Datasets:
microsoft
/
FStarDataSet

Dataset card Data Studio Files Community
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Prims.Tot
val va_codegen_success_Prefetchnta : v:va_operand_opr64 -> Tot va_pbool
[ { "abbrev": true, "full_module": "Vale.X64.Machine_Semantics_s", "short_module": "S" }, { "abbrev": true, "full_module": "Vale.X64.Instructions_s", "short_module": "I" }, { "abbrev": false, "full_module": "Vale.X64.Stack_i", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.Memory", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.Taint_Semantics", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.InsLemmas", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.StateLemmas", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.CPU_Features_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.QuickCode", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.Decls", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.State", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.Machine_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Arch.Types", "short_module": null }, { "abbrev": false, "full_module": "Vale.Arch.HeapImpl", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Types_s", "short_module": null }, { "abbrev": false, "full_module": "FStar.Mul", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]
false
let va_codegen_success_Prefetchnta v = (va_ttrue ())
val va_codegen_success_Prefetchnta : v:va_operand_opr64 -> Tot va_pbool let va_codegen_success_Prefetchnta v =
false
null
false
(va_ttrue ())
{ "checked_file": "Vale.X64.InsBasic.fst.checked", "dependencies": [ "Vale.X64.Taint_Semantics.fst.checked", "Vale.X64.StateLemmas.fsti.checked", "Vale.X64.Stack_i.fsti.checked", "Vale.X64.Memory.fsti.checked", "Vale.X64.Machine_Semantics_s.fst.checked", "Vale.X64.Instructions_s.fsti.checked", "Vale.X64.InsLemmas.fsti.checked", "Vale.X64.Decls.fst.checked", "Vale.X64.CPU_Features_s.fst.checked", "Vale.Arch.Types.fsti.checked", "prims.fst.checked", "FStar.UInt.fsti.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Math.Lemmas.fst.checked" ], "interface_file": true, "source_file": "Vale.X64.InsBasic.fst" }
[ "total" ]
[ "Vale.X64.Decls.va_operand_opr64", "Vale.X64.Decls.va_ttrue", "Vale.X64.Decls.va_pbool" ]
[]
module Vale.X64.InsBasic open Vale.X64 open Vale.X64.StateLemmas open Vale.X64.InsLemmas open Vale.X64.Taint_Semantics open Vale.X64.CPU_Features_s open Vale.X64.Memory open Vale.X64.Stack_i module I = Vale.X64.Instructions_s module S = Vale.X64.Machine_Semantics_s friend Vale.X64.Decls #reset-options "--initial_fuel 5 --max_fuel 5 --max_ifuel 2 --z3rlimit 20" //-- Mov64 [@ "opaque_to_smt"] let va_code_Mov64 dst src = (mk_ins (make_instr_annotate (I.ins_Mov64) (S.AnnotateMov64 ()) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Mov64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Mov64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Mov64) (va_code_Mov64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr_annotate (I.ins_Mov64) (S.AnnotateMov64 ()) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr_annotate (I.ins_Mov64) (S.AnnotateMov64 ()) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Mov64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Mov64 (va_code_Mov64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0))); va_lemma_norm_mods ([va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cmovc64 [@ "opaque_to_smt"] let va_code_Cmovc64 dst src = (mk_ins (make_instr (I.ins_Cmovc64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Cmovc64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cmovc64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Cmovc64) (va_code_Cmovc64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cmovc64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cmovc64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cmovc64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cmovc64 (va_code_Cmovc64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0))); va_lemma_norm_mods ([va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Add64 [@ "opaque_to_smt"] let va_code_Add64 dst src = (mk_ins (make_instr (I.ins_Add64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Add64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Add64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Add64) (va_code_Add64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Add64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Add64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Add64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Add64 (va_code_Add64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Add64Wrap [@ "opaque_to_smt"] let va_code_Add64Wrap dst src = (mk_ins (make_instr (I.ins_Add64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Add64Wrap dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Add64Wrap va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Add64Wrap) (va_code_Add64Wrap dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Add64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Add64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Add64Wrap dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Add64Wrap (va_code_Add64Wrap dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- AddLea64 [@ "opaque_to_smt"] let va_code_AddLea64 dst src1 src2 = (mk_ins (make_instr (I.ins_AddLea64) dst src1 src2)) [@ "opaque_to_smt"] let va_codegen_success_AddLea64 dst src1 src2 = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_AddLea64 va_b0 va_s0 dst src1 src2 = va_reveal_opaque (`%va_code_AddLea64) (va_code_AddLea64 dst src1 src2); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_AddLea64) dst src1 src2)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_AddLea64) dst src1 src2)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_AddLea64 dst src1 src2 va_s0 va_k = let (va_sM, va_f0) = va_lemma_AddLea64 (va_code_AddLea64 dst src1 src2) va_s0 dst src1 src2 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0))); va_lemma_norm_mods ([va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Adc64 [@ "opaque_to_smt"] let va_code_Adc64 dst src = (mk_ins (make_instr (I.ins_AddCarry64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Adc64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Adc64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Adc64) (va_code_Adc64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_AddCarry64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_AddCarry64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Adc64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Adc64 (va_code_Adc64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Adc64Wrap [@ "opaque_to_smt"] let va_code_Adc64Wrap dst src = (mk_ins (make_instr (I.ins_AddCarry64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Adc64Wrap dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Adc64Wrap va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Adc64Wrap) (va_code_Adc64Wrap dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_AddCarry64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_AddCarry64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Adc64Wrap dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Adc64Wrap (va_code_Adc64Wrap dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Adcx64Wrap #push-options "--smtencoding.nl_arith_repr boxwrap" [@ "opaque_to_smt"] let va_code_Adcx64Wrap dst src = (mk_ins (make_instr (I.ins_Adcx64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Adcx64Wrap dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Adcx64Wrap va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Adcx64Wrap) (va_code_Adcx64Wrap dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Adcx64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Adcx64) dst src)) va_s0 in assert (Vale.Arch.Types.add_wrap64 (Vale.Arch.Types.add_wrap64 (va_eval_dst_opr64 va_old_s dst) (va_eval_opr64 va_old_s src)) (if Vale.X64.Decls.cf (va_get_flags va_old_s) then 1 else 0) == (va_eval_dst_opr64 va_old_s dst + va_eval_opr64 va_old_s src + (if Vale.X64.Decls.cf (va_get_flags va_old_s) then 1 else 0)) `op_Modulus` pow2_64); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Adcx64Wrap dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Adcx64Wrap (va_code_Adcx64Wrap dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) #pop-options //-- //-- Adox64Wrap [@ "opaque_to_smt"] let va_code_Adox64Wrap dst src = (mk_ins (make_instr (I.ins_Adox64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Adox64Wrap dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Adox64Wrap va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Adox64Wrap) (va_code_Adox64Wrap dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Adox64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Adox64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Adox64Wrap dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Adox64Wrap (va_code_Adox64Wrap dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Sub64 [@ "opaque_to_smt"] let va_code_Sub64 dst src = (mk_ins (make_instr (I.ins_Sub64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Sub64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Sub64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Sub64) (va_code_Sub64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Sub64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Sub64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Sub64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Sub64 (va_code_Sub64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Sub64Wrap [@ "opaque_to_smt"] let va_code_Sub64Wrap dst src = (mk_ins (make_instr (I.ins_Sub64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Sub64Wrap dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Sub64Wrap va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Sub64Wrap) (va_code_Sub64Wrap dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Sub64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Sub64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Sub64Wrap dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Sub64Wrap (va_code_Sub64Wrap dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Sbb64 [@ "opaque_to_smt"] let va_code_Sbb64 dst src = (mk_ins (make_instr (I.ins_Sbb64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Sbb64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Sbb64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Sbb64) (va_code_Sbb64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Sbb64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Sbb64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Sbb64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Sbb64 (va_code_Sbb64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- #restart-solver #push-options "--max_fuel 0 --max_ifuel 0 --using_facts_from 'Prims FStar.UInt'" let lemma_fundamental_div_mod (a b:nat64) : Lemma (pow2_64 * (FStar.UInt.mul_div #64 a b) + (FStar.UInt.mul_mod #64 a b) == a * b) = FStar.Math.Lemmas.lemma_div_mod (a * b) pow2_64 #pop-options //-- lemma_fundamental_div_mod //-- //-- Mul64Wrap [@ "opaque_to_smt"] let va_code_Mul64Wrap src = (mk_ins (make_instr (I.ins_Mul64) src)) [@ "opaque_to_smt"] let va_codegen_success_Mul64Wrap src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Mul64Wrap va_b0 va_s0 src = va_reveal_opaque (`%va_code_Mul64Wrap) (va_code_Mul64Wrap src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Mul64) src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Mul64) src)) va_s0 in lemma_fundamental_div_mod (va_get_reg64 rRax va_old_s) (va_eval_opr64 va_old_s src); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Mul64Wrap src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Mul64Wrap (va_code_Mul64Wrap src) va_s0 src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRax va_sM (va_update_flags va_sM (va_update_ok va_sM va_s0))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRax; va_Mod_flags]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Mulx64 [@ "opaque_to_smt"] let va_code_Mulx64 dst_hi dst_lo src = (mk_ins (make_instr (I.ins_Mulx64) dst_hi dst_lo src)) [@ "opaque_to_smt"] let va_codegen_success_Mulx64 dst_hi dst_lo src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Mulx64 va_b0 va_s0 dst_hi dst_lo src = va_reveal_opaque (`%va_code_Mulx64) (va_code_Mulx64 dst_hi dst_lo src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Mulx64) dst_hi dst_lo src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Mulx64) dst_hi dst_lo src)) va_s0 in lemma_fundamental_div_mod (va_get_reg64 rRdx va_old_s) (va_eval_opr64 va_old_s src); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Mulx64 dst_hi dst_lo src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Mulx64 (va_code_Mulx64 dst_hi dst_lo src) va_s0 dst_hi dst_lo src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst_lo va_sM (va_update_operand_dst_opr64 dst_hi va_sM va_s0)))); va_lemma_norm_mods ([va_mod_dst_opr64 dst_lo; va_mod_dst_opr64 dst_hi]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- lemma_mul_nat //-- //-- lemma_mul_in_bounds //-- //-- IMul64 [@ "opaque_to_smt"] let va_code_IMul64 dst src = (mk_ins (make_instr (I.ins_IMul64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_IMul64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_IMul64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_IMul64) (va_code_IMul64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_IMul64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_IMul64) dst src)) va_s0 in lemma_mul_nat (va_eval_dst_opr64 va_old_s dst) (va_eval_opr64 va_old_s src); lemma_mul_in_bounds (va_eval_dst_opr64 va_old_s dst) (va_eval_opr64 va_old_s src); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_IMul64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_IMul64 (va_code_IMul64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Xor64 [@ "opaque_to_smt"] let va_code_Xor64 dst src = (mk_ins (make_instr_annotate (I.ins_Xor64) (S.AnnotateXor64 ()) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Xor64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Xor64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Xor64) (va_code_Xor64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr_annotate (I.ins_Xor64) (S.AnnotateXor64 ()) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr_annotate (I.ins_Xor64) (S.AnnotateXor64 ()) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Xor64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Xor64 (va_code_Xor64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- And64 [@ "opaque_to_smt"] let va_code_And64 dst src = (mk_ins (make_instr (I.ins_And64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_And64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_And64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_And64) (va_code_And64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_And64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_And64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_And64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_And64 (va_code_And64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Shl64 [@ "opaque_to_smt"] let va_code_Shl64 dst amt = (mk_ins (make_instr (I.ins_Shl64) dst amt)) [@ "opaque_to_smt"] let va_codegen_success_Shl64 dst amt = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Shl64 va_b0 va_s0 dst amt = va_reveal_opaque (`%va_code_Shl64) (va_code_Shl64 dst amt); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Shl64) dst amt)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Shl64) dst amt)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Shl64 dst amt va_s0 va_k = let (va_sM, va_f0) = va_lemma_Shl64 (va_code_Shl64 dst amt) va_s0 dst amt in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Shr64 [@ "opaque_to_smt"] let va_code_Shr64 dst amt = (mk_ins (make_instr (I.ins_Shr64) dst amt)) [@ "opaque_to_smt"] let va_codegen_success_Shr64 dst amt = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Shr64 va_b0 va_s0 dst amt = va_reveal_opaque (`%va_code_Shr64) (va_code_Shr64 dst amt); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Shr64) dst amt)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Shr64) dst amt)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Shr64 dst amt va_s0 va_k = let (va_sM, va_f0) = va_lemma_Shr64 (va_code_Shr64 dst amt) va_s0 dst amt in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_AES [@ "opaque_to_smt"] let va_code_Cpuid_AES () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_AES () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_AES va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_AES) (va_code_Cpuid_AES ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_AES va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_AES (va_code_Cpuid_AES ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Sha [@ "opaque_to_smt"] let va_code_Cpuid_Sha () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Sha () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Sha va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Sha) (va_code_Cpuid_Sha ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Sha va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Sha (va_code_Cpuid_Sha ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Adx_Bmi2 [@ "opaque_to_smt"] let va_code_Cpuid_Adx_Bmi2 () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Adx_Bmi2 () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Adx_Bmi2 va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Adx_Bmi2) (va_code_Cpuid_Adx_Bmi2 ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Adx_Bmi2 va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Adx_Bmi2 (va_code_Cpuid_Adx_Bmi2 ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Avx [@ "opaque_to_smt"] let va_code_Cpuid_Avx () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Avx () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Avx va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Avx) (va_code_Cpuid_Avx ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Avx va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Avx (va_code_Cpuid_Avx ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Avx2 [@ "opaque_to_smt"] let va_code_Cpuid_Avx2 () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Avx2 () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Avx2 va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Avx2) (va_code_Cpuid_Avx2 ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Avx2 va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Avx2 (va_code_Cpuid_Avx2 ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Sse [@ "opaque_to_smt"] let va_code_Cpuid_Sse () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Sse () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Sse va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Sse) (va_code_Cpuid_Sse ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Sse va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Sse (va_code_Cpuid_Sse ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Movbe [@ "opaque_to_smt"] let va_code_Cpuid_Movbe () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Movbe () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Movbe va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Movbe) (va_code_Cpuid_Movbe ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Movbe va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Movbe (va_code_Cpuid_Movbe ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Rdrand [@ "opaque_to_smt"] let va_code_Cpuid_Rdrand () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Rdrand () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Rdrand va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Rdrand) (va_code_Cpuid_Rdrand ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Rdrand va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Rdrand (va_code_Cpuid_Rdrand ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Avx512 [@ "opaque_to_smt"] let va_code_Cpuid_Avx512 () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Avx512 () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Avx512 va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Avx512) (va_code_Cpuid_Avx512 ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Avx512 va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Avx512 (va_code_Cpuid_Avx512 ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Osxsave [@ "opaque_to_smt"] let va_code_Cpuid_Osxsave () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Osxsave () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Osxsave va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Osxsave) (va_code_Cpuid_Osxsave ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Osxsave va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Osxsave (va_code_Cpuid_Osxsave ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Xgetbv_Avx [@ "opaque_to_smt"] let va_code_Xgetbv_Avx () = (mk_ins (make_instr (I.ins_Xgetbv))) [@ "opaque_to_smt"] let va_codegen_success_Xgetbv_Avx () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Xgetbv_Avx va_b0 va_s0 = va_reveal_opaque (`%va_code_Xgetbv_Avx) (va_code_Xgetbv_Avx ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Xgetbv))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Xgetbv))) va_s0 in Vale.X64.CPU_Features_s.xgetbv_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Xgetbv_Avx va_s0 va_k = let (va_sM, va_f0) = va_lemma_Xgetbv_Avx (va_code_Xgetbv_Avx ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Xgetbv_Avx512 [@ "opaque_to_smt"] let va_code_Xgetbv_Avx512 () = (mk_ins (make_instr (I.ins_Xgetbv))) [@ "opaque_to_smt"] let va_codegen_success_Xgetbv_Avx512 () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Xgetbv_Avx512 va_b0 va_s0 = va_reveal_opaque (`%va_code_Xgetbv_Avx512) (va_code_Xgetbv_Avx512 ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Xgetbv))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Xgetbv))) va_s0 in Vale.X64.CPU_Features_s.xgetbv_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Xgetbv_Avx512 va_s0 va_k = let (va_sM, va_f0) = va_lemma_Xgetbv_Avx512 (va_code_Xgetbv_Avx512 ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Nat64Equal [@ "opaque_to_smt"] let va_code_Nat64Equal dst src = (va_Block (va_CCons (va_code_Sub64Wrap (va_coerce_reg_opr64_to_dst_opr64 src) (va_const_opr64 18446744073709551615)) (va_CCons (va_code_Mov64 (va_coerce_reg_opr64_to_dst_opr64 dst) (va_const_opr64 0)) (va_CCons (va_code_Adc64 (va_coerce_reg_opr64_to_dst_opr64 dst) (va_const_opr64 0)) (va_CNil ()))))) [@ "opaque_to_smt"] let va_codegen_success_Nat64Equal dst src = (va_pbool_and (va_codegen_success_Sub64Wrap (va_coerce_reg_opr64_to_dst_opr64 src) (va_const_opr64 18446744073709551615)) (va_pbool_and (va_codegen_success_Mov64 (va_coerce_reg_opr64_to_dst_opr64 dst) (va_const_opr64 0)) (va_pbool_and (va_codegen_success_Adc64 (va_coerce_reg_opr64_to_dst_opr64 dst) (va_const_opr64 0)) (va_ttrue ())))) [@"opaque_to_smt"] let va_lemma_Nat64Equal va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Nat64Equal) (va_code_Nat64Equal dst src); let (va_old_s:va_state) = va_s0 in let (va_b1:va_codes) = va_get_block va_b0 in let (va_s2, va_fc2) = va_lemma_Sub64Wrap (va_hd va_b1) va_s0 (va_coerce_reg_opr64_to_dst_opr64 src) (va_const_opr64 18446744073709551615) in let va_b2 = va_tl va_b1 in let (va_s3, va_fc3) = va_lemma_Mov64 (va_hd va_b2) va_s2 (va_coerce_reg_opr64_to_dst_opr64 dst) (va_const_opr64 0) in let va_b3 = va_tl va_b2 in let (va_s4, va_fc4) = va_lemma_Adc64 (va_hd va_b3) va_s3 (va_coerce_reg_opr64_to_dst_opr64 dst) (va_const_opr64 0) in let va_b4 = va_tl va_b3 in let (va_sM, va_f4) = va_lemma_empty_total va_s4 va_b4 in let va_f3 = va_lemma_merge_total va_b3 va_s3 va_fc4 va_s4 va_f4 va_sM in let va_f2 = va_lemma_merge_total va_b2 va_s2 va_fc3 va_s3 va_f3 va_sM in let va_fM = va_lemma_merge_total va_b1 va_s0 va_fc2 va_s2 va_f2 va_sM in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Nat64Equal dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Nat64Equal (va_code_Nat64Equal dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_reg_opr64 src va_sM (va_update_operand_reg_opr64 dst va_sM va_s0))))); va_lemma_norm_mods ([va_Mod_flags; va_mod_reg_opr64 src; va_mod_reg_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Comment [@ "opaque_to_smt"] let va_code_Comment c = (mk_ins (make_instr_annotate (I.ins_Comment c) (S.AnnotateComment c))) [@ "opaque_to_smt"] let va_codegen_success_Comment c = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Comment va_b0 va_s0 c = va_reveal_opaque (`%va_code_Comment) (va_code_Comment c); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr_annotate (I.ins_Comment c) (S.AnnotateComment c))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr_annotate (I.ins_Comment c) (S.AnnotateComment c))) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Comment c va_s0 va_k = let (va_sM, va_f0) = va_lemma_Comment (va_code_Comment c) va_s0 c in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_ok va_sM va_s0)); va_lemma_norm_mods ([]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- LargeComment [@ "opaque_to_smt"] let va_code_LargeComment c = (mk_ins (make_instr_annotate (I.ins_LargeComment c) (S.AnnotateLargeComment c))) [@ "opaque_to_smt"] let va_codegen_success_LargeComment c = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_LargeComment va_b0 va_s0 c = va_reveal_opaque (`%va_code_LargeComment) (va_code_LargeComment c); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr_annotate (I.ins_LargeComment c) (S.AnnotateLargeComment c))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr_annotate (I.ins_LargeComment c) (S.AnnotateLargeComment c))) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_LargeComment c va_s0 va_k = let (va_sM, va_f0) = va_lemma_LargeComment (va_code_LargeComment c) va_s0 c in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_ok va_sM va_s0)); va_lemma_norm_mods ([]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- NoNewline [@ "opaque_to_smt"] let va_code_NoNewline () = (mk_ins (make_instr_annotate (I.ins_Space 0) (S.AnnotateSpace 0))) [@ "opaque_to_smt"] let va_codegen_success_NoNewline () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_NoNewline va_b0 va_s0 = va_reveal_opaque (`%va_code_NoNewline) (va_code_NoNewline ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr_annotate (I.ins_Space 0) (S.AnnotateSpace 0))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr_annotate (I.ins_Space 0) (S.AnnotateSpace 0))) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_NoNewline va_s0 va_k = let (va_sM, va_f0) = va_lemma_NoNewline (va_code_NoNewline ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_ok va_sM va_s0)); va_lemma_norm_mods ([]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Newline [@ "opaque_to_smt"] let va_code_Newline () = (mk_ins (make_instr_annotate (I.ins_Newline) (S.AnnotateNewline ()))) [@ "opaque_to_smt"] let va_codegen_success_Newline () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Newline va_b0 va_s0 = va_reveal_opaque (`%va_code_Newline) (va_code_Newline ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr_annotate (I.ins_Newline) (S.AnnotateNewline ()))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr_annotate (I.ins_Newline) (S.AnnotateNewline ()))) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Newline va_s0 va_k = let (va_sM, va_f0) = va_lemma_Newline (va_code_Newline ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_ok va_sM va_s0)); va_lemma_norm_mods ([]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Space [@ "opaque_to_smt"] let va_code_Space n = (mk_ins (make_instr_annotate (I.ins_Space n) (S.AnnotateSpace n))) [@ "opaque_to_smt"] let va_codegen_success_Space n = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Space va_b0 va_s0 n = va_reveal_opaque (`%va_code_Space) (va_code_Space n); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr_annotate (I.ins_Space n) (S.AnnotateSpace n))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr_annotate (I.ins_Space n) (S.AnnotateSpace n))) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Space n va_s0 va_k = let (va_sM, va_f0) = va_lemma_Space (va_code_Space n) va_s0 n in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_ok va_sM va_s0)); va_lemma_norm_mods ([]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Prefetchnta [@ "opaque_to_smt"] let va_code_Prefetchnta v = (mk_ins (make_instr_annotate (I.ins_Prefetchnta) (S.AnnotatePrefetchnta ()) v)) [@ "opaque_to_smt"]
false
true
Vale.X64.InsBasic.fst
{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 5, "initial_ifuel": 0, "max_fuel": 5, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": true, "smtencoding_l_arith_repr": "native", "smtencoding_nl_arith_repr": "wrapped", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": false, "z3cliopt": [ "smt.arith.nl=false", "smt.QI.EAGER_THRESHOLD=100", "smt.CASE_SPLIT=3" ], "z3refresh": false, "z3rlimit": 20, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }
null
val va_codegen_success_Prefetchnta : v:va_operand_opr64 -> Tot va_pbool
[]
Vale.X64.InsBasic.va_codegen_success_Prefetchnta
{ "file_name": "obj/Vale.X64.InsBasic.fst", "git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e", "git_url": "https://github.com/hacl-star/hacl-star.git", "project_name": "hacl-star" }
v: Vale.X64.Decls.va_operand_opr64 -> Vale.X64.Decls.va_pbool
{ "end_col": 15, "end_line": 1195, "start_col": 2, "start_line": 1195 }
Prims.Ghost
val va_lemma_Sbb64 : va_b0:va_code -> va_s0:va_state -> dst:va_operand_dst_opr64 -> src:va_operand_opr64 -> Ghost (va_state & va_fuel) (requires (va_require_total va_b0 (va_code_Sbb64 dst src) va_s0 /\ va_is_dst_dst_opr64 dst va_s0 /\ va_is_src_opr64 src va_s0 /\ va_get_ok va_s0 /\ Vale.X64.Decls.valid_cf (va_get_flags va_s0))) (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\ va_eval_dst_opr64 va_sM dst == Vale.Arch.Types.sub_wrap64 (va_eval_dst_opr64 va_s0 dst) (Vale.Arch.Types.add_wrap64 (va_eval_opr64 va_s0 src) (if Vale.X64.Decls.cf (va_get_flags va_s0) then 1 else 0)) /\ Vale.X64.Decls.updated_cf (va_get_flags va_sM) (va_eval_dst_opr64 va_s0 dst - (va_eval_opr64 va_s0 src + (if Vale.X64.Decls.cf (va_get_flags va_s0) then 1 else 0)) < 0) /\ va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))))
[ { "abbrev": true, "full_module": "Vale.X64.Machine_Semantics_s", "short_module": "S" }, { "abbrev": true, "full_module": "Vale.X64.Instructions_s", "short_module": "I" }, { "abbrev": false, "full_module": "Vale.X64.Stack_i", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.Memory", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.Taint_Semantics", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.InsLemmas", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.StateLemmas", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.CPU_Features_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.QuickCode", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.Decls", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.State", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.Machine_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Arch.Types", "short_module": null }, { "abbrev": false, "full_module": "Vale.Arch.HeapImpl", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Types_s", "short_module": null }, { "abbrev": false, "full_module": "FStar.Mul", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]
false
let va_lemma_Sbb64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Sbb64) (va_code_Sbb64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Sbb64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Sbb64) dst src)) va_s0 in (va_sM, va_fM)
val va_lemma_Sbb64 : va_b0:va_code -> va_s0:va_state -> dst:va_operand_dst_opr64 -> src:va_operand_opr64 -> Ghost (va_state & va_fuel) (requires (va_require_total va_b0 (va_code_Sbb64 dst src) va_s0 /\ va_is_dst_dst_opr64 dst va_s0 /\ va_is_src_opr64 src va_s0 /\ va_get_ok va_s0 /\ Vale.X64.Decls.valid_cf (va_get_flags va_s0))) (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\ va_eval_dst_opr64 va_sM dst == Vale.Arch.Types.sub_wrap64 (va_eval_dst_opr64 va_s0 dst) (Vale.Arch.Types.add_wrap64 (va_eval_opr64 va_s0 src) (if Vale.X64.Decls.cf (va_get_flags va_s0) then 1 else 0)) /\ Vale.X64.Decls.updated_cf (va_get_flags va_sM) (va_eval_dst_opr64 va_s0 dst - (va_eval_opr64 va_s0 src + (if Vale.X64.Decls.cf (va_get_flags va_s0) then 1 else 0)) < 0) /\ va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0))))) let va_lemma_Sbb64 va_b0 va_s0 dst src =
false
null
false
va_reveal_opaque (`%va_code_Sbb64) (va_code_Sbb64 dst src); let va_old_s:va_state = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Sbb64) dst src)) va_s0; let va_sM, va_fM = va_eval_ins (mk_ins (make_instr (I.ins_Sbb64) dst src)) va_s0 in (va_sM, va_fM)
{ "checked_file": "Vale.X64.InsBasic.fst.checked", "dependencies": [ "Vale.X64.Taint_Semantics.fst.checked", "Vale.X64.StateLemmas.fsti.checked", "Vale.X64.Stack_i.fsti.checked", "Vale.X64.Memory.fsti.checked", "Vale.X64.Machine_Semantics_s.fst.checked", "Vale.X64.Instructions_s.fsti.checked", "Vale.X64.InsLemmas.fsti.checked", "Vale.X64.Decls.fst.checked", "Vale.X64.CPU_Features_s.fst.checked", "Vale.Arch.Types.fsti.checked", "prims.fst.checked", "FStar.UInt.fsti.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Math.Lemmas.fst.checked" ], "interface_file": true, "source_file": "Vale.X64.InsBasic.fst" }
[]
[ "Vale.X64.Decls.va_code", "Vale.X64.Decls.va_state", "Vale.X64.Decls.va_operand_dst_opr64", "Vale.X64.Decls.va_operand_opr64", "Vale.X64.State.vale_state", "Vale.X64.Lemmas.fuel", "FStar.Pervasives.Native.Mktuple2", "Vale.X64.Decls.va_fuel", "FStar.Pervasives.Native.tuple2", "Prims.nat", "Vale.X64.Decls.va_eval_ins", "Vale.X64.Taint_Semantics.mk_ins", "Vale.X64.InsLemmas.make_instr", "Prims.Cons", "Vale.X64.Instruction_s.instr_out", "Vale.X64.Instruction_s.inOut", "Vale.X64.Instruction_s.opFlagsCf", "Vale.X64.Instruction_s.op64", "Prims.Nil", "Vale.X64.Instruction_s.instr_operand", "Vale.X64.Instruction_s.HavocFlags", "Vale.X64.Instructions_s.ins_Sbb64", "Prims.unit", "Vale.X64.Decls.va_ins_lemma", "Vale.X64.Decls.va_reveal_opaque", "Vale.X64.InsBasic.va_code_Sbb64" ]
[]
module Vale.X64.InsBasic open Vale.X64 open Vale.X64.StateLemmas open Vale.X64.InsLemmas open Vale.X64.Taint_Semantics open Vale.X64.CPU_Features_s open Vale.X64.Memory open Vale.X64.Stack_i module I = Vale.X64.Instructions_s module S = Vale.X64.Machine_Semantics_s friend Vale.X64.Decls #reset-options "--initial_fuel 5 --max_fuel 5 --max_ifuel 2 --z3rlimit 20" //-- Mov64 [@ "opaque_to_smt"] let va_code_Mov64 dst src = (mk_ins (make_instr_annotate (I.ins_Mov64) (S.AnnotateMov64 ()) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Mov64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Mov64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Mov64) (va_code_Mov64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr_annotate (I.ins_Mov64) (S.AnnotateMov64 ()) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr_annotate (I.ins_Mov64) (S.AnnotateMov64 ()) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Mov64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Mov64 (va_code_Mov64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0))); va_lemma_norm_mods ([va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cmovc64 [@ "opaque_to_smt"] let va_code_Cmovc64 dst src = (mk_ins (make_instr (I.ins_Cmovc64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Cmovc64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cmovc64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Cmovc64) (va_code_Cmovc64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cmovc64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cmovc64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cmovc64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cmovc64 (va_code_Cmovc64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0))); va_lemma_norm_mods ([va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Add64 [@ "opaque_to_smt"] let va_code_Add64 dst src = (mk_ins (make_instr (I.ins_Add64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Add64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Add64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Add64) (va_code_Add64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Add64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Add64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Add64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Add64 (va_code_Add64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Add64Wrap [@ "opaque_to_smt"] let va_code_Add64Wrap dst src = (mk_ins (make_instr (I.ins_Add64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Add64Wrap dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Add64Wrap va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Add64Wrap) (va_code_Add64Wrap dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Add64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Add64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Add64Wrap dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Add64Wrap (va_code_Add64Wrap dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- AddLea64 [@ "opaque_to_smt"] let va_code_AddLea64 dst src1 src2 = (mk_ins (make_instr (I.ins_AddLea64) dst src1 src2)) [@ "opaque_to_smt"] let va_codegen_success_AddLea64 dst src1 src2 = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_AddLea64 va_b0 va_s0 dst src1 src2 = va_reveal_opaque (`%va_code_AddLea64) (va_code_AddLea64 dst src1 src2); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_AddLea64) dst src1 src2)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_AddLea64) dst src1 src2)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_AddLea64 dst src1 src2 va_s0 va_k = let (va_sM, va_f0) = va_lemma_AddLea64 (va_code_AddLea64 dst src1 src2) va_s0 dst src1 src2 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0))); va_lemma_norm_mods ([va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Adc64 [@ "opaque_to_smt"] let va_code_Adc64 dst src = (mk_ins (make_instr (I.ins_AddCarry64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Adc64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Adc64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Adc64) (va_code_Adc64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_AddCarry64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_AddCarry64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Adc64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Adc64 (va_code_Adc64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Adc64Wrap [@ "opaque_to_smt"] let va_code_Adc64Wrap dst src = (mk_ins (make_instr (I.ins_AddCarry64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Adc64Wrap dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Adc64Wrap va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Adc64Wrap) (va_code_Adc64Wrap dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_AddCarry64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_AddCarry64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Adc64Wrap dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Adc64Wrap (va_code_Adc64Wrap dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Adcx64Wrap #push-options "--smtencoding.nl_arith_repr boxwrap" [@ "opaque_to_smt"] let va_code_Adcx64Wrap dst src = (mk_ins (make_instr (I.ins_Adcx64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Adcx64Wrap dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Adcx64Wrap va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Adcx64Wrap) (va_code_Adcx64Wrap dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Adcx64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Adcx64) dst src)) va_s0 in assert (Vale.Arch.Types.add_wrap64 (Vale.Arch.Types.add_wrap64 (va_eval_dst_opr64 va_old_s dst) (va_eval_opr64 va_old_s src)) (if Vale.X64.Decls.cf (va_get_flags va_old_s) then 1 else 0) == (va_eval_dst_opr64 va_old_s dst + va_eval_opr64 va_old_s src + (if Vale.X64.Decls.cf (va_get_flags va_old_s) then 1 else 0)) `op_Modulus` pow2_64); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Adcx64Wrap dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Adcx64Wrap (va_code_Adcx64Wrap dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) #pop-options //-- //-- Adox64Wrap [@ "opaque_to_smt"] let va_code_Adox64Wrap dst src = (mk_ins (make_instr (I.ins_Adox64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Adox64Wrap dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Adox64Wrap va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Adox64Wrap) (va_code_Adox64Wrap dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Adox64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Adox64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Adox64Wrap dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Adox64Wrap (va_code_Adox64Wrap dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Sub64 [@ "opaque_to_smt"] let va_code_Sub64 dst src = (mk_ins (make_instr (I.ins_Sub64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Sub64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Sub64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Sub64) (va_code_Sub64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Sub64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Sub64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Sub64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Sub64 (va_code_Sub64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Sub64Wrap [@ "opaque_to_smt"] let va_code_Sub64Wrap dst src = (mk_ins (make_instr (I.ins_Sub64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Sub64Wrap dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Sub64Wrap va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Sub64Wrap) (va_code_Sub64Wrap dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Sub64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Sub64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Sub64Wrap dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Sub64Wrap (va_code_Sub64Wrap dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Sbb64 [@ "opaque_to_smt"] let va_code_Sbb64 dst src = (mk_ins (make_instr (I.ins_Sbb64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Sbb64 dst src = (va_ttrue ()) [@"opaque_to_smt"]
false
false
Vale.X64.InsBasic.fst
{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 5, "initial_ifuel": 0, "max_fuel": 5, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": true, "smtencoding_l_arith_repr": "native", "smtencoding_nl_arith_repr": "wrapped", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": false, "z3cliopt": [ "smt.arith.nl=false", "smt.QI.EAGER_THRESHOLD=100", "smt.CASE_SPLIT=3" ], "z3refresh": false, "z3rlimit": 20, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }
null
val va_lemma_Sbb64 : va_b0:va_code -> va_s0:va_state -> dst:va_operand_dst_opr64 -> src:va_operand_opr64 -> Ghost (va_state & va_fuel) (requires (va_require_total va_b0 (va_code_Sbb64 dst src) va_s0 /\ va_is_dst_dst_opr64 dst va_s0 /\ va_is_src_opr64 src va_s0 /\ va_get_ok va_s0 /\ Vale.X64.Decls.valid_cf (va_get_flags va_s0))) (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\ va_eval_dst_opr64 va_sM dst == Vale.Arch.Types.sub_wrap64 (va_eval_dst_opr64 va_s0 dst) (Vale.Arch.Types.add_wrap64 (va_eval_opr64 va_s0 src) (if Vale.X64.Decls.cf (va_get_flags va_s0) then 1 else 0)) /\ Vale.X64.Decls.updated_cf (va_get_flags va_sM) (va_eval_dst_opr64 va_s0 dst - (va_eval_opr64 va_s0 src + (if Vale.X64.Decls.cf (va_get_flags va_s0) then 1 else 0)) < 0) /\ va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))))
[]
Vale.X64.InsBasic.va_lemma_Sbb64
{ "file_name": "obj/Vale.X64.InsBasic.fst", "git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e", "git_url": "https://github.com/hacl-star/hacl-star.git", "project_name": "hacl-star" }
va_b0: Vale.X64.Decls.va_code -> va_s0: Vale.X64.Decls.va_state -> dst: Vale.X64.Decls.va_operand_dst_opr64 -> src: Vale.X64.Decls.va_operand_opr64 -> Prims.Ghost (Vale.X64.Decls.va_state * Vale.X64.Decls.va_fuel)
{ "end_col": 16, "end_line": 363, "start_col": 2, "start_line": 359 }
Prims.Ghost
val va_lemma_IMul64 : va_b0:va_code -> va_s0:va_state -> dst:va_operand_dst_opr64 -> src:va_operand_opr64 -> Ghost (va_state & va_fuel) (requires (va_require_total va_b0 (va_code_IMul64 dst src) va_s0 /\ va_is_dst_dst_opr64 dst va_s0 /\ va_is_src_opr64 src va_s0 /\ va_get_ok va_s0 /\ va_mul_nat (va_eval_dst_opr64 va_s0 dst) (va_eval_opr64 va_s0 src) < pow2_64)) (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\ va_eval_dst_opr64 va_sM dst == va_mul_nat (va_eval_dst_opr64 va_s0 dst) (va_eval_opr64 va_s0 src) /\ va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))))
[ { "abbrev": true, "full_module": "Vale.X64.Machine_Semantics_s", "short_module": "S" }, { "abbrev": true, "full_module": "Vale.X64.Instructions_s", "short_module": "I" }, { "abbrev": false, "full_module": "Vale.X64.Stack_i", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.Memory", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.Taint_Semantics", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.InsLemmas", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.StateLemmas", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.CPU_Features_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.QuickCode", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.Decls", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.State", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.Machine_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Arch.Types", "short_module": null }, { "abbrev": false, "full_module": "Vale.Arch.HeapImpl", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Types_s", "short_module": null }, { "abbrev": false, "full_module": "FStar.Mul", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]
false
let va_lemma_IMul64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_IMul64) (va_code_IMul64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_IMul64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_IMul64) dst src)) va_s0 in lemma_mul_nat (va_eval_dst_opr64 va_old_s dst) (va_eval_opr64 va_old_s src); lemma_mul_in_bounds (va_eval_dst_opr64 va_old_s dst) (va_eval_opr64 va_old_s src); (va_sM, va_fM)
val va_lemma_IMul64 : va_b0:va_code -> va_s0:va_state -> dst:va_operand_dst_opr64 -> src:va_operand_opr64 -> Ghost (va_state & va_fuel) (requires (va_require_total va_b0 (va_code_IMul64 dst src) va_s0 /\ va_is_dst_dst_opr64 dst va_s0 /\ va_is_src_opr64 src va_s0 /\ va_get_ok va_s0 /\ va_mul_nat (va_eval_dst_opr64 va_s0 dst) (va_eval_opr64 va_s0 src) < pow2_64)) (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\ va_eval_dst_opr64 va_sM dst == va_mul_nat (va_eval_dst_opr64 va_s0 dst) (va_eval_opr64 va_s0 src) /\ va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0))))) let va_lemma_IMul64 va_b0 va_s0 dst src =
false
null
false
va_reveal_opaque (`%va_code_IMul64) (va_code_IMul64 dst src); let va_old_s:va_state = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_IMul64) dst src)) va_s0; let va_sM, va_fM = va_eval_ins (mk_ins (make_instr (I.ins_IMul64) dst src)) va_s0 in lemma_mul_nat (va_eval_dst_opr64 va_old_s dst) (va_eval_opr64 va_old_s src); lemma_mul_in_bounds (va_eval_dst_opr64 va_old_s dst) (va_eval_opr64 va_old_s src); (va_sM, va_fM)
{ "checked_file": "Vale.X64.InsBasic.fst.checked", "dependencies": [ "Vale.X64.Taint_Semantics.fst.checked", "Vale.X64.StateLemmas.fsti.checked", "Vale.X64.Stack_i.fsti.checked", "Vale.X64.Memory.fsti.checked", "Vale.X64.Machine_Semantics_s.fst.checked", "Vale.X64.Instructions_s.fsti.checked", "Vale.X64.InsLemmas.fsti.checked", "Vale.X64.Decls.fst.checked", "Vale.X64.CPU_Features_s.fst.checked", "Vale.Arch.Types.fsti.checked", "prims.fst.checked", "FStar.UInt.fsti.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Math.Lemmas.fst.checked" ], "interface_file": true, "source_file": "Vale.X64.InsBasic.fst" }
[]
[ "Vale.X64.Decls.va_code", "Vale.X64.Decls.va_state", "Vale.X64.Decls.va_operand_dst_opr64", "Vale.X64.Decls.va_operand_opr64", "Vale.X64.State.vale_state", "Vale.X64.Lemmas.fuel", "FStar.Pervasives.Native.Mktuple2", "Vale.X64.Decls.va_fuel", "Prims.unit", "Vale.X64.Decls.lemma_mul_in_bounds", "Vale.X64.Decls.va_eval_dst_opr64", "Vale.X64.Decls.va_eval_opr64", "Vale.X64.Decls.lemma_mul_nat", "FStar.Pervasives.Native.tuple2", "Prims.nat", "Vale.X64.Decls.va_eval_ins", "Vale.X64.Taint_Semantics.mk_ins", "Vale.X64.InsLemmas.make_instr", "Prims.Cons", "Vale.X64.Instruction_s.instr_out", "Vale.X64.Instruction_s.inOut", "Vale.X64.Instruction_s.op64", "Prims.Nil", "Vale.X64.Instruction_s.instr_operand", "Vale.X64.Instruction_s.HavocFlags", "Vale.X64.Instructions_s.ins_IMul64", "Vale.X64.Decls.va_ins_lemma", "Vale.X64.Decls.va_reveal_opaque", "Vale.X64.InsBasic.va_code_IMul64" ]
[]
module Vale.X64.InsBasic open Vale.X64 open Vale.X64.StateLemmas open Vale.X64.InsLemmas open Vale.X64.Taint_Semantics open Vale.X64.CPU_Features_s open Vale.X64.Memory open Vale.X64.Stack_i module I = Vale.X64.Instructions_s module S = Vale.X64.Machine_Semantics_s friend Vale.X64.Decls #reset-options "--initial_fuel 5 --max_fuel 5 --max_ifuel 2 --z3rlimit 20" //-- Mov64 [@ "opaque_to_smt"] let va_code_Mov64 dst src = (mk_ins (make_instr_annotate (I.ins_Mov64) (S.AnnotateMov64 ()) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Mov64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Mov64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Mov64) (va_code_Mov64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr_annotate (I.ins_Mov64) (S.AnnotateMov64 ()) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr_annotate (I.ins_Mov64) (S.AnnotateMov64 ()) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Mov64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Mov64 (va_code_Mov64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0))); va_lemma_norm_mods ([va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cmovc64 [@ "opaque_to_smt"] let va_code_Cmovc64 dst src = (mk_ins (make_instr (I.ins_Cmovc64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Cmovc64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cmovc64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Cmovc64) (va_code_Cmovc64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cmovc64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cmovc64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cmovc64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cmovc64 (va_code_Cmovc64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0))); va_lemma_norm_mods ([va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Add64 [@ "opaque_to_smt"] let va_code_Add64 dst src = (mk_ins (make_instr (I.ins_Add64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Add64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Add64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Add64) (va_code_Add64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Add64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Add64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Add64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Add64 (va_code_Add64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Add64Wrap [@ "opaque_to_smt"] let va_code_Add64Wrap dst src = (mk_ins (make_instr (I.ins_Add64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Add64Wrap dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Add64Wrap va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Add64Wrap) (va_code_Add64Wrap dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Add64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Add64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Add64Wrap dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Add64Wrap (va_code_Add64Wrap dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- AddLea64 [@ "opaque_to_smt"] let va_code_AddLea64 dst src1 src2 = (mk_ins (make_instr (I.ins_AddLea64) dst src1 src2)) [@ "opaque_to_smt"] let va_codegen_success_AddLea64 dst src1 src2 = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_AddLea64 va_b0 va_s0 dst src1 src2 = va_reveal_opaque (`%va_code_AddLea64) (va_code_AddLea64 dst src1 src2); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_AddLea64) dst src1 src2)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_AddLea64) dst src1 src2)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_AddLea64 dst src1 src2 va_s0 va_k = let (va_sM, va_f0) = va_lemma_AddLea64 (va_code_AddLea64 dst src1 src2) va_s0 dst src1 src2 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0))); va_lemma_norm_mods ([va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Adc64 [@ "opaque_to_smt"] let va_code_Adc64 dst src = (mk_ins (make_instr (I.ins_AddCarry64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Adc64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Adc64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Adc64) (va_code_Adc64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_AddCarry64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_AddCarry64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Adc64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Adc64 (va_code_Adc64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Adc64Wrap [@ "opaque_to_smt"] let va_code_Adc64Wrap dst src = (mk_ins (make_instr (I.ins_AddCarry64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Adc64Wrap dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Adc64Wrap va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Adc64Wrap) (va_code_Adc64Wrap dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_AddCarry64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_AddCarry64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Adc64Wrap dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Adc64Wrap (va_code_Adc64Wrap dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Adcx64Wrap #push-options "--smtencoding.nl_arith_repr boxwrap" [@ "opaque_to_smt"] let va_code_Adcx64Wrap dst src = (mk_ins (make_instr (I.ins_Adcx64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Adcx64Wrap dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Adcx64Wrap va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Adcx64Wrap) (va_code_Adcx64Wrap dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Adcx64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Adcx64) dst src)) va_s0 in assert (Vale.Arch.Types.add_wrap64 (Vale.Arch.Types.add_wrap64 (va_eval_dst_opr64 va_old_s dst) (va_eval_opr64 va_old_s src)) (if Vale.X64.Decls.cf (va_get_flags va_old_s) then 1 else 0) == (va_eval_dst_opr64 va_old_s dst + va_eval_opr64 va_old_s src + (if Vale.X64.Decls.cf (va_get_flags va_old_s) then 1 else 0)) `op_Modulus` pow2_64); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Adcx64Wrap dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Adcx64Wrap (va_code_Adcx64Wrap dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) #pop-options //-- //-- Adox64Wrap [@ "opaque_to_smt"] let va_code_Adox64Wrap dst src = (mk_ins (make_instr (I.ins_Adox64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Adox64Wrap dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Adox64Wrap va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Adox64Wrap) (va_code_Adox64Wrap dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Adox64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Adox64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Adox64Wrap dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Adox64Wrap (va_code_Adox64Wrap dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Sub64 [@ "opaque_to_smt"] let va_code_Sub64 dst src = (mk_ins (make_instr (I.ins_Sub64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Sub64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Sub64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Sub64) (va_code_Sub64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Sub64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Sub64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Sub64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Sub64 (va_code_Sub64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Sub64Wrap [@ "opaque_to_smt"] let va_code_Sub64Wrap dst src = (mk_ins (make_instr (I.ins_Sub64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Sub64Wrap dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Sub64Wrap va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Sub64Wrap) (va_code_Sub64Wrap dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Sub64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Sub64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Sub64Wrap dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Sub64Wrap (va_code_Sub64Wrap dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Sbb64 [@ "opaque_to_smt"] let va_code_Sbb64 dst src = (mk_ins (make_instr (I.ins_Sbb64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Sbb64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Sbb64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Sbb64) (va_code_Sbb64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Sbb64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Sbb64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Sbb64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Sbb64 (va_code_Sbb64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- #restart-solver #push-options "--max_fuel 0 --max_ifuel 0 --using_facts_from 'Prims FStar.UInt'" let lemma_fundamental_div_mod (a b:nat64) : Lemma (pow2_64 * (FStar.UInt.mul_div #64 a b) + (FStar.UInt.mul_mod #64 a b) == a * b) = FStar.Math.Lemmas.lemma_div_mod (a * b) pow2_64 #pop-options //-- lemma_fundamental_div_mod //-- //-- Mul64Wrap [@ "opaque_to_smt"] let va_code_Mul64Wrap src = (mk_ins (make_instr (I.ins_Mul64) src)) [@ "opaque_to_smt"] let va_codegen_success_Mul64Wrap src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Mul64Wrap va_b0 va_s0 src = va_reveal_opaque (`%va_code_Mul64Wrap) (va_code_Mul64Wrap src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Mul64) src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Mul64) src)) va_s0 in lemma_fundamental_div_mod (va_get_reg64 rRax va_old_s) (va_eval_opr64 va_old_s src); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Mul64Wrap src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Mul64Wrap (va_code_Mul64Wrap src) va_s0 src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRax va_sM (va_update_flags va_sM (va_update_ok va_sM va_s0))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRax; va_Mod_flags]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Mulx64 [@ "opaque_to_smt"] let va_code_Mulx64 dst_hi dst_lo src = (mk_ins (make_instr (I.ins_Mulx64) dst_hi dst_lo src)) [@ "opaque_to_smt"] let va_codegen_success_Mulx64 dst_hi dst_lo src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Mulx64 va_b0 va_s0 dst_hi dst_lo src = va_reveal_opaque (`%va_code_Mulx64) (va_code_Mulx64 dst_hi dst_lo src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Mulx64) dst_hi dst_lo src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Mulx64) dst_hi dst_lo src)) va_s0 in lemma_fundamental_div_mod (va_get_reg64 rRdx va_old_s) (va_eval_opr64 va_old_s src); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Mulx64 dst_hi dst_lo src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Mulx64 (va_code_Mulx64 dst_hi dst_lo src) va_s0 dst_hi dst_lo src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst_lo va_sM (va_update_operand_dst_opr64 dst_hi va_sM va_s0)))); va_lemma_norm_mods ([va_mod_dst_opr64 dst_lo; va_mod_dst_opr64 dst_hi]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- lemma_mul_nat //-- //-- lemma_mul_in_bounds //-- //-- IMul64 [@ "opaque_to_smt"] let va_code_IMul64 dst src = (mk_ins (make_instr (I.ins_IMul64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_IMul64 dst src = (va_ttrue ()) [@"opaque_to_smt"]
false
false
Vale.X64.InsBasic.fst
{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 5, "initial_ifuel": 0, "max_fuel": 5, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": true, "smtencoding_l_arith_repr": "native", "smtencoding_nl_arith_repr": "wrapped", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": false, "z3cliopt": [ "smt.arith.nl=false", "smt.QI.EAGER_THRESHOLD=100", "smt.CASE_SPLIT=3" ], "z3refresh": false, "z3rlimit": 20, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }
null
val va_lemma_IMul64 : va_b0:va_code -> va_s0:va_state -> dst:va_operand_dst_opr64 -> src:va_operand_opr64 -> Ghost (va_state & va_fuel) (requires (va_require_total va_b0 (va_code_IMul64 dst src) va_s0 /\ va_is_dst_dst_opr64 dst va_s0 /\ va_is_src_opr64 src va_s0 /\ va_get_ok va_s0 /\ va_mul_nat (va_eval_dst_opr64 va_s0 dst) (va_eval_opr64 va_s0 src) < pow2_64)) (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\ va_eval_dst_opr64 va_sM dst == va_mul_nat (va_eval_dst_opr64 va_s0 dst) (va_eval_opr64 va_s0 src) /\ va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))))
[]
Vale.X64.InsBasic.va_lemma_IMul64
{ "file_name": "obj/Vale.X64.InsBasic.fst", "git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e", "git_url": "https://github.com/hacl-star/hacl-star.git", "project_name": "hacl-star" }
va_b0: Vale.X64.Decls.va_code -> va_s0: Vale.X64.Decls.va_state -> dst: Vale.X64.Decls.va_operand_dst_opr64 -> src: Vale.X64.Decls.va_operand_opr64 -> Prims.Ghost (Vale.X64.Decls.va_state * Vale.X64.Decls.va_fuel)
{ "end_col": 16, "end_line": 470, "start_col": 2, "start_line": 464 }
Prims.Ghost
val va_lemma_Cpuid_Sha : va_b0:va_code -> va_s0:va_state -> Ghost (va_state & va_fuel) (requires (va_require_total va_b0 (va_code_Cpuid_Sha ()) va_s0 /\ va_get_ok va_s0 /\ va_get_reg64 rRax va_s0 = 7 /\ va_get_reg64 rRcx va_s0 = 0)) (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\ Vale.Arch.Types.iand64 (va_get_reg64 rRbx va_sM) 536870912 > 0 == sha_enabled /\ va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))))
[ { "abbrev": true, "full_module": "Vale.X64.Machine_Semantics_s", "short_module": "S" }, { "abbrev": true, "full_module": "Vale.X64.Instructions_s", "short_module": "I" }, { "abbrev": false, "full_module": "Vale.X64.Stack_i", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.Memory", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.Taint_Semantics", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.InsLemmas", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.StateLemmas", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.CPU_Features_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.QuickCode", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.Decls", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.State", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.Machine_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Arch.Types", "short_module": null }, { "abbrev": false, "full_module": "Vale.Arch.HeapImpl", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Types_s", "short_module": null }, { "abbrev": false, "full_module": "FStar.Mul", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]
false
let va_lemma_Cpuid_Sha va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Sha) (va_code_Cpuid_Sha ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM)
val va_lemma_Cpuid_Sha : va_b0:va_code -> va_s0:va_state -> Ghost (va_state & va_fuel) (requires (va_require_total va_b0 (va_code_Cpuid_Sha ()) va_s0 /\ va_get_ok va_s0 /\ va_get_reg64 rRax va_s0 = 7 /\ va_get_reg64 rRcx va_s0 = 0)) (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\ Vale.Arch.Types.iand64 (va_get_reg64 rRbx va_sM) 536870912 > 0 == sha_enabled /\ va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0))))))) let va_lemma_Cpuid_Sha va_b0 va_s0 =
false
null
false
va_reveal_opaque (`%va_code_Cpuid_Sha) (va_code_Cpuid_Sha ()); let va_old_s:va_state = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let va_sM, va_fM = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM)
{ "checked_file": "Vale.X64.InsBasic.fst.checked", "dependencies": [ "Vale.X64.Taint_Semantics.fst.checked", "Vale.X64.StateLemmas.fsti.checked", "Vale.X64.Stack_i.fsti.checked", "Vale.X64.Memory.fsti.checked", "Vale.X64.Machine_Semantics_s.fst.checked", "Vale.X64.Instructions_s.fsti.checked", "Vale.X64.InsLemmas.fsti.checked", "Vale.X64.Decls.fst.checked", "Vale.X64.CPU_Features_s.fst.checked", "Vale.Arch.Types.fsti.checked", "prims.fst.checked", "FStar.UInt.fsti.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Math.Lemmas.fst.checked" ], "interface_file": true, "source_file": "Vale.X64.InsBasic.fst" }
[]
[ "Vale.X64.Decls.va_code", "Vale.X64.Decls.va_state", "Vale.X64.State.vale_state", "Vale.X64.Lemmas.fuel", "FStar.Pervasives.Native.Mktuple2", "Vale.X64.Decls.va_fuel", "Prims.unit", "Vale.X64.CPU_Features_s.cpuid_features", "FStar.Pervasives.Native.tuple2", "Prims.nat", "Vale.X64.Decls.va_eval_ins", "Vale.X64.Taint_Semantics.mk_ins", "Vale.X64.InsLemmas.make_instr", "Prims.Cons", "Vale.X64.Instruction_s.instr_out", "Vale.X64.Instruction_s.inOut", "Vale.X64.Instruction_s.one64Reg", "Vale.X64.Machine_s.rRax", "Vale.X64.Instruction_s.out", "Vale.X64.Machine_s.rRbx", "Vale.X64.Machine_s.rRcx", "Vale.X64.Machine_s.rRdx", "Prims.Nil", "Vale.X64.Instruction_s.instr_operand", "Vale.X64.Instruction_s.PreserveFlags", "Vale.X64.Instructions_s.ins_Cpuid", "Vale.X64.Decls.va_ins_lemma", "Vale.X64.Decls.va_reveal_opaque", "Vale.X64.InsBasic.va_code_Cpuid_Sha" ]
[]
module Vale.X64.InsBasic open Vale.X64 open Vale.X64.StateLemmas open Vale.X64.InsLemmas open Vale.X64.Taint_Semantics open Vale.X64.CPU_Features_s open Vale.X64.Memory open Vale.X64.Stack_i module I = Vale.X64.Instructions_s module S = Vale.X64.Machine_Semantics_s friend Vale.X64.Decls #reset-options "--initial_fuel 5 --max_fuel 5 --max_ifuel 2 --z3rlimit 20" //-- Mov64 [@ "opaque_to_smt"] let va_code_Mov64 dst src = (mk_ins (make_instr_annotate (I.ins_Mov64) (S.AnnotateMov64 ()) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Mov64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Mov64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Mov64) (va_code_Mov64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr_annotate (I.ins_Mov64) (S.AnnotateMov64 ()) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr_annotate (I.ins_Mov64) (S.AnnotateMov64 ()) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Mov64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Mov64 (va_code_Mov64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0))); va_lemma_norm_mods ([va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cmovc64 [@ "opaque_to_smt"] let va_code_Cmovc64 dst src = (mk_ins (make_instr (I.ins_Cmovc64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Cmovc64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cmovc64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Cmovc64) (va_code_Cmovc64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cmovc64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cmovc64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cmovc64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cmovc64 (va_code_Cmovc64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0))); va_lemma_norm_mods ([va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Add64 [@ "opaque_to_smt"] let va_code_Add64 dst src = (mk_ins (make_instr (I.ins_Add64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Add64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Add64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Add64) (va_code_Add64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Add64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Add64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Add64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Add64 (va_code_Add64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Add64Wrap [@ "opaque_to_smt"] let va_code_Add64Wrap dst src = (mk_ins (make_instr (I.ins_Add64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Add64Wrap dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Add64Wrap va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Add64Wrap) (va_code_Add64Wrap dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Add64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Add64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Add64Wrap dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Add64Wrap (va_code_Add64Wrap dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- AddLea64 [@ "opaque_to_smt"] let va_code_AddLea64 dst src1 src2 = (mk_ins (make_instr (I.ins_AddLea64) dst src1 src2)) [@ "opaque_to_smt"] let va_codegen_success_AddLea64 dst src1 src2 = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_AddLea64 va_b0 va_s0 dst src1 src2 = va_reveal_opaque (`%va_code_AddLea64) (va_code_AddLea64 dst src1 src2); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_AddLea64) dst src1 src2)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_AddLea64) dst src1 src2)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_AddLea64 dst src1 src2 va_s0 va_k = let (va_sM, va_f0) = va_lemma_AddLea64 (va_code_AddLea64 dst src1 src2) va_s0 dst src1 src2 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0))); va_lemma_norm_mods ([va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Adc64 [@ "opaque_to_smt"] let va_code_Adc64 dst src = (mk_ins (make_instr (I.ins_AddCarry64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Adc64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Adc64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Adc64) (va_code_Adc64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_AddCarry64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_AddCarry64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Adc64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Adc64 (va_code_Adc64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Adc64Wrap [@ "opaque_to_smt"] let va_code_Adc64Wrap dst src = (mk_ins (make_instr (I.ins_AddCarry64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Adc64Wrap dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Adc64Wrap va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Adc64Wrap) (va_code_Adc64Wrap dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_AddCarry64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_AddCarry64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Adc64Wrap dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Adc64Wrap (va_code_Adc64Wrap dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Adcx64Wrap #push-options "--smtencoding.nl_arith_repr boxwrap" [@ "opaque_to_smt"] let va_code_Adcx64Wrap dst src = (mk_ins (make_instr (I.ins_Adcx64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Adcx64Wrap dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Adcx64Wrap va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Adcx64Wrap) (va_code_Adcx64Wrap dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Adcx64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Adcx64) dst src)) va_s0 in assert (Vale.Arch.Types.add_wrap64 (Vale.Arch.Types.add_wrap64 (va_eval_dst_opr64 va_old_s dst) (va_eval_opr64 va_old_s src)) (if Vale.X64.Decls.cf (va_get_flags va_old_s) then 1 else 0) == (va_eval_dst_opr64 va_old_s dst + va_eval_opr64 va_old_s src + (if Vale.X64.Decls.cf (va_get_flags va_old_s) then 1 else 0)) `op_Modulus` pow2_64); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Adcx64Wrap dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Adcx64Wrap (va_code_Adcx64Wrap dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) #pop-options //-- //-- Adox64Wrap [@ "opaque_to_smt"] let va_code_Adox64Wrap dst src = (mk_ins (make_instr (I.ins_Adox64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Adox64Wrap dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Adox64Wrap va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Adox64Wrap) (va_code_Adox64Wrap dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Adox64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Adox64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Adox64Wrap dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Adox64Wrap (va_code_Adox64Wrap dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Sub64 [@ "opaque_to_smt"] let va_code_Sub64 dst src = (mk_ins (make_instr (I.ins_Sub64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Sub64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Sub64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Sub64) (va_code_Sub64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Sub64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Sub64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Sub64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Sub64 (va_code_Sub64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Sub64Wrap [@ "opaque_to_smt"] let va_code_Sub64Wrap dst src = (mk_ins (make_instr (I.ins_Sub64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Sub64Wrap dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Sub64Wrap va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Sub64Wrap) (va_code_Sub64Wrap dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Sub64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Sub64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Sub64Wrap dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Sub64Wrap (va_code_Sub64Wrap dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Sbb64 [@ "opaque_to_smt"] let va_code_Sbb64 dst src = (mk_ins (make_instr (I.ins_Sbb64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Sbb64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Sbb64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Sbb64) (va_code_Sbb64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Sbb64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Sbb64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Sbb64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Sbb64 (va_code_Sbb64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- #restart-solver #push-options "--max_fuel 0 --max_ifuel 0 --using_facts_from 'Prims FStar.UInt'" let lemma_fundamental_div_mod (a b:nat64) : Lemma (pow2_64 * (FStar.UInt.mul_div #64 a b) + (FStar.UInt.mul_mod #64 a b) == a * b) = FStar.Math.Lemmas.lemma_div_mod (a * b) pow2_64 #pop-options //-- lemma_fundamental_div_mod //-- //-- Mul64Wrap [@ "opaque_to_smt"] let va_code_Mul64Wrap src = (mk_ins (make_instr (I.ins_Mul64) src)) [@ "opaque_to_smt"] let va_codegen_success_Mul64Wrap src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Mul64Wrap va_b0 va_s0 src = va_reveal_opaque (`%va_code_Mul64Wrap) (va_code_Mul64Wrap src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Mul64) src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Mul64) src)) va_s0 in lemma_fundamental_div_mod (va_get_reg64 rRax va_old_s) (va_eval_opr64 va_old_s src); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Mul64Wrap src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Mul64Wrap (va_code_Mul64Wrap src) va_s0 src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRax va_sM (va_update_flags va_sM (va_update_ok va_sM va_s0))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRax; va_Mod_flags]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Mulx64 [@ "opaque_to_smt"] let va_code_Mulx64 dst_hi dst_lo src = (mk_ins (make_instr (I.ins_Mulx64) dst_hi dst_lo src)) [@ "opaque_to_smt"] let va_codegen_success_Mulx64 dst_hi dst_lo src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Mulx64 va_b0 va_s0 dst_hi dst_lo src = va_reveal_opaque (`%va_code_Mulx64) (va_code_Mulx64 dst_hi dst_lo src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Mulx64) dst_hi dst_lo src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Mulx64) dst_hi dst_lo src)) va_s0 in lemma_fundamental_div_mod (va_get_reg64 rRdx va_old_s) (va_eval_opr64 va_old_s src); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Mulx64 dst_hi dst_lo src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Mulx64 (va_code_Mulx64 dst_hi dst_lo src) va_s0 dst_hi dst_lo src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst_lo va_sM (va_update_operand_dst_opr64 dst_hi va_sM va_s0)))); va_lemma_norm_mods ([va_mod_dst_opr64 dst_lo; va_mod_dst_opr64 dst_hi]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- lemma_mul_nat //-- //-- lemma_mul_in_bounds //-- //-- IMul64 [@ "opaque_to_smt"] let va_code_IMul64 dst src = (mk_ins (make_instr (I.ins_IMul64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_IMul64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_IMul64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_IMul64) (va_code_IMul64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_IMul64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_IMul64) dst src)) va_s0 in lemma_mul_nat (va_eval_dst_opr64 va_old_s dst) (va_eval_opr64 va_old_s src); lemma_mul_in_bounds (va_eval_dst_opr64 va_old_s dst) (va_eval_opr64 va_old_s src); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_IMul64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_IMul64 (va_code_IMul64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Xor64 [@ "opaque_to_smt"] let va_code_Xor64 dst src = (mk_ins (make_instr_annotate (I.ins_Xor64) (S.AnnotateXor64 ()) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Xor64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Xor64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Xor64) (va_code_Xor64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr_annotate (I.ins_Xor64) (S.AnnotateXor64 ()) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr_annotate (I.ins_Xor64) (S.AnnotateXor64 ()) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Xor64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Xor64 (va_code_Xor64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- And64 [@ "opaque_to_smt"] let va_code_And64 dst src = (mk_ins (make_instr (I.ins_And64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_And64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_And64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_And64) (va_code_And64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_And64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_And64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_And64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_And64 (va_code_And64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Shl64 [@ "opaque_to_smt"] let va_code_Shl64 dst amt = (mk_ins (make_instr (I.ins_Shl64) dst amt)) [@ "opaque_to_smt"] let va_codegen_success_Shl64 dst amt = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Shl64 va_b0 va_s0 dst amt = va_reveal_opaque (`%va_code_Shl64) (va_code_Shl64 dst amt); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Shl64) dst amt)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Shl64) dst amt)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Shl64 dst amt va_s0 va_k = let (va_sM, va_f0) = va_lemma_Shl64 (va_code_Shl64 dst amt) va_s0 dst amt in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Shr64 [@ "opaque_to_smt"] let va_code_Shr64 dst amt = (mk_ins (make_instr (I.ins_Shr64) dst amt)) [@ "opaque_to_smt"] let va_codegen_success_Shr64 dst amt = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Shr64 va_b0 va_s0 dst amt = va_reveal_opaque (`%va_code_Shr64) (va_code_Shr64 dst amt); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Shr64) dst amt)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Shr64) dst amt)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Shr64 dst amt va_s0 va_k = let (va_sM, va_f0) = va_lemma_Shr64 (va_code_Shr64 dst amt) va_s0 dst amt in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_AES [@ "opaque_to_smt"] let va_code_Cpuid_AES () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_AES () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_AES va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_AES) (va_code_Cpuid_AES ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_AES va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_AES (va_code_Cpuid_AES ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Sha [@ "opaque_to_smt"] let va_code_Cpuid_Sha () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Sha () = (va_ttrue ()) [@"opaque_to_smt"]
false
false
Vale.X64.InsBasic.fst
{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 5, "initial_ifuel": 0, "max_fuel": 5, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": true, "smtencoding_l_arith_repr": "native", "smtencoding_nl_arith_repr": "wrapped", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": false, "z3cliopt": [ "smt.arith.nl=false", "smt.QI.EAGER_THRESHOLD=100", "smt.CASE_SPLIT=3" ], "z3refresh": false, "z3rlimit": 20, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }
null
val va_lemma_Cpuid_Sha : va_b0:va_code -> va_s0:va_state -> Ghost (va_state & va_fuel) (requires (va_require_total va_b0 (va_code_Cpuid_Sha ()) va_s0 /\ va_get_ok va_s0 /\ va_get_reg64 rRax va_s0 = 7 /\ va_get_reg64 rRcx va_s0 = 0)) (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\ Vale.Arch.Types.iand64 (va_get_reg64 rRbx va_sM) 536870912 > 0 == sha_enabled /\ va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))))
[]
Vale.X64.InsBasic.va_lemma_Cpuid_Sha
{ "file_name": "obj/Vale.X64.InsBasic.fst", "git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e", "git_url": "https://github.com/hacl-star/hacl-star.git", "project_name": "hacl-star" }
va_b0: Vale.X64.Decls.va_code -> va_s0: Vale.X64.Decls.va_state -> Prims.Ghost (Vale.X64.Decls.va_state * Vale.X64.Decls.va_fuel)
{ "end_col": 16, "end_line": 654, "start_col": 2, "start_line": 649 }
Prims.Ghost
val va_lemma_Cpuid_Adx_Bmi2 : va_b0:va_code -> va_s0:va_state -> Ghost (va_state & va_fuel) (requires (va_require_total va_b0 (va_code_Cpuid_Adx_Bmi2 ()) va_s0 /\ va_get_ok va_s0 /\ va_get_reg64 rRax va_s0 = 7 /\ va_get_reg64 rRcx va_s0 = 0)) (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\ Vale.Arch.Types.iand64 (va_get_reg64 rRbx va_sM) 256 > 0 == bmi2_enabled /\ Vale.Arch.Types.iand64 (va_get_reg64 rRbx va_sM) 524288 > 0 == adx_enabled /\ va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))))
[ { "abbrev": true, "full_module": "Vale.X64.Machine_Semantics_s", "short_module": "S" }, { "abbrev": true, "full_module": "Vale.X64.Instructions_s", "short_module": "I" }, { "abbrev": false, "full_module": "Vale.X64.Stack_i", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.Memory", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.Taint_Semantics", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.InsLemmas", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.StateLemmas", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.CPU_Features_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.QuickCode", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.Decls", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.State", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.Machine_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Arch.Types", "short_module": null }, { "abbrev": false, "full_module": "Vale.Arch.HeapImpl", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Types_s", "short_module": null }, { "abbrev": false, "full_module": "FStar.Mul", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]
false
let va_lemma_Cpuid_Adx_Bmi2 va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Adx_Bmi2) (va_code_Cpuid_Adx_Bmi2 ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM)
val va_lemma_Cpuid_Adx_Bmi2 : va_b0:va_code -> va_s0:va_state -> Ghost (va_state & va_fuel) (requires (va_require_total va_b0 (va_code_Cpuid_Adx_Bmi2 ()) va_s0 /\ va_get_ok va_s0 /\ va_get_reg64 rRax va_s0 = 7 /\ va_get_reg64 rRcx va_s0 = 0)) (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\ Vale.Arch.Types.iand64 (va_get_reg64 rRbx va_sM) 256 > 0 == bmi2_enabled /\ Vale.Arch.Types.iand64 (va_get_reg64 rRbx va_sM) 524288 > 0 == adx_enabled /\ va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0))))))) let va_lemma_Cpuid_Adx_Bmi2 va_b0 va_s0 =
false
null
false
va_reveal_opaque (`%va_code_Cpuid_Adx_Bmi2) (va_code_Cpuid_Adx_Bmi2 ()); let va_old_s:va_state = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let va_sM, va_fM = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM)
{ "checked_file": "Vale.X64.InsBasic.fst.checked", "dependencies": [ "Vale.X64.Taint_Semantics.fst.checked", "Vale.X64.StateLemmas.fsti.checked", "Vale.X64.Stack_i.fsti.checked", "Vale.X64.Memory.fsti.checked", "Vale.X64.Machine_Semantics_s.fst.checked", "Vale.X64.Instructions_s.fsti.checked", "Vale.X64.InsLemmas.fsti.checked", "Vale.X64.Decls.fst.checked", "Vale.X64.CPU_Features_s.fst.checked", "Vale.Arch.Types.fsti.checked", "prims.fst.checked", "FStar.UInt.fsti.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Math.Lemmas.fst.checked" ], "interface_file": true, "source_file": "Vale.X64.InsBasic.fst" }
[]
[ "Vale.X64.Decls.va_code", "Vale.X64.Decls.va_state", "Vale.X64.State.vale_state", "Vale.X64.Lemmas.fuel", "FStar.Pervasives.Native.Mktuple2", "Vale.X64.Decls.va_fuel", "Prims.unit", "Vale.X64.CPU_Features_s.cpuid_features", "FStar.Pervasives.Native.tuple2", "Prims.nat", "Vale.X64.Decls.va_eval_ins", "Vale.X64.Taint_Semantics.mk_ins", "Vale.X64.InsLemmas.make_instr", "Prims.Cons", "Vale.X64.Instruction_s.instr_out", "Vale.X64.Instruction_s.inOut", "Vale.X64.Instruction_s.one64Reg", "Vale.X64.Machine_s.rRax", "Vale.X64.Instruction_s.out", "Vale.X64.Machine_s.rRbx", "Vale.X64.Machine_s.rRcx", "Vale.X64.Machine_s.rRdx", "Prims.Nil", "Vale.X64.Instruction_s.instr_operand", "Vale.X64.Instruction_s.PreserveFlags", "Vale.X64.Instructions_s.ins_Cpuid", "Vale.X64.Decls.va_ins_lemma", "Vale.X64.Decls.va_reveal_opaque", "Vale.X64.InsBasic.va_code_Cpuid_Adx_Bmi2" ]
[]
module Vale.X64.InsBasic open Vale.X64 open Vale.X64.StateLemmas open Vale.X64.InsLemmas open Vale.X64.Taint_Semantics open Vale.X64.CPU_Features_s open Vale.X64.Memory open Vale.X64.Stack_i module I = Vale.X64.Instructions_s module S = Vale.X64.Machine_Semantics_s friend Vale.X64.Decls #reset-options "--initial_fuel 5 --max_fuel 5 --max_ifuel 2 --z3rlimit 20" //-- Mov64 [@ "opaque_to_smt"] let va_code_Mov64 dst src = (mk_ins (make_instr_annotate (I.ins_Mov64) (S.AnnotateMov64 ()) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Mov64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Mov64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Mov64) (va_code_Mov64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr_annotate (I.ins_Mov64) (S.AnnotateMov64 ()) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr_annotate (I.ins_Mov64) (S.AnnotateMov64 ()) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Mov64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Mov64 (va_code_Mov64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0))); va_lemma_norm_mods ([va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cmovc64 [@ "opaque_to_smt"] let va_code_Cmovc64 dst src = (mk_ins (make_instr (I.ins_Cmovc64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Cmovc64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cmovc64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Cmovc64) (va_code_Cmovc64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cmovc64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cmovc64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cmovc64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cmovc64 (va_code_Cmovc64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0))); va_lemma_norm_mods ([va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Add64 [@ "opaque_to_smt"] let va_code_Add64 dst src = (mk_ins (make_instr (I.ins_Add64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Add64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Add64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Add64) (va_code_Add64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Add64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Add64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Add64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Add64 (va_code_Add64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Add64Wrap [@ "opaque_to_smt"] let va_code_Add64Wrap dst src = (mk_ins (make_instr (I.ins_Add64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Add64Wrap dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Add64Wrap va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Add64Wrap) (va_code_Add64Wrap dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Add64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Add64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Add64Wrap dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Add64Wrap (va_code_Add64Wrap dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- AddLea64 [@ "opaque_to_smt"] let va_code_AddLea64 dst src1 src2 = (mk_ins (make_instr (I.ins_AddLea64) dst src1 src2)) [@ "opaque_to_smt"] let va_codegen_success_AddLea64 dst src1 src2 = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_AddLea64 va_b0 va_s0 dst src1 src2 = va_reveal_opaque (`%va_code_AddLea64) (va_code_AddLea64 dst src1 src2); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_AddLea64) dst src1 src2)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_AddLea64) dst src1 src2)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_AddLea64 dst src1 src2 va_s0 va_k = let (va_sM, va_f0) = va_lemma_AddLea64 (va_code_AddLea64 dst src1 src2) va_s0 dst src1 src2 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0))); va_lemma_norm_mods ([va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Adc64 [@ "opaque_to_smt"] let va_code_Adc64 dst src = (mk_ins (make_instr (I.ins_AddCarry64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Adc64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Adc64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Adc64) (va_code_Adc64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_AddCarry64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_AddCarry64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Adc64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Adc64 (va_code_Adc64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Adc64Wrap [@ "opaque_to_smt"] let va_code_Adc64Wrap dst src = (mk_ins (make_instr (I.ins_AddCarry64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Adc64Wrap dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Adc64Wrap va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Adc64Wrap) (va_code_Adc64Wrap dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_AddCarry64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_AddCarry64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Adc64Wrap dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Adc64Wrap (va_code_Adc64Wrap dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Adcx64Wrap #push-options "--smtencoding.nl_arith_repr boxwrap" [@ "opaque_to_smt"] let va_code_Adcx64Wrap dst src = (mk_ins (make_instr (I.ins_Adcx64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Adcx64Wrap dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Adcx64Wrap va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Adcx64Wrap) (va_code_Adcx64Wrap dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Adcx64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Adcx64) dst src)) va_s0 in assert (Vale.Arch.Types.add_wrap64 (Vale.Arch.Types.add_wrap64 (va_eval_dst_opr64 va_old_s dst) (va_eval_opr64 va_old_s src)) (if Vale.X64.Decls.cf (va_get_flags va_old_s) then 1 else 0) == (va_eval_dst_opr64 va_old_s dst + va_eval_opr64 va_old_s src + (if Vale.X64.Decls.cf (va_get_flags va_old_s) then 1 else 0)) `op_Modulus` pow2_64); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Adcx64Wrap dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Adcx64Wrap (va_code_Adcx64Wrap dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) #pop-options //-- //-- Adox64Wrap [@ "opaque_to_smt"] let va_code_Adox64Wrap dst src = (mk_ins (make_instr (I.ins_Adox64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Adox64Wrap dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Adox64Wrap va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Adox64Wrap) (va_code_Adox64Wrap dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Adox64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Adox64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Adox64Wrap dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Adox64Wrap (va_code_Adox64Wrap dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Sub64 [@ "opaque_to_smt"] let va_code_Sub64 dst src = (mk_ins (make_instr (I.ins_Sub64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Sub64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Sub64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Sub64) (va_code_Sub64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Sub64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Sub64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Sub64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Sub64 (va_code_Sub64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Sub64Wrap [@ "opaque_to_smt"] let va_code_Sub64Wrap dst src = (mk_ins (make_instr (I.ins_Sub64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Sub64Wrap dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Sub64Wrap va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Sub64Wrap) (va_code_Sub64Wrap dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Sub64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Sub64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Sub64Wrap dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Sub64Wrap (va_code_Sub64Wrap dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Sbb64 [@ "opaque_to_smt"] let va_code_Sbb64 dst src = (mk_ins (make_instr (I.ins_Sbb64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Sbb64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Sbb64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Sbb64) (va_code_Sbb64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Sbb64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Sbb64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Sbb64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Sbb64 (va_code_Sbb64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- #restart-solver #push-options "--max_fuel 0 --max_ifuel 0 --using_facts_from 'Prims FStar.UInt'" let lemma_fundamental_div_mod (a b:nat64) : Lemma (pow2_64 * (FStar.UInt.mul_div #64 a b) + (FStar.UInt.mul_mod #64 a b) == a * b) = FStar.Math.Lemmas.lemma_div_mod (a * b) pow2_64 #pop-options //-- lemma_fundamental_div_mod //-- //-- Mul64Wrap [@ "opaque_to_smt"] let va_code_Mul64Wrap src = (mk_ins (make_instr (I.ins_Mul64) src)) [@ "opaque_to_smt"] let va_codegen_success_Mul64Wrap src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Mul64Wrap va_b0 va_s0 src = va_reveal_opaque (`%va_code_Mul64Wrap) (va_code_Mul64Wrap src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Mul64) src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Mul64) src)) va_s0 in lemma_fundamental_div_mod (va_get_reg64 rRax va_old_s) (va_eval_opr64 va_old_s src); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Mul64Wrap src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Mul64Wrap (va_code_Mul64Wrap src) va_s0 src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRax va_sM (va_update_flags va_sM (va_update_ok va_sM va_s0))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRax; va_Mod_flags]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Mulx64 [@ "opaque_to_smt"] let va_code_Mulx64 dst_hi dst_lo src = (mk_ins (make_instr (I.ins_Mulx64) dst_hi dst_lo src)) [@ "opaque_to_smt"] let va_codegen_success_Mulx64 dst_hi dst_lo src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Mulx64 va_b0 va_s0 dst_hi dst_lo src = va_reveal_opaque (`%va_code_Mulx64) (va_code_Mulx64 dst_hi dst_lo src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Mulx64) dst_hi dst_lo src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Mulx64) dst_hi dst_lo src)) va_s0 in lemma_fundamental_div_mod (va_get_reg64 rRdx va_old_s) (va_eval_opr64 va_old_s src); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Mulx64 dst_hi dst_lo src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Mulx64 (va_code_Mulx64 dst_hi dst_lo src) va_s0 dst_hi dst_lo src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst_lo va_sM (va_update_operand_dst_opr64 dst_hi va_sM va_s0)))); va_lemma_norm_mods ([va_mod_dst_opr64 dst_lo; va_mod_dst_opr64 dst_hi]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- lemma_mul_nat //-- //-- lemma_mul_in_bounds //-- //-- IMul64 [@ "opaque_to_smt"] let va_code_IMul64 dst src = (mk_ins (make_instr (I.ins_IMul64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_IMul64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_IMul64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_IMul64) (va_code_IMul64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_IMul64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_IMul64) dst src)) va_s0 in lemma_mul_nat (va_eval_dst_opr64 va_old_s dst) (va_eval_opr64 va_old_s src); lemma_mul_in_bounds (va_eval_dst_opr64 va_old_s dst) (va_eval_opr64 va_old_s src); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_IMul64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_IMul64 (va_code_IMul64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Xor64 [@ "opaque_to_smt"] let va_code_Xor64 dst src = (mk_ins (make_instr_annotate (I.ins_Xor64) (S.AnnotateXor64 ()) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Xor64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Xor64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Xor64) (va_code_Xor64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr_annotate (I.ins_Xor64) (S.AnnotateXor64 ()) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr_annotate (I.ins_Xor64) (S.AnnotateXor64 ()) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Xor64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Xor64 (va_code_Xor64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- And64 [@ "opaque_to_smt"] let va_code_And64 dst src = (mk_ins (make_instr (I.ins_And64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_And64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_And64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_And64) (va_code_And64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_And64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_And64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_And64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_And64 (va_code_And64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Shl64 [@ "opaque_to_smt"] let va_code_Shl64 dst amt = (mk_ins (make_instr (I.ins_Shl64) dst amt)) [@ "opaque_to_smt"] let va_codegen_success_Shl64 dst amt = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Shl64 va_b0 va_s0 dst amt = va_reveal_opaque (`%va_code_Shl64) (va_code_Shl64 dst amt); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Shl64) dst amt)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Shl64) dst amt)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Shl64 dst amt va_s0 va_k = let (va_sM, va_f0) = va_lemma_Shl64 (va_code_Shl64 dst amt) va_s0 dst amt in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Shr64 [@ "opaque_to_smt"] let va_code_Shr64 dst amt = (mk_ins (make_instr (I.ins_Shr64) dst amt)) [@ "opaque_to_smt"] let va_codegen_success_Shr64 dst amt = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Shr64 va_b0 va_s0 dst amt = va_reveal_opaque (`%va_code_Shr64) (va_code_Shr64 dst amt); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Shr64) dst amt)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Shr64) dst amt)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Shr64 dst amt va_s0 va_k = let (va_sM, va_f0) = va_lemma_Shr64 (va_code_Shr64 dst amt) va_s0 dst amt in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_AES [@ "opaque_to_smt"] let va_code_Cpuid_AES () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_AES () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_AES va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_AES) (va_code_Cpuid_AES ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_AES va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_AES (va_code_Cpuid_AES ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Sha [@ "opaque_to_smt"] let va_code_Cpuid_Sha () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Sha () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Sha va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Sha) (va_code_Cpuid_Sha ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Sha va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Sha (va_code_Cpuid_Sha ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Adx_Bmi2 [@ "opaque_to_smt"] let va_code_Cpuid_Adx_Bmi2 () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Adx_Bmi2 () = (va_ttrue ()) [@"opaque_to_smt"]
false
false
Vale.X64.InsBasic.fst
{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 5, "initial_ifuel": 0, "max_fuel": 5, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": true, "smtencoding_l_arith_repr": "native", "smtencoding_nl_arith_repr": "wrapped", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": false, "z3cliopt": [ "smt.arith.nl=false", "smt.QI.EAGER_THRESHOLD=100", "smt.CASE_SPLIT=3" ], "z3refresh": false, "z3rlimit": 20, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }
null
val va_lemma_Cpuid_Adx_Bmi2 : va_b0:va_code -> va_s0:va_state -> Ghost (va_state & va_fuel) (requires (va_require_total va_b0 (va_code_Cpuid_Adx_Bmi2 ()) va_s0 /\ va_get_ok va_s0 /\ va_get_reg64 rRax va_s0 = 7 /\ va_get_reg64 rRcx va_s0 = 0)) (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\ Vale.Arch.Types.iand64 (va_get_reg64 rRbx va_sM) 256 > 0 == bmi2_enabled /\ Vale.Arch.Types.iand64 (va_get_reg64 rRbx va_sM) 524288 > 0 == adx_enabled /\ va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))))
[]
Vale.X64.InsBasic.va_lemma_Cpuid_Adx_Bmi2
{ "file_name": "obj/Vale.X64.InsBasic.fst", "git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e", "git_url": "https://github.com/hacl-star/hacl-star.git", "project_name": "hacl-star" }
va_b0: Vale.X64.Decls.va_code -> va_s0: Vale.X64.Decls.va_state -> Prims.Ghost (Vale.X64.Decls.va_state * Vale.X64.Decls.va_fuel)
{ "end_col": 16, "end_line": 686, "start_col": 2, "start_line": 681 }
Prims.Ghost
val va_wpProof_Cpuid_Avx512 : va_s0:va_state -> va_k:(va_state -> unit -> Type0) -> Ghost (va_state & va_fuel & unit) (requires (va_t_require va_s0 /\ va_wp_Cpuid_Avx512 va_s0 va_k)) (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Cpuid_Avx512 ()) ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_s0 va_k ((va_sM, va_f0, va_g))))
[ { "abbrev": true, "full_module": "Vale.X64.Machine_Semantics_s", "short_module": "S" }, { "abbrev": true, "full_module": "Vale.X64.Instructions_s", "short_module": "I" }, { "abbrev": false, "full_module": "Vale.X64.Stack_i", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.Memory", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.Taint_Semantics", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.InsLemmas", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.StateLemmas", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.CPU_Features_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.QuickCode", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.Decls", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.State", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.Machine_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Arch.Types", "short_module": null }, { "abbrev": false, "full_module": "Vale.Arch.HeapImpl", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Types_s", "short_module": null }, { "abbrev": false, "full_module": "FStar.Mul", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]
false
let va_wpProof_Cpuid_Avx512 va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Avx512 (va_code_Cpuid_Avx512 ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g)
val va_wpProof_Cpuid_Avx512 : va_s0:va_state -> va_k:(va_state -> unit -> Type0) -> Ghost (va_state & va_fuel & unit) (requires (va_t_require va_s0 /\ va_wp_Cpuid_Avx512 va_s0 va_k)) (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Cpuid_Avx512 ()) ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_s0 va_k ((va_sM, va_f0, va_g)))) let va_wpProof_Cpuid_Avx512 va_s0 va_k =
false
null
false
let va_sM, va_f0 = va_lemma_Cpuid_Avx512 (va_code_Cpuid_Avx512 ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0))))) ); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g)
{ "checked_file": "Vale.X64.InsBasic.fst.checked", "dependencies": [ "Vale.X64.Taint_Semantics.fst.checked", "Vale.X64.StateLemmas.fsti.checked", "Vale.X64.Stack_i.fsti.checked", "Vale.X64.Memory.fsti.checked", "Vale.X64.Machine_Semantics_s.fst.checked", "Vale.X64.Instructions_s.fsti.checked", "Vale.X64.InsLemmas.fsti.checked", "Vale.X64.Decls.fst.checked", "Vale.X64.CPU_Features_s.fst.checked", "Vale.Arch.Types.fsti.checked", "prims.fst.checked", "FStar.UInt.fsti.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Math.Lemmas.fst.checked" ], "interface_file": true, "source_file": "Vale.X64.InsBasic.fst" }
[]
[ "Vale.X64.Decls.va_state", "Prims.unit", "Vale.X64.Decls.va_fuel", "FStar.Pervasives.Native.Mktuple3", "Vale.X64.QuickCode.va_lemma_norm_mods", "Prims.Cons", "Vale.X64.QuickCode.mod_t", "Vale.X64.QuickCode.va_Mod_reg64", "Vale.X64.Machine_s.rRdx", "Vale.X64.Machine_s.rRcx", "Vale.X64.Machine_s.rRbx", "Vale.X64.Machine_s.rRax", "Prims.Nil", "Prims._assert", "Vale.X64.Decls.va_state_eq", "Vale.X64.Decls.va_update_reg64", "Vale.X64.Decls.va_update_ok", "Vale.X64.Decls.va_lemma_upd_update", "FStar.Pervasives.Native.tuple3", "FStar.Pervasives.Native.tuple2", "Vale.X64.State.vale_state", "Vale.X64.InsBasic.va_lemma_Cpuid_Avx512", "Vale.X64.InsBasic.va_code_Cpuid_Avx512" ]
[]
module Vale.X64.InsBasic open Vale.X64 open Vale.X64.StateLemmas open Vale.X64.InsLemmas open Vale.X64.Taint_Semantics open Vale.X64.CPU_Features_s open Vale.X64.Memory open Vale.X64.Stack_i module I = Vale.X64.Instructions_s module S = Vale.X64.Machine_Semantics_s friend Vale.X64.Decls #reset-options "--initial_fuel 5 --max_fuel 5 --max_ifuel 2 --z3rlimit 20" //-- Mov64 [@ "opaque_to_smt"] let va_code_Mov64 dst src = (mk_ins (make_instr_annotate (I.ins_Mov64) (S.AnnotateMov64 ()) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Mov64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Mov64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Mov64) (va_code_Mov64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr_annotate (I.ins_Mov64) (S.AnnotateMov64 ()) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr_annotate (I.ins_Mov64) (S.AnnotateMov64 ()) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Mov64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Mov64 (va_code_Mov64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0))); va_lemma_norm_mods ([va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cmovc64 [@ "opaque_to_smt"] let va_code_Cmovc64 dst src = (mk_ins (make_instr (I.ins_Cmovc64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Cmovc64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cmovc64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Cmovc64) (va_code_Cmovc64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cmovc64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cmovc64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cmovc64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cmovc64 (va_code_Cmovc64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0))); va_lemma_norm_mods ([va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Add64 [@ "opaque_to_smt"] let va_code_Add64 dst src = (mk_ins (make_instr (I.ins_Add64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Add64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Add64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Add64) (va_code_Add64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Add64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Add64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Add64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Add64 (va_code_Add64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Add64Wrap [@ "opaque_to_smt"] let va_code_Add64Wrap dst src = (mk_ins (make_instr (I.ins_Add64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Add64Wrap dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Add64Wrap va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Add64Wrap) (va_code_Add64Wrap dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Add64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Add64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Add64Wrap dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Add64Wrap (va_code_Add64Wrap dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- AddLea64 [@ "opaque_to_smt"] let va_code_AddLea64 dst src1 src2 = (mk_ins (make_instr (I.ins_AddLea64) dst src1 src2)) [@ "opaque_to_smt"] let va_codegen_success_AddLea64 dst src1 src2 = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_AddLea64 va_b0 va_s0 dst src1 src2 = va_reveal_opaque (`%va_code_AddLea64) (va_code_AddLea64 dst src1 src2); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_AddLea64) dst src1 src2)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_AddLea64) dst src1 src2)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_AddLea64 dst src1 src2 va_s0 va_k = let (va_sM, va_f0) = va_lemma_AddLea64 (va_code_AddLea64 dst src1 src2) va_s0 dst src1 src2 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0))); va_lemma_norm_mods ([va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Adc64 [@ "opaque_to_smt"] let va_code_Adc64 dst src = (mk_ins (make_instr (I.ins_AddCarry64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Adc64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Adc64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Adc64) (va_code_Adc64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_AddCarry64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_AddCarry64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Adc64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Adc64 (va_code_Adc64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Adc64Wrap [@ "opaque_to_smt"] let va_code_Adc64Wrap dst src = (mk_ins (make_instr (I.ins_AddCarry64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Adc64Wrap dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Adc64Wrap va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Adc64Wrap) (va_code_Adc64Wrap dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_AddCarry64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_AddCarry64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Adc64Wrap dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Adc64Wrap (va_code_Adc64Wrap dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Adcx64Wrap #push-options "--smtencoding.nl_arith_repr boxwrap" [@ "opaque_to_smt"] let va_code_Adcx64Wrap dst src = (mk_ins (make_instr (I.ins_Adcx64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Adcx64Wrap dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Adcx64Wrap va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Adcx64Wrap) (va_code_Adcx64Wrap dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Adcx64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Adcx64) dst src)) va_s0 in assert (Vale.Arch.Types.add_wrap64 (Vale.Arch.Types.add_wrap64 (va_eval_dst_opr64 va_old_s dst) (va_eval_opr64 va_old_s src)) (if Vale.X64.Decls.cf (va_get_flags va_old_s) then 1 else 0) == (va_eval_dst_opr64 va_old_s dst + va_eval_opr64 va_old_s src + (if Vale.X64.Decls.cf (va_get_flags va_old_s) then 1 else 0)) `op_Modulus` pow2_64); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Adcx64Wrap dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Adcx64Wrap (va_code_Adcx64Wrap dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) #pop-options //-- //-- Adox64Wrap [@ "opaque_to_smt"] let va_code_Adox64Wrap dst src = (mk_ins (make_instr (I.ins_Adox64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Adox64Wrap dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Adox64Wrap va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Adox64Wrap) (va_code_Adox64Wrap dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Adox64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Adox64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Adox64Wrap dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Adox64Wrap (va_code_Adox64Wrap dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Sub64 [@ "opaque_to_smt"] let va_code_Sub64 dst src = (mk_ins (make_instr (I.ins_Sub64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Sub64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Sub64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Sub64) (va_code_Sub64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Sub64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Sub64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Sub64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Sub64 (va_code_Sub64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Sub64Wrap [@ "opaque_to_smt"] let va_code_Sub64Wrap dst src = (mk_ins (make_instr (I.ins_Sub64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Sub64Wrap dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Sub64Wrap va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Sub64Wrap) (va_code_Sub64Wrap dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Sub64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Sub64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Sub64Wrap dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Sub64Wrap (va_code_Sub64Wrap dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Sbb64 [@ "opaque_to_smt"] let va_code_Sbb64 dst src = (mk_ins (make_instr (I.ins_Sbb64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Sbb64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Sbb64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Sbb64) (va_code_Sbb64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Sbb64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Sbb64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Sbb64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Sbb64 (va_code_Sbb64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- #restart-solver #push-options "--max_fuel 0 --max_ifuel 0 --using_facts_from 'Prims FStar.UInt'" let lemma_fundamental_div_mod (a b:nat64) : Lemma (pow2_64 * (FStar.UInt.mul_div #64 a b) + (FStar.UInt.mul_mod #64 a b) == a * b) = FStar.Math.Lemmas.lemma_div_mod (a * b) pow2_64 #pop-options //-- lemma_fundamental_div_mod //-- //-- Mul64Wrap [@ "opaque_to_smt"] let va_code_Mul64Wrap src = (mk_ins (make_instr (I.ins_Mul64) src)) [@ "opaque_to_smt"] let va_codegen_success_Mul64Wrap src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Mul64Wrap va_b0 va_s0 src = va_reveal_opaque (`%va_code_Mul64Wrap) (va_code_Mul64Wrap src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Mul64) src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Mul64) src)) va_s0 in lemma_fundamental_div_mod (va_get_reg64 rRax va_old_s) (va_eval_opr64 va_old_s src); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Mul64Wrap src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Mul64Wrap (va_code_Mul64Wrap src) va_s0 src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRax va_sM (va_update_flags va_sM (va_update_ok va_sM va_s0))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRax; va_Mod_flags]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Mulx64 [@ "opaque_to_smt"] let va_code_Mulx64 dst_hi dst_lo src = (mk_ins (make_instr (I.ins_Mulx64) dst_hi dst_lo src)) [@ "opaque_to_smt"] let va_codegen_success_Mulx64 dst_hi dst_lo src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Mulx64 va_b0 va_s0 dst_hi dst_lo src = va_reveal_opaque (`%va_code_Mulx64) (va_code_Mulx64 dst_hi dst_lo src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Mulx64) dst_hi dst_lo src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Mulx64) dst_hi dst_lo src)) va_s0 in lemma_fundamental_div_mod (va_get_reg64 rRdx va_old_s) (va_eval_opr64 va_old_s src); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Mulx64 dst_hi dst_lo src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Mulx64 (va_code_Mulx64 dst_hi dst_lo src) va_s0 dst_hi dst_lo src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst_lo va_sM (va_update_operand_dst_opr64 dst_hi va_sM va_s0)))); va_lemma_norm_mods ([va_mod_dst_opr64 dst_lo; va_mod_dst_opr64 dst_hi]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- lemma_mul_nat //-- //-- lemma_mul_in_bounds //-- //-- IMul64 [@ "opaque_to_smt"] let va_code_IMul64 dst src = (mk_ins (make_instr (I.ins_IMul64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_IMul64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_IMul64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_IMul64) (va_code_IMul64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_IMul64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_IMul64) dst src)) va_s0 in lemma_mul_nat (va_eval_dst_opr64 va_old_s dst) (va_eval_opr64 va_old_s src); lemma_mul_in_bounds (va_eval_dst_opr64 va_old_s dst) (va_eval_opr64 va_old_s src); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_IMul64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_IMul64 (va_code_IMul64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Xor64 [@ "opaque_to_smt"] let va_code_Xor64 dst src = (mk_ins (make_instr_annotate (I.ins_Xor64) (S.AnnotateXor64 ()) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Xor64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Xor64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Xor64) (va_code_Xor64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr_annotate (I.ins_Xor64) (S.AnnotateXor64 ()) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr_annotate (I.ins_Xor64) (S.AnnotateXor64 ()) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Xor64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Xor64 (va_code_Xor64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- And64 [@ "opaque_to_smt"] let va_code_And64 dst src = (mk_ins (make_instr (I.ins_And64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_And64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_And64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_And64) (va_code_And64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_And64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_And64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_And64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_And64 (va_code_And64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Shl64 [@ "opaque_to_smt"] let va_code_Shl64 dst amt = (mk_ins (make_instr (I.ins_Shl64) dst amt)) [@ "opaque_to_smt"] let va_codegen_success_Shl64 dst amt = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Shl64 va_b0 va_s0 dst amt = va_reveal_opaque (`%va_code_Shl64) (va_code_Shl64 dst amt); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Shl64) dst amt)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Shl64) dst amt)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Shl64 dst amt va_s0 va_k = let (va_sM, va_f0) = va_lemma_Shl64 (va_code_Shl64 dst amt) va_s0 dst amt in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Shr64 [@ "opaque_to_smt"] let va_code_Shr64 dst amt = (mk_ins (make_instr (I.ins_Shr64) dst amt)) [@ "opaque_to_smt"] let va_codegen_success_Shr64 dst amt = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Shr64 va_b0 va_s0 dst amt = va_reveal_opaque (`%va_code_Shr64) (va_code_Shr64 dst amt); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Shr64) dst amt)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Shr64) dst amt)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Shr64 dst amt va_s0 va_k = let (va_sM, va_f0) = va_lemma_Shr64 (va_code_Shr64 dst amt) va_s0 dst amt in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_AES [@ "opaque_to_smt"] let va_code_Cpuid_AES () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_AES () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_AES va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_AES) (va_code_Cpuid_AES ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_AES va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_AES (va_code_Cpuid_AES ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Sha [@ "opaque_to_smt"] let va_code_Cpuid_Sha () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Sha () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Sha va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Sha) (va_code_Cpuid_Sha ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Sha va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Sha (va_code_Cpuid_Sha ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Adx_Bmi2 [@ "opaque_to_smt"] let va_code_Cpuid_Adx_Bmi2 () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Adx_Bmi2 () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Adx_Bmi2 va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Adx_Bmi2) (va_code_Cpuid_Adx_Bmi2 ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Adx_Bmi2 va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Adx_Bmi2 (va_code_Cpuid_Adx_Bmi2 ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Avx [@ "opaque_to_smt"] let va_code_Cpuid_Avx () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Avx () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Avx va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Avx) (va_code_Cpuid_Avx ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Avx va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Avx (va_code_Cpuid_Avx ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Avx2 [@ "opaque_to_smt"] let va_code_Cpuid_Avx2 () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Avx2 () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Avx2 va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Avx2) (va_code_Cpuid_Avx2 ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Avx2 va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Avx2 (va_code_Cpuid_Avx2 ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Sse [@ "opaque_to_smt"] let va_code_Cpuid_Sse () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Sse () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Sse va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Sse) (va_code_Cpuid_Sse ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Sse va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Sse (va_code_Cpuid_Sse ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Movbe [@ "opaque_to_smt"] let va_code_Cpuid_Movbe () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Movbe () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Movbe va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Movbe) (va_code_Cpuid_Movbe ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Movbe va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Movbe (va_code_Cpuid_Movbe ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Rdrand [@ "opaque_to_smt"] let va_code_Cpuid_Rdrand () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Rdrand () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Rdrand va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Rdrand) (va_code_Cpuid_Rdrand ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Rdrand va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Rdrand (va_code_Cpuid_Rdrand ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Avx512 [@ "opaque_to_smt"] let va_code_Cpuid_Avx512 () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Avx512 () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Avx512 va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Avx512) (va_code_Cpuid_Avx512 ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM)
false
false
Vale.X64.InsBasic.fst
{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 5, "initial_ifuel": 0, "max_fuel": 5, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": true, "smtencoding_l_arith_repr": "native", "smtencoding_nl_arith_repr": "wrapped", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": false, "z3cliopt": [ "smt.arith.nl=false", "smt.QI.EAGER_THRESHOLD=100", "smt.CASE_SPLIT=3" ], "z3refresh": false, "z3rlimit": 20, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }
null
val va_wpProof_Cpuid_Avx512 : va_s0:va_state -> va_k:(va_state -> unit -> Type0) -> Ghost (va_state & va_fuel & unit) (requires (va_t_require va_s0 /\ va_wp_Cpuid_Avx512 va_s0 va_k)) (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Cpuid_Avx512 ()) ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_s0 va_k ((va_sM, va_f0, va_g))))
[]
Vale.X64.InsBasic.va_wpProof_Cpuid_Avx512
{ "file_name": "obj/Vale.X64.InsBasic.fst", "git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e", "git_url": "https://github.com/hacl-star/hacl-star.git", "project_name": "hacl-star" }
va_s0: Vale.X64.Decls.va_state -> va_k: (_: Vale.X64.Decls.va_state -> _: Prims.unit -> Type0) -> Prims.Ghost ((Vale.X64.Decls.va_state * Vale.X64.Decls.va_fuel) * Prims.unit)
{ "end_col": 22, "end_line": 890, "start_col": 40, "start_line": 882 }
Prims.Ghost
val va_lemma_Cpuid_Avx2 : va_b0:va_code -> va_s0:va_state -> Ghost (va_state & va_fuel) (requires (va_require_total va_b0 (va_code_Cpuid_Avx2 ()) va_s0 /\ va_get_ok va_s0 /\ va_get_reg64 rRax va_s0 = 7 /\ va_get_reg64 rRcx va_s0 = 0)) (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\ Vale.Arch.Types.iand64 (va_get_reg64 rRbx va_sM) 32 > 0 == avx2_cpuid_enabled /\ va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))))
[ { "abbrev": true, "full_module": "Vale.X64.Machine_Semantics_s", "short_module": "S" }, { "abbrev": true, "full_module": "Vale.X64.Instructions_s", "short_module": "I" }, { "abbrev": false, "full_module": "Vale.X64.Stack_i", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.Memory", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.Taint_Semantics", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.InsLemmas", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.StateLemmas", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.CPU_Features_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.QuickCode", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.Decls", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.State", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.Machine_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Arch.Types", "short_module": null }, { "abbrev": false, "full_module": "Vale.Arch.HeapImpl", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Types_s", "short_module": null }, { "abbrev": false, "full_module": "FStar.Mul", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]
false
let va_lemma_Cpuid_Avx2 va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Avx2) (va_code_Cpuid_Avx2 ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM)
val va_lemma_Cpuid_Avx2 : va_b0:va_code -> va_s0:va_state -> Ghost (va_state & va_fuel) (requires (va_require_total va_b0 (va_code_Cpuid_Avx2 ()) va_s0 /\ va_get_ok va_s0 /\ va_get_reg64 rRax va_s0 = 7 /\ va_get_reg64 rRcx va_s0 = 0)) (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\ Vale.Arch.Types.iand64 (va_get_reg64 rRbx va_sM) 32 > 0 == avx2_cpuid_enabled /\ va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0))))))) let va_lemma_Cpuid_Avx2 va_b0 va_s0 =
false
null
false
va_reveal_opaque (`%va_code_Cpuid_Avx2) (va_code_Cpuid_Avx2 ()); let va_old_s:va_state = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let va_sM, va_fM = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM)
{ "checked_file": "Vale.X64.InsBasic.fst.checked", "dependencies": [ "Vale.X64.Taint_Semantics.fst.checked", "Vale.X64.StateLemmas.fsti.checked", "Vale.X64.Stack_i.fsti.checked", "Vale.X64.Memory.fsti.checked", "Vale.X64.Machine_Semantics_s.fst.checked", "Vale.X64.Instructions_s.fsti.checked", "Vale.X64.InsLemmas.fsti.checked", "Vale.X64.Decls.fst.checked", "Vale.X64.CPU_Features_s.fst.checked", "Vale.Arch.Types.fsti.checked", "prims.fst.checked", "FStar.UInt.fsti.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Math.Lemmas.fst.checked" ], "interface_file": true, "source_file": "Vale.X64.InsBasic.fst" }
[]
[ "Vale.X64.Decls.va_code", "Vale.X64.Decls.va_state", "Vale.X64.State.vale_state", "Vale.X64.Lemmas.fuel", "FStar.Pervasives.Native.Mktuple2", "Vale.X64.Decls.va_fuel", "Prims.unit", "Vale.X64.CPU_Features_s.cpuid_features", "FStar.Pervasives.Native.tuple2", "Prims.nat", "Vale.X64.Decls.va_eval_ins", "Vale.X64.Taint_Semantics.mk_ins", "Vale.X64.InsLemmas.make_instr", "Prims.Cons", "Vale.X64.Instruction_s.instr_out", "Vale.X64.Instruction_s.inOut", "Vale.X64.Instruction_s.one64Reg", "Vale.X64.Machine_s.rRax", "Vale.X64.Instruction_s.out", "Vale.X64.Machine_s.rRbx", "Vale.X64.Machine_s.rRcx", "Vale.X64.Machine_s.rRdx", "Prims.Nil", "Vale.X64.Instruction_s.instr_operand", "Vale.X64.Instruction_s.PreserveFlags", "Vale.X64.Instructions_s.ins_Cpuid", "Vale.X64.Decls.va_ins_lemma", "Vale.X64.Decls.va_reveal_opaque", "Vale.X64.InsBasic.va_code_Cpuid_Avx2" ]
[]
module Vale.X64.InsBasic open Vale.X64 open Vale.X64.StateLemmas open Vale.X64.InsLemmas open Vale.X64.Taint_Semantics open Vale.X64.CPU_Features_s open Vale.X64.Memory open Vale.X64.Stack_i module I = Vale.X64.Instructions_s module S = Vale.X64.Machine_Semantics_s friend Vale.X64.Decls #reset-options "--initial_fuel 5 --max_fuel 5 --max_ifuel 2 --z3rlimit 20" //-- Mov64 [@ "opaque_to_smt"] let va_code_Mov64 dst src = (mk_ins (make_instr_annotate (I.ins_Mov64) (S.AnnotateMov64 ()) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Mov64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Mov64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Mov64) (va_code_Mov64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr_annotate (I.ins_Mov64) (S.AnnotateMov64 ()) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr_annotate (I.ins_Mov64) (S.AnnotateMov64 ()) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Mov64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Mov64 (va_code_Mov64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0))); va_lemma_norm_mods ([va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cmovc64 [@ "opaque_to_smt"] let va_code_Cmovc64 dst src = (mk_ins (make_instr (I.ins_Cmovc64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Cmovc64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cmovc64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Cmovc64) (va_code_Cmovc64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cmovc64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cmovc64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cmovc64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cmovc64 (va_code_Cmovc64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0))); va_lemma_norm_mods ([va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Add64 [@ "opaque_to_smt"] let va_code_Add64 dst src = (mk_ins (make_instr (I.ins_Add64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Add64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Add64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Add64) (va_code_Add64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Add64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Add64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Add64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Add64 (va_code_Add64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Add64Wrap [@ "opaque_to_smt"] let va_code_Add64Wrap dst src = (mk_ins (make_instr (I.ins_Add64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Add64Wrap dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Add64Wrap va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Add64Wrap) (va_code_Add64Wrap dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Add64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Add64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Add64Wrap dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Add64Wrap (va_code_Add64Wrap dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- AddLea64 [@ "opaque_to_smt"] let va_code_AddLea64 dst src1 src2 = (mk_ins (make_instr (I.ins_AddLea64) dst src1 src2)) [@ "opaque_to_smt"] let va_codegen_success_AddLea64 dst src1 src2 = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_AddLea64 va_b0 va_s0 dst src1 src2 = va_reveal_opaque (`%va_code_AddLea64) (va_code_AddLea64 dst src1 src2); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_AddLea64) dst src1 src2)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_AddLea64) dst src1 src2)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_AddLea64 dst src1 src2 va_s0 va_k = let (va_sM, va_f0) = va_lemma_AddLea64 (va_code_AddLea64 dst src1 src2) va_s0 dst src1 src2 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0))); va_lemma_norm_mods ([va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Adc64 [@ "opaque_to_smt"] let va_code_Adc64 dst src = (mk_ins (make_instr (I.ins_AddCarry64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Adc64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Adc64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Adc64) (va_code_Adc64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_AddCarry64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_AddCarry64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Adc64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Adc64 (va_code_Adc64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Adc64Wrap [@ "opaque_to_smt"] let va_code_Adc64Wrap dst src = (mk_ins (make_instr (I.ins_AddCarry64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Adc64Wrap dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Adc64Wrap va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Adc64Wrap) (va_code_Adc64Wrap dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_AddCarry64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_AddCarry64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Adc64Wrap dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Adc64Wrap (va_code_Adc64Wrap dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Adcx64Wrap #push-options "--smtencoding.nl_arith_repr boxwrap" [@ "opaque_to_smt"] let va_code_Adcx64Wrap dst src = (mk_ins (make_instr (I.ins_Adcx64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Adcx64Wrap dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Adcx64Wrap va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Adcx64Wrap) (va_code_Adcx64Wrap dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Adcx64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Adcx64) dst src)) va_s0 in assert (Vale.Arch.Types.add_wrap64 (Vale.Arch.Types.add_wrap64 (va_eval_dst_opr64 va_old_s dst) (va_eval_opr64 va_old_s src)) (if Vale.X64.Decls.cf (va_get_flags va_old_s) then 1 else 0) == (va_eval_dst_opr64 va_old_s dst + va_eval_opr64 va_old_s src + (if Vale.X64.Decls.cf (va_get_flags va_old_s) then 1 else 0)) `op_Modulus` pow2_64); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Adcx64Wrap dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Adcx64Wrap (va_code_Adcx64Wrap dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) #pop-options //-- //-- Adox64Wrap [@ "opaque_to_smt"] let va_code_Adox64Wrap dst src = (mk_ins (make_instr (I.ins_Adox64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Adox64Wrap dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Adox64Wrap va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Adox64Wrap) (va_code_Adox64Wrap dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Adox64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Adox64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Adox64Wrap dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Adox64Wrap (va_code_Adox64Wrap dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Sub64 [@ "opaque_to_smt"] let va_code_Sub64 dst src = (mk_ins (make_instr (I.ins_Sub64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Sub64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Sub64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Sub64) (va_code_Sub64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Sub64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Sub64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Sub64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Sub64 (va_code_Sub64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Sub64Wrap [@ "opaque_to_smt"] let va_code_Sub64Wrap dst src = (mk_ins (make_instr (I.ins_Sub64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Sub64Wrap dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Sub64Wrap va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Sub64Wrap) (va_code_Sub64Wrap dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Sub64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Sub64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Sub64Wrap dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Sub64Wrap (va_code_Sub64Wrap dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Sbb64 [@ "opaque_to_smt"] let va_code_Sbb64 dst src = (mk_ins (make_instr (I.ins_Sbb64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Sbb64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Sbb64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Sbb64) (va_code_Sbb64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Sbb64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Sbb64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Sbb64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Sbb64 (va_code_Sbb64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- #restart-solver #push-options "--max_fuel 0 --max_ifuel 0 --using_facts_from 'Prims FStar.UInt'" let lemma_fundamental_div_mod (a b:nat64) : Lemma (pow2_64 * (FStar.UInt.mul_div #64 a b) + (FStar.UInt.mul_mod #64 a b) == a * b) = FStar.Math.Lemmas.lemma_div_mod (a * b) pow2_64 #pop-options //-- lemma_fundamental_div_mod //-- //-- Mul64Wrap [@ "opaque_to_smt"] let va_code_Mul64Wrap src = (mk_ins (make_instr (I.ins_Mul64) src)) [@ "opaque_to_smt"] let va_codegen_success_Mul64Wrap src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Mul64Wrap va_b0 va_s0 src = va_reveal_opaque (`%va_code_Mul64Wrap) (va_code_Mul64Wrap src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Mul64) src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Mul64) src)) va_s0 in lemma_fundamental_div_mod (va_get_reg64 rRax va_old_s) (va_eval_opr64 va_old_s src); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Mul64Wrap src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Mul64Wrap (va_code_Mul64Wrap src) va_s0 src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRax va_sM (va_update_flags va_sM (va_update_ok va_sM va_s0))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRax; va_Mod_flags]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Mulx64 [@ "opaque_to_smt"] let va_code_Mulx64 dst_hi dst_lo src = (mk_ins (make_instr (I.ins_Mulx64) dst_hi dst_lo src)) [@ "opaque_to_smt"] let va_codegen_success_Mulx64 dst_hi dst_lo src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Mulx64 va_b0 va_s0 dst_hi dst_lo src = va_reveal_opaque (`%va_code_Mulx64) (va_code_Mulx64 dst_hi dst_lo src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Mulx64) dst_hi dst_lo src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Mulx64) dst_hi dst_lo src)) va_s0 in lemma_fundamental_div_mod (va_get_reg64 rRdx va_old_s) (va_eval_opr64 va_old_s src); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Mulx64 dst_hi dst_lo src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Mulx64 (va_code_Mulx64 dst_hi dst_lo src) va_s0 dst_hi dst_lo src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst_lo va_sM (va_update_operand_dst_opr64 dst_hi va_sM va_s0)))); va_lemma_norm_mods ([va_mod_dst_opr64 dst_lo; va_mod_dst_opr64 dst_hi]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- lemma_mul_nat //-- //-- lemma_mul_in_bounds //-- //-- IMul64 [@ "opaque_to_smt"] let va_code_IMul64 dst src = (mk_ins (make_instr (I.ins_IMul64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_IMul64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_IMul64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_IMul64) (va_code_IMul64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_IMul64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_IMul64) dst src)) va_s0 in lemma_mul_nat (va_eval_dst_opr64 va_old_s dst) (va_eval_opr64 va_old_s src); lemma_mul_in_bounds (va_eval_dst_opr64 va_old_s dst) (va_eval_opr64 va_old_s src); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_IMul64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_IMul64 (va_code_IMul64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Xor64 [@ "opaque_to_smt"] let va_code_Xor64 dst src = (mk_ins (make_instr_annotate (I.ins_Xor64) (S.AnnotateXor64 ()) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Xor64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Xor64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Xor64) (va_code_Xor64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr_annotate (I.ins_Xor64) (S.AnnotateXor64 ()) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr_annotate (I.ins_Xor64) (S.AnnotateXor64 ()) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Xor64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Xor64 (va_code_Xor64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- And64 [@ "opaque_to_smt"] let va_code_And64 dst src = (mk_ins (make_instr (I.ins_And64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_And64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_And64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_And64) (va_code_And64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_And64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_And64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_And64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_And64 (va_code_And64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Shl64 [@ "opaque_to_smt"] let va_code_Shl64 dst amt = (mk_ins (make_instr (I.ins_Shl64) dst amt)) [@ "opaque_to_smt"] let va_codegen_success_Shl64 dst amt = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Shl64 va_b0 va_s0 dst amt = va_reveal_opaque (`%va_code_Shl64) (va_code_Shl64 dst amt); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Shl64) dst amt)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Shl64) dst amt)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Shl64 dst amt va_s0 va_k = let (va_sM, va_f0) = va_lemma_Shl64 (va_code_Shl64 dst amt) va_s0 dst amt in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Shr64 [@ "opaque_to_smt"] let va_code_Shr64 dst amt = (mk_ins (make_instr (I.ins_Shr64) dst amt)) [@ "opaque_to_smt"] let va_codegen_success_Shr64 dst amt = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Shr64 va_b0 va_s0 dst amt = va_reveal_opaque (`%va_code_Shr64) (va_code_Shr64 dst amt); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Shr64) dst amt)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Shr64) dst amt)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Shr64 dst amt va_s0 va_k = let (va_sM, va_f0) = va_lemma_Shr64 (va_code_Shr64 dst amt) va_s0 dst amt in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_AES [@ "opaque_to_smt"] let va_code_Cpuid_AES () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_AES () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_AES va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_AES) (va_code_Cpuid_AES ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_AES va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_AES (va_code_Cpuid_AES ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Sha [@ "opaque_to_smt"] let va_code_Cpuid_Sha () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Sha () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Sha va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Sha) (va_code_Cpuid_Sha ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Sha va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Sha (va_code_Cpuid_Sha ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Adx_Bmi2 [@ "opaque_to_smt"] let va_code_Cpuid_Adx_Bmi2 () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Adx_Bmi2 () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Adx_Bmi2 va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Adx_Bmi2) (va_code_Cpuid_Adx_Bmi2 ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Adx_Bmi2 va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Adx_Bmi2 (va_code_Cpuid_Adx_Bmi2 ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Avx [@ "opaque_to_smt"] let va_code_Cpuid_Avx () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Avx () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Avx va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Avx) (va_code_Cpuid_Avx ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Avx va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Avx (va_code_Cpuid_Avx ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Avx2 [@ "opaque_to_smt"] let va_code_Cpuid_Avx2 () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Avx2 () = (va_ttrue ()) [@"opaque_to_smt"]
false
false
Vale.X64.InsBasic.fst
{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 5, "initial_ifuel": 0, "max_fuel": 5, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": true, "smtencoding_l_arith_repr": "native", "smtencoding_nl_arith_repr": "wrapped", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": false, "z3cliopt": [ "smt.arith.nl=false", "smt.QI.EAGER_THRESHOLD=100", "smt.CASE_SPLIT=3" ], "z3refresh": false, "z3rlimit": 20, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }
null
val va_lemma_Cpuid_Avx2 : va_b0:va_code -> va_s0:va_state -> Ghost (va_state & va_fuel) (requires (va_require_total va_b0 (va_code_Cpuid_Avx2 ()) va_s0 /\ va_get_ok va_s0 /\ va_get_reg64 rRax va_s0 = 7 /\ va_get_reg64 rRcx va_s0 = 0)) (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\ Vale.Arch.Types.iand64 (va_get_reg64 rRbx va_sM) 32 > 0 == avx2_cpuid_enabled /\ va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))))
[]
Vale.X64.InsBasic.va_lemma_Cpuid_Avx2
{ "file_name": "obj/Vale.X64.InsBasic.fst", "git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e", "git_url": "https://github.com/hacl-star/hacl-star.git", "project_name": "hacl-star" }
va_b0: Vale.X64.Decls.va_code -> va_s0: Vale.X64.Decls.va_state -> Prims.Ghost (Vale.X64.Decls.va_state * Vale.X64.Decls.va_fuel)
{ "end_col": 16, "end_line": 750, "start_col": 2, "start_line": 745 }
Prims.Ghost
val va_wpProof_Cpuid_Osxsave : va_s0:va_state -> va_k:(va_state -> unit -> Type0) -> Ghost (va_state & va_fuel & unit) (requires (va_t_require va_s0 /\ va_wp_Cpuid_Osxsave va_s0 va_k)) (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Cpuid_Osxsave ()) ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_s0 va_k ((va_sM, va_f0, va_g))))
[ { "abbrev": true, "full_module": "Vale.X64.Machine_Semantics_s", "short_module": "S" }, { "abbrev": true, "full_module": "Vale.X64.Instructions_s", "short_module": "I" }, { "abbrev": false, "full_module": "Vale.X64.Stack_i", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.Memory", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.Taint_Semantics", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.InsLemmas", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.StateLemmas", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.CPU_Features_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.QuickCode", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.Decls", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.State", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.Machine_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Arch.Types", "short_module": null }, { "abbrev": false, "full_module": "Vale.Arch.HeapImpl", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Types_s", "short_module": null }, { "abbrev": false, "full_module": "FStar.Mul", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]
false
let va_wpProof_Cpuid_Osxsave va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Osxsave (va_code_Cpuid_Osxsave ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g)
val va_wpProof_Cpuid_Osxsave : va_s0:va_state -> va_k:(va_state -> unit -> Type0) -> Ghost (va_state & va_fuel & unit) (requires (va_t_require va_s0 /\ va_wp_Cpuid_Osxsave va_s0 va_k)) (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Cpuid_Osxsave ()) ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_s0 va_k ((va_sM, va_f0, va_g)))) let va_wpProof_Cpuid_Osxsave va_s0 va_k =
false
null
false
let va_sM, va_f0 = va_lemma_Cpuid_Osxsave (va_code_Cpuid_Osxsave ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0))))) ); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g)
{ "checked_file": "Vale.X64.InsBasic.fst.checked", "dependencies": [ "Vale.X64.Taint_Semantics.fst.checked", "Vale.X64.StateLemmas.fsti.checked", "Vale.X64.Stack_i.fsti.checked", "Vale.X64.Memory.fsti.checked", "Vale.X64.Machine_Semantics_s.fst.checked", "Vale.X64.Instructions_s.fsti.checked", "Vale.X64.InsLemmas.fsti.checked", "Vale.X64.Decls.fst.checked", "Vale.X64.CPU_Features_s.fst.checked", "Vale.Arch.Types.fsti.checked", "prims.fst.checked", "FStar.UInt.fsti.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Math.Lemmas.fst.checked" ], "interface_file": true, "source_file": "Vale.X64.InsBasic.fst" }
[]
[ "Vale.X64.Decls.va_state", "Prims.unit", "Vale.X64.Decls.va_fuel", "FStar.Pervasives.Native.Mktuple3", "Vale.X64.QuickCode.va_lemma_norm_mods", "Prims.Cons", "Vale.X64.QuickCode.mod_t", "Vale.X64.QuickCode.va_Mod_reg64", "Vale.X64.Machine_s.rRdx", "Vale.X64.Machine_s.rRcx", "Vale.X64.Machine_s.rRbx", "Vale.X64.Machine_s.rRax", "Prims.Nil", "Prims._assert", "Vale.X64.Decls.va_state_eq", "Vale.X64.Decls.va_update_reg64", "Vale.X64.Decls.va_update_ok", "Vale.X64.Decls.va_lemma_upd_update", "FStar.Pervasives.Native.tuple3", "FStar.Pervasives.Native.tuple2", "Vale.X64.State.vale_state", "Vale.X64.InsBasic.va_lemma_Cpuid_Osxsave", "Vale.X64.InsBasic.va_code_Cpuid_Osxsave" ]
[]
module Vale.X64.InsBasic open Vale.X64 open Vale.X64.StateLemmas open Vale.X64.InsLemmas open Vale.X64.Taint_Semantics open Vale.X64.CPU_Features_s open Vale.X64.Memory open Vale.X64.Stack_i module I = Vale.X64.Instructions_s module S = Vale.X64.Machine_Semantics_s friend Vale.X64.Decls #reset-options "--initial_fuel 5 --max_fuel 5 --max_ifuel 2 --z3rlimit 20" //-- Mov64 [@ "opaque_to_smt"] let va_code_Mov64 dst src = (mk_ins (make_instr_annotate (I.ins_Mov64) (S.AnnotateMov64 ()) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Mov64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Mov64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Mov64) (va_code_Mov64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr_annotate (I.ins_Mov64) (S.AnnotateMov64 ()) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr_annotate (I.ins_Mov64) (S.AnnotateMov64 ()) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Mov64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Mov64 (va_code_Mov64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0))); va_lemma_norm_mods ([va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cmovc64 [@ "opaque_to_smt"] let va_code_Cmovc64 dst src = (mk_ins (make_instr (I.ins_Cmovc64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Cmovc64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cmovc64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Cmovc64) (va_code_Cmovc64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cmovc64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cmovc64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cmovc64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cmovc64 (va_code_Cmovc64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0))); va_lemma_norm_mods ([va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Add64 [@ "opaque_to_smt"] let va_code_Add64 dst src = (mk_ins (make_instr (I.ins_Add64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Add64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Add64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Add64) (va_code_Add64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Add64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Add64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Add64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Add64 (va_code_Add64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Add64Wrap [@ "opaque_to_smt"] let va_code_Add64Wrap dst src = (mk_ins (make_instr (I.ins_Add64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Add64Wrap dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Add64Wrap va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Add64Wrap) (va_code_Add64Wrap dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Add64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Add64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Add64Wrap dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Add64Wrap (va_code_Add64Wrap dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- AddLea64 [@ "opaque_to_smt"] let va_code_AddLea64 dst src1 src2 = (mk_ins (make_instr (I.ins_AddLea64) dst src1 src2)) [@ "opaque_to_smt"] let va_codegen_success_AddLea64 dst src1 src2 = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_AddLea64 va_b0 va_s0 dst src1 src2 = va_reveal_opaque (`%va_code_AddLea64) (va_code_AddLea64 dst src1 src2); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_AddLea64) dst src1 src2)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_AddLea64) dst src1 src2)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_AddLea64 dst src1 src2 va_s0 va_k = let (va_sM, va_f0) = va_lemma_AddLea64 (va_code_AddLea64 dst src1 src2) va_s0 dst src1 src2 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0))); va_lemma_norm_mods ([va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Adc64 [@ "opaque_to_smt"] let va_code_Adc64 dst src = (mk_ins (make_instr (I.ins_AddCarry64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Adc64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Adc64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Adc64) (va_code_Adc64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_AddCarry64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_AddCarry64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Adc64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Adc64 (va_code_Adc64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Adc64Wrap [@ "opaque_to_smt"] let va_code_Adc64Wrap dst src = (mk_ins (make_instr (I.ins_AddCarry64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Adc64Wrap dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Adc64Wrap va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Adc64Wrap) (va_code_Adc64Wrap dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_AddCarry64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_AddCarry64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Adc64Wrap dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Adc64Wrap (va_code_Adc64Wrap dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Adcx64Wrap #push-options "--smtencoding.nl_arith_repr boxwrap" [@ "opaque_to_smt"] let va_code_Adcx64Wrap dst src = (mk_ins (make_instr (I.ins_Adcx64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Adcx64Wrap dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Adcx64Wrap va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Adcx64Wrap) (va_code_Adcx64Wrap dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Adcx64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Adcx64) dst src)) va_s0 in assert (Vale.Arch.Types.add_wrap64 (Vale.Arch.Types.add_wrap64 (va_eval_dst_opr64 va_old_s dst) (va_eval_opr64 va_old_s src)) (if Vale.X64.Decls.cf (va_get_flags va_old_s) then 1 else 0) == (va_eval_dst_opr64 va_old_s dst + va_eval_opr64 va_old_s src + (if Vale.X64.Decls.cf (va_get_flags va_old_s) then 1 else 0)) `op_Modulus` pow2_64); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Adcx64Wrap dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Adcx64Wrap (va_code_Adcx64Wrap dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) #pop-options //-- //-- Adox64Wrap [@ "opaque_to_smt"] let va_code_Adox64Wrap dst src = (mk_ins (make_instr (I.ins_Adox64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Adox64Wrap dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Adox64Wrap va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Adox64Wrap) (va_code_Adox64Wrap dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Adox64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Adox64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Adox64Wrap dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Adox64Wrap (va_code_Adox64Wrap dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Sub64 [@ "opaque_to_smt"] let va_code_Sub64 dst src = (mk_ins (make_instr (I.ins_Sub64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Sub64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Sub64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Sub64) (va_code_Sub64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Sub64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Sub64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Sub64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Sub64 (va_code_Sub64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Sub64Wrap [@ "opaque_to_smt"] let va_code_Sub64Wrap dst src = (mk_ins (make_instr (I.ins_Sub64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Sub64Wrap dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Sub64Wrap va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Sub64Wrap) (va_code_Sub64Wrap dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Sub64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Sub64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Sub64Wrap dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Sub64Wrap (va_code_Sub64Wrap dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Sbb64 [@ "opaque_to_smt"] let va_code_Sbb64 dst src = (mk_ins (make_instr (I.ins_Sbb64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Sbb64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Sbb64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Sbb64) (va_code_Sbb64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Sbb64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Sbb64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Sbb64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Sbb64 (va_code_Sbb64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- #restart-solver #push-options "--max_fuel 0 --max_ifuel 0 --using_facts_from 'Prims FStar.UInt'" let lemma_fundamental_div_mod (a b:nat64) : Lemma (pow2_64 * (FStar.UInt.mul_div #64 a b) + (FStar.UInt.mul_mod #64 a b) == a * b) = FStar.Math.Lemmas.lemma_div_mod (a * b) pow2_64 #pop-options //-- lemma_fundamental_div_mod //-- //-- Mul64Wrap [@ "opaque_to_smt"] let va_code_Mul64Wrap src = (mk_ins (make_instr (I.ins_Mul64) src)) [@ "opaque_to_smt"] let va_codegen_success_Mul64Wrap src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Mul64Wrap va_b0 va_s0 src = va_reveal_opaque (`%va_code_Mul64Wrap) (va_code_Mul64Wrap src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Mul64) src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Mul64) src)) va_s0 in lemma_fundamental_div_mod (va_get_reg64 rRax va_old_s) (va_eval_opr64 va_old_s src); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Mul64Wrap src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Mul64Wrap (va_code_Mul64Wrap src) va_s0 src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRax va_sM (va_update_flags va_sM (va_update_ok va_sM va_s0))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRax; va_Mod_flags]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Mulx64 [@ "opaque_to_smt"] let va_code_Mulx64 dst_hi dst_lo src = (mk_ins (make_instr (I.ins_Mulx64) dst_hi dst_lo src)) [@ "opaque_to_smt"] let va_codegen_success_Mulx64 dst_hi dst_lo src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Mulx64 va_b0 va_s0 dst_hi dst_lo src = va_reveal_opaque (`%va_code_Mulx64) (va_code_Mulx64 dst_hi dst_lo src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Mulx64) dst_hi dst_lo src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Mulx64) dst_hi dst_lo src)) va_s0 in lemma_fundamental_div_mod (va_get_reg64 rRdx va_old_s) (va_eval_opr64 va_old_s src); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Mulx64 dst_hi dst_lo src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Mulx64 (va_code_Mulx64 dst_hi dst_lo src) va_s0 dst_hi dst_lo src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst_lo va_sM (va_update_operand_dst_opr64 dst_hi va_sM va_s0)))); va_lemma_norm_mods ([va_mod_dst_opr64 dst_lo; va_mod_dst_opr64 dst_hi]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- lemma_mul_nat //-- //-- lemma_mul_in_bounds //-- //-- IMul64 [@ "opaque_to_smt"] let va_code_IMul64 dst src = (mk_ins (make_instr (I.ins_IMul64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_IMul64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_IMul64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_IMul64) (va_code_IMul64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_IMul64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_IMul64) dst src)) va_s0 in lemma_mul_nat (va_eval_dst_opr64 va_old_s dst) (va_eval_opr64 va_old_s src); lemma_mul_in_bounds (va_eval_dst_opr64 va_old_s dst) (va_eval_opr64 va_old_s src); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_IMul64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_IMul64 (va_code_IMul64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Xor64 [@ "opaque_to_smt"] let va_code_Xor64 dst src = (mk_ins (make_instr_annotate (I.ins_Xor64) (S.AnnotateXor64 ()) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Xor64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Xor64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Xor64) (va_code_Xor64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr_annotate (I.ins_Xor64) (S.AnnotateXor64 ()) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr_annotate (I.ins_Xor64) (S.AnnotateXor64 ()) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Xor64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Xor64 (va_code_Xor64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- And64 [@ "opaque_to_smt"] let va_code_And64 dst src = (mk_ins (make_instr (I.ins_And64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_And64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_And64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_And64) (va_code_And64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_And64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_And64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_And64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_And64 (va_code_And64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Shl64 [@ "opaque_to_smt"] let va_code_Shl64 dst amt = (mk_ins (make_instr (I.ins_Shl64) dst amt)) [@ "opaque_to_smt"] let va_codegen_success_Shl64 dst amt = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Shl64 va_b0 va_s0 dst amt = va_reveal_opaque (`%va_code_Shl64) (va_code_Shl64 dst amt); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Shl64) dst amt)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Shl64) dst amt)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Shl64 dst amt va_s0 va_k = let (va_sM, va_f0) = va_lemma_Shl64 (va_code_Shl64 dst amt) va_s0 dst amt in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Shr64 [@ "opaque_to_smt"] let va_code_Shr64 dst amt = (mk_ins (make_instr (I.ins_Shr64) dst amt)) [@ "opaque_to_smt"] let va_codegen_success_Shr64 dst amt = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Shr64 va_b0 va_s0 dst amt = va_reveal_opaque (`%va_code_Shr64) (va_code_Shr64 dst amt); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Shr64) dst amt)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Shr64) dst amt)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Shr64 dst amt va_s0 va_k = let (va_sM, va_f0) = va_lemma_Shr64 (va_code_Shr64 dst amt) va_s0 dst amt in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_AES [@ "opaque_to_smt"] let va_code_Cpuid_AES () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_AES () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_AES va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_AES) (va_code_Cpuid_AES ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_AES va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_AES (va_code_Cpuid_AES ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Sha [@ "opaque_to_smt"] let va_code_Cpuid_Sha () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Sha () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Sha va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Sha) (va_code_Cpuid_Sha ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Sha va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Sha (va_code_Cpuid_Sha ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Adx_Bmi2 [@ "opaque_to_smt"] let va_code_Cpuid_Adx_Bmi2 () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Adx_Bmi2 () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Adx_Bmi2 va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Adx_Bmi2) (va_code_Cpuid_Adx_Bmi2 ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Adx_Bmi2 va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Adx_Bmi2 (va_code_Cpuid_Adx_Bmi2 ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Avx [@ "opaque_to_smt"] let va_code_Cpuid_Avx () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Avx () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Avx va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Avx) (va_code_Cpuid_Avx ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Avx va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Avx (va_code_Cpuid_Avx ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Avx2 [@ "opaque_to_smt"] let va_code_Cpuid_Avx2 () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Avx2 () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Avx2 va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Avx2) (va_code_Cpuid_Avx2 ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Avx2 va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Avx2 (va_code_Cpuid_Avx2 ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Sse [@ "opaque_to_smt"] let va_code_Cpuid_Sse () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Sse () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Sse va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Sse) (va_code_Cpuid_Sse ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Sse va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Sse (va_code_Cpuid_Sse ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Movbe [@ "opaque_to_smt"] let va_code_Cpuid_Movbe () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Movbe () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Movbe va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Movbe) (va_code_Cpuid_Movbe ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Movbe va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Movbe (va_code_Cpuid_Movbe ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Rdrand [@ "opaque_to_smt"] let va_code_Cpuid_Rdrand () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Rdrand () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Rdrand va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Rdrand) (va_code_Cpuid_Rdrand ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Rdrand va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Rdrand (va_code_Cpuid_Rdrand ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Avx512 [@ "opaque_to_smt"] let va_code_Cpuid_Avx512 () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Avx512 () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Avx512 va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Avx512) (va_code_Cpuid_Avx512 ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Avx512 va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Avx512 (va_code_Cpuid_Avx512 ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Osxsave [@ "opaque_to_smt"] let va_code_Cpuid_Osxsave () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Osxsave () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Osxsave va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Osxsave) (va_code_Cpuid_Osxsave ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM)
false
false
Vale.X64.InsBasic.fst
{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 5, "initial_ifuel": 0, "max_fuel": 5, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": true, "smtencoding_l_arith_repr": "native", "smtencoding_nl_arith_repr": "wrapped", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": false, "z3cliopt": [ "smt.arith.nl=false", "smt.QI.EAGER_THRESHOLD=100", "smt.CASE_SPLIT=3" ], "z3refresh": false, "z3rlimit": 20, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }
null
val va_wpProof_Cpuid_Osxsave : va_s0:va_state -> va_k:(va_state -> unit -> Type0) -> Ghost (va_state & va_fuel & unit) (requires (va_t_require va_s0 /\ va_wp_Cpuid_Osxsave va_s0 va_k)) (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Cpuid_Osxsave ()) ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_s0 va_k ((va_sM, va_f0, va_g))))
[]
Vale.X64.InsBasic.va_wpProof_Cpuid_Osxsave
{ "file_name": "obj/Vale.X64.InsBasic.fst", "git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e", "git_url": "https://github.com/hacl-star/hacl-star.git", "project_name": "hacl-star" }
va_s0: Vale.X64.Decls.va_state -> va_k: (_: Vale.X64.Decls.va_state -> _: Prims.unit -> Type0) -> Prims.Ghost ((Vale.X64.Decls.va_state * Vale.X64.Decls.va_fuel) * Prims.unit)
{ "end_col": 22, "end_line": 922, "start_col": 41, "start_line": 914 }
Prims.Ghost
val va_lemma_Cpuid_Movbe : va_b0:va_code -> va_s0:va_state -> Ghost (va_state & va_fuel) (requires (va_require_total va_b0 (va_code_Cpuid_Movbe ()) va_s0 /\ va_get_ok va_s0 /\ va_get_reg64 rRax va_s0 = 1)) (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\ Vale.Arch.Types.iand64 (va_get_reg64 rRcx va_sM) 4194304 > 0 == movbe_enabled /\ va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))))
[ { "abbrev": true, "full_module": "Vale.X64.Machine_Semantics_s", "short_module": "S" }, { "abbrev": true, "full_module": "Vale.X64.Instructions_s", "short_module": "I" }, { "abbrev": false, "full_module": "Vale.X64.Stack_i", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.Memory", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.Taint_Semantics", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.InsLemmas", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.StateLemmas", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.CPU_Features_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.QuickCode", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.Decls", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.State", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.Machine_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Arch.Types", "short_module": null }, { "abbrev": false, "full_module": "Vale.Arch.HeapImpl", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Types_s", "short_module": null }, { "abbrev": false, "full_module": "FStar.Mul", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]
false
let va_lemma_Cpuid_Movbe va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Movbe) (va_code_Cpuid_Movbe ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM)
val va_lemma_Cpuid_Movbe : va_b0:va_code -> va_s0:va_state -> Ghost (va_state & va_fuel) (requires (va_require_total va_b0 (va_code_Cpuid_Movbe ()) va_s0 /\ va_get_ok va_s0 /\ va_get_reg64 rRax va_s0 = 1)) (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\ Vale.Arch.Types.iand64 (va_get_reg64 rRcx va_sM) 4194304 > 0 == movbe_enabled /\ va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0))))))) let va_lemma_Cpuid_Movbe va_b0 va_s0 =
false
null
false
va_reveal_opaque (`%va_code_Cpuid_Movbe) (va_code_Cpuid_Movbe ()); let va_old_s:va_state = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let va_sM, va_fM = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM)
{ "checked_file": "Vale.X64.InsBasic.fst.checked", "dependencies": [ "Vale.X64.Taint_Semantics.fst.checked", "Vale.X64.StateLemmas.fsti.checked", "Vale.X64.Stack_i.fsti.checked", "Vale.X64.Memory.fsti.checked", "Vale.X64.Machine_Semantics_s.fst.checked", "Vale.X64.Instructions_s.fsti.checked", "Vale.X64.InsLemmas.fsti.checked", "Vale.X64.Decls.fst.checked", "Vale.X64.CPU_Features_s.fst.checked", "Vale.Arch.Types.fsti.checked", "prims.fst.checked", "FStar.UInt.fsti.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Math.Lemmas.fst.checked" ], "interface_file": true, "source_file": "Vale.X64.InsBasic.fst" }
[]
[ "Vale.X64.Decls.va_code", "Vale.X64.Decls.va_state", "Vale.X64.State.vale_state", "Vale.X64.Lemmas.fuel", "FStar.Pervasives.Native.Mktuple2", "Vale.X64.Decls.va_fuel", "Prims.unit", "Vale.X64.CPU_Features_s.cpuid_features", "FStar.Pervasives.Native.tuple2", "Prims.nat", "Vale.X64.Decls.va_eval_ins", "Vale.X64.Taint_Semantics.mk_ins", "Vale.X64.InsLemmas.make_instr", "Prims.Cons", "Vale.X64.Instruction_s.instr_out", "Vale.X64.Instruction_s.inOut", "Vale.X64.Instruction_s.one64Reg", "Vale.X64.Machine_s.rRax", "Vale.X64.Instruction_s.out", "Vale.X64.Machine_s.rRbx", "Vale.X64.Machine_s.rRcx", "Vale.X64.Machine_s.rRdx", "Prims.Nil", "Vale.X64.Instruction_s.instr_operand", "Vale.X64.Instruction_s.PreserveFlags", "Vale.X64.Instructions_s.ins_Cpuid", "Vale.X64.Decls.va_ins_lemma", "Vale.X64.Decls.va_reveal_opaque", "Vale.X64.InsBasic.va_code_Cpuid_Movbe" ]
[]
module Vale.X64.InsBasic open Vale.X64 open Vale.X64.StateLemmas open Vale.X64.InsLemmas open Vale.X64.Taint_Semantics open Vale.X64.CPU_Features_s open Vale.X64.Memory open Vale.X64.Stack_i module I = Vale.X64.Instructions_s module S = Vale.X64.Machine_Semantics_s friend Vale.X64.Decls #reset-options "--initial_fuel 5 --max_fuel 5 --max_ifuel 2 --z3rlimit 20" //-- Mov64 [@ "opaque_to_smt"] let va_code_Mov64 dst src = (mk_ins (make_instr_annotate (I.ins_Mov64) (S.AnnotateMov64 ()) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Mov64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Mov64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Mov64) (va_code_Mov64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr_annotate (I.ins_Mov64) (S.AnnotateMov64 ()) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr_annotate (I.ins_Mov64) (S.AnnotateMov64 ()) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Mov64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Mov64 (va_code_Mov64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0))); va_lemma_norm_mods ([va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cmovc64 [@ "opaque_to_smt"] let va_code_Cmovc64 dst src = (mk_ins (make_instr (I.ins_Cmovc64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Cmovc64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cmovc64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Cmovc64) (va_code_Cmovc64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cmovc64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cmovc64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cmovc64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cmovc64 (va_code_Cmovc64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0))); va_lemma_norm_mods ([va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Add64 [@ "opaque_to_smt"] let va_code_Add64 dst src = (mk_ins (make_instr (I.ins_Add64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Add64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Add64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Add64) (va_code_Add64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Add64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Add64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Add64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Add64 (va_code_Add64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Add64Wrap [@ "opaque_to_smt"] let va_code_Add64Wrap dst src = (mk_ins (make_instr (I.ins_Add64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Add64Wrap dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Add64Wrap va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Add64Wrap) (va_code_Add64Wrap dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Add64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Add64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Add64Wrap dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Add64Wrap (va_code_Add64Wrap dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- AddLea64 [@ "opaque_to_smt"] let va_code_AddLea64 dst src1 src2 = (mk_ins (make_instr (I.ins_AddLea64) dst src1 src2)) [@ "opaque_to_smt"] let va_codegen_success_AddLea64 dst src1 src2 = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_AddLea64 va_b0 va_s0 dst src1 src2 = va_reveal_opaque (`%va_code_AddLea64) (va_code_AddLea64 dst src1 src2); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_AddLea64) dst src1 src2)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_AddLea64) dst src1 src2)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_AddLea64 dst src1 src2 va_s0 va_k = let (va_sM, va_f0) = va_lemma_AddLea64 (va_code_AddLea64 dst src1 src2) va_s0 dst src1 src2 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0))); va_lemma_norm_mods ([va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Adc64 [@ "opaque_to_smt"] let va_code_Adc64 dst src = (mk_ins (make_instr (I.ins_AddCarry64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Adc64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Adc64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Adc64) (va_code_Adc64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_AddCarry64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_AddCarry64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Adc64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Adc64 (va_code_Adc64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Adc64Wrap [@ "opaque_to_smt"] let va_code_Adc64Wrap dst src = (mk_ins (make_instr (I.ins_AddCarry64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Adc64Wrap dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Adc64Wrap va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Adc64Wrap) (va_code_Adc64Wrap dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_AddCarry64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_AddCarry64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Adc64Wrap dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Adc64Wrap (va_code_Adc64Wrap dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Adcx64Wrap #push-options "--smtencoding.nl_arith_repr boxwrap" [@ "opaque_to_smt"] let va_code_Adcx64Wrap dst src = (mk_ins (make_instr (I.ins_Adcx64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Adcx64Wrap dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Adcx64Wrap va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Adcx64Wrap) (va_code_Adcx64Wrap dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Adcx64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Adcx64) dst src)) va_s0 in assert (Vale.Arch.Types.add_wrap64 (Vale.Arch.Types.add_wrap64 (va_eval_dst_opr64 va_old_s dst) (va_eval_opr64 va_old_s src)) (if Vale.X64.Decls.cf (va_get_flags va_old_s) then 1 else 0) == (va_eval_dst_opr64 va_old_s dst + va_eval_opr64 va_old_s src + (if Vale.X64.Decls.cf (va_get_flags va_old_s) then 1 else 0)) `op_Modulus` pow2_64); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Adcx64Wrap dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Adcx64Wrap (va_code_Adcx64Wrap dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) #pop-options //-- //-- Adox64Wrap [@ "opaque_to_smt"] let va_code_Adox64Wrap dst src = (mk_ins (make_instr (I.ins_Adox64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Adox64Wrap dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Adox64Wrap va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Adox64Wrap) (va_code_Adox64Wrap dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Adox64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Adox64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Adox64Wrap dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Adox64Wrap (va_code_Adox64Wrap dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Sub64 [@ "opaque_to_smt"] let va_code_Sub64 dst src = (mk_ins (make_instr (I.ins_Sub64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Sub64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Sub64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Sub64) (va_code_Sub64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Sub64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Sub64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Sub64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Sub64 (va_code_Sub64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Sub64Wrap [@ "opaque_to_smt"] let va_code_Sub64Wrap dst src = (mk_ins (make_instr (I.ins_Sub64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Sub64Wrap dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Sub64Wrap va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Sub64Wrap) (va_code_Sub64Wrap dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Sub64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Sub64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Sub64Wrap dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Sub64Wrap (va_code_Sub64Wrap dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Sbb64 [@ "opaque_to_smt"] let va_code_Sbb64 dst src = (mk_ins (make_instr (I.ins_Sbb64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Sbb64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Sbb64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Sbb64) (va_code_Sbb64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Sbb64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Sbb64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Sbb64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Sbb64 (va_code_Sbb64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- #restart-solver #push-options "--max_fuel 0 --max_ifuel 0 --using_facts_from 'Prims FStar.UInt'" let lemma_fundamental_div_mod (a b:nat64) : Lemma (pow2_64 * (FStar.UInt.mul_div #64 a b) + (FStar.UInt.mul_mod #64 a b) == a * b) = FStar.Math.Lemmas.lemma_div_mod (a * b) pow2_64 #pop-options //-- lemma_fundamental_div_mod //-- //-- Mul64Wrap [@ "opaque_to_smt"] let va_code_Mul64Wrap src = (mk_ins (make_instr (I.ins_Mul64) src)) [@ "opaque_to_smt"] let va_codegen_success_Mul64Wrap src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Mul64Wrap va_b0 va_s0 src = va_reveal_opaque (`%va_code_Mul64Wrap) (va_code_Mul64Wrap src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Mul64) src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Mul64) src)) va_s0 in lemma_fundamental_div_mod (va_get_reg64 rRax va_old_s) (va_eval_opr64 va_old_s src); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Mul64Wrap src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Mul64Wrap (va_code_Mul64Wrap src) va_s0 src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRax va_sM (va_update_flags va_sM (va_update_ok va_sM va_s0))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRax; va_Mod_flags]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Mulx64 [@ "opaque_to_smt"] let va_code_Mulx64 dst_hi dst_lo src = (mk_ins (make_instr (I.ins_Mulx64) dst_hi dst_lo src)) [@ "opaque_to_smt"] let va_codegen_success_Mulx64 dst_hi dst_lo src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Mulx64 va_b0 va_s0 dst_hi dst_lo src = va_reveal_opaque (`%va_code_Mulx64) (va_code_Mulx64 dst_hi dst_lo src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Mulx64) dst_hi dst_lo src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Mulx64) dst_hi dst_lo src)) va_s0 in lemma_fundamental_div_mod (va_get_reg64 rRdx va_old_s) (va_eval_opr64 va_old_s src); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Mulx64 dst_hi dst_lo src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Mulx64 (va_code_Mulx64 dst_hi dst_lo src) va_s0 dst_hi dst_lo src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst_lo va_sM (va_update_operand_dst_opr64 dst_hi va_sM va_s0)))); va_lemma_norm_mods ([va_mod_dst_opr64 dst_lo; va_mod_dst_opr64 dst_hi]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- lemma_mul_nat //-- //-- lemma_mul_in_bounds //-- //-- IMul64 [@ "opaque_to_smt"] let va_code_IMul64 dst src = (mk_ins (make_instr (I.ins_IMul64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_IMul64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_IMul64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_IMul64) (va_code_IMul64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_IMul64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_IMul64) dst src)) va_s0 in lemma_mul_nat (va_eval_dst_opr64 va_old_s dst) (va_eval_opr64 va_old_s src); lemma_mul_in_bounds (va_eval_dst_opr64 va_old_s dst) (va_eval_opr64 va_old_s src); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_IMul64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_IMul64 (va_code_IMul64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Xor64 [@ "opaque_to_smt"] let va_code_Xor64 dst src = (mk_ins (make_instr_annotate (I.ins_Xor64) (S.AnnotateXor64 ()) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Xor64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Xor64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Xor64) (va_code_Xor64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr_annotate (I.ins_Xor64) (S.AnnotateXor64 ()) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr_annotate (I.ins_Xor64) (S.AnnotateXor64 ()) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Xor64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Xor64 (va_code_Xor64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- And64 [@ "opaque_to_smt"] let va_code_And64 dst src = (mk_ins (make_instr (I.ins_And64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_And64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_And64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_And64) (va_code_And64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_And64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_And64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_And64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_And64 (va_code_And64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Shl64 [@ "opaque_to_smt"] let va_code_Shl64 dst amt = (mk_ins (make_instr (I.ins_Shl64) dst amt)) [@ "opaque_to_smt"] let va_codegen_success_Shl64 dst amt = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Shl64 va_b0 va_s0 dst amt = va_reveal_opaque (`%va_code_Shl64) (va_code_Shl64 dst amt); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Shl64) dst amt)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Shl64) dst amt)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Shl64 dst amt va_s0 va_k = let (va_sM, va_f0) = va_lemma_Shl64 (va_code_Shl64 dst amt) va_s0 dst amt in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Shr64 [@ "opaque_to_smt"] let va_code_Shr64 dst amt = (mk_ins (make_instr (I.ins_Shr64) dst amt)) [@ "opaque_to_smt"] let va_codegen_success_Shr64 dst amt = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Shr64 va_b0 va_s0 dst amt = va_reveal_opaque (`%va_code_Shr64) (va_code_Shr64 dst amt); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Shr64) dst amt)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Shr64) dst amt)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Shr64 dst amt va_s0 va_k = let (va_sM, va_f0) = va_lemma_Shr64 (va_code_Shr64 dst amt) va_s0 dst amt in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_AES [@ "opaque_to_smt"] let va_code_Cpuid_AES () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_AES () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_AES va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_AES) (va_code_Cpuid_AES ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_AES va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_AES (va_code_Cpuid_AES ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Sha [@ "opaque_to_smt"] let va_code_Cpuid_Sha () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Sha () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Sha va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Sha) (va_code_Cpuid_Sha ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Sha va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Sha (va_code_Cpuid_Sha ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Adx_Bmi2 [@ "opaque_to_smt"] let va_code_Cpuid_Adx_Bmi2 () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Adx_Bmi2 () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Adx_Bmi2 va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Adx_Bmi2) (va_code_Cpuid_Adx_Bmi2 ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Adx_Bmi2 va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Adx_Bmi2 (va_code_Cpuid_Adx_Bmi2 ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Avx [@ "opaque_to_smt"] let va_code_Cpuid_Avx () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Avx () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Avx va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Avx) (va_code_Cpuid_Avx ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Avx va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Avx (va_code_Cpuid_Avx ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Avx2 [@ "opaque_to_smt"] let va_code_Cpuid_Avx2 () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Avx2 () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Avx2 va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Avx2) (va_code_Cpuid_Avx2 ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Avx2 va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Avx2 (va_code_Cpuid_Avx2 ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Sse [@ "opaque_to_smt"] let va_code_Cpuid_Sse () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Sse () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Sse va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Sse) (va_code_Cpuid_Sse ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Sse va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Sse (va_code_Cpuid_Sse ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Movbe [@ "opaque_to_smt"] let va_code_Cpuid_Movbe () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Movbe () = (va_ttrue ()) [@"opaque_to_smt"]
false
false
Vale.X64.InsBasic.fst
{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 5, "initial_ifuel": 0, "max_fuel": 5, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": true, "smtencoding_l_arith_repr": "native", "smtencoding_nl_arith_repr": "wrapped", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": false, "z3cliopt": [ "smt.arith.nl=false", "smt.QI.EAGER_THRESHOLD=100", "smt.CASE_SPLIT=3" ], "z3refresh": false, "z3rlimit": 20, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }
null
val va_lemma_Cpuid_Movbe : va_b0:va_code -> va_s0:va_state -> Ghost (va_state & va_fuel) (requires (va_require_total va_b0 (va_code_Cpuid_Movbe ()) va_s0 /\ va_get_ok va_s0 /\ va_get_reg64 rRax va_s0 = 1)) (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\ Vale.Arch.Types.iand64 (va_get_reg64 rRcx va_sM) 4194304 > 0 == movbe_enabled /\ va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))))
[]
Vale.X64.InsBasic.va_lemma_Cpuid_Movbe
{ "file_name": "obj/Vale.X64.InsBasic.fst", "git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e", "git_url": "https://github.com/hacl-star/hacl-star.git", "project_name": "hacl-star" }
va_b0: Vale.X64.Decls.va_code -> va_s0: Vale.X64.Decls.va_state -> Prims.Ghost (Vale.X64.Decls.va_state * Vale.X64.Decls.va_fuel)
{ "end_col": 16, "end_line": 814, "start_col": 2, "start_line": 809 }
Prims.Ghost
val va_wpProof_Xgetbv_Avx : va_s0:va_state -> va_k:(va_state -> unit -> Type0) -> Ghost (va_state & va_fuel & unit) (requires (va_t_require va_s0 /\ va_wp_Xgetbv_Avx va_s0 va_k)) (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Xgetbv_Avx ()) ([va_Mod_reg64 rRdx; va_Mod_reg64 rRax]) va_s0 va_k ((va_sM, va_f0, va_g))))
[ { "abbrev": true, "full_module": "Vale.X64.Machine_Semantics_s", "short_module": "S" }, { "abbrev": true, "full_module": "Vale.X64.Instructions_s", "short_module": "I" }, { "abbrev": false, "full_module": "Vale.X64.Stack_i", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.Memory", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.Taint_Semantics", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.InsLemmas", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.StateLemmas", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.CPU_Features_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.QuickCode", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.Decls", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.State", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.Machine_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Arch.Types", "short_module": null }, { "abbrev": false, "full_module": "Vale.Arch.HeapImpl", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Types_s", "short_module": null }, { "abbrev": false, "full_module": "FStar.Mul", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]
false
let va_wpProof_Xgetbv_Avx va_s0 va_k = let (va_sM, va_f0) = va_lemma_Xgetbv_Avx (va_code_Xgetbv_Avx ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g)
val va_wpProof_Xgetbv_Avx : va_s0:va_state -> va_k:(va_state -> unit -> Type0) -> Ghost (va_state & va_fuel & unit) (requires (va_t_require va_s0 /\ va_wp_Xgetbv_Avx va_s0 va_k)) (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Xgetbv_Avx ()) ([va_Mod_reg64 rRdx; va_Mod_reg64 rRax]) va_s0 va_k ((va_sM, va_f0, va_g)))) let va_wpProof_Xgetbv_Avx va_s0 va_k =
false
null
false
let va_sM, va_f0 = va_lemma_Xgetbv_Avx (va_code_Xgetbv_Avx ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g)
{ "checked_file": "Vale.X64.InsBasic.fst.checked", "dependencies": [ "Vale.X64.Taint_Semantics.fst.checked", "Vale.X64.StateLemmas.fsti.checked", "Vale.X64.Stack_i.fsti.checked", "Vale.X64.Memory.fsti.checked", "Vale.X64.Machine_Semantics_s.fst.checked", "Vale.X64.Instructions_s.fsti.checked", "Vale.X64.InsLemmas.fsti.checked", "Vale.X64.Decls.fst.checked", "Vale.X64.CPU_Features_s.fst.checked", "Vale.Arch.Types.fsti.checked", "prims.fst.checked", "FStar.UInt.fsti.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Math.Lemmas.fst.checked" ], "interface_file": true, "source_file": "Vale.X64.InsBasic.fst" }
[]
[ "Vale.X64.Decls.va_state", "Prims.unit", "Vale.X64.Decls.va_fuel", "FStar.Pervasives.Native.Mktuple3", "Vale.X64.QuickCode.va_lemma_norm_mods", "Prims.Cons", "Vale.X64.QuickCode.mod_t", "Vale.X64.QuickCode.va_Mod_reg64", "Vale.X64.Machine_s.rRdx", "Vale.X64.Machine_s.rRax", "Prims.Nil", "Prims._assert", "Vale.X64.Decls.va_state_eq", "Vale.X64.Decls.va_update_reg64", "Vale.X64.Decls.va_update_ok", "Vale.X64.Decls.va_lemma_upd_update", "FStar.Pervasives.Native.tuple3", "FStar.Pervasives.Native.tuple2", "Vale.X64.State.vale_state", "Vale.X64.InsBasic.va_lemma_Xgetbv_Avx", "Vale.X64.InsBasic.va_code_Xgetbv_Avx" ]
[]
module Vale.X64.InsBasic open Vale.X64 open Vale.X64.StateLemmas open Vale.X64.InsLemmas open Vale.X64.Taint_Semantics open Vale.X64.CPU_Features_s open Vale.X64.Memory open Vale.X64.Stack_i module I = Vale.X64.Instructions_s module S = Vale.X64.Machine_Semantics_s friend Vale.X64.Decls #reset-options "--initial_fuel 5 --max_fuel 5 --max_ifuel 2 --z3rlimit 20" //-- Mov64 [@ "opaque_to_smt"] let va_code_Mov64 dst src = (mk_ins (make_instr_annotate (I.ins_Mov64) (S.AnnotateMov64 ()) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Mov64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Mov64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Mov64) (va_code_Mov64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr_annotate (I.ins_Mov64) (S.AnnotateMov64 ()) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr_annotate (I.ins_Mov64) (S.AnnotateMov64 ()) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Mov64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Mov64 (va_code_Mov64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0))); va_lemma_norm_mods ([va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cmovc64 [@ "opaque_to_smt"] let va_code_Cmovc64 dst src = (mk_ins (make_instr (I.ins_Cmovc64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Cmovc64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cmovc64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Cmovc64) (va_code_Cmovc64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cmovc64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cmovc64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cmovc64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cmovc64 (va_code_Cmovc64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0))); va_lemma_norm_mods ([va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Add64 [@ "opaque_to_smt"] let va_code_Add64 dst src = (mk_ins (make_instr (I.ins_Add64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Add64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Add64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Add64) (va_code_Add64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Add64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Add64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Add64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Add64 (va_code_Add64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Add64Wrap [@ "opaque_to_smt"] let va_code_Add64Wrap dst src = (mk_ins (make_instr (I.ins_Add64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Add64Wrap dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Add64Wrap va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Add64Wrap) (va_code_Add64Wrap dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Add64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Add64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Add64Wrap dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Add64Wrap (va_code_Add64Wrap dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- AddLea64 [@ "opaque_to_smt"] let va_code_AddLea64 dst src1 src2 = (mk_ins (make_instr (I.ins_AddLea64) dst src1 src2)) [@ "opaque_to_smt"] let va_codegen_success_AddLea64 dst src1 src2 = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_AddLea64 va_b0 va_s0 dst src1 src2 = va_reveal_opaque (`%va_code_AddLea64) (va_code_AddLea64 dst src1 src2); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_AddLea64) dst src1 src2)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_AddLea64) dst src1 src2)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_AddLea64 dst src1 src2 va_s0 va_k = let (va_sM, va_f0) = va_lemma_AddLea64 (va_code_AddLea64 dst src1 src2) va_s0 dst src1 src2 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0))); va_lemma_norm_mods ([va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Adc64 [@ "opaque_to_smt"] let va_code_Adc64 dst src = (mk_ins (make_instr (I.ins_AddCarry64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Adc64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Adc64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Adc64) (va_code_Adc64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_AddCarry64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_AddCarry64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Adc64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Adc64 (va_code_Adc64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Adc64Wrap [@ "opaque_to_smt"] let va_code_Adc64Wrap dst src = (mk_ins (make_instr (I.ins_AddCarry64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Adc64Wrap dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Adc64Wrap va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Adc64Wrap) (va_code_Adc64Wrap dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_AddCarry64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_AddCarry64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Adc64Wrap dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Adc64Wrap (va_code_Adc64Wrap dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Adcx64Wrap #push-options "--smtencoding.nl_arith_repr boxwrap" [@ "opaque_to_smt"] let va_code_Adcx64Wrap dst src = (mk_ins (make_instr (I.ins_Adcx64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Adcx64Wrap dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Adcx64Wrap va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Adcx64Wrap) (va_code_Adcx64Wrap dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Adcx64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Adcx64) dst src)) va_s0 in assert (Vale.Arch.Types.add_wrap64 (Vale.Arch.Types.add_wrap64 (va_eval_dst_opr64 va_old_s dst) (va_eval_opr64 va_old_s src)) (if Vale.X64.Decls.cf (va_get_flags va_old_s) then 1 else 0) == (va_eval_dst_opr64 va_old_s dst + va_eval_opr64 va_old_s src + (if Vale.X64.Decls.cf (va_get_flags va_old_s) then 1 else 0)) `op_Modulus` pow2_64); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Adcx64Wrap dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Adcx64Wrap (va_code_Adcx64Wrap dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) #pop-options //-- //-- Adox64Wrap [@ "opaque_to_smt"] let va_code_Adox64Wrap dst src = (mk_ins (make_instr (I.ins_Adox64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Adox64Wrap dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Adox64Wrap va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Adox64Wrap) (va_code_Adox64Wrap dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Adox64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Adox64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Adox64Wrap dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Adox64Wrap (va_code_Adox64Wrap dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Sub64 [@ "opaque_to_smt"] let va_code_Sub64 dst src = (mk_ins (make_instr (I.ins_Sub64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Sub64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Sub64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Sub64) (va_code_Sub64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Sub64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Sub64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Sub64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Sub64 (va_code_Sub64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Sub64Wrap [@ "opaque_to_smt"] let va_code_Sub64Wrap dst src = (mk_ins (make_instr (I.ins_Sub64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Sub64Wrap dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Sub64Wrap va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Sub64Wrap) (va_code_Sub64Wrap dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Sub64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Sub64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Sub64Wrap dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Sub64Wrap (va_code_Sub64Wrap dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Sbb64 [@ "opaque_to_smt"] let va_code_Sbb64 dst src = (mk_ins (make_instr (I.ins_Sbb64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Sbb64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Sbb64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Sbb64) (va_code_Sbb64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Sbb64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Sbb64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Sbb64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Sbb64 (va_code_Sbb64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- #restart-solver #push-options "--max_fuel 0 --max_ifuel 0 --using_facts_from 'Prims FStar.UInt'" let lemma_fundamental_div_mod (a b:nat64) : Lemma (pow2_64 * (FStar.UInt.mul_div #64 a b) + (FStar.UInt.mul_mod #64 a b) == a * b) = FStar.Math.Lemmas.lemma_div_mod (a * b) pow2_64 #pop-options //-- lemma_fundamental_div_mod //-- //-- Mul64Wrap [@ "opaque_to_smt"] let va_code_Mul64Wrap src = (mk_ins (make_instr (I.ins_Mul64) src)) [@ "opaque_to_smt"] let va_codegen_success_Mul64Wrap src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Mul64Wrap va_b0 va_s0 src = va_reveal_opaque (`%va_code_Mul64Wrap) (va_code_Mul64Wrap src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Mul64) src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Mul64) src)) va_s0 in lemma_fundamental_div_mod (va_get_reg64 rRax va_old_s) (va_eval_opr64 va_old_s src); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Mul64Wrap src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Mul64Wrap (va_code_Mul64Wrap src) va_s0 src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRax va_sM (va_update_flags va_sM (va_update_ok va_sM va_s0))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRax; va_Mod_flags]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Mulx64 [@ "opaque_to_smt"] let va_code_Mulx64 dst_hi dst_lo src = (mk_ins (make_instr (I.ins_Mulx64) dst_hi dst_lo src)) [@ "opaque_to_smt"] let va_codegen_success_Mulx64 dst_hi dst_lo src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Mulx64 va_b0 va_s0 dst_hi dst_lo src = va_reveal_opaque (`%va_code_Mulx64) (va_code_Mulx64 dst_hi dst_lo src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Mulx64) dst_hi dst_lo src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Mulx64) dst_hi dst_lo src)) va_s0 in lemma_fundamental_div_mod (va_get_reg64 rRdx va_old_s) (va_eval_opr64 va_old_s src); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Mulx64 dst_hi dst_lo src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Mulx64 (va_code_Mulx64 dst_hi dst_lo src) va_s0 dst_hi dst_lo src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst_lo va_sM (va_update_operand_dst_opr64 dst_hi va_sM va_s0)))); va_lemma_norm_mods ([va_mod_dst_opr64 dst_lo; va_mod_dst_opr64 dst_hi]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- lemma_mul_nat //-- //-- lemma_mul_in_bounds //-- //-- IMul64 [@ "opaque_to_smt"] let va_code_IMul64 dst src = (mk_ins (make_instr (I.ins_IMul64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_IMul64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_IMul64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_IMul64) (va_code_IMul64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_IMul64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_IMul64) dst src)) va_s0 in lemma_mul_nat (va_eval_dst_opr64 va_old_s dst) (va_eval_opr64 va_old_s src); lemma_mul_in_bounds (va_eval_dst_opr64 va_old_s dst) (va_eval_opr64 va_old_s src); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_IMul64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_IMul64 (va_code_IMul64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Xor64 [@ "opaque_to_smt"] let va_code_Xor64 dst src = (mk_ins (make_instr_annotate (I.ins_Xor64) (S.AnnotateXor64 ()) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Xor64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Xor64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Xor64) (va_code_Xor64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr_annotate (I.ins_Xor64) (S.AnnotateXor64 ()) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr_annotate (I.ins_Xor64) (S.AnnotateXor64 ()) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Xor64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Xor64 (va_code_Xor64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- And64 [@ "opaque_to_smt"] let va_code_And64 dst src = (mk_ins (make_instr (I.ins_And64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_And64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_And64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_And64) (va_code_And64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_And64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_And64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_And64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_And64 (va_code_And64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Shl64 [@ "opaque_to_smt"] let va_code_Shl64 dst amt = (mk_ins (make_instr (I.ins_Shl64) dst amt)) [@ "opaque_to_smt"] let va_codegen_success_Shl64 dst amt = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Shl64 va_b0 va_s0 dst amt = va_reveal_opaque (`%va_code_Shl64) (va_code_Shl64 dst amt); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Shl64) dst amt)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Shl64) dst amt)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Shl64 dst amt va_s0 va_k = let (va_sM, va_f0) = va_lemma_Shl64 (va_code_Shl64 dst amt) va_s0 dst amt in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Shr64 [@ "opaque_to_smt"] let va_code_Shr64 dst amt = (mk_ins (make_instr (I.ins_Shr64) dst amt)) [@ "opaque_to_smt"] let va_codegen_success_Shr64 dst amt = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Shr64 va_b0 va_s0 dst amt = va_reveal_opaque (`%va_code_Shr64) (va_code_Shr64 dst amt); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Shr64) dst amt)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Shr64) dst amt)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Shr64 dst amt va_s0 va_k = let (va_sM, va_f0) = va_lemma_Shr64 (va_code_Shr64 dst amt) va_s0 dst amt in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_AES [@ "opaque_to_smt"] let va_code_Cpuid_AES () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_AES () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_AES va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_AES) (va_code_Cpuid_AES ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_AES va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_AES (va_code_Cpuid_AES ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Sha [@ "opaque_to_smt"] let va_code_Cpuid_Sha () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Sha () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Sha va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Sha) (va_code_Cpuid_Sha ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Sha va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Sha (va_code_Cpuid_Sha ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Adx_Bmi2 [@ "opaque_to_smt"] let va_code_Cpuid_Adx_Bmi2 () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Adx_Bmi2 () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Adx_Bmi2 va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Adx_Bmi2) (va_code_Cpuid_Adx_Bmi2 ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Adx_Bmi2 va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Adx_Bmi2 (va_code_Cpuid_Adx_Bmi2 ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Avx [@ "opaque_to_smt"] let va_code_Cpuid_Avx () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Avx () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Avx va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Avx) (va_code_Cpuid_Avx ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Avx va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Avx (va_code_Cpuid_Avx ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Avx2 [@ "opaque_to_smt"] let va_code_Cpuid_Avx2 () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Avx2 () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Avx2 va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Avx2) (va_code_Cpuid_Avx2 ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Avx2 va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Avx2 (va_code_Cpuid_Avx2 ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Sse [@ "opaque_to_smt"] let va_code_Cpuid_Sse () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Sse () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Sse va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Sse) (va_code_Cpuid_Sse ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Sse va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Sse (va_code_Cpuid_Sse ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Movbe [@ "opaque_to_smt"] let va_code_Cpuid_Movbe () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Movbe () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Movbe va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Movbe) (va_code_Cpuid_Movbe ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Movbe va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Movbe (va_code_Cpuid_Movbe ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Rdrand [@ "opaque_to_smt"] let va_code_Cpuid_Rdrand () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Rdrand () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Rdrand va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Rdrand) (va_code_Cpuid_Rdrand ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Rdrand va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Rdrand (va_code_Cpuid_Rdrand ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Avx512 [@ "opaque_to_smt"] let va_code_Cpuid_Avx512 () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Avx512 () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Avx512 va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Avx512) (va_code_Cpuid_Avx512 ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Avx512 va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Avx512 (va_code_Cpuid_Avx512 ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Osxsave [@ "opaque_to_smt"] let va_code_Cpuid_Osxsave () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Osxsave () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Osxsave va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Osxsave) (va_code_Cpuid_Osxsave ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Osxsave va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Osxsave (va_code_Cpuid_Osxsave ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Xgetbv_Avx [@ "opaque_to_smt"] let va_code_Xgetbv_Avx () = (mk_ins (make_instr (I.ins_Xgetbv))) [@ "opaque_to_smt"] let va_codegen_success_Xgetbv_Avx () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Xgetbv_Avx va_b0 va_s0 = va_reveal_opaque (`%va_code_Xgetbv_Avx) (va_code_Xgetbv_Avx ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Xgetbv))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Xgetbv))) va_s0 in Vale.X64.CPU_Features_s.xgetbv_features (); (va_sM, va_fM)
false
false
Vale.X64.InsBasic.fst
{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 5, "initial_ifuel": 0, "max_fuel": 5, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": true, "smtencoding_l_arith_repr": "native", "smtencoding_nl_arith_repr": "wrapped", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": false, "z3cliopt": [ "smt.arith.nl=false", "smt.QI.EAGER_THRESHOLD=100", "smt.CASE_SPLIT=3" ], "z3refresh": false, "z3rlimit": 20, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }
null
val va_wpProof_Xgetbv_Avx : va_s0:va_state -> va_k:(va_state -> unit -> Type0) -> Ghost (va_state & va_fuel & unit) (requires (va_t_require va_s0 /\ va_wp_Xgetbv_Avx va_s0 va_k)) (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Xgetbv_Avx ()) ([va_Mod_reg64 rRdx; va_Mod_reg64 rRax]) va_s0 va_k ((va_sM, va_f0, va_g))))
[]
Vale.X64.InsBasic.va_wpProof_Xgetbv_Avx
{ "file_name": "obj/Vale.X64.InsBasic.fst", "git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e", "git_url": "https://github.com/hacl-star/hacl-star.git", "project_name": "hacl-star" }
va_s0: Vale.X64.Decls.va_state -> va_k: (_: Vale.X64.Decls.va_state -> _: Prims.unit -> Type0) -> Prims.Ghost ((Vale.X64.Decls.va_state * Vale.X64.Decls.va_fuel) * Prims.unit)
{ "end_col": 22, "end_line": 953, "start_col": 38, "start_line": 946 }
Prims.Ghost
val va_lemma_Cpuid_Rdrand : va_b0:va_code -> va_s0:va_state -> Ghost (va_state & va_fuel) (requires (va_require_total va_b0 (va_code_Cpuid_Rdrand ()) va_s0 /\ va_get_ok va_s0 /\ va_get_reg64 rRax va_s0 = 1)) (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\ Vale.Arch.Types.iand64 (va_get_reg64 rRcx va_sM) 1073741824 > 0 == rdrand_enabled /\ va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))))
[ { "abbrev": true, "full_module": "Vale.X64.Machine_Semantics_s", "short_module": "S" }, { "abbrev": true, "full_module": "Vale.X64.Instructions_s", "short_module": "I" }, { "abbrev": false, "full_module": "Vale.X64.Stack_i", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.Memory", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.Taint_Semantics", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.InsLemmas", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.StateLemmas", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.CPU_Features_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.QuickCode", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.Decls", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.State", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.Machine_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Arch.Types", "short_module": null }, { "abbrev": false, "full_module": "Vale.Arch.HeapImpl", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Types_s", "short_module": null }, { "abbrev": false, "full_module": "FStar.Mul", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]
false
let va_lemma_Cpuid_Rdrand va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Rdrand) (va_code_Cpuid_Rdrand ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM)
val va_lemma_Cpuid_Rdrand : va_b0:va_code -> va_s0:va_state -> Ghost (va_state & va_fuel) (requires (va_require_total va_b0 (va_code_Cpuid_Rdrand ()) va_s0 /\ va_get_ok va_s0 /\ va_get_reg64 rRax va_s0 = 1)) (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\ Vale.Arch.Types.iand64 (va_get_reg64 rRcx va_sM) 1073741824 > 0 == rdrand_enabled /\ va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0))))))) let va_lemma_Cpuid_Rdrand va_b0 va_s0 =
false
null
false
va_reveal_opaque (`%va_code_Cpuid_Rdrand) (va_code_Cpuid_Rdrand ()); let va_old_s:va_state = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let va_sM, va_fM = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM)
{ "checked_file": "Vale.X64.InsBasic.fst.checked", "dependencies": [ "Vale.X64.Taint_Semantics.fst.checked", "Vale.X64.StateLemmas.fsti.checked", "Vale.X64.Stack_i.fsti.checked", "Vale.X64.Memory.fsti.checked", "Vale.X64.Machine_Semantics_s.fst.checked", "Vale.X64.Instructions_s.fsti.checked", "Vale.X64.InsLemmas.fsti.checked", "Vale.X64.Decls.fst.checked", "Vale.X64.CPU_Features_s.fst.checked", "Vale.Arch.Types.fsti.checked", "prims.fst.checked", "FStar.UInt.fsti.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Math.Lemmas.fst.checked" ], "interface_file": true, "source_file": "Vale.X64.InsBasic.fst" }
[]
[ "Vale.X64.Decls.va_code", "Vale.X64.Decls.va_state", "Vale.X64.State.vale_state", "Vale.X64.Lemmas.fuel", "FStar.Pervasives.Native.Mktuple2", "Vale.X64.Decls.va_fuel", "Prims.unit", "Vale.X64.CPU_Features_s.cpuid_features", "FStar.Pervasives.Native.tuple2", "Prims.nat", "Vale.X64.Decls.va_eval_ins", "Vale.X64.Taint_Semantics.mk_ins", "Vale.X64.InsLemmas.make_instr", "Prims.Cons", "Vale.X64.Instruction_s.instr_out", "Vale.X64.Instruction_s.inOut", "Vale.X64.Instruction_s.one64Reg", "Vale.X64.Machine_s.rRax", "Vale.X64.Instruction_s.out", "Vale.X64.Machine_s.rRbx", "Vale.X64.Machine_s.rRcx", "Vale.X64.Machine_s.rRdx", "Prims.Nil", "Vale.X64.Instruction_s.instr_operand", "Vale.X64.Instruction_s.PreserveFlags", "Vale.X64.Instructions_s.ins_Cpuid", "Vale.X64.Decls.va_ins_lemma", "Vale.X64.Decls.va_reveal_opaque", "Vale.X64.InsBasic.va_code_Cpuid_Rdrand" ]
[]
module Vale.X64.InsBasic open Vale.X64 open Vale.X64.StateLemmas open Vale.X64.InsLemmas open Vale.X64.Taint_Semantics open Vale.X64.CPU_Features_s open Vale.X64.Memory open Vale.X64.Stack_i module I = Vale.X64.Instructions_s module S = Vale.X64.Machine_Semantics_s friend Vale.X64.Decls #reset-options "--initial_fuel 5 --max_fuel 5 --max_ifuel 2 --z3rlimit 20" //-- Mov64 [@ "opaque_to_smt"] let va_code_Mov64 dst src = (mk_ins (make_instr_annotate (I.ins_Mov64) (S.AnnotateMov64 ()) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Mov64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Mov64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Mov64) (va_code_Mov64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr_annotate (I.ins_Mov64) (S.AnnotateMov64 ()) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr_annotate (I.ins_Mov64) (S.AnnotateMov64 ()) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Mov64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Mov64 (va_code_Mov64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0))); va_lemma_norm_mods ([va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cmovc64 [@ "opaque_to_smt"] let va_code_Cmovc64 dst src = (mk_ins (make_instr (I.ins_Cmovc64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Cmovc64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cmovc64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Cmovc64) (va_code_Cmovc64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cmovc64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cmovc64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cmovc64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cmovc64 (va_code_Cmovc64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0))); va_lemma_norm_mods ([va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Add64 [@ "opaque_to_smt"] let va_code_Add64 dst src = (mk_ins (make_instr (I.ins_Add64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Add64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Add64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Add64) (va_code_Add64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Add64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Add64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Add64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Add64 (va_code_Add64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Add64Wrap [@ "opaque_to_smt"] let va_code_Add64Wrap dst src = (mk_ins (make_instr (I.ins_Add64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Add64Wrap dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Add64Wrap va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Add64Wrap) (va_code_Add64Wrap dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Add64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Add64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Add64Wrap dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Add64Wrap (va_code_Add64Wrap dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- AddLea64 [@ "opaque_to_smt"] let va_code_AddLea64 dst src1 src2 = (mk_ins (make_instr (I.ins_AddLea64) dst src1 src2)) [@ "opaque_to_smt"] let va_codegen_success_AddLea64 dst src1 src2 = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_AddLea64 va_b0 va_s0 dst src1 src2 = va_reveal_opaque (`%va_code_AddLea64) (va_code_AddLea64 dst src1 src2); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_AddLea64) dst src1 src2)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_AddLea64) dst src1 src2)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_AddLea64 dst src1 src2 va_s0 va_k = let (va_sM, va_f0) = va_lemma_AddLea64 (va_code_AddLea64 dst src1 src2) va_s0 dst src1 src2 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0))); va_lemma_norm_mods ([va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Adc64 [@ "opaque_to_smt"] let va_code_Adc64 dst src = (mk_ins (make_instr (I.ins_AddCarry64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Adc64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Adc64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Adc64) (va_code_Adc64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_AddCarry64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_AddCarry64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Adc64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Adc64 (va_code_Adc64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Adc64Wrap [@ "opaque_to_smt"] let va_code_Adc64Wrap dst src = (mk_ins (make_instr (I.ins_AddCarry64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Adc64Wrap dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Adc64Wrap va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Adc64Wrap) (va_code_Adc64Wrap dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_AddCarry64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_AddCarry64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Adc64Wrap dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Adc64Wrap (va_code_Adc64Wrap dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Adcx64Wrap #push-options "--smtencoding.nl_arith_repr boxwrap" [@ "opaque_to_smt"] let va_code_Adcx64Wrap dst src = (mk_ins (make_instr (I.ins_Adcx64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Adcx64Wrap dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Adcx64Wrap va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Adcx64Wrap) (va_code_Adcx64Wrap dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Adcx64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Adcx64) dst src)) va_s0 in assert (Vale.Arch.Types.add_wrap64 (Vale.Arch.Types.add_wrap64 (va_eval_dst_opr64 va_old_s dst) (va_eval_opr64 va_old_s src)) (if Vale.X64.Decls.cf (va_get_flags va_old_s) then 1 else 0) == (va_eval_dst_opr64 va_old_s dst + va_eval_opr64 va_old_s src + (if Vale.X64.Decls.cf (va_get_flags va_old_s) then 1 else 0)) `op_Modulus` pow2_64); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Adcx64Wrap dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Adcx64Wrap (va_code_Adcx64Wrap dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) #pop-options //-- //-- Adox64Wrap [@ "opaque_to_smt"] let va_code_Adox64Wrap dst src = (mk_ins (make_instr (I.ins_Adox64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Adox64Wrap dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Adox64Wrap va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Adox64Wrap) (va_code_Adox64Wrap dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Adox64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Adox64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Adox64Wrap dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Adox64Wrap (va_code_Adox64Wrap dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Sub64 [@ "opaque_to_smt"] let va_code_Sub64 dst src = (mk_ins (make_instr (I.ins_Sub64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Sub64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Sub64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Sub64) (va_code_Sub64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Sub64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Sub64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Sub64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Sub64 (va_code_Sub64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Sub64Wrap [@ "opaque_to_smt"] let va_code_Sub64Wrap dst src = (mk_ins (make_instr (I.ins_Sub64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Sub64Wrap dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Sub64Wrap va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Sub64Wrap) (va_code_Sub64Wrap dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Sub64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Sub64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Sub64Wrap dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Sub64Wrap (va_code_Sub64Wrap dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Sbb64 [@ "opaque_to_smt"] let va_code_Sbb64 dst src = (mk_ins (make_instr (I.ins_Sbb64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Sbb64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Sbb64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Sbb64) (va_code_Sbb64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Sbb64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Sbb64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Sbb64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Sbb64 (va_code_Sbb64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- #restart-solver #push-options "--max_fuel 0 --max_ifuel 0 --using_facts_from 'Prims FStar.UInt'" let lemma_fundamental_div_mod (a b:nat64) : Lemma (pow2_64 * (FStar.UInt.mul_div #64 a b) + (FStar.UInt.mul_mod #64 a b) == a * b) = FStar.Math.Lemmas.lemma_div_mod (a * b) pow2_64 #pop-options //-- lemma_fundamental_div_mod //-- //-- Mul64Wrap [@ "opaque_to_smt"] let va_code_Mul64Wrap src = (mk_ins (make_instr (I.ins_Mul64) src)) [@ "opaque_to_smt"] let va_codegen_success_Mul64Wrap src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Mul64Wrap va_b0 va_s0 src = va_reveal_opaque (`%va_code_Mul64Wrap) (va_code_Mul64Wrap src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Mul64) src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Mul64) src)) va_s0 in lemma_fundamental_div_mod (va_get_reg64 rRax va_old_s) (va_eval_opr64 va_old_s src); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Mul64Wrap src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Mul64Wrap (va_code_Mul64Wrap src) va_s0 src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRax va_sM (va_update_flags va_sM (va_update_ok va_sM va_s0))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRax; va_Mod_flags]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Mulx64 [@ "opaque_to_smt"] let va_code_Mulx64 dst_hi dst_lo src = (mk_ins (make_instr (I.ins_Mulx64) dst_hi dst_lo src)) [@ "opaque_to_smt"] let va_codegen_success_Mulx64 dst_hi dst_lo src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Mulx64 va_b0 va_s0 dst_hi dst_lo src = va_reveal_opaque (`%va_code_Mulx64) (va_code_Mulx64 dst_hi dst_lo src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Mulx64) dst_hi dst_lo src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Mulx64) dst_hi dst_lo src)) va_s0 in lemma_fundamental_div_mod (va_get_reg64 rRdx va_old_s) (va_eval_opr64 va_old_s src); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Mulx64 dst_hi dst_lo src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Mulx64 (va_code_Mulx64 dst_hi dst_lo src) va_s0 dst_hi dst_lo src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst_lo va_sM (va_update_operand_dst_opr64 dst_hi va_sM va_s0)))); va_lemma_norm_mods ([va_mod_dst_opr64 dst_lo; va_mod_dst_opr64 dst_hi]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- lemma_mul_nat //-- //-- lemma_mul_in_bounds //-- //-- IMul64 [@ "opaque_to_smt"] let va_code_IMul64 dst src = (mk_ins (make_instr (I.ins_IMul64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_IMul64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_IMul64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_IMul64) (va_code_IMul64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_IMul64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_IMul64) dst src)) va_s0 in lemma_mul_nat (va_eval_dst_opr64 va_old_s dst) (va_eval_opr64 va_old_s src); lemma_mul_in_bounds (va_eval_dst_opr64 va_old_s dst) (va_eval_opr64 va_old_s src); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_IMul64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_IMul64 (va_code_IMul64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Xor64 [@ "opaque_to_smt"] let va_code_Xor64 dst src = (mk_ins (make_instr_annotate (I.ins_Xor64) (S.AnnotateXor64 ()) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Xor64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Xor64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Xor64) (va_code_Xor64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr_annotate (I.ins_Xor64) (S.AnnotateXor64 ()) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr_annotate (I.ins_Xor64) (S.AnnotateXor64 ()) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Xor64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Xor64 (va_code_Xor64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- And64 [@ "opaque_to_smt"] let va_code_And64 dst src = (mk_ins (make_instr (I.ins_And64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_And64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_And64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_And64) (va_code_And64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_And64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_And64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_And64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_And64 (va_code_And64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Shl64 [@ "opaque_to_smt"] let va_code_Shl64 dst amt = (mk_ins (make_instr (I.ins_Shl64) dst amt)) [@ "opaque_to_smt"] let va_codegen_success_Shl64 dst amt = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Shl64 va_b0 va_s0 dst amt = va_reveal_opaque (`%va_code_Shl64) (va_code_Shl64 dst amt); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Shl64) dst amt)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Shl64) dst amt)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Shl64 dst amt va_s0 va_k = let (va_sM, va_f0) = va_lemma_Shl64 (va_code_Shl64 dst amt) va_s0 dst amt in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Shr64 [@ "opaque_to_smt"] let va_code_Shr64 dst amt = (mk_ins (make_instr (I.ins_Shr64) dst amt)) [@ "opaque_to_smt"] let va_codegen_success_Shr64 dst amt = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Shr64 va_b0 va_s0 dst amt = va_reveal_opaque (`%va_code_Shr64) (va_code_Shr64 dst amt); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Shr64) dst amt)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Shr64) dst amt)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Shr64 dst amt va_s0 va_k = let (va_sM, va_f0) = va_lemma_Shr64 (va_code_Shr64 dst amt) va_s0 dst amt in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_AES [@ "opaque_to_smt"] let va_code_Cpuid_AES () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_AES () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_AES va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_AES) (va_code_Cpuid_AES ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_AES va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_AES (va_code_Cpuid_AES ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Sha [@ "opaque_to_smt"] let va_code_Cpuid_Sha () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Sha () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Sha va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Sha) (va_code_Cpuid_Sha ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Sha va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Sha (va_code_Cpuid_Sha ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Adx_Bmi2 [@ "opaque_to_smt"] let va_code_Cpuid_Adx_Bmi2 () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Adx_Bmi2 () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Adx_Bmi2 va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Adx_Bmi2) (va_code_Cpuid_Adx_Bmi2 ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Adx_Bmi2 va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Adx_Bmi2 (va_code_Cpuid_Adx_Bmi2 ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Avx [@ "opaque_to_smt"] let va_code_Cpuid_Avx () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Avx () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Avx va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Avx) (va_code_Cpuid_Avx ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Avx va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Avx (va_code_Cpuid_Avx ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Avx2 [@ "opaque_to_smt"] let va_code_Cpuid_Avx2 () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Avx2 () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Avx2 va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Avx2) (va_code_Cpuid_Avx2 ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Avx2 va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Avx2 (va_code_Cpuid_Avx2 ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Sse [@ "opaque_to_smt"] let va_code_Cpuid_Sse () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Sse () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Sse va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Sse) (va_code_Cpuid_Sse ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Sse va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Sse (va_code_Cpuid_Sse ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Movbe [@ "opaque_to_smt"] let va_code_Cpuid_Movbe () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Movbe () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Movbe va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Movbe) (va_code_Cpuid_Movbe ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Movbe va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Movbe (va_code_Cpuid_Movbe ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Rdrand [@ "opaque_to_smt"] let va_code_Cpuid_Rdrand () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Rdrand () = (va_ttrue ()) [@"opaque_to_smt"]
false
false
Vale.X64.InsBasic.fst
{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 5, "initial_ifuel": 0, "max_fuel": 5, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": true, "smtencoding_l_arith_repr": "native", "smtencoding_nl_arith_repr": "wrapped", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": false, "z3cliopt": [ "smt.arith.nl=false", "smt.QI.EAGER_THRESHOLD=100", "smt.CASE_SPLIT=3" ], "z3refresh": false, "z3rlimit": 20, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }
null
val va_lemma_Cpuid_Rdrand : va_b0:va_code -> va_s0:va_state -> Ghost (va_state & va_fuel) (requires (va_require_total va_b0 (va_code_Cpuid_Rdrand ()) va_s0 /\ va_get_ok va_s0 /\ va_get_reg64 rRax va_s0 = 1)) (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\ Vale.Arch.Types.iand64 (va_get_reg64 rRcx va_sM) 1073741824 > 0 == rdrand_enabled /\ va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))))
[]
Vale.X64.InsBasic.va_lemma_Cpuid_Rdrand
{ "file_name": "obj/Vale.X64.InsBasic.fst", "git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e", "git_url": "https://github.com/hacl-star/hacl-star.git", "project_name": "hacl-star" }
va_b0: Vale.X64.Decls.va_code -> va_s0: Vale.X64.Decls.va_state -> Prims.Ghost (Vale.X64.Decls.va_state * Vale.X64.Decls.va_fuel)
{ "end_col": 16, "end_line": 846, "start_col": 2, "start_line": 841 }
Prims.Ghost
val va_lemma_Xgetbv_Avx : va_b0:va_code -> va_s0:va_state -> Ghost (va_state & va_fuel) (requires (va_require_total va_b0 (va_code_Xgetbv_Avx ()) va_s0 /\ va_get_ok va_s0 /\ osxsave_enabled /\ va_get_reg64 rRcx va_s0 = 0)) (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\ Vale.Arch.Types.iand64 (va_get_reg64 rRax va_sM) 2 > 0 == sse_xcr0_enabled /\ Vale.Arch.Types.iand64 (va_get_reg64 rRax va_sM) 4 > 0 == avx_xcr0_enabled /\ va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))
[ { "abbrev": true, "full_module": "Vale.X64.Machine_Semantics_s", "short_module": "S" }, { "abbrev": true, "full_module": "Vale.X64.Instructions_s", "short_module": "I" }, { "abbrev": false, "full_module": "Vale.X64.Stack_i", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.Memory", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.Taint_Semantics", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.InsLemmas", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.StateLemmas", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.CPU_Features_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.QuickCode", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.Decls", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.State", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.Machine_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Arch.Types", "short_module": null }, { "abbrev": false, "full_module": "Vale.Arch.HeapImpl", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Types_s", "short_module": null }, { "abbrev": false, "full_module": "FStar.Mul", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]
false
let va_lemma_Xgetbv_Avx va_b0 va_s0 = va_reveal_opaque (`%va_code_Xgetbv_Avx) (va_code_Xgetbv_Avx ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Xgetbv))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Xgetbv))) va_s0 in Vale.X64.CPU_Features_s.xgetbv_features (); (va_sM, va_fM)
val va_lemma_Xgetbv_Avx : va_b0:va_code -> va_s0:va_state -> Ghost (va_state & va_fuel) (requires (va_require_total va_b0 (va_code_Xgetbv_Avx ()) va_s0 /\ va_get_ok va_s0 /\ osxsave_enabled /\ va_get_reg64 rRcx va_s0 = 0)) (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\ Vale.Arch.Types.iand64 (va_get_reg64 rRax va_sM) 2 > 0 == sse_xcr0_enabled /\ Vale.Arch.Types.iand64 (va_get_reg64 rRax va_sM) 4 > 0 == avx_xcr0_enabled /\ va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0))))) let va_lemma_Xgetbv_Avx va_b0 va_s0 =
false
null
false
va_reveal_opaque (`%va_code_Xgetbv_Avx) (va_code_Xgetbv_Avx ()); let va_old_s:va_state = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Xgetbv))) va_s0; let va_sM, va_fM = va_eval_ins (mk_ins (make_instr (I.ins_Xgetbv))) va_s0 in Vale.X64.CPU_Features_s.xgetbv_features (); (va_sM, va_fM)
{ "checked_file": "Vale.X64.InsBasic.fst.checked", "dependencies": [ "Vale.X64.Taint_Semantics.fst.checked", "Vale.X64.StateLemmas.fsti.checked", "Vale.X64.Stack_i.fsti.checked", "Vale.X64.Memory.fsti.checked", "Vale.X64.Machine_Semantics_s.fst.checked", "Vale.X64.Instructions_s.fsti.checked", "Vale.X64.InsLemmas.fsti.checked", "Vale.X64.Decls.fst.checked", "Vale.X64.CPU_Features_s.fst.checked", "Vale.Arch.Types.fsti.checked", "prims.fst.checked", "FStar.UInt.fsti.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Math.Lemmas.fst.checked" ], "interface_file": true, "source_file": "Vale.X64.InsBasic.fst" }
[]
[ "Vale.X64.Decls.va_code", "Vale.X64.Decls.va_state", "Vale.X64.State.vale_state", "Vale.X64.Lemmas.fuel", "FStar.Pervasives.Native.Mktuple2", "Vale.X64.Decls.va_fuel", "Prims.unit", "Vale.X64.CPU_Features_s.xgetbv_features", "FStar.Pervasives.Native.tuple2", "Prims.nat", "Vale.X64.Decls.va_eval_ins", "Vale.X64.Taint_Semantics.mk_ins", "Vale.X64.InsLemmas.make_instr", "Prims.Cons", "Vale.X64.Instruction_s.instr_out", "Vale.X64.Instruction_s.out", "Vale.X64.Instruction_s.one64Reg", "Vale.X64.Machine_s.rRax", "Vale.X64.Machine_s.rRdx", "Prims.Nil", "Vale.X64.Instruction_s.instr_operand", "Vale.X64.Machine_s.rRcx", "Vale.X64.Instruction_s.PreserveFlags", "Vale.X64.Instructions_s.ins_Xgetbv", "Vale.X64.Decls.va_ins_lemma", "Vale.X64.Decls.va_reveal_opaque", "Vale.X64.InsBasic.va_code_Xgetbv_Avx" ]
[]
module Vale.X64.InsBasic open Vale.X64 open Vale.X64.StateLemmas open Vale.X64.InsLemmas open Vale.X64.Taint_Semantics open Vale.X64.CPU_Features_s open Vale.X64.Memory open Vale.X64.Stack_i module I = Vale.X64.Instructions_s module S = Vale.X64.Machine_Semantics_s friend Vale.X64.Decls #reset-options "--initial_fuel 5 --max_fuel 5 --max_ifuel 2 --z3rlimit 20" //-- Mov64 [@ "opaque_to_smt"] let va_code_Mov64 dst src = (mk_ins (make_instr_annotate (I.ins_Mov64) (S.AnnotateMov64 ()) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Mov64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Mov64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Mov64) (va_code_Mov64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr_annotate (I.ins_Mov64) (S.AnnotateMov64 ()) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr_annotate (I.ins_Mov64) (S.AnnotateMov64 ()) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Mov64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Mov64 (va_code_Mov64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0))); va_lemma_norm_mods ([va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cmovc64 [@ "opaque_to_smt"] let va_code_Cmovc64 dst src = (mk_ins (make_instr (I.ins_Cmovc64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Cmovc64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cmovc64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Cmovc64) (va_code_Cmovc64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cmovc64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cmovc64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cmovc64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cmovc64 (va_code_Cmovc64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0))); va_lemma_norm_mods ([va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Add64 [@ "opaque_to_smt"] let va_code_Add64 dst src = (mk_ins (make_instr (I.ins_Add64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Add64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Add64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Add64) (va_code_Add64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Add64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Add64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Add64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Add64 (va_code_Add64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Add64Wrap [@ "opaque_to_smt"] let va_code_Add64Wrap dst src = (mk_ins (make_instr (I.ins_Add64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Add64Wrap dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Add64Wrap va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Add64Wrap) (va_code_Add64Wrap dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Add64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Add64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Add64Wrap dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Add64Wrap (va_code_Add64Wrap dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- AddLea64 [@ "opaque_to_smt"] let va_code_AddLea64 dst src1 src2 = (mk_ins (make_instr (I.ins_AddLea64) dst src1 src2)) [@ "opaque_to_smt"] let va_codegen_success_AddLea64 dst src1 src2 = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_AddLea64 va_b0 va_s0 dst src1 src2 = va_reveal_opaque (`%va_code_AddLea64) (va_code_AddLea64 dst src1 src2); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_AddLea64) dst src1 src2)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_AddLea64) dst src1 src2)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_AddLea64 dst src1 src2 va_s0 va_k = let (va_sM, va_f0) = va_lemma_AddLea64 (va_code_AddLea64 dst src1 src2) va_s0 dst src1 src2 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0))); va_lemma_norm_mods ([va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Adc64 [@ "opaque_to_smt"] let va_code_Adc64 dst src = (mk_ins (make_instr (I.ins_AddCarry64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Adc64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Adc64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Adc64) (va_code_Adc64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_AddCarry64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_AddCarry64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Adc64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Adc64 (va_code_Adc64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Adc64Wrap [@ "opaque_to_smt"] let va_code_Adc64Wrap dst src = (mk_ins (make_instr (I.ins_AddCarry64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Adc64Wrap dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Adc64Wrap va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Adc64Wrap) (va_code_Adc64Wrap dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_AddCarry64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_AddCarry64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Adc64Wrap dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Adc64Wrap (va_code_Adc64Wrap dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Adcx64Wrap #push-options "--smtencoding.nl_arith_repr boxwrap" [@ "opaque_to_smt"] let va_code_Adcx64Wrap dst src = (mk_ins (make_instr (I.ins_Adcx64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Adcx64Wrap dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Adcx64Wrap va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Adcx64Wrap) (va_code_Adcx64Wrap dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Adcx64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Adcx64) dst src)) va_s0 in assert (Vale.Arch.Types.add_wrap64 (Vale.Arch.Types.add_wrap64 (va_eval_dst_opr64 va_old_s dst) (va_eval_opr64 va_old_s src)) (if Vale.X64.Decls.cf (va_get_flags va_old_s) then 1 else 0) == (va_eval_dst_opr64 va_old_s dst + va_eval_opr64 va_old_s src + (if Vale.X64.Decls.cf (va_get_flags va_old_s) then 1 else 0)) `op_Modulus` pow2_64); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Adcx64Wrap dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Adcx64Wrap (va_code_Adcx64Wrap dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) #pop-options //-- //-- Adox64Wrap [@ "opaque_to_smt"] let va_code_Adox64Wrap dst src = (mk_ins (make_instr (I.ins_Adox64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Adox64Wrap dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Adox64Wrap va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Adox64Wrap) (va_code_Adox64Wrap dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Adox64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Adox64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Adox64Wrap dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Adox64Wrap (va_code_Adox64Wrap dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Sub64 [@ "opaque_to_smt"] let va_code_Sub64 dst src = (mk_ins (make_instr (I.ins_Sub64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Sub64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Sub64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Sub64) (va_code_Sub64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Sub64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Sub64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Sub64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Sub64 (va_code_Sub64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Sub64Wrap [@ "opaque_to_smt"] let va_code_Sub64Wrap dst src = (mk_ins (make_instr (I.ins_Sub64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Sub64Wrap dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Sub64Wrap va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Sub64Wrap) (va_code_Sub64Wrap dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Sub64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Sub64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Sub64Wrap dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Sub64Wrap (va_code_Sub64Wrap dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Sbb64 [@ "opaque_to_smt"] let va_code_Sbb64 dst src = (mk_ins (make_instr (I.ins_Sbb64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Sbb64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Sbb64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Sbb64) (va_code_Sbb64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Sbb64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Sbb64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Sbb64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Sbb64 (va_code_Sbb64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- #restart-solver #push-options "--max_fuel 0 --max_ifuel 0 --using_facts_from 'Prims FStar.UInt'" let lemma_fundamental_div_mod (a b:nat64) : Lemma (pow2_64 * (FStar.UInt.mul_div #64 a b) + (FStar.UInt.mul_mod #64 a b) == a * b) = FStar.Math.Lemmas.lemma_div_mod (a * b) pow2_64 #pop-options //-- lemma_fundamental_div_mod //-- //-- Mul64Wrap [@ "opaque_to_smt"] let va_code_Mul64Wrap src = (mk_ins (make_instr (I.ins_Mul64) src)) [@ "opaque_to_smt"] let va_codegen_success_Mul64Wrap src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Mul64Wrap va_b0 va_s0 src = va_reveal_opaque (`%va_code_Mul64Wrap) (va_code_Mul64Wrap src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Mul64) src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Mul64) src)) va_s0 in lemma_fundamental_div_mod (va_get_reg64 rRax va_old_s) (va_eval_opr64 va_old_s src); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Mul64Wrap src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Mul64Wrap (va_code_Mul64Wrap src) va_s0 src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRax va_sM (va_update_flags va_sM (va_update_ok va_sM va_s0))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRax; va_Mod_flags]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Mulx64 [@ "opaque_to_smt"] let va_code_Mulx64 dst_hi dst_lo src = (mk_ins (make_instr (I.ins_Mulx64) dst_hi dst_lo src)) [@ "opaque_to_smt"] let va_codegen_success_Mulx64 dst_hi dst_lo src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Mulx64 va_b0 va_s0 dst_hi dst_lo src = va_reveal_opaque (`%va_code_Mulx64) (va_code_Mulx64 dst_hi dst_lo src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Mulx64) dst_hi dst_lo src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Mulx64) dst_hi dst_lo src)) va_s0 in lemma_fundamental_div_mod (va_get_reg64 rRdx va_old_s) (va_eval_opr64 va_old_s src); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Mulx64 dst_hi dst_lo src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Mulx64 (va_code_Mulx64 dst_hi dst_lo src) va_s0 dst_hi dst_lo src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst_lo va_sM (va_update_operand_dst_opr64 dst_hi va_sM va_s0)))); va_lemma_norm_mods ([va_mod_dst_opr64 dst_lo; va_mod_dst_opr64 dst_hi]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- lemma_mul_nat //-- //-- lemma_mul_in_bounds //-- //-- IMul64 [@ "opaque_to_smt"] let va_code_IMul64 dst src = (mk_ins (make_instr (I.ins_IMul64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_IMul64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_IMul64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_IMul64) (va_code_IMul64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_IMul64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_IMul64) dst src)) va_s0 in lemma_mul_nat (va_eval_dst_opr64 va_old_s dst) (va_eval_opr64 va_old_s src); lemma_mul_in_bounds (va_eval_dst_opr64 va_old_s dst) (va_eval_opr64 va_old_s src); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_IMul64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_IMul64 (va_code_IMul64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Xor64 [@ "opaque_to_smt"] let va_code_Xor64 dst src = (mk_ins (make_instr_annotate (I.ins_Xor64) (S.AnnotateXor64 ()) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Xor64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Xor64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Xor64) (va_code_Xor64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr_annotate (I.ins_Xor64) (S.AnnotateXor64 ()) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr_annotate (I.ins_Xor64) (S.AnnotateXor64 ()) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Xor64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Xor64 (va_code_Xor64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- And64 [@ "opaque_to_smt"] let va_code_And64 dst src = (mk_ins (make_instr (I.ins_And64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_And64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_And64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_And64) (va_code_And64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_And64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_And64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_And64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_And64 (va_code_And64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Shl64 [@ "opaque_to_smt"] let va_code_Shl64 dst amt = (mk_ins (make_instr (I.ins_Shl64) dst amt)) [@ "opaque_to_smt"] let va_codegen_success_Shl64 dst amt = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Shl64 va_b0 va_s0 dst amt = va_reveal_opaque (`%va_code_Shl64) (va_code_Shl64 dst amt); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Shl64) dst amt)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Shl64) dst amt)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Shl64 dst amt va_s0 va_k = let (va_sM, va_f0) = va_lemma_Shl64 (va_code_Shl64 dst amt) va_s0 dst amt in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Shr64 [@ "opaque_to_smt"] let va_code_Shr64 dst amt = (mk_ins (make_instr (I.ins_Shr64) dst amt)) [@ "opaque_to_smt"] let va_codegen_success_Shr64 dst amt = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Shr64 va_b0 va_s0 dst amt = va_reveal_opaque (`%va_code_Shr64) (va_code_Shr64 dst amt); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Shr64) dst amt)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Shr64) dst amt)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Shr64 dst amt va_s0 va_k = let (va_sM, va_f0) = va_lemma_Shr64 (va_code_Shr64 dst amt) va_s0 dst amt in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_AES [@ "opaque_to_smt"] let va_code_Cpuid_AES () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_AES () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_AES va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_AES) (va_code_Cpuid_AES ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_AES va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_AES (va_code_Cpuid_AES ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Sha [@ "opaque_to_smt"] let va_code_Cpuid_Sha () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Sha () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Sha va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Sha) (va_code_Cpuid_Sha ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Sha va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Sha (va_code_Cpuid_Sha ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Adx_Bmi2 [@ "opaque_to_smt"] let va_code_Cpuid_Adx_Bmi2 () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Adx_Bmi2 () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Adx_Bmi2 va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Adx_Bmi2) (va_code_Cpuid_Adx_Bmi2 ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Adx_Bmi2 va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Adx_Bmi2 (va_code_Cpuid_Adx_Bmi2 ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Avx [@ "opaque_to_smt"] let va_code_Cpuid_Avx () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Avx () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Avx va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Avx) (va_code_Cpuid_Avx ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Avx va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Avx (va_code_Cpuid_Avx ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Avx2 [@ "opaque_to_smt"] let va_code_Cpuid_Avx2 () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Avx2 () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Avx2 va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Avx2) (va_code_Cpuid_Avx2 ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Avx2 va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Avx2 (va_code_Cpuid_Avx2 ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Sse [@ "opaque_to_smt"] let va_code_Cpuid_Sse () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Sse () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Sse va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Sse) (va_code_Cpuid_Sse ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Sse va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Sse (va_code_Cpuid_Sse ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Movbe [@ "opaque_to_smt"] let va_code_Cpuid_Movbe () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Movbe () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Movbe va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Movbe) (va_code_Cpuid_Movbe ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Movbe va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Movbe (va_code_Cpuid_Movbe ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Rdrand [@ "opaque_to_smt"] let va_code_Cpuid_Rdrand () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Rdrand () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Rdrand va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Rdrand) (va_code_Cpuid_Rdrand ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Rdrand va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Rdrand (va_code_Cpuid_Rdrand ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Avx512 [@ "opaque_to_smt"] let va_code_Cpuid_Avx512 () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Avx512 () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Avx512 va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Avx512) (va_code_Cpuid_Avx512 ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Avx512 va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Avx512 (va_code_Cpuid_Avx512 ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Osxsave [@ "opaque_to_smt"] let va_code_Cpuid_Osxsave () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Osxsave () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Osxsave va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Osxsave) (va_code_Cpuid_Osxsave ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Osxsave va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Osxsave (va_code_Cpuid_Osxsave ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Xgetbv_Avx [@ "opaque_to_smt"] let va_code_Xgetbv_Avx () = (mk_ins (make_instr (I.ins_Xgetbv))) [@ "opaque_to_smt"] let va_codegen_success_Xgetbv_Avx () = (va_ttrue ()) [@"opaque_to_smt"]
false
false
Vale.X64.InsBasic.fst
{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 5, "initial_ifuel": 0, "max_fuel": 5, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": true, "smtencoding_l_arith_repr": "native", "smtencoding_nl_arith_repr": "wrapped", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": false, "z3cliopt": [ "smt.arith.nl=false", "smt.QI.EAGER_THRESHOLD=100", "smt.CASE_SPLIT=3" ], "z3refresh": false, "z3rlimit": 20, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }
null
val va_lemma_Xgetbv_Avx : va_b0:va_code -> va_s0:va_state -> Ghost (va_state & va_fuel) (requires (va_require_total va_b0 (va_code_Xgetbv_Avx ()) va_s0 /\ va_get_ok va_s0 /\ osxsave_enabled /\ va_get_reg64 rRcx va_s0 = 0)) (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\ Vale.Arch.Types.iand64 (va_get_reg64 rRax va_sM) 2 > 0 == sse_xcr0_enabled /\ Vale.Arch.Types.iand64 (va_get_reg64 rRax va_sM) 4 > 0 == avx_xcr0_enabled /\ va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))
[]
Vale.X64.InsBasic.va_lemma_Xgetbv_Avx
{ "file_name": "obj/Vale.X64.InsBasic.fst", "git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e", "git_url": "https://github.com/hacl-star/hacl-star.git", "project_name": "hacl-star" }
va_b0: Vale.X64.Decls.va_code -> va_s0: Vale.X64.Decls.va_state -> Prims.Ghost (Vale.X64.Decls.va_state * Vale.X64.Decls.va_fuel)
{ "end_col": 16, "end_line": 942, "start_col": 2, "start_line": 937 }
Prims.Ghost
val va_lemma_Cpuid_Osxsave : va_b0:va_code -> va_s0:va_state -> Ghost (va_state & va_fuel) (requires (va_require_total va_b0 (va_code_Cpuid_Osxsave ()) va_s0 /\ va_get_ok va_s0 /\ va_get_reg64 rRax va_s0 = 1)) (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\ Vale.Arch.Types.iand64 (va_get_reg64 rRcx va_sM) 134217728 > 0 == osxsave_enabled /\ va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))))
[ { "abbrev": true, "full_module": "Vale.X64.Machine_Semantics_s", "short_module": "S" }, { "abbrev": true, "full_module": "Vale.X64.Instructions_s", "short_module": "I" }, { "abbrev": false, "full_module": "Vale.X64.Stack_i", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.Memory", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.Taint_Semantics", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.InsLemmas", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.StateLemmas", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.CPU_Features_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.QuickCode", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.Decls", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.State", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.Machine_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Arch.Types", "short_module": null }, { "abbrev": false, "full_module": "Vale.Arch.HeapImpl", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Types_s", "short_module": null }, { "abbrev": false, "full_module": "FStar.Mul", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]
false
let va_lemma_Cpuid_Osxsave va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Osxsave) (va_code_Cpuid_Osxsave ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM)
val va_lemma_Cpuid_Osxsave : va_b0:va_code -> va_s0:va_state -> Ghost (va_state & va_fuel) (requires (va_require_total va_b0 (va_code_Cpuid_Osxsave ()) va_s0 /\ va_get_ok va_s0 /\ va_get_reg64 rRax va_s0 = 1)) (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\ Vale.Arch.Types.iand64 (va_get_reg64 rRcx va_sM) 134217728 > 0 == osxsave_enabled /\ va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0))))))) let va_lemma_Cpuid_Osxsave va_b0 va_s0 =
false
null
false
va_reveal_opaque (`%va_code_Cpuid_Osxsave) (va_code_Cpuid_Osxsave ()); let va_old_s:va_state = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let va_sM, va_fM = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM)
{ "checked_file": "Vale.X64.InsBasic.fst.checked", "dependencies": [ "Vale.X64.Taint_Semantics.fst.checked", "Vale.X64.StateLemmas.fsti.checked", "Vale.X64.Stack_i.fsti.checked", "Vale.X64.Memory.fsti.checked", "Vale.X64.Machine_Semantics_s.fst.checked", "Vale.X64.Instructions_s.fsti.checked", "Vale.X64.InsLemmas.fsti.checked", "Vale.X64.Decls.fst.checked", "Vale.X64.CPU_Features_s.fst.checked", "Vale.Arch.Types.fsti.checked", "prims.fst.checked", "FStar.UInt.fsti.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Math.Lemmas.fst.checked" ], "interface_file": true, "source_file": "Vale.X64.InsBasic.fst" }
[]
[ "Vale.X64.Decls.va_code", "Vale.X64.Decls.va_state", "Vale.X64.State.vale_state", "Vale.X64.Lemmas.fuel", "FStar.Pervasives.Native.Mktuple2", "Vale.X64.Decls.va_fuel", "Prims.unit", "Vale.X64.CPU_Features_s.cpuid_features", "FStar.Pervasives.Native.tuple2", "Prims.nat", "Vale.X64.Decls.va_eval_ins", "Vale.X64.Taint_Semantics.mk_ins", "Vale.X64.InsLemmas.make_instr", "Prims.Cons", "Vale.X64.Instruction_s.instr_out", "Vale.X64.Instruction_s.inOut", "Vale.X64.Instruction_s.one64Reg", "Vale.X64.Machine_s.rRax", "Vale.X64.Instruction_s.out", "Vale.X64.Machine_s.rRbx", "Vale.X64.Machine_s.rRcx", "Vale.X64.Machine_s.rRdx", "Prims.Nil", "Vale.X64.Instruction_s.instr_operand", "Vale.X64.Instruction_s.PreserveFlags", "Vale.X64.Instructions_s.ins_Cpuid", "Vale.X64.Decls.va_ins_lemma", "Vale.X64.Decls.va_reveal_opaque", "Vale.X64.InsBasic.va_code_Cpuid_Osxsave" ]
[]
module Vale.X64.InsBasic open Vale.X64 open Vale.X64.StateLemmas open Vale.X64.InsLemmas open Vale.X64.Taint_Semantics open Vale.X64.CPU_Features_s open Vale.X64.Memory open Vale.X64.Stack_i module I = Vale.X64.Instructions_s module S = Vale.X64.Machine_Semantics_s friend Vale.X64.Decls #reset-options "--initial_fuel 5 --max_fuel 5 --max_ifuel 2 --z3rlimit 20" //-- Mov64 [@ "opaque_to_smt"] let va_code_Mov64 dst src = (mk_ins (make_instr_annotate (I.ins_Mov64) (S.AnnotateMov64 ()) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Mov64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Mov64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Mov64) (va_code_Mov64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr_annotate (I.ins_Mov64) (S.AnnotateMov64 ()) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr_annotate (I.ins_Mov64) (S.AnnotateMov64 ()) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Mov64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Mov64 (va_code_Mov64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0))); va_lemma_norm_mods ([va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cmovc64 [@ "opaque_to_smt"] let va_code_Cmovc64 dst src = (mk_ins (make_instr (I.ins_Cmovc64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Cmovc64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cmovc64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Cmovc64) (va_code_Cmovc64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cmovc64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cmovc64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cmovc64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cmovc64 (va_code_Cmovc64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0))); va_lemma_norm_mods ([va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Add64 [@ "opaque_to_smt"] let va_code_Add64 dst src = (mk_ins (make_instr (I.ins_Add64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Add64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Add64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Add64) (va_code_Add64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Add64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Add64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Add64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Add64 (va_code_Add64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Add64Wrap [@ "opaque_to_smt"] let va_code_Add64Wrap dst src = (mk_ins (make_instr (I.ins_Add64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Add64Wrap dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Add64Wrap va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Add64Wrap) (va_code_Add64Wrap dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Add64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Add64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Add64Wrap dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Add64Wrap (va_code_Add64Wrap dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- AddLea64 [@ "opaque_to_smt"] let va_code_AddLea64 dst src1 src2 = (mk_ins (make_instr (I.ins_AddLea64) dst src1 src2)) [@ "opaque_to_smt"] let va_codegen_success_AddLea64 dst src1 src2 = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_AddLea64 va_b0 va_s0 dst src1 src2 = va_reveal_opaque (`%va_code_AddLea64) (va_code_AddLea64 dst src1 src2); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_AddLea64) dst src1 src2)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_AddLea64) dst src1 src2)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_AddLea64 dst src1 src2 va_s0 va_k = let (va_sM, va_f0) = va_lemma_AddLea64 (va_code_AddLea64 dst src1 src2) va_s0 dst src1 src2 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0))); va_lemma_norm_mods ([va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Adc64 [@ "opaque_to_smt"] let va_code_Adc64 dst src = (mk_ins (make_instr (I.ins_AddCarry64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Adc64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Adc64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Adc64) (va_code_Adc64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_AddCarry64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_AddCarry64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Adc64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Adc64 (va_code_Adc64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Adc64Wrap [@ "opaque_to_smt"] let va_code_Adc64Wrap dst src = (mk_ins (make_instr (I.ins_AddCarry64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Adc64Wrap dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Adc64Wrap va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Adc64Wrap) (va_code_Adc64Wrap dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_AddCarry64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_AddCarry64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Adc64Wrap dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Adc64Wrap (va_code_Adc64Wrap dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Adcx64Wrap #push-options "--smtencoding.nl_arith_repr boxwrap" [@ "opaque_to_smt"] let va_code_Adcx64Wrap dst src = (mk_ins (make_instr (I.ins_Adcx64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Adcx64Wrap dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Adcx64Wrap va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Adcx64Wrap) (va_code_Adcx64Wrap dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Adcx64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Adcx64) dst src)) va_s0 in assert (Vale.Arch.Types.add_wrap64 (Vale.Arch.Types.add_wrap64 (va_eval_dst_opr64 va_old_s dst) (va_eval_opr64 va_old_s src)) (if Vale.X64.Decls.cf (va_get_flags va_old_s) then 1 else 0) == (va_eval_dst_opr64 va_old_s dst + va_eval_opr64 va_old_s src + (if Vale.X64.Decls.cf (va_get_flags va_old_s) then 1 else 0)) `op_Modulus` pow2_64); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Adcx64Wrap dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Adcx64Wrap (va_code_Adcx64Wrap dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) #pop-options //-- //-- Adox64Wrap [@ "opaque_to_smt"] let va_code_Adox64Wrap dst src = (mk_ins (make_instr (I.ins_Adox64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Adox64Wrap dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Adox64Wrap va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Adox64Wrap) (va_code_Adox64Wrap dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Adox64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Adox64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Adox64Wrap dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Adox64Wrap (va_code_Adox64Wrap dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Sub64 [@ "opaque_to_smt"] let va_code_Sub64 dst src = (mk_ins (make_instr (I.ins_Sub64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Sub64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Sub64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Sub64) (va_code_Sub64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Sub64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Sub64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Sub64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Sub64 (va_code_Sub64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Sub64Wrap [@ "opaque_to_smt"] let va_code_Sub64Wrap dst src = (mk_ins (make_instr (I.ins_Sub64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Sub64Wrap dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Sub64Wrap va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Sub64Wrap) (va_code_Sub64Wrap dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Sub64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Sub64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Sub64Wrap dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Sub64Wrap (va_code_Sub64Wrap dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Sbb64 [@ "opaque_to_smt"] let va_code_Sbb64 dst src = (mk_ins (make_instr (I.ins_Sbb64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Sbb64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Sbb64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Sbb64) (va_code_Sbb64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Sbb64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Sbb64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Sbb64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Sbb64 (va_code_Sbb64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- #restart-solver #push-options "--max_fuel 0 --max_ifuel 0 --using_facts_from 'Prims FStar.UInt'" let lemma_fundamental_div_mod (a b:nat64) : Lemma (pow2_64 * (FStar.UInt.mul_div #64 a b) + (FStar.UInt.mul_mod #64 a b) == a * b) = FStar.Math.Lemmas.lemma_div_mod (a * b) pow2_64 #pop-options //-- lemma_fundamental_div_mod //-- //-- Mul64Wrap [@ "opaque_to_smt"] let va_code_Mul64Wrap src = (mk_ins (make_instr (I.ins_Mul64) src)) [@ "opaque_to_smt"] let va_codegen_success_Mul64Wrap src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Mul64Wrap va_b0 va_s0 src = va_reveal_opaque (`%va_code_Mul64Wrap) (va_code_Mul64Wrap src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Mul64) src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Mul64) src)) va_s0 in lemma_fundamental_div_mod (va_get_reg64 rRax va_old_s) (va_eval_opr64 va_old_s src); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Mul64Wrap src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Mul64Wrap (va_code_Mul64Wrap src) va_s0 src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRax va_sM (va_update_flags va_sM (va_update_ok va_sM va_s0))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRax; va_Mod_flags]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Mulx64 [@ "opaque_to_smt"] let va_code_Mulx64 dst_hi dst_lo src = (mk_ins (make_instr (I.ins_Mulx64) dst_hi dst_lo src)) [@ "opaque_to_smt"] let va_codegen_success_Mulx64 dst_hi dst_lo src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Mulx64 va_b0 va_s0 dst_hi dst_lo src = va_reveal_opaque (`%va_code_Mulx64) (va_code_Mulx64 dst_hi dst_lo src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Mulx64) dst_hi dst_lo src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Mulx64) dst_hi dst_lo src)) va_s0 in lemma_fundamental_div_mod (va_get_reg64 rRdx va_old_s) (va_eval_opr64 va_old_s src); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Mulx64 dst_hi dst_lo src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Mulx64 (va_code_Mulx64 dst_hi dst_lo src) va_s0 dst_hi dst_lo src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst_lo va_sM (va_update_operand_dst_opr64 dst_hi va_sM va_s0)))); va_lemma_norm_mods ([va_mod_dst_opr64 dst_lo; va_mod_dst_opr64 dst_hi]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- lemma_mul_nat //-- //-- lemma_mul_in_bounds //-- //-- IMul64 [@ "opaque_to_smt"] let va_code_IMul64 dst src = (mk_ins (make_instr (I.ins_IMul64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_IMul64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_IMul64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_IMul64) (va_code_IMul64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_IMul64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_IMul64) dst src)) va_s0 in lemma_mul_nat (va_eval_dst_opr64 va_old_s dst) (va_eval_opr64 va_old_s src); lemma_mul_in_bounds (va_eval_dst_opr64 va_old_s dst) (va_eval_opr64 va_old_s src); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_IMul64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_IMul64 (va_code_IMul64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Xor64 [@ "opaque_to_smt"] let va_code_Xor64 dst src = (mk_ins (make_instr_annotate (I.ins_Xor64) (S.AnnotateXor64 ()) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Xor64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Xor64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Xor64) (va_code_Xor64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr_annotate (I.ins_Xor64) (S.AnnotateXor64 ()) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr_annotate (I.ins_Xor64) (S.AnnotateXor64 ()) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Xor64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Xor64 (va_code_Xor64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- And64 [@ "opaque_to_smt"] let va_code_And64 dst src = (mk_ins (make_instr (I.ins_And64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_And64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_And64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_And64) (va_code_And64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_And64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_And64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_And64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_And64 (va_code_And64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Shl64 [@ "opaque_to_smt"] let va_code_Shl64 dst amt = (mk_ins (make_instr (I.ins_Shl64) dst amt)) [@ "opaque_to_smt"] let va_codegen_success_Shl64 dst amt = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Shl64 va_b0 va_s0 dst amt = va_reveal_opaque (`%va_code_Shl64) (va_code_Shl64 dst amt); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Shl64) dst amt)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Shl64) dst amt)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Shl64 dst amt va_s0 va_k = let (va_sM, va_f0) = va_lemma_Shl64 (va_code_Shl64 dst amt) va_s0 dst amt in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Shr64 [@ "opaque_to_smt"] let va_code_Shr64 dst amt = (mk_ins (make_instr (I.ins_Shr64) dst amt)) [@ "opaque_to_smt"] let va_codegen_success_Shr64 dst amt = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Shr64 va_b0 va_s0 dst amt = va_reveal_opaque (`%va_code_Shr64) (va_code_Shr64 dst amt); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Shr64) dst amt)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Shr64) dst amt)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Shr64 dst amt va_s0 va_k = let (va_sM, va_f0) = va_lemma_Shr64 (va_code_Shr64 dst amt) va_s0 dst amt in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_AES [@ "opaque_to_smt"] let va_code_Cpuid_AES () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_AES () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_AES va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_AES) (va_code_Cpuid_AES ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_AES va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_AES (va_code_Cpuid_AES ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Sha [@ "opaque_to_smt"] let va_code_Cpuid_Sha () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Sha () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Sha va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Sha) (va_code_Cpuid_Sha ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Sha va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Sha (va_code_Cpuid_Sha ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Adx_Bmi2 [@ "opaque_to_smt"] let va_code_Cpuid_Adx_Bmi2 () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Adx_Bmi2 () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Adx_Bmi2 va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Adx_Bmi2) (va_code_Cpuid_Adx_Bmi2 ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Adx_Bmi2 va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Adx_Bmi2 (va_code_Cpuid_Adx_Bmi2 ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Avx [@ "opaque_to_smt"] let va_code_Cpuid_Avx () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Avx () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Avx va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Avx) (va_code_Cpuid_Avx ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Avx va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Avx (va_code_Cpuid_Avx ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Avx2 [@ "opaque_to_smt"] let va_code_Cpuid_Avx2 () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Avx2 () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Avx2 va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Avx2) (va_code_Cpuid_Avx2 ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Avx2 va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Avx2 (va_code_Cpuid_Avx2 ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Sse [@ "opaque_to_smt"] let va_code_Cpuid_Sse () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Sse () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Sse va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Sse) (va_code_Cpuid_Sse ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Sse va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Sse (va_code_Cpuid_Sse ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Movbe [@ "opaque_to_smt"] let va_code_Cpuid_Movbe () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Movbe () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Movbe va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Movbe) (va_code_Cpuid_Movbe ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Movbe va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Movbe (va_code_Cpuid_Movbe ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Rdrand [@ "opaque_to_smt"] let va_code_Cpuid_Rdrand () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Rdrand () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Rdrand va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Rdrand) (va_code_Cpuid_Rdrand ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Rdrand va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Rdrand (va_code_Cpuid_Rdrand ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Avx512 [@ "opaque_to_smt"] let va_code_Cpuid_Avx512 () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Avx512 () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Avx512 va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Avx512) (va_code_Cpuid_Avx512 ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Avx512 va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Avx512 (va_code_Cpuid_Avx512 ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Osxsave [@ "opaque_to_smt"] let va_code_Cpuid_Osxsave () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Osxsave () = (va_ttrue ()) [@"opaque_to_smt"]
false
false
Vale.X64.InsBasic.fst
{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 5, "initial_ifuel": 0, "max_fuel": 5, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": true, "smtencoding_l_arith_repr": "native", "smtencoding_nl_arith_repr": "wrapped", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": false, "z3cliopt": [ "smt.arith.nl=false", "smt.QI.EAGER_THRESHOLD=100", "smt.CASE_SPLIT=3" ], "z3refresh": false, "z3rlimit": 20, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }
null
val va_lemma_Cpuid_Osxsave : va_b0:va_code -> va_s0:va_state -> Ghost (va_state & va_fuel) (requires (va_require_total va_b0 (va_code_Cpuid_Osxsave ()) va_s0 /\ va_get_ok va_s0 /\ va_get_reg64 rRax va_s0 = 1)) (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\ Vale.Arch.Types.iand64 (va_get_reg64 rRcx va_sM) 134217728 > 0 == osxsave_enabled /\ va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))))
[]
Vale.X64.InsBasic.va_lemma_Cpuid_Osxsave
{ "file_name": "obj/Vale.X64.InsBasic.fst", "git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e", "git_url": "https://github.com/hacl-star/hacl-star.git", "project_name": "hacl-star" }
va_b0: Vale.X64.Decls.va_code -> va_s0: Vale.X64.Decls.va_state -> Prims.Ghost (Vale.X64.Decls.va_state * Vale.X64.Decls.va_fuel)
{ "end_col": 16, "end_line": 910, "start_col": 2, "start_line": 905 }
Prims.Ghost
val va_wpProof_Xgetbv_Avx512 : va_s0:va_state -> va_k:(va_state -> unit -> Type0) -> Ghost (va_state & va_fuel & unit) (requires (va_t_require va_s0 /\ va_wp_Xgetbv_Avx512 va_s0 va_k)) (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Xgetbv_Avx512 ()) ([va_Mod_reg64 rRdx; va_Mod_reg64 rRax]) va_s0 va_k ((va_sM, va_f0, va_g))))
[ { "abbrev": true, "full_module": "Vale.X64.Machine_Semantics_s", "short_module": "S" }, { "abbrev": true, "full_module": "Vale.X64.Instructions_s", "short_module": "I" }, { "abbrev": false, "full_module": "Vale.X64.Stack_i", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.Memory", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.Taint_Semantics", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.InsLemmas", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.StateLemmas", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.CPU_Features_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.QuickCode", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.Decls", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.State", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.Machine_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Arch.Types", "short_module": null }, { "abbrev": false, "full_module": "Vale.Arch.HeapImpl", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Types_s", "short_module": null }, { "abbrev": false, "full_module": "FStar.Mul", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]
false
let va_wpProof_Xgetbv_Avx512 va_s0 va_k = let (va_sM, va_f0) = va_lemma_Xgetbv_Avx512 (va_code_Xgetbv_Avx512 ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g)
val va_wpProof_Xgetbv_Avx512 : va_s0:va_state -> va_k:(va_state -> unit -> Type0) -> Ghost (va_state & va_fuel & unit) (requires (va_t_require va_s0 /\ va_wp_Xgetbv_Avx512 va_s0 va_k)) (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Xgetbv_Avx512 ()) ([va_Mod_reg64 rRdx; va_Mod_reg64 rRax]) va_s0 va_k ((va_sM, va_f0, va_g)))) let va_wpProof_Xgetbv_Avx512 va_s0 va_k =
false
null
false
let va_sM, va_f0 = va_lemma_Xgetbv_Avx512 (va_code_Xgetbv_Avx512 ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g)
{ "checked_file": "Vale.X64.InsBasic.fst.checked", "dependencies": [ "Vale.X64.Taint_Semantics.fst.checked", "Vale.X64.StateLemmas.fsti.checked", "Vale.X64.Stack_i.fsti.checked", "Vale.X64.Memory.fsti.checked", "Vale.X64.Machine_Semantics_s.fst.checked", "Vale.X64.Instructions_s.fsti.checked", "Vale.X64.InsLemmas.fsti.checked", "Vale.X64.Decls.fst.checked", "Vale.X64.CPU_Features_s.fst.checked", "Vale.Arch.Types.fsti.checked", "prims.fst.checked", "FStar.UInt.fsti.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Math.Lemmas.fst.checked" ], "interface_file": true, "source_file": "Vale.X64.InsBasic.fst" }
[]
[ "Vale.X64.Decls.va_state", "Prims.unit", "Vale.X64.Decls.va_fuel", "FStar.Pervasives.Native.Mktuple3", "Vale.X64.QuickCode.va_lemma_norm_mods", "Prims.Cons", "Vale.X64.QuickCode.mod_t", "Vale.X64.QuickCode.va_Mod_reg64", "Vale.X64.Machine_s.rRdx", "Vale.X64.Machine_s.rRax", "Prims.Nil", "Prims._assert", "Vale.X64.Decls.va_state_eq", "Vale.X64.Decls.va_update_reg64", "Vale.X64.Decls.va_update_ok", "Vale.X64.Decls.va_lemma_upd_update", "FStar.Pervasives.Native.tuple3", "FStar.Pervasives.Native.tuple2", "Vale.X64.State.vale_state", "Vale.X64.InsBasic.va_lemma_Xgetbv_Avx512", "Vale.X64.InsBasic.va_code_Xgetbv_Avx512" ]
[]
module Vale.X64.InsBasic open Vale.X64 open Vale.X64.StateLemmas open Vale.X64.InsLemmas open Vale.X64.Taint_Semantics open Vale.X64.CPU_Features_s open Vale.X64.Memory open Vale.X64.Stack_i module I = Vale.X64.Instructions_s module S = Vale.X64.Machine_Semantics_s friend Vale.X64.Decls #reset-options "--initial_fuel 5 --max_fuel 5 --max_ifuel 2 --z3rlimit 20" //-- Mov64 [@ "opaque_to_smt"] let va_code_Mov64 dst src = (mk_ins (make_instr_annotate (I.ins_Mov64) (S.AnnotateMov64 ()) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Mov64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Mov64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Mov64) (va_code_Mov64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr_annotate (I.ins_Mov64) (S.AnnotateMov64 ()) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr_annotate (I.ins_Mov64) (S.AnnotateMov64 ()) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Mov64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Mov64 (va_code_Mov64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0))); va_lemma_norm_mods ([va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cmovc64 [@ "opaque_to_smt"] let va_code_Cmovc64 dst src = (mk_ins (make_instr (I.ins_Cmovc64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Cmovc64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cmovc64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Cmovc64) (va_code_Cmovc64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cmovc64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cmovc64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cmovc64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cmovc64 (va_code_Cmovc64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0))); va_lemma_norm_mods ([va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Add64 [@ "opaque_to_smt"] let va_code_Add64 dst src = (mk_ins (make_instr (I.ins_Add64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Add64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Add64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Add64) (va_code_Add64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Add64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Add64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Add64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Add64 (va_code_Add64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Add64Wrap [@ "opaque_to_smt"] let va_code_Add64Wrap dst src = (mk_ins (make_instr (I.ins_Add64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Add64Wrap dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Add64Wrap va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Add64Wrap) (va_code_Add64Wrap dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Add64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Add64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Add64Wrap dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Add64Wrap (va_code_Add64Wrap dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- AddLea64 [@ "opaque_to_smt"] let va_code_AddLea64 dst src1 src2 = (mk_ins (make_instr (I.ins_AddLea64) dst src1 src2)) [@ "opaque_to_smt"] let va_codegen_success_AddLea64 dst src1 src2 = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_AddLea64 va_b0 va_s0 dst src1 src2 = va_reveal_opaque (`%va_code_AddLea64) (va_code_AddLea64 dst src1 src2); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_AddLea64) dst src1 src2)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_AddLea64) dst src1 src2)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_AddLea64 dst src1 src2 va_s0 va_k = let (va_sM, va_f0) = va_lemma_AddLea64 (va_code_AddLea64 dst src1 src2) va_s0 dst src1 src2 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0))); va_lemma_norm_mods ([va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Adc64 [@ "opaque_to_smt"] let va_code_Adc64 dst src = (mk_ins (make_instr (I.ins_AddCarry64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Adc64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Adc64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Adc64) (va_code_Adc64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_AddCarry64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_AddCarry64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Adc64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Adc64 (va_code_Adc64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Adc64Wrap [@ "opaque_to_smt"] let va_code_Adc64Wrap dst src = (mk_ins (make_instr (I.ins_AddCarry64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Adc64Wrap dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Adc64Wrap va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Adc64Wrap) (va_code_Adc64Wrap dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_AddCarry64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_AddCarry64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Adc64Wrap dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Adc64Wrap (va_code_Adc64Wrap dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Adcx64Wrap #push-options "--smtencoding.nl_arith_repr boxwrap" [@ "opaque_to_smt"] let va_code_Adcx64Wrap dst src = (mk_ins (make_instr (I.ins_Adcx64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Adcx64Wrap dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Adcx64Wrap va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Adcx64Wrap) (va_code_Adcx64Wrap dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Adcx64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Adcx64) dst src)) va_s0 in assert (Vale.Arch.Types.add_wrap64 (Vale.Arch.Types.add_wrap64 (va_eval_dst_opr64 va_old_s dst) (va_eval_opr64 va_old_s src)) (if Vale.X64.Decls.cf (va_get_flags va_old_s) then 1 else 0) == (va_eval_dst_opr64 va_old_s dst + va_eval_opr64 va_old_s src + (if Vale.X64.Decls.cf (va_get_flags va_old_s) then 1 else 0)) `op_Modulus` pow2_64); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Adcx64Wrap dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Adcx64Wrap (va_code_Adcx64Wrap dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) #pop-options //-- //-- Adox64Wrap [@ "opaque_to_smt"] let va_code_Adox64Wrap dst src = (mk_ins (make_instr (I.ins_Adox64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Adox64Wrap dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Adox64Wrap va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Adox64Wrap) (va_code_Adox64Wrap dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Adox64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Adox64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Adox64Wrap dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Adox64Wrap (va_code_Adox64Wrap dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Sub64 [@ "opaque_to_smt"] let va_code_Sub64 dst src = (mk_ins (make_instr (I.ins_Sub64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Sub64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Sub64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Sub64) (va_code_Sub64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Sub64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Sub64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Sub64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Sub64 (va_code_Sub64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Sub64Wrap [@ "opaque_to_smt"] let va_code_Sub64Wrap dst src = (mk_ins (make_instr (I.ins_Sub64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Sub64Wrap dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Sub64Wrap va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Sub64Wrap) (va_code_Sub64Wrap dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Sub64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Sub64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Sub64Wrap dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Sub64Wrap (va_code_Sub64Wrap dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Sbb64 [@ "opaque_to_smt"] let va_code_Sbb64 dst src = (mk_ins (make_instr (I.ins_Sbb64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Sbb64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Sbb64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Sbb64) (va_code_Sbb64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Sbb64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Sbb64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Sbb64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Sbb64 (va_code_Sbb64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- #restart-solver #push-options "--max_fuel 0 --max_ifuel 0 --using_facts_from 'Prims FStar.UInt'" let lemma_fundamental_div_mod (a b:nat64) : Lemma (pow2_64 * (FStar.UInt.mul_div #64 a b) + (FStar.UInt.mul_mod #64 a b) == a * b) = FStar.Math.Lemmas.lemma_div_mod (a * b) pow2_64 #pop-options //-- lemma_fundamental_div_mod //-- //-- Mul64Wrap [@ "opaque_to_smt"] let va_code_Mul64Wrap src = (mk_ins (make_instr (I.ins_Mul64) src)) [@ "opaque_to_smt"] let va_codegen_success_Mul64Wrap src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Mul64Wrap va_b0 va_s0 src = va_reveal_opaque (`%va_code_Mul64Wrap) (va_code_Mul64Wrap src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Mul64) src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Mul64) src)) va_s0 in lemma_fundamental_div_mod (va_get_reg64 rRax va_old_s) (va_eval_opr64 va_old_s src); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Mul64Wrap src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Mul64Wrap (va_code_Mul64Wrap src) va_s0 src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRax va_sM (va_update_flags va_sM (va_update_ok va_sM va_s0))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRax; va_Mod_flags]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Mulx64 [@ "opaque_to_smt"] let va_code_Mulx64 dst_hi dst_lo src = (mk_ins (make_instr (I.ins_Mulx64) dst_hi dst_lo src)) [@ "opaque_to_smt"] let va_codegen_success_Mulx64 dst_hi dst_lo src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Mulx64 va_b0 va_s0 dst_hi dst_lo src = va_reveal_opaque (`%va_code_Mulx64) (va_code_Mulx64 dst_hi dst_lo src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Mulx64) dst_hi dst_lo src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Mulx64) dst_hi dst_lo src)) va_s0 in lemma_fundamental_div_mod (va_get_reg64 rRdx va_old_s) (va_eval_opr64 va_old_s src); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Mulx64 dst_hi dst_lo src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Mulx64 (va_code_Mulx64 dst_hi dst_lo src) va_s0 dst_hi dst_lo src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst_lo va_sM (va_update_operand_dst_opr64 dst_hi va_sM va_s0)))); va_lemma_norm_mods ([va_mod_dst_opr64 dst_lo; va_mod_dst_opr64 dst_hi]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- lemma_mul_nat //-- //-- lemma_mul_in_bounds //-- //-- IMul64 [@ "opaque_to_smt"] let va_code_IMul64 dst src = (mk_ins (make_instr (I.ins_IMul64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_IMul64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_IMul64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_IMul64) (va_code_IMul64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_IMul64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_IMul64) dst src)) va_s0 in lemma_mul_nat (va_eval_dst_opr64 va_old_s dst) (va_eval_opr64 va_old_s src); lemma_mul_in_bounds (va_eval_dst_opr64 va_old_s dst) (va_eval_opr64 va_old_s src); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_IMul64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_IMul64 (va_code_IMul64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Xor64 [@ "opaque_to_smt"] let va_code_Xor64 dst src = (mk_ins (make_instr_annotate (I.ins_Xor64) (S.AnnotateXor64 ()) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Xor64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Xor64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Xor64) (va_code_Xor64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr_annotate (I.ins_Xor64) (S.AnnotateXor64 ()) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr_annotate (I.ins_Xor64) (S.AnnotateXor64 ()) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Xor64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Xor64 (va_code_Xor64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- And64 [@ "opaque_to_smt"] let va_code_And64 dst src = (mk_ins (make_instr (I.ins_And64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_And64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_And64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_And64) (va_code_And64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_And64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_And64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_And64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_And64 (va_code_And64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Shl64 [@ "opaque_to_smt"] let va_code_Shl64 dst amt = (mk_ins (make_instr (I.ins_Shl64) dst amt)) [@ "opaque_to_smt"] let va_codegen_success_Shl64 dst amt = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Shl64 va_b0 va_s0 dst amt = va_reveal_opaque (`%va_code_Shl64) (va_code_Shl64 dst amt); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Shl64) dst amt)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Shl64) dst amt)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Shl64 dst amt va_s0 va_k = let (va_sM, va_f0) = va_lemma_Shl64 (va_code_Shl64 dst amt) va_s0 dst amt in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Shr64 [@ "opaque_to_smt"] let va_code_Shr64 dst amt = (mk_ins (make_instr (I.ins_Shr64) dst amt)) [@ "opaque_to_smt"] let va_codegen_success_Shr64 dst amt = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Shr64 va_b0 va_s0 dst amt = va_reveal_opaque (`%va_code_Shr64) (va_code_Shr64 dst amt); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Shr64) dst amt)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Shr64) dst amt)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Shr64 dst amt va_s0 va_k = let (va_sM, va_f0) = va_lemma_Shr64 (va_code_Shr64 dst amt) va_s0 dst amt in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_AES [@ "opaque_to_smt"] let va_code_Cpuid_AES () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_AES () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_AES va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_AES) (va_code_Cpuid_AES ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_AES va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_AES (va_code_Cpuid_AES ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Sha [@ "opaque_to_smt"] let va_code_Cpuid_Sha () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Sha () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Sha va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Sha) (va_code_Cpuid_Sha ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Sha va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Sha (va_code_Cpuid_Sha ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Adx_Bmi2 [@ "opaque_to_smt"] let va_code_Cpuid_Adx_Bmi2 () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Adx_Bmi2 () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Adx_Bmi2 va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Adx_Bmi2) (va_code_Cpuid_Adx_Bmi2 ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Adx_Bmi2 va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Adx_Bmi2 (va_code_Cpuid_Adx_Bmi2 ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Avx [@ "opaque_to_smt"] let va_code_Cpuid_Avx () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Avx () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Avx va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Avx) (va_code_Cpuid_Avx ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Avx va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Avx (va_code_Cpuid_Avx ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Avx2 [@ "opaque_to_smt"] let va_code_Cpuid_Avx2 () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Avx2 () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Avx2 va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Avx2) (va_code_Cpuid_Avx2 ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Avx2 va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Avx2 (va_code_Cpuid_Avx2 ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Sse [@ "opaque_to_smt"] let va_code_Cpuid_Sse () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Sse () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Sse va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Sse) (va_code_Cpuid_Sse ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Sse va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Sse (va_code_Cpuid_Sse ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Movbe [@ "opaque_to_smt"] let va_code_Cpuid_Movbe () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Movbe () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Movbe va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Movbe) (va_code_Cpuid_Movbe ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Movbe va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Movbe (va_code_Cpuid_Movbe ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Rdrand [@ "opaque_to_smt"] let va_code_Cpuid_Rdrand () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Rdrand () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Rdrand va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Rdrand) (va_code_Cpuid_Rdrand ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Rdrand va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Rdrand (va_code_Cpuid_Rdrand ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Avx512 [@ "opaque_to_smt"] let va_code_Cpuid_Avx512 () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Avx512 () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Avx512 va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Avx512) (va_code_Cpuid_Avx512 ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Avx512 va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Avx512 (va_code_Cpuid_Avx512 ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Osxsave [@ "opaque_to_smt"] let va_code_Cpuid_Osxsave () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Osxsave () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Osxsave va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Osxsave) (va_code_Cpuid_Osxsave ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Osxsave va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Osxsave (va_code_Cpuid_Osxsave ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Xgetbv_Avx [@ "opaque_to_smt"] let va_code_Xgetbv_Avx () = (mk_ins (make_instr (I.ins_Xgetbv))) [@ "opaque_to_smt"] let va_codegen_success_Xgetbv_Avx () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Xgetbv_Avx va_b0 va_s0 = va_reveal_opaque (`%va_code_Xgetbv_Avx) (va_code_Xgetbv_Avx ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Xgetbv))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Xgetbv))) va_s0 in Vale.X64.CPU_Features_s.xgetbv_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Xgetbv_Avx va_s0 va_k = let (va_sM, va_f0) = va_lemma_Xgetbv_Avx (va_code_Xgetbv_Avx ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Xgetbv_Avx512 [@ "opaque_to_smt"] let va_code_Xgetbv_Avx512 () = (mk_ins (make_instr (I.ins_Xgetbv))) [@ "opaque_to_smt"] let va_codegen_success_Xgetbv_Avx512 () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Xgetbv_Avx512 va_b0 va_s0 = va_reveal_opaque (`%va_code_Xgetbv_Avx512) (va_code_Xgetbv_Avx512 ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Xgetbv))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Xgetbv))) va_s0 in Vale.X64.CPU_Features_s.xgetbv_features (); (va_sM, va_fM)
false
false
Vale.X64.InsBasic.fst
{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 5, "initial_ifuel": 0, "max_fuel": 5, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": true, "smtencoding_l_arith_repr": "native", "smtencoding_nl_arith_repr": "wrapped", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": false, "z3cliopt": [ "smt.arith.nl=false", "smt.QI.EAGER_THRESHOLD=100", "smt.CASE_SPLIT=3" ], "z3refresh": false, "z3rlimit": 20, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }
null
val va_wpProof_Xgetbv_Avx512 : va_s0:va_state -> va_k:(va_state -> unit -> Type0) -> Ghost (va_state & va_fuel & unit) (requires (va_t_require va_s0 /\ va_wp_Xgetbv_Avx512 va_s0 va_k)) (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Xgetbv_Avx512 ()) ([va_Mod_reg64 rRdx; va_Mod_reg64 rRax]) va_s0 va_k ((va_sM, va_f0, va_g))))
[]
Vale.X64.InsBasic.va_wpProof_Xgetbv_Avx512
{ "file_name": "obj/Vale.X64.InsBasic.fst", "git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e", "git_url": "https://github.com/hacl-star/hacl-star.git", "project_name": "hacl-star" }
va_s0: Vale.X64.Decls.va_state -> va_k: (_: Vale.X64.Decls.va_state -> _: Prims.unit -> Type0) -> Prims.Ghost ((Vale.X64.Decls.va_state * Vale.X64.Decls.va_fuel) * Prims.unit)
{ "end_col": 22, "end_line": 984, "start_col": 41, "start_line": 977 }
Prims.Ghost
val va_lemma_Mulx64 : va_b0:va_code -> va_s0:va_state -> dst_hi:va_operand_dst_opr64 -> dst_lo:va_operand_dst_opr64 -> src:va_operand_opr64 -> Ghost (va_state & va_fuel) (requires (va_require_total va_b0 (va_code_Mulx64 dst_hi dst_lo src) va_s0 /\ va_is_dst_dst_opr64 dst_hi va_s0 /\ va_is_dst_dst_opr64 dst_lo va_s0 /\ va_is_src_opr64 src va_s0 /\ va_get_ok va_s0 /\ bmi2_enabled /\ dst_hi =!= dst_lo)) (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\ va_mul_nat pow2_64 (va_eval_dst_opr64 va_sM dst_hi) + va_eval_dst_opr64 va_sM dst_lo == va_mul_nat (va_get_reg64 rRdx va_s0) (va_eval_opr64 va_s0 src) /\ va_state_eq va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst_lo va_sM (va_update_operand_dst_opr64 dst_hi va_sM va_s0)))))
[ { "abbrev": true, "full_module": "Vale.X64.Machine_Semantics_s", "short_module": "S" }, { "abbrev": true, "full_module": "Vale.X64.Instructions_s", "short_module": "I" }, { "abbrev": false, "full_module": "Vale.X64.Stack_i", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.Memory", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.Taint_Semantics", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.InsLemmas", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.StateLemmas", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.CPU_Features_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.QuickCode", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.Decls", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.State", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.Machine_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Arch.Types", "short_module": null }, { "abbrev": false, "full_module": "Vale.Arch.HeapImpl", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Types_s", "short_module": null }, { "abbrev": false, "full_module": "FStar.Mul", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]
false
let va_lemma_Mulx64 va_b0 va_s0 dst_hi dst_lo src = va_reveal_opaque (`%va_code_Mulx64) (va_code_Mulx64 dst_hi dst_lo src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Mulx64) dst_hi dst_lo src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Mulx64) dst_hi dst_lo src)) va_s0 in lemma_fundamental_div_mod (va_get_reg64 rRdx va_old_s) (va_eval_opr64 va_old_s src); (va_sM, va_fM)
val va_lemma_Mulx64 : va_b0:va_code -> va_s0:va_state -> dst_hi:va_operand_dst_opr64 -> dst_lo:va_operand_dst_opr64 -> src:va_operand_opr64 -> Ghost (va_state & va_fuel) (requires (va_require_total va_b0 (va_code_Mulx64 dst_hi dst_lo src) va_s0 /\ va_is_dst_dst_opr64 dst_hi va_s0 /\ va_is_dst_dst_opr64 dst_lo va_s0 /\ va_is_src_opr64 src va_s0 /\ va_get_ok va_s0 /\ bmi2_enabled /\ dst_hi =!= dst_lo)) (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\ va_mul_nat pow2_64 (va_eval_dst_opr64 va_sM dst_hi) + va_eval_dst_opr64 va_sM dst_lo == va_mul_nat (va_get_reg64 rRdx va_s0) (va_eval_opr64 va_s0 src) /\ va_state_eq va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst_lo va_sM (va_update_operand_dst_opr64 dst_hi va_sM va_s0))))) let va_lemma_Mulx64 va_b0 va_s0 dst_hi dst_lo src =
false
null
false
va_reveal_opaque (`%va_code_Mulx64) (va_code_Mulx64 dst_hi dst_lo src); let va_old_s:va_state = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Mulx64) dst_hi dst_lo src)) va_s0; let va_sM, va_fM = va_eval_ins (mk_ins (make_instr (I.ins_Mulx64) dst_hi dst_lo src)) va_s0 in lemma_fundamental_div_mod (va_get_reg64 rRdx va_old_s) (va_eval_opr64 va_old_s src); (va_sM, va_fM)
{ "checked_file": "Vale.X64.InsBasic.fst.checked", "dependencies": [ "Vale.X64.Taint_Semantics.fst.checked", "Vale.X64.StateLemmas.fsti.checked", "Vale.X64.Stack_i.fsti.checked", "Vale.X64.Memory.fsti.checked", "Vale.X64.Machine_Semantics_s.fst.checked", "Vale.X64.Instructions_s.fsti.checked", "Vale.X64.InsLemmas.fsti.checked", "Vale.X64.Decls.fst.checked", "Vale.X64.CPU_Features_s.fst.checked", "Vale.Arch.Types.fsti.checked", "prims.fst.checked", "FStar.UInt.fsti.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Math.Lemmas.fst.checked" ], "interface_file": true, "source_file": "Vale.X64.InsBasic.fst" }
[]
[ "Vale.X64.Decls.va_code", "Vale.X64.Decls.va_state", "Vale.X64.Decls.va_operand_dst_opr64", "Vale.X64.Decls.va_operand_opr64", "Vale.X64.State.vale_state", "Vale.X64.Lemmas.fuel", "FStar.Pervasives.Native.Mktuple2", "Vale.X64.Decls.va_fuel", "Prims.unit", "Vale.X64.InsBasic.lemma_fundamental_div_mod", "Vale.X64.Decls.va_get_reg64", "Vale.X64.Machine_s.rRdx", "Vale.X64.Decls.va_eval_opr64", "FStar.Pervasives.Native.tuple2", "Prims.nat", "Vale.X64.Decls.va_eval_ins", "Vale.X64.Taint_Semantics.mk_ins", "Vale.X64.InsLemmas.make_instr", "Prims.Cons", "Vale.X64.Instruction_s.instr_out", "Vale.X64.Instruction_s.out", "Vale.X64.Instruction_s.op64", "Prims.Nil", "Vale.X64.Instruction_s.instr_operand", "Vale.X64.Instruction_s.one64Reg", "Vale.X64.Instruction_s.PreserveFlags", "Vale.X64.Instructions_s.ins_Mulx64", "Vale.X64.Decls.va_ins_lemma", "Vale.X64.Decls.va_reveal_opaque", "Vale.X64.InsBasic.va_code_Mulx64" ]
[]
module Vale.X64.InsBasic open Vale.X64 open Vale.X64.StateLemmas open Vale.X64.InsLemmas open Vale.X64.Taint_Semantics open Vale.X64.CPU_Features_s open Vale.X64.Memory open Vale.X64.Stack_i module I = Vale.X64.Instructions_s module S = Vale.X64.Machine_Semantics_s friend Vale.X64.Decls #reset-options "--initial_fuel 5 --max_fuel 5 --max_ifuel 2 --z3rlimit 20" //-- Mov64 [@ "opaque_to_smt"] let va_code_Mov64 dst src = (mk_ins (make_instr_annotate (I.ins_Mov64) (S.AnnotateMov64 ()) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Mov64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Mov64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Mov64) (va_code_Mov64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr_annotate (I.ins_Mov64) (S.AnnotateMov64 ()) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr_annotate (I.ins_Mov64) (S.AnnotateMov64 ()) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Mov64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Mov64 (va_code_Mov64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0))); va_lemma_norm_mods ([va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cmovc64 [@ "opaque_to_smt"] let va_code_Cmovc64 dst src = (mk_ins (make_instr (I.ins_Cmovc64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Cmovc64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cmovc64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Cmovc64) (va_code_Cmovc64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cmovc64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cmovc64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cmovc64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cmovc64 (va_code_Cmovc64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0))); va_lemma_norm_mods ([va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Add64 [@ "opaque_to_smt"] let va_code_Add64 dst src = (mk_ins (make_instr (I.ins_Add64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Add64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Add64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Add64) (va_code_Add64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Add64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Add64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Add64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Add64 (va_code_Add64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Add64Wrap [@ "opaque_to_smt"] let va_code_Add64Wrap dst src = (mk_ins (make_instr (I.ins_Add64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Add64Wrap dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Add64Wrap va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Add64Wrap) (va_code_Add64Wrap dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Add64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Add64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Add64Wrap dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Add64Wrap (va_code_Add64Wrap dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- AddLea64 [@ "opaque_to_smt"] let va_code_AddLea64 dst src1 src2 = (mk_ins (make_instr (I.ins_AddLea64) dst src1 src2)) [@ "opaque_to_smt"] let va_codegen_success_AddLea64 dst src1 src2 = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_AddLea64 va_b0 va_s0 dst src1 src2 = va_reveal_opaque (`%va_code_AddLea64) (va_code_AddLea64 dst src1 src2); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_AddLea64) dst src1 src2)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_AddLea64) dst src1 src2)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_AddLea64 dst src1 src2 va_s0 va_k = let (va_sM, va_f0) = va_lemma_AddLea64 (va_code_AddLea64 dst src1 src2) va_s0 dst src1 src2 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0))); va_lemma_norm_mods ([va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Adc64 [@ "opaque_to_smt"] let va_code_Adc64 dst src = (mk_ins (make_instr (I.ins_AddCarry64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Adc64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Adc64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Adc64) (va_code_Adc64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_AddCarry64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_AddCarry64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Adc64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Adc64 (va_code_Adc64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Adc64Wrap [@ "opaque_to_smt"] let va_code_Adc64Wrap dst src = (mk_ins (make_instr (I.ins_AddCarry64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Adc64Wrap dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Adc64Wrap va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Adc64Wrap) (va_code_Adc64Wrap dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_AddCarry64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_AddCarry64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Adc64Wrap dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Adc64Wrap (va_code_Adc64Wrap dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Adcx64Wrap #push-options "--smtencoding.nl_arith_repr boxwrap" [@ "opaque_to_smt"] let va_code_Adcx64Wrap dst src = (mk_ins (make_instr (I.ins_Adcx64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Adcx64Wrap dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Adcx64Wrap va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Adcx64Wrap) (va_code_Adcx64Wrap dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Adcx64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Adcx64) dst src)) va_s0 in assert (Vale.Arch.Types.add_wrap64 (Vale.Arch.Types.add_wrap64 (va_eval_dst_opr64 va_old_s dst) (va_eval_opr64 va_old_s src)) (if Vale.X64.Decls.cf (va_get_flags va_old_s) then 1 else 0) == (va_eval_dst_opr64 va_old_s dst + va_eval_opr64 va_old_s src + (if Vale.X64.Decls.cf (va_get_flags va_old_s) then 1 else 0)) `op_Modulus` pow2_64); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Adcx64Wrap dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Adcx64Wrap (va_code_Adcx64Wrap dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) #pop-options //-- //-- Adox64Wrap [@ "opaque_to_smt"] let va_code_Adox64Wrap dst src = (mk_ins (make_instr (I.ins_Adox64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Adox64Wrap dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Adox64Wrap va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Adox64Wrap) (va_code_Adox64Wrap dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Adox64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Adox64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Adox64Wrap dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Adox64Wrap (va_code_Adox64Wrap dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Sub64 [@ "opaque_to_smt"] let va_code_Sub64 dst src = (mk_ins (make_instr (I.ins_Sub64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Sub64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Sub64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Sub64) (va_code_Sub64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Sub64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Sub64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Sub64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Sub64 (va_code_Sub64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Sub64Wrap [@ "opaque_to_smt"] let va_code_Sub64Wrap dst src = (mk_ins (make_instr (I.ins_Sub64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Sub64Wrap dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Sub64Wrap va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Sub64Wrap) (va_code_Sub64Wrap dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Sub64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Sub64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Sub64Wrap dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Sub64Wrap (va_code_Sub64Wrap dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Sbb64 [@ "opaque_to_smt"] let va_code_Sbb64 dst src = (mk_ins (make_instr (I.ins_Sbb64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Sbb64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Sbb64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Sbb64) (va_code_Sbb64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Sbb64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Sbb64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Sbb64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Sbb64 (va_code_Sbb64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- #restart-solver #push-options "--max_fuel 0 --max_ifuel 0 --using_facts_from 'Prims FStar.UInt'" let lemma_fundamental_div_mod (a b:nat64) : Lemma (pow2_64 * (FStar.UInt.mul_div #64 a b) + (FStar.UInt.mul_mod #64 a b) == a * b) = FStar.Math.Lemmas.lemma_div_mod (a * b) pow2_64 #pop-options //-- lemma_fundamental_div_mod //-- //-- Mul64Wrap [@ "opaque_to_smt"] let va_code_Mul64Wrap src = (mk_ins (make_instr (I.ins_Mul64) src)) [@ "opaque_to_smt"] let va_codegen_success_Mul64Wrap src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Mul64Wrap va_b0 va_s0 src = va_reveal_opaque (`%va_code_Mul64Wrap) (va_code_Mul64Wrap src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Mul64) src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Mul64) src)) va_s0 in lemma_fundamental_div_mod (va_get_reg64 rRax va_old_s) (va_eval_opr64 va_old_s src); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Mul64Wrap src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Mul64Wrap (va_code_Mul64Wrap src) va_s0 src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRax va_sM (va_update_flags va_sM (va_update_ok va_sM va_s0))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRax; va_Mod_flags]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Mulx64 [@ "opaque_to_smt"] let va_code_Mulx64 dst_hi dst_lo src = (mk_ins (make_instr (I.ins_Mulx64) dst_hi dst_lo src)) [@ "opaque_to_smt"] let va_codegen_success_Mulx64 dst_hi dst_lo src = (va_ttrue ()) [@"opaque_to_smt"]
false
false
Vale.X64.InsBasic.fst
{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 5, "initial_ifuel": 0, "max_fuel": 5, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": true, "smtencoding_l_arith_repr": "native", "smtencoding_nl_arith_repr": "wrapped", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": false, "z3cliopt": [ "smt.arith.nl=false", "smt.QI.EAGER_THRESHOLD=100", "smt.CASE_SPLIT=3" ], "z3refresh": false, "z3rlimit": 20, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }
null
val va_lemma_Mulx64 : va_b0:va_code -> va_s0:va_state -> dst_hi:va_operand_dst_opr64 -> dst_lo:va_operand_dst_opr64 -> src:va_operand_opr64 -> Ghost (va_state & va_fuel) (requires (va_require_total va_b0 (va_code_Mulx64 dst_hi dst_lo src) va_s0 /\ va_is_dst_dst_opr64 dst_hi va_s0 /\ va_is_dst_dst_opr64 dst_lo va_s0 /\ va_is_src_opr64 src va_s0 /\ va_get_ok va_s0 /\ bmi2_enabled /\ dst_hi =!= dst_lo)) (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\ va_mul_nat pow2_64 (va_eval_dst_opr64 va_sM dst_hi) + va_eval_dst_opr64 va_sM dst_lo == va_mul_nat (va_get_reg64 rRdx va_s0) (va_eval_opr64 va_s0 src) /\ va_state_eq va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst_lo va_sM (va_update_operand_dst_opr64 dst_hi va_sM va_s0)))))
[]
Vale.X64.InsBasic.va_lemma_Mulx64
{ "file_name": "obj/Vale.X64.InsBasic.fst", "git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e", "git_url": "https://github.com/hacl-star/hacl-star.git", "project_name": "hacl-star" }
va_b0: Vale.X64.Decls.va_code -> va_s0: Vale.X64.Decls.va_state -> dst_hi: Vale.X64.Decls.va_operand_dst_opr64 -> dst_lo: Vale.X64.Decls.va_operand_dst_opr64 -> src: Vale.X64.Decls.va_operand_opr64 -> Prims.Ghost (Vale.X64.Decls.va_state * Vale.X64.Decls.va_fuel)
{ "end_col": 16, "end_line": 434, "start_col": 2, "start_line": 429 }
Prims.Ghost
val va_wpProof_Comment : c:string -> va_s0:va_state -> va_k:(va_state -> unit -> Type0) -> Ghost (va_state & va_fuel & unit) (requires (va_t_require va_s0 /\ va_wp_Comment c va_s0 va_k)) (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Comment c) ([]) va_s0 va_k ((va_sM, va_f0, va_g))))
[ { "abbrev": true, "full_module": "Vale.X64.Machine_Semantics_s", "short_module": "S" }, { "abbrev": true, "full_module": "Vale.X64.Instructions_s", "short_module": "I" }, { "abbrev": false, "full_module": "Vale.X64.Stack_i", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.Memory", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.Taint_Semantics", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.InsLemmas", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.StateLemmas", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.CPU_Features_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.QuickCode", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.Decls", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.State", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.Machine_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Arch.Types", "short_module": null }, { "abbrev": false, "full_module": "Vale.Arch.HeapImpl", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Types_s", "short_module": null }, { "abbrev": false, "full_module": "FStar.Mul", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]
false
let va_wpProof_Comment c va_s0 va_k = let (va_sM, va_f0) = va_lemma_Comment (va_code_Comment c) va_s0 c in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_ok va_sM va_s0)); va_lemma_norm_mods ([]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g)
val va_wpProof_Comment : c:string -> va_s0:va_state -> va_k:(va_state -> unit -> Type0) -> Ghost (va_state & va_fuel & unit) (requires (va_t_require va_s0 /\ va_wp_Comment c va_s0 va_k)) (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Comment c) ([]) va_s0 va_k ((va_sM, va_f0, va_g)))) let va_wpProof_Comment c va_s0 va_k =
false
null
false
let va_sM, va_f0 = va_lemma_Comment (va_code_Comment c) va_s0 c in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_ok va_sM va_s0)); va_lemma_norm_mods ([]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g)
{ "checked_file": "Vale.X64.InsBasic.fst.checked", "dependencies": [ "Vale.X64.Taint_Semantics.fst.checked", "Vale.X64.StateLemmas.fsti.checked", "Vale.X64.Stack_i.fsti.checked", "Vale.X64.Memory.fsti.checked", "Vale.X64.Machine_Semantics_s.fst.checked", "Vale.X64.Instructions_s.fsti.checked", "Vale.X64.InsLemmas.fsti.checked", "Vale.X64.Decls.fst.checked", "Vale.X64.CPU_Features_s.fst.checked", "Vale.Arch.Types.fsti.checked", "prims.fst.checked", "FStar.UInt.fsti.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Math.Lemmas.fst.checked" ], "interface_file": true, "source_file": "Vale.X64.InsBasic.fst" }
[]
[ "Prims.string", "Vale.X64.Decls.va_state", "Prims.unit", "Vale.X64.Decls.va_fuel", "FStar.Pervasives.Native.Mktuple3", "Vale.X64.QuickCode.va_lemma_norm_mods", "Prims.Nil", "Vale.X64.QuickCode.mod_t", "Prims._assert", "Vale.X64.Decls.va_state_eq", "Vale.X64.Decls.va_update_ok", "Vale.X64.Decls.va_lemma_upd_update", "FStar.Pervasives.Native.tuple3", "FStar.Pervasives.Native.tuple2", "Vale.X64.State.vale_state", "Vale.X64.InsBasic.va_lemma_Comment", "Vale.X64.InsBasic.va_code_Comment" ]
[]
module Vale.X64.InsBasic open Vale.X64 open Vale.X64.StateLemmas open Vale.X64.InsLemmas open Vale.X64.Taint_Semantics open Vale.X64.CPU_Features_s open Vale.X64.Memory open Vale.X64.Stack_i module I = Vale.X64.Instructions_s module S = Vale.X64.Machine_Semantics_s friend Vale.X64.Decls #reset-options "--initial_fuel 5 --max_fuel 5 --max_ifuel 2 --z3rlimit 20" //-- Mov64 [@ "opaque_to_smt"] let va_code_Mov64 dst src = (mk_ins (make_instr_annotate (I.ins_Mov64) (S.AnnotateMov64 ()) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Mov64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Mov64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Mov64) (va_code_Mov64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr_annotate (I.ins_Mov64) (S.AnnotateMov64 ()) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr_annotate (I.ins_Mov64) (S.AnnotateMov64 ()) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Mov64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Mov64 (va_code_Mov64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0))); va_lemma_norm_mods ([va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cmovc64 [@ "opaque_to_smt"] let va_code_Cmovc64 dst src = (mk_ins (make_instr (I.ins_Cmovc64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Cmovc64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cmovc64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Cmovc64) (va_code_Cmovc64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cmovc64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cmovc64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cmovc64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cmovc64 (va_code_Cmovc64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0))); va_lemma_norm_mods ([va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Add64 [@ "opaque_to_smt"] let va_code_Add64 dst src = (mk_ins (make_instr (I.ins_Add64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Add64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Add64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Add64) (va_code_Add64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Add64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Add64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Add64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Add64 (va_code_Add64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Add64Wrap [@ "opaque_to_smt"] let va_code_Add64Wrap dst src = (mk_ins (make_instr (I.ins_Add64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Add64Wrap dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Add64Wrap va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Add64Wrap) (va_code_Add64Wrap dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Add64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Add64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Add64Wrap dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Add64Wrap (va_code_Add64Wrap dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- AddLea64 [@ "opaque_to_smt"] let va_code_AddLea64 dst src1 src2 = (mk_ins (make_instr (I.ins_AddLea64) dst src1 src2)) [@ "opaque_to_smt"] let va_codegen_success_AddLea64 dst src1 src2 = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_AddLea64 va_b0 va_s0 dst src1 src2 = va_reveal_opaque (`%va_code_AddLea64) (va_code_AddLea64 dst src1 src2); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_AddLea64) dst src1 src2)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_AddLea64) dst src1 src2)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_AddLea64 dst src1 src2 va_s0 va_k = let (va_sM, va_f0) = va_lemma_AddLea64 (va_code_AddLea64 dst src1 src2) va_s0 dst src1 src2 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0))); va_lemma_norm_mods ([va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Adc64 [@ "opaque_to_smt"] let va_code_Adc64 dst src = (mk_ins (make_instr (I.ins_AddCarry64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Adc64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Adc64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Adc64) (va_code_Adc64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_AddCarry64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_AddCarry64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Adc64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Adc64 (va_code_Adc64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Adc64Wrap [@ "opaque_to_smt"] let va_code_Adc64Wrap dst src = (mk_ins (make_instr (I.ins_AddCarry64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Adc64Wrap dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Adc64Wrap va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Adc64Wrap) (va_code_Adc64Wrap dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_AddCarry64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_AddCarry64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Adc64Wrap dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Adc64Wrap (va_code_Adc64Wrap dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Adcx64Wrap #push-options "--smtencoding.nl_arith_repr boxwrap" [@ "opaque_to_smt"] let va_code_Adcx64Wrap dst src = (mk_ins (make_instr (I.ins_Adcx64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Adcx64Wrap dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Adcx64Wrap va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Adcx64Wrap) (va_code_Adcx64Wrap dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Adcx64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Adcx64) dst src)) va_s0 in assert (Vale.Arch.Types.add_wrap64 (Vale.Arch.Types.add_wrap64 (va_eval_dst_opr64 va_old_s dst) (va_eval_opr64 va_old_s src)) (if Vale.X64.Decls.cf (va_get_flags va_old_s) then 1 else 0) == (va_eval_dst_opr64 va_old_s dst + va_eval_opr64 va_old_s src + (if Vale.X64.Decls.cf (va_get_flags va_old_s) then 1 else 0)) `op_Modulus` pow2_64); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Adcx64Wrap dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Adcx64Wrap (va_code_Adcx64Wrap dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) #pop-options //-- //-- Adox64Wrap [@ "opaque_to_smt"] let va_code_Adox64Wrap dst src = (mk_ins (make_instr (I.ins_Adox64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Adox64Wrap dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Adox64Wrap va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Adox64Wrap) (va_code_Adox64Wrap dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Adox64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Adox64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Adox64Wrap dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Adox64Wrap (va_code_Adox64Wrap dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Sub64 [@ "opaque_to_smt"] let va_code_Sub64 dst src = (mk_ins (make_instr (I.ins_Sub64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Sub64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Sub64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Sub64) (va_code_Sub64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Sub64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Sub64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Sub64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Sub64 (va_code_Sub64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Sub64Wrap [@ "opaque_to_smt"] let va_code_Sub64Wrap dst src = (mk_ins (make_instr (I.ins_Sub64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Sub64Wrap dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Sub64Wrap va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Sub64Wrap) (va_code_Sub64Wrap dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Sub64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Sub64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Sub64Wrap dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Sub64Wrap (va_code_Sub64Wrap dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Sbb64 [@ "opaque_to_smt"] let va_code_Sbb64 dst src = (mk_ins (make_instr (I.ins_Sbb64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Sbb64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Sbb64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Sbb64) (va_code_Sbb64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Sbb64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Sbb64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Sbb64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Sbb64 (va_code_Sbb64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- #restart-solver #push-options "--max_fuel 0 --max_ifuel 0 --using_facts_from 'Prims FStar.UInt'" let lemma_fundamental_div_mod (a b:nat64) : Lemma (pow2_64 * (FStar.UInt.mul_div #64 a b) + (FStar.UInt.mul_mod #64 a b) == a * b) = FStar.Math.Lemmas.lemma_div_mod (a * b) pow2_64 #pop-options //-- lemma_fundamental_div_mod //-- //-- Mul64Wrap [@ "opaque_to_smt"] let va_code_Mul64Wrap src = (mk_ins (make_instr (I.ins_Mul64) src)) [@ "opaque_to_smt"] let va_codegen_success_Mul64Wrap src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Mul64Wrap va_b0 va_s0 src = va_reveal_opaque (`%va_code_Mul64Wrap) (va_code_Mul64Wrap src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Mul64) src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Mul64) src)) va_s0 in lemma_fundamental_div_mod (va_get_reg64 rRax va_old_s) (va_eval_opr64 va_old_s src); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Mul64Wrap src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Mul64Wrap (va_code_Mul64Wrap src) va_s0 src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRax va_sM (va_update_flags va_sM (va_update_ok va_sM va_s0))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRax; va_Mod_flags]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Mulx64 [@ "opaque_to_smt"] let va_code_Mulx64 dst_hi dst_lo src = (mk_ins (make_instr (I.ins_Mulx64) dst_hi dst_lo src)) [@ "opaque_to_smt"] let va_codegen_success_Mulx64 dst_hi dst_lo src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Mulx64 va_b0 va_s0 dst_hi dst_lo src = va_reveal_opaque (`%va_code_Mulx64) (va_code_Mulx64 dst_hi dst_lo src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Mulx64) dst_hi dst_lo src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Mulx64) dst_hi dst_lo src)) va_s0 in lemma_fundamental_div_mod (va_get_reg64 rRdx va_old_s) (va_eval_opr64 va_old_s src); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Mulx64 dst_hi dst_lo src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Mulx64 (va_code_Mulx64 dst_hi dst_lo src) va_s0 dst_hi dst_lo src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst_lo va_sM (va_update_operand_dst_opr64 dst_hi va_sM va_s0)))); va_lemma_norm_mods ([va_mod_dst_opr64 dst_lo; va_mod_dst_opr64 dst_hi]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- lemma_mul_nat //-- //-- lemma_mul_in_bounds //-- //-- IMul64 [@ "opaque_to_smt"] let va_code_IMul64 dst src = (mk_ins (make_instr (I.ins_IMul64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_IMul64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_IMul64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_IMul64) (va_code_IMul64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_IMul64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_IMul64) dst src)) va_s0 in lemma_mul_nat (va_eval_dst_opr64 va_old_s dst) (va_eval_opr64 va_old_s src); lemma_mul_in_bounds (va_eval_dst_opr64 va_old_s dst) (va_eval_opr64 va_old_s src); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_IMul64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_IMul64 (va_code_IMul64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Xor64 [@ "opaque_to_smt"] let va_code_Xor64 dst src = (mk_ins (make_instr_annotate (I.ins_Xor64) (S.AnnotateXor64 ()) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Xor64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Xor64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Xor64) (va_code_Xor64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr_annotate (I.ins_Xor64) (S.AnnotateXor64 ()) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr_annotate (I.ins_Xor64) (S.AnnotateXor64 ()) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Xor64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Xor64 (va_code_Xor64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- And64 [@ "opaque_to_smt"] let va_code_And64 dst src = (mk_ins (make_instr (I.ins_And64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_And64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_And64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_And64) (va_code_And64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_And64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_And64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_And64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_And64 (va_code_And64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Shl64 [@ "opaque_to_smt"] let va_code_Shl64 dst amt = (mk_ins (make_instr (I.ins_Shl64) dst amt)) [@ "opaque_to_smt"] let va_codegen_success_Shl64 dst amt = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Shl64 va_b0 va_s0 dst amt = va_reveal_opaque (`%va_code_Shl64) (va_code_Shl64 dst amt); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Shl64) dst amt)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Shl64) dst amt)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Shl64 dst amt va_s0 va_k = let (va_sM, va_f0) = va_lemma_Shl64 (va_code_Shl64 dst amt) va_s0 dst amt in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Shr64 [@ "opaque_to_smt"] let va_code_Shr64 dst amt = (mk_ins (make_instr (I.ins_Shr64) dst amt)) [@ "opaque_to_smt"] let va_codegen_success_Shr64 dst amt = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Shr64 va_b0 va_s0 dst amt = va_reveal_opaque (`%va_code_Shr64) (va_code_Shr64 dst amt); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Shr64) dst amt)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Shr64) dst amt)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Shr64 dst amt va_s0 va_k = let (va_sM, va_f0) = va_lemma_Shr64 (va_code_Shr64 dst amt) va_s0 dst amt in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_AES [@ "opaque_to_smt"] let va_code_Cpuid_AES () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_AES () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_AES va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_AES) (va_code_Cpuid_AES ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_AES va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_AES (va_code_Cpuid_AES ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Sha [@ "opaque_to_smt"] let va_code_Cpuid_Sha () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Sha () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Sha va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Sha) (va_code_Cpuid_Sha ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Sha va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Sha (va_code_Cpuid_Sha ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Adx_Bmi2 [@ "opaque_to_smt"] let va_code_Cpuid_Adx_Bmi2 () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Adx_Bmi2 () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Adx_Bmi2 va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Adx_Bmi2) (va_code_Cpuid_Adx_Bmi2 ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Adx_Bmi2 va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Adx_Bmi2 (va_code_Cpuid_Adx_Bmi2 ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Avx [@ "opaque_to_smt"] let va_code_Cpuid_Avx () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Avx () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Avx va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Avx) (va_code_Cpuid_Avx ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Avx va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Avx (va_code_Cpuid_Avx ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Avx2 [@ "opaque_to_smt"] let va_code_Cpuid_Avx2 () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Avx2 () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Avx2 va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Avx2) (va_code_Cpuid_Avx2 ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Avx2 va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Avx2 (va_code_Cpuid_Avx2 ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Sse [@ "opaque_to_smt"] let va_code_Cpuid_Sse () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Sse () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Sse va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Sse) (va_code_Cpuid_Sse ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Sse va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Sse (va_code_Cpuid_Sse ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Movbe [@ "opaque_to_smt"] let va_code_Cpuid_Movbe () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Movbe () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Movbe va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Movbe) (va_code_Cpuid_Movbe ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Movbe va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Movbe (va_code_Cpuid_Movbe ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Rdrand [@ "opaque_to_smt"] let va_code_Cpuid_Rdrand () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Rdrand () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Rdrand va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Rdrand) (va_code_Cpuid_Rdrand ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Rdrand va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Rdrand (va_code_Cpuid_Rdrand ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Avx512 [@ "opaque_to_smt"] let va_code_Cpuid_Avx512 () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Avx512 () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Avx512 va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Avx512) (va_code_Cpuid_Avx512 ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Avx512 va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Avx512 (va_code_Cpuid_Avx512 ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Osxsave [@ "opaque_to_smt"] let va_code_Cpuid_Osxsave () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Osxsave () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Osxsave va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Osxsave) (va_code_Cpuid_Osxsave ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Osxsave va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Osxsave (va_code_Cpuid_Osxsave ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Xgetbv_Avx [@ "opaque_to_smt"] let va_code_Xgetbv_Avx () = (mk_ins (make_instr (I.ins_Xgetbv))) [@ "opaque_to_smt"] let va_codegen_success_Xgetbv_Avx () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Xgetbv_Avx va_b0 va_s0 = va_reveal_opaque (`%va_code_Xgetbv_Avx) (va_code_Xgetbv_Avx ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Xgetbv))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Xgetbv))) va_s0 in Vale.X64.CPU_Features_s.xgetbv_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Xgetbv_Avx va_s0 va_k = let (va_sM, va_f0) = va_lemma_Xgetbv_Avx (va_code_Xgetbv_Avx ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Xgetbv_Avx512 [@ "opaque_to_smt"] let va_code_Xgetbv_Avx512 () = (mk_ins (make_instr (I.ins_Xgetbv))) [@ "opaque_to_smt"] let va_codegen_success_Xgetbv_Avx512 () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Xgetbv_Avx512 va_b0 va_s0 = va_reveal_opaque (`%va_code_Xgetbv_Avx512) (va_code_Xgetbv_Avx512 ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Xgetbv))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Xgetbv))) va_s0 in Vale.X64.CPU_Features_s.xgetbv_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Xgetbv_Avx512 va_s0 va_k = let (va_sM, va_f0) = va_lemma_Xgetbv_Avx512 (va_code_Xgetbv_Avx512 ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Nat64Equal [@ "opaque_to_smt"] let va_code_Nat64Equal dst src = (va_Block (va_CCons (va_code_Sub64Wrap (va_coerce_reg_opr64_to_dst_opr64 src) (va_const_opr64 18446744073709551615)) (va_CCons (va_code_Mov64 (va_coerce_reg_opr64_to_dst_opr64 dst) (va_const_opr64 0)) (va_CCons (va_code_Adc64 (va_coerce_reg_opr64_to_dst_opr64 dst) (va_const_opr64 0)) (va_CNil ()))))) [@ "opaque_to_smt"] let va_codegen_success_Nat64Equal dst src = (va_pbool_and (va_codegen_success_Sub64Wrap (va_coerce_reg_opr64_to_dst_opr64 src) (va_const_opr64 18446744073709551615)) (va_pbool_and (va_codegen_success_Mov64 (va_coerce_reg_opr64_to_dst_opr64 dst) (va_const_opr64 0)) (va_pbool_and (va_codegen_success_Adc64 (va_coerce_reg_opr64_to_dst_opr64 dst) (va_const_opr64 0)) (va_ttrue ())))) [@"opaque_to_smt"] let va_lemma_Nat64Equal va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Nat64Equal) (va_code_Nat64Equal dst src); let (va_old_s:va_state) = va_s0 in let (va_b1:va_codes) = va_get_block va_b0 in let (va_s2, va_fc2) = va_lemma_Sub64Wrap (va_hd va_b1) va_s0 (va_coerce_reg_opr64_to_dst_opr64 src) (va_const_opr64 18446744073709551615) in let va_b2 = va_tl va_b1 in let (va_s3, va_fc3) = va_lemma_Mov64 (va_hd va_b2) va_s2 (va_coerce_reg_opr64_to_dst_opr64 dst) (va_const_opr64 0) in let va_b3 = va_tl va_b2 in let (va_s4, va_fc4) = va_lemma_Adc64 (va_hd va_b3) va_s3 (va_coerce_reg_opr64_to_dst_opr64 dst) (va_const_opr64 0) in let va_b4 = va_tl va_b3 in let (va_sM, va_f4) = va_lemma_empty_total va_s4 va_b4 in let va_f3 = va_lemma_merge_total va_b3 va_s3 va_fc4 va_s4 va_f4 va_sM in let va_f2 = va_lemma_merge_total va_b2 va_s2 va_fc3 va_s3 va_f3 va_sM in let va_fM = va_lemma_merge_total va_b1 va_s0 va_fc2 va_s2 va_f2 va_sM in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Nat64Equal dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Nat64Equal (va_code_Nat64Equal dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_reg_opr64 src va_sM (va_update_operand_reg_opr64 dst va_sM va_s0))))); va_lemma_norm_mods ([va_Mod_flags; va_mod_reg_opr64 src; va_mod_reg_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Comment [@ "opaque_to_smt"] let va_code_Comment c = (mk_ins (make_instr_annotate (I.ins_Comment c) (S.AnnotateComment c))) [@ "opaque_to_smt"] let va_codegen_success_Comment c = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Comment va_b0 va_s0 c = va_reveal_opaque (`%va_code_Comment) (va_code_Comment c); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr_annotate (I.ins_Comment c) (S.AnnotateComment c))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr_annotate (I.ins_Comment c) (S.AnnotateComment c))) va_s0 in (va_sM, va_fM)
false
false
Vale.X64.InsBasic.fst
{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 5, "initial_ifuel": 0, "max_fuel": 5, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": true, "smtencoding_l_arith_repr": "native", "smtencoding_nl_arith_repr": "wrapped", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": false, "z3cliopt": [ "smt.arith.nl=false", "smt.QI.EAGER_THRESHOLD=100", "smt.CASE_SPLIT=3" ], "z3refresh": false, "z3rlimit": 20, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }
null
val va_wpProof_Comment : c:string -> va_s0:va_state -> va_k:(va_state -> unit -> Type0) -> Ghost (va_state & va_fuel & unit) (requires (va_t_require va_s0 /\ va_wp_Comment c va_s0 va_k)) (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Comment c) ([]) va_s0 va_k ((va_sM, va_f0, va_g))))
[]
Vale.X64.InsBasic.va_wpProof_Comment
{ "file_name": "obj/Vale.X64.InsBasic.fst", "git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e", "git_url": "https://github.com/hacl-star/hacl-star.git", "project_name": "hacl-star" }
c: Prims.string -> va_s0: Vale.X64.Decls.va_state -> va_k: (_: Vale.X64.Decls.va_state -> _: Prims.unit -> Type0) -> Prims.Ghost ((Vale.X64.Decls.va_state * Vale.X64.Decls.va_fuel) * Prims.unit)
{ "end_col": 22, "end_line": 1063, "start_col": 37, "start_line": 1057 }
Prims.Ghost
val va_lemma_Xgetbv_Avx512 : va_b0:va_code -> va_s0:va_state -> Ghost (va_state & va_fuel) (requires (va_require_total va_b0 (va_code_Xgetbv_Avx512 ()) va_s0 /\ va_get_ok va_s0 /\ osxsave_enabled /\ va_get_reg64 rRcx va_s0 = 0)) (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\ Vale.Arch.Types.iand64 (va_get_reg64 rRax va_sM) 32 > 0 == opmask_xcr0_enabled /\ Vale.Arch.Types.iand64 (va_get_reg64 rRax va_sM) 64 > 0 == zmm_hi256_xcr0_enabled /\ Vale.Arch.Types.iand64 (va_get_reg64 rRax va_sM) 128 > 0 == hi16_zmm_xcr0_enabled /\ va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))
[ { "abbrev": true, "full_module": "Vale.X64.Machine_Semantics_s", "short_module": "S" }, { "abbrev": true, "full_module": "Vale.X64.Instructions_s", "short_module": "I" }, { "abbrev": false, "full_module": "Vale.X64.Stack_i", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.Memory", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.Taint_Semantics", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.InsLemmas", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.StateLemmas", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.CPU_Features_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.QuickCode", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.Decls", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.State", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.Machine_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Arch.Types", "short_module": null }, { "abbrev": false, "full_module": "Vale.Arch.HeapImpl", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Types_s", "short_module": null }, { "abbrev": false, "full_module": "FStar.Mul", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]
false
let va_lemma_Xgetbv_Avx512 va_b0 va_s0 = va_reveal_opaque (`%va_code_Xgetbv_Avx512) (va_code_Xgetbv_Avx512 ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Xgetbv))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Xgetbv))) va_s0 in Vale.X64.CPU_Features_s.xgetbv_features (); (va_sM, va_fM)
val va_lemma_Xgetbv_Avx512 : va_b0:va_code -> va_s0:va_state -> Ghost (va_state & va_fuel) (requires (va_require_total va_b0 (va_code_Xgetbv_Avx512 ()) va_s0 /\ va_get_ok va_s0 /\ osxsave_enabled /\ va_get_reg64 rRcx va_s0 = 0)) (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\ Vale.Arch.Types.iand64 (va_get_reg64 rRax va_sM) 32 > 0 == opmask_xcr0_enabled /\ Vale.Arch.Types.iand64 (va_get_reg64 rRax va_sM) 64 > 0 == zmm_hi256_xcr0_enabled /\ Vale.Arch.Types.iand64 (va_get_reg64 rRax va_sM) 128 > 0 == hi16_zmm_xcr0_enabled /\ va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0))))) let va_lemma_Xgetbv_Avx512 va_b0 va_s0 =
false
null
false
va_reveal_opaque (`%va_code_Xgetbv_Avx512) (va_code_Xgetbv_Avx512 ()); let va_old_s:va_state = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Xgetbv))) va_s0; let va_sM, va_fM = va_eval_ins (mk_ins (make_instr (I.ins_Xgetbv))) va_s0 in Vale.X64.CPU_Features_s.xgetbv_features (); (va_sM, va_fM)
{ "checked_file": "Vale.X64.InsBasic.fst.checked", "dependencies": [ "Vale.X64.Taint_Semantics.fst.checked", "Vale.X64.StateLemmas.fsti.checked", "Vale.X64.Stack_i.fsti.checked", "Vale.X64.Memory.fsti.checked", "Vale.X64.Machine_Semantics_s.fst.checked", "Vale.X64.Instructions_s.fsti.checked", "Vale.X64.InsLemmas.fsti.checked", "Vale.X64.Decls.fst.checked", "Vale.X64.CPU_Features_s.fst.checked", "Vale.Arch.Types.fsti.checked", "prims.fst.checked", "FStar.UInt.fsti.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Math.Lemmas.fst.checked" ], "interface_file": true, "source_file": "Vale.X64.InsBasic.fst" }
[]
[ "Vale.X64.Decls.va_code", "Vale.X64.Decls.va_state", "Vale.X64.State.vale_state", "Vale.X64.Lemmas.fuel", "FStar.Pervasives.Native.Mktuple2", "Vale.X64.Decls.va_fuel", "Prims.unit", "Vale.X64.CPU_Features_s.xgetbv_features", "FStar.Pervasives.Native.tuple2", "Prims.nat", "Vale.X64.Decls.va_eval_ins", "Vale.X64.Taint_Semantics.mk_ins", "Vale.X64.InsLemmas.make_instr", "Prims.Cons", "Vale.X64.Instruction_s.instr_out", "Vale.X64.Instruction_s.out", "Vale.X64.Instruction_s.one64Reg", "Vale.X64.Machine_s.rRax", "Vale.X64.Machine_s.rRdx", "Prims.Nil", "Vale.X64.Instruction_s.instr_operand", "Vale.X64.Machine_s.rRcx", "Vale.X64.Instruction_s.PreserveFlags", "Vale.X64.Instructions_s.ins_Xgetbv", "Vale.X64.Decls.va_ins_lemma", "Vale.X64.Decls.va_reveal_opaque", "Vale.X64.InsBasic.va_code_Xgetbv_Avx512" ]
[]
module Vale.X64.InsBasic open Vale.X64 open Vale.X64.StateLemmas open Vale.X64.InsLemmas open Vale.X64.Taint_Semantics open Vale.X64.CPU_Features_s open Vale.X64.Memory open Vale.X64.Stack_i module I = Vale.X64.Instructions_s module S = Vale.X64.Machine_Semantics_s friend Vale.X64.Decls #reset-options "--initial_fuel 5 --max_fuel 5 --max_ifuel 2 --z3rlimit 20" //-- Mov64 [@ "opaque_to_smt"] let va_code_Mov64 dst src = (mk_ins (make_instr_annotate (I.ins_Mov64) (S.AnnotateMov64 ()) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Mov64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Mov64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Mov64) (va_code_Mov64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr_annotate (I.ins_Mov64) (S.AnnotateMov64 ()) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr_annotate (I.ins_Mov64) (S.AnnotateMov64 ()) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Mov64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Mov64 (va_code_Mov64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0))); va_lemma_norm_mods ([va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cmovc64 [@ "opaque_to_smt"] let va_code_Cmovc64 dst src = (mk_ins (make_instr (I.ins_Cmovc64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Cmovc64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cmovc64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Cmovc64) (va_code_Cmovc64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cmovc64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cmovc64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cmovc64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cmovc64 (va_code_Cmovc64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0))); va_lemma_norm_mods ([va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Add64 [@ "opaque_to_smt"] let va_code_Add64 dst src = (mk_ins (make_instr (I.ins_Add64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Add64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Add64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Add64) (va_code_Add64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Add64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Add64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Add64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Add64 (va_code_Add64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Add64Wrap [@ "opaque_to_smt"] let va_code_Add64Wrap dst src = (mk_ins (make_instr (I.ins_Add64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Add64Wrap dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Add64Wrap va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Add64Wrap) (va_code_Add64Wrap dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Add64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Add64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Add64Wrap dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Add64Wrap (va_code_Add64Wrap dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- AddLea64 [@ "opaque_to_smt"] let va_code_AddLea64 dst src1 src2 = (mk_ins (make_instr (I.ins_AddLea64) dst src1 src2)) [@ "opaque_to_smt"] let va_codegen_success_AddLea64 dst src1 src2 = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_AddLea64 va_b0 va_s0 dst src1 src2 = va_reveal_opaque (`%va_code_AddLea64) (va_code_AddLea64 dst src1 src2); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_AddLea64) dst src1 src2)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_AddLea64) dst src1 src2)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_AddLea64 dst src1 src2 va_s0 va_k = let (va_sM, va_f0) = va_lemma_AddLea64 (va_code_AddLea64 dst src1 src2) va_s0 dst src1 src2 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0))); va_lemma_norm_mods ([va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Adc64 [@ "opaque_to_smt"] let va_code_Adc64 dst src = (mk_ins (make_instr (I.ins_AddCarry64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Adc64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Adc64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Adc64) (va_code_Adc64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_AddCarry64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_AddCarry64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Adc64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Adc64 (va_code_Adc64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Adc64Wrap [@ "opaque_to_smt"] let va_code_Adc64Wrap dst src = (mk_ins (make_instr (I.ins_AddCarry64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Adc64Wrap dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Adc64Wrap va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Adc64Wrap) (va_code_Adc64Wrap dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_AddCarry64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_AddCarry64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Adc64Wrap dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Adc64Wrap (va_code_Adc64Wrap dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Adcx64Wrap #push-options "--smtencoding.nl_arith_repr boxwrap" [@ "opaque_to_smt"] let va_code_Adcx64Wrap dst src = (mk_ins (make_instr (I.ins_Adcx64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Adcx64Wrap dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Adcx64Wrap va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Adcx64Wrap) (va_code_Adcx64Wrap dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Adcx64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Adcx64) dst src)) va_s0 in assert (Vale.Arch.Types.add_wrap64 (Vale.Arch.Types.add_wrap64 (va_eval_dst_opr64 va_old_s dst) (va_eval_opr64 va_old_s src)) (if Vale.X64.Decls.cf (va_get_flags va_old_s) then 1 else 0) == (va_eval_dst_opr64 va_old_s dst + va_eval_opr64 va_old_s src + (if Vale.X64.Decls.cf (va_get_flags va_old_s) then 1 else 0)) `op_Modulus` pow2_64); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Adcx64Wrap dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Adcx64Wrap (va_code_Adcx64Wrap dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) #pop-options //-- //-- Adox64Wrap [@ "opaque_to_smt"] let va_code_Adox64Wrap dst src = (mk_ins (make_instr (I.ins_Adox64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Adox64Wrap dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Adox64Wrap va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Adox64Wrap) (va_code_Adox64Wrap dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Adox64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Adox64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Adox64Wrap dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Adox64Wrap (va_code_Adox64Wrap dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Sub64 [@ "opaque_to_smt"] let va_code_Sub64 dst src = (mk_ins (make_instr (I.ins_Sub64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Sub64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Sub64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Sub64) (va_code_Sub64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Sub64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Sub64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Sub64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Sub64 (va_code_Sub64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Sub64Wrap [@ "opaque_to_smt"] let va_code_Sub64Wrap dst src = (mk_ins (make_instr (I.ins_Sub64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Sub64Wrap dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Sub64Wrap va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Sub64Wrap) (va_code_Sub64Wrap dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Sub64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Sub64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Sub64Wrap dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Sub64Wrap (va_code_Sub64Wrap dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Sbb64 [@ "opaque_to_smt"] let va_code_Sbb64 dst src = (mk_ins (make_instr (I.ins_Sbb64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Sbb64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Sbb64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Sbb64) (va_code_Sbb64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Sbb64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Sbb64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Sbb64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Sbb64 (va_code_Sbb64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- #restart-solver #push-options "--max_fuel 0 --max_ifuel 0 --using_facts_from 'Prims FStar.UInt'" let lemma_fundamental_div_mod (a b:nat64) : Lemma (pow2_64 * (FStar.UInt.mul_div #64 a b) + (FStar.UInt.mul_mod #64 a b) == a * b) = FStar.Math.Lemmas.lemma_div_mod (a * b) pow2_64 #pop-options //-- lemma_fundamental_div_mod //-- //-- Mul64Wrap [@ "opaque_to_smt"] let va_code_Mul64Wrap src = (mk_ins (make_instr (I.ins_Mul64) src)) [@ "opaque_to_smt"] let va_codegen_success_Mul64Wrap src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Mul64Wrap va_b0 va_s0 src = va_reveal_opaque (`%va_code_Mul64Wrap) (va_code_Mul64Wrap src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Mul64) src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Mul64) src)) va_s0 in lemma_fundamental_div_mod (va_get_reg64 rRax va_old_s) (va_eval_opr64 va_old_s src); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Mul64Wrap src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Mul64Wrap (va_code_Mul64Wrap src) va_s0 src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRax va_sM (va_update_flags va_sM (va_update_ok va_sM va_s0))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRax; va_Mod_flags]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Mulx64 [@ "opaque_to_smt"] let va_code_Mulx64 dst_hi dst_lo src = (mk_ins (make_instr (I.ins_Mulx64) dst_hi dst_lo src)) [@ "opaque_to_smt"] let va_codegen_success_Mulx64 dst_hi dst_lo src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Mulx64 va_b0 va_s0 dst_hi dst_lo src = va_reveal_opaque (`%va_code_Mulx64) (va_code_Mulx64 dst_hi dst_lo src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Mulx64) dst_hi dst_lo src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Mulx64) dst_hi dst_lo src)) va_s0 in lemma_fundamental_div_mod (va_get_reg64 rRdx va_old_s) (va_eval_opr64 va_old_s src); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Mulx64 dst_hi dst_lo src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Mulx64 (va_code_Mulx64 dst_hi dst_lo src) va_s0 dst_hi dst_lo src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst_lo va_sM (va_update_operand_dst_opr64 dst_hi va_sM va_s0)))); va_lemma_norm_mods ([va_mod_dst_opr64 dst_lo; va_mod_dst_opr64 dst_hi]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- lemma_mul_nat //-- //-- lemma_mul_in_bounds //-- //-- IMul64 [@ "opaque_to_smt"] let va_code_IMul64 dst src = (mk_ins (make_instr (I.ins_IMul64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_IMul64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_IMul64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_IMul64) (va_code_IMul64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_IMul64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_IMul64) dst src)) va_s0 in lemma_mul_nat (va_eval_dst_opr64 va_old_s dst) (va_eval_opr64 va_old_s src); lemma_mul_in_bounds (va_eval_dst_opr64 va_old_s dst) (va_eval_opr64 va_old_s src); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_IMul64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_IMul64 (va_code_IMul64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Xor64 [@ "opaque_to_smt"] let va_code_Xor64 dst src = (mk_ins (make_instr_annotate (I.ins_Xor64) (S.AnnotateXor64 ()) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Xor64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Xor64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Xor64) (va_code_Xor64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr_annotate (I.ins_Xor64) (S.AnnotateXor64 ()) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr_annotate (I.ins_Xor64) (S.AnnotateXor64 ()) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Xor64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Xor64 (va_code_Xor64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- And64 [@ "opaque_to_smt"] let va_code_And64 dst src = (mk_ins (make_instr (I.ins_And64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_And64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_And64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_And64) (va_code_And64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_And64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_And64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_And64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_And64 (va_code_And64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Shl64 [@ "opaque_to_smt"] let va_code_Shl64 dst amt = (mk_ins (make_instr (I.ins_Shl64) dst amt)) [@ "opaque_to_smt"] let va_codegen_success_Shl64 dst amt = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Shl64 va_b0 va_s0 dst amt = va_reveal_opaque (`%va_code_Shl64) (va_code_Shl64 dst amt); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Shl64) dst amt)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Shl64) dst amt)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Shl64 dst amt va_s0 va_k = let (va_sM, va_f0) = va_lemma_Shl64 (va_code_Shl64 dst amt) va_s0 dst amt in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Shr64 [@ "opaque_to_smt"] let va_code_Shr64 dst amt = (mk_ins (make_instr (I.ins_Shr64) dst amt)) [@ "opaque_to_smt"] let va_codegen_success_Shr64 dst amt = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Shr64 va_b0 va_s0 dst amt = va_reveal_opaque (`%va_code_Shr64) (va_code_Shr64 dst amt); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Shr64) dst amt)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Shr64) dst amt)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Shr64 dst amt va_s0 va_k = let (va_sM, va_f0) = va_lemma_Shr64 (va_code_Shr64 dst amt) va_s0 dst amt in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_AES [@ "opaque_to_smt"] let va_code_Cpuid_AES () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_AES () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_AES va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_AES) (va_code_Cpuid_AES ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_AES va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_AES (va_code_Cpuid_AES ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Sha [@ "opaque_to_smt"] let va_code_Cpuid_Sha () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Sha () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Sha va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Sha) (va_code_Cpuid_Sha ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Sha va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Sha (va_code_Cpuid_Sha ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Adx_Bmi2 [@ "opaque_to_smt"] let va_code_Cpuid_Adx_Bmi2 () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Adx_Bmi2 () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Adx_Bmi2 va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Adx_Bmi2) (va_code_Cpuid_Adx_Bmi2 ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Adx_Bmi2 va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Adx_Bmi2 (va_code_Cpuid_Adx_Bmi2 ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Avx [@ "opaque_to_smt"] let va_code_Cpuid_Avx () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Avx () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Avx va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Avx) (va_code_Cpuid_Avx ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Avx va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Avx (va_code_Cpuid_Avx ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Avx2 [@ "opaque_to_smt"] let va_code_Cpuid_Avx2 () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Avx2 () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Avx2 va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Avx2) (va_code_Cpuid_Avx2 ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Avx2 va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Avx2 (va_code_Cpuid_Avx2 ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Sse [@ "opaque_to_smt"] let va_code_Cpuid_Sse () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Sse () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Sse va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Sse) (va_code_Cpuid_Sse ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Sse va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Sse (va_code_Cpuid_Sse ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Movbe [@ "opaque_to_smt"] let va_code_Cpuid_Movbe () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Movbe () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Movbe va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Movbe) (va_code_Cpuid_Movbe ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Movbe va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Movbe (va_code_Cpuid_Movbe ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Rdrand [@ "opaque_to_smt"] let va_code_Cpuid_Rdrand () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Rdrand () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Rdrand va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Rdrand) (va_code_Cpuid_Rdrand ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Rdrand va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Rdrand (va_code_Cpuid_Rdrand ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Avx512 [@ "opaque_to_smt"] let va_code_Cpuid_Avx512 () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Avx512 () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Avx512 va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Avx512) (va_code_Cpuid_Avx512 ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Avx512 va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Avx512 (va_code_Cpuid_Avx512 ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Osxsave [@ "opaque_to_smt"] let va_code_Cpuid_Osxsave () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Osxsave () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Osxsave va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Osxsave) (va_code_Cpuid_Osxsave ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Osxsave va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Osxsave (va_code_Cpuid_Osxsave ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Xgetbv_Avx [@ "opaque_to_smt"] let va_code_Xgetbv_Avx () = (mk_ins (make_instr (I.ins_Xgetbv))) [@ "opaque_to_smt"] let va_codegen_success_Xgetbv_Avx () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Xgetbv_Avx va_b0 va_s0 = va_reveal_opaque (`%va_code_Xgetbv_Avx) (va_code_Xgetbv_Avx ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Xgetbv))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Xgetbv))) va_s0 in Vale.X64.CPU_Features_s.xgetbv_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Xgetbv_Avx va_s0 va_k = let (va_sM, va_f0) = va_lemma_Xgetbv_Avx (va_code_Xgetbv_Avx ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Xgetbv_Avx512 [@ "opaque_to_smt"] let va_code_Xgetbv_Avx512 () = (mk_ins (make_instr (I.ins_Xgetbv))) [@ "opaque_to_smt"] let va_codegen_success_Xgetbv_Avx512 () = (va_ttrue ()) [@"opaque_to_smt"]
false
false
Vale.X64.InsBasic.fst
{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 5, "initial_ifuel": 0, "max_fuel": 5, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": true, "smtencoding_l_arith_repr": "native", "smtencoding_nl_arith_repr": "wrapped", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": false, "z3cliopt": [ "smt.arith.nl=false", "smt.QI.EAGER_THRESHOLD=100", "smt.CASE_SPLIT=3" ], "z3refresh": false, "z3rlimit": 20, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }
null
val va_lemma_Xgetbv_Avx512 : va_b0:va_code -> va_s0:va_state -> Ghost (va_state & va_fuel) (requires (va_require_total va_b0 (va_code_Xgetbv_Avx512 ()) va_s0 /\ va_get_ok va_s0 /\ osxsave_enabled /\ va_get_reg64 rRcx va_s0 = 0)) (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\ Vale.Arch.Types.iand64 (va_get_reg64 rRax va_sM) 32 > 0 == opmask_xcr0_enabled /\ Vale.Arch.Types.iand64 (va_get_reg64 rRax va_sM) 64 > 0 == zmm_hi256_xcr0_enabled /\ Vale.Arch.Types.iand64 (va_get_reg64 rRax va_sM) 128 > 0 == hi16_zmm_xcr0_enabled /\ va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))
[]
Vale.X64.InsBasic.va_lemma_Xgetbv_Avx512
{ "file_name": "obj/Vale.X64.InsBasic.fst", "git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e", "git_url": "https://github.com/hacl-star/hacl-star.git", "project_name": "hacl-star" }
va_b0: Vale.X64.Decls.va_code -> va_s0: Vale.X64.Decls.va_state -> Prims.Ghost (Vale.X64.Decls.va_state * Vale.X64.Decls.va_fuel)
{ "end_col": 16, "end_line": 973, "start_col": 2, "start_line": 968 }
Prims.Ghost
val va_lemma_Comment : va_b0:va_code -> va_s0:va_state -> c:string -> Ghost (va_state & va_fuel) (requires (va_require_total va_b0 (va_code_Comment c) va_s0 /\ va_get_ok va_s0)) (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\ va_state_eq va_sM (va_update_ok va_sM va_s0)))
[ { "abbrev": true, "full_module": "Vale.X64.Machine_Semantics_s", "short_module": "S" }, { "abbrev": true, "full_module": "Vale.X64.Instructions_s", "short_module": "I" }, { "abbrev": false, "full_module": "Vale.X64.Stack_i", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.Memory", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.Taint_Semantics", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.InsLemmas", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.StateLemmas", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.CPU_Features_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.QuickCode", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.Decls", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.State", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.Machine_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Arch.Types", "short_module": null }, { "abbrev": false, "full_module": "Vale.Arch.HeapImpl", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Types_s", "short_module": null }, { "abbrev": false, "full_module": "FStar.Mul", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]
false
let va_lemma_Comment va_b0 va_s0 c = va_reveal_opaque (`%va_code_Comment) (va_code_Comment c); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr_annotate (I.ins_Comment c) (S.AnnotateComment c))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr_annotate (I.ins_Comment c) (S.AnnotateComment c))) va_s0 in (va_sM, va_fM)
val va_lemma_Comment : va_b0:va_code -> va_s0:va_state -> c:string -> Ghost (va_state & va_fuel) (requires (va_require_total va_b0 (va_code_Comment c) va_s0 /\ va_get_ok va_s0)) (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\ va_state_eq va_sM (va_update_ok va_sM va_s0))) let va_lemma_Comment va_b0 va_s0 c =
false
null
false
va_reveal_opaque (`%va_code_Comment) (va_code_Comment c); let va_old_s:va_state = va_s0 in va_ins_lemma (mk_ins (make_instr_annotate (I.ins_Comment c) (S.AnnotateComment c))) va_s0; let va_sM, va_fM = va_eval_ins (mk_ins (make_instr_annotate (I.ins_Comment c) (S.AnnotateComment c))) va_s0 in (va_sM, va_fM)
{ "checked_file": "Vale.X64.InsBasic.fst.checked", "dependencies": [ "Vale.X64.Taint_Semantics.fst.checked", "Vale.X64.StateLemmas.fsti.checked", "Vale.X64.Stack_i.fsti.checked", "Vale.X64.Memory.fsti.checked", "Vale.X64.Machine_Semantics_s.fst.checked", "Vale.X64.Instructions_s.fsti.checked", "Vale.X64.InsLemmas.fsti.checked", "Vale.X64.Decls.fst.checked", "Vale.X64.CPU_Features_s.fst.checked", "Vale.Arch.Types.fsti.checked", "prims.fst.checked", "FStar.UInt.fsti.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Math.Lemmas.fst.checked" ], "interface_file": true, "source_file": "Vale.X64.InsBasic.fst" }
[]
[ "Vale.X64.Decls.va_code", "Vale.X64.Decls.va_state", "Prims.string", "Vale.X64.State.vale_state", "Vale.X64.Lemmas.fuel", "FStar.Pervasives.Native.Mktuple2", "Vale.X64.Decls.va_fuel", "FStar.Pervasives.Native.tuple2", "Prims.nat", "Vale.X64.Decls.va_eval_ins", "Vale.X64.Taint_Semantics.mk_ins", "Vale.X64.InsLemmas.make_instr_annotate", "Prims.Nil", "Vale.X64.Instruction_s.instr_out", "Vale.X64.Instruction_s.instr_operand", "Vale.X64.Instruction_s.PreserveFlags", "Vale.X64.Instructions_s.ins_Comment", "Vale.X64.Machine_Semantics_s.AnnotateComment", "Vale.X64.Instruction_s.InstrTypeRecord", "Prims.unit", "Vale.X64.Decls.va_ins_lemma", "Vale.X64.Decls.va_reveal_opaque", "Vale.X64.InsBasic.va_code_Comment" ]
[]
module Vale.X64.InsBasic open Vale.X64 open Vale.X64.StateLemmas open Vale.X64.InsLemmas open Vale.X64.Taint_Semantics open Vale.X64.CPU_Features_s open Vale.X64.Memory open Vale.X64.Stack_i module I = Vale.X64.Instructions_s module S = Vale.X64.Machine_Semantics_s friend Vale.X64.Decls #reset-options "--initial_fuel 5 --max_fuel 5 --max_ifuel 2 --z3rlimit 20" //-- Mov64 [@ "opaque_to_smt"] let va_code_Mov64 dst src = (mk_ins (make_instr_annotate (I.ins_Mov64) (S.AnnotateMov64 ()) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Mov64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Mov64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Mov64) (va_code_Mov64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr_annotate (I.ins_Mov64) (S.AnnotateMov64 ()) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr_annotate (I.ins_Mov64) (S.AnnotateMov64 ()) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Mov64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Mov64 (va_code_Mov64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0))); va_lemma_norm_mods ([va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cmovc64 [@ "opaque_to_smt"] let va_code_Cmovc64 dst src = (mk_ins (make_instr (I.ins_Cmovc64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Cmovc64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cmovc64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Cmovc64) (va_code_Cmovc64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cmovc64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cmovc64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cmovc64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cmovc64 (va_code_Cmovc64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0))); va_lemma_norm_mods ([va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Add64 [@ "opaque_to_smt"] let va_code_Add64 dst src = (mk_ins (make_instr (I.ins_Add64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Add64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Add64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Add64) (va_code_Add64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Add64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Add64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Add64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Add64 (va_code_Add64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Add64Wrap [@ "opaque_to_smt"] let va_code_Add64Wrap dst src = (mk_ins (make_instr (I.ins_Add64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Add64Wrap dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Add64Wrap va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Add64Wrap) (va_code_Add64Wrap dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Add64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Add64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Add64Wrap dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Add64Wrap (va_code_Add64Wrap dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- AddLea64 [@ "opaque_to_smt"] let va_code_AddLea64 dst src1 src2 = (mk_ins (make_instr (I.ins_AddLea64) dst src1 src2)) [@ "opaque_to_smt"] let va_codegen_success_AddLea64 dst src1 src2 = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_AddLea64 va_b0 va_s0 dst src1 src2 = va_reveal_opaque (`%va_code_AddLea64) (va_code_AddLea64 dst src1 src2); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_AddLea64) dst src1 src2)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_AddLea64) dst src1 src2)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_AddLea64 dst src1 src2 va_s0 va_k = let (va_sM, va_f0) = va_lemma_AddLea64 (va_code_AddLea64 dst src1 src2) va_s0 dst src1 src2 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0))); va_lemma_norm_mods ([va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Adc64 [@ "opaque_to_smt"] let va_code_Adc64 dst src = (mk_ins (make_instr (I.ins_AddCarry64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Adc64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Adc64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Adc64) (va_code_Adc64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_AddCarry64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_AddCarry64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Adc64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Adc64 (va_code_Adc64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Adc64Wrap [@ "opaque_to_smt"] let va_code_Adc64Wrap dst src = (mk_ins (make_instr (I.ins_AddCarry64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Adc64Wrap dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Adc64Wrap va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Adc64Wrap) (va_code_Adc64Wrap dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_AddCarry64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_AddCarry64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Adc64Wrap dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Adc64Wrap (va_code_Adc64Wrap dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Adcx64Wrap #push-options "--smtencoding.nl_arith_repr boxwrap" [@ "opaque_to_smt"] let va_code_Adcx64Wrap dst src = (mk_ins (make_instr (I.ins_Adcx64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Adcx64Wrap dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Adcx64Wrap va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Adcx64Wrap) (va_code_Adcx64Wrap dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Adcx64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Adcx64) dst src)) va_s0 in assert (Vale.Arch.Types.add_wrap64 (Vale.Arch.Types.add_wrap64 (va_eval_dst_opr64 va_old_s dst) (va_eval_opr64 va_old_s src)) (if Vale.X64.Decls.cf (va_get_flags va_old_s) then 1 else 0) == (va_eval_dst_opr64 va_old_s dst + va_eval_opr64 va_old_s src + (if Vale.X64.Decls.cf (va_get_flags va_old_s) then 1 else 0)) `op_Modulus` pow2_64); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Adcx64Wrap dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Adcx64Wrap (va_code_Adcx64Wrap dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) #pop-options //-- //-- Adox64Wrap [@ "opaque_to_smt"] let va_code_Adox64Wrap dst src = (mk_ins (make_instr (I.ins_Adox64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Adox64Wrap dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Adox64Wrap va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Adox64Wrap) (va_code_Adox64Wrap dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Adox64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Adox64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Adox64Wrap dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Adox64Wrap (va_code_Adox64Wrap dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Sub64 [@ "opaque_to_smt"] let va_code_Sub64 dst src = (mk_ins (make_instr (I.ins_Sub64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Sub64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Sub64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Sub64) (va_code_Sub64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Sub64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Sub64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Sub64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Sub64 (va_code_Sub64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Sub64Wrap [@ "opaque_to_smt"] let va_code_Sub64Wrap dst src = (mk_ins (make_instr (I.ins_Sub64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Sub64Wrap dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Sub64Wrap va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Sub64Wrap) (va_code_Sub64Wrap dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Sub64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Sub64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Sub64Wrap dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Sub64Wrap (va_code_Sub64Wrap dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Sbb64 [@ "opaque_to_smt"] let va_code_Sbb64 dst src = (mk_ins (make_instr (I.ins_Sbb64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Sbb64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Sbb64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Sbb64) (va_code_Sbb64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Sbb64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Sbb64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Sbb64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Sbb64 (va_code_Sbb64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- #restart-solver #push-options "--max_fuel 0 --max_ifuel 0 --using_facts_from 'Prims FStar.UInt'" let lemma_fundamental_div_mod (a b:nat64) : Lemma (pow2_64 * (FStar.UInt.mul_div #64 a b) + (FStar.UInt.mul_mod #64 a b) == a * b) = FStar.Math.Lemmas.lemma_div_mod (a * b) pow2_64 #pop-options //-- lemma_fundamental_div_mod //-- //-- Mul64Wrap [@ "opaque_to_smt"] let va_code_Mul64Wrap src = (mk_ins (make_instr (I.ins_Mul64) src)) [@ "opaque_to_smt"] let va_codegen_success_Mul64Wrap src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Mul64Wrap va_b0 va_s0 src = va_reveal_opaque (`%va_code_Mul64Wrap) (va_code_Mul64Wrap src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Mul64) src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Mul64) src)) va_s0 in lemma_fundamental_div_mod (va_get_reg64 rRax va_old_s) (va_eval_opr64 va_old_s src); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Mul64Wrap src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Mul64Wrap (va_code_Mul64Wrap src) va_s0 src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRax va_sM (va_update_flags va_sM (va_update_ok va_sM va_s0))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRax; va_Mod_flags]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Mulx64 [@ "opaque_to_smt"] let va_code_Mulx64 dst_hi dst_lo src = (mk_ins (make_instr (I.ins_Mulx64) dst_hi dst_lo src)) [@ "opaque_to_smt"] let va_codegen_success_Mulx64 dst_hi dst_lo src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Mulx64 va_b0 va_s0 dst_hi dst_lo src = va_reveal_opaque (`%va_code_Mulx64) (va_code_Mulx64 dst_hi dst_lo src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Mulx64) dst_hi dst_lo src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Mulx64) dst_hi dst_lo src)) va_s0 in lemma_fundamental_div_mod (va_get_reg64 rRdx va_old_s) (va_eval_opr64 va_old_s src); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Mulx64 dst_hi dst_lo src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Mulx64 (va_code_Mulx64 dst_hi dst_lo src) va_s0 dst_hi dst_lo src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst_lo va_sM (va_update_operand_dst_opr64 dst_hi va_sM va_s0)))); va_lemma_norm_mods ([va_mod_dst_opr64 dst_lo; va_mod_dst_opr64 dst_hi]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- lemma_mul_nat //-- //-- lemma_mul_in_bounds //-- //-- IMul64 [@ "opaque_to_smt"] let va_code_IMul64 dst src = (mk_ins (make_instr (I.ins_IMul64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_IMul64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_IMul64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_IMul64) (va_code_IMul64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_IMul64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_IMul64) dst src)) va_s0 in lemma_mul_nat (va_eval_dst_opr64 va_old_s dst) (va_eval_opr64 va_old_s src); lemma_mul_in_bounds (va_eval_dst_opr64 va_old_s dst) (va_eval_opr64 va_old_s src); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_IMul64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_IMul64 (va_code_IMul64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Xor64 [@ "opaque_to_smt"] let va_code_Xor64 dst src = (mk_ins (make_instr_annotate (I.ins_Xor64) (S.AnnotateXor64 ()) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Xor64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Xor64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Xor64) (va_code_Xor64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr_annotate (I.ins_Xor64) (S.AnnotateXor64 ()) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr_annotate (I.ins_Xor64) (S.AnnotateXor64 ()) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Xor64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Xor64 (va_code_Xor64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- And64 [@ "opaque_to_smt"] let va_code_And64 dst src = (mk_ins (make_instr (I.ins_And64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_And64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_And64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_And64) (va_code_And64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_And64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_And64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_And64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_And64 (va_code_And64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Shl64 [@ "opaque_to_smt"] let va_code_Shl64 dst amt = (mk_ins (make_instr (I.ins_Shl64) dst amt)) [@ "opaque_to_smt"] let va_codegen_success_Shl64 dst amt = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Shl64 va_b0 va_s0 dst amt = va_reveal_opaque (`%va_code_Shl64) (va_code_Shl64 dst amt); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Shl64) dst amt)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Shl64) dst amt)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Shl64 dst amt va_s0 va_k = let (va_sM, va_f0) = va_lemma_Shl64 (va_code_Shl64 dst amt) va_s0 dst amt in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Shr64 [@ "opaque_to_smt"] let va_code_Shr64 dst amt = (mk_ins (make_instr (I.ins_Shr64) dst amt)) [@ "opaque_to_smt"] let va_codegen_success_Shr64 dst amt = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Shr64 va_b0 va_s0 dst amt = va_reveal_opaque (`%va_code_Shr64) (va_code_Shr64 dst amt); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Shr64) dst amt)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Shr64) dst amt)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Shr64 dst amt va_s0 va_k = let (va_sM, va_f0) = va_lemma_Shr64 (va_code_Shr64 dst amt) va_s0 dst amt in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_AES [@ "opaque_to_smt"] let va_code_Cpuid_AES () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_AES () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_AES va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_AES) (va_code_Cpuid_AES ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_AES va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_AES (va_code_Cpuid_AES ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Sha [@ "opaque_to_smt"] let va_code_Cpuid_Sha () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Sha () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Sha va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Sha) (va_code_Cpuid_Sha ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Sha va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Sha (va_code_Cpuid_Sha ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Adx_Bmi2 [@ "opaque_to_smt"] let va_code_Cpuid_Adx_Bmi2 () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Adx_Bmi2 () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Adx_Bmi2 va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Adx_Bmi2) (va_code_Cpuid_Adx_Bmi2 ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Adx_Bmi2 va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Adx_Bmi2 (va_code_Cpuid_Adx_Bmi2 ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Avx [@ "opaque_to_smt"] let va_code_Cpuid_Avx () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Avx () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Avx va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Avx) (va_code_Cpuid_Avx ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Avx va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Avx (va_code_Cpuid_Avx ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Avx2 [@ "opaque_to_smt"] let va_code_Cpuid_Avx2 () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Avx2 () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Avx2 va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Avx2) (va_code_Cpuid_Avx2 ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Avx2 va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Avx2 (va_code_Cpuid_Avx2 ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Sse [@ "opaque_to_smt"] let va_code_Cpuid_Sse () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Sse () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Sse va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Sse) (va_code_Cpuid_Sse ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Sse va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Sse (va_code_Cpuid_Sse ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Movbe [@ "opaque_to_smt"] let va_code_Cpuid_Movbe () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Movbe () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Movbe va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Movbe) (va_code_Cpuid_Movbe ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Movbe va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Movbe (va_code_Cpuid_Movbe ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Rdrand [@ "opaque_to_smt"] let va_code_Cpuid_Rdrand () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Rdrand () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Rdrand va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Rdrand) (va_code_Cpuid_Rdrand ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Rdrand va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Rdrand (va_code_Cpuid_Rdrand ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Avx512 [@ "opaque_to_smt"] let va_code_Cpuid_Avx512 () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Avx512 () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Avx512 va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Avx512) (va_code_Cpuid_Avx512 ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Avx512 va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Avx512 (va_code_Cpuid_Avx512 ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Osxsave [@ "opaque_to_smt"] let va_code_Cpuid_Osxsave () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Osxsave () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Osxsave va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Osxsave) (va_code_Cpuid_Osxsave ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Osxsave va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Osxsave (va_code_Cpuid_Osxsave ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Xgetbv_Avx [@ "opaque_to_smt"] let va_code_Xgetbv_Avx () = (mk_ins (make_instr (I.ins_Xgetbv))) [@ "opaque_to_smt"] let va_codegen_success_Xgetbv_Avx () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Xgetbv_Avx va_b0 va_s0 = va_reveal_opaque (`%va_code_Xgetbv_Avx) (va_code_Xgetbv_Avx ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Xgetbv))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Xgetbv))) va_s0 in Vale.X64.CPU_Features_s.xgetbv_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Xgetbv_Avx va_s0 va_k = let (va_sM, va_f0) = va_lemma_Xgetbv_Avx (va_code_Xgetbv_Avx ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Xgetbv_Avx512 [@ "opaque_to_smt"] let va_code_Xgetbv_Avx512 () = (mk_ins (make_instr (I.ins_Xgetbv))) [@ "opaque_to_smt"] let va_codegen_success_Xgetbv_Avx512 () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Xgetbv_Avx512 va_b0 va_s0 = va_reveal_opaque (`%va_code_Xgetbv_Avx512) (va_code_Xgetbv_Avx512 ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Xgetbv))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Xgetbv))) va_s0 in Vale.X64.CPU_Features_s.xgetbv_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Xgetbv_Avx512 va_s0 va_k = let (va_sM, va_f0) = va_lemma_Xgetbv_Avx512 (va_code_Xgetbv_Avx512 ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Nat64Equal [@ "opaque_to_smt"] let va_code_Nat64Equal dst src = (va_Block (va_CCons (va_code_Sub64Wrap (va_coerce_reg_opr64_to_dst_opr64 src) (va_const_opr64 18446744073709551615)) (va_CCons (va_code_Mov64 (va_coerce_reg_opr64_to_dst_opr64 dst) (va_const_opr64 0)) (va_CCons (va_code_Adc64 (va_coerce_reg_opr64_to_dst_opr64 dst) (va_const_opr64 0)) (va_CNil ()))))) [@ "opaque_to_smt"] let va_codegen_success_Nat64Equal dst src = (va_pbool_and (va_codegen_success_Sub64Wrap (va_coerce_reg_opr64_to_dst_opr64 src) (va_const_opr64 18446744073709551615)) (va_pbool_and (va_codegen_success_Mov64 (va_coerce_reg_opr64_to_dst_opr64 dst) (va_const_opr64 0)) (va_pbool_and (va_codegen_success_Adc64 (va_coerce_reg_opr64_to_dst_opr64 dst) (va_const_opr64 0)) (va_ttrue ())))) [@"opaque_to_smt"] let va_lemma_Nat64Equal va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Nat64Equal) (va_code_Nat64Equal dst src); let (va_old_s:va_state) = va_s0 in let (va_b1:va_codes) = va_get_block va_b0 in let (va_s2, va_fc2) = va_lemma_Sub64Wrap (va_hd va_b1) va_s0 (va_coerce_reg_opr64_to_dst_opr64 src) (va_const_opr64 18446744073709551615) in let va_b2 = va_tl va_b1 in let (va_s3, va_fc3) = va_lemma_Mov64 (va_hd va_b2) va_s2 (va_coerce_reg_opr64_to_dst_opr64 dst) (va_const_opr64 0) in let va_b3 = va_tl va_b2 in let (va_s4, va_fc4) = va_lemma_Adc64 (va_hd va_b3) va_s3 (va_coerce_reg_opr64_to_dst_opr64 dst) (va_const_opr64 0) in let va_b4 = va_tl va_b3 in let (va_sM, va_f4) = va_lemma_empty_total va_s4 va_b4 in let va_f3 = va_lemma_merge_total va_b3 va_s3 va_fc4 va_s4 va_f4 va_sM in let va_f2 = va_lemma_merge_total va_b2 va_s2 va_fc3 va_s3 va_f3 va_sM in let va_fM = va_lemma_merge_total va_b1 va_s0 va_fc2 va_s2 va_f2 va_sM in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Nat64Equal dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Nat64Equal (va_code_Nat64Equal dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_reg_opr64 src va_sM (va_update_operand_reg_opr64 dst va_sM va_s0))))); va_lemma_norm_mods ([va_Mod_flags; va_mod_reg_opr64 src; va_mod_reg_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Comment [@ "opaque_to_smt"] let va_code_Comment c = (mk_ins (make_instr_annotate (I.ins_Comment c) (S.AnnotateComment c))) [@ "opaque_to_smt"] let va_codegen_success_Comment c = (va_ttrue ()) [@"opaque_to_smt"]
false
false
Vale.X64.InsBasic.fst
{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 5, "initial_ifuel": 0, "max_fuel": 5, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": true, "smtencoding_l_arith_repr": "native", "smtencoding_nl_arith_repr": "wrapped", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": false, "z3cliopt": [ "smt.arith.nl=false", "smt.QI.EAGER_THRESHOLD=100", "smt.CASE_SPLIT=3" ], "z3refresh": false, "z3rlimit": 20, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }
null
val va_lemma_Comment : va_b0:va_code -> va_s0:va_state -> c:string -> Ghost (va_state & va_fuel) (requires (va_require_total va_b0 (va_code_Comment c) va_s0 /\ va_get_ok va_s0)) (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\ va_state_eq va_sM (va_update_ok va_sM va_s0)))
[]
Vale.X64.InsBasic.va_lemma_Comment
{ "file_name": "obj/Vale.X64.InsBasic.fst", "git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e", "git_url": "https://github.com/hacl-star/hacl-star.git", "project_name": "hacl-star" }
va_b0: Vale.X64.Decls.va_code -> va_s0: Vale.X64.Decls.va_state -> c: Prims.string -> Prims.Ghost (Vale.X64.Decls.va_state * Vale.X64.Decls.va_fuel)
{ "end_col": 16, "end_line": 1053, "start_col": 2, "start_line": 1048 }
Prims.Ghost
val va_lemma_Nat64Equal : va_b0:va_code -> va_s0:va_state -> dst:va_operand_reg_opr64 -> src:va_operand_reg_opr64 -> Ghost (va_state & va_fuel) (requires (va_require_total va_b0 (va_code_Nat64Equal dst src) va_s0 /\ va_is_dst_reg_opr64 dst va_s0 /\ va_is_dst_reg_opr64 src va_s0 /\ va_get_ok va_s0)) (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\ (if (va_eval_reg_opr64 va_s0 src = 18446744073709551615) then (va_eval_reg_opr64 va_sM dst = 0) else (va_eval_reg_opr64 va_sM dst = 1)) /\ va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_reg_opr64 src va_sM (va_update_operand_reg_opr64 dst va_sM va_s0))))))
[ { "abbrev": true, "full_module": "Vale.X64.Machine_Semantics_s", "short_module": "S" }, { "abbrev": true, "full_module": "Vale.X64.Instructions_s", "short_module": "I" }, { "abbrev": false, "full_module": "Vale.X64.Stack_i", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.Memory", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.Taint_Semantics", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.InsLemmas", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.StateLemmas", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.CPU_Features_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.QuickCode", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.Decls", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.State", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.Machine_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Arch.Types", "short_module": null }, { "abbrev": false, "full_module": "Vale.Arch.HeapImpl", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Types_s", "short_module": null }, { "abbrev": false, "full_module": "FStar.Mul", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]
false
let va_lemma_Nat64Equal va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Nat64Equal) (va_code_Nat64Equal dst src); let (va_old_s:va_state) = va_s0 in let (va_b1:va_codes) = va_get_block va_b0 in let (va_s2, va_fc2) = va_lemma_Sub64Wrap (va_hd va_b1) va_s0 (va_coerce_reg_opr64_to_dst_opr64 src) (va_const_opr64 18446744073709551615) in let va_b2 = va_tl va_b1 in let (va_s3, va_fc3) = va_lemma_Mov64 (va_hd va_b2) va_s2 (va_coerce_reg_opr64_to_dst_opr64 dst) (va_const_opr64 0) in let va_b3 = va_tl va_b2 in let (va_s4, va_fc4) = va_lemma_Adc64 (va_hd va_b3) va_s3 (va_coerce_reg_opr64_to_dst_opr64 dst) (va_const_opr64 0) in let va_b4 = va_tl va_b3 in let (va_sM, va_f4) = va_lemma_empty_total va_s4 va_b4 in let va_f3 = va_lemma_merge_total va_b3 va_s3 va_fc4 va_s4 va_f4 va_sM in let va_f2 = va_lemma_merge_total va_b2 va_s2 va_fc3 va_s3 va_f3 va_sM in let va_fM = va_lemma_merge_total va_b1 va_s0 va_fc2 va_s2 va_f2 va_sM in (va_sM, va_fM)
val va_lemma_Nat64Equal : va_b0:va_code -> va_s0:va_state -> dst:va_operand_reg_opr64 -> src:va_operand_reg_opr64 -> Ghost (va_state & va_fuel) (requires (va_require_total va_b0 (va_code_Nat64Equal dst src) va_s0 /\ va_is_dst_reg_opr64 dst va_s0 /\ va_is_dst_reg_opr64 src va_s0 /\ va_get_ok va_s0)) (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\ (if (va_eval_reg_opr64 va_s0 src = 18446744073709551615) then (va_eval_reg_opr64 va_sM dst = 0) else (va_eval_reg_opr64 va_sM dst = 1)) /\ va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_reg_opr64 src va_sM (va_update_operand_reg_opr64 dst va_sM va_s0)))))) let va_lemma_Nat64Equal va_b0 va_s0 dst src =
false
null
false
va_reveal_opaque (`%va_code_Nat64Equal) (va_code_Nat64Equal dst src); let va_old_s:va_state = va_s0 in let va_b1:va_codes = va_get_block va_b0 in let va_s2, va_fc2 = va_lemma_Sub64Wrap (va_hd va_b1) va_s0 (va_coerce_reg_opr64_to_dst_opr64 src) (va_const_opr64 18446744073709551615) in let va_b2 = va_tl va_b1 in let va_s3, va_fc3 = va_lemma_Mov64 (va_hd va_b2) va_s2 (va_coerce_reg_opr64_to_dst_opr64 dst) (va_const_opr64 0) in let va_b3 = va_tl va_b2 in let va_s4, va_fc4 = va_lemma_Adc64 (va_hd va_b3) va_s3 (va_coerce_reg_opr64_to_dst_opr64 dst) (va_const_opr64 0) in let va_b4 = va_tl va_b3 in let va_sM, va_f4 = va_lemma_empty_total va_s4 va_b4 in let va_f3 = va_lemma_merge_total va_b3 va_s3 va_fc4 va_s4 va_f4 va_sM in let va_f2 = va_lemma_merge_total va_b2 va_s2 va_fc3 va_s3 va_f3 va_sM in let va_fM = va_lemma_merge_total va_b1 va_s0 va_fc2 va_s2 va_f2 va_sM in (va_sM, va_fM)
{ "checked_file": "Vale.X64.InsBasic.fst.checked", "dependencies": [ "Vale.X64.Taint_Semantics.fst.checked", "Vale.X64.StateLemmas.fsti.checked", "Vale.X64.Stack_i.fsti.checked", "Vale.X64.Memory.fsti.checked", "Vale.X64.Machine_Semantics_s.fst.checked", "Vale.X64.Instructions_s.fsti.checked", "Vale.X64.InsLemmas.fsti.checked", "Vale.X64.Decls.fst.checked", "Vale.X64.CPU_Features_s.fst.checked", "Vale.Arch.Types.fsti.checked", "prims.fst.checked", "FStar.UInt.fsti.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Math.Lemmas.fst.checked" ], "interface_file": true, "source_file": "Vale.X64.InsBasic.fst" }
[]
[ "Vale.X64.Decls.va_code", "Vale.X64.Decls.va_state", "Vale.X64.Decls.va_operand_reg_opr64", "Vale.X64.Decls.va_fuel", "FStar.Pervasives.Native.Mktuple2", "Vale.X64.Decls.va_lemma_merge_total", "FStar.Pervasives.Native.tuple2", "Vale.X64.State.vale_state", "Vale.X64.Decls.va_lemma_empty_total", "Prims.list", "Vale.X64.Machine_s.precode", "Vale.X64.Decls.ins", "Vale.X64.Decls.ocmp", "Vale.X64.Decls.va_tl", "Vale.X64.InsBasic.va_lemma_Adc64", "Vale.X64.Decls.va_hd", "Vale.X64.Decls.va_coerce_reg_opr64_to_dst_opr64", "Vale.X64.Decls.va_const_opr64", "Vale.X64.InsBasic.va_lemma_Mov64", "Vale.X64.InsBasic.va_lemma_Sub64Wrap", "Vale.X64.Decls.va_get_block", "Prims.unit", "Vale.X64.Decls.va_reveal_opaque", "Vale.X64.InsBasic.va_code_Nat64Equal" ]
[]
module Vale.X64.InsBasic open Vale.X64 open Vale.X64.StateLemmas open Vale.X64.InsLemmas open Vale.X64.Taint_Semantics open Vale.X64.CPU_Features_s open Vale.X64.Memory open Vale.X64.Stack_i module I = Vale.X64.Instructions_s module S = Vale.X64.Machine_Semantics_s friend Vale.X64.Decls #reset-options "--initial_fuel 5 --max_fuel 5 --max_ifuel 2 --z3rlimit 20" //-- Mov64 [@ "opaque_to_smt"] let va_code_Mov64 dst src = (mk_ins (make_instr_annotate (I.ins_Mov64) (S.AnnotateMov64 ()) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Mov64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Mov64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Mov64) (va_code_Mov64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr_annotate (I.ins_Mov64) (S.AnnotateMov64 ()) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr_annotate (I.ins_Mov64) (S.AnnotateMov64 ()) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Mov64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Mov64 (va_code_Mov64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0))); va_lemma_norm_mods ([va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cmovc64 [@ "opaque_to_smt"] let va_code_Cmovc64 dst src = (mk_ins (make_instr (I.ins_Cmovc64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Cmovc64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cmovc64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Cmovc64) (va_code_Cmovc64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cmovc64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cmovc64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cmovc64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cmovc64 (va_code_Cmovc64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0))); va_lemma_norm_mods ([va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Add64 [@ "opaque_to_smt"] let va_code_Add64 dst src = (mk_ins (make_instr (I.ins_Add64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Add64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Add64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Add64) (va_code_Add64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Add64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Add64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Add64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Add64 (va_code_Add64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Add64Wrap [@ "opaque_to_smt"] let va_code_Add64Wrap dst src = (mk_ins (make_instr (I.ins_Add64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Add64Wrap dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Add64Wrap va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Add64Wrap) (va_code_Add64Wrap dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Add64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Add64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Add64Wrap dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Add64Wrap (va_code_Add64Wrap dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- AddLea64 [@ "opaque_to_smt"] let va_code_AddLea64 dst src1 src2 = (mk_ins (make_instr (I.ins_AddLea64) dst src1 src2)) [@ "opaque_to_smt"] let va_codegen_success_AddLea64 dst src1 src2 = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_AddLea64 va_b0 va_s0 dst src1 src2 = va_reveal_opaque (`%va_code_AddLea64) (va_code_AddLea64 dst src1 src2); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_AddLea64) dst src1 src2)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_AddLea64) dst src1 src2)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_AddLea64 dst src1 src2 va_s0 va_k = let (va_sM, va_f0) = va_lemma_AddLea64 (va_code_AddLea64 dst src1 src2) va_s0 dst src1 src2 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0))); va_lemma_norm_mods ([va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Adc64 [@ "opaque_to_smt"] let va_code_Adc64 dst src = (mk_ins (make_instr (I.ins_AddCarry64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Adc64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Adc64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Adc64) (va_code_Adc64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_AddCarry64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_AddCarry64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Adc64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Adc64 (va_code_Adc64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Adc64Wrap [@ "opaque_to_smt"] let va_code_Adc64Wrap dst src = (mk_ins (make_instr (I.ins_AddCarry64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Adc64Wrap dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Adc64Wrap va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Adc64Wrap) (va_code_Adc64Wrap dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_AddCarry64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_AddCarry64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Adc64Wrap dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Adc64Wrap (va_code_Adc64Wrap dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Adcx64Wrap #push-options "--smtencoding.nl_arith_repr boxwrap" [@ "opaque_to_smt"] let va_code_Adcx64Wrap dst src = (mk_ins (make_instr (I.ins_Adcx64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Adcx64Wrap dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Adcx64Wrap va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Adcx64Wrap) (va_code_Adcx64Wrap dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Adcx64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Adcx64) dst src)) va_s0 in assert (Vale.Arch.Types.add_wrap64 (Vale.Arch.Types.add_wrap64 (va_eval_dst_opr64 va_old_s dst) (va_eval_opr64 va_old_s src)) (if Vale.X64.Decls.cf (va_get_flags va_old_s) then 1 else 0) == (va_eval_dst_opr64 va_old_s dst + va_eval_opr64 va_old_s src + (if Vale.X64.Decls.cf (va_get_flags va_old_s) then 1 else 0)) `op_Modulus` pow2_64); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Adcx64Wrap dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Adcx64Wrap (va_code_Adcx64Wrap dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) #pop-options //-- //-- Adox64Wrap [@ "opaque_to_smt"] let va_code_Adox64Wrap dst src = (mk_ins (make_instr (I.ins_Adox64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Adox64Wrap dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Adox64Wrap va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Adox64Wrap) (va_code_Adox64Wrap dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Adox64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Adox64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Adox64Wrap dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Adox64Wrap (va_code_Adox64Wrap dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Sub64 [@ "opaque_to_smt"] let va_code_Sub64 dst src = (mk_ins (make_instr (I.ins_Sub64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Sub64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Sub64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Sub64) (va_code_Sub64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Sub64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Sub64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Sub64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Sub64 (va_code_Sub64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Sub64Wrap [@ "opaque_to_smt"] let va_code_Sub64Wrap dst src = (mk_ins (make_instr (I.ins_Sub64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Sub64Wrap dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Sub64Wrap va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Sub64Wrap) (va_code_Sub64Wrap dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Sub64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Sub64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Sub64Wrap dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Sub64Wrap (va_code_Sub64Wrap dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Sbb64 [@ "opaque_to_smt"] let va_code_Sbb64 dst src = (mk_ins (make_instr (I.ins_Sbb64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Sbb64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Sbb64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Sbb64) (va_code_Sbb64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Sbb64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Sbb64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Sbb64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Sbb64 (va_code_Sbb64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- #restart-solver #push-options "--max_fuel 0 --max_ifuel 0 --using_facts_from 'Prims FStar.UInt'" let lemma_fundamental_div_mod (a b:nat64) : Lemma (pow2_64 * (FStar.UInt.mul_div #64 a b) + (FStar.UInt.mul_mod #64 a b) == a * b) = FStar.Math.Lemmas.lemma_div_mod (a * b) pow2_64 #pop-options //-- lemma_fundamental_div_mod //-- //-- Mul64Wrap [@ "opaque_to_smt"] let va_code_Mul64Wrap src = (mk_ins (make_instr (I.ins_Mul64) src)) [@ "opaque_to_smt"] let va_codegen_success_Mul64Wrap src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Mul64Wrap va_b0 va_s0 src = va_reveal_opaque (`%va_code_Mul64Wrap) (va_code_Mul64Wrap src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Mul64) src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Mul64) src)) va_s0 in lemma_fundamental_div_mod (va_get_reg64 rRax va_old_s) (va_eval_opr64 va_old_s src); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Mul64Wrap src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Mul64Wrap (va_code_Mul64Wrap src) va_s0 src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRax va_sM (va_update_flags va_sM (va_update_ok va_sM va_s0))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRax; va_Mod_flags]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Mulx64 [@ "opaque_to_smt"] let va_code_Mulx64 dst_hi dst_lo src = (mk_ins (make_instr (I.ins_Mulx64) dst_hi dst_lo src)) [@ "opaque_to_smt"] let va_codegen_success_Mulx64 dst_hi dst_lo src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Mulx64 va_b0 va_s0 dst_hi dst_lo src = va_reveal_opaque (`%va_code_Mulx64) (va_code_Mulx64 dst_hi dst_lo src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Mulx64) dst_hi dst_lo src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Mulx64) dst_hi dst_lo src)) va_s0 in lemma_fundamental_div_mod (va_get_reg64 rRdx va_old_s) (va_eval_opr64 va_old_s src); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Mulx64 dst_hi dst_lo src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Mulx64 (va_code_Mulx64 dst_hi dst_lo src) va_s0 dst_hi dst_lo src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst_lo va_sM (va_update_operand_dst_opr64 dst_hi va_sM va_s0)))); va_lemma_norm_mods ([va_mod_dst_opr64 dst_lo; va_mod_dst_opr64 dst_hi]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- lemma_mul_nat //-- //-- lemma_mul_in_bounds //-- //-- IMul64 [@ "opaque_to_smt"] let va_code_IMul64 dst src = (mk_ins (make_instr (I.ins_IMul64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_IMul64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_IMul64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_IMul64) (va_code_IMul64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_IMul64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_IMul64) dst src)) va_s0 in lemma_mul_nat (va_eval_dst_opr64 va_old_s dst) (va_eval_opr64 va_old_s src); lemma_mul_in_bounds (va_eval_dst_opr64 va_old_s dst) (va_eval_opr64 va_old_s src); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_IMul64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_IMul64 (va_code_IMul64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Xor64 [@ "opaque_to_smt"] let va_code_Xor64 dst src = (mk_ins (make_instr_annotate (I.ins_Xor64) (S.AnnotateXor64 ()) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Xor64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Xor64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Xor64) (va_code_Xor64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr_annotate (I.ins_Xor64) (S.AnnotateXor64 ()) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr_annotate (I.ins_Xor64) (S.AnnotateXor64 ()) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Xor64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Xor64 (va_code_Xor64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- And64 [@ "opaque_to_smt"] let va_code_And64 dst src = (mk_ins (make_instr (I.ins_And64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_And64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_And64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_And64) (va_code_And64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_And64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_And64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_And64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_And64 (va_code_And64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Shl64 [@ "opaque_to_smt"] let va_code_Shl64 dst amt = (mk_ins (make_instr (I.ins_Shl64) dst amt)) [@ "opaque_to_smt"] let va_codegen_success_Shl64 dst amt = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Shl64 va_b0 va_s0 dst amt = va_reveal_opaque (`%va_code_Shl64) (va_code_Shl64 dst amt); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Shl64) dst amt)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Shl64) dst amt)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Shl64 dst amt va_s0 va_k = let (va_sM, va_f0) = va_lemma_Shl64 (va_code_Shl64 dst amt) va_s0 dst amt in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Shr64 [@ "opaque_to_smt"] let va_code_Shr64 dst amt = (mk_ins (make_instr (I.ins_Shr64) dst amt)) [@ "opaque_to_smt"] let va_codegen_success_Shr64 dst amt = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Shr64 va_b0 va_s0 dst amt = va_reveal_opaque (`%va_code_Shr64) (va_code_Shr64 dst amt); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Shr64) dst amt)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Shr64) dst amt)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Shr64 dst amt va_s0 va_k = let (va_sM, va_f0) = va_lemma_Shr64 (va_code_Shr64 dst amt) va_s0 dst amt in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_AES [@ "opaque_to_smt"] let va_code_Cpuid_AES () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_AES () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_AES va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_AES) (va_code_Cpuid_AES ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_AES va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_AES (va_code_Cpuid_AES ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Sha [@ "opaque_to_smt"] let va_code_Cpuid_Sha () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Sha () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Sha va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Sha) (va_code_Cpuid_Sha ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Sha va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Sha (va_code_Cpuid_Sha ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Adx_Bmi2 [@ "opaque_to_smt"] let va_code_Cpuid_Adx_Bmi2 () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Adx_Bmi2 () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Adx_Bmi2 va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Adx_Bmi2) (va_code_Cpuid_Adx_Bmi2 ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Adx_Bmi2 va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Adx_Bmi2 (va_code_Cpuid_Adx_Bmi2 ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Avx [@ "opaque_to_smt"] let va_code_Cpuid_Avx () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Avx () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Avx va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Avx) (va_code_Cpuid_Avx ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Avx va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Avx (va_code_Cpuid_Avx ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Avx2 [@ "opaque_to_smt"] let va_code_Cpuid_Avx2 () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Avx2 () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Avx2 va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Avx2) (va_code_Cpuid_Avx2 ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Avx2 va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Avx2 (va_code_Cpuid_Avx2 ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Sse [@ "opaque_to_smt"] let va_code_Cpuid_Sse () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Sse () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Sse va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Sse) (va_code_Cpuid_Sse ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Sse va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Sse (va_code_Cpuid_Sse ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Movbe [@ "opaque_to_smt"] let va_code_Cpuid_Movbe () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Movbe () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Movbe va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Movbe) (va_code_Cpuid_Movbe ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Movbe va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Movbe (va_code_Cpuid_Movbe ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Rdrand [@ "opaque_to_smt"] let va_code_Cpuid_Rdrand () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Rdrand () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Rdrand va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Rdrand) (va_code_Cpuid_Rdrand ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Rdrand va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Rdrand (va_code_Cpuid_Rdrand ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Avx512 [@ "opaque_to_smt"] let va_code_Cpuid_Avx512 () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Avx512 () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Avx512 va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Avx512) (va_code_Cpuid_Avx512 ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Avx512 va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Avx512 (va_code_Cpuid_Avx512 ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Osxsave [@ "opaque_to_smt"] let va_code_Cpuid_Osxsave () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Osxsave () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Osxsave va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Osxsave) (va_code_Cpuid_Osxsave ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Osxsave va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Osxsave (va_code_Cpuid_Osxsave ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Xgetbv_Avx [@ "opaque_to_smt"] let va_code_Xgetbv_Avx () = (mk_ins (make_instr (I.ins_Xgetbv))) [@ "opaque_to_smt"] let va_codegen_success_Xgetbv_Avx () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Xgetbv_Avx va_b0 va_s0 = va_reveal_opaque (`%va_code_Xgetbv_Avx) (va_code_Xgetbv_Avx ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Xgetbv))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Xgetbv))) va_s0 in Vale.X64.CPU_Features_s.xgetbv_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Xgetbv_Avx va_s0 va_k = let (va_sM, va_f0) = va_lemma_Xgetbv_Avx (va_code_Xgetbv_Avx ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Xgetbv_Avx512 [@ "opaque_to_smt"] let va_code_Xgetbv_Avx512 () = (mk_ins (make_instr (I.ins_Xgetbv))) [@ "opaque_to_smt"] let va_codegen_success_Xgetbv_Avx512 () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Xgetbv_Avx512 va_b0 va_s0 = va_reveal_opaque (`%va_code_Xgetbv_Avx512) (va_code_Xgetbv_Avx512 ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Xgetbv))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Xgetbv))) va_s0 in Vale.X64.CPU_Features_s.xgetbv_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Xgetbv_Avx512 va_s0 va_k = let (va_sM, va_f0) = va_lemma_Xgetbv_Avx512 (va_code_Xgetbv_Avx512 ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Nat64Equal [@ "opaque_to_smt"] let va_code_Nat64Equal dst src = (va_Block (va_CCons (va_code_Sub64Wrap (va_coerce_reg_opr64_to_dst_opr64 src) (va_const_opr64 18446744073709551615)) (va_CCons (va_code_Mov64 (va_coerce_reg_opr64_to_dst_opr64 dst) (va_const_opr64 0)) (va_CCons (va_code_Adc64 (va_coerce_reg_opr64_to_dst_opr64 dst) (va_const_opr64 0)) (va_CNil ()))))) [@ "opaque_to_smt"] let va_codegen_success_Nat64Equal dst src = (va_pbool_and (va_codegen_success_Sub64Wrap (va_coerce_reg_opr64_to_dst_opr64 src) (va_const_opr64 18446744073709551615)) (va_pbool_and (va_codegen_success_Mov64 (va_coerce_reg_opr64_to_dst_opr64 dst) (va_const_opr64 0)) (va_pbool_and (va_codegen_success_Adc64 (va_coerce_reg_opr64_to_dst_opr64 dst) (va_const_opr64 0)) (va_ttrue ())))) [@"opaque_to_smt"]
false
false
Vale.X64.InsBasic.fst
{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 5, "initial_ifuel": 0, "max_fuel": 5, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": true, "smtencoding_l_arith_repr": "native", "smtencoding_nl_arith_repr": "wrapped", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": false, "z3cliopt": [ "smt.arith.nl=false", "smt.QI.EAGER_THRESHOLD=100", "smt.CASE_SPLIT=3" ], "z3refresh": false, "z3rlimit": 20, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }
null
val va_lemma_Nat64Equal : va_b0:va_code -> va_s0:va_state -> dst:va_operand_reg_opr64 -> src:va_operand_reg_opr64 -> Ghost (va_state & va_fuel) (requires (va_require_total va_b0 (va_code_Nat64Equal dst src) va_s0 /\ va_is_dst_reg_opr64 dst va_s0 /\ va_is_dst_reg_opr64 src va_s0 /\ va_get_ok va_s0)) (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\ (if (va_eval_reg_opr64 va_s0 src = 18446744073709551615) then (va_eval_reg_opr64 va_sM dst = 0) else (va_eval_reg_opr64 va_sM dst = 1)) /\ va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_reg_opr64 src va_sM (va_update_operand_reg_opr64 dst va_sM va_s0))))))
[]
Vale.X64.InsBasic.va_lemma_Nat64Equal
{ "file_name": "obj/Vale.X64.InsBasic.fst", "git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e", "git_url": "https://github.com/hacl-star/hacl-star.git", "project_name": "hacl-star" }
va_b0: Vale.X64.Decls.va_code -> va_s0: Vale.X64.Decls.va_state -> dst: Vale.X64.Decls.va_operand_reg_opr64 -> src: Vale.X64.Decls.va_operand_reg_opr64 -> Prims.Ghost (Vale.X64.Decls.va_state * Vale.X64.Decls.va_fuel)
{ "end_col": 16, "end_line": 1022, "start_col": 2, "start_line": 1006 }
Prims.Ghost
val va_lemma_Xor64 : va_b0:va_code -> va_s0:va_state -> dst:va_operand_dst_opr64 -> src:va_operand_opr64 -> Ghost (va_state & va_fuel) (requires (va_require_total va_b0 (va_code_Xor64 dst src) va_s0 /\ va_is_dst_dst_opr64 dst va_s0 /\ va_is_src_opr64 src va_s0 /\ va_get_ok va_s0)) (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\ va_eval_dst_opr64 va_sM dst == Vale.Arch.Types.ixor64 (va_eval_dst_opr64 va_s0 dst) (va_eval_opr64 va_s0 src) /\ ~(Vale.X64.Decls.overflow (va_get_flags va_sM)) /\ ~(Vale.X64.Decls.cf (va_get_flags va_sM)) /\ Vale.X64.Decls.valid_cf (va_get_flags va_sM) /\ Vale.X64.Decls.valid_of (va_get_flags va_sM) /\ va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))))
[ { "abbrev": true, "full_module": "Vale.X64.Machine_Semantics_s", "short_module": "S" }, { "abbrev": true, "full_module": "Vale.X64.Instructions_s", "short_module": "I" }, { "abbrev": false, "full_module": "Vale.X64.Stack_i", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.Memory", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.Taint_Semantics", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.InsLemmas", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.StateLemmas", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.CPU_Features_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.QuickCode", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.Decls", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.State", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.Machine_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Arch.Types", "short_module": null }, { "abbrev": false, "full_module": "Vale.Arch.HeapImpl", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Types_s", "short_module": null }, { "abbrev": false, "full_module": "FStar.Mul", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]
false
let va_lemma_Xor64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Xor64) (va_code_Xor64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr_annotate (I.ins_Xor64) (S.AnnotateXor64 ()) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr_annotate (I.ins_Xor64) (S.AnnotateXor64 ()) dst src)) va_s0 in (va_sM, va_fM)
val va_lemma_Xor64 : va_b0:va_code -> va_s0:va_state -> dst:va_operand_dst_opr64 -> src:va_operand_opr64 -> Ghost (va_state & va_fuel) (requires (va_require_total va_b0 (va_code_Xor64 dst src) va_s0 /\ va_is_dst_dst_opr64 dst va_s0 /\ va_is_src_opr64 src va_s0 /\ va_get_ok va_s0)) (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\ va_eval_dst_opr64 va_sM dst == Vale.Arch.Types.ixor64 (va_eval_dst_opr64 va_s0 dst) (va_eval_opr64 va_s0 src) /\ ~(Vale.X64.Decls.overflow (va_get_flags va_sM)) /\ ~(Vale.X64.Decls.cf (va_get_flags va_sM)) /\ Vale.X64.Decls.valid_cf (va_get_flags va_sM) /\ Vale.X64.Decls.valid_of (va_get_flags va_sM) /\ va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0))))) let va_lemma_Xor64 va_b0 va_s0 dst src =
false
null
false
va_reveal_opaque (`%va_code_Xor64) (va_code_Xor64 dst src); let va_old_s:va_state = va_s0 in va_ins_lemma (mk_ins (make_instr_annotate (I.ins_Xor64) (S.AnnotateXor64 ()) dst src)) va_s0; let va_sM, va_fM = va_eval_ins (mk_ins (make_instr_annotate (I.ins_Xor64) (S.AnnotateXor64 ()) dst src)) va_s0 in (va_sM, va_fM)
{ "checked_file": "Vale.X64.InsBasic.fst.checked", "dependencies": [ "Vale.X64.Taint_Semantics.fst.checked", "Vale.X64.StateLemmas.fsti.checked", "Vale.X64.Stack_i.fsti.checked", "Vale.X64.Memory.fsti.checked", "Vale.X64.Machine_Semantics_s.fst.checked", "Vale.X64.Instructions_s.fsti.checked", "Vale.X64.InsLemmas.fsti.checked", "Vale.X64.Decls.fst.checked", "Vale.X64.CPU_Features_s.fst.checked", "Vale.Arch.Types.fsti.checked", "prims.fst.checked", "FStar.UInt.fsti.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Math.Lemmas.fst.checked" ], "interface_file": true, "source_file": "Vale.X64.InsBasic.fst" }
[]
[ "Vale.X64.Decls.va_code", "Vale.X64.Decls.va_state", "Vale.X64.Decls.va_operand_dst_opr64", "Vale.X64.Decls.va_operand_opr64", "Vale.X64.State.vale_state", "Vale.X64.Lemmas.fuel", "FStar.Pervasives.Native.Mktuple2", "Vale.X64.Decls.va_fuel", "FStar.Pervasives.Native.tuple2", "Prims.nat", "Vale.X64.Decls.va_eval_ins", "Vale.X64.Taint_Semantics.mk_ins", "Vale.X64.InsLemmas.make_instr_annotate", "Prims.Cons", "Vale.X64.Instruction_s.instr_out", "Vale.X64.Instruction_s.inOut", "Vale.X64.Instruction_s.op64", "Vale.X64.Instruction_s.out", "Vale.X64.Instruction_s.opFlagsCf", "Vale.X64.Instruction_s.opFlagsOf", "Prims.Nil", "Vale.X64.Instruction_s.instr_operand", "Vale.X64.Instruction_s.HavocFlags", "Vale.X64.Instructions_s.ins_Xor64", "Vale.X64.Machine_Semantics_s.AnnotateXor64", "Vale.X64.Instruction_s.InstrTypeRecord", "Prims.unit", "Vale.X64.Decls.va_ins_lemma", "Vale.X64.Decls.va_reveal_opaque", "Vale.X64.InsBasic.va_code_Xor64" ]
[]
module Vale.X64.InsBasic open Vale.X64 open Vale.X64.StateLemmas open Vale.X64.InsLemmas open Vale.X64.Taint_Semantics open Vale.X64.CPU_Features_s open Vale.X64.Memory open Vale.X64.Stack_i module I = Vale.X64.Instructions_s module S = Vale.X64.Machine_Semantics_s friend Vale.X64.Decls #reset-options "--initial_fuel 5 --max_fuel 5 --max_ifuel 2 --z3rlimit 20" //-- Mov64 [@ "opaque_to_smt"] let va_code_Mov64 dst src = (mk_ins (make_instr_annotate (I.ins_Mov64) (S.AnnotateMov64 ()) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Mov64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Mov64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Mov64) (va_code_Mov64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr_annotate (I.ins_Mov64) (S.AnnotateMov64 ()) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr_annotate (I.ins_Mov64) (S.AnnotateMov64 ()) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Mov64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Mov64 (va_code_Mov64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0))); va_lemma_norm_mods ([va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cmovc64 [@ "opaque_to_smt"] let va_code_Cmovc64 dst src = (mk_ins (make_instr (I.ins_Cmovc64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Cmovc64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cmovc64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Cmovc64) (va_code_Cmovc64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cmovc64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cmovc64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cmovc64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cmovc64 (va_code_Cmovc64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0))); va_lemma_norm_mods ([va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Add64 [@ "opaque_to_smt"] let va_code_Add64 dst src = (mk_ins (make_instr (I.ins_Add64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Add64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Add64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Add64) (va_code_Add64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Add64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Add64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Add64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Add64 (va_code_Add64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Add64Wrap [@ "opaque_to_smt"] let va_code_Add64Wrap dst src = (mk_ins (make_instr (I.ins_Add64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Add64Wrap dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Add64Wrap va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Add64Wrap) (va_code_Add64Wrap dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Add64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Add64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Add64Wrap dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Add64Wrap (va_code_Add64Wrap dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- AddLea64 [@ "opaque_to_smt"] let va_code_AddLea64 dst src1 src2 = (mk_ins (make_instr (I.ins_AddLea64) dst src1 src2)) [@ "opaque_to_smt"] let va_codegen_success_AddLea64 dst src1 src2 = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_AddLea64 va_b0 va_s0 dst src1 src2 = va_reveal_opaque (`%va_code_AddLea64) (va_code_AddLea64 dst src1 src2); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_AddLea64) dst src1 src2)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_AddLea64) dst src1 src2)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_AddLea64 dst src1 src2 va_s0 va_k = let (va_sM, va_f0) = va_lemma_AddLea64 (va_code_AddLea64 dst src1 src2) va_s0 dst src1 src2 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0))); va_lemma_norm_mods ([va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Adc64 [@ "opaque_to_smt"] let va_code_Adc64 dst src = (mk_ins (make_instr (I.ins_AddCarry64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Adc64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Adc64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Adc64) (va_code_Adc64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_AddCarry64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_AddCarry64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Adc64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Adc64 (va_code_Adc64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Adc64Wrap [@ "opaque_to_smt"] let va_code_Adc64Wrap dst src = (mk_ins (make_instr (I.ins_AddCarry64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Adc64Wrap dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Adc64Wrap va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Adc64Wrap) (va_code_Adc64Wrap dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_AddCarry64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_AddCarry64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Adc64Wrap dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Adc64Wrap (va_code_Adc64Wrap dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Adcx64Wrap #push-options "--smtencoding.nl_arith_repr boxwrap" [@ "opaque_to_smt"] let va_code_Adcx64Wrap dst src = (mk_ins (make_instr (I.ins_Adcx64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Adcx64Wrap dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Adcx64Wrap va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Adcx64Wrap) (va_code_Adcx64Wrap dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Adcx64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Adcx64) dst src)) va_s0 in assert (Vale.Arch.Types.add_wrap64 (Vale.Arch.Types.add_wrap64 (va_eval_dst_opr64 va_old_s dst) (va_eval_opr64 va_old_s src)) (if Vale.X64.Decls.cf (va_get_flags va_old_s) then 1 else 0) == (va_eval_dst_opr64 va_old_s dst + va_eval_opr64 va_old_s src + (if Vale.X64.Decls.cf (va_get_flags va_old_s) then 1 else 0)) `op_Modulus` pow2_64); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Adcx64Wrap dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Adcx64Wrap (va_code_Adcx64Wrap dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) #pop-options //-- //-- Adox64Wrap [@ "opaque_to_smt"] let va_code_Adox64Wrap dst src = (mk_ins (make_instr (I.ins_Adox64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Adox64Wrap dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Adox64Wrap va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Adox64Wrap) (va_code_Adox64Wrap dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Adox64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Adox64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Adox64Wrap dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Adox64Wrap (va_code_Adox64Wrap dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Sub64 [@ "opaque_to_smt"] let va_code_Sub64 dst src = (mk_ins (make_instr (I.ins_Sub64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Sub64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Sub64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Sub64) (va_code_Sub64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Sub64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Sub64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Sub64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Sub64 (va_code_Sub64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Sub64Wrap [@ "opaque_to_smt"] let va_code_Sub64Wrap dst src = (mk_ins (make_instr (I.ins_Sub64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Sub64Wrap dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Sub64Wrap va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Sub64Wrap) (va_code_Sub64Wrap dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Sub64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Sub64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Sub64Wrap dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Sub64Wrap (va_code_Sub64Wrap dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Sbb64 [@ "opaque_to_smt"] let va_code_Sbb64 dst src = (mk_ins (make_instr (I.ins_Sbb64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Sbb64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Sbb64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Sbb64) (va_code_Sbb64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Sbb64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Sbb64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Sbb64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Sbb64 (va_code_Sbb64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- #restart-solver #push-options "--max_fuel 0 --max_ifuel 0 --using_facts_from 'Prims FStar.UInt'" let lemma_fundamental_div_mod (a b:nat64) : Lemma (pow2_64 * (FStar.UInt.mul_div #64 a b) + (FStar.UInt.mul_mod #64 a b) == a * b) = FStar.Math.Lemmas.lemma_div_mod (a * b) pow2_64 #pop-options //-- lemma_fundamental_div_mod //-- //-- Mul64Wrap [@ "opaque_to_smt"] let va_code_Mul64Wrap src = (mk_ins (make_instr (I.ins_Mul64) src)) [@ "opaque_to_smt"] let va_codegen_success_Mul64Wrap src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Mul64Wrap va_b0 va_s0 src = va_reveal_opaque (`%va_code_Mul64Wrap) (va_code_Mul64Wrap src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Mul64) src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Mul64) src)) va_s0 in lemma_fundamental_div_mod (va_get_reg64 rRax va_old_s) (va_eval_opr64 va_old_s src); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Mul64Wrap src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Mul64Wrap (va_code_Mul64Wrap src) va_s0 src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRax va_sM (va_update_flags va_sM (va_update_ok va_sM va_s0))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRax; va_Mod_flags]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Mulx64 [@ "opaque_to_smt"] let va_code_Mulx64 dst_hi dst_lo src = (mk_ins (make_instr (I.ins_Mulx64) dst_hi dst_lo src)) [@ "opaque_to_smt"] let va_codegen_success_Mulx64 dst_hi dst_lo src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Mulx64 va_b0 va_s0 dst_hi dst_lo src = va_reveal_opaque (`%va_code_Mulx64) (va_code_Mulx64 dst_hi dst_lo src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Mulx64) dst_hi dst_lo src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Mulx64) dst_hi dst_lo src)) va_s0 in lemma_fundamental_div_mod (va_get_reg64 rRdx va_old_s) (va_eval_opr64 va_old_s src); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Mulx64 dst_hi dst_lo src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Mulx64 (va_code_Mulx64 dst_hi dst_lo src) va_s0 dst_hi dst_lo src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst_lo va_sM (va_update_operand_dst_opr64 dst_hi va_sM va_s0)))); va_lemma_norm_mods ([va_mod_dst_opr64 dst_lo; va_mod_dst_opr64 dst_hi]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- lemma_mul_nat //-- //-- lemma_mul_in_bounds //-- //-- IMul64 [@ "opaque_to_smt"] let va_code_IMul64 dst src = (mk_ins (make_instr (I.ins_IMul64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_IMul64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_IMul64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_IMul64) (va_code_IMul64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_IMul64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_IMul64) dst src)) va_s0 in lemma_mul_nat (va_eval_dst_opr64 va_old_s dst) (va_eval_opr64 va_old_s src); lemma_mul_in_bounds (va_eval_dst_opr64 va_old_s dst) (va_eval_opr64 va_old_s src); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_IMul64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_IMul64 (va_code_IMul64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Xor64 [@ "opaque_to_smt"] let va_code_Xor64 dst src = (mk_ins (make_instr_annotate (I.ins_Xor64) (S.AnnotateXor64 ()) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Xor64 dst src = (va_ttrue ()) [@"opaque_to_smt"]
false
false
Vale.X64.InsBasic.fst
{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 5, "initial_ifuel": 0, "max_fuel": 5, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": true, "smtencoding_l_arith_repr": "native", "smtencoding_nl_arith_repr": "wrapped", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": false, "z3cliopt": [ "smt.arith.nl=false", "smt.QI.EAGER_THRESHOLD=100", "smt.CASE_SPLIT=3" ], "z3refresh": false, "z3rlimit": 20, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }
null
val va_lemma_Xor64 : va_b0:va_code -> va_s0:va_state -> dst:va_operand_dst_opr64 -> src:va_operand_opr64 -> Ghost (va_state & va_fuel) (requires (va_require_total va_b0 (va_code_Xor64 dst src) va_s0 /\ va_is_dst_dst_opr64 dst va_s0 /\ va_is_src_opr64 src va_s0 /\ va_get_ok va_s0)) (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\ va_eval_dst_opr64 va_sM dst == Vale.Arch.Types.ixor64 (va_eval_dst_opr64 va_s0 dst) (va_eval_opr64 va_s0 src) /\ ~(Vale.X64.Decls.overflow (va_get_flags va_sM)) /\ ~(Vale.X64.Decls.cf (va_get_flags va_sM)) /\ Vale.X64.Decls.valid_cf (va_get_flags va_sM) /\ Vale.X64.Decls.valid_of (va_get_flags va_sM) /\ va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))))
[]
Vale.X64.InsBasic.va_lemma_Xor64
{ "file_name": "obj/Vale.X64.InsBasic.fst", "git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e", "git_url": "https://github.com/hacl-star/hacl-star.git", "project_name": "hacl-star" }
va_b0: Vale.X64.Decls.va_code -> va_s0: Vale.X64.Decls.va_state -> dst: Vale.X64.Decls.va_operand_dst_opr64 -> src: Vale.X64.Decls.va_operand_opr64 -> Prims.Ghost (Vale.X64.Decls.va_state * Vale.X64.Decls.va_fuel)
{ "end_col": 16, "end_line": 501, "start_col": 2, "start_line": 496 }
Prims.Ghost
val va_wpProof_LargeComment : c:string -> va_s0:va_state -> va_k:(va_state -> unit -> Type0) -> Ghost (va_state & va_fuel & unit) (requires (va_t_require va_s0 /\ va_wp_LargeComment c va_s0 va_k)) (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_LargeComment c) ([]) va_s0 va_k ((va_sM, va_f0, va_g))))
[ { "abbrev": true, "full_module": "Vale.X64.Machine_Semantics_s", "short_module": "S" }, { "abbrev": true, "full_module": "Vale.X64.Instructions_s", "short_module": "I" }, { "abbrev": false, "full_module": "Vale.X64.Stack_i", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.Memory", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.Taint_Semantics", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.InsLemmas", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.StateLemmas", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.CPU_Features_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.QuickCode", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.Decls", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.State", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.Machine_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Arch.Types", "short_module": null }, { "abbrev": false, "full_module": "Vale.Arch.HeapImpl", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Types_s", "short_module": null }, { "abbrev": false, "full_module": "FStar.Mul", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]
false
let va_wpProof_LargeComment c va_s0 va_k = let (va_sM, va_f0) = va_lemma_LargeComment (va_code_LargeComment c) va_s0 c in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_ok va_sM va_s0)); va_lemma_norm_mods ([]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g)
val va_wpProof_LargeComment : c:string -> va_s0:va_state -> va_k:(va_state -> unit -> Type0) -> Ghost (va_state & va_fuel & unit) (requires (va_t_require va_s0 /\ va_wp_LargeComment c va_s0 va_k)) (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_LargeComment c) ([]) va_s0 va_k ((va_sM, va_f0, va_g)))) let va_wpProof_LargeComment c va_s0 va_k =
false
null
false
let va_sM, va_f0 = va_lemma_LargeComment (va_code_LargeComment c) va_s0 c in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_ok va_sM va_s0)); va_lemma_norm_mods ([]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g)
{ "checked_file": "Vale.X64.InsBasic.fst.checked", "dependencies": [ "Vale.X64.Taint_Semantics.fst.checked", "Vale.X64.StateLemmas.fsti.checked", "Vale.X64.Stack_i.fsti.checked", "Vale.X64.Memory.fsti.checked", "Vale.X64.Machine_Semantics_s.fst.checked", "Vale.X64.Instructions_s.fsti.checked", "Vale.X64.InsLemmas.fsti.checked", "Vale.X64.Decls.fst.checked", "Vale.X64.CPU_Features_s.fst.checked", "Vale.Arch.Types.fsti.checked", "prims.fst.checked", "FStar.UInt.fsti.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Math.Lemmas.fst.checked" ], "interface_file": true, "source_file": "Vale.X64.InsBasic.fst" }
[]
[ "Prims.string", "Vale.X64.Decls.va_state", "Prims.unit", "Vale.X64.Decls.va_fuel", "FStar.Pervasives.Native.Mktuple3", "Vale.X64.QuickCode.va_lemma_norm_mods", "Prims.Nil", "Vale.X64.QuickCode.mod_t", "Prims._assert", "Vale.X64.Decls.va_state_eq", "Vale.X64.Decls.va_update_ok", "Vale.X64.Decls.va_lemma_upd_update", "FStar.Pervasives.Native.tuple3", "FStar.Pervasives.Native.tuple2", "Vale.X64.State.vale_state", "Vale.X64.InsBasic.va_lemma_LargeComment", "Vale.X64.InsBasic.va_code_LargeComment" ]
[]
module Vale.X64.InsBasic open Vale.X64 open Vale.X64.StateLemmas open Vale.X64.InsLemmas open Vale.X64.Taint_Semantics open Vale.X64.CPU_Features_s open Vale.X64.Memory open Vale.X64.Stack_i module I = Vale.X64.Instructions_s module S = Vale.X64.Machine_Semantics_s friend Vale.X64.Decls #reset-options "--initial_fuel 5 --max_fuel 5 --max_ifuel 2 --z3rlimit 20" //-- Mov64 [@ "opaque_to_smt"] let va_code_Mov64 dst src = (mk_ins (make_instr_annotate (I.ins_Mov64) (S.AnnotateMov64 ()) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Mov64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Mov64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Mov64) (va_code_Mov64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr_annotate (I.ins_Mov64) (S.AnnotateMov64 ()) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr_annotate (I.ins_Mov64) (S.AnnotateMov64 ()) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Mov64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Mov64 (va_code_Mov64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0))); va_lemma_norm_mods ([va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cmovc64 [@ "opaque_to_smt"] let va_code_Cmovc64 dst src = (mk_ins (make_instr (I.ins_Cmovc64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Cmovc64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cmovc64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Cmovc64) (va_code_Cmovc64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cmovc64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cmovc64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cmovc64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cmovc64 (va_code_Cmovc64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0))); va_lemma_norm_mods ([va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Add64 [@ "opaque_to_smt"] let va_code_Add64 dst src = (mk_ins (make_instr (I.ins_Add64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Add64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Add64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Add64) (va_code_Add64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Add64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Add64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Add64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Add64 (va_code_Add64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Add64Wrap [@ "opaque_to_smt"] let va_code_Add64Wrap dst src = (mk_ins (make_instr (I.ins_Add64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Add64Wrap dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Add64Wrap va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Add64Wrap) (va_code_Add64Wrap dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Add64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Add64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Add64Wrap dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Add64Wrap (va_code_Add64Wrap dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- AddLea64 [@ "opaque_to_smt"] let va_code_AddLea64 dst src1 src2 = (mk_ins (make_instr (I.ins_AddLea64) dst src1 src2)) [@ "opaque_to_smt"] let va_codegen_success_AddLea64 dst src1 src2 = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_AddLea64 va_b0 va_s0 dst src1 src2 = va_reveal_opaque (`%va_code_AddLea64) (va_code_AddLea64 dst src1 src2); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_AddLea64) dst src1 src2)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_AddLea64) dst src1 src2)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_AddLea64 dst src1 src2 va_s0 va_k = let (va_sM, va_f0) = va_lemma_AddLea64 (va_code_AddLea64 dst src1 src2) va_s0 dst src1 src2 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0))); va_lemma_norm_mods ([va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Adc64 [@ "opaque_to_smt"] let va_code_Adc64 dst src = (mk_ins (make_instr (I.ins_AddCarry64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Adc64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Adc64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Adc64) (va_code_Adc64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_AddCarry64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_AddCarry64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Adc64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Adc64 (va_code_Adc64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Adc64Wrap [@ "opaque_to_smt"] let va_code_Adc64Wrap dst src = (mk_ins (make_instr (I.ins_AddCarry64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Adc64Wrap dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Adc64Wrap va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Adc64Wrap) (va_code_Adc64Wrap dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_AddCarry64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_AddCarry64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Adc64Wrap dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Adc64Wrap (va_code_Adc64Wrap dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Adcx64Wrap #push-options "--smtencoding.nl_arith_repr boxwrap" [@ "opaque_to_smt"] let va_code_Adcx64Wrap dst src = (mk_ins (make_instr (I.ins_Adcx64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Adcx64Wrap dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Adcx64Wrap va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Adcx64Wrap) (va_code_Adcx64Wrap dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Adcx64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Adcx64) dst src)) va_s0 in assert (Vale.Arch.Types.add_wrap64 (Vale.Arch.Types.add_wrap64 (va_eval_dst_opr64 va_old_s dst) (va_eval_opr64 va_old_s src)) (if Vale.X64.Decls.cf (va_get_flags va_old_s) then 1 else 0) == (va_eval_dst_opr64 va_old_s dst + va_eval_opr64 va_old_s src + (if Vale.X64.Decls.cf (va_get_flags va_old_s) then 1 else 0)) `op_Modulus` pow2_64); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Adcx64Wrap dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Adcx64Wrap (va_code_Adcx64Wrap dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) #pop-options //-- //-- Adox64Wrap [@ "opaque_to_smt"] let va_code_Adox64Wrap dst src = (mk_ins (make_instr (I.ins_Adox64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Adox64Wrap dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Adox64Wrap va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Adox64Wrap) (va_code_Adox64Wrap dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Adox64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Adox64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Adox64Wrap dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Adox64Wrap (va_code_Adox64Wrap dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Sub64 [@ "opaque_to_smt"] let va_code_Sub64 dst src = (mk_ins (make_instr (I.ins_Sub64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Sub64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Sub64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Sub64) (va_code_Sub64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Sub64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Sub64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Sub64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Sub64 (va_code_Sub64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Sub64Wrap [@ "opaque_to_smt"] let va_code_Sub64Wrap dst src = (mk_ins (make_instr (I.ins_Sub64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Sub64Wrap dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Sub64Wrap va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Sub64Wrap) (va_code_Sub64Wrap dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Sub64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Sub64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Sub64Wrap dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Sub64Wrap (va_code_Sub64Wrap dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Sbb64 [@ "opaque_to_smt"] let va_code_Sbb64 dst src = (mk_ins (make_instr (I.ins_Sbb64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Sbb64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Sbb64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Sbb64) (va_code_Sbb64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Sbb64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Sbb64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Sbb64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Sbb64 (va_code_Sbb64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- #restart-solver #push-options "--max_fuel 0 --max_ifuel 0 --using_facts_from 'Prims FStar.UInt'" let lemma_fundamental_div_mod (a b:nat64) : Lemma (pow2_64 * (FStar.UInt.mul_div #64 a b) + (FStar.UInt.mul_mod #64 a b) == a * b) = FStar.Math.Lemmas.lemma_div_mod (a * b) pow2_64 #pop-options //-- lemma_fundamental_div_mod //-- //-- Mul64Wrap [@ "opaque_to_smt"] let va_code_Mul64Wrap src = (mk_ins (make_instr (I.ins_Mul64) src)) [@ "opaque_to_smt"] let va_codegen_success_Mul64Wrap src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Mul64Wrap va_b0 va_s0 src = va_reveal_opaque (`%va_code_Mul64Wrap) (va_code_Mul64Wrap src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Mul64) src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Mul64) src)) va_s0 in lemma_fundamental_div_mod (va_get_reg64 rRax va_old_s) (va_eval_opr64 va_old_s src); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Mul64Wrap src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Mul64Wrap (va_code_Mul64Wrap src) va_s0 src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRax va_sM (va_update_flags va_sM (va_update_ok va_sM va_s0))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRax; va_Mod_flags]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Mulx64 [@ "opaque_to_smt"] let va_code_Mulx64 dst_hi dst_lo src = (mk_ins (make_instr (I.ins_Mulx64) dst_hi dst_lo src)) [@ "opaque_to_smt"] let va_codegen_success_Mulx64 dst_hi dst_lo src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Mulx64 va_b0 va_s0 dst_hi dst_lo src = va_reveal_opaque (`%va_code_Mulx64) (va_code_Mulx64 dst_hi dst_lo src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Mulx64) dst_hi dst_lo src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Mulx64) dst_hi dst_lo src)) va_s0 in lemma_fundamental_div_mod (va_get_reg64 rRdx va_old_s) (va_eval_opr64 va_old_s src); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Mulx64 dst_hi dst_lo src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Mulx64 (va_code_Mulx64 dst_hi dst_lo src) va_s0 dst_hi dst_lo src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst_lo va_sM (va_update_operand_dst_opr64 dst_hi va_sM va_s0)))); va_lemma_norm_mods ([va_mod_dst_opr64 dst_lo; va_mod_dst_opr64 dst_hi]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- lemma_mul_nat //-- //-- lemma_mul_in_bounds //-- //-- IMul64 [@ "opaque_to_smt"] let va_code_IMul64 dst src = (mk_ins (make_instr (I.ins_IMul64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_IMul64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_IMul64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_IMul64) (va_code_IMul64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_IMul64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_IMul64) dst src)) va_s0 in lemma_mul_nat (va_eval_dst_opr64 va_old_s dst) (va_eval_opr64 va_old_s src); lemma_mul_in_bounds (va_eval_dst_opr64 va_old_s dst) (va_eval_opr64 va_old_s src); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_IMul64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_IMul64 (va_code_IMul64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Xor64 [@ "opaque_to_smt"] let va_code_Xor64 dst src = (mk_ins (make_instr_annotate (I.ins_Xor64) (S.AnnotateXor64 ()) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Xor64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Xor64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Xor64) (va_code_Xor64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr_annotate (I.ins_Xor64) (S.AnnotateXor64 ()) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr_annotate (I.ins_Xor64) (S.AnnotateXor64 ()) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Xor64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Xor64 (va_code_Xor64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- And64 [@ "opaque_to_smt"] let va_code_And64 dst src = (mk_ins (make_instr (I.ins_And64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_And64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_And64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_And64) (va_code_And64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_And64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_And64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_And64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_And64 (va_code_And64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Shl64 [@ "opaque_to_smt"] let va_code_Shl64 dst amt = (mk_ins (make_instr (I.ins_Shl64) dst amt)) [@ "opaque_to_smt"] let va_codegen_success_Shl64 dst amt = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Shl64 va_b0 va_s0 dst amt = va_reveal_opaque (`%va_code_Shl64) (va_code_Shl64 dst amt); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Shl64) dst amt)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Shl64) dst amt)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Shl64 dst amt va_s0 va_k = let (va_sM, va_f0) = va_lemma_Shl64 (va_code_Shl64 dst amt) va_s0 dst amt in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Shr64 [@ "opaque_to_smt"] let va_code_Shr64 dst amt = (mk_ins (make_instr (I.ins_Shr64) dst amt)) [@ "opaque_to_smt"] let va_codegen_success_Shr64 dst amt = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Shr64 va_b0 va_s0 dst amt = va_reveal_opaque (`%va_code_Shr64) (va_code_Shr64 dst amt); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Shr64) dst amt)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Shr64) dst amt)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Shr64 dst amt va_s0 va_k = let (va_sM, va_f0) = va_lemma_Shr64 (va_code_Shr64 dst amt) va_s0 dst amt in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_AES [@ "opaque_to_smt"] let va_code_Cpuid_AES () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_AES () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_AES va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_AES) (va_code_Cpuid_AES ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_AES va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_AES (va_code_Cpuid_AES ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Sha [@ "opaque_to_smt"] let va_code_Cpuid_Sha () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Sha () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Sha va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Sha) (va_code_Cpuid_Sha ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Sha va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Sha (va_code_Cpuid_Sha ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Adx_Bmi2 [@ "opaque_to_smt"] let va_code_Cpuid_Adx_Bmi2 () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Adx_Bmi2 () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Adx_Bmi2 va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Adx_Bmi2) (va_code_Cpuid_Adx_Bmi2 ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Adx_Bmi2 va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Adx_Bmi2 (va_code_Cpuid_Adx_Bmi2 ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Avx [@ "opaque_to_smt"] let va_code_Cpuid_Avx () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Avx () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Avx va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Avx) (va_code_Cpuid_Avx ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Avx va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Avx (va_code_Cpuid_Avx ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Avx2 [@ "opaque_to_smt"] let va_code_Cpuid_Avx2 () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Avx2 () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Avx2 va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Avx2) (va_code_Cpuid_Avx2 ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Avx2 va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Avx2 (va_code_Cpuid_Avx2 ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Sse [@ "opaque_to_smt"] let va_code_Cpuid_Sse () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Sse () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Sse va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Sse) (va_code_Cpuid_Sse ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Sse va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Sse (va_code_Cpuid_Sse ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Movbe [@ "opaque_to_smt"] let va_code_Cpuid_Movbe () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Movbe () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Movbe va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Movbe) (va_code_Cpuid_Movbe ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Movbe va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Movbe (va_code_Cpuid_Movbe ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Rdrand [@ "opaque_to_smt"] let va_code_Cpuid_Rdrand () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Rdrand () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Rdrand va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Rdrand) (va_code_Cpuid_Rdrand ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Rdrand va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Rdrand (va_code_Cpuid_Rdrand ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Avx512 [@ "opaque_to_smt"] let va_code_Cpuid_Avx512 () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Avx512 () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Avx512 va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Avx512) (va_code_Cpuid_Avx512 ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Avx512 va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Avx512 (va_code_Cpuid_Avx512 ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Osxsave [@ "opaque_to_smt"] let va_code_Cpuid_Osxsave () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Osxsave () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Osxsave va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Osxsave) (va_code_Cpuid_Osxsave ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Osxsave va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Osxsave (va_code_Cpuid_Osxsave ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Xgetbv_Avx [@ "opaque_to_smt"] let va_code_Xgetbv_Avx () = (mk_ins (make_instr (I.ins_Xgetbv))) [@ "opaque_to_smt"] let va_codegen_success_Xgetbv_Avx () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Xgetbv_Avx va_b0 va_s0 = va_reveal_opaque (`%va_code_Xgetbv_Avx) (va_code_Xgetbv_Avx ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Xgetbv))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Xgetbv))) va_s0 in Vale.X64.CPU_Features_s.xgetbv_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Xgetbv_Avx va_s0 va_k = let (va_sM, va_f0) = va_lemma_Xgetbv_Avx (va_code_Xgetbv_Avx ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Xgetbv_Avx512 [@ "opaque_to_smt"] let va_code_Xgetbv_Avx512 () = (mk_ins (make_instr (I.ins_Xgetbv))) [@ "opaque_to_smt"] let va_codegen_success_Xgetbv_Avx512 () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Xgetbv_Avx512 va_b0 va_s0 = va_reveal_opaque (`%va_code_Xgetbv_Avx512) (va_code_Xgetbv_Avx512 ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Xgetbv))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Xgetbv))) va_s0 in Vale.X64.CPU_Features_s.xgetbv_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Xgetbv_Avx512 va_s0 va_k = let (va_sM, va_f0) = va_lemma_Xgetbv_Avx512 (va_code_Xgetbv_Avx512 ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Nat64Equal [@ "opaque_to_smt"] let va_code_Nat64Equal dst src = (va_Block (va_CCons (va_code_Sub64Wrap (va_coerce_reg_opr64_to_dst_opr64 src) (va_const_opr64 18446744073709551615)) (va_CCons (va_code_Mov64 (va_coerce_reg_opr64_to_dst_opr64 dst) (va_const_opr64 0)) (va_CCons (va_code_Adc64 (va_coerce_reg_opr64_to_dst_opr64 dst) (va_const_opr64 0)) (va_CNil ()))))) [@ "opaque_to_smt"] let va_codegen_success_Nat64Equal dst src = (va_pbool_and (va_codegen_success_Sub64Wrap (va_coerce_reg_opr64_to_dst_opr64 src) (va_const_opr64 18446744073709551615)) (va_pbool_and (va_codegen_success_Mov64 (va_coerce_reg_opr64_to_dst_opr64 dst) (va_const_opr64 0)) (va_pbool_and (va_codegen_success_Adc64 (va_coerce_reg_opr64_to_dst_opr64 dst) (va_const_opr64 0)) (va_ttrue ())))) [@"opaque_to_smt"] let va_lemma_Nat64Equal va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Nat64Equal) (va_code_Nat64Equal dst src); let (va_old_s:va_state) = va_s0 in let (va_b1:va_codes) = va_get_block va_b0 in let (va_s2, va_fc2) = va_lemma_Sub64Wrap (va_hd va_b1) va_s0 (va_coerce_reg_opr64_to_dst_opr64 src) (va_const_opr64 18446744073709551615) in let va_b2 = va_tl va_b1 in let (va_s3, va_fc3) = va_lemma_Mov64 (va_hd va_b2) va_s2 (va_coerce_reg_opr64_to_dst_opr64 dst) (va_const_opr64 0) in let va_b3 = va_tl va_b2 in let (va_s4, va_fc4) = va_lemma_Adc64 (va_hd va_b3) va_s3 (va_coerce_reg_opr64_to_dst_opr64 dst) (va_const_opr64 0) in let va_b4 = va_tl va_b3 in let (va_sM, va_f4) = va_lemma_empty_total va_s4 va_b4 in let va_f3 = va_lemma_merge_total va_b3 va_s3 va_fc4 va_s4 va_f4 va_sM in let va_f2 = va_lemma_merge_total va_b2 va_s2 va_fc3 va_s3 va_f3 va_sM in let va_fM = va_lemma_merge_total va_b1 va_s0 va_fc2 va_s2 va_f2 va_sM in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Nat64Equal dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Nat64Equal (va_code_Nat64Equal dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_reg_opr64 src va_sM (va_update_operand_reg_opr64 dst va_sM va_s0))))); va_lemma_norm_mods ([va_Mod_flags; va_mod_reg_opr64 src; va_mod_reg_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Comment [@ "opaque_to_smt"] let va_code_Comment c = (mk_ins (make_instr_annotate (I.ins_Comment c) (S.AnnotateComment c))) [@ "opaque_to_smt"] let va_codegen_success_Comment c = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Comment va_b0 va_s0 c = va_reveal_opaque (`%va_code_Comment) (va_code_Comment c); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr_annotate (I.ins_Comment c) (S.AnnotateComment c))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr_annotate (I.ins_Comment c) (S.AnnotateComment c))) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Comment c va_s0 va_k = let (va_sM, va_f0) = va_lemma_Comment (va_code_Comment c) va_s0 c in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_ok va_sM va_s0)); va_lemma_norm_mods ([]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- LargeComment [@ "opaque_to_smt"] let va_code_LargeComment c = (mk_ins (make_instr_annotate (I.ins_LargeComment c) (S.AnnotateLargeComment c))) [@ "opaque_to_smt"] let va_codegen_success_LargeComment c = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_LargeComment va_b0 va_s0 c = va_reveal_opaque (`%va_code_LargeComment) (va_code_LargeComment c); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr_annotate (I.ins_LargeComment c) (S.AnnotateLargeComment c))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr_annotate (I.ins_LargeComment c) (S.AnnotateLargeComment c))) va_s0 in (va_sM, va_fM)
false
false
Vale.X64.InsBasic.fst
{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 5, "initial_ifuel": 0, "max_fuel": 5, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": true, "smtencoding_l_arith_repr": "native", "smtencoding_nl_arith_repr": "wrapped", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": false, "z3cliopt": [ "smt.arith.nl=false", "smt.QI.EAGER_THRESHOLD=100", "smt.CASE_SPLIT=3" ], "z3refresh": false, "z3rlimit": 20, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }
null
val va_wpProof_LargeComment : c:string -> va_s0:va_state -> va_k:(va_state -> unit -> Type0) -> Ghost (va_state & va_fuel & unit) (requires (va_t_require va_s0 /\ va_wp_LargeComment c va_s0 va_k)) (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_LargeComment c) ([]) va_s0 va_k ((va_sM, va_f0, va_g))))
[]
Vale.X64.InsBasic.va_wpProof_LargeComment
{ "file_name": "obj/Vale.X64.InsBasic.fst", "git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e", "git_url": "https://github.com/hacl-star/hacl-star.git", "project_name": "hacl-star" }
c: Prims.string -> va_s0: Vale.X64.Decls.va_state -> va_k: (_: Vale.X64.Decls.va_state -> _: Prims.unit -> Type0) -> Prims.Ghost ((Vale.X64.Decls.va_state * Vale.X64.Decls.va_fuel) * Prims.unit)
{ "end_col": 22, "end_line": 1094, "start_col": 42, "start_line": 1088 }
Prims.Ghost
val va_lemma_LargeComment : va_b0:va_code -> va_s0:va_state -> c:string -> Ghost (va_state & va_fuel) (requires (va_require_total va_b0 (va_code_LargeComment c) va_s0 /\ va_get_ok va_s0)) (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\ va_state_eq va_sM (va_update_ok va_sM va_s0)))
[ { "abbrev": true, "full_module": "Vale.X64.Machine_Semantics_s", "short_module": "S" }, { "abbrev": true, "full_module": "Vale.X64.Instructions_s", "short_module": "I" }, { "abbrev": false, "full_module": "Vale.X64.Stack_i", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.Memory", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.Taint_Semantics", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.InsLemmas", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.StateLemmas", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.CPU_Features_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.QuickCode", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.Decls", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.State", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.Machine_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Arch.Types", "short_module": null }, { "abbrev": false, "full_module": "Vale.Arch.HeapImpl", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Types_s", "short_module": null }, { "abbrev": false, "full_module": "FStar.Mul", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]
false
let va_lemma_LargeComment va_b0 va_s0 c = va_reveal_opaque (`%va_code_LargeComment) (va_code_LargeComment c); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr_annotate (I.ins_LargeComment c) (S.AnnotateLargeComment c))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr_annotate (I.ins_LargeComment c) (S.AnnotateLargeComment c))) va_s0 in (va_sM, va_fM)
val va_lemma_LargeComment : va_b0:va_code -> va_s0:va_state -> c:string -> Ghost (va_state & va_fuel) (requires (va_require_total va_b0 (va_code_LargeComment c) va_s0 /\ va_get_ok va_s0)) (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\ va_state_eq va_sM (va_update_ok va_sM va_s0))) let va_lemma_LargeComment va_b0 va_s0 c =
false
null
false
va_reveal_opaque (`%va_code_LargeComment) (va_code_LargeComment c); let va_old_s:va_state = va_s0 in va_ins_lemma (mk_ins (make_instr_annotate (I.ins_LargeComment c) (S.AnnotateLargeComment c))) va_s0; let va_sM, va_fM = va_eval_ins (mk_ins (make_instr_annotate (I.ins_LargeComment c) (S.AnnotateLargeComment c))) va_s0 in (va_sM, va_fM)
{ "checked_file": "Vale.X64.InsBasic.fst.checked", "dependencies": [ "Vale.X64.Taint_Semantics.fst.checked", "Vale.X64.StateLemmas.fsti.checked", "Vale.X64.Stack_i.fsti.checked", "Vale.X64.Memory.fsti.checked", "Vale.X64.Machine_Semantics_s.fst.checked", "Vale.X64.Instructions_s.fsti.checked", "Vale.X64.InsLemmas.fsti.checked", "Vale.X64.Decls.fst.checked", "Vale.X64.CPU_Features_s.fst.checked", "Vale.Arch.Types.fsti.checked", "prims.fst.checked", "FStar.UInt.fsti.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Math.Lemmas.fst.checked" ], "interface_file": true, "source_file": "Vale.X64.InsBasic.fst" }
[]
[ "Vale.X64.Decls.va_code", "Vale.X64.Decls.va_state", "Prims.string", "Vale.X64.State.vale_state", "Vale.X64.Lemmas.fuel", "FStar.Pervasives.Native.Mktuple2", "Vale.X64.Decls.va_fuel", "FStar.Pervasives.Native.tuple2", "Prims.nat", "Vale.X64.Decls.va_eval_ins", "Vale.X64.Taint_Semantics.mk_ins", "Vale.X64.InsLemmas.make_instr_annotate", "Prims.Nil", "Vale.X64.Instruction_s.instr_out", "Vale.X64.Instruction_s.instr_operand", "Vale.X64.Instruction_s.PreserveFlags", "Vale.X64.Instructions_s.ins_LargeComment", "Vale.X64.Machine_Semantics_s.AnnotateLargeComment", "Vale.X64.Instruction_s.InstrTypeRecord", "Prims.unit", "Vale.X64.Decls.va_ins_lemma", "Vale.X64.Decls.va_reveal_opaque", "Vale.X64.InsBasic.va_code_LargeComment" ]
[]
module Vale.X64.InsBasic open Vale.X64 open Vale.X64.StateLemmas open Vale.X64.InsLemmas open Vale.X64.Taint_Semantics open Vale.X64.CPU_Features_s open Vale.X64.Memory open Vale.X64.Stack_i module I = Vale.X64.Instructions_s module S = Vale.X64.Machine_Semantics_s friend Vale.X64.Decls #reset-options "--initial_fuel 5 --max_fuel 5 --max_ifuel 2 --z3rlimit 20" //-- Mov64 [@ "opaque_to_smt"] let va_code_Mov64 dst src = (mk_ins (make_instr_annotate (I.ins_Mov64) (S.AnnotateMov64 ()) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Mov64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Mov64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Mov64) (va_code_Mov64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr_annotate (I.ins_Mov64) (S.AnnotateMov64 ()) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr_annotate (I.ins_Mov64) (S.AnnotateMov64 ()) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Mov64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Mov64 (va_code_Mov64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0))); va_lemma_norm_mods ([va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cmovc64 [@ "opaque_to_smt"] let va_code_Cmovc64 dst src = (mk_ins (make_instr (I.ins_Cmovc64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Cmovc64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cmovc64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Cmovc64) (va_code_Cmovc64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cmovc64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cmovc64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cmovc64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cmovc64 (va_code_Cmovc64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0))); va_lemma_norm_mods ([va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Add64 [@ "opaque_to_smt"] let va_code_Add64 dst src = (mk_ins (make_instr (I.ins_Add64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Add64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Add64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Add64) (va_code_Add64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Add64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Add64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Add64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Add64 (va_code_Add64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Add64Wrap [@ "opaque_to_smt"] let va_code_Add64Wrap dst src = (mk_ins (make_instr (I.ins_Add64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Add64Wrap dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Add64Wrap va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Add64Wrap) (va_code_Add64Wrap dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Add64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Add64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Add64Wrap dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Add64Wrap (va_code_Add64Wrap dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- AddLea64 [@ "opaque_to_smt"] let va_code_AddLea64 dst src1 src2 = (mk_ins (make_instr (I.ins_AddLea64) dst src1 src2)) [@ "opaque_to_smt"] let va_codegen_success_AddLea64 dst src1 src2 = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_AddLea64 va_b0 va_s0 dst src1 src2 = va_reveal_opaque (`%va_code_AddLea64) (va_code_AddLea64 dst src1 src2); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_AddLea64) dst src1 src2)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_AddLea64) dst src1 src2)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_AddLea64 dst src1 src2 va_s0 va_k = let (va_sM, va_f0) = va_lemma_AddLea64 (va_code_AddLea64 dst src1 src2) va_s0 dst src1 src2 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0))); va_lemma_norm_mods ([va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Adc64 [@ "opaque_to_smt"] let va_code_Adc64 dst src = (mk_ins (make_instr (I.ins_AddCarry64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Adc64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Adc64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Adc64) (va_code_Adc64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_AddCarry64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_AddCarry64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Adc64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Adc64 (va_code_Adc64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Adc64Wrap [@ "opaque_to_smt"] let va_code_Adc64Wrap dst src = (mk_ins (make_instr (I.ins_AddCarry64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Adc64Wrap dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Adc64Wrap va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Adc64Wrap) (va_code_Adc64Wrap dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_AddCarry64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_AddCarry64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Adc64Wrap dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Adc64Wrap (va_code_Adc64Wrap dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Adcx64Wrap #push-options "--smtencoding.nl_arith_repr boxwrap" [@ "opaque_to_smt"] let va_code_Adcx64Wrap dst src = (mk_ins (make_instr (I.ins_Adcx64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Adcx64Wrap dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Adcx64Wrap va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Adcx64Wrap) (va_code_Adcx64Wrap dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Adcx64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Adcx64) dst src)) va_s0 in assert (Vale.Arch.Types.add_wrap64 (Vale.Arch.Types.add_wrap64 (va_eval_dst_opr64 va_old_s dst) (va_eval_opr64 va_old_s src)) (if Vale.X64.Decls.cf (va_get_flags va_old_s) then 1 else 0) == (va_eval_dst_opr64 va_old_s dst + va_eval_opr64 va_old_s src + (if Vale.X64.Decls.cf (va_get_flags va_old_s) then 1 else 0)) `op_Modulus` pow2_64); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Adcx64Wrap dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Adcx64Wrap (va_code_Adcx64Wrap dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) #pop-options //-- //-- Adox64Wrap [@ "opaque_to_smt"] let va_code_Adox64Wrap dst src = (mk_ins (make_instr (I.ins_Adox64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Adox64Wrap dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Adox64Wrap va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Adox64Wrap) (va_code_Adox64Wrap dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Adox64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Adox64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Adox64Wrap dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Adox64Wrap (va_code_Adox64Wrap dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Sub64 [@ "opaque_to_smt"] let va_code_Sub64 dst src = (mk_ins (make_instr (I.ins_Sub64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Sub64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Sub64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Sub64) (va_code_Sub64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Sub64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Sub64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Sub64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Sub64 (va_code_Sub64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Sub64Wrap [@ "opaque_to_smt"] let va_code_Sub64Wrap dst src = (mk_ins (make_instr (I.ins_Sub64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Sub64Wrap dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Sub64Wrap va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Sub64Wrap) (va_code_Sub64Wrap dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Sub64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Sub64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Sub64Wrap dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Sub64Wrap (va_code_Sub64Wrap dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Sbb64 [@ "opaque_to_smt"] let va_code_Sbb64 dst src = (mk_ins (make_instr (I.ins_Sbb64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Sbb64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Sbb64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Sbb64) (va_code_Sbb64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Sbb64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Sbb64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Sbb64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Sbb64 (va_code_Sbb64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- #restart-solver #push-options "--max_fuel 0 --max_ifuel 0 --using_facts_from 'Prims FStar.UInt'" let lemma_fundamental_div_mod (a b:nat64) : Lemma (pow2_64 * (FStar.UInt.mul_div #64 a b) + (FStar.UInt.mul_mod #64 a b) == a * b) = FStar.Math.Lemmas.lemma_div_mod (a * b) pow2_64 #pop-options //-- lemma_fundamental_div_mod //-- //-- Mul64Wrap [@ "opaque_to_smt"] let va_code_Mul64Wrap src = (mk_ins (make_instr (I.ins_Mul64) src)) [@ "opaque_to_smt"] let va_codegen_success_Mul64Wrap src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Mul64Wrap va_b0 va_s0 src = va_reveal_opaque (`%va_code_Mul64Wrap) (va_code_Mul64Wrap src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Mul64) src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Mul64) src)) va_s0 in lemma_fundamental_div_mod (va_get_reg64 rRax va_old_s) (va_eval_opr64 va_old_s src); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Mul64Wrap src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Mul64Wrap (va_code_Mul64Wrap src) va_s0 src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRax va_sM (va_update_flags va_sM (va_update_ok va_sM va_s0))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRax; va_Mod_flags]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Mulx64 [@ "opaque_to_smt"] let va_code_Mulx64 dst_hi dst_lo src = (mk_ins (make_instr (I.ins_Mulx64) dst_hi dst_lo src)) [@ "opaque_to_smt"] let va_codegen_success_Mulx64 dst_hi dst_lo src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Mulx64 va_b0 va_s0 dst_hi dst_lo src = va_reveal_opaque (`%va_code_Mulx64) (va_code_Mulx64 dst_hi dst_lo src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Mulx64) dst_hi dst_lo src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Mulx64) dst_hi dst_lo src)) va_s0 in lemma_fundamental_div_mod (va_get_reg64 rRdx va_old_s) (va_eval_opr64 va_old_s src); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Mulx64 dst_hi dst_lo src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Mulx64 (va_code_Mulx64 dst_hi dst_lo src) va_s0 dst_hi dst_lo src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst_lo va_sM (va_update_operand_dst_opr64 dst_hi va_sM va_s0)))); va_lemma_norm_mods ([va_mod_dst_opr64 dst_lo; va_mod_dst_opr64 dst_hi]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- lemma_mul_nat //-- //-- lemma_mul_in_bounds //-- //-- IMul64 [@ "opaque_to_smt"] let va_code_IMul64 dst src = (mk_ins (make_instr (I.ins_IMul64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_IMul64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_IMul64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_IMul64) (va_code_IMul64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_IMul64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_IMul64) dst src)) va_s0 in lemma_mul_nat (va_eval_dst_opr64 va_old_s dst) (va_eval_opr64 va_old_s src); lemma_mul_in_bounds (va_eval_dst_opr64 va_old_s dst) (va_eval_opr64 va_old_s src); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_IMul64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_IMul64 (va_code_IMul64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Xor64 [@ "opaque_to_smt"] let va_code_Xor64 dst src = (mk_ins (make_instr_annotate (I.ins_Xor64) (S.AnnotateXor64 ()) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Xor64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Xor64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Xor64) (va_code_Xor64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr_annotate (I.ins_Xor64) (S.AnnotateXor64 ()) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr_annotate (I.ins_Xor64) (S.AnnotateXor64 ()) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Xor64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Xor64 (va_code_Xor64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- And64 [@ "opaque_to_smt"] let va_code_And64 dst src = (mk_ins (make_instr (I.ins_And64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_And64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_And64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_And64) (va_code_And64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_And64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_And64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_And64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_And64 (va_code_And64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Shl64 [@ "opaque_to_smt"] let va_code_Shl64 dst amt = (mk_ins (make_instr (I.ins_Shl64) dst amt)) [@ "opaque_to_smt"] let va_codegen_success_Shl64 dst amt = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Shl64 va_b0 va_s0 dst amt = va_reveal_opaque (`%va_code_Shl64) (va_code_Shl64 dst amt); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Shl64) dst amt)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Shl64) dst amt)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Shl64 dst amt va_s0 va_k = let (va_sM, va_f0) = va_lemma_Shl64 (va_code_Shl64 dst amt) va_s0 dst amt in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Shr64 [@ "opaque_to_smt"] let va_code_Shr64 dst amt = (mk_ins (make_instr (I.ins_Shr64) dst amt)) [@ "opaque_to_smt"] let va_codegen_success_Shr64 dst amt = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Shr64 va_b0 va_s0 dst amt = va_reveal_opaque (`%va_code_Shr64) (va_code_Shr64 dst amt); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Shr64) dst amt)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Shr64) dst amt)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Shr64 dst amt va_s0 va_k = let (va_sM, va_f0) = va_lemma_Shr64 (va_code_Shr64 dst amt) va_s0 dst amt in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_AES [@ "opaque_to_smt"] let va_code_Cpuid_AES () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_AES () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_AES va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_AES) (va_code_Cpuid_AES ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_AES va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_AES (va_code_Cpuid_AES ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Sha [@ "opaque_to_smt"] let va_code_Cpuid_Sha () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Sha () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Sha va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Sha) (va_code_Cpuid_Sha ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Sha va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Sha (va_code_Cpuid_Sha ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Adx_Bmi2 [@ "opaque_to_smt"] let va_code_Cpuid_Adx_Bmi2 () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Adx_Bmi2 () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Adx_Bmi2 va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Adx_Bmi2) (va_code_Cpuid_Adx_Bmi2 ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Adx_Bmi2 va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Adx_Bmi2 (va_code_Cpuid_Adx_Bmi2 ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Avx [@ "opaque_to_smt"] let va_code_Cpuid_Avx () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Avx () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Avx va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Avx) (va_code_Cpuid_Avx ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Avx va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Avx (va_code_Cpuid_Avx ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Avx2 [@ "opaque_to_smt"] let va_code_Cpuid_Avx2 () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Avx2 () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Avx2 va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Avx2) (va_code_Cpuid_Avx2 ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Avx2 va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Avx2 (va_code_Cpuid_Avx2 ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Sse [@ "opaque_to_smt"] let va_code_Cpuid_Sse () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Sse () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Sse va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Sse) (va_code_Cpuid_Sse ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Sse va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Sse (va_code_Cpuid_Sse ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Movbe [@ "opaque_to_smt"] let va_code_Cpuid_Movbe () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Movbe () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Movbe va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Movbe) (va_code_Cpuid_Movbe ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Movbe va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Movbe (va_code_Cpuid_Movbe ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Rdrand [@ "opaque_to_smt"] let va_code_Cpuid_Rdrand () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Rdrand () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Rdrand va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Rdrand) (va_code_Cpuid_Rdrand ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Rdrand va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Rdrand (va_code_Cpuid_Rdrand ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Avx512 [@ "opaque_to_smt"] let va_code_Cpuid_Avx512 () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Avx512 () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Avx512 va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Avx512) (va_code_Cpuid_Avx512 ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Avx512 va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Avx512 (va_code_Cpuid_Avx512 ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Osxsave [@ "opaque_to_smt"] let va_code_Cpuid_Osxsave () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Osxsave () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Osxsave va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Osxsave) (va_code_Cpuid_Osxsave ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Osxsave va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Osxsave (va_code_Cpuid_Osxsave ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Xgetbv_Avx [@ "opaque_to_smt"] let va_code_Xgetbv_Avx () = (mk_ins (make_instr (I.ins_Xgetbv))) [@ "opaque_to_smt"] let va_codegen_success_Xgetbv_Avx () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Xgetbv_Avx va_b0 va_s0 = va_reveal_opaque (`%va_code_Xgetbv_Avx) (va_code_Xgetbv_Avx ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Xgetbv))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Xgetbv))) va_s0 in Vale.X64.CPU_Features_s.xgetbv_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Xgetbv_Avx va_s0 va_k = let (va_sM, va_f0) = va_lemma_Xgetbv_Avx (va_code_Xgetbv_Avx ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Xgetbv_Avx512 [@ "opaque_to_smt"] let va_code_Xgetbv_Avx512 () = (mk_ins (make_instr (I.ins_Xgetbv))) [@ "opaque_to_smt"] let va_codegen_success_Xgetbv_Avx512 () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Xgetbv_Avx512 va_b0 va_s0 = va_reveal_opaque (`%va_code_Xgetbv_Avx512) (va_code_Xgetbv_Avx512 ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Xgetbv))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Xgetbv))) va_s0 in Vale.X64.CPU_Features_s.xgetbv_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Xgetbv_Avx512 va_s0 va_k = let (va_sM, va_f0) = va_lemma_Xgetbv_Avx512 (va_code_Xgetbv_Avx512 ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Nat64Equal [@ "opaque_to_smt"] let va_code_Nat64Equal dst src = (va_Block (va_CCons (va_code_Sub64Wrap (va_coerce_reg_opr64_to_dst_opr64 src) (va_const_opr64 18446744073709551615)) (va_CCons (va_code_Mov64 (va_coerce_reg_opr64_to_dst_opr64 dst) (va_const_opr64 0)) (va_CCons (va_code_Adc64 (va_coerce_reg_opr64_to_dst_opr64 dst) (va_const_opr64 0)) (va_CNil ()))))) [@ "opaque_to_smt"] let va_codegen_success_Nat64Equal dst src = (va_pbool_and (va_codegen_success_Sub64Wrap (va_coerce_reg_opr64_to_dst_opr64 src) (va_const_opr64 18446744073709551615)) (va_pbool_and (va_codegen_success_Mov64 (va_coerce_reg_opr64_to_dst_opr64 dst) (va_const_opr64 0)) (va_pbool_and (va_codegen_success_Adc64 (va_coerce_reg_opr64_to_dst_opr64 dst) (va_const_opr64 0)) (va_ttrue ())))) [@"opaque_to_smt"] let va_lemma_Nat64Equal va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Nat64Equal) (va_code_Nat64Equal dst src); let (va_old_s:va_state) = va_s0 in let (va_b1:va_codes) = va_get_block va_b0 in let (va_s2, va_fc2) = va_lemma_Sub64Wrap (va_hd va_b1) va_s0 (va_coerce_reg_opr64_to_dst_opr64 src) (va_const_opr64 18446744073709551615) in let va_b2 = va_tl va_b1 in let (va_s3, va_fc3) = va_lemma_Mov64 (va_hd va_b2) va_s2 (va_coerce_reg_opr64_to_dst_opr64 dst) (va_const_opr64 0) in let va_b3 = va_tl va_b2 in let (va_s4, va_fc4) = va_lemma_Adc64 (va_hd va_b3) va_s3 (va_coerce_reg_opr64_to_dst_opr64 dst) (va_const_opr64 0) in let va_b4 = va_tl va_b3 in let (va_sM, va_f4) = va_lemma_empty_total va_s4 va_b4 in let va_f3 = va_lemma_merge_total va_b3 va_s3 va_fc4 va_s4 va_f4 va_sM in let va_f2 = va_lemma_merge_total va_b2 va_s2 va_fc3 va_s3 va_f3 va_sM in let va_fM = va_lemma_merge_total va_b1 va_s0 va_fc2 va_s2 va_f2 va_sM in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Nat64Equal dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Nat64Equal (va_code_Nat64Equal dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_reg_opr64 src va_sM (va_update_operand_reg_opr64 dst va_sM va_s0))))); va_lemma_norm_mods ([va_Mod_flags; va_mod_reg_opr64 src; va_mod_reg_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Comment [@ "opaque_to_smt"] let va_code_Comment c = (mk_ins (make_instr_annotate (I.ins_Comment c) (S.AnnotateComment c))) [@ "opaque_to_smt"] let va_codegen_success_Comment c = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Comment va_b0 va_s0 c = va_reveal_opaque (`%va_code_Comment) (va_code_Comment c); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr_annotate (I.ins_Comment c) (S.AnnotateComment c))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr_annotate (I.ins_Comment c) (S.AnnotateComment c))) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Comment c va_s0 va_k = let (va_sM, va_f0) = va_lemma_Comment (va_code_Comment c) va_s0 c in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_ok va_sM va_s0)); va_lemma_norm_mods ([]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- LargeComment [@ "opaque_to_smt"] let va_code_LargeComment c = (mk_ins (make_instr_annotate (I.ins_LargeComment c) (S.AnnotateLargeComment c))) [@ "opaque_to_smt"] let va_codegen_success_LargeComment c = (va_ttrue ()) [@"opaque_to_smt"]
false
false
Vale.X64.InsBasic.fst
{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 5, "initial_ifuel": 0, "max_fuel": 5, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": true, "smtencoding_l_arith_repr": "native", "smtencoding_nl_arith_repr": "wrapped", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": false, "z3cliopt": [ "smt.arith.nl=false", "smt.QI.EAGER_THRESHOLD=100", "smt.CASE_SPLIT=3" ], "z3refresh": false, "z3rlimit": 20, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }
null
val va_lemma_LargeComment : va_b0:va_code -> va_s0:va_state -> c:string -> Ghost (va_state & va_fuel) (requires (va_require_total va_b0 (va_code_LargeComment c) va_s0 /\ va_get_ok va_s0)) (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\ va_state_eq va_sM (va_update_ok va_sM va_s0)))
[]
Vale.X64.InsBasic.va_lemma_LargeComment
{ "file_name": "obj/Vale.X64.InsBasic.fst", "git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e", "git_url": "https://github.com/hacl-star/hacl-star.git", "project_name": "hacl-star" }
va_b0: Vale.X64.Decls.va_code -> va_s0: Vale.X64.Decls.va_state -> c: Prims.string -> Prims.Ghost (Vale.X64.Decls.va_state * Vale.X64.Decls.va_fuel)
{ "end_col": 16, "end_line": 1084, "start_col": 2, "start_line": 1078 }
Prims.Ghost
val va_wpProof_Newline : va_s0:va_state -> va_k:(va_state -> unit -> Type0) -> Ghost (va_state & va_fuel & unit) (requires (va_t_require va_s0 /\ va_wp_Newline va_s0 va_k)) (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Newline ()) ([]) va_s0 va_k ((va_sM, va_f0, va_g))))
[ { "abbrev": true, "full_module": "Vale.X64.Machine_Semantics_s", "short_module": "S" }, { "abbrev": true, "full_module": "Vale.X64.Instructions_s", "short_module": "I" }, { "abbrev": false, "full_module": "Vale.X64.Stack_i", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.Memory", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.Taint_Semantics", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.InsLemmas", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.StateLemmas", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.CPU_Features_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.QuickCode", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.Decls", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.State", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.Machine_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Arch.Types", "short_module": null }, { "abbrev": false, "full_module": "Vale.Arch.HeapImpl", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Types_s", "short_module": null }, { "abbrev": false, "full_module": "FStar.Mul", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]
false
let va_wpProof_Newline va_s0 va_k = let (va_sM, va_f0) = va_lemma_Newline (va_code_Newline ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_ok va_sM va_s0)); va_lemma_norm_mods ([]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g)
val va_wpProof_Newline : va_s0:va_state -> va_k:(va_state -> unit -> Type0) -> Ghost (va_state & va_fuel & unit) (requires (va_t_require va_s0 /\ va_wp_Newline va_s0 va_k)) (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Newline ()) ([]) va_s0 va_k ((va_sM, va_f0, va_g)))) let va_wpProof_Newline va_s0 va_k =
false
null
false
let va_sM, va_f0 = va_lemma_Newline (va_code_Newline ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_ok va_sM va_s0)); va_lemma_norm_mods ([]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g)
{ "checked_file": "Vale.X64.InsBasic.fst.checked", "dependencies": [ "Vale.X64.Taint_Semantics.fst.checked", "Vale.X64.StateLemmas.fsti.checked", "Vale.X64.Stack_i.fsti.checked", "Vale.X64.Memory.fsti.checked", "Vale.X64.Machine_Semantics_s.fst.checked", "Vale.X64.Instructions_s.fsti.checked", "Vale.X64.InsLemmas.fsti.checked", "Vale.X64.Decls.fst.checked", "Vale.X64.CPU_Features_s.fst.checked", "Vale.Arch.Types.fsti.checked", "prims.fst.checked", "FStar.UInt.fsti.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Math.Lemmas.fst.checked" ], "interface_file": true, "source_file": "Vale.X64.InsBasic.fst" }
[]
[ "Vale.X64.Decls.va_state", "Prims.unit", "Vale.X64.Decls.va_fuel", "FStar.Pervasives.Native.Mktuple3", "Vale.X64.QuickCode.va_lemma_norm_mods", "Prims.Nil", "Vale.X64.QuickCode.mod_t", "Prims._assert", "Vale.X64.Decls.va_state_eq", "Vale.X64.Decls.va_update_ok", "Vale.X64.Decls.va_lemma_upd_update", "FStar.Pervasives.Native.tuple3", "FStar.Pervasives.Native.tuple2", "Vale.X64.State.vale_state", "Vale.X64.InsBasic.va_lemma_Newline", "Vale.X64.InsBasic.va_code_Newline" ]
[]
module Vale.X64.InsBasic open Vale.X64 open Vale.X64.StateLemmas open Vale.X64.InsLemmas open Vale.X64.Taint_Semantics open Vale.X64.CPU_Features_s open Vale.X64.Memory open Vale.X64.Stack_i module I = Vale.X64.Instructions_s module S = Vale.X64.Machine_Semantics_s friend Vale.X64.Decls #reset-options "--initial_fuel 5 --max_fuel 5 --max_ifuel 2 --z3rlimit 20" //-- Mov64 [@ "opaque_to_smt"] let va_code_Mov64 dst src = (mk_ins (make_instr_annotate (I.ins_Mov64) (S.AnnotateMov64 ()) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Mov64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Mov64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Mov64) (va_code_Mov64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr_annotate (I.ins_Mov64) (S.AnnotateMov64 ()) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr_annotate (I.ins_Mov64) (S.AnnotateMov64 ()) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Mov64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Mov64 (va_code_Mov64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0))); va_lemma_norm_mods ([va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cmovc64 [@ "opaque_to_smt"] let va_code_Cmovc64 dst src = (mk_ins (make_instr (I.ins_Cmovc64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Cmovc64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cmovc64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Cmovc64) (va_code_Cmovc64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cmovc64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cmovc64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cmovc64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cmovc64 (va_code_Cmovc64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0))); va_lemma_norm_mods ([va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Add64 [@ "opaque_to_smt"] let va_code_Add64 dst src = (mk_ins (make_instr (I.ins_Add64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Add64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Add64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Add64) (va_code_Add64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Add64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Add64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Add64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Add64 (va_code_Add64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Add64Wrap [@ "opaque_to_smt"] let va_code_Add64Wrap dst src = (mk_ins (make_instr (I.ins_Add64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Add64Wrap dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Add64Wrap va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Add64Wrap) (va_code_Add64Wrap dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Add64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Add64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Add64Wrap dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Add64Wrap (va_code_Add64Wrap dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- AddLea64 [@ "opaque_to_smt"] let va_code_AddLea64 dst src1 src2 = (mk_ins (make_instr (I.ins_AddLea64) dst src1 src2)) [@ "opaque_to_smt"] let va_codegen_success_AddLea64 dst src1 src2 = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_AddLea64 va_b0 va_s0 dst src1 src2 = va_reveal_opaque (`%va_code_AddLea64) (va_code_AddLea64 dst src1 src2); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_AddLea64) dst src1 src2)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_AddLea64) dst src1 src2)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_AddLea64 dst src1 src2 va_s0 va_k = let (va_sM, va_f0) = va_lemma_AddLea64 (va_code_AddLea64 dst src1 src2) va_s0 dst src1 src2 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0))); va_lemma_norm_mods ([va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Adc64 [@ "opaque_to_smt"] let va_code_Adc64 dst src = (mk_ins (make_instr (I.ins_AddCarry64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Adc64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Adc64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Adc64) (va_code_Adc64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_AddCarry64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_AddCarry64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Adc64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Adc64 (va_code_Adc64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Adc64Wrap [@ "opaque_to_smt"] let va_code_Adc64Wrap dst src = (mk_ins (make_instr (I.ins_AddCarry64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Adc64Wrap dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Adc64Wrap va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Adc64Wrap) (va_code_Adc64Wrap dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_AddCarry64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_AddCarry64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Adc64Wrap dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Adc64Wrap (va_code_Adc64Wrap dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Adcx64Wrap #push-options "--smtencoding.nl_arith_repr boxwrap" [@ "opaque_to_smt"] let va_code_Adcx64Wrap dst src = (mk_ins (make_instr (I.ins_Adcx64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Adcx64Wrap dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Adcx64Wrap va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Adcx64Wrap) (va_code_Adcx64Wrap dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Adcx64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Adcx64) dst src)) va_s0 in assert (Vale.Arch.Types.add_wrap64 (Vale.Arch.Types.add_wrap64 (va_eval_dst_opr64 va_old_s dst) (va_eval_opr64 va_old_s src)) (if Vale.X64.Decls.cf (va_get_flags va_old_s) then 1 else 0) == (va_eval_dst_opr64 va_old_s dst + va_eval_opr64 va_old_s src + (if Vale.X64.Decls.cf (va_get_flags va_old_s) then 1 else 0)) `op_Modulus` pow2_64); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Adcx64Wrap dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Adcx64Wrap (va_code_Adcx64Wrap dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) #pop-options //-- //-- Adox64Wrap [@ "opaque_to_smt"] let va_code_Adox64Wrap dst src = (mk_ins (make_instr (I.ins_Adox64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Adox64Wrap dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Adox64Wrap va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Adox64Wrap) (va_code_Adox64Wrap dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Adox64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Adox64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Adox64Wrap dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Adox64Wrap (va_code_Adox64Wrap dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Sub64 [@ "opaque_to_smt"] let va_code_Sub64 dst src = (mk_ins (make_instr (I.ins_Sub64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Sub64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Sub64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Sub64) (va_code_Sub64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Sub64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Sub64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Sub64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Sub64 (va_code_Sub64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Sub64Wrap [@ "opaque_to_smt"] let va_code_Sub64Wrap dst src = (mk_ins (make_instr (I.ins_Sub64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Sub64Wrap dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Sub64Wrap va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Sub64Wrap) (va_code_Sub64Wrap dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Sub64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Sub64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Sub64Wrap dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Sub64Wrap (va_code_Sub64Wrap dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Sbb64 [@ "opaque_to_smt"] let va_code_Sbb64 dst src = (mk_ins (make_instr (I.ins_Sbb64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Sbb64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Sbb64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Sbb64) (va_code_Sbb64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Sbb64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Sbb64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Sbb64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Sbb64 (va_code_Sbb64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- #restart-solver #push-options "--max_fuel 0 --max_ifuel 0 --using_facts_from 'Prims FStar.UInt'" let lemma_fundamental_div_mod (a b:nat64) : Lemma (pow2_64 * (FStar.UInt.mul_div #64 a b) + (FStar.UInt.mul_mod #64 a b) == a * b) = FStar.Math.Lemmas.lemma_div_mod (a * b) pow2_64 #pop-options //-- lemma_fundamental_div_mod //-- //-- Mul64Wrap [@ "opaque_to_smt"] let va_code_Mul64Wrap src = (mk_ins (make_instr (I.ins_Mul64) src)) [@ "opaque_to_smt"] let va_codegen_success_Mul64Wrap src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Mul64Wrap va_b0 va_s0 src = va_reveal_opaque (`%va_code_Mul64Wrap) (va_code_Mul64Wrap src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Mul64) src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Mul64) src)) va_s0 in lemma_fundamental_div_mod (va_get_reg64 rRax va_old_s) (va_eval_opr64 va_old_s src); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Mul64Wrap src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Mul64Wrap (va_code_Mul64Wrap src) va_s0 src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRax va_sM (va_update_flags va_sM (va_update_ok va_sM va_s0))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRax; va_Mod_flags]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Mulx64 [@ "opaque_to_smt"] let va_code_Mulx64 dst_hi dst_lo src = (mk_ins (make_instr (I.ins_Mulx64) dst_hi dst_lo src)) [@ "opaque_to_smt"] let va_codegen_success_Mulx64 dst_hi dst_lo src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Mulx64 va_b0 va_s0 dst_hi dst_lo src = va_reveal_opaque (`%va_code_Mulx64) (va_code_Mulx64 dst_hi dst_lo src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Mulx64) dst_hi dst_lo src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Mulx64) dst_hi dst_lo src)) va_s0 in lemma_fundamental_div_mod (va_get_reg64 rRdx va_old_s) (va_eval_opr64 va_old_s src); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Mulx64 dst_hi dst_lo src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Mulx64 (va_code_Mulx64 dst_hi dst_lo src) va_s0 dst_hi dst_lo src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst_lo va_sM (va_update_operand_dst_opr64 dst_hi va_sM va_s0)))); va_lemma_norm_mods ([va_mod_dst_opr64 dst_lo; va_mod_dst_opr64 dst_hi]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- lemma_mul_nat //-- //-- lemma_mul_in_bounds //-- //-- IMul64 [@ "opaque_to_smt"] let va_code_IMul64 dst src = (mk_ins (make_instr (I.ins_IMul64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_IMul64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_IMul64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_IMul64) (va_code_IMul64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_IMul64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_IMul64) dst src)) va_s0 in lemma_mul_nat (va_eval_dst_opr64 va_old_s dst) (va_eval_opr64 va_old_s src); lemma_mul_in_bounds (va_eval_dst_opr64 va_old_s dst) (va_eval_opr64 va_old_s src); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_IMul64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_IMul64 (va_code_IMul64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Xor64 [@ "opaque_to_smt"] let va_code_Xor64 dst src = (mk_ins (make_instr_annotate (I.ins_Xor64) (S.AnnotateXor64 ()) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Xor64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Xor64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Xor64) (va_code_Xor64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr_annotate (I.ins_Xor64) (S.AnnotateXor64 ()) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr_annotate (I.ins_Xor64) (S.AnnotateXor64 ()) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Xor64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Xor64 (va_code_Xor64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- And64 [@ "opaque_to_smt"] let va_code_And64 dst src = (mk_ins (make_instr (I.ins_And64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_And64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_And64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_And64) (va_code_And64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_And64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_And64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_And64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_And64 (va_code_And64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Shl64 [@ "opaque_to_smt"] let va_code_Shl64 dst amt = (mk_ins (make_instr (I.ins_Shl64) dst amt)) [@ "opaque_to_smt"] let va_codegen_success_Shl64 dst amt = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Shl64 va_b0 va_s0 dst amt = va_reveal_opaque (`%va_code_Shl64) (va_code_Shl64 dst amt); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Shl64) dst amt)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Shl64) dst amt)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Shl64 dst amt va_s0 va_k = let (va_sM, va_f0) = va_lemma_Shl64 (va_code_Shl64 dst amt) va_s0 dst amt in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Shr64 [@ "opaque_to_smt"] let va_code_Shr64 dst amt = (mk_ins (make_instr (I.ins_Shr64) dst amt)) [@ "opaque_to_smt"] let va_codegen_success_Shr64 dst amt = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Shr64 va_b0 va_s0 dst amt = va_reveal_opaque (`%va_code_Shr64) (va_code_Shr64 dst amt); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Shr64) dst amt)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Shr64) dst amt)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Shr64 dst amt va_s0 va_k = let (va_sM, va_f0) = va_lemma_Shr64 (va_code_Shr64 dst amt) va_s0 dst amt in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_AES [@ "opaque_to_smt"] let va_code_Cpuid_AES () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_AES () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_AES va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_AES) (va_code_Cpuid_AES ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_AES va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_AES (va_code_Cpuid_AES ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Sha [@ "opaque_to_smt"] let va_code_Cpuid_Sha () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Sha () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Sha va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Sha) (va_code_Cpuid_Sha ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Sha va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Sha (va_code_Cpuid_Sha ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Adx_Bmi2 [@ "opaque_to_smt"] let va_code_Cpuid_Adx_Bmi2 () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Adx_Bmi2 () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Adx_Bmi2 va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Adx_Bmi2) (va_code_Cpuid_Adx_Bmi2 ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Adx_Bmi2 va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Adx_Bmi2 (va_code_Cpuid_Adx_Bmi2 ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Avx [@ "opaque_to_smt"] let va_code_Cpuid_Avx () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Avx () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Avx va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Avx) (va_code_Cpuid_Avx ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Avx va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Avx (va_code_Cpuid_Avx ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Avx2 [@ "opaque_to_smt"] let va_code_Cpuid_Avx2 () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Avx2 () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Avx2 va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Avx2) (va_code_Cpuid_Avx2 ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Avx2 va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Avx2 (va_code_Cpuid_Avx2 ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Sse [@ "opaque_to_smt"] let va_code_Cpuid_Sse () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Sse () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Sse va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Sse) (va_code_Cpuid_Sse ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Sse va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Sse (va_code_Cpuid_Sse ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Movbe [@ "opaque_to_smt"] let va_code_Cpuid_Movbe () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Movbe () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Movbe va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Movbe) (va_code_Cpuid_Movbe ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Movbe va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Movbe (va_code_Cpuid_Movbe ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Rdrand [@ "opaque_to_smt"] let va_code_Cpuid_Rdrand () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Rdrand () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Rdrand va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Rdrand) (va_code_Cpuid_Rdrand ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Rdrand va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Rdrand (va_code_Cpuid_Rdrand ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Avx512 [@ "opaque_to_smt"] let va_code_Cpuid_Avx512 () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Avx512 () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Avx512 va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Avx512) (va_code_Cpuid_Avx512 ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Avx512 va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Avx512 (va_code_Cpuid_Avx512 ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Osxsave [@ "opaque_to_smt"] let va_code_Cpuid_Osxsave () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Osxsave () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Osxsave va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Osxsave) (va_code_Cpuid_Osxsave ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Osxsave va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Osxsave (va_code_Cpuid_Osxsave ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Xgetbv_Avx [@ "opaque_to_smt"] let va_code_Xgetbv_Avx () = (mk_ins (make_instr (I.ins_Xgetbv))) [@ "opaque_to_smt"] let va_codegen_success_Xgetbv_Avx () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Xgetbv_Avx va_b0 va_s0 = va_reveal_opaque (`%va_code_Xgetbv_Avx) (va_code_Xgetbv_Avx ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Xgetbv))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Xgetbv))) va_s0 in Vale.X64.CPU_Features_s.xgetbv_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Xgetbv_Avx va_s0 va_k = let (va_sM, va_f0) = va_lemma_Xgetbv_Avx (va_code_Xgetbv_Avx ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Xgetbv_Avx512 [@ "opaque_to_smt"] let va_code_Xgetbv_Avx512 () = (mk_ins (make_instr (I.ins_Xgetbv))) [@ "opaque_to_smt"] let va_codegen_success_Xgetbv_Avx512 () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Xgetbv_Avx512 va_b0 va_s0 = va_reveal_opaque (`%va_code_Xgetbv_Avx512) (va_code_Xgetbv_Avx512 ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Xgetbv))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Xgetbv))) va_s0 in Vale.X64.CPU_Features_s.xgetbv_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Xgetbv_Avx512 va_s0 va_k = let (va_sM, va_f0) = va_lemma_Xgetbv_Avx512 (va_code_Xgetbv_Avx512 ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Nat64Equal [@ "opaque_to_smt"] let va_code_Nat64Equal dst src = (va_Block (va_CCons (va_code_Sub64Wrap (va_coerce_reg_opr64_to_dst_opr64 src) (va_const_opr64 18446744073709551615)) (va_CCons (va_code_Mov64 (va_coerce_reg_opr64_to_dst_opr64 dst) (va_const_opr64 0)) (va_CCons (va_code_Adc64 (va_coerce_reg_opr64_to_dst_opr64 dst) (va_const_opr64 0)) (va_CNil ()))))) [@ "opaque_to_smt"] let va_codegen_success_Nat64Equal dst src = (va_pbool_and (va_codegen_success_Sub64Wrap (va_coerce_reg_opr64_to_dst_opr64 src) (va_const_opr64 18446744073709551615)) (va_pbool_and (va_codegen_success_Mov64 (va_coerce_reg_opr64_to_dst_opr64 dst) (va_const_opr64 0)) (va_pbool_and (va_codegen_success_Adc64 (va_coerce_reg_opr64_to_dst_opr64 dst) (va_const_opr64 0)) (va_ttrue ())))) [@"opaque_to_smt"] let va_lemma_Nat64Equal va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Nat64Equal) (va_code_Nat64Equal dst src); let (va_old_s:va_state) = va_s0 in let (va_b1:va_codes) = va_get_block va_b0 in let (va_s2, va_fc2) = va_lemma_Sub64Wrap (va_hd va_b1) va_s0 (va_coerce_reg_opr64_to_dst_opr64 src) (va_const_opr64 18446744073709551615) in let va_b2 = va_tl va_b1 in let (va_s3, va_fc3) = va_lemma_Mov64 (va_hd va_b2) va_s2 (va_coerce_reg_opr64_to_dst_opr64 dst) (va_const_opr64 0) in let va_b3 = va_tl va_b2 in let (va_s4, va_fc4) = va_lemma_Adc64 (va_hd va_b3) va_s3 (va_coerce_reg_opr64_to_dst_opr64 dst) (va_const_opr64 0) in let va_b4 = va_tl va_b3 in let (va_sM, va_f4) = va_lemma_empty_total va_s4 va_b4 in let va_f3 = va_lemma_merge_total va_b3 va_s3 va_fc4 va_s4 va_f4 va_sM in let va_f2 = va_lemma_merge_total va_b2 va_s2 va_fc3 va_s3 va_f3 va_sM in let va_fM = va_lemma_merge_total va_b1 va_s0 va_fc2 va_s2 va_f2 va_sM in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Nat64Equal dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Nat64Equal (va_code_Nat64Equal dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_reg_opr64 src va_sM (va_update_operand_reg_opr64 dst va_sM va_s0))))); va_lemma_norm_mods ([va_Mod_flags; va_mod_reg_opr64 src; va_mod_reg_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Comment [@ "opaque_to_smt"] let va_code_Comment c = (mk_ins (make_instr_annotate (I.ins_Comment c) (S.AnnotateComment c))) [@ "opaque_to_smt"] let va_codegen_success_Comment c = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Comment va_b0 va_s0 c = va_reveal_opaque (`%va_code_Comment) (va_code_Comment c); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr_annotate (I.ins_Comment c) (S.AnnotateComment c))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr_annotate (I.ins_Comment c) (S.AnnotateComment c))) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Comment c va_s0 va_k = let (va_sM, va_f0) = va_lemma_Comment (va_code_Comment c) va_s0 c in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_ok va_sM va_s0)); va_lemma_norm_mods ([]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- LargeComment [@ "opaque_to_smt"] let va_code_LargeComment c = (mk_ins (make_instr_annotate (I.ins_LargeComment c) (S.AnnotateLargeComment c))) [@ "opaque_to_smt"] let va_codegen_success_LargeComment c = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_LargeComment va_b0 va_s0 c = va_reveal_opaque (`%va_code_LargeComment) (va_code_LargeComment c); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr_annotate (I.ins_LargeComment c) (S.AnnotateLargeComment c))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr_annotate (I.ins_LargeComment c) (S.AnnotateLargeComment c))) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_LargeComment c va_s0 va_k = let (va_sM, va_f0) = va_lemma_LargeComment (va_code_LargeComment c) va_s0 c in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_ok va_sM va_s0)); va_lemma_norm_mods ([]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- NoNewline [@ "opaque_to_smt"] let va_code_NoNewline () = (mk_ins (make_instr_annotate (I.ins_Space 0) (S.AnnotateSpace 0))) [@ "opaque_to_smt"] let va_codegen_success_NoNewline () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_NoNewline va_b0 va_s0 = va_reveal_opaque (`%va_code_NoNewline) (va_code_NoNewline ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr_annotate (I.ins_Space 0) (S.AnnotateSpace 0))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr_annotate (I.ins_Space 0) (S.AnnotateSpace 0))) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_NoNewline va_s0 va_k = let (va_sM, va_f0) = va_lemma_NoNewline (va_code_NoNewline ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_ok va_sM va_s0)); va_lemma_norm_mods ([]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Newline [@ "opaque_to_smt"] let va_code_Newline () = (mk_ins (make_instr_annotate (I.ins_Newline) (S.AnnotateNewline ()))) [@ "opaque_to_smt"] let va_codegen_success_Newline () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Newline va_b0 va_s0 = va_reveal_opaque (`%va_code_Newline) (va_code_Newline ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr_annotate (I.ins_Newline) (S.AnnotateNewline ()))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr_annotate (I.ins_Newline) (S.AnnotateNewline ()))) va_s0 in (va_sM, va_fM)
false
false
Vale.X64.InsBasic.fst
{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 5, "initial_ifuel": 0, "max_fuel": 5, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": true, "smtencoding_l_arith_repr": "native", "smtencoding_nl_arith_repr": "wrapped", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": false, "z3cliopt": [ "smt.arith.nl=false", "smt.QI.EAGER_THRESHOLD=100", "smt.CASE_SPLIT=3" ], "z3refresh": false, "z3rlimit": 20, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }
null
val va_wpProof_Newline : va_s0:va_state -> va_k:(va_state -> unit -> Type0) -> Ghost (va_state & va_fuel & unit) (requires (va_t_require va_s0 /\ va_wp_Newline va_s0 va_k)) (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Newline ()) ([]) va_s0 va_k ((va_sM, va_f0, va_g))))
[]
Vale.X64.InsBasic.va_wpProof_Newline
{ "file_name": "obj/Vale.X64.InsBasic.fst", "git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e", "git_url": "https://github.com/hacl-star/hacl-star.git", "project_name": "hacl-star" }
va_s0: Vale.X64.Decls.va_state -> va_k: (_: Vale.X64.Decls.va_state -> _: Prims.unit -> Type0) -> Prims.Ghost ((Vale.X64.Decls.va_state * Vale.X64.Decls.va_fuel) * Prims.unit)
{ "end_col": 22, "end_line": 1154, "start_col": 35, "start_line": 1148 }
Prims.Ghost
val va_lemma_Newline : va_b0:va_code -> va_s0:va_state -> Ghost (va_state & va_fuel) (requires (va_require_total va_b0 (va_code_Newline ()) va_s0 /\ va_get_ok va_s0)) (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\ va_state_eq va_sM (va_update_ok va_sM va_s0)))
[ { "abbrev": true, "full_module": "Vale.X64.Machine_Semantics_s", "short_module": "S" }, { "abbrev": true, "full_module": "Vale.X64.Instructions_s", "short_module": "I" }, { "abbrev": false, "full_module": "Vale.X64.Stack_i", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.Memory", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.Taint_Semantics", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.InsLemmas", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.StateLemmas", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.CPU_Features_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.QuickCode", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.Decls", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.State", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.Machine_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Arch.Types", "short_module": null }, { "abbrev": false, "full_module": "Vale.Arch.HeapImpl", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Types_s", "short_module": null }, { "abbrev": false, "full_module": "FStar.Mul", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]
false
let va_lemma_Newline va_b0 va_s0 = va_reveal_opaque (`%va_code_Newline) (va_code_Newline ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr_annotate (I.ins_Newline) (S.AnnotateNewline ()))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr_annotate (I.ins_Newline) (S.AnnotateNewline ()))) va_s0 in (va_sM, va_fM)
val va_lemma_Newline : va_b0:va_code -> va_s0:va_state -> Ghost (va_state & va_fuel) (requires (va_require_total va_b0 (va_code_Newline ()) va_s0 /\ va_get_ok va_s0)) (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\ va_state_eq va_sM (va_update_ok va_sM va_s0))) let va_lemma_Newline va_b0 va_s0 =
false
null
false
va_reveal_opaque (`%va_code_Newline) (va_code_Newline ()); let va_old_s:va_state = va_s0 in va_ins_lemma (mk_ins (make_instr_annotate (I.ins_Newline) (S.AnnotateNewline ()))) va_s0; let va_sM, va_fM = va_eval_ins (mk_ins (make_instr_annotate (I.ins_Newline) (S.AnnotateNewline ()))) va_s0 in (va_sM, va_fM)
{ "checked_file": "Vale.X64.InsBasic.fst.checked", "dependencies": [ "Vale.X64.Taint_Semantics.fst.checked", "Vale.X64.StateLemmas.fsti.checked", "Vale.X64.Stack_i.fsti.checked", "Vale.X64.Memory.fsti.checked", "Vale.X64.Machine_Semantics_s.fst.checked", "Vale.X64.Instructions_s.fsti.checked", "Vale.X64.InsLemmas.fsti.checked", "Vale.X64.Decls.fst.checked", "Vale.X64.CPU_Features_s.fst.checked", "Vale.Arch.Types.fsti.checked", "prims.fst.checked", "FStar.UInt.fsti.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Math.Lemmas.fst.checked" ], "interface_file": true, "source_file": "Vale.X64.InsBasic.fst" }
[]
[ "Vale.X64.Decls.va_code", "Vale.X64.Decls.va_state", "Vale.X64.State.vale_state", "Vale.X64.Lemmas.fuel", "FStar.Pervasives.Native.Mktuple2", "Vale.X64.Decls.va_fuel", "FStar.Pervasives.Native.tuple2", "Prims.nat", "Vale.X64.Decls.va_eval_ins", "Vale.X64.Taint_Semantics.mk_ins", "Vale.X64.InsLemmas.make_instr_annotate", "Prims.Nil", "Vale.X64.Instruction_s.instr_out", "Vale.X64.Instruction_s.instr_operand", "Vale.X64.Instruction_s.PreserveFlags", "Vale.X64.Instructions_s.ins_Newline", "Vale.X64.Machine_Semantics_s.AnnotateNewline", "Vale.X64.Instruction_s.InstrTypeRecord", "Prims.unit", "Vale.X64.Decls.va_ins_lemma", "Vale.X64.Decls.va_reveal_opaque", "Vale.X64.InsBasic.va_code_Newline" ]
[]
module Vale.X64.InsBasic open Vale.X64 open Vale.X64.StateLemmas open Vale.X64.InsLemmas open Vale.X64.Taint_Semantics open Vale.X64.CPU_Features_s open Vale.X64.Memory open Vale.X64.Stack_i module I = Vale.X64.Instructions_s module S = Vale.X64.Machine_Semantics_s friend Vale.X64.Decls #reset-options "--initial_fuel 5 --max_fuel 5 --max_ifuel 2 --z3rlimit 20" //-- Mov64 [@ "opaque_to_smt"] let va_code_Mov64 dst src = (mk_ins (make_instr_annotate (I.ins_Mov64) (S.AnnotateMov64 ()) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Mov64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Mov64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Mov64) (va_code_Mov64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr_annotate (I.ins_Mov64) (S.AnnotateMov64 ()) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr_annotate (I.ins_Mov64) (S.AnnotateMov64 ()) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Mov64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Mov64 (va_code_Mov64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0))); va_lemma_norm_mods ([va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cmovc64 [@ "opaque_to_smt"] let va_code_Cmovc64 dst src = (mk_ins (make_instr (I.ins_Cmovc64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Cmovc64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cmovc64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Cmovc64) (va_code_Cmovc64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cmovc64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cmovc64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cmovc64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cmovc64 (va_code_Cmovc64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0))); va_lemma_norm_mods ([va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Add64 [@ "opaque_to_smt"] let va_code_Add64 dst src = (mk_ins (make_instr (I.ins_Add64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Add64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Add64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Add64) (va_code_Add64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Add64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Add64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Add64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Add64 (va_code_Add64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Add64Wrap [@ "opaque_to_smt"] let va_code_Add64Wrap dst src = (mk_ins (make_instr (I.ins_Add64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Add64Wrap dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Add64Wrap va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Add64Wrap) (va_code_Add64Wrap dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Add64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Add64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Add64Wrap dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Add64Wrap (va_code_Add64Wrap dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- AddLea64 [@ "opaque_to_smt"] let va_code_AddLea64 dst src1 src2 = (mk_ins (make_instr (I.ins_AddLea64) dst src1 src2)) [@ "opaque_to_smt"] let va_codegen_success_AddLea64 dst src1 src2 = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_AddLea64 va_b0 va_s0 dst src1 src2 = va_reveal_opaque (`%va_code_AddLea64) (va_code_AddLea64 dst src1 src2); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_AddLea64) dst src1 src2)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_AddLea64) dst src1 src2)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_AddLea64 dst src1 src2 va_s0 va_k = let (va_sM, va_f0) = va_lemma_AddLea64 (va_code_AddLea64 dst src1 src2) va_s0 dst src1 src2 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0))); va_lemma_norm_mods ([va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Adc64 [@ "opaque_to_smt"] let va_code_Adc64 dst src = (mk_ins (make_instr (I.ins_AddCarry64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Adc64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Adc64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Adc64) (va_code_Adc64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_AddCarry64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_AddCarry64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Adc64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Adc64 (va_code_Adc64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Adc64Wrap [@ "opaque_to_smt"] let va_code_Adc64Wrap dst src = (mk_ins (make_instr (I.ins_AddCarry64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Adc64Wrap dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Adc64Wrap va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Adc64Wrap) (va_code_Adc64Wrap dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_AddCarry64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_AddCarry64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Adc64Wrap dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Adc64Wrap (va_code_Adc64Wrap dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Adcx64Wrap #push-options "--smtencoding.nl_arith_repr boxwrap" [@ "opaque_to_smt"] let va_code_Adcx64Wrap dst src = (mk_ins (make_instr (I.ins_Adcx64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Adcx64Wrap dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Adcx64Wrap va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Adcx64Wrap) (va_code_Adcx64Wrap dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Adcx64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Adcx64) dst src)) va_s0 in assert (Vale.Arch.Types.add_wrap64 (Vale.Arch.Types.add_wrap64 (va_eval_dst_opr64 va_old_s dst) (va_eval_opr64 va_old_s src)) (if Vale.X64.Decls.cf (va_get_flags va_old_s) then 1 else 0) == (va_eval_dst_opr64 va_old_s dst + va_eval_opr64 va_old_s src + (if Vale.X64.Decls.cf (va_get_flags va_old_s) then 1 else 0)) `op_Modulus` pow2_64); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Adcx64Wrap dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Adcx64Wrap (va_code_Adcx64Wrap dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) #pop-options //-- //-- Adox64Wrap [@ "opaque_to_smt"] let va_code_Adox64Wrap dst src = (mk_ins (make_instr (I.ins_Adox64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Adox64Wrap dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Adox64Wrap va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Adox64Wrap) (va_code_Adox64Wrap dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Adox64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Adox64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Adox64Wrap dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Adox64Wrap (va_code_Adox64Wrap dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Sub64 [@ "opaque_to_smt"] let va_code_Sub64 dst src = (mk_ins (make_instr (I.ins_Sub64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Sub64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Sub64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Sub64) (va_code_Sub64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Sub64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Sub64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Sub64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Sub64 (va_code_Sub64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Sub64Wrap [@ "opaque_to_smt"] let va_code_Sub64Wrap dst src = (mk_ins (make_instr (I.ins_Sub64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Sub64Wrap dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Sub64Wrap va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Sub64Wrap) (va_code_Sub64Wrap dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Sub64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Sub64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Sub64Wrap dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Sub64Wrap (va_code_Sub64Wrap dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Sbb64 [@ "opaque_to_smt"] let va_code_Sbb64 dst src = (mk_ins (make_instr (I.ins_Sbb64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Sbb64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Sbb64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Sbb64) (va_code_Sbb64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Sbb64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Sbb64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Sbb64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Sbb64 (va_code_Sbb64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- #restart-solver #push-options "--max_fuel 0 --max_ifuel 0 --using_facts_from 'Prims FStar.UInt'" let lemma_fundamental_div_mod (a b:nat64) : Lemma (pow2_64 * (FStar.UInt.mul_div #64 a b) + (FStar.UInt.mul_mod #64 a b) == a * b) = FStar.Math.Lemmas.lemma_div_mod (a * b) pow2_64 #pop-options //-- lemma_fundamental_div_mod //-- //-- Mul64Wrap [@ "opaque_to_smt"] let va_code_Mul64Wrap src = (mk_ins (make_instr (I.ins_Mul64) src)) [@ "opaque_to_smt"] let va_codegen_success_Mul64Wrap src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Mul64Wrap va_b0 va_s0 src = va_reveal_opaque (`%va_code_Mul64Wrap) (va_code_Mul64Wrap src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Mul64) src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Mul64) src)) va_s0 in lemma_fundamental_div_mod (va_get_reg64 rRax va_old_s) (va_eval_opr64 va_old_s src); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Mul64Wrap src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Mul64Wrap (va_code_Mul64Wrap src) va_s0 src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRax va_sM (va_update_flags va_sM (va_update_ok va_sM va_s0))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRax; va_Mod_flags]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Mulx64 [@ "opaque_to_smt"] let va_code_Mulx64 dst_hi dst_lo src = (mk_ins (make_instr (I.ins_Mulx64) dst_hi dst_lo src)) [@ "opaque_to_smt"] let va_codegen_success_Mulx64 dst_hi dst_lo src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Mulx64 va_b0 va_s0 dst_hi dst_lo src = va_reveal_opaque (`%va_code_Mulx64) (va_code_Mulx64 dst_hi dst_lo src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Mulx64) dst_hi dst_lo src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Mulx64) dst_hi dst_lo src)) va_s0 in lemma_fundamental_div_mod (va_get_reg64 rRdx va_old_s) (va_eval_opr64 va_old_s src); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Mulx64 dst_hi dst_lo src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Mulx64 (va_code_Mulx64 dst_hi dst_lo src) va_s0 dst_hi dst_lo src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst_lo va_sM (va_update_operand_dst_opr64 dst_hi va_sM va_s0)))); va_lemma_norm_mods ([va_mod_dst_opr64 dst_lo; va_mod_dst_opr64 dst_hi]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- lemma_mul_nat //-- //-- lemma_mul_in_bounds //-- //-- IMul64 [@ "opaque_to_smt"] let va_code_IMul64 dst src = (mk_ins (make_instr (I.ins_IMul64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_IMul64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_IMul64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_IMul64) (va_code_IMul64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_IMul64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_IMul64) dst src)) va_s0 in lemma_mul_nat (va_eval_dst_opr64 va_old_s dst) (va_eval_opr64 va_old_s src); lemma_mul_in_bounds (va_eval_dst_opr64 va_old_s dst) (va_eval_opr64 va_old_s src); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_IMul64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_IMul64 (va_code_IMul64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Xor64 [@ "opaque_to_smt"] let va_code_Xor64 dst src = (mk_ins (make_instr_annotate (I.ins_Xor64) (S.AnnotateXor64 ()) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Xor64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Xor64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Xor64) (va_code_Xor64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr_annotate (I.ins_Xor64) (S.AnnotateXor64 ()) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr_annotate (I.ins_Xor64) (S.AnnotateXor64 ()) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Xor64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Xor64 (va_code_Xor64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- And64 [@ "opaque_to_smt"] let va_code_And64 dst src = (mk_ins (make_instr (I.ins_And64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_And64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_And64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_And64) (va_code_And64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_And64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_And64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_And64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_And64 (va_code_And64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Shl64 [@ "opaque_to_smt"] let va_code_Shl64 dst amt = (mk_ins (make_instr (I.ins_Shl64) dst amt)) [@ "opaque_to_smt"] let va_codegen_success_Shl64 dst amt = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Shl64 va_b0 va_s0 dst amt = va_reveal_opaque (`%va_code_Shl64) (va_code_Shl64 dst amt); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Shl64) dst amt)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Shl64) dst amt)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Shl64 dst amt va_s0 va_k = let (va_sM, va_f0) = va_lemma_Shl64 (va_code_Shl64 dst amt) va_s0 dst amt in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Shr64 [@ "opaque_to_smt"] let va_code_Shr64 dst amt = (mk_ins (make_instr (I.ins_Shr64) dst amt)) [@ "opaque_to_smt"] let va_codegen_success_Shr64 dst amt = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Shr64 va_b0 va_s0 dst amt = va_reveal_opaque (`%va_code_Shr64) (va_code_Shr64 dst amt); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Shr64) dst amt)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Shr64) dst amt)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Shr64 dst amt va_s0 va_k = let (va_sM, va_f0) = va_lemma_Shr64 (va_code_Shr64 dst amt) va_s0 dst amt in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_AES [@ "opaque_to_smt"] let va_code_Cpuid_AES () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_AES () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_AES va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_AES) (va_code_Cpuid_AES ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_AES va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_AES (va_code_Cpuid_AES ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Sha [@ "opaque_to_smt"] let va_code_Cpuid_Sha () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Sha () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Sha va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Sha) (va_code_Cpuid_Sha ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Sha va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Sha (va_code_Cpuid_Sha ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Adx_Bmi2 [@ "opaque_to_smt"] let va_code_Cpuid_Adx_Bmi2 () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Adx_Bmi2 () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Adx_Bmi2 va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Adx_Bmi2) (va_code_Cpuid_Adx_Bmi2 ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Adx_Bmi2 va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Adx_Bmi2 (va_code_Cpuid_Adx_Bmi2 ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Avx [@ "opaque_to_smt"] let va_code_Cpuid_Avx () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Avx () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Avx va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Avx) (va_code_Cpuid_Avx ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Avx va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Avx (va_code_Cpuid_Avx ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Avx2 [@ "opaque_to_smt"] let va_code_Cpuid_Avx2 () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Avx2 () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Avx2 va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Avx2) (va_code_Cpuid_Avx2 ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Avx2 va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Avx2 (va_code_Cpuid_Avx2 ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Sse [@ "opaque_to_smt"] let va_code_Cpuid_Sse () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Sse () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Sse va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Sse) (va_code_Cpuid_Sse ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Sse va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Sse (va_code_Cpuid_Sse ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Movbe [@ "opaque_to_smt"] let va_code_Cpuid_Movbe () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Movbe () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Movbe va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Movbe) (va_code_Cpuid_Movbe ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Movbe va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Movbe (va_code_Cpuid_Movbe ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Rdrand [@ "opaque_to_smt"] let va_code_Cpuid_Rdrand () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Rdrand () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Rdrand va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Rdrand) (va_code_Cpuid_Rdrand ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Rdrand va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Rdrand (va_code_Cpuid_Rdrand ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Avx512 [@ "opaque_to_smt"] let va_code_Cpuid_Avx512 () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Avx512 () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Avx512 va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Avx512) (va_code_Cpuid_Avx512 ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Avx512 va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Avx512 (va_code_Cpuid_Avx512 ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Osxsave [@ "opaque_to_smt"] let va_code_Cpuid_Osxsave () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Osxsave () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Osxsave va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Osxsave) (va_code_Cpuid_Osxsave ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Osxsave va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Osxsave (va_code_Cpuid_Osxsave ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Xgetbv_Avx [@ "opaque_to_smt"] let va_code_Xgetbv_Avx () = (mk_ins (make_instr (I.ins_Xgetbv))) [@ "opaque_to_smt"] let va_codegen_success_Xgetbv_Avx () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Xgetbv_Avx va_b0 va_s0 = va_reveal_opaque (`%va_code_Xgetbv_Avx) (va_code_Xgetbv_Avx ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Xgetbv))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Xgetbv))) va_s0 in Vale.X64.CPU_Features_s.xgetbv_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Xgetbv_Avx va_s0 va_k = let (va_sM, va_f0) = va_lemma_Xgetbv_Avx (va_code_Xgetbv_Avx ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Xgetbv_Avx512 [@ "opaque_to_smt"] let va_code_Xgetbv_Avx512 () = (mk_ins (make_instr (I.ins_Xgetbv))) [@ "opaque_to_smt"] let va_codegen_success_Xgetbv_Avx512 () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Xgetbv_Avx512 va_b0 va_s0 = va_reveal_opaque (`%va_code_Xgetbv_Avx512) (va_code_Xgetbv_Avx512 ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Xgetbv))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Xgetbv))) va_s0 in Vale.X64.CPU_Features_s.xgetbv_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Xgetbv_Avx512 va_s0 va_k = let (va_sM, va_f0) = va_lemma_Xgetbv_Avx512 (va_code_Xgetbv_Avx512 ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Nat64Equal [@ "opaque_to_smt"] let va_code_Nat64Equal dst src = (va_Block (va_CCons (va_code_Sub64Wrap (va_coerce_reg_opr64_to_dst_opr64 src) (va_const_opr64 18446744073709551615)) (va_CCons (va_code_Mov64 (va_coerce_reg_opr64_to_dst_opr64 dst) (va_const_opr64 0)) (va_CCons (va_code_Adc64 (va_coerce_reg_opr64_to_dst_opr64 dst) (va_const_opr64 0)) (va_CNil ()))))) [@ "opaque_to_smt"] let va_codegen_success_Nat64Equal dst src = (va_pbool_and (va_codegen_success_Sub64Wrap (va_coerce_reg_opr64_to_dst_opr64 src) (va_const_opr64 18446744073709551615)) (va_pbool_and (va_codegen_success_Mov64 (va_coerce_reg_opr64_to_dst_opr64 dst) (va_const_opr64 0)) (va_pbool_and (va_codegen_success_Adc64 (va_coerce_reg_opr64_to_dst_opr64 dst) (va_const_opr64 0)) (va_ttrue ())))) [@"opaque_to_smt"] let va_lemma_Nat64Equal va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Nat64Equal) (va_code_Nat64Equal dst src); let (va_old_s:va_state) = va_s0 in let (va_b1:va_codes) = va_get_block va_b0 in let (va_s2, va_fc2) = va_lemma_Sub64Wrap (va_hd va_b1) va_s0 (va_coerce_reg_opr64_to_dst_opr64 src) (va_const_opr64 18446744073709551615) in let va_b2 = va_tl va_b1 in let (va_s3, va_fc3) = va_lemma_Mov64 (va_hd va_b2) va_s2 (va_coerce_reg_opr64_to_dst_opr64 dst) (va_const_opr64 0) in let va_b3 = va_tl va_b2 in let (va_s4, va_fc4) = va_lemma_Adc64 (va_hd va_b3) va_s3 (va_coerce_reg_opr64_to_dst_opr64 dst) (va_const_opr64 0) in let va_b4 = va_tl va_b3 in let (va_sM, va_f4) = va_lemma_empty_total va_s4 va_b4 in let va_f3 = va_lemma_merge_total va_b3 va_s3 va_fc4 va_s4 va_f4 va_sM in let va_f2 = va_lemma_merge_total va_b2 va_s2 va_fc3 va_s3 va_f3 va_sM in let va_fM = va_lemma_merge_total va_b1 va_s0 va_fc2 va_s2 va_f2 va_sM in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Nat64Equal dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Nat64Equal (va_code_Nat64Equal dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_reg_opr64 src va_sM (va_update_operand_reg_opr64 dst va_sM va_s0))))); va_lemma_norm_mods ([va_Mod_flags; va_mod_reg_opr64 src; va_mod_reg_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Comment [@ "opaque_to_smt"] let va_code_Comment c = (mk_ins (make_instr_annotate (I.ins_Comment c) (S.AnnotateComment c))) [@ "opaque_to_smt"] let va_codegen_success_Comment c = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Comment va_b0 va_s0 c = va_reveal_opaque (`%va_code_Comment) (va_code_Comment c); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr_annotate (I.ins_Comment c) (S.AnnotateComment c))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr_annotate (I.ins_Comment c) (S.AnnotateComment c))) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Comment c va_s0 va_k = let (va_sM, va_f0) = va_lemma_Comment (va_code_Comment c) va_s0 c in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_ok va_sM va_s0)); va_lemma_norm_mods ([]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- LargeComment [@ "opaque_to_smt"] let va_code_LargeComment c = (mk_ins (make_instr_annotate (I.ins_LargeComment c) (S.AnnotateLargeComment c))) [@ "opaque_to_smt"] let va_codegen_success_LargeComment c = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_LargeComment va_b0 va_s0 c = va_reveal_opaque (`%va_code_LargeComment) (va_code_LargeComment c); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr_annotate (I.ins_LargeComment c) (S.AnnotateLargeComment c))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr_annotate (I.ins_LargeComment c) (S.AnnotateLargeComment c))) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_LargeComment c va_s0 va_k = let (va_sM, va_f0) = va_lemma_LargeComment (va_code_LargeComment c) va_s0 c in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_ok va_sM va_s0)); va_lemma_norm_mods ([]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- NoNewline [@ "opaque_to_smt"] let va_code_NoNewline () = (mk_ins (make_instr_annotate (I.ins_Space 0) (S.AnnotateSpace 0))) [@ "opaque_to_smt"] let va_codegen_success_NoNewline () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_NoNewline va_b0 va_s0 = va_reveal_opaque (`%va_code_NoNewline) (va_code_NoNewline ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr_annotate (I.ins_Space 0) (S.AnnotateSpace 0))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr_annotate (I.ins_Space 0) (S.AnnotateSpace 0))) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_NoNewline va_s0 va_k = let (va_sM, va_f0) = va_lemma_NoNewline (va_code_NoNewline ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_ok va_sM va_s0)); va_lemma_norm_mods ([]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Newline [@ "opaque_to_smt"] let va_code_Newline () = (mk_ins (make_instr_annotate (I.ins_Newline) (S.AnnotateNewline ()))) [@ "opaque_to_smt"] let va_codegen_success_Newline () = (va_ttrue ()) [@"opaque_to_smt"]
false
false
Vale.X64.InsBasic.fst
{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 5, "initial_ifuel": 0, "max_fuel": 5, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": true, "smtencoding_l_arith_repr": "native", "smtencoding_nl_arith_repr": "wrapped", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": false, "z3cliopt": [ "smt.arith.nl=false", "smt.QI.EAGER_THRESHOLD=100", "smt.CASE_SPLIT=3" ], "z3refresh": false, "z3rlimit": 20, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }
null
val va_lemma_Newline : va_b0:va_code -> va_s0:va_state -> Ghost (va_state & va_fuel) (requires (va_require_total va_b0 (va_code_Newline ()) va_s0 /\ va_get_ok va_s0)) (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\ va_state_eq va_sM (va_update_ok va_sM va_s0)))
[]
Vale.X64.InsBasic.va_lemma_Newline
{ "file_name": "obj/Vale.X64.InsBasic.fst", "git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e", "git_url": "https://github.com/hacl-star/hacl-star.git", "project_name": "hacl-star" }
va_b0: Vale.X64.Decls.va_code -> va_s0: Vale.X64.Decls.va_state -> Prims.Ghost (Vale.X64.Decls.va_state * Vale.X64.Decls.va_fuel)
{ "end_col": 16, "end_line": 1144, "start_col": 2, "start_line": 1139 }
Prims.Ghost
val va_lemma_NoNewline : va_b0:va_code -> va_s0:va_state -> Ghost (va_state & va_fuel) (requires (va_require_total va_b0 (va_code_NoNewline ()) va_s0 /\ va_get_ok va_s0)) (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\ va_state_eq va_sM (va_update_ok va_sM va_s0)))
[ { "abbrev": true, "full_module": "Vale.X64.Machine_Semantics_s", "short_module": "S" }, { "abbrev": true, "full_module": "Vale.X64.Instructions_s", "short_module": "I" }, { "abbrev": false, "full_module": "Vale.X64.Stack_i", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.Memory", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.Taint_Semantics", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.InsLemmas", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.StateLemmas", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.CPU_Features_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.QuickCode", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.Decls", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.State", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.Machine_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Arch.Types", "short_module": null }, { "abbrev": false, "full_module": "Vale.Arch.HeapImpl", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Types_s", "short_module": null }, { "abbrev": false, "full_module": "FStar.Mul", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]
false
let va_lemma_NoNewline va_b0 va_s0 = va_reveal_opaque (`%va_code_NoNewline) (va_code_NoNewline ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr_annotate (I.ins_Space 0) (S.AnnotateSpace 0))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr_annotate (I.ins_Space 0) (S.AnnotateSpace 0))) va_s0 in (va_sM, va_fM)
val va_lemma_NoNewline : va_b0:va_code -> va_s0:va_state -> Ghost (va_state & va_fuel) (requires (va_require_total va_b0 (va_code_NoNewline ()) va_s0 /\ va_get_ok va_s0)) (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\ va_state_eq va_sM (va_update_ok va_sM va_s0))) let va_lemma_NoNewline va_b0 va_s0 =
false
null
false
va_reveal_opaque (`%va_code_NoNewline) (va_code_NoNewline ()); let va_old_s:va_state = va_s0 in va_ins_lemma (mk_ins (make_instr_annotate (I.ins_Space 0) (S.AnnotateSpace 0))) va_s0; let va_sM, va_fM = va_eval_ins (mk_ins (make_instr_annotate (I.ins_Space 0) (S.AnnotateSpace 0))) va_s0 in (va_sM, va_fM)
{ "checked_file": "Vale.X64.InsBasic.fst.checked", "dependencies": [ "Vale.X64.Taint_Semantics.fst.checked", "Vale.X64.StateLemmas.fsti.checked", "Vale.X64.Stack_i.fsti.checked", "Vale.X64.Memory.fsti.checked", "Vale.X64.Machine_Semantics_s.fst.checked", "Vale.X64.Instructions_s.fsti.checked", "Vale.X64.InsLemmas.fsti.checked", "Vale.X64.Decls.fst.checked", "Vale.X64.CPU_Features_s.fst.checked", "Vale.Arch.Types.fsti.checked", "prims.fst.checked", "FStar.UInt.fsti.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Math.Lemmas.fst.checked" ], "interface_file": true, "source_file": "Vale.X64.InsBasic.fst" }
[]
[ "Vale.X64.Decls.va_code", "Vale.X64.Decls.va_state", "Vale.X64.State.vale_state", "Vale.X64.Lemmas.fuel", "FStar.Pervasives.Native.Mktuple2", "Vale.X64.Decls.va_fuel", "FStar.Pervasives.Native.tuple2", "Prims.nat", "Vale.X64.Decls.va_eval_ins", "Vale.X64.Taint_Semantics.mk_ins", "Vale.X64.InsLemmas.make_instr_annotate", "Prims.Nil", "Vale.X64.Instruction_s.instr_out", "Vale.X64.Instruction_s.instr_operand", "Vale.X64.Instruction_s.PreserveFlags", "Vale.X64.Instructions_s.ins_Space", "Vale.X64.Machine_Semantics_s.AnnotateSpace", "Vale.X64.Instruction_s.InstrTypeRecord", "Prims.unit", "Vale.X64.Decls.va_ins_lemma", "Vale.X64.Decls.va_reveal_opaque", "Vale.X64.InsBasic.va_code_NoNewline" ]
[]
module Vale.X64.InsBasic open Vale.X64 open Vale.X64.StateLemmas open Vale.X64.InsLemmas open Vale.X64.Taint_Semantics open Vale.X64.CPU_Features_s open Vale.X64.Memory open Vale.X64.Stack_i module I = Vale.X64.Instructions_s module S = Vale.X64.Machine_Semantics_s friend Vale.X64.Decls #reset-options "--initial_fuel 5 --max_fuel 5 --max_ifuel 2 --z3rlimit 20" //-- Mov64 [@ "opaque_to_smt"] let va_code_Mov64 dst src = (mk_ins (make_instr_annotate (I.ins_Mov64) (S.AnnotateMov64 ()) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Mov64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Mov64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Mov64) (va_code_Mov64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr_annotate (I.ins_Mov64) (S.AnnotateMov64 ()) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr_annotate (I.ins_Mov64) (S.AnnotateMov64 ()) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Mov64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Mov64 (va_code_Mov64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0))); va_lemma_norm_mods ([va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cmovc64 [@ "opaque_to_smt"] let va_code_Cmovc64 dst src = (mk_ins (make_instr (I.ins_Cmovc64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Cmovc64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cmovc64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Cmovc64) (va_code_Cmovc64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cmovc64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cmovc64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cmovc64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cmovc64 (va_code_Cmovc64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0))); va_lemma_norm_mods ([va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Add64 [@ "opaque_to_smt"] let va_code_Add64 dst src = (mk_ins (make_instr (I.ins_Add64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Add64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Add64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Add64) (va_code_Add64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Add64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Add64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Add64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Add64 (va_code_Add64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Add64Wrap [@ "opaque_to_smt"] let va_code_Add64Wrap dst src = (mk_ins (make_instr (I.ins_Add64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Add64Wrap dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Add64Wrap va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Add64Wrap) (va_code_Add64Wrap dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Add64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Add64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Add64Wrap dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Add64Wrap (va_code_Add64Wrap dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- AddLea64 [@ "opaque_to_smt"] let va_code_AddLea64 dst src1 src2 = (mk_ins (make_instr (I.ins_AddLea64) dst src1 src2)) [@ "opaque_to_smt"] let va_codegen_success_AddLea64 dst src1 src2 = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_AddLea64 va_b0 va_s0 dst src1 src2 = va_reveal_opaque (`%va_code_AddLea64) (va_code_AddLea64 dst src1 src2); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_AddLea64) dst src1 src2)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_AddLea64) dst src1 src2)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_AddLea64 dst src1 src2 va_s0 va_k = let (va_sM, va_f0) = va_lemma_AddLea64 (va_code_AddLea64 dst src1 src2) va_s0 dst src1 src2 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0))); va_lemma_norm_mods ([va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Adc64 [@ "opaque_to_smt"] let va_code_Adc64 dst src = (mk_ins (make_instr (I.ins_AddCarry64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Adc64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Adc64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Adc64) (va_code_Adc64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_AddCarry64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_AddCarry64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Adc64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Adc64 (va_code_Adc64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Adc64Wrap [@ "opaque_to_smt"] let va_code_Adc64Wrap dst src = (mk_ins (make_instr (I.ins_AddCarry64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Adc64Wrap dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Adc64Wrap va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Adc64Wrap) (va_code_Adc64Wrap dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_AddCarry64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_AddCarry64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Adc64Wrap dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Adc64Wrap (va_code_Adc64Wrap dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Adcx64Wrap #push-options "--smtencoding.nl_arith_repr boxwrap" [@ "opaque_to_smt"] let va_code_Adcx64Wrap dst src = (mk_ins (make_instr (I.ins_Adcx64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Adcx64Wrap dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Adcx64Wrap va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Adcx64Wrap) (va_code_Adcx64Wrap dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Adcx64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Adcx64) dst src)) va_s0 in assert (Vale.Arch.Types.add_wrap64 (Vale.Arch.Types.add_wrap64 (va_eval_dst_opr64 va_old_s dst) (va_eval_opr64 va_old_s src)) (if Vale.X64.Decls.cf (va_get_flags va_old_s) then 1 else 0) == (va_eval_dst_opr64 va_old_s dst + va_eval_opr64 va_old_s src + (if Vale.X64.Decls.cf (va_get_flags va_old_s) then 1 else 0)) `op_Modulus` pow2_64); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Adcx64Wrap dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Adcx64Wrap (va_code_Adcx64Wrap dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) #pop-options //-- //-- Adox64Wrap [@ "opaque_to_smt"] let va_code_Adox64Wrap dst src = (mk_ins (make_instr (I.ins_Adox64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Adox64Wrap dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Adox64Wrap va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Adox64Wrap) (va_code_Adox64Wrap dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Adox64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Adox64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Adox64Wrap dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Adox64Wrap (va_code_Adox64Wrap dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Sub64 [@ "opaque_to_smt"] let va_code_Sub64 dst src = (mk_ins (make_instr (I.ins_Sub64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Sub64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Sub64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Sub64) (va_code_Sub64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Sub64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Sub64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Sub64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Sub64 (va_code_Sub64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Sub64Wrap [@ "opaque_to_smt"] let va_code_Sub64Wrap dst src = (mk_ins (make_instr (I.ins_Sub64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Sub64Wrap dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Sub64Wrap va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Sub64Wrap) (va_code_Sub64Wrap dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Sub64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Sub64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Sub64Wrap dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Sub64Wrap (va_code_Sub64Wrap dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Sbb64 [@ "opaque_to_smt"] let va_code_Sbb64 dst src = (mk_ins (make_instr (I.ins_Sbb64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Sbb64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Sbb64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Sbb64) (va_code_Sbb64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Sbb64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Sbb64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Sbb64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Sbb64 (va_code_Sbb64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- #restart-solver #push-options "--max_fuel 0 --max_ifuel 0 --using_facts_from 'Prims FStar.UInt'" let lemma_fundamental_div_mod (a b:nat64) : Lemma (pow2_64 * (FStar.UInt.mul_div #64 a b) + (FStar.UInt.mul_mod #64 a b) == a * b) = FStar.Math.Lemmas.lemma_div_mod (a * b) pow2_64 #pop-options //-- lemma_fundamental_div_mod //-- //-- Mul64Wrap [@ "opaque_to_smt"] let va_code_Mul64Wrap src = (mk_ins (make_instr (I.ins_Mul64) src)) [@ "opaque_to_smt"] let va_codegen_success_Mul64Wrap src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Mul64Wrap va_b0 va_s0 src = va_reveal_opaque (`%va_code_Mul64Wrap) (va_code_Mul64Wrap src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Mul64) src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Mul64) src)) va_s0 in lemma_fundamental_div_mod (va_get_reg64 rRax va_old_s) (va_eval_opr64 va_old_s src); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Mul64Wrap src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Mul64Wrap (va_code_Mul64Wrap src) va_s0 src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRax va_sM (va_update_flags va_sM (va_update_ok va_sM va_s0))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRax; va_Mod_flags]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Mulx64 [@ "opaque_to_smt"] let va_code_Mulx64 dst_hi dst_lo src = (mk_ins (make_instr (I.ins_Mulx64) dst_hi dst_lo src)) [@ "opaque_to_smt"] let va_codegen_success_Mulx64 dst_hi dst_lo src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Mulx64 va_b0 va_s0 dst_hi dst_lo src = va_reveal_opaque (`%va_code_Mulx64) (va_code_Mulx64 dst_hi dst_lo src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Mulx64) dst_hi dst_lo src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Mulx64) dst_hi dst_lo src)) va_s0 in lemma_fundamental_div_mod (va_get_reg64 rRdx va_old_s) (va_eval_opr64 va_old_s src); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Mulx64 dst_hi dst_lo src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Mulx64 (va_code_Mulx64 dst_hi dst_lo src) va_s0 dst_hi dst_lo src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst_lo va_sM (va_update_operand_dst_opr64 dst_hi va_sM va_s0)))); va_lemma_norm_mods ([va_mod_dst_opr64 dst_lo; va_mod_dst_opr64 dst_hi]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- lemma_mul_nat //-- //-- lemma_mul_in_bounds //-- //-- IMul64 [@ "opaque_to_smt"] let va_code_IMul64 dst src = (mk_ins (make_instr (I.ins_IMul64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_IMul64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_IMul64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_IMul64) (va_code_IMul64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_IMul64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_IMul64) dst src)) va_s0 in lemma_mul_nat (va_eval_dst_opr64 va_old_s dst) (va_eval_opr64 va_old_s src); lemma_mul_in_bounds (va_eval_dst_opr64 va_old_s dst) (va_eval_opr64 va_old_s src); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_IMul64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_IMul64 (va_code_IMul64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Xor64 [@ "opaque_to_smt"] let va_code_Xor64 dst src = (mk_ins (make_instr_annotate (I.ins_Xor64) (S.AnnotateXor64 ()) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Xor64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Xor64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Xor64) (va_code_Xor64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr_annotate (I.ins_Xor64) (S.AnnotateXor64 ()) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr_annotate (I.ins_Xor64) (S.AnnotateXor64 ()) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Xor64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Xor64 (va_code_Xor64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- And64 [@ "opaque_to_smt"] let va_code_And64 dst src = (mk_ins (make_instr (I.ins_And64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_And64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_And64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_And64) (va_code_And64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_And64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_And64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_And64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_And64 (va_code_And64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Shl64 [@ "opaque_to_smt"] let va_code_Shl64 dst amt = (mk_ins (make_instr (I.ins_Shl64) dst amt)) [@ "opaque_to_smt"] let va_codegen_success_Shl64 dst amt = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Shl64 va_b0 va_s0 dst amt = va_reveal_opaque (`%va_code_Shl64) (va_code_Shl64 dst amt); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Shl64) dst amt)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Shl64) dst amt)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Shl64 dst amt va_s0 va_k = let (va_sM, va_f0) = va_lemma_Shl64 (va_code_Shl64 dst amt) va_s0 dst amt in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Shr64 [@ "opaque_to_smt"] let va_code_Shr64 dst amt = (mk_ins (make_instr (I.ins_Shr64) dst amt)) [@ "opaque_to_smt"] let va_codegen_success_Shr64 dst amt = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Shr64 va_b0 va_s0 dst amt = va_reveal_opaque (`%va_code_Shr64) (va_code_Shr64 dst amt); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Shr64) dst amt)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Shr64) dst amt)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Shr64 dst amt va_s0 va_k = let (va_sM, va_f0) = va_lemma_Shr64 (va_code_Shr64 dst amt) va_s0 dst amt in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_AES [@ "opaque_to_smt"] let va_code_Cpuid_AES () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_AES () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_AES va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_AES) (va_code_Cpuid_AES ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_AES va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_AES (va_code_Cpuid_AES ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Sha [@ "opaque_to_smt"] let va_code_Cpuid_Sha () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Sha () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Sha va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Sha) (va_code_Cpuid_Sha ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Sha va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Sha (va_code_Cpuid_Sha ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Adx_Bmi2 [@ "opaque_to_smt"] let va_code_Cpuid_Adx_Bmi2 () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Adx_Bmi2 () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Adx_Bmi2 va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Adx_Bmi2) (va_code_Cpuid_Adx_Bmi2 ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Adx_Bmi2 va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Adx_Bmi2 (va_code_Cpuid_Adx_Bmi2 ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Avx [@ "opaque_to_smt"] let va_code_Cpuid_Avx () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Avx () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Avx va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Avx) (va_code_Cpuid_Avx ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Avx va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Avx (va_code_Cpuid_Avx ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Avx2 [@ "opaque_to_smt"] let va_code_Cpuid_Avx2 () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Avx2 () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Avx2 va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Avx2) (va_code_Cpuid_Avx2 ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Avx2 va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Avx2 (va_code_Cpuid_Avx2 ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Sse [@ "opaque_to_smt"] let va_code_Cpuid_Sse () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Sse () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Sse va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Sse) (va_code_Cpuid_Sse ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Sse va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Sse (va_code_Cpuid_Sse ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Movbe [@ "opaque_to_smt"] let va_code_Cpuid_Movbe () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Movbe () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Movbe va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Movbe) (va_code_Cpuid_Movbe ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Movbe va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Movbe (va_code_Cpuid_Movbe ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Rdrand [@ "opaque_to_smt"] let va_code_Cpuid_Rdrand () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Rdrand () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Rdrand va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Rdrand) (va_code_Cpuid_Rdrand ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Rdrand va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Rdrand (va_code_Cpuid_Rdrand ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Avx512 [@ "opaque_to_smt"] let va_code_Cpuid_Avx512 () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Avx512 () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Avx512 va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Avx512) (va_code_Cpuid_Avx512 ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Avx512 va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Avx512 (va_code_Cpuid_Avx512 ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Osxsave [@ "opaque_to_smt"] let va_code_Cpuid_Osxsave () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Osxsave () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Osxsave va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Osxsave) (va_code_Cpuid_Osxsave ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Osxsave va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Osxsave (va_code_Cpuid_Osxsave ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Xgetbv_Avx [@ "opaque_to_smt"] let va_code_Xgetbv_Avx () = (mk_ins (make_instr (I.ins_Xgetbv))) [@ "opaque_to_smt"] let va_codegen_success_Xgetbv_Avx () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Xgetbv_Avx va_b0 va_s0 = va_reveal_opaque (`%va_code_Xgetbv_Avx) (va_code_Xgetbv_Avx ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Xgetbv))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Xgetbv))) va_s0 in Vale.X64.CPU_Features_s.xgetbv_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Xgetbv_Avx va_s0 va_k = let (va_sM, va_f0) = va_lemma_Xgetbv_Avx (va_code_Xgetbv_Avx ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Xgetbv_Avx512 [@ "opaque_to_smt"] let va_code_Xgetbv_Avx512 () = (mk_ins (make_instr (I.ins_Xgetbv))) [@ "opaque_to_smt"] let va_codegen_success_Xgetbv_Avx512 () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Xgetbv_Avx512 va_b0 va_s0 = va_reveal_opaque (`%va_code_Xgetbv_Avx512) (va_code_Xgetbv_Avx512 ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Xgetbv))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Xgetbv))) va_s0 in Vale.X64.CPU_Features_s.xgetbv_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Xgetbv_Avx512 va_s0 va_k = let (va_sM, va_f0) = va_lemma_Xgetbv_Avx512 (va_code_Xgetbv_Avx512 ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Nat64Equal [@ "opaque_to_smt"] let va_code_Nat64Equal dst src = (va_Block (va_CCons (va_code_Sub64Wrap (va_coerce_reg_opr64_to_dst_opr64 src) (va_const_opr64 18446744073709551615)) (va_CCons (va_code_Mov64 (va_coerce_reg_opr64_to_dst_opr64 dst) (va_const_opr64 0)) (va_CCons (va_code_Adc64 (va_coerce_reg_opr64_to_dst_opr64 dst) (va_const_opr64 0)) (va_CNil ()))))) [@ "opaque_to_smt"] let va_codegen_success_Nat64Equal dst src = (va_pbool_and (va_codegen_success_Sub64Wrap (va_coerce_reg_opr64_to_dst_opr64 src) (va_const_opr64 18446744073709551615)) (va_pbool_and (va_codegen_success_Mov64 (va_coerce_reg_opr64_to_dst_opr64 dst) (va_const_opr64 0)) (va_pbool_and (va_codegen_success_Adc64 (va_coerce_reg_opr64_to_dst_opr64 dst) (va_const_opr64 0)) (va_ttrue ())))) [@"opaque_to_smt"] let va_lemma_Nat64Equal va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Nat64Equal) (va_code_Nat64Equal dst src); let (va_old_s:va_state) = va_s0 in let (va_b1:va_codes) = va_get_block va_b0 in let (va_s2, va_fc2) = va_lemma_Sub64Wrap (va_hd va_b1) va_s0 (va_coerce_reg_opr64_to_dst_opr64 src) (va_const_opr64 18446744073709551615) in let va_b2 = va_tl va_b1 in let (va_s3, va_fc3) = va_lemma_Mov64 (va_hd va_b2) va_s2 (va_coerce_reg_opr64_to_dst_opr64 dst) (va_const_opr64 0) in let va_b3 = va_tl va_b2 in let (va_s4, va_fc4) = va_lemma_Adc64 (va_hd va_b3) va_s3 (va_coerce_reg_opr64_to_dst_opr64 dst) (va_const_opr64 0) in let va_b4 = va_tl va_b3 in let (va_sM, va_f4) = va_lemma_empty_total va_s4 va_b4 in let va_f3 = va_lemma_merge_total va_b3 va_s3 va_fc4 va_s4 va_f4 va_sM in let va_f2 = va_lemma_merge_total va_b2 va_s2 va_fc3 va_s3 va_f3 va_sM in let va_fM = va_lemma_merge_total va_b1 va_s0 va_fc2 va_s2 va_f2 va_sM in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Nat64Equal dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Nat64Equal (va_code_Nat64Equal dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_reg_opr64 src va_sM (va_update_operand_reg_opr64 dst va_sM va_s0))))); va_lemma_norm_mods ([va_Mod_flags; va_mod_reg_opr64 src; va_mod_reg_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Comment [@ "opaque_to_smt"] let va_code_Comment c = (mk_ins (make_instr_annotate (I.ins_Comment c) (S.AnnotateComment c))) [@ "opaque_to_smt"] let va_codegen_success_Comment c = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Comment va_b0 va_s0 c = va_reveal_opaque (`%va_code_Comment) (va_code_Comment c); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr_annotate (I.ins_Comment c) (S.AnnotateComment c))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr_annotate (I.ins_Comment c) (S.AnnotateComment c))) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Comment c va_s0 va_k = let (va_sM, va_f0) = va_lemma_Comment (va_code_Comment c) va_s0 c in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_ok va_sM va_s0)); va_lemma_norm_mods ([]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- LargeComment [@ "opaque_to_smt"] let va_code_LargeComment c = (mk_ins (make_instr_annotate (I.ins_LargeComment c) (S.AnnotateLargeComment c))) [@ "opaque_to_smt"] let va_codegen_success_LargeComment c = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_LargeComment va_b0 va_s0 c = va_reveal_opaque (`%va_code_LargeComment) (va_code_LargeComment c); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr_annotate (I.ins_LargeComment c) (S.AnnotateLargeComment c))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr_annotate (I.ins_LargeComment c) (S.AnnotateLargeComment c))) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_LargeComment c va_s0 va_k = let (va_sM, va_f0) = va_lemma_LargeComment (va_code_LargeComment c) va_s0 c in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_ok va_sM va_s0)); va_lemma_norm_mods ([]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- NoNewline [@ "opaque_to_smt"] let va_code_NoNewline () = (mk_ins (make_instr_annotate (I.ins_Space 0) (S.AnnotateSpace 0))) [@ "opaque_to_smt"] let va_codegen_success_NoNewline () = (va_ttrue ()) [@"opaque_to_smt"]
false
false
Vale.X64.InsBasic.fst
{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 5, "initial_ifuel": 0, "max_fuel": 5, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": true, "smtencoding_l_arith_repr": "native", "smtencoding_nl_arith_repr": "wrapped", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": false, "z3cliopt": [ "smt.arith.nl=false", "smt.QI.EAGER_THRESHOLD=100", "smt.CASE_SPLIT=3" ], "z3refresh": false, "z3rlimit": 20, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }
null
val va_lemma_NoNewline : va_b0:va_code -> va_s0:va_state -> Ghost (va_state & va_fuel) (requires (va_require_total va_b0 (va_code_NoNewline ()) va_s0 /\ va_get_ok va_s0)) (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\ va_state_eq va_sM (va_update_ok va_sM va_s0)))
[]
Vale.X64.InsBasic.va_lemma_NoNewline
{ "file_name": "obj/Vale.X64.InsBasic.fst", "git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e", "git_url": "https://github.com/hacl-star/hacl-star.git", "project_name": "hacl-star" }
va_b0: Vale.X64.Decls.va_code -> va_s0: Vale.X64.Decls.va_state -> Prims.Ghost (Vale.X64.Decls.va_state * Vale.X64.Decls.va_fuel)
{ "end_col": 16, "end_line": 1114, "start_col": 2, "start_line": 1109 }
Prims.Ghost
val va_wpProof_Space : n:nat -> va_s0:va_state -> va_k:(va_state -> unit -> Type0) -> Ghost (va_state & va_fuel & unit) (requires (va_t_require va_s0 /\ va_wp_Space n va_s0 va_k)) (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Space n) ([]) va_s0 va_k ((va_sM, va_f0, va_g))))
[ { "abbrev": true, "full_module": "Vale.X64.Machine_Semantics_s", "short_module": "S" }, { "abbrev": true, "full_module": "Vale.X64.Instructions_s", "short_module": "I" }, { "abbrev": false, "full_module": "Vale.X64.Stack_i", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.Memory", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.Taint_Semantics", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.InsLemmas", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.StateLemmas", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.CPU_Features_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.QuickCode", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.Decls", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.State", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.Machine_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Arch.Types", "short_module": null }, { "abbrev": false, "full_module": "Vale.Arch.HeapImpl", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Types_s", "short_module": null }, { "abbrev": false, "full_module": "FStar.Mul", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]
false
let va_wpProof_Space n va_s0 va_k = let (va_sM, va_f0) = va_lemma_Space (va_code_Space n) va_s0 n in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_ok va_sM va_s0)); va_lemma_norm_mods ([]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g)
val va_wpProof_Space : n:nat -> va_s0:va_state -> va_k:(va_state -> unit -> Type0) -> Ghost (va_state & va_fuel & unit) (requires (va_t_require va_s0 /\ va_wp_Space n va_s0 va_k)) (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Space n) ([]) va_s0 va_k ((va_sM, va_f0, va_g)))) let va_wpProof_Space n va_s0 va_k =
false
null
false
let va_sM, va_f0 = va_lemma_Space (va_code_Space n) va_s0 n in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_ok va_sM va_s0)); va_lemma_norm_mods ([]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g)
{ "checked_file": "Vale.X64.InsBasic.fst.checked", "dependencies": [ "Vale.X64.Taint_Semantics.fst.checked", "Vale.X64.StateLemmas.fsti.checked", "Vale.X64.Stack_i.fsti.checked", "Vale.X64.Memory.fsti.checked", "Vale.X64.Machine_Semantics_s.fst.checked", "Vale.X64.Instructions_s.fsti.checked", "Vale.X64.InsLemmas.fsti.checked", "Vale.X64.Decls.fst.checked", "Vale.X64.CPU_Features_s.fst.checked", "Vale.Arch.Types.fsti.checked", "prims.fst.checked", "FStar.UInt.fsti.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Math.Lemmas.fst.checked" ], "interface_file": true, "source_file": "Vale.X64.InsBasic.fst" }
[]
[ "Prims.nat", "Vale.X64.Decls.va_state", "Prims.unit", "Vale.X64.Decls.va_fuel", "FStar.Pervasives.Native.Mktuple3", "Vale.X64.QuickCode.va_lemma_norm_mods", "Prims.Nil", "Vale.X64.QuickCode.mod_t", "Prims._assert", "Vale.X64.Decls.va_state_eq", "Vale.X64.Decls.va_update_ok", "Vale.X64.Decls.va_lemma_upd_update", "FStar.Pervasives.Native.tuple3", "FStar.Pervasives.Native.tuple2", "Vale.X64.State.vale_state", "Vale.X64.InsBasic.va_lemma_Space", "Vale.X64.InsBasic.va_code_Space" ]
[]
module Vale.X64.InsBasic open Vale.X64 open Vale.X64.StateLemmas open Vale.X64.InsLemmas open Vale.X64.Taint_Semantics open Vale.X64.CPU_Features_s open Vale.X64.Memory open Vale.X64.Stack_i module I = Vale.X64.Instructions_s module S = Vale.X64.Machine_Semantics_s friend Vale.X64.Decls #reset-options "--initial_fuel 5 --max_fuel 5 --max_ifuel 2 --z3rlimit 20" //-- Mov64 [@ "opaque_to_smt"] let va_code_Mov64 dst src = (mk_ins (make_instr_annotate (I.ins_Mov64) (S.AnnotateMov64 ()) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Mov64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Mov64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Mov64) (va_code_Mov64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr_annotate (I.ins_Mov64) (S.AnnotateMov64 ()) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr_annotate (I.ins_Mov64) (S.AnnotateMov64 ()) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Mov64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Mov64 (va_code_Mov64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0))); va_lemma_norm_mods ([va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cmovc64 [@ "opaque_to_smt"] let va_code_Cmovc64 dst src = (mk_ins (make_instr (I.ins_Cmovc64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Cmovc64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cmovc64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Cmovc64) (va_code_Cmovc64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cmovc64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cmovc64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cmovc64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cmovc64 (va_code_Cmovc64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0))); va_lemma_norm_mods ([va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Add64 [@ "opaque_to_smt"] let va_code_Add64 dst src = (mk_ins (make_instr (I.ins_Add64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Add64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Add64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Add64) (va_code_Add64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Add64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Add64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Add64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Add64 (va_code_Add64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Add64Wrap [@ "opaque_to_smt"] let va_code_Add64Wrap dst src = (mk_ins (make_instr (I.ins_Add64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Add64Wrap dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Add64Wrap va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Add64Wrap) (va_code_Add64Wrap dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Add64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Add64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Add64Wrap dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Add64Wrap (va_code_Add64Wrap dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- AddLea64 [@ "opaque_to_smt"] let va_code_AddLea64 dst src1 src2 = (mk_ins (make_instr (I.ins_AddLea64) dst src1 src2)) [@ "opaque_to_smt"] let va_codegen_success_AddLea64 dst src1 src2 = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_AddLea64 va_b0 va_s0 dst src1 src2 = va_reveal_opaque (`%va_code_AddLea64) (va_code_AddLea64 dst src1 src2); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_AddLea64) dst src1 src2)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_AddLea64) dst src1 src2)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_AddLea64 dst src1 src2 va_s0 va_k = let (va_sM, va_f0) = va_lemma_AddLea64 (va_code_AddLea64 dst src1 src2) va_s0 dst src1 src2 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0))); va_lemma_norm_mods ([va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Adc64 [@ "opaque_to_smt"] let va_code_Adc64 dst src = (mk_ins (make_instr (I.ins_AddCarry64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Adc64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Adc64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Adc64) (va_code_Adc64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_AddCarry64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_AddCarry64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Adc64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Adc64 (va_code_Adc64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Adc64Wrap [@ "opaque_to_smt"] let va_code_Adc64Wrap dst src = (mk_ins (make_instr (I.ins_AddCarry64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Adc64Wrap dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Adc64Wrap va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Adc64Wrap) (va_code_Adc64Wrap dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_AddCarry64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_AddCarry64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Adc64Wrap dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Adc64Wrap (va_code_Adc64Wrap dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Adcx64Wrap #push-options "--smtencoding.nl_arith_repr boxwrap" [@ "opaque_to_smt"] let va_code_Adcx64Wrap dst src = (mk_ins (make_instr (I.ins_Adcx64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Adcx64Wrap dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Adcx64Wrap va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Adcx64Wrap) (va_code_Adcx64Wrap dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Adcx64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Adcx64) dst src)) va_s0 in assert (Vale.Arch.Types.add_wrap64 (Vale.Arch.Types.add_wrap64 (va_eval_dst_opr64 va_old_s dst) (va_eval_opr64 va_old_s src)) (if Vale.X64.Decls.cf (va_get_flags va_old_s) then 1 else 0) == (va_eval_dst_opr64 va_old_s dst + va_eval_opr64 va_old_s src + (if Vale.X64.Decls.cf (va_get_flags va_old_s) then 1 else 0)) `op_Modulus` pow2_64); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Adcx64Wrap dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Adcx64Wrap (va_code_Adcx64Wrap dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) #pop-options //-- //-- Adox64Wrap [@ "opaque_to_smt"] let va_code_Adox64Wrap dst src = (mk_ins (make_instr (I.ins_Adox64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Adox64Wrap dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Adox64Wrap va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Adox64Wrap) (va_code_Adox64Wrap dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Adox64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Adox64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Adox64Wrap dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Adox64Wrap (va_code_Adox64Wrap dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Sub64 [@ "opaque_to_smt"] let va_code_Sub64 dst src = (mk_ins (make_instr (I.ins_Sub64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Sub64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Sub64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Sub64) (va_code_Sub64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Sub64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Sub64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Sub64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Sub64 (va_code_Sub64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Sub64Wrap [@ "opaque_to_smt"] let va_code_Sub64Wrap dst src = (mk_ins (make_instr (I.ins_Sub64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Sub64Wrap dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Sub64Wrap va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Sub64Wrap) (va_code_Sub64Wrap dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Sub64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Sub64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Sub64Wrap dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Sub64Wrap (va_code_Sub64Wrap dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Sbb64 [@ "opaque_to_smt"] let va_code_Sbb64 dst src = (mk_ins (make_instr (I.ins_Sbb64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Sbb64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Sbb64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Sbb64) (va_code_Sbb64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Sbb64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Sbb64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Sbb64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Sbb64 (va_code_Sbb64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- #restart-solver #push-options "--max_fuel 0 --max_ifuel 0 --using_facts_from 'Prims FStar.UInt'" let lemma_fundamental_div_mod (a b:nat64) : Lemma (pow2_64 * (FStar.UInt.mul_div #64 a b) + (FStar.UInt.mul_mod #64 a b) == a * b) = FStar.Math.Lemmas.lemma_div_mod (a * b) pow2_64 #pop-options //-- lemma_fundamental_div_mod //-- //-- Mul64Wrap [@ "opaque_to_smt"] let va_code_Mul64Wrap src = (mk_ins (make_instr (I.ins_Mul64) src)) [@ "opaque_to_smt"] let va_codegen_success_Mul64Wrap src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Mul64Wrap va_b0 va_s0 src = va_reveal_opaque (`%va_code_Mul64Wrap) (va_code_Mul64Wrap src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Mul64) src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Mul64) src)) va_s0 in lemma_fundamental_div_mod (va_get_reg64 rRax va_old_s) (va_eval_opr64 va_old_s src); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Mul64Wrap src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Mul64Wrap (va_code_Mul64Wrap src) va_s0 src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRax va_sM (va_update_flags va_sM (va_update_ok va_sM va_s0))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRax; va_Mod_flags]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Mulx64 [@ "opaque_to_smt"] let va_code_Mulx64 dst_hi dst_lo src = (mk_ins (make_instr (I.ins_Mulx64) dst_hi dst_lo src)) [@ "opaque_to_smt"] let va_codegen_success_Mulx64 dst_hi dst_lo src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Mulx64 va_b0 va_s0 dst_hi dst_lo src = va_reveal_opaque (`%va_code_Mulx64) (va_code_Mulx64 dst_hi dst_lo src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Mulx64) dst_hi dst_lo src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Mulx64) dst_hi dst_lo src)) va_s0 in lemma_fundamental_div_mod (va_get_reg64 rRdx va_old_s) (va_eval_opr64 va_old_s src); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Mulx64 dst_hi dst_lo src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Mulx64 (va_code_Mulx64 dst_hi dst_lo src) va_s0 dst_hi dst_lo src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst_lo va_sM (va_update_operand_dst_opr64 dst_hi va_sM va_s0)))); va_lemma_norm_mods ([va_mod_dst_opr64 dst_lo; va_mod_dst_opr64 dst_hi]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- lemma_mul_nat //-- //-- lemma_mul_in_bounds //-- //-- IMul64 [@ "opaque_to_smt"] let va_code_IMul64 dst src = (mk_ins (make_instr (I.ins_IMul64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_IMul64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_IMul64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_IMul64) (va_code_IMul64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_IMul64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_IMul64) dst src)) va_s0 in lemma_mul_nat (va_eval_dst_opr64 va_old_s dst) (va_eval_opr64 va_old_s src); lemma_mul_in_bounds (va_eval_dst_opr64 va_old_s dst) (va_eval_opr64 va_old_s src); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_IMul64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_IMul64 (va_code_IMul64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Xor64 [@ "opaque_to_smt"] let va_code_Xor64 dst src = (mk_ins (make_instr_annotate (I.ins_Xor64) (S.AnnotateXor64 ()) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Xor64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Xor64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Xor64) (va_code_Xor64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr_annotate (I.ins_Xor64) (S.AnnotateXor64 ()) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr_annotate (I.ins_Xor64) (S.AnnotateXor64 ()) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Xor64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Xor64 (va_code_Xor64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- And64 [@ "opaque_to_smt"] let va_code_And64 dst src = (mk_ins (make_instr (I.ins_And64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_And64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_And64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_And64) (va_code_And64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_And64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_And64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_And64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_And64 (va_code_And64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Shl64 [@ "opaque_to_smt"] let va_code_Shl64 dst amt = (mk_ins (make_instr (I.ins_Shl64) dst amt)) [@ "opaque_to_smt"] let va_codegen_success_Shl64 dst amt = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Shl64 va_b0 va_s0 dst amt = va_reveal_opaque (`%va_code_Shl64) (va_code_Shl64 dst amt); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Shl64) dst amt)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Shl64) dst amt)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Shl64 dst amt va_s0 va_k = let (va_sM, va_f0) = va_lemma_Shl64 (va_code_Shl64 dst amt) va_s0 dst amt in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Shr64 [@ "opaque_to_smt"] let va_code_Shr64 dst amt = (mk_ins (make_instr (I.ins_Shr64) dst amt)) [@ "opaque_to_smt"] let va_codegen_success_Shr64 dst amt = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Shr64 va_b0 va_s0 dst amt = va_reveal_opaque (`%va_code_Shr64) (va_code_Shr64 dst amt); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Shr64) dst amt)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Shr64) dst amt)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Shr64 dst amt va_s0 va_k = let (va_sM, va_f0) = va_lemma_Shr64 (va_code_Shr64 dst amt) va_s0 dst amt in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_AES [@ "opaque_to_smt"] let va_code_Cpuid_AES () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_AES () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_AES va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_AES) (va_code_Cpuid_AES ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_AES va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_AES (va_code_Cpuid_AES ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Sha [@ "opaque_to_smt"] let va_code_Cpuid_Sha () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Sha () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Sha va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Sha) (va_code_Cpuid_Sha ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Sha va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Sha (va_code_Cpuid_Sha ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Adx_Bmi2 [@ "opaque_to_smt"] let va_code_Cpuid_Adx_Bmi2 () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Adx_Bmi2 () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Adx_Bmi2 va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Adx_Bmi2) (va_code_Cpuid_Adx_Bmi2 ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Adx_Bmi2 va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Adx_Bmi2 (va_code_Cpuid_Adx_Bmi2 ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Avx [@ "opaque_to_smt"] let va_code_Cpuid_Avx () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Avx () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Avx va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Avx) (va_code_Cpuid_Avx ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Avx va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Avx (va_code_Cpuid_Avx ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Avx2 [@ "opaque_to_smt"] let va_code_Cpuid_Avx2 () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Avx2 () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Avx2 va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Avx2) (va_code_Cpuid_Avx2 ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Avx2 va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Avx2 (va_code_Cpuid_Avx2 ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Sse [@ "opaque_to_smt"] let va_code_Cpuid_Sse () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Sse () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Sse va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Sse) (va_code_Cpuid_Sse ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Sse va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Sse (va_code_Cpuid_Sse ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Movbe [@ "opaque_to_smt"] let va_code_Cpuid_Movbe () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Movbe () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Movbe va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Movbe) (va_code_Cpuid_Movbe ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Movbe va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Movbe (va_code_Cpuid_Movbe ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Rdrand [@ "opaque_to_smt"] let va_code_Cpuid_Rdrand () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Rdrand () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Rdrand va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Rdrand) (va_code_Cpuid_Rdrand ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Rdrand va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Rdrand (va_code_Cpuid_Rdrand ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Avx512 [@ "opaque_to_smt"] let va_code_Cpuid_Avx512 () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Avx512 () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Avx512 va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Avx512) (va_code_Cpuid_Avx512 ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Avx512 va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Avx512 (va_code_Cpuid_Avx512 ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Osxsave [@ "opaque_to_smt"] let va_code_Cpuid_Osxsave () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Osxsave () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Osxsave va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Osxsave) (va_code_Cpuid_Osxsave ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Osxsave va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Osxsave (va_code_Cpuid_Osxsave ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Xgetbv_Avx [@ "opaque_to_smt"] let va_code_Xgetbv_Avx () = (mk_ins (make_instr (I.ins_Xgetbv))) [@ "opaque_to_smt"] let va_codegen_success_Xgetbv_Avx () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Xgetbv_Avx va_b0 va_s0 = va_reveal_opaque (`%va_code_Xgetbv_Avx) (va_code_Xgetbv_Avx ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Xgetbv))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Xgetbv))) va_s0 in Vale.X64.CPU_Features_s.xgetbv_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Xgetbv_Avx va_s0 va_k = let (va_sM, va_f0) = va_lemma_Xgetbv_Avx (va_code_Xgetbv_Avx ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Xgetbv_Avx512 [@ "opaque_to_smt"] let va_code_Xgetbv_Avx512 () = (mk_ins (make_instr (I.ins_Xgetbv))) [@ "opaque_to_smt"] let va_codegen_success_Xgetbv_Avx512 () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Xgetbv_Avx512 va_b0 va_s0 = va_reveal_opaque (`%va_code_Xgetbv_Avx512) (va_code_Xgetbv_Avx512 ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Xgetbv))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Xgetbv))) va_s0 in Vale.X64.CPU_Features_s.xgetbv_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Xgetbv_Avx512 va_s0 va_k = let (va_sM, va_f0) = va_lemma_Xgetbv_Avx512 (va_code_Xgetbv_Avx512 ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Nat64Equal [@ "opaque_to_smt"] let va_code_Nat64Equal dst src = (va_Block (va_CCons (va_code_Sub64Wrap (va_coerce_reg_opr64_to_dst_opr64 src) (va_const_opr64 18446744073709551615)) (va_CCons (va_code_Mov64 (va_coerce_reg_opr64_to_dst_opr64 dst) (va_const_opr64 0)) (va_CCons (va_code_Adc64 (va_coerce_reg_opr64_to_dst_opr64 dst) (va_const_opr64 0)) (va_CNil ()))))) [@ "opaque_to_smt"] let va_codegen_success_Nat64Equal dst src = (va_pbool_and (va_codegen_success_Sub64Wrap (va_coerce_reg_opr64_to_dst_opr64 src) (va_const_opr64 18446744073709551615)) (va_pbool_and (va_codegen_success_Mov64 (va_coerce_reg_opr64_to_dst_opr64 dst) (va_const_opr64 0)) (va_pbool_and (va_codegen_success_Adc64 (va_coerce_reg_opr64_to_dst_opr64 dst) (va_const_opr64 0)) (va_ttrue ())))) [@"opaque_to_smt"] let va_lemma_Nat64Equal va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Nat64Equal) (va_code_Nat64Equal dst src); let (va_old_s:va_state) = va_s0 in let (va_b1:va_codes) = va_get_block va_b0 in let (va_s2, va_fc2) = va_lemma_Sub64Wrap (va_hd va_b1) va_s0 (va_coerce_reg_opr64_to_dst_opr64 src) (va_const_opr64 18446744073709551615) in let va_b2 = va_tl va_b1 in let (va_s3, va_fc3) = va_lemma_Mov64 (va_hd va_b2) va_s2 (va_coerce_reg_opr64_to_dst_opr64 dst) (va_const_opr64 0) in let va_b3 = va_tl va_b2 in let (va_s4, va_fc4) = va_lemma_Adc64 (va_hd va_b3) va_s3 (va_coerce_reg_opr64_to_dst_opr64 dst) (va_const_opr64 0) in let va_b4 = va_tl va_b3 in let (va_sM, va_f4) = va_lemma_empty_total va_s4 va_b4 in let va_f3 = va_lemma_merge_total va_b3 va_s3 va_fc4 va_s4 va_f4 va_sM in let va_f2 = va_lemma_merge_total va_b2 va_s2 va_fc3 va_s3 va_f3 va_sM in let va_fM = va_lemma_merge_total va_b1 va_s0 va_fc2 va_s2 va_f2 va_sM in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Nat64Equal dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Nat64Equal (va_code_Nat64Equal dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_reg_opr64 src va_sM (va_update_operand_reg_opr64 dst va_sM va_s0))))); va_lemma_norm_mods ([va_Mod_flags; va_mod_reg_opr64 src; va_mod_reg_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Comment [@ "opaque_to_smt"] let va_code_Comment c = (mk_ins (make_instr_annotate (I.ins_Comment c) (S.AnnotateComment c))) [@ "opaque_to_smt"] let va_codegen_success_Comment c = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Comment va_b0 va_s0 c = va_reveal_opaque (`%va_code_Comment) (va_code_Comment c); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr_annotate (I.ins_Comment c) (S.AnnotateComment c))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr_annotate (I.ins_Comment c) (S.AnnotateComment c))) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Comment c va_s0 va_k = let (va_sM, va_f0) = va_lemma_Comment (va_code_Comment c) va_s0 c in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_ok va_sM va_s0)); va_lemma_norm_mods ([]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- LargeComment [@ "opaque_to_smt"] let va_code_LargeComment c = (mk_ins (make_instr_annotate (I.ins_LargeComment c) (S.AnnotateLargeComment c))) [@ "opaque_to_smt"] let va_codegen_success_LargeComment c = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_LargeComment va_b0 va_s0 c = va_reveal_opaque (`%va_code_LargeComment) (va_code_LargeComment c); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr_annotate (I.ins_LargeComment c) (S.AnnotateLargeComment c))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr_annotate (I.ins_LargeComment c) (S.AnnotateLargeComment c))) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_LargeComment c va_s0 va_k = let (va_sM, va_f0) = va_lemma_LargeComment (va_code_LargeComment c) va_s0 c in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_ok va_sM va_s0)); va_lemma_norm_mods ([]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- NoNewline [@ "opaque_to_smt"] let va_code_NoNewline () = (mk_ins (make_instr_annotate (I.ins_Space 0) (S.AnnotateSpace 0))) [@ "opaque_to_smt"] let va_codegen_success_NoNewline () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_NoNewline va_b0 va_s0 = va_reveal_opaque (`%va_code_NoNewline) (va_code_NoNewline ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr_annotate (I.ins_Space 0) (S.AnnotateSpace 0))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr_annotate (I.ins_Space 0) (S.AnnotateSpace 0))) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_NoNewline va_s0 va_k = let (va_sM, va_f0) = va_lemma_NoNewline (va_code_NoNewline ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_ok va_sM va_s0)); va_lemma_norm_mods ([]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Newline [@ "opaque_to_smt"] let va_code_Newline () = (mk_ins (make_instr_annotate (I.ins_Newline) (S.AnnotateNewline ()))) [@ "opaque_to_smt"] let va_codegen_success_Newline () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Newline va_b0 va_s0 = va_reveal_opaque (`%va_code_Newline) (va_code_Newline ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr_annotate (I.ins_Newline) (S.AnnotateNewline ()))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr_annotate (I.ins_Newline) (S.AnnotateNewline ()))) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Newline va_s0 va_k = let (va_sM, va_f0) = va_lemma_Newline (va_code_Newline ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_ok va_sM va_s0)); va_lemma_norm_mods ([]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Space [@ "opaque_to_smt"] let va_code_Space n = (mk_ins (make_instr_annotate (I.ins_Space n) (S.AnnotateSpace n))) [@ "opaque_to_smt"] let va_codegen_success_Space n = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Space va_b0 va_s0 n = va_reveal_opaque (`%va_code_Space) (va_code_Space n); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr_annotate (I.ins_Space n) (S.AnnotateSpace n))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr_annotate (I.ins_Space n) (S.AnnotateSpace n))) va_s0 in (va_sM, va_fM)
false
false
Vale.X64.InsBasic.fst
{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 5, "initial_ifuel": 0, "max_fuel": 5, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": true, "smtencoding_l_arith_repr": "native", "smtencoding_nl_arith_repr": "wrapped", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": false, "z3cliopt": [ "smt.arith.nl=false", "smt.QI.EAGER_THRESHOLD=100", "smt.CASE_SPLIT=3" ], "z3refresh": false, "z3rlimit": 20, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }
null
val va_wpProof_Space : n:nat -> va_s0:va_state -> va_k:(va_state -> unit -> Type0) -> Ghost (va_state & va_fuel & unit) (requires (va_t_require va_s0 /\ va_wp_Space n va_s0 va_k)) (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Space n) ([]) va_s0 va_k ((va_sM, va_f0, va_g))))
[]
Vale.X64.InsBasic.va_wpProof_Space
{ "file_name": "obj/Vale.X64.InsBasic.fst", "git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e", "git_url": "https://github.com/hacl-star/hacl-star.git", "project_name": "hacl-star" }
n: Prims.nat -> va_s0: Vale.X64.Decls.va_state -> va_k: (_: Vale.X64.Decls.va_state -> _: Prims.unit -> Type0) -> Prims.Ghost ((Vale.X64.Decls.va_state * Vale.X64.Decls.va_fuel) * Prims.unit)
{ "end_col": 22, "end_line": 1184, "start_col": 35, "start_line": 1178 }
Prims.Ghost
val va_lemma_Space : va_b0:va_code -> va_s0:va_state -> n:nat -> Ghost (va_state & va_fuel) (requires (va_require_total va_b0 (va_code_Space n) va_s0 /\ va_get_ok va_s0)) (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\ va_state_eq va_sM (va_update_ok va_sM va_s0)))
[ { "abbrev": true, "full_module": "Vale.X64.Machine_Semantics_s", "short_module": "S" }, { "abbrev": true, "full_module": "Vale.X64.Instructions_s", "short_module": "I" }, { "abbrev": false, "full_module": "Vale.X64.Stack_i", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.Memory", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.Taint_Semantics", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.InsLemmas", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.StateLemmas", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.CPU_Features_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.QuickCode", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.Decls", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.State", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.Machine_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Arch.Types", "short_module": null }, { "abbrev": false, "full_module": "Vale.Arch.HeapImpl", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Types_s", "short_module": null }, { "abbrev": false, "full_module": "FStar.Mul", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]
false
let va_lemma_Space va_b0 va_s0 n = va_reveal_opaque (`%va_code_Space) (va_code_Space n); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr_annotate (I.ins_Space n) (S.AnnotateSpace n))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr_annotate (I.ins_Space n) (S.AnnotateSpace n))) va_s0 in (va_sM, va_fM)
val va_lemma_Space : va_b0:va_code -> va_s0:va_state -> n:nat -> Ghost (va_state & va_fuel) (requires (va_require_total va_b0 (va_code_Space n) va_s0 /\ va_get_ok va_s0)) (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\ va_state_eq va_sM (va_update_ok va_sM va_s0))) let va_lemma_Space va_b0 va_s0 n =
false
null
false
va_reveal_opaque (`%va_code_Space) (va_code_Space n); let va_old_s:va_state = va_s0 in va_ins_lemma (mk_ins (make_instr_annotate (I.ins_Space n) (S.AnnotateSpace n))) va_s0; let va_sM, va_fM = va_eval_ins (mk_ins (make_instr_annotate (I.ins_Space n) (S.AnnotateSpace n))) va_s0 in (va_sM, va_fM)
{ "checked_file": "Vale.X64.InsBasic.fst.checked", "dependencies": [ "Vale.X64.Taint_Semantics.fst.checked", "Vale.X64.StateLemmas.fsti.checked", "Vale.X64.Stack_i.fsti.checked", "Vale.X64.Memory.fsti.checked", "Vale.X64.Machine_Semantics_s.fst.checked", "Vale.X64.Instructions_s.fsti.checked", "Vale.X64.InsLemmas.fsti.checked", "Vale.X64.Decls.fst.checked", "Vale.X64.CPU_Features_s.fst.checked", "Vale.Arch.Types.fsti.checked", "prims.fst.checked", "FStar.UInt.fsti.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Math.Lemmas.fst.checked" ], "interface_file": true, "source_file": "Vale.X64.InsBasic.fst" }
[]
[ "Vale.X64.Decls.va_code", "Vale.X64.Decls.va_state", "Prims.nat", "Vale.X64.State.vale_state", "Vale.X64.Lemmas.fuel", "FStar.Pervasives.Native.Mktuple2", "Vale.X64.Decls.va_fuel", "FStar.Pervasives.Native.tuple2", "Vale.X64.Decls.va_eval_ins", "Vale.X64.Taint_Semantics.mk_ins", "Vale.X64.InsLemmas.make_instr_annotate", "Prims.Nil", "Vale.X64.Instruction_s.instr_out", "Vale.X64.Instruction_s.instr_operand", "Vale.X64.Instruction_s.PreserveFlags", "Vale.X64.Instructions_s.ins_Space", "Vale.X64.Machine_Semantics_s.AnnotateSpace", "Vale.X64.Instruction_s.InstrTypeRecord", "Prims.unit", "Vale.X64.Decls.va_ins_lemma", "Vale.X64.Decls.va_reveal_opaque", "Vale.X64.InsBasic.va_code_Space" ]
[]
module Vale.X64.InsBasic open Vale.X64 open Vale.X64.StateLemmas open Vale.X64.InsLemmas open Vale.X64.Taint_Semantics open Vale.X64.CPU_Features_s open Vale.X64.Memory open Vale.X64.Stack_i module I = Vale.X64.Instructions_s module S = Vale.X64.Machine_Semantics_s friend Vale.X64.Decls #reset-options "--initial_fuel 5 --max_fuel 5 --max_ifuel 2 --z3rlimit 20" //-- Mov64 [@ "opaque_to_smt"] let va_code_Mov64 dst src = (mk_ins (make_instr_annotate (I.ins_Mov64) (S.AnnotateMov64 ()) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Mov64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Mov64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Mov64) (va_code_Mov64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr_annotate (I.ins_Mov64) (S.AnnotateMov64 ()) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr_annotate (I.ins_Mov64) (S.AnnotateMov64 ()) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Mov64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Mov64 (va_code_Mov64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0))); va_lemma_norm_mods ([va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cmovc64 [@ "opaque_to_smt"] let va_code_Cmovc64 dst src = (mk_ins (make_instr (I.ins_Cmovc64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Cmovc64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cmovc64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Cmovc64) (va_code_Cmovc64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cmovc64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cmovc64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cmovc64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cmovc64 (va_code_Cmovc64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0))); va_lemma_norm_mods ([va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Add64 [@ "opaque_to_smt"] let va_code_Add64 dst src = (mk_ins (make_instr (I.ins_Add64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Add64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Add64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Add64) (va_code_Add64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Add64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Add64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Add64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Add64 (va_code_Add64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Add64Wrap [@ "opaque_to_smt"] let va_code_Add64Wrap dst src = (mk_ins (make_instr (I.ins_Add64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Add64Wrap dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Add64Wrap va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Add64Wrap) (va_code_Add64Wrap dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Add64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Add64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Add64Wrap dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Add64Wrap (va_code_Add64Wrap dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- AddLea64 [@ "opaque_to_smt"] let va_code_AddLea64 dst src1 src2 = (mk_ins (make_instr (I.ins_AddLea64) dst src1 src2)) [@ "opaque_to_smt"] let va_codegen_success_AddLea64 dst src1 src2 = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_AddLea64 va_b0 va_s0 dst src1 src2 = va_reveal_opaque (`%va_code_AddLea64) (va_code_AddLea64 dst src1 src2); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_AddLea64) dst src1 src2)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_AddLea64) dst src1 src2)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_AddLea64 dst src1 src2 va_s0 va_k = let (va_sM, va_f0) = va_lemma_AddLea64 (va_code_AddLea64 dst src1 src2) va_s0 dst src1 src2 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0))); va_lemma_norm_mods ([va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Adc64 [@ "opaque_to_smt"] let va_code_Adc64 dst src = (mk_ins (make_instr (I.ins_AddCarry64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Adc64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Adc64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Adc64) (va_code_Adc64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_AddCarry64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_AddCarry64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Adc64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Adc64 (va_code_Adc64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Adc64Wrap [@ "opaque_to_smt"] let va_code_Adc64Wrap dst src = (mk_ins (make_instr (I.ins_AddCarry64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Adc64Wrap dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Adc64Wrap va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Adc64Wrap) (va_code_Adc64Wrap dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_AddCarry64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_AddCarry64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Adc64Wrap dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Adc64Wrap (va_code_Adc64Wrap dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Adcx64Wrap #push-options "--smtencoding.nl_arith_repr boxwrap" [@ "opaque_to_smt"] let va_code_Adcx64Wrap dst src = (mk_ins (make_instr (I.ins_Adcx64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Adcx64Wrap dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Adcx64Wrap va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Adcx64Wrap) (va_code_Adcx64Wrap dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Adcx64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Adcx64) dst src)) va_s0 in assert (Vale.Arch.Types.add_wrap64 (Vale.Arch.Types.add_wrap64 (va_eval_dst_opr64 va_old_s dst) (va_eval_opr64 va_old_s src)) (if Vale.X64.Decls.cf (va_get_flags va_old_s) then 1 else 0) == (va_eval_dst_opr64 va_old_s dst + va_eval_opr64 va_old_s src + (if Vale.X64.Decls.cf (va_get_flags va_old_s) then 1 else 0)) `op_Modulus` pow2_64); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Adcx64Wrap dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Adcx64Wrap (va_code_Adcx64Wrap dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) #pop-options //-- //-- Adox64Wrap [@ "opaque_to_smt"] let va_code_Adox64Wrap dst src = (mk_ins (make_instr (I.ins_Adox64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Adox64Wrap dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Adox64Wrap va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Adox64Wrap) (va_code_Adox64Wrap dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Adox64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Adox64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Adox64Wrap dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Adox64Wrap (va_code_Adox64Wrap dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Sub64 [@ "opaque_to_smt"] let va_code_Sub64 dst src = (mk_ins (make_instr (I.ins_Sub64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Sub64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Sub64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Sub64) (va_code_Sub64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Sub64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Sub64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Sub64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Sub64 (va_code_Sub64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Sub64Wrap [@ "opaque_to_smt"] let va_code_Sub64Wrap dst src = (mk_ins (make_instr (I.ins_Sub64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Sub64Wrap dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Sub64Wrap va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Sub64Wrap) (va_code_Sub64Wrap dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Sub64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Sub64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Sub64Wrap dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Sub64Wrap (va_code_Sub64Wrap dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Sbb64 [@ "opaque_to_smt"] let va_code_Sbb64 dst src = (mk_ins (make_instr (I.ins_Sbb64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Sbb64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Sbb64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Sbb64) (va_code_Sbb64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Sbb64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Sbb64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Sbb64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Sbb64 (va_code_Sbb64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- #restart-solver #push-options "--max_fuel 0 --max_ifuel 0 --using_facts_from 'Prims FStar.UInt'" let lemma_fundamental_div_mod (a b:nat64) : Lemma (pow2_64 * (FStar.UInt.mul_div #64 a b) + (FStar.UInt.mul_mod #64 a b) == a * b) = FStar.Math.Lemmas.lemma_div_mod (a * b) pow2_64 #pop-options //-- lemma_fundamental_div_mod //-- //-- Mul64Wrap [@ "opaque_to_smt"] let va_code_Mul64Wrap src = (mk_ins (make_instr (I.ins_Mul64) src)) [@ "opaque_to_smt"] let va_codegen_success_Mul64Wrap src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Mul64Wrap va_b0 va_s0 src = va_reveal_opaque (`%va_code_Mul64Wrap) (va_code_Mul64Wrap src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Mul64) src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Mul64) src)) va_s0 in lemma_fundamental_div_mod (va_get_reg64 rRax va_old_s) (va_eval_opr64 va_old_s src); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Mul64Wrap src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Mul64Wrap (va_code_Mul64Wrap src) va_s0 src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRax va_sM (va_update_flags va_sM (va_update_ok va_sM va_s0))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRax; va_Mod_flags]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Mulx64 [@ "opaque_to_smt"] let va_code_Mulx64 dst_hi dst_lo src = (mk_ins (make_instr (I.ins_Mulx64) dst_hi dst_lo src)) [@ "opaque_to_smt"] let va_codegen_success_Mulx64 dst_hi dst_lo src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Mulx64 va_b0 va_s0 dst_hi dst_lo src = va_reveal_opaque (`%va_code_Mulx64) (va_code_Mulx64 dst_hi dst_lo src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Mulx64) dst_hi dst_lo src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Mulx64) dst_hi dst_lo src)) va_s0 in lemma_fundamental_div_mod (va_get_reg64 rRdx va_old_s) (va_eval_opr64 va_old_s src); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Mulx64 dst_hi dst_lo src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Mulx64 (va_code_Mulx64 dst_hi dst_lo src) va_s0 dst_hi dst_lo src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst_lo va_sM (va_update_operand_dst_opr64 dst_hi va_sM va_s0)))); va_lemma_norm_mods ([va_mod_dst_opr64 dst_lo; va_mod_dst_opr64 dst_hi]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- lemma_mul_nat //-- //-- lemma_mul_in_bounds //-- //-- IMul64 [@ "opaque_to_smt"] let va_code_IMul64 dst src = (mk_ins (make_instr (I.ins_IMul64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_IMul64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_IMul64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_IMul64) (va_code_IMul64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_IMul64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_IMul64) dst src)) va_s0 in lemma_mul_nat (va_eval_dst_opr64 va_old_s dst) (va_eval_opr64 va_old_s src); lemma_mul_in_bounds (va_eval_dst_opr64 va_old_s dst) (va_eval_opr64 va_old_s src); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_IMul64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_IMul64 (va_code_IMul64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Xor64 [@ "opaque_to_smt"] let va_code_Xor64 dst src = (mk_ins (make_instr_annotate (I.ins_Xor64) (S.AnnotateXor64 ()) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Xor64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Xor64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Xor64) (va_code_Xor64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr_annotate (I.ins_Xor64) (S.AnnotateXor64 ()) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr_annotate (I.ins_Xor64) (S.AnnotateXor64 ()) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Xor64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Xor64 (va_code_Xor64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- And64 [@ "opaque_to_smt"] let va_code_And64 dst src = (mk_ins (make_instr (I.ins_And64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_And64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_And64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_And64) (va_code_And64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_And64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_And64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_And64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_And64 (va_code_And64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Shl64 [@ "opaque_to_smt"] let va_code_Shl64 dst amt = (mk_ins (make_instr (I.ins_Shl64) dst amt)) [@ "opaque_to_smt"] let va_codegen_success_Shl64 dst amt = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Shl64 va_b0 va_s0 dst amt = va_reveal_opaque (`%va_code_Shl64) (va_code_Shl64 dst amt); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Shl64) dst amt)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Shl64) dst amt)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Shl64 dst amt va_s0 va_k = let (va_sM, va_f0) = va_lemma_Shl64 (va_code_Shl64 dst amt) va_s0 dst amt in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Shr64 [@ "opaque_to_smt"] let va_code_Shr64 dst amt = (mk_ins (make_instr (I.ins_Shr64) dst amt)) [@ "opaque_to_smt"] let va_codegen_success_Shr64 dst amt = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Shr64 va_b0 va_s0 dst amt = va_reveal_opaque (`%va_code_Shr64) (va_code_Shr64 dst amt); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Shr64) dst amt)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Shr64) dst amt)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Shr64 dst amt va_s0 va_k = let (va_sM, va_f0) = va_lemma_Shr64 (va_code_Shr64 dst amt) va_s0 dst amt in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_AES [@ "opaque_to_smt"] let va_code_Cpuid_AES () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_AES () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_AES va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_AES) (va_code_Cpuid_AES ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_AES va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_AES (va_code_Cpuid_AES ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Sha [@ "opaque_to_smt"] let va_code_Cpuid_Sha () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Sha () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Sha va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Sha) (va_code_Cpuid_Sha ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Sha va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Sha (va_code_Cpuid_Sha ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Adx_Bmi2 [@ "opaque_to_smt"] let va_code_Cpuid_Adx_Bmi2 () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Adx_Bmi2 () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Adx_Bmi2 va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Adx_Bmi2) (va_code_Cpuid_Adx_Bmi2 ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Adx_Bmi2 va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Adx_Bmi2 (va_code_Cpuid_Adx_Bmi2 ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Avx [@ "opaque_to_smt"] let va_code_Cpuid_Avx () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Avx () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Avx va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Avx) (va_code_Cpuid_Avx ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Avx va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Avx (va_code_Cpuid_Avx ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Avx2 [@ "opaque_to_smt"] let va_code_Cpuid_Avx2 () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Avx2 () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Avx2 va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Avx2) (va_code_Cpuid_Avx2 ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Avx2 va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Avx2 (va_code_Cpuid_Avx2 ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Sse [@ "opaque_to_smt"] let va_code_Cpuid_Sse () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Sse () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Sse va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Sse) (va_code_Cpuid_Sse ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Sse va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Sse (va_code_Cpuid_Sse ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Movbe [@ "opaque_to_smt"] let va_code_Cpuid_Movbe () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Movbe () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Movbe va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Movbe) (va_code_Cpuid_Movbe ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Movbe va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Movbe (va_code_Cpuid_Movbe ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Rdrand [@ "opaque_to_smt"] let va_code_Cpuid_Rdrand () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Rdrand () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Rdrand va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Rdrand) (va_code_Cpuid_Rdrand ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Rdrand va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Rdrand (va_code_Cpuid_Rdrand ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Avx512 [@ "opaque_to_smt"] let va_code_Cpuid_Avx512 () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Avx512 () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Avx512 va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Avx512) (va_code_Cpuid_Avx512 ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Avx512 va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Avx512 (va_code_Cpuid_Avx512 ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Osxsave [@ "opaque_to_smt"] let va_code_Cpuid_Osxsave () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Osxsave () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Osxsave va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Osxsave) (va_code_Cpuid_Osxsave ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Osxsave va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Osxsave (va_code_Cpuid_Osxsave ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Xgetbv_Avx [@ "opaque_to_smt"] let va_code_Xgetbv_Avx () = (mk_ins (make_instr (I.ins_Xgetbv))) [@ "opaque_to_smt"] let va_codegen_success_Xgetbv_Avx () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Xgetbv_Avx va_b0 va_s0 = va_reveal_opaque (`%va_code_Xgetbv_Avx) (va_code_Xgetbv_Avx ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Xgetbv))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Xgetbv))) va_s0 in Vale.X64.CPU_Features_s.xgetbv_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Xgetbv_Avx va_s0 va_k = let (va_sM, va_f0) = va_lemma_Xgetbv_Avx (va_code_Xgetbv_Avx ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Xgetbv_Avx512 [@ "opaque_to_smt"] let va_code_Xgetbv_Avx512 () = (mk_ins (make_instr (I.ins_Xgetbv))) [@ "opaque_to_smt"] let va_codegen_success_Xgetbv_Avx512 () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Xgetbv_Avx512 va_b0 va_s0 = va_reveal_opaque (`%va_code_Xgetbv_Avx512) (va_code_Xgetbv_Avx512 ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Xgetbv))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Xgetbv))) va_s0 in Vale.X64.CPU_Features_s.xgetbv_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Xgetbv_Avx512 va_s0 va_k = let (va_sM, va_f0) = va_lemma_Xgetbv_Avx512 (va_code_Xgetbv_Avx512 ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Nat64Equal [@ "opaque_to_smt"] let va_code_Nat64Equal dst src = (va_Block (va_CCons (va_code_Sub64Wrap (va_coerce_reg_opr64_to_dst_opr64 src) (va_const_opr64 18446744073709551615)) (va_CCons (va_code_Mov64 (va_coerce_reg_opr64_to_dst_opr64 dst) (va_const_opr64 0)) (va_CCons (va_code_Adc64 (va_coerce_reg_opr64_to_dst_opr64 dst) (va_const_opr64 0)) (va_CNil ()))))) [@ "opaque_to_smt"] let va_codegen_success_Nat64Equal dst src = (va_pbool_and (va_codegen_success_Sub64Wrap (va_coerce_reg_opr64_to_dst_opr64 src) (va_const_opr64 18446744073709551615)) (va_pbool_and (va_codegen_success_Mov64 (va_coerce_reg_opr64_to_dst_opr64 dst) (va_const_opr64 0)) (va_pbool_and (va_codegen_success_Adc64 (va_coerce_reg_opr64_to_dst_opr64 dst) (va_const_opr64 0)) (va_ttrue ())))) [@"opaque_to_smt"] let va_lemma_Nat64Equal va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Nat64Equal) (va_code_Nat64Equal dst src); let (va_old_s:va_state) = va_s0 in let (va_b1:va_codes) = va_get_block va_b0 in let (va_s2, va_fc2) = va_lemma_Sub64Wrap (va_hd va_b1) va_s0 (va_coerce_reg_opr64_to_dst_opr64 src) (va_const_opr64 18446744073709551615) in let va_b2 = va_tl va_b1 in let (va_s3, va_fc3) = va_lemma_Mov64 (va_hd va_b2) va_s2 (va_coerce_reg_opr64_to_dst_opr64 dst) (va_const_opr64 0) in let va_b3 = va_tl va_b2 in let (va_s4, va_fc4) = va_lemma_Adc64 (va_hd va_b3) va_s3 (va_coerce_reg_opr64_to_dst_opr64 dst) (va_const_opr64 0) in let va_b4 = va_tl va_b3 in let (va_sM, va_f4) = va_lemma_empty_total va_s4 va_b4 in let va_f3 = va_lemma_merge_total va_b3 va_s3 va_fc4 va_s4 va_f4 va_sM in let va_f2 = va_lemma_merge_total va_b2 va_s2 va_fc3 va_s3 va_f3 va_sM in let va_fM = va_lemma_merge_total va_b1 va_s0 va_fc2 va_s2 va_f2 va_sM in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Nat64Equal dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Nat64Equal (va_code_Nat64Equal dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_reg_opr64 src va_sM (va_update_operand_reg_opr64 dst va_sM va_s0))))); va_lemma_norm_mods ([va_Mod_flags; va_mod_reg_opr64 src; va_mod_reg_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Comment [@ "opaque_to_smt"] let va_code_Comment c = (mk_ins (make_instr_annotate (I.ins_Comment c) (S.AnnotateComment c))) [@ "opaque_to_smt"] let va_codegen_success_Comment c = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Comment va_b0 va_s0 c = va_reveal_opaque (`%va_code_Comment) (va_code_Comment c); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr_annotate (I.ins_Comment c) (S.AnnotateComment c))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr_annotate (I.ins_Comment c) (S.AnnotateComment c))) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Comment c va_s0 va_k = let (va_sM, va_f0) = va_lemma_Comment (va_code_Comment c) va_s0 c in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_ok va_sM va_s0)); va_lemma_norm_mods ([]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- LargeComment [@ "opaque_to_smt"] let va_code_LargeComment c = (mk_ins (make_instr_annotate (I.ins_LargeComment c) (S.AnnotateLargeComment c))) [@ "opaque_to_smt"] let va_codegen_success_LargeComment c = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_LargeComment va_b0 va_s0 c = va_reveal_opaque (`%va_code_LargeComment) (va_code_LargeComment c); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr_annotate (I.ins_LargeComment c) (S.AnnotateLargeComment c))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr_annotate (I.ins_LargeComment c) (S.AnnotateLargeComment c))) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_LargeComment c va_s0 va_k = let (va_sM, va_f0) = va_lemma_LargeComment (va_code_LargeComment c) va_s0 c in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_ok va_sM va_s0)); va_lemma_norm_mods ([]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- NoNewline [@ "opaque_to_smt"] let va_code_NoNewline () = (mk_ins (make_instr_annotate (I.ins_Space 0) (S.AnnotateSpace 0))) [@ "opaque_to_smt"] let va_codegen_success_NoNewline () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_NoNewline va_b0 va_s0 = va_reveal_opaque (`%va_code_NoNewline) (va_code_NoNewline ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr_annotate (I.ins_Space 0) (S.AnnotateSpace 0))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr_annotate (I.ins_Space 0) (S.AnnotateSpace 0))) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_NoNewline va_s0 va_k = let (va_sM, va_f0) = va_lemma_NoNewline (va_code_NoNewline ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_ok va_sM va_s0)); va_lemma_norm_mods ([]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Newline [@ "opaque_to_smt"] let va_code_Newline () = (mk_ins (make_instr_annotate (I.ins_Newline) (S.AnnotateNewline ()))) [@ "opaque_to_smt"] let va_codegen_success_Newline () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Newline va_b0 va_s0 = va_reveal_opaque (`%va_code_Newline) (va_code_Newline ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr_annotate (I.ins_Newline) (S.AnnotateNewline ()))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr_annotate (I.ins_Newline) (S.AnnotateNewline ()))) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Newline va_s0 va_k = let (va_sM, va_f0) = va_lemma_Newline (va_code_Newline ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_ok va_sM va_s0)); va_lemma_norm_mods ([]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Space [@ "opaque_to_smt"] let va_code_Space n = (mk_ins (make_instr_annotate (I.ins_Space n) (S.AnnotateSpace n))) [@ "opaque_to_smt"] let va_codegen_success_Space n = (va_ttrue ()) [@"opaque_to_smt"]
false
false
Vale.X64.InsBasic.fst
{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 5, "initial_ifuel": 0, "max_fuel": 5, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": true, "smtencoding_l_arith_repr": "native", "smtencoding_nl_arith_repr": "wrapped", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": false, "z3cliopt": [ "smt.arith.nl=false", "smt.QI.EAGER_THRESHOLD=100", "smt.CASE_SPLIT=3" ], "z3refresh": false, "z3rlimit": 20, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }
null
val va_lemma_Space : va_b0:va_code -> va_s0:va_state -> n:nat -> Ghost (va_state & va_fuel) (requires (va_require_total va_b0 (va_code_Space n) va_s0 /\ va_get_ok va_s0)) (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\ va_state_eq va_sM (va_update_ok va_sM va_s0)))
[]
Vale.X64.InsBasic.va_lemma_Space
{ "file_name": "obj/Vale.X64.InsBasic.fst", "git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e", "git_url": "https://github.com/hacl-star/hacl-star.git", "project_name": "hacl-star" }
va_b0: Vale.X64.Decls.va_code -> va_s0: Vale.X64.Decls.va_state -> n: Prims.nat -> Prims.Ghost (Vale.X64.Decls.va_state * Vale.X64.Decls.va_fuel)
{ "end_col": 16, "end_line": 1174, "start_col": 2, "start_line": 1169 }
Prims.Ghost
val va_wpProof_Prefetchnta : v:va_operand_opr64 -> va_s0:va_state -> va_k:(va_state -> unit -> Type0) -> Ghost (va_state & va_fuel & unit) (requires (va_t_require va_s0 /\ va_wp_Prefetchnta v va_s0 va_k)) (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Prefetchnta v) ([]) va_s0 va_k ((va_sM, va_f0, va_g))))
[ { "abbrev": true, "full_module": "Vale.X64.Machine_Semantics_s", "short_module": "S" }, { "abbrev": true, "full_module": "Vale.X64.Instructions_s", "short_module": "I" }, { "abbrev": false, "full_module": "Vale.X64.Stack_i", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.Memory", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.Taint_Semantics", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.InsLemmas", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.StateLemmas", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.CPU_Features_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.QuickCode", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.Decls", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.State", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64.Machine_s", "short_module": null }, { "abbrev": false, "full_module": "Vale.Arch.Types", "short_module": null }, { "abbrev": false, "full_module": "Vale.Arch.HeapImpl", "short_module": null }, { "abbrev": false, "full_module": "Vale.Def.Types_s", "short_module": null }, { "abbrev": false, "full_module": "FStar.Mul", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64", "short_module": null }, { "abbrev": false, "full_module": "Vale.X64", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]
false
let va_wpProof_Prefetchnta v va_s0 va_k = let (va_sM, va_f0) = va_lemma_Prefetchnta (va_code_Prefetchnta v) va_s0 v in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_ok va_sM va_s0)); va_lemma_norm_mods ([]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g)
val va_wpProof_Prefetchnta : v:va_operand_opr64 -> va_s0:va_state -> va_k:(va_state -> unit -> Type0) -> Ghost (va_state & va_fuel & unit) (requires (va_t_require va_s0 /\ va_wp_Prefetchnta v va_s0 va_k)) (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Prefetchnta v) ([]) va_s0 va_k ((va_sM, va_f0, va_g)))) let va_wpProof_Prefetchnta v va_s0 va_k =
false
null
false
let va_sM, va_f0 = va_lemma_Prefetchnta (va_code_Prefetchnta v) va_s0 v in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_ok va_sM va_s0)); va_lemma_norm_mods ([]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g)
{ "checked_file": "Vale.X64.InsBasic.fst.checked", "dependencies": [ "Vale.X64.Taint_Semantics.fst.checked", "Vale.X64.StateLemmas.fsti.checked", "Vale.X64.Stack_i.fsti.checked", "Vale.X64.Memory.fsti.checked", "Vale.X64.Machine_Semantics_s.fst.checked", "Vale.X64.Instructions_s.fsti.checked", "Vale.X64.InsLemmas.fsti.checked", "Vale.X64.Decls.fst.checked", "Vale.X64.CPU_Features_s.fst.checked", "Vale.Arch.Types.fsti.checked", "prims.fst.checked", "FStar.UInt.fsti.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Math.Lemmas.fst.checked" ], "interface_file": true, "source_file": "Vale.X64.InsBasic.fst" }
[]
[ "Vale.X64.Decls.va_operand_opr64", "Vale.X64.Decls.va_state", "Prims.unit", "Vale.X64.Decls.va_fuel", "FStar.Pervasives.Native.Mktuple3", "Vale.X64.QuickCode.va_lemma_norm_mods", "Prims.Nil", "Vale.X64.QuickCode.mod_t", "Prims._assert", "Vale.X64.Decls.va_state_eq", "Vale.X64.Decls.va_update_ok", "Vale.X64.Decls.va_lemma_upd_update", "FStar.Pervasives.Native.tuple3", "FStar.Pervasives.Native.tuple2", "Vale.X64.State.vale_state", "Vale.X64.InsBasic.va_lemma_Prefetchnta", "Vale.X64.InsBasic.va_code_Prefetchnta" ]
[]
module Vale.X64.InsBasic open Vale.X64 open Vale.X64.StateLemmas open Vale.X64.InsLemmas open Vale.X64.Taint_Semantics open Vale.X64.CPU_Features_s open Vale.X64.Memory open Vale.X64.Stack_i module I = Vale.X64.Instructions_s module S = Vale.X64.Machine_Semantics_s friend Vale.X64.Decls #reset-options "--initial_fuel 5 --max_fuel 5 --max_ifuel 2 --z3rlimit 20" //-- Mov64 [@ "opaque_to_smt"] let va_code_Mov64 dst src = (mk_ins (make_instr_annotate (I.ins_Mov64) (S.AnnotateMov64 ()) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Mov64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Mov64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Mov64) (va_code_Mov64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr_annotate (I.ins_Mov64) (S.AnnotateMov64 ()) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr_annotate (I.ins_Mov64) (S.AnnotateMov64 ()) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Mov64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Mov64 (va_code_Mov64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0))); va_lemma_norm_mods ([va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cmovc64 [@ "opaque_to_smt"] let va_code_Cmovc64 dst src = (mk_ins (make_instr (I.ins_Cmovc64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Cmovc64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cmovc64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Cmovc64) (va_code_Cmovc64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cmovc64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cmovc64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cmovc64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cmovc64 (va_code_Cmovc64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0))); va_lemma_norm_mods ([va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Add64 [@ "opaque_to_smt"] let va_code_Add64 dst src = (mk_ins (make_instr (I.ins_Add64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Add64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Add64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Add64) (va_code_Add64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Add64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Add64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Add64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Add64 (va_code_Add64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Add64Wrap [@ "opaque_to_smt"] let va_code_Add64Wrap dst src = (mk_ins (make_instr (I.ins_Add64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Add64Wrap dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Add64Wrap va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Add64Wrap) (va_code_Add64Wrap dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Add64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Add64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Add64Wrap dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Add64Wrap (va_code_Add64Wrap dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- AddLea64 [@ "opaque_to_smt"] let va_code_AddLea64 dst src1 src2 = (mk_ins (make_instr (I.ins_AddLea64) dst src1 src2)) [@ "opaque_to_smt"] let va_codegen_success_AddLea64 dst src1 src2 = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_AddLea64 va_b0 va_s0 dst src1 src2 = va_reveal_opaque (`%va_code_AddLea64) (va_code_AddLea64 dst src1 src2); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_AddLea64) dst src1 src2)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_AddLea64) dst src1 src2)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_AddLea64 dst src1 src2 va_s0 va_k = let (va_sM, va_f0) = va_lemma_AddLea64 (va_code_AddLea64 dst src1 src2) va_s0 dst src1 src2 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0))); va_lemma_norm_mods ([va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Adc64 [@ "opaque_to_smt"] let va_code_Adc64 dst src = (mk_ins (make_instr (I.ins_AddCarry64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Adc64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Adc64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Adc64) (va_code_Adc64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_AddCarry64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_AddCarry64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Adc64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Adc64 (va_code_Adc64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Adc64Wrap [@ "opaque_to_smt"] let va_code_Adc64Wrap dst src = (mk_ins (make_instr (I.ins_AddCarry64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Adc64Wrap dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Adc64Wrap va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Adc64Wrap) (va_code_Adc64Wrap dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_AddCarry64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_AddCarry64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Adc64Wrap dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Adc64Wrap (va_code_Adc64Wrap dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Adcx64Wrap #push-options "--smtencoding.nl_arith_repr boxwrap" [@ "opaque_to_smt"] let va_code_Adcx64Wrap dst src = (mk_ins (make_instr (I.ins_Adcx64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Adcx64Wrap dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Adcx64Wrap va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Adcx64Wrap) (va_code_Adcx64Wrap dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Adcx64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Adcx64) dst src)) va_s0 in assert (Vale.Arch.Types.add_wrap64 (Vale.Arch.Types.add_wrap64 (va_eval_dst_opr64 va_old_s dst) (va_eval_opr64 va_old_s src)) (if Vale.X64.Decls.cf (va_get_flags va_old_s) then 1 else 0) == (va_eval_dst_opr64 va_old_s dst + va_eval_opr64 va_old_s src + (if Vale.X64.Decls.cf (va_get_flags va_old_s) then 1 else 0)) `op_Modulus` pow2_64); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Adcx64Wrap dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Adcx64Wrap (va_code_Adcx64Wrap dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) #pop-options //-- //-- Adox64Wrap [@ "opaque_to_smt"] let va_code_Adox64Wrap dst src = (mk_ins (make_instr (I.ins_Adox64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Adox64Wrap dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Adox64Wrap va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Adox64Wrap) (va_code_Adox64Wrap dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Adox64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Adox64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Adox64Wrap dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Adox64Wrap (va_code_Adox64Wrap dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Sub64 [@ "opaque_to_smt"] let va_code_Sub64 dst src = (mk_ins (make_instr (I.ins_Sub64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Sub64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Sub64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Sub64) (va_code_Sub64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Sub64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Sub64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Sub64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Sub64 (va_code_Sub64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Sub64Wrap [@ "opaque_to_smt"] let va_code_Sub64Wrap dst src = (mk_ins (make_instr (I.ins_Sub64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Sub64Wrap dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Sub64Wrap va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Sub64Wrap) (va_code_Sub64Wrap dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Sub64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Sub64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Sub64Wrap dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Sub64Wrap (va_code_Sub64Wrap dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Sbb64 [@ "opaque_to_smt"] let va_code_Sbb64 dst src = (mk_ins (make_instr (I.ins_Sbb64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Sbb64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Sbb64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Sbb64) (va_code_Sbb64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Sbb64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Sbb64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Sbb64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Sbb64 (va_code_Sbb64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- #restart-solver #push-options "--max_fuel 0 --max_ifuel 0 --using_facts_from 'Prims FStar.UInt'" let lemma_fundamental_div_mod (a b:nat64) : Lemma (pow2_64 * (FStar.UInt.mul_div #64 a b) + (FStar.UInt.mul_mod #64 a b) == a * b) = FStar.Math.Lemmas.lemma_div_mod (a * b) pow2_64 #pop-options //-- lemma_fundamental_div_mod //-- //-- Mul64Wrap [@ "opaque_to_smt"] let va_code_Mul64Wrap src = (mk_ins (make_instr (I.ins_Mul64) src)) [@ "opaque_to_smt"] let va_codegen_success_Mul64Wrap src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Mul64Wrap va_b0 va_s0 src = va_reveal_opaque (`%va_code_Mul64Wrap) (va_code_Mul64Wrap src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Mul64) src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Mul64) src)) va_s0 in lemma_fundamental_div_mod (va_get_reg64 rRax va_old_s) (va_eval_opr64 va_old_s src); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Mul64Wrap src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Mul64Wrap (va_code_Mul64Wrap src) va_s0 src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRax va_sM (va_update_flags va_sM (va_update_ok va_sM va_s0))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRax; va_Mod_flags]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Mulx64 [@ "opaque_to_smt"] let va_code_Mulx64 dst_hi dst_lo src = (mk_ins (make_instr (I.ins_Mulx64) dst_hi dst_lo src)) [@ "opaque_to_smt"] let va_codegen_success_Mulx64 dst_hi dst_lo src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Mulx64 va_b0 va_s0 dst_hi dst_lo src = va_reveal_opaque (`%va_code_Mulx64) (va_code_Mulx64 dst_hi dst_lo src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Mulx64) dst_hi dst_lo src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Mulx64) dst_hi dst_lo src)) va_s0 in lemma_fundamental_div_mod (va_get_reg64 rRdx va_old_s) (va_eval_opr64 va_old_s src); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Mulx64 dst_hi dst_lo src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Mulx64 (va_code_Mulx64 dst_hi dst_lo src) va_s0 dst_hi dst_lo src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst_lo va_sM (va_update_operand_dst_opr64 dst_hi va_sM va_s0)))); va_lemma_norm_mods ([va_mod_dst_opr64 dst_lo; va_mod_dst_opr64 dst_hi]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- lemma_mul_nat //-- //-- lemma_mul_in_bounds //-- //-- IMul64 [@ "opaque_to_smt"] let va_code_IMul64 dst src = (mk_ins (make_instr (I.ins_IMul64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_IMul64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_IMul64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_IMul64) (va_code_IMul64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_IMul64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_IMul64) dst src)) va_s0 in lemma_mul_nat (va_eval_dst_opr64 va_old_s dst) (va_eval_opr64 va_old_s src); lemma_mul_in_bounds (va_eval_dst_opr64 va_old_s dst) (va_eval_opr64 va_old_s src); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_IMul64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_IMul64 (va_code_IMul64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Xor64 [@ "opaque_to_smt"] let va_code_Xor64 dst src = (mk_ins (make_instr_annotate (I.ins_Xor64) (S.AnnotateXor64 ()) dst src)) [@ "opaque_to_smt"] let va_codegen_success_Xor64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Xor64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Xor64) (va_code_Xor64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr_annotate (I.ins_Xor64) (S.AnnotateXor64 ()) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr_annotate (I.ins_Xor64) (S.AnnotateXor64 ()) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Xor64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Xor64 (va_code_Xor64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- And64 [@ "opaque_to_smt"] let va_code_And64 dst src = (mk_ins (make_instr (I.ins_And64) dst src)) [@ "opaque_to_smt"] let va_codegen_success_And64 dst src = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_And64 va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_And64) (va_code_And64 dst src); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_And64) dst src)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_And64) dst src)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_And64 dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_And64 (va_code_And64 dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Shl64 [@ "opaque_to_smt"] let va_code_Shl64 dst amt = (mk_ins (make_instr (I.ins_Shl64) dst amt)) [@ "opaque_to_smt"] let va_codegen_success_Shl64 dst amt = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Shl64 va_b0 va_s0 dst amt = va_reveal_opaque (`%va_code_Shl64) (va_code_Shl64 dst amt); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Shl64) dst amt)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Shl64) dst amt)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Shl64 dst amt va_s0 va_k = let (va_sM, va_f0) = va_lemma_Shl64 (va_code_Shl64 dst amt) va_s0 dst amt in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Shr64 [@ "opaque_to_smt"] let va_code_Shr64 dst amt = (mk_ins (make_instr (I.ins_Shr64) dst amt)) [@ "opaque_to_smt"] let va_codegen_success_Shr64 dst amt = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Shr64 va_b0 va_s0 dst amt = va_reveal_opaque (`%va_code_Shr64) (va_code_Shr64 dst amt); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Shr64) dst amt)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Shr64) dst amt)) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Shr64 dst amt va_s0 va_k = let (va_sM, va_f0) = va_lemma_Shr64 (va_code_Shr64 dst amt) va_s0 dst amt in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_dst_opr64 dst va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_flags; va_mod_dst_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_AES [@ "opaque_to_smt"] let va_code_Cpuid_AES () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_AES () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_AES va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_AES) (va_code_Cpuid_AES ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_AES va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_AES (va_code_Cpuid_AES ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Sha [@ "opaque_to_smt"] let va_code_Cpuid_Sha () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Sha () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Sha va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Sha) (va_code_Cpuid_Sha ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Sha va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Sha (va_code_Cpuid_Sha ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Adx_Bmi2 [@ "opaque_to_smt"] let va_code_Cpuid_Adx_Bmi2 () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Adx_Bmi2 () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Adx_Bmi2 va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Adx_Bmi2) (va_code_Cpuid_Adx_Bmi2 ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Adx_Bmi2 va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Adx_Bmi2 (va_code_Cpuid_Adx_Bmi2 ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Avx [@ "opaque_to_smt"] let va_code_Cpuid_Avx () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Avx () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Avx va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Avx) (va_code_Cpuid_Avx ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Avx va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Avx (va_code_Cpuid_Avx ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Avx2 [@ "opaque_to_smt"] let va_code_Cpuid_Avx2 () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Avx2 () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Avx2 va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Avx2) (va_code_Cpuid_Avx2 ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Avx2 va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Avx2 (va_code_Cpuid_Avx2 ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Sse [@ "opaque_to_smt"] let va_code_Cpuid_Sse () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Sse () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Sse va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Sse) (va_code_Cpuid_Sse ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Sse va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Sse (va_code_Cpuid_Sse ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Movbe [@ "opaque_to_smt"] let va_code_Cpuid_Movbe () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Movbe () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Movbe va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Movbe) (va_code_Cpuid_Movbe ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Movbe va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Movbe (va_code_Cpuid_Movbe ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Rdrand [@ "opaque_to_smt"] let va_code_Cpuid_Rdrand () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Rdrand () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Rdrand va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Rdrand) (va_code_Cpuid_Rdrand ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Rdrand va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Rdrand (va_code_Cpuid_Rdrand ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Avx512 [@ "opaque_to_smt"] let va_code_Cpuid_Avx512 () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Avx512 () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Avx512 va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Avx512) (va_code_Cpuid_Avx512 ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Avx512 va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Avx512 (va_code_Cpuid_Avx512 ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Cpuid_Osxsave [@ "opaque_to_smt"] let va_code_Cpuid_Osxsave () = (mk_ins (make_instr (I.ins_Cpuid))) [@ "opaque_to_smt"] let va_codegen_success_Cpuid_Osxsave () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Cpuid_Osxsave va_b0 va_s0 = va_reveal_opaque (`%va_code_Cpuid_Osxsave) (va_code_Cpuid_Osxsave ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Cpuid))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Cpuid))) va_s0 in Vale.X64.CPU_Features_s.cpuid_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Cpuid_Osxsave va_s0 va_k = let (va_sM, va_f0) = va_lemma_Cpuid_Osxsave (va_code_Cpuid_Osxsave ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRcx va_sM (va_update_reg64 rRbx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRcx; va_Mod_reg64 rRbx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Xgetbv_Avx [@ "opaque_to_smt"] let va_code_Xgetbv_Avx () = (mk_ins (make_instr (I.ins_Xgetbv))) [@ "opaque_to_smt"] let va_codegen_success_Xgetbv_Avx () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Xgetbv_Avx va_b0 va_s0 = va_reveal_opaque (`%va_code_Xgetbv_Avx) (va_code_Xgetbv_Avx ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Xgetbv))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Xgetbv))) va_s0 in Vale.X64.CPU_Features_s.xgetbv_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Xgetbv_Avx va_s0 va_k = let (va_sM, va_f0) = va_lemma_Xgetbv_Avx (va_code_Xgetbv_Avx ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Xgetbv_Avx512 [@ "opaque_to_smt"] let va_code_Xgetbv_Avx512 () = (mk_ins (make_instr (I.ins_Xgetbv))) [@ "opaque_to_smt"] let va_codegen_success_Xgetbv_Avx512 () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Xgetbv_Avx512 va_b0 va_s0 = va_reveal_opaque (`%va_code_Xgetbv_Avx512) (va_code_Xgetbv_Avx512 ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr (I.ins_Xgetbv))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr (I.ins_Xgetbv))) va_s0 in Vale.X64.CPU_Features_s.xgetbv_features (); (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Xgetbv_Avx512 va_s0 va_k = let (va_sM, va_f0) = va_lemma_Xgetbv_Avx512 (va_code_Xgetbv_Avx512 ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_reg64 rRdx va_sM (va_update_reg64 rRax va_sM (va_update_ok va_sM va_s0)))); va_lemma_norm_mods ([va_Mod_reg64 rRdx; va_Mod_reg64 rRax]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Nat64Equal [@ "opaque_to_smt"] let va_code_Nat64Equal dst src = (va_Block (va_CCons (va_code_Sub64Wrap (va_coerce_reg_opr64_to_dst_opr64 src) (va_const_opr64 18446744073709551615)) (va_CCons (va_code_Mov64 (va_coerce_reg_opr64_to_dst_opr64 dst) (va_const_opr64 0)) (va_CCons (va_code_Adc64 (va_coerce_reg_opr64_to_dst_opr64 dst) (va_const_opr64 0)) (va_CNil ()))))) [@ "opaque_to_smt"] let va_codegen_success_Nat64Equal dst src = (va_pbool_and (va_codegen_success_Sub64Wrap (va_coerce_reg_opr64_to_dst_opr64 src) (va_const_opr64 18446744073709551615)) (va_pbool_and (va_codegen_success_Mov64 (va_coerce_reg_opr64_to_dst_opr64 dst) (va_const_opr64 0)) (va_pbool_and (va_codegen_success_Adc64 (va_coerce_reg_opr64_to_dst_opr64 dst) (va_const_opr64 0)) (va_ttrue ())))) [@"opaque_to_smt"] let va_lemma_Nat64Equal va_b0 va_s0 dst src = va_reveal_opaque (`%va_code_Nat64Equal) (va_code_Nat64Equal dst src); let (va_old_s:va_state) = va_s0 in let (va_b1:va_codes) = va_get_block va_b0 in let (va_s2, va_fc2) = va_lemma_Sub64Wrap (va_hd va_b1) va_s0 (va_coerce_reg_opr64_to_dst_opr64 src) (va_const_opr64 18446744073709551615) in let va_b2 = va_tl va_b1 in let (va_s3, va_fc3) = va_lemma_Mov64 (va_hd va_b2) va_s2 (va_coerce_reg_opr64_to_dst_opr64 dst) (va_const_opr64 0) in let va_b3 = va_tl va_b2 in let (va_s4, va_fc4) = va_lemma_Adc64 (va_hd va_b3) va_s3 (va_coerce_reg_opr64_to_dst_opr64 dst) (va_const_opr64 0) in let va_b4 = va_tl va_b3 in let (va_sM, va_f4) = va_lemma_empty_total va_s4 va_b4 in let va_f3 = va_lemma_merge_total va_b3 va_s3 va_fc4 va_s4 va_f4 va_sM in let va_f2 = va_lemma_merge_total va_b2 va_s2 va_fc3 va_s3 va_f3 va_sM in let va_fM = va_lemma_merge_total va_b1 va_s0 va_fc2 va_s2 va_f2 va_sM in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Nat64Equal dst src va_s0 va_k = let (va_sM, va_f0) = va_lemma_Nat64Equal (va_code_Nat64Equal dst src) va_s0 dst src in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_flags va_sM (va_update_ok va_sM (va_update_operand_reg_opr64 src va_sM (va_update_operand_reg_opr64 dst va_sM va_s0))))); va_lemma_norm_mods ([va_Mod_flags; va_mod_reg_opr64 src; va_mod_reg_opr64 dst]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Comment [@ "opaque_to_smt"] let va_code_Comment c = (mk_ins (make_instr_annotate (I.ins_Comment c) (S.AnnotateComment c))) [@ "opaque_to_smt"] let va_codegen_success_Comment c = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Comment va_b0 va_s0 c = va_reveal_opaque (`%va_code_Comment) (va_code_Comment c); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr_annotate (I.ins_Comment c) (S.AnnotateComment c))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr_annotate (I.ins_Comment c) (S.AnnotateComment c))) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Comment c va_s0 va_k = let (va_sM, va_f0) = va_lemma_Comment (va_code_Comment c) va_s0 c in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_ok va_sM va_s0)); va_lemma_norm_mods ([]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- LargeComment [@ "opaque_to_smt"] let va_code_LargeComment c = (mk_ins (make_instr_annotate (I.ins_LargeComment c) (S.AnnotateLargeComment c))) [@ "opaque_to_smt"] let va_codegen_success_LargeComment c = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_LargeComment va_b0 va_s0 c = va_reveal_opaque (`%va_code_LargeComment) (va_code_LargeComment c); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr_annotate (I.ins_LargeComment c) (S.AnnotateLargeComment c))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr_annotate (I.ins_LargeComment c) (S.AnnotateLargeComment c))) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_LargeComment c va_s0 va_k = let (va_sM, va_f0) = va_lemma_LargeComment (va_code_LargeComment c) va_s0 c in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_ok va_sM va_s0)); va_lemma_norm_mods ([]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- NoNewline [@ "opaque_to_smt"] let va_code_NoNewline () = (mk_ins (make_instr_annotate (I.ins_Space 0) (S.AnnotateSpace 0))) [@ "opaque_to_smt"] let va_codegen_success_NoNewline () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_NoNewline va_b0 va_s0 = va_reveal_opaque (`%va_code_NoNewline) (va_code_NoNewline ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr_annotate (I.ins_Space 0) (S.AnnotateSpace 0))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr_annotate (I.ins_Space 0) (S.AnnotateSpace 0))) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_NoNewline va_s0 va_k = let (va_sM, va_f0) = va_lemma_NoNewline (va_code_NoNewline ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_ok va_sM va_s0)); va_lemma_norm_mods ([]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Newline [@ "opaque_to_smt"] let va_code_Newline () = (mk_ins (make_instr_annotate (I.ins_Newline) (S.AnnotateNewline ()))) [@ "opaque_to_smt"] let va_codegen_success_Newline () = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Newline va_b0 va_s0 = va_reveal_opaque (`%va_code_Newline) (va_code_Newline ()); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr_annotate (I.ins_Newline) (S.AnnotateNewline ()))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr_annotate (I.ins_Newline) (S.AnnotateNewline ()))) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Newline va_s0 va_k = let (va_sM, va_f0) = va_lemma_Newline (va_code_Newline ()) va_s0 in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_ok va_sM va_s0)); va_lemma_norm_mods ([]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Space [@ "opaque_to_smt"] let va_code_Space n = (mk_ins (make_instr_annotate (I.ins_Space n) (S.AnnotateSpace n))) [@ "opaque_to_smt"] let va_codegen_success_Space n = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Space va_b0 va_s0 n = va_reveal_opaque (`%va_code_Space) (va_code_Space n); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr_annotate (I.ins_Space n) (S.AnnotateSpace n))) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr_annotate (I.ins_Space n) (S.AnnotateSpace n))) va_s0 in (va_sM, va_fM) [@"opaque_to_smt"] let va_wpProof_Space n va_s0 va_k = let (va_sM, va_f0) = va_lemma_Space (va_code_Space n) va_s0 n in va_lemma_upd_update va_sM; assert (va_state_eq va_sM (va_update_ok va_sM va_s0)); va_lemma_norm_mods ([]) va_sM va_s0; let va_g = () in (va_sM, va_f0, va_g) //-- //-- Prefetchnta [@ "opaque_to_smt"] let va_code_Prefetchnta v = (mk_ins (make_instr_annotate (I.ins_Prefetchnta) (S.AnnotatePrefetchnta ()) v)) [@ "opaque_to_smt"] let va_codegen_success_Prefetchnta v = (va_ttrue ()) [@"opaque_to_smt"] let va_lemma_Prefetchnta va_b0 va_s0 v = va_reveal_opaque (`%va_code_Prefetchnta) (va_code_Prefetchnta v); let (va_old_s:va_state) = va_s0 in va_ins_lemma (mk_ins (make_instr_annotate (I.ins_Prefetchnta) (S.AnnotatePrefetchnta ()) v)) va_s0; let (va_sM, va_fM) = va_eval_ins (mk_ins (make_instr_annotate (I.ins_Prefetchnta) (S.AnnotatePrefetchnta ()) v)) va_s0 in (va_sM, va_fM)
false
false
Vale.X64.InsBasic.fst
{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 5, "initial_ifuel": 0, "max_fuel": 5, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": true, "smtencoding_l_arith_repr": "native", "smtencoding_nl_arith_repr": "wrapped", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": false, "z3cliopt": [ "smt.arith.nl=false", "smt.QI.EAGER_THRESHOLD=100", "smt.CASE_SPLIT=3" ], "z3refresh": false, "z3rlimit": 20, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }
null
val va_wpProof_Prefetchnta : v:va_operand_opr64 -> va_s0:va_state -> va_k:(va_state -> unit -> Type0) -> Ghost (va_state & va_fuel & unit) (requires (va_t_require va_s0 /\ va_wp_Prefetchnta v va_s0 va_k)) (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_Prefetchnta v) ([]) va_s0 va_k ((va_sM, va_f0, va_g))))
[]
Vale.X64.InsBasic.va_wpProof_Prefetchnta
{ "file_name": "obj/Vale.X64.InsBasic.fst", "git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e", "git_url": "https://github.com/hacl-star/hacl-star.git", "project_name": "hacl-star" }
v: Vale.X64.Decls.va_operand_opr64 -> va_s0: Vale.X64.Decls.va_state -> va_k: (_: Vale.X64.Decls.va_state -> _: Prims.unit -> Type0) -> Prims.Ghost ((Vale.X64.Decls.va_state * Vale.X64.Decls.va_fuel) * Prims.unit)
{ "end_col": 22, "end_line": 1215, "start_col": 41, "start_line": 1209 }
Prims.Tot
[ { "abbrev": true, "full_module": "Spec.Agile.Hash", "short_module": "Hash" }, { "abbrev": true, "full_module": "Lib.Sequence", "short_module": "LSeq" }, { "abbrev": true, "full_module": "Lib.ByteSequence", "short_module": "BSeq" }, { "abbrev": true, "full_module": "Spec.RSAPSS", "short_module": "S" }, { "abbrev": true, "full_module": "FStar.HyperStack.ST", "short_module": "ST" }, { "abbrev": false, "full_module": "Hacl.Bignum.Definitions", "short_module": null }, { "abbrev": false, "full_module": "Lib.Buffer", "short_module": null }, { "abbrev": false, "full_module": "Lib.IntTypes", "short_module": null }, { "abbrev": false, "full_module": "FStar.Mul", "short_module": null }, { "abbrev": false, "full_module": "FStar.HyperStack.ST", "short_module": null }, { "abbrev": false, "full_module": "FStar.HyperStack", "short_module": null }, { "abbrev": false, "full_module": "Hacl.Impl.RSAPSS", "short_module": null }, { "abbrev": false, "full_module": "Hacl.Impl.RSAPSS", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]
false
let less_than_max_input_length = Spec.Hash.Definitions.less_than_max_input_length
let less_than_max_input_length =
false
null
false
Spec.Hash.Definitions.less_than_max_input_length
{ "checked_file": "Hacl.Impl.RSAPSS.MGF.fst.checked", "dependencies": [ "Spec.RSAPSS.fst.checked", "Spec.Hash.Definitions.fst.checked", "Spec.Agile.Hash.fsti.checked", "prims.fst.checked", "Lib.Sequence.fsti.checked", "Lib.IntTypes.fsti.checked", "Lib.ByteSequence.fsti.checked", "Lib.Buffer.fsti.checked", "Hacl.Streaming.SHA2.fst.checked", "Hacl.Hash.Definitions.fst.checked", "Hacl.Bignum.Definitions.fst.checked", "FStar.UInt32.fsti.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Mul.fst.checked", "FStar.HyperStack.ST.fsti.checked", "FStar.HyperStack.fst.checked" ], "interface_file": false, "source_file": "Hacl.Impl.RSAPSS.MGF.fst" }
[ "total" ]
[ "Spec.Hash.Definitions.less_than_max_input_length" ]
[]
module Hacl.Impl.RSAPSS.MGF open FStar.HyperStack open FStar.HyperStack.ST open FStar.Mul open Lib.IntTypes open Lib.Buffer open Hacl.Bignum.Definitions module ST = FStar.HyperStack.ST module S = Spec.RSAPSS module BSeq = Lib.ByteSequence module LSeq = Lib.Sequence module Hash = Spec.Agile.Hash #reset-options "--z3rlimit 50 --fuel 0 --ifuel 0" val hash_len: a:Hash.hash_alg{S.hash_is_supported a} -> Tot (res:size_t{v res == Hash.hash_length a}) [@CInline] let hash_len a = Hacl.Hash.Definitions.hash_len a inline_for_extraction noextract let max_input_length = Hash.max_input_length
false
true
Hacl.Impl.RSAPSS.MGF.fst
{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 0, "initial_ifuel": 0, "max_fuel": 0, "max_ifuel": 0, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": false, "z3cliopt": [], "z3refresh": false, "z3rlimit": 50, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }
null
val less_than_max_input_length : l: Prims.int -> a: Spec.Hash.Definitions.hash_alg -> Prims.bool
[]
Hacl.Impl.RSAPSS.MGF.less_than_max_input_length
{ "file_name": "code/rsapss/Hacl.Impl.RSAPSS.MGF.fst", "git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e", "git_url": "https://github.com/hacl-star/hacl-star.git", "project_name": "hacl-star" }
l: Prims.int -> a: Spec.Hash.Definitions.hash_alg -> Prims.bool
{ "end_col": 81, "end_line": 30, "start_col": 33, "start_line": 30 }
Prims.Tot
[ { "abbrev": true, "full_module": "Spec.Agile.Hash", "short_module": "Hash" }, { "abbrev": true, "full_module": "Lib.Sequence", "short_module": "LSeq" }, { "abbrev": true, "full_module": "Lib.ByteSequence", "short_module": "BSeq" }, { "abbrev": true, "full_module": "Spec.RSAPSS", "short_module": "S" }, { "abbrev": true, "full_module": "FStar.HyperStack.ST", "short_module": "ST" }, { "abbrev": false, "full_module": "Hacl.Bignum.Definitions", "short_module": null }, { "abbrev": false, "full_module": "Lib.Buffer", "short_module": null }, { "abbrev": false, "full_module": "Lib.IntTypes", "short_module": null }, { "abbrev": false, "full_module": "FStar.Mul", "short_module": null }, { "abbrev": false, "full_module": "FStar.HyperStack.ST", "short_module": null }, { "abbrev": false, "full_module": "FStar.HyperStack", "short_module": null }, { "abbrev": false, "full_module": "Hacl.Impl.RSAPSS", "short_module": null }, { "abbrev": false, "full_module": "Hacl.Impl.RSAPSS", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]
false
let max_input_length = Hash.max_input_length
let max_input_length =
false
null
false
Hash.max_input_length
{ "checked_file": "Hacl.Impl.RSAPSS.MGF.fst.checked", "dependencies": [ "Spec.RSAPSS.fst.checked", "Spec.Hash.Definitions.fst.checked", "Spec.Agile.Hash.fsti.checked", "prims.fst.checked", "Lib.Sequence.fsti.checked", "Lib.IntTypes.fsti.checked", "Lib.ByteSequence.fsti.checked", "Lib.Buffer.fsti.checked", "Hacl.Streaming.SHA2.fst.checked", "Hacl.Hash.Definitions.fst.checked", "Hacl.Bignum.Definitions.fst.checked", "FStar.UInt32.fsti.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Mul.fst.checked", "FStar.HyperStack.ST.fsti.checked", "FStar.HyperStack.fst.checked" ], "interface_file": false, "source_file": "Hacl.Impl.RSAPSS.MGF.fst" }
[ "total" ]
[ "Spec.Hash.Definitions.max_input_length" ]
[]
module Hacl.Impl.RSAPSS.MGF open FStar.HyperStack open FStar.HyperStack.ST open FStar.Mul open Lib.IntTypes open Lib.Buffer open Hacl.Bignum.Definitions module ST = FStar.HyperStack.ST module S = Spec.RSAPSS module BSeq = Lib.ByteSequence module LSeq = Lib.Sequence module Hash = Spec.Agile.Hash #reset-options "--z3rlimit 50 --fuel 0 --ifuel 0" val hash_len: a:Hash.hash_alg{S.hash_is_supported a} -> Tot (res:size_t{v res == Hash.hash_length a}) [@CInline] let hash_len a = Hacl.Hash.Definitions.hash_len a
false
true
Hacl.Impl.RSAPSS.MGF.fst
{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 0, "initial_ifuel": 0, "max_fuel": 0, "max_ifuel": 0, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": false, "z3cliopt": [], "z3refresh": false, "z3rlimit": 50, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }
null
val max_input_length : _: Spec.Hash.Definitions.hash_alg -> FStar.Pervasives.Native.option Prims.pos
[]
Hacl.Impl.RSAPSS.MGF.max_input_length
{ "file_name": "code/rsapss/Hacl.Impl.RSAPSS.MGF.fst", "git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e", "git_url": "https://github.com/hacl-star/hacl-star.git", "project_name": "hacl-star" }
_: Spec.Hash.Definitions.hash_alg -> FStar.Pervasives.Native.option Prims.pos
{ "end_col": 44, "end_line": 27, "start_col": 23, "start_line": 27 }
Prims.Tot
[ { "abbrev": true, "full_module": "Spec.Agile.Hash", "short_module": "Hash" }, { "abbrev": true, "full_module": "Lib.Sequence", "short_module": "LSeq" }, { "abbrev": true, "full_module": "Lib.ByteSequence", "short_module": "BSeq" }, { "abbrev": true, "full_module": "Spec.RSAPSS", "short_module": "S" }, { "abbrev": true, "full_module": "FStar.HyperStack.ST", "short_module": "ST" }, { "abbrev": false, "full_module": "Hacl.Bignum.Definitions", "short_module": null }, { "abbrev": false, "full_module": "Lib.Buffer", "short_module": null }, { "abbrev": false, "full_module": "Lib.IntTypes", "short_module": null }, { "abbrev": false, "full_module": "FStar.Mul", "short_module": null }, { "abbrev": false, "full_module": "FStar.HyperStack.ST", "short_module": null }, { "abbrev": false, "full_module": "FStar.HyperStack", "short_module": null }, { "abbrev": false, "full_module": "Hacl.Impl.RSAPSS", "short_module": null }, { "abbrev": false, "full_module": "Hacl.Impl.RSAPSS", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]
false
let mgf_hash_st (a:Hash.hash_alg{S.hash_is_supported a}) = len:size_t{v len + 4 <= max_size_t /\ (v len + 4) `less_than_max_input_length` a} -> mgfseed:lbuffer uint8 len -> maskLen:size_t{0 < v maskLen /\ S.blocks (v maskLen) (Hash.hash_length a) * Hash.hash_length a < pow2 32} -> res:lbuffer uint8 maskLen -> Stack unit (requires fun h -> live h mgfseed /\ live h res /\ disjoint res mgfseed) (ensures fun h0 _ h1 -> modifies (loc res) h0 h1 /\ as_seq h1 res == S.mgf_hash a (v len) (as_seq h0 mgfseed) (v maskLen))
let mgf_hash_st (a: Hash.hash_alg{S.hash_is_supported a}) =
false
null
false
len: size_t{v len + 4 <= max_size_t /\ (v len + 4) `less_than_max_input_length` a} -> mgfseed: lbuffer uint8 len -> maskLen: size_t {0 < v maskLen /\ S.blocks (v maskLen) (Hash.hash_length a) * Hash.hash_length a < pow2 32} -> res: lbuffer uint8 maskLen -> Stack unit (requires fun h -> live h mgfseed /\ live h res /\ disjoint res mgfseed) (ensures fun h0 _ h1 -> modifies (loc res) h0 h1 /\ as_seq h1 res == S.mgf_hash a (v len) (as_seq h0 mgfseed) (v maskLen))
{ "checked_file": "Hacl.Impl.RSAPSS.MGF.fst.checked", "dependencies": [ "Spec.RSAPSS.fst.checked", "Spec.Hash.Definitions.fst.checked", "Spec.Agile.Hash.fsti.checked", "prims.fst.checked", "Lib.Sequence.fsti.checked", "Lib.IntTypes.fsti.checked", "Lib.ByteSequence.fsti.checked", "Lib.Buffer.fsti.checked", "Hacl.Streaming.SHA2.fst.checked", "Hacl.Hash.Definitions.fst.checked", "Hacl.Bignum.Definitions.fst.checked", "FStar.UInt32.fsti.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Mul.fst.checked", "FStar.HyperStack.ST.fsti.checked", "FStar.HyperStack.fst.checked" ], "interface_file": false, "source_file": "Hacl.Impl.RSAPSS.MGF.fst" }
[ "total" ]
[ "Spec.Hash.Definitions.hash_alg", "Prims.b2t", "Spec.RSAPSS.hash_is_supported", "Lib.IntTypes.size_t", "Prims.l_and", "Prims.op_LessThanOrEqual", "Prims.op_Addition", "Lib.IntTypes.v", "Lib.IntTypes.U32", "Lib.IntTypes.PUB", "Lib.IntTypes.max_size_t", "Hacl.Impl.RSAPSS.MGF.less_than_max_input_length", "Lib.Buffer.lbuffer", "Lib.IntTypes.uint8", "Prims.op_LessThan", "FStar.Mul.op_Star", "Spec.RSAPSS.blocks", "Spec.Hash.Definitions.hash_length", "Prims.pow2", "Prims.unit", "FStar.Monotonic.HyperStack.mem", "Lib.Buffer.live", "Lib.Buffer.MUT", "Lib.Buffer.disjoint", "Lib.Buffer.modifies", "Lib.Buffer.loc", "Prims.eq2", "Lib.Sequence.lseq", "Lib.Buffer.as_seq", "Spec.RSAPSS.mgf_hash" ]
[]
module Hacl.Impl.RSAPSS.MGF open FStar.HyperStack open FStar.HyperStack.ST open FStar.Mul open Lib.IntTypes open Lib.Buffer open Hacl.Bignum.Definitions module ST = FStar.HyperStack.ST module S = Spec.RSAPSS module BSeq = Lib.ByteSequence module LSeq = Lib.Sequence module Hash = Spec.Agile.Hash #reset-options "--z3rlimit 50 --fuel 0 --ifuel 0" val hash_len: a:Hash.hash_alg{S.hash_is_supported a} -> Tot (res:size_t{v res == Hash.hash_length a}) [@CInline] let hash_len a = Hacl.Hash.Definitions.hash_len a inline_for_extraction noextract let max_input_length = Hash.max_input_length inline_for_extraction noextract let less_than_max_input_length = Spec.Hash.Definitions.less_than_max_input_length val hash: a:Hash.hash_alg{S.hash_is_supported a} -> mHash:lbuffer uint8 (hash_len a) -> msgLen:size_t{v msgLen `less_than_max_input_length` a} -> msg:lbuffer uint8 msgLen -> Stack unit (requires fun h -> live h mHash /\ live h msg /\ disjoint msg mHash) (ensures fun h0 _ h1 -> modifies (loc mHash) h0 h1 /\ as_seq h1 mHash == Hash.hash a (as_seq h0 msg)) [@CInline] let hash a mHash msgLen msg = match a with | Hash.SHA2_256 -> Hacl.Streaming.SHA2.hash_256 msg msgLen mHash | Hash.SHA2_384 -> Hacl.Streaming.SHA2.hash_384 msg msgLen mHash | Hash.SHA2_512 -> Hacl.Streaming.SHA2.hash_512 msg msgLen mHash (* Mask Generation Function *) inline_for_extraction noextract val counter_to_bytes: i:size_t -> counter:lbuffer uint8 4ul -> Stack unit (requires fun h -> live h counter) (ensures fun h0 _ h1 -> modifies (loc counter) h0 h1 /\ as_seq h1 counter == BSeq.nat_to_intseq_be 4 (v i)) let counter_to_bytes i c = let h0 = ST.get () in c.(0ul) <- to_u8 (i >>. 24ul); c.(1ul) <- to_u8 (i >>. 16ul); c.(2ul) <- to_u8 (i >>. 8ul); c.(3ul) <- to_u8 i; let h1 = ST.get () in BSeq.index_nat_to_intseq_be #U8 #SEC 4 (v i) 0; BSeq.index_nat_to_intseq_be #U8 #SEC 4 (v i) 1; BSeq.index_nat_to_intseq_be #U8 #SEC 4 (v i) 2; BSeq.index_nat_to_intseq_be #U8 #SEC 4 (v i) 3; LSeq.eq_intro (as_seq h1 c) (BSeq.nat_to_intseq_be 4 (v i)) inline_for_extraction noextract val mgf_hash_f: a:Hash.hash_alg{S.hash_is_supported a} -> len:size_t{v len + 4 <= max_size_t /\ (v len + 4) `less_than_max_input_length` a} -> i:size_t -> mgfseed_counter:lbuffer uint8 (len +! 4ul) -> block:lbuffer uint8 (hash_len a) -> Stack unit (requires fun h -> live h mgfseed_counter /\ live h block /\ disjoint mgfseed_counter block) (ensures fun h0 _ h1 -> modifies (loc mgfseed_counter |+| loc block) h0 h1 /\ (as_seq h1 mgfseed_counter, as_seq h1 block) == S.mgf_hash_f a (v len) (v i) (as_seq h0 mgfseed_counter)) let mgf_hash_f a len i mgfseed_counter block = let h0 = ST.get () in update_sub_f h0 mgfseed_counter len 4ul (fun h -> BSeq.nat_to_intseq_be 4 (v i)) (fun _ -> let c = sub mgfseed_counter len 4ul in counter_to_bytes i c); hash a block (len +! 4ul) mgfseed_counter inline_for_extraction noextract
false
false
Hacl.Impl.RSAPSS.MGF.fst
{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 0, "initial_ifuel": 0, "max_fuel": 0, "max_ifuel": 0, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": false, "z3cliopt": [], "z3refresh": false, "z3rlimit": 50, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }
null
val mgf_hash_st : a: Spec.Hash.Definitions.hash_alg{Spec.RSAPSS.hash_is_supported a} -> Type0
[]
Hacl.Impl.RSAPSS.MGF.mgf_hash_st
{ "file_name": "code/rsapss/Hacl.Impl.RSAPSS.MGF.fst", "git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e", "git_url": "https://github.com/hacl-star/hacl-star.git", "project_name": "hacl-star" }
a: Spec.Hash.Definitions.hash_alg{Spec.RSAPSS.hash_is_supported a} -> Type0
{ "end_col": 74, "end_line": 105, "start_col": 2, "start_line": 98 }
Prims.Tot
val hash_len: a:Hash.hash_alg{S.hash_is_supported a} -> Tot (res:size_t{v res == Hash.hash_length a})
[ { "abbrev": true, "full_module": "Spec.Agile.Hash", "short_module": "Hash" }, { "abbrev": true, "full_module": "Lib.Sequence", "short_module": "LSeq" }, { "abbrev": true, "full_module": "Lib.ByteSequence", "short_module": "BSeq" }, { "abbrev": true, "full_module": "Spec.RSAPSS", "short_module": "S" }, { "abbrev": true, "full_module": "FStar.HyperStack.ST", "short_module": "ST" }, { "abbrev": false, "full_module": "Hacl.Bignum.Definitions", "short_module": null }, { "abbrev": false, "full_module": "Lib.Buffer", "short_module": null }, { "abbrev": false, "full_module": "Lib.IntTypes", "short_module": null }, { "abbrev": false, "full_module": "FStar.Mul", "short_module": null }, { "abbrev": false, "full_module": "FStar.HyperStack.ST", "short_module": null }, { "abbrev": false, "full_module": "FStar.HyperStack", "short_module": null }, { "abbrev": false, "full_module": "Hacl.Impl.RSAPSS", "short_module": null }, { "abbrev": false, "full_module": "Hacl.Impl.RSAPSS", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]
false
let hash_len a = Hacl.Hash.Definitions.hash_len a
val hash_len: a:Hash.hash_alg{S.hash_is_supported a} -> Tot (res:size_t{v res == Hash.hash_length a}) let hash_len a =
false
null
false
Hacl.Hash.Definitions.hash_len a
{ "checked_file": "Hacl.Impl.RSAPSS.MGF.fst.checked", "dependencies": [ "Spec.RSAPSS.fst.checked", "Spec.Hash.Definitions.fst.checked", "Spec.Agile.Hash.fsti.checked", "prims.fst.checked", "Lib.Sequence.fsti.checked", "Lib.IntTypes.fsti.checked", "Lib.ByteSequence.fsti.checked", "Lib.Buffer.fsti.checked", "Hacl.Streaming.SHA2.fst.checked", "Hacl.Hash.Definitions.fst.checked", "Hacl.Bignum.Definitions.fst.checked", "FStar.UInt32.fsti.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Mul.fst.checked", "FStar.HyperStack.ST.fsti.checked", "FStar.HyperStack.fst.checked" ], "interface_file": false, "source_file": "Hacl.Impl.RSAPSS.MGF.fst" }
[ "total" ]
[ "Spec.Hash.Definitions.hash_alg", "Prims.b2t", "Spec.RSAPSS.hash_is_supported", "Hacl.Hash.Definitions.hash_len", "Lib.IntTypes.size_t", "Prims.eq2", "Prims.int", "Prims.l_or", "Lib.IntTypes.range", "Lib.IntTypes.U32", "Prims.l_and", "Prims.op_GreaterThanOrEqual", "Prims.op_LessThanOrEqual", "Lib.IntTypes.max_size_t", "Prims.op_GreaterThan", "Lib.IntTypes.v", "Lib.IntTypes.PUB", "Spec.Hash.Definitions.hash_length" ]
[]
module Hacl.Impl.RSAPSS.MGF open FStar.HyperStack open FStar.HyperStack.ST open FStar.Mul open Lib.IntTypes open Lib.Buffer open Hacl.Bignum.Definitions module ST = FStar.HyperStack.ST module S = Spec.RSAPSS module BSeq = Lib.ByteSequence module LSeq = Lib.Sequence module Hash = Spec.Agile.Hash #reset-options "--z3rlimit 50 --fuel 0 --ifuel 0" val hash_len: a:Hash.hash_alg{S.hash_is_supported a} -> Tot (res:size_t{v res == Hash.hash_length a}) [@CInline]
false
false
Hacl.Impl.RSAPSS.MGF.fst
{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 0, "initial_ifuel": 0, "max_fuel": 0, "max_ifuel": 0, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": false, "z3cliopt": [], "z3refresh": false, "z3rlimit": 50, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }
null
val hash_len: a:Hash.hash_alg{S.hash_is_supported a} -> Tot (res:size_t{v res == Hash.hash_length a})
[]
Hacl.Impl.RSAPSS.MGF.hash_len
{ "file_name": "code/rsapss/Hacl.Impl.RSAPSS.MGF.fst", "git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e", "git_url": "https://github.com/hacl-star/hacl-star.git", "project_name": "hacl-star" }
a: Spec.Hash.Definitions.hash_alg{Spec.RSAPSS.hash_is_supported a} -> res: Lib.IntTypes.size_t{Lib.IntTypes.v res == Spec.Hash.Definitions.hash_length a}
{ "end_col": 34, "end_line": 24, "start_col": 2, "start_line": 24 }
FStar.HyperStack.ST.Stack
val hash: a:Hash.hash_alg{S.hash_is_supported a} -> mHash:lbuffer uint8 (hash_len a) -> msgLen:size_t{v msgLen `less_than_max_input_length` a} -> msg:lbuffer uint8 msgLen -> Stack unit (requires fun h -> live h mHash /\ live h msg /\ disjoint msg mHash) (ensures fun h0 _ h1 -> modifies (loc mHash) h0 h1 /\ as_seq h1 mHash == Hash.hash a (as_seq h0 msg))
[ { "abbrev": true, "full_module": "Spec.Agile.Hash", "short_module": "Hash" }, { "abbrev": true, "full_module": "Lib.Sequence", "short_module": "LSeq" }, { "abbrev": true, "full_module": "Lib.ByteSequence", "short_module": "BSeq" }, { "abbrev": true, "full_module": "Spec.RSAPSS", "short_module": "S" }, { "abbrev": true, "full_module": "FStar.HyperStack.ST", "short_module": "ST" }, { "abbrev": false, "full_module": "Hacl.Bignum.Definitions", "short_module": null }, { "abbrev": false, "full_module": "Lib.Buffer", "short_module": null }, { "abbrev": false, "full_module": "Lib.IntTypes", "short_module": null }, { "abbrev": false, "full_module": "FStar.Mul", "short_module": null }, { "abbrev": false, "full_module": "FStar.HyperStack.ST", "short_module": null }, { "abbrev": false, "full_module": "FStar.HyperStack", "short_module": null }, { "abbrev": false, "full_module": "Hacl.Impl.RSAPSS", "short_module": null }, { "abbrev": false, "full_module": "Hacl.Impl.RSAPSS", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]
false
let hash a mHash msgLen msg = match a with | Hash.SHA2_256 -> Hacl.Streaming.SHA2.hash_256 msg msgLen mHash | Hash.SHA2_384 -> Hacl.Streaming.SHA2.hash_384 msg msgLen mHash | Hash.SHA2_512 -> Hacl.Streaming.SHA2.hash_512 msg msgLen mHash
val hash: a:Hash.hash_alg{S.hash_is_supported a} -> mHash:lbuffer uint8 (hash_len a) -> msgLen:size_t{v msgLen `less_than_max_input_length` a} -> msg:lbuffer uint8 msgLen -> Stack unit (requires fun h -> live h mHash /\ live h msg /\ disjoint msg mHash) (ensures fun h0 _ h1 -> modifies (loc mHash) h0 h1 /\ as_seq h1 mHash == Hash.hash a (as_seq h0 msg)) let hash a mHash msgLen msg =
true
null
false
match a with | Hash.SHA2_256 -> Hacl.Streaming.SHA2.hash_256 msg msgLen mHash | Hash.SHA2_384 -> Hacl.Streaming.SHA2.hash_384 msg msgLen mHash | Hash.SHA2_512 -> Hacl.Streaming.SHA2.hash_512 msg msgLen mHash
{ "checked_file": "Hacl.Impl.RSAPSS.MGF.fst.checked", "dependencies": [ "Spec.RSAPSS.fst.checked", "Spec.Hash.Definitions.fst.checked", "Spec.Agile.Hash.fsti.checked", "prims.fst.checked", "Lib.Sequence.fsti.checked", "Lib.IntTypes.fsti.checked", "Lib.ByteSequence.fsti.checked", "Lib.Buffer.fsti.checked", "Hacl.Streaming.SHA2.fst.checked", "Hacl.Hash.Definitions.fst.checked", "Hacl.Bignum.Definitions.fst.checked", "FStar.UInt32.fsti.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Mul.fst.checked", "FStar.HyperStack.ST.fsti.checked", "FStar.HyperStack.fst.checked" ], "interface_file": false, "source_file": "Hacl.Impl.RSAPSS.MGF.fst" }
[]
[ "Spec.Hash.Definitions.hash_alg", "Prims.b2t", "Spec.RSAPSS.hash_is_supported", "Lib.Buffer.lbuffer", "Lib.IntTypes.uint8", "Hacl.Impl.RSAPSS.MGF.hash_len", "Lib.IntTypes.size_t", "Hacl.Impl.RSAPSS.MGF.less_than_max_input_length", "Lib.IntTypes.v", "Lib.IntTypes.U32", "Lib.IntTypes.PUB", "Hacl.Streaming.SHA2.hash_256", "Prims.unit", "Hacl.Streaming.SHA2.hash_384", "Hacl.Streaming.SHA2.hash_512" ]
[]
module Hacl.Impl.RSAPSS.MGF open FStar.HyperStack open FStar.HyperStack.ST open FStar.Mul open Lib.IntTypes open Lib.Buffer open Hacl.Bignum.Definitions module ST = FStar.HyperStack.ST module S = Spec.RSAPSS module BSeq = Lib.ByteSequence module LSeq = Lib.Sequence module Hash = Spec.Agile.Hash #reset-options "--z3rlimit 50 --fuel 0 --ifuel 0" val hash_len: a:Hash.hash_alg{S.hash_is_supported a} -> Tot (res:size_t{v res == Hash.hash_length a}) [@CInline] let hash_len a = Hacl.Hash.Definitions.hash_len a inline_for_extraction noextract let max_input_length = Hash.max_input_length inline_for_extraction noextract let less_than_max_input_length = Spec.Hash.Definitions.less_than_max_input_length val hash: a:Hash.hash_alg{S.hash_is_supported a} -> mHash:lbuffer uint8 (hash_len a) -> msgLen:size_t{v msgLen `less_than_max_input_length` a} -> msg:lbuffer uint8 msgLen -> Stack unit (requires fun h -> live h mHash /\ live h msg /\ disjoint msg mHash) (ensures fun h0 _ h1 -> modifies (loc mHash) h0 h1 /\ as_seq h1 mHash == Hash.hash a (as_seq h0 msg)) [@CInline]
false
false
Hacl.Impl.RSAPSS.MGF.fst
{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 0, "initial_ifuel": 0, "max_fuel": 0, "max_ifuel": 0, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": false, "z3cliopt": [], "z3refresh": false, "z3rlimit": 50, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }
null
val hash: a:Hash.hash_alg{S.hash_is_supported a} -> mHash:lbuffer uint8 (hash_len a) -> msgLen:size_t{v msgLen `less_than_max_input_length` a} -> msg:lbuffer uint8 msgLen -> Stack unit (requires fun h -> live h mHash /\ live h msg /\ disjoint msg mHash) (ensures fun h0 _ h1 -> modifies (loc mHash) h0 h1 /\ as_seq h1 mHash == Hash.hash a (as_seq h0 msg))
[]
Hacl.Impl.RSAPSS.MGF.hash
{ "file_name": "code/rsapss/Hacl.Impl.RSAPSS.MGF.fst", "git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e", "git_url": "https://github.com/hacl-star/hacl-star.git", "project_name": "hacl-star" }
a: Spec.Hash.Definitions.hash_alg{Spec.RSAPSS.hash_is_supported a} -> mHash: Lib.Buffer.lbuffer Lib.IntTypes.uint8 (Hacl.Impl.RSAPSS.MGF.hash_len a) -> msgLen: Lib.IntTypes.size_t{Hacl.Impl.RSAPSS.MGF.less_than_max_input_length (Lib.IntTypes.v msgLen) a} -> msg: Lib.Buffer.lbuffer Lib.IntTypes.uint8 msgLen -> FStar.HyperStack.ST.Stack Prims.unit
{ "end_col": 66, "end_line": 47, "start_col": 2, "start_line": 44 }
FStar.HyperStack.ST.Stack
val counter_to_bytes: i:size_t -> counter:lbuffer uint8 4ul -> Stack unit (requires fun h -> live h counter) (ensures fun h0 _ h1 -> modifies (loc counter) h0 h1 /\ as_seq h1 counter == BSeq.nat_to_intseq_be 4 (v i))
[ { "abbrev": true, "full_module": "Spec.Agile.Hash", "short_module": "Hash" }, { "abbrev": true, "full_module": "Lib.Sequence", "short_module": "LSeq" }, { "abbrev": true, "full_module": "Lib.ByteSequence", "short_module": "BSeq" }, { "abbrev": true, "full_module": "Spec.RSAPSS", "short_module": "S" }, { "abbrev": true, "full_module": "FStar.HyperStack.ST", "short_module": "ST" }, { "abbrev": false, "full_module": "Hacl.Bignum.Definitions", "short_module": null }, { "abbrev": false, "full_module": "Lib.Buffer", "short_module": null }, { "abbrev": false, "full_module": "Lib.IntTypes", "short_module": null }, { "abbrev": false, "full_module": "FStar.Mul", "short_module": null }, { "abbrev": false, "full_module": "FStar.HyperStack.ST", "short_module": null }, { "abbrev": false, "full_module": "FStar.HyperStack", "short_module": null }, { "abbrev": false, "full_module": "Hacl.Impl.RSAPSS", "short_module": null }, { "abbrev": false, "full_module": "Hacl.Impl.RSAPSS", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]
false
let counter_to_bytes i c = let h0 = ST.get () in c.(0ul) <- to_u8 (i >>. 24ul); c.(1ul) <- to_u8 (i >>. 16ul); c.(2ul) <- to_u8 (i >>. 8ul); c.(3ul) <- to_u8 i; let h1 = ST.get () in BSeq.index_nat_to_intseq_be #U8 #SEC 4 (v i) 0; BSeq.index_nat_to_intseq_be #U8 #SEC 4 (v i) 1; BSeq.index_nat_to_intseq_be #U8 #SEC 4 (v i) 2; BSeq.index_nat_to_intseq_be #U8 #SEC 4 (v i) 3; LSeq.eq_intro (as_seq h1 c) (BSeq.nat_to_intseq_be 4 (v i))
val counter_to_bytes: i:size_t -> counter:lbuffer uint8 4ul -> Stack unit (requires fun h -> live h counter) (ensures fun h0 _ h1 -> modifies (loc counter) h0 h1 /\ as_seq h1 counter == BSeq.nat_to_intseq_be 4 (v i)) let counter_to_bytes i c =
true
null
false
let h0 = ST.get () in c.(0ul) <- to_u8 (i >>. 24ul); c.(1ul) <- to_u8 (i >>. 16ul); c.(2ul) <- to_u8 (i >>. 8ul); c.(3ul) <- to_u8 i; let h1 = ST.get () in BSeq.index_nat_to_intseq_be #U8 #SEC 4 (v i) 0; BSeq.index_nat_to_intseq_be #U8 #SEC 4 (v i) 1; BSeq.index_nat_to_intseq_be #U8 #SEC 4 (v i) 2; BSeq.index_nat_to_intseq_be #U8 #SEC 4 (v i) 3; LSeq.eq_intro (as_seq h1 c) (BSeq.nat_to_intseq_be 4 (v i))
{ "checked_file": "Hacl.Impl.RSAPSS.MGF.fst.checked", "dependencies": [ "Spec.RSAPSS.fst.checked", "Spec.Hash.Definitions.fst.checked", "Spec.Agile.Hash.fsti.checked", "prims.fst.checked", "Lib.Sequence.fsti.checked", "Lib.IntTypes.fsti.checked", "Lib.ByteSequence.fsti.checked", "Lib.Buffer.fsti.checked", "Hacl.Streaming.SHA2.fst.checked", "Hacl.Hash.Definitions.fst.checked", "Hacl.Bignum.Definitions.fst.checked", "FStar.UInt32.fsti.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Mul.fst.checked", "FStar.HyperStack.ST.fsti.checked", "FStar.HyperStack.fst.checked" ], "interface_file": false, "source_file": "Hacl.Impl.RSAPSS.MGF.fst" }
[]
[ "Lib.IntTypes.size_t", "Lib.Buffer.lbuffer", "Lib.IntTypes.uint8", "FStar.UInt32.__uint_to_t", "Lib.Sequence.eq_intro", "Lib.IntTypes.v", "Lib.IntTypes.U32", "Lib.IntTypes.PUB", "Lib.Buffer.as_seq", "Lib.Buffer.MUT", "Lib.ByteSequence.nat_to_intseq_be", "Lib.IntTypes.U8", "Lib.IntTypes.SEC", "Prims.unit", "Lib.ByteSequence.index_nat_to_intseq_be", "FStar.Monotonic.HyperStack.mem", "FStar.HyperStack.ST.get", "Lib.Buffer.op_Array_Assignment", "Lib.IntTypes.to_u8", "Lib.IntTypes.op_Greater_Greater_Dot" ]
[]
module Hacl.Impl.RSAPSS.MGF open FStar.HyperStack open FStar.HyperStack.ST open FStar.Mul open Lib.IntTypes open Lib.Buffer open Hacl.Bignum.Definitions module ST = FStar.HyperStack.ST module S = Spec.RSAPSS module BSeq = Lib.ByteSequence module LSeq = Lib.Sequence module Hash = Spec.Agile.Hash #reset-options "--z3rlimit 50 --fuel 0 --ifuel 0" val hash_len: a:Hash.hash_alg{S.hash_is_supported a} -> Tot (res:size_t{v res == Hash.hash_length a}) [@CInline] let hash_len a = Hacl.Hash.Definitions.hash_len a inline_for_extraction noextract let max_input_length = Hash.max_input_length inline_for_extraction noextract let less_than_max_input_length = Spec.Hash.Definitions.less_than_max_input_length val hash: a:Hash.hash_alg{S.hash_is_supported a} -> mHash:lbuffer uint8 (hash_len a) -> msgLen:size_t{v msgLen `less_than_max_input_length` a} -> msg:lbuffer uint8 msgLen -> Stack unit (requires fun h -> live h mHash /\ live h msg /\ disjoint msg mHash) (ensures fun h0 _ h1 -> modifies (loc mHash) h0 h1 /\ as_seq h1 mHash == Hash.hash a (as_seq h0 msg)) [@CInline] let hash a mHash msgLen msg = match a with | Hash.SHA2_256 -> Hacl.Streaming.SHA2.hash_256 msg msgLen mHash | Hash.SHA2_384 -> Hacl.Streaming.SHA2.hash_384 msg msgLen mHash | Hash.SHA2_512 -> Hacl.Streaming.SHA2.hash_512 msg msgLen mHash (* Mask Generation Function *) inline_for_extraction noextract val counter_to_bytes: i:size_t -> counter:lbuffer uint8 4ul -> Stack unit (requires fun h -> live h counter) (ensures fun h0 _ h1 -> modifies (loc counter) h0 h1 /\ as_seq h1 counter == BSeq.nat_to_intseq_be 4 (v i))
false
false
Hacl.Impl.RSAPSS.MGF.fst
{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 0, "initial_ifuel": 0, "max_fuel": 0, "max_ifuel": 0, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": false, "z3cliopt": [], "z3refresh": false, "z3rlimit": 50, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }
null
val counter_to_bytes: i:size_t -> counter:lbuffer uint8 4ul -> Stack unit (requires fun h -> live h counter) (ensures fun h0 _ h1 -> modifies (loc counter) h0 h1 /\ as_seq h1 counter == BSeq.nat_to_intseq_be 4 (v i))
[]
Hacl.Impl.RSAPSS.MGF.counter_to_bytes
{ "file_name": "code/rsapss/Hacl.Impl.RSAPSS.MGF.fst", "git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e", "git_url": "https://github.com/hacl-star/hacl-star.git", "project_name": "hacl-star" }
i: Lib.IntTypes.size_t -> counter: Lib.Buffer.lbuffer Lib.IntTypes.uint8 4ul -> FStar.HyperStack.ST.Stack Prims.unit
{ "end_col": 61, "end_line": 71, "start_col": 26, "start_line": 60 }
FStar.HyperStack.ST.Stack
val mgf_hash_f: a:Hash.hash_alg{S.hash_is_supported a} -> len:size_t{v len + 4 <= max_size_t /\ (v len + 4) `less_than_max_input_length` a} -> i:size_t -> mgfseed_counter:lbuffer uint8 (len +! 4ul) -> block:lbuffer uint8 (hash_len a) -> Stack unit (requires fun h -> live h mgfseed_counter /\ live h block /\ disjoint mgfseed_counter block) (ensures fun h0 _ h1 -> modifies (loc mgfseed_counter |+| loc block) h0 h1 /\ (as_seq h1 mgfseed_counter, as_seq h1 block) == S.mgf_hash_f a (v len) (v i) (as_seq h0 mgfseed_counter))
[ { "abbrev": true, "full_module": "Spec.Agile.Hash", "short_module": "Hash" }, { "abbrev": true, "full_module": "Lib.Sequence", "short_module": "LSeq" }, { "abbrev": true, "full_module": "Lib.ByteSequence", "short_module": "BSeq" }, { "abbrev": true, "full_module": "Spec.RSAPSS", "short_module": "S" }, { "abbrev": true, "full_module": "FStar.HyperStack.ST", "short_module": "ST" }, { "abbrev": false, "full_module": "Hacl.Bignum.Definitions", "short_module": null }, { "abbrev": false, "full_module": "Lib.Buffer", "short_module": null }, { "abbrev": false, "full_module": "Lib.IntTypes", "short_module": null }, { "abbrev": false, "full_module": "FStar.Mul", "short_module": null }, { "abbrev": false, "full_module": "FStar.HyperStack.ST", "short_module": null }, { "abbrev": false, "full_module": "FStar.HyperStack", "short_module": null }, { "abbrev": false, "full_module": "Hacl.Impl.RSAPSS", "short_module": null }, { "abbrev": false, "full_module": "Hacl.Impl.RSAPSS", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]
false
let mgf_hash_f a len i mgfseed_counter block = let h0 = ST.get () in update_sub_f h0 mgfseed_counter len 4ul (fun h -> BSeq.nat_to_intseq_be 4 (v i)) (fun _ -> let c = sub mgfseed_counter len 4ul in counter_to_bytes i c); hash a block (len +! 4ul) mgfseed_counter
val mgf_hash_f: a:Hash.hash_alg{S.hash_is_supported a} -> len:size_t{v len + 4 <= max_size_t /\ (v len + 4) `less_than_max_input_length` a} -> i:size_t -> mgfseed_counter:lbuffer uint8 (len +! 4ul) -> block:lbuffer uint8 (hash_len a) -> Stack unit (requires fun h -> live h mgfseed_counter /\ live h block /\ disjoint mgfseed_counter block) (ensures fun h0 _ h1 -> modifies (loc mgfseed_counter |+| loc block) h0 h1 /\ (as_seq h1 mgfseed_counter, as_seq h1 block) == S.mgf_hash_f a (v len) (v i) (as_seq h0 mgfseed_counter)) let mgf_hash_f a len i mgfseed_counter block =
true
null
false
let h0 = ST.get () in update_sub_f h0 mgfseed_counter len 4ul (fun h -> BSeq.nat_to_intseq_be 4 (v i)) (fun _ -> let c = sub mgfseed_counter len 4ul in counter_to_bytes i c); hash a block (len +! 4ul) mgfseed_counter
{ "checked_file": "Hacl.Impl.RSAPSS.MGF.fst.checked", "dependencies": [ "Spec.RSAPSS.fst.checked", "Spec.Hash.Definitions.fst.checked", "Spec.Agile.Hash.fsti.checked", "prims.fst.checked", "Lib.Sequence.fsti.checked", "Lib.IntTypes.fsti.checked", "Lib.ByteSequence.fsti.checked", "Lib.Buffer.fsti.checked", "Hacl.Streaming.SHA2.fst.checked", "Hacl.Hash.Definitions.fst.checked", "Hacl.Bignum.Definitions.fst.checked", "FStar.UInt32.fsti.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Mul.fst.checked", "FStar.HyperStack.ST.fsti.checked", "FStar.HyperStack.fst.checked" ], "interface_file": false, "source_file": "Hacl.Impl.RSAPSS.MGF.fst" }
[]
[ "Spec.Hash.Definitions.hash_alg", "Prims.b2t", "Spec.RSAPSS.hash_is_supported", "Lib.IntTypes.size_t", "Prims.l_and", "Prims.op_LessThanOrEqual", "Prims.op_Addition", "Lib.IntTypes.v", "Lib.IntTypes.U32", "Lib.IntTypes.PUB", "Lib.IntTypes.max_size_t", "Hacl.Impl.RSAPSS.MGF.less_than_max_input_length", "Lib.Buffer.lbuffer", "Lib.IntTypes.uint8", "Lib.IntTypes.op_Plus_Bang", "FStar.UInt32.__uint_to_t", "Hacl.Impl.RSAPSS.MGF.hash_len", "Hacl.Impl.RSAPSS.MGF.hash", "Prims.unit", "Lib.Buffer.update_sub_f", "FStar.Monotonic.HyperStack.mem", "Lib.ByteSequence.nat_to_intseq_be", "Lib.IntTypes.U8", "Lib.IntTypes.SEC", "Lib.Sequence.lseq", "Hacl.Impl.RSAPSS.MGF.counter_to_bytes", "Lib.Buffer.lbuffer_t", "Lib.Buffer.MUT", "Lib.IntTypes.int_t", "FStar.UInt32.uint_to_t", "FStar.UInt32.t", "Lib.Buffer.sub", "FStar.HyperStack.ST.get" ]
[]
module Hacl.Impl.RSAPSS.MGF open FStar.HyperStack open FStar.HyperStack.ST open FStar.Mul open Lib.IntTypes open Lib.Buffer open Hacl.Bignum.Definitions module ST = FStar.HyperStack.ST module S = Spec.RSAPSS module BSeq = Lib.ByteSequence module LSeq = Lib.Sequence module Hash = Spec.Agile.Hash #reset-options "--z3rlimit 50 --fuel 0 --ifuel 0" val hash_len: a:Hash.hash_alg{S.hash_is_supported a} -> Tot (res:size_t{v res == Hash.hash_length a}) [@CInline] let hash_len a = Hacl.Hash.Definitions.hash_len a inline_for_extraction noextract let max_input_length = Hash.max_input_length inline_for_extraction noextract let less_than_max_input_length = Spec.Hash.Definitions.less_than_max_input_length val hash: a:Hash.hash_alg{S.hash_is_supported a} -> mHash:lbuffer uint8 (hash_len a) -> msgLen:size_t{v msgLen `less_than_max_input_length` a} -> msg:lbuffer uint8 msgLen -> Stack unit (requires fun h -> live h mHash /\ live h msg /\ disjoint msg mHash) (ensures fun h0 _ h1 -> modifies (loc mHash) h0 h1 /\ as_seq h1 mHash == Hash.hash a (as_seq h0 msg)) [@CInline] let hash a mHash msgLen msg = match a with | Hash.SHA2_256 -> Hacl.Streaming.SHA2.hash_256 msg msgLen mHash | Hash.SHA2_384 -> Hacl.Streaming.SHA2.hash_384 msg msgLen mHash | Hash.SHA2_512 -> Hacl.Streaming.SHA2.hash_512 msg msgLen mHash (* Mask Generation Function *) inline_for_extraction noextract val counter_to_bytes: i:size_t -> counter:lbuffer uint8 4ul -> Stack unit (requires fun h -> live h counter) (ensures fun h0 _ h1 -> modifies (loc counter) h0 h1 /\ as_seq h1 counter == BSeq.nat_to_intseq_be 4 (v i)) let counter_to_bytes i c = let h0 = ST.get () in c.(0ul) <- to_u8 (i >>. 24ul); c.(1ul) <- to_u8 (i >>. 16ul); c.(2ul) <- to_u8 (i >>. 8ul); c.(3ul) <- to_u8 i; let h1 = ST.get () in BSeq.index_nat_to_intseq_be #U8 #SEC 4 (v i) 0; BSeq.index_nat_to_intseq_be #U8 #SEC 4 (v i) 1; BSeq.index_nat_to_intseq_be #U8 #SEC 4 (v i) 2; BSeq.index_nat_to_intseq_be #U8 #SEC 4 (v i) 3; LSeq.eq_intro (as_seq h1 c) (BSeq.nat_to_intseq_be 4 (v i)) inline_for_extraction noextract val mgf_hash_f: a:Hash.hash_alg{S.hash_is_supported a} -> len:size_t{v len + 4 <= max_size_t /\ (v len + 4) `less_than_max_input_length` a} -> i:size_t -> mgfseed_counter:lbuffer uint8 (len +! 4ul) -> block:lbuffer uint8 (hash_len a) -> Stack unit (requires fun h -> live h mgfseed_counter /\ live h block /\ disjoint mgfseed_counter block) (ensures fun h0 _ h1 -> modifies (loc mgfseed_counter |+| loc block) h0 h1 /\ (as_seq h1 mgfseed_counter, as_seq h1 block) == S.mgf_hash_f a (v len) (v i) (as_seq h0 mgfseed_counter))
false
false
Hacl.Impl.RSAPSS.MGF.fst
{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 0, "initial_ifuel": 0, "max_fuel": 0, "max_ifuel": 0, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": false, "z3cliopt": [], "z3refresh": false, "z3rlimit": 50, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }
null
val mgf_hash_f: a:Hash.hash_alg{S.hash_is_supported a} -> len:size_t{v len + 4 <= max_size_t /\ (v len + 4) `less_than_max_input_length` a} -> i:size_t -> mgfseed_counter:lbuffer uint8 (len +! 4ul) -> block:lbuffer uint8 (hash_len a) -> Stack unit (requires fun h -> live h mgfseed_counter /\ live h block /\ disjoint mgfseed_counter block) (ensures fun h0 _ h1 -> modifies (loc mgfseed_counter |+| loc block) h0 h1 /\ (as_seq h1 mgfseed_counter, as_seq h1 block) == S.mgf_hash_f a (v len) (v i) (as_seq h0 mgfseed_counter))
[]
Hacl.Impl.RSAPSS.MGF.mgf_hash_f
{ "file_name": "code/rsapss/Hacl.Impl.RSAPSS.MGF.fst", "git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e", "git_url": "https://github.com/hacl-star/hacl-star.git", "project_name": "hacl-star" }
a: Spec.Hash.Definitions.hash_alg{Spec.RSAPSS.hash_is_supported a} -> len: Lib.IntTypes.size_t { Lib.IntTypes.v len + 4 <= Lib.IntTypes.max_size_t /\ Hacl.Impl.RSAPSS.MGF.less_than_max_input_length (Lib.IntTypes.v len + 4) a } -> i: Lib.IntTypes.size_t -> mgfseed_counter: Lib.Buffer.lbuffer Lib.IntTypes.uint8 (len +! 4ul) -> block: Lib.Buffer.lbuffer Lib.IntTypes.uint8 (Hacl.Impl.RSAPSS.MGF.hash_len a) -> FStar.HyperStack.ST.Stack Prims.unit
{ "end_col": 43, "end_line": 93, "start_col": 46, "start_line": 86 }
Prims.Tot
val mgf_hash: a:Hash.hash_alg{S.hash_is_supported a} -> mgf_hash_st a
[ { "abbrev": true, "full_module": "Spec.Agile.Hash", "short_module": "Hash" }, { "abbrev": true, "full_module": "Lib.Sequence", "short_module": "LSeq" }, { "abbrev": true, "full_module": "Lib.ByteSequence", "short_module": "BSeq" }, { "abbrev": true, "full_module": "Spec.RSAPSS", "short_module": "S" }, { "abbrev": true, "full_module": "FStar.HyperStack.ST", "short_module": "ST" }, { "abbrev": false, "full_module": "Hacl.Bignum.Definitions", "short_module": null }, { "abbrev": false, "full_module": "Lib.Buffer", "short_module": null }, { "abbrev": false, "full_module": "Lib.IntTypes", "short_module": null }, { "abbrev": false, "full_module": "FStar.Mul", "short_module": null }, { "abbrev": false, "full_module": "FStar.HyperStack.ST", "short_module": null }, { "abbrev": false, "full_module": "FStar.HyperStack", "short_module": null }, { "abbrev": false, "full_module": "Hacl.Impl.RSAPSS", "short_module": null }, { "abbrev": false, "full_module": "Hacl.Impl.RSAPSS", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]
false
let mgf_hash a len mgfseed maskLen res = push_frame (); let mgfseed_counter = create (len +! 4ul) (u8 0) in update_sub mgfseed_counter 0ul len mgfseed; let hLen = hash_len a in let n = blocks maskLen hLen in let accLen = n *! hLen in let acc = create accLen (u8 0) in [@ inline_let] let a_spec = S.mgf_hash_a (v len) (v n) in let h0 = ST.get () in fill_blocks h0 hLen n acc a_spec (fun h i -> as_seq h mgfseed_counter) (fun _ -> loc mgfseed_counter) (fun h0 -> S.mgf_hash_f a (v len)) (fun i -> let acc_i = sub acc (i *! hLen) hLen in mgf_hash_f a len i mgfseed_counter acc_i); copy res (sub acc 0ul maskLen); pop_frame ()
val mgf_hash: a:Hash.hash_alg{S.hash_is_supported a} -> mgf_hash_st a let mgf_hash a len mgfseed maskLen res =
false
null
false
push_frame (); let mgfseed_counter = create (len +! 4ul) (u8 0) in update_sub mgfseed_counter 0ul len mgfseed; let hLen = hash_len a in let n = blocks maskLen hLen in let accLen = n *! hLen in let acc = create accLen (u8 0) in [@@ inline_let ]let a_spec = S.mgf_hash_a (v len) (v n) in let h0 = ST.get () in fill_blocks h0 hLen n acc a_spec (fun h i -> as_seq h mgfseed_counter) (fun _ -> loc mgfseed_counter) (fun h0 -> S.mgf_hash_f a (v len)) (fun i -> let acc_i = sub acc (i *! hLen) hLen in mgf_hash_f a len i mgfseed_counter acc_i); copy res (sub acc 0ul maskLen); pop_frame ()
{ "checked_file": "Hacl.Impl.RSAPSS.MGF.fst.checked", "dependencies": [ "Spec.RSAPSS.fst.checked", "Spec.Hash.Definitions.fst.checked", "Spec.Agile.Hash.fsti.checked", "prims.fst.checked", "Lib.Sequence.fsti.checked", "Lib.IntTypes.fsti.checked", "Lib.ByteSequence.fsti.checked", "Lib.Buffer.fsti.checked", "Hacl.Streaming.SHA2.fst.checked", "Hacl.Hash.Definitions.fst.checked", "Hacl.Bignum.Definitions.fst.checked", "FStar.UInt32.fsti.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Mul.fst.checked", "FStar.HyperStack.ST.fsti.checked", "FStar.HyperStack.fst.checked" ], "interface_file": false, "source_file": "Hacl.Impl.RSAPSS.MGF.fst" }
[ "total" ]
[ "Spec.Hash.Definitions.hash_alg", "Prims.b2t", "Spec.RSAPSS.hash_is_supported", "Lib.IntTypes.size_t", "Prims.l_and", "Prims.op_LessThanOrEqual", "Prims.op_Addition", "Lib.IntTypes.v", "Lib.IntTypes.U32", "Lib.IntTypes.PUB", "Lib.IntTypes.max_size_t", "Hacl.Impl.RSAPSS.MGF.less_than_max_input_length", "Lib.Buffer.lbuffer", "Lib.IntTypes.uint8", "Prims.op_LessThan", "FStar.Mul.op_Star", "Spec.RSAPSS.blocks", "Spec.Hash.Definitions.hash_length", "Prims.pow2", "FStar.HyperStack.ST.pop_frame", "Prims.unit", "Lib.Buffer.copy", "Lib.Buffer.MUT", "Lib.Buffer.lbuffer_t", "Lib.IntTypes.int_t", "Lib.IntTypes.U8", "Lib.IntTypes.SEC", "Lib.Buffer.sub", "Lib.IntTypes.uint_t", "FStar.UInt32.__uint_to_t", "Lib.Buffer.fill_blocks", "FStar.Monotonic.HyperStack.mem", "Lib.IntTypes.size_nat", "Lib.Buffer.as_seq", "Lib.IntTypes.op_Plus_Bang", "Lib.Buffer.loc", "LowStar.Monotonic.Buffer.loc", "LowStar.Monotonic.Buffer.loc_disjoint", "LowStar.Monotonic.Buffer.loc_includes", "LowStar.Monotonic.Buffer.address_liveness_insensitive_locs", "Spec.RSAPSS.mgf_hash_f", "FStar.Pervasives.Native.tuple2", "Lib.Sequence.lseq", "Hacl.Impl.RSAPSS.MGF.mgf_hash_f", "Lib.IntTypes.op_Star_Bang", "FStar.HyperStack.ST.get", "Prims.nat", "Spec.RSAPSS.mgf_hash_a", "Lib.Buffer.create", "Lib.IntTypes.u8", "Prims.eq2", "Prims.int", "Prims.l_or", "Lib.IntTypes.range", "Prims.op_GreaterThan", "Prims.op_Subtraction", "Prims.op_Multiply", "Hacl.Spec.Bignum.Definitions.blocks", "Hacl.Bignum.Definitions.blocks", "Prims.op_GreaterThanOrEqual", "Hacl.Impl.RSAPSS.MGF.hash_len", "Lib.Buffer.update_sub", "Lib.IntTypes.add", "FStar.UInt32.uint_to_t", "FStar.UInt32.t", "FStar.HyperStack.ST.push_frame" ]
[]
module Hacl.Impl.RSAPSS.MGF open FStar.HyperStack open FStar.HyperStack.ST open FStar.Mul open Lib.IntTypes open Lib.Buffer open Hacl.Bignum.Definitions module ST = FStar.HyperStack.ST module S = Spec.RSAPSS module BSeq = Lib.ByteSequence module LSeq = Lib.Sequence module Hash = Spec.Agile.Hash #reset-options "--z3rlimit 50 --fuel 0 --ifuel 0" val hash_len: a:Hash.hash_alg{S.hash_is_supported a} -> Tot (res:size_t{v res == Hash.hash_length a}) [@CInline] let hash_len a = Hacl.Hash.Definitions.hash_len a inline_for_extraction noextract let max_input_length = Hash.max_input_length inline_for_extraction noextract let less_than_max_input_length = Spec.Hash.Definitions.less_than_max_input_length val hash: a:Hash.hash_alg{S.hash_is_supported a} -> mHash:lbuffer uint8 (hash_len a) -> msgLen:size_t{v msgLen `less_than_max_input_length` a} -> msg:lbuffer uint8 msgLen -> Stack unit (requires fun h -> live h mHash /\ live h msg /\ disjoint msg mHash) (ensures fun h0 _ h1 -> modifies (loc mHash) h0 h1 /\ as_seq h1 mHash == Hash.hash a (as_seq h0 msg)) [@CInline] let hash a mHash msgLen msg = match a with | Hash.SHA2_256 -> Hacl.Streaming.SHA2.hash_256 msg msgLen mHash | Hash.SHA2_384 -> Hacl.Streaming.SHA2.hash_384 msg msgLen mHash | Hash.SHA2_512 -> Hacl.Streaming.SHA2.hash_512 msg msgLen mHash (* Mask Generation Function *) inline_for_extraction noextract val counter_to_bytes: i:size_t -> counter:lbuffer uint8 4ul -> Stack unit (requires fun h -> live h counter) (ensures fun h0 _ h1 -> modifies (loc counter) h0 h1 /\ as_seq h1 counter == BSeq.nat_to_intseq_be 4 (v i)) let counter_to_bytes i c = let h0 = ST.get () in c.(0ul) <- to_u8 (i >>. 24ul); c.(1ul) <- to_u8 (i >>. 16ul); c.(2ul) <- to_u8 (i >>. 8ul); c.(3ul) <- to_u8 i; let h1 = ST.get () in BSeq.index_nat_to_intseq_be #U8 #SEC 4 (v i) 0; BSeq.index_nat_to_intseq_be #U8 #SEC 4 (v i) 1; BSeq.index_nat_to_intseq_be #U8 #SEC 4 (v i) 2; BSeq.index_nat_to_intseq_be #U8 #SEC 4 (v i) 3; LSeq.eq_intro (as_seq h1 c) (BSeq.nat_to_intseq_be 4 (v i)) inline_for_extraction noextract val mgf_hash_f: a:Hash.hash_alg{S.hash_is_supported a} -> len:size_t{v len + 4 <= max_size_t /\ (v len + 4) `less_than_max_input_length` a} -> i:size_t -> mgfseed_counter:lbuffer uint8 (len +! 4ul) -> block:lbuffer uint8 (hash_len a) -> Stack unit (requires fun h -> live h mgfseed_counter /\ live h block /\ disjoint mgfseed_counter block) (ensures fun h0 _ h1 -> modifies (loc mgfseed_counter |+| loc block) h0 h1 /\ (as_seq h1 mgfseed_counter, as_seq h1 block) == S.mgf_hash_f a (v len) (v i) (as_seq h0 mgfseed_counter)) let mgf_hash_f a len i mgfseed_counter block = let h0 = ST.get () in update_sub_f h0 mgfseed_counter len 4ul (fun h -> BSeq.nat_to_intseq_be 4 (v i)) (fun _ -> let c = sub mgfseed_counter len 4ul in counter_to_bytes i c); hash a block (len +! 4ul) mgfseed_counter inline_for_extraction noextract let mgf_hash_st (a:Hash.hash_alg{S.hash_is_supported a}) = len:size_t{v len + 4 <= max_size_t /\ (v len + 4) `less_than_max_input_length` a} -> mgfseed:lbuffer uint8 len -> maskLen:size_t{0 < v maskLen /\ S.blocks (v maskLen) (Hash.hash_length a) * Hash.hash_length a < pow2 32} -> res:lbuffer uint8 maskLen -> Stack unit (requires fun h -> live h mgfseed /\ live h res /\ disjoint res mgfseed) (ensures fun h0 _ h1 -> modifies (loc res) h0 h1 /\ as_seq h1 res == S.mgf_hash a (v len) (as_seq h0 mgfseed) (v maskLen)) #push-options "--z3rlimit 100" val mgf_hash: a:Hash.hash_alg{S.hash_is_supported a} -> mgf_hash_st a [@CInline]
false
false
Hacl.Impl.RSAPSS.MGF.fst
{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 0, "initial_ifuel": 0, "max_fuel": 0, "max_ifuel": 0, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": false, "z3cliopt": [], "z3refresh": false, "z3rlimit": 100, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }
null
val mgf_hash: a:Hash.hash_alg{S.hash_is_supported a} -> mgf_hash_st a
[]
Hacl.Impl.RSAPSS.MGF.mgf_hash
{ "file_name": "code/rsapss/Hacl.Impl.RSAPSS.MGF.fst", "git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e", "git_url": "https://github.com/hacl-star/hacl-star.git", "project_name": "hacl-star" }
a: Spec.Hash.Definitions.hash_alg{Spec.RSAPSS.hash_is_supported a} -> Hacl.Impl.RSAPSS.MGF.mgf_hash_st a
{ "end_col": 14, "end_line": 130, "start_col": 2, "start_line": 111 }
Prims.Tot
val cs:S.ciphersuite
[ { "abbrev": true, "full_module": "Spec.Agile.Hash", "short_module": "Hash" }, { "abbrev": true, "full_module": "Spec.Agile.AEAD", "short_module": "AEAD" }, { "abbrev": true, "full_module": "Spec.Agile.DH", "short_module": "DH" }, { "abbrev": true, "full_module": "Spec.Agile.HPKE", "short_module": "S" }, { "abbrev": false, "full_module": "Hacl.Impl.HPKE", "short_module": null }, { "abbrev": false, "full_module": "Hacl.HPKE", "short_module": null }, { "abbrev": false, "full_module": "Hacl.HPKE", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]
false
let cs:S.ciphersuite = (DH.DH_Curve25519, Hash.SHA2_256, S.Seal AEAD.CHACHA20_POLY1305, Hash.SHA2_256)
val cs:S.ciphersuite let cs:S.ciphersuite =
false
null
false
(DH.DH_Curve25519, Hash.SHA2_256, S.Seal AEAD.CHACHA20_POLY1305, Hash.SHA2_256)
{ "checked_file": "Hacl.HPKE.Curve51_CP128_SHA256.fsti.checked", "dependencies": [ "Spec.Agile.HPKE.fsti.checked", "Spec.Agile.Hash.fsti.checked", "Spec.Agile.DH.fst.checked", "Spec.Agile.AEAD.fsti.checked", "prims.fst.checked", "Hacl.Impl.HPKE.fsti.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked" ], "interface_file": false, "source_file": "Hacl.HPKE.Curve51_CP128_SHA256.fsti" }
[ "total" ]
[ "FStar.Pervasives.Native.Mktuple4", "Spec.Agile.DH.algorithm", "Spec.Agile.HPKE.hash_algorithm", "Spec.Agile.HPKE.aead", "Spec.Hash.Definitions.hash_alg", "Spec.Agile.DH.DH_Curve25519", "Spec.Hash.Definitions.SHA2_256", "Spec.Agile.HPKE.Seal", "Spec.Agile.AEAD.CHACHA20_POLY1305" ]
[]
module Hacl.HPKE.Curve51_CP128_SHA256 open Hacl.Impl.HPKE module S = Spec.Agile.HPKE module DH = Spec.Agile.DH module AEAD = Spec.Agile.AEAD module Hash = Spec.Agile.Hash
false
true
Hacl.HPKE.Curve51_CP128_SHA256.fsti
{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 1, "max_fuel": 8, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": false, "z3cliopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }
null
val cs:S.ciphersuite
[]
Hacl.HPKE.Curve51_CP128_SHA256.cs
{ "file_name": "code/hpke/Hacl.HPKE.Curve51_CP128_SHA256.fsti", "git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e", "git_url": "https://github.com/hacl-star/hacl-star.git", "project_name": "hacl-star" }
Spec.Agile.HPKE.ciphersuite
{ "end_col": 102, "end_line": 10, "start_col": 23, "start_line": 10 }
Prims.Tot
val add1_: add1_t True
[ { "abbrev": true, "full_module": "Hacl.Spec.Bignum.Definitions", "short_module": "SD" }, { "abbrev": true, "full_module": "Hacl.Spec.Bignum", "short_module": "SB" }, { "abbrev": true, "full_module": "Hacl.Bignum.Definitions", "short_module": "BD" }, { "abbrev": true, "full_module": "Hacl.Bignum", "short_module": "BN" }, { "abbrev": true, "full_module": "Hacl.Spec.Curve25519.Field64.Core", "short_module": "CC" }, { "abbrev": true, "full_module": "Hacl.Spec.Curve25519.Field64.Definition", "short_module": "CD" }, { "abbrev": true, "full_module": "Lib.Sequence", "short_module": "LSeq" }, { "abbrev": true, "full_module": "Lib.ByteSequence", "short_module": "BSeq" }, { "abbrev": true, "full_module": "FStar.HyperStack.ST", "short_module": "ST" }, { "abbrev": true, "full_module": "Lib.Buffer", "short_module": "B" }, { "abbrev": false, "full_module": "Lib.Buffer", "short_module": null }, { "abbrev": false, "full_module": "Lib.IntTypes", "short_module": null }, { "abbrev": false, "full_module": "Lib.Sequence", "short_module": null }, { "abbrev": false, "full_module": "FStar.Mul", "short_module": null }, { "abbrev": false, "full_module": "FStar.HyperStack.All", "short_module": null }, { "abbrev": false, "full_module": "FStar.HyperStack", "short_module": null }, { "abbrev": false, "full_module": "Hacl.Impl.Curve25519.Fields.Core", "short_module": null }, { "abbrev": false, "full_module": "Hacl.Impl.Curve25519.Field64", "short_module": null }, { "abbrev": false, "full_module": "Hacl.Impl.Curve25519.Field64", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]
false
let add1_ out f1 f2 = let h0 = ST.get () in let c = BN.bn_add1 4ul f1 f2 out in let h1 = ST.get () in assert (let c1, r1 = CC.add1 (as_seq h0 f1) f2 in c == c1 /\ as_seq h1 out == r1); CD.bn_v_is_as_nat (as_seq h0 f1); CD.bn_v_is_as_nat (as_seq h1 out); c
val add1_: add1_t True let add1_ out f1 f2 =
false
null
false
let h0 = ST.get () in let c = BN.bn_add1 4ul f1 f2 out in let h1 = ST.get () in assert (let c1, r1 = CC.add1 (as_seq h0 f1) f2 in c == c1 /\ as_seq h1 out == r1); CD.bn_v_is_as_nat (as_seq h0 f1); CD.bn_v_is_as_nat (as_seq h1 out); c
{ "checked_file": "Hacl.Impl.Curve25519.Field64.Hacl.fst.checked", "dependencies": [ "prims.fst.checked", "Lib.Sequence.fsti.checked", "Lib.Loops.fsti.checked", "Lib.IntTypes.fsti.checked", "Lib.ByteSequence.fsti.checked", "Lib.Buffer.fsti.checked", "Hacl.Spec.Curve25519.Field64.Definition.fst.checked", "Hacl.Spec.Curve25519.Field64.Core.fst.checked", "Hacl.Spec.Bignum.Lib.fst.checked", "Hacl.Spec.Bignum.Definitions.fst.checked", "Hacl.Spec.Bignum.fsti.checked", "Hacl.Bignum.Definitions.fst.checked", "Hacl.Bignum.fsti.checked", "FStar.UInt32.fsti.checked", "FStar.Pervasives.fsti.checked", "FStar.Mul.fst.checked", "FStar.HyperStack.ST.fsti.checked", "FStar.HyperStack.All.fst.checked", "FStar.HyperStack.fst.checked" ], "interface_file": true, "source_file": "Hacl.Impl.Curve25519.Field64.Hacl.fst" }
[ "total" ]
[ "Hacl.Impl.Curve25519.Fields.Core.felem", "Hacl.Impl.Curve25519.Fields.Core.M64", "Lib.IntTypes.uint64", "FStar.Ghost.hide", "Prims.unit", "Hacl.Spec.Curve25519.Field64.Definition.bn_v_is_as_nat", "Lib.Buffer.as_seq", "Lib.Buffer.MUT", "Hacl.Impl.Curve25519.Fields.Core.limb", "Hacl.Impl.Curve25519.Fields.Core.nlimb", "Prims._assert", "Hacl.Spec.Curve25519.Field64.Core.felem", "Prims.l_and", "Prims.eq2", "Lib.IntTypes.sec_int_t", "Lib.IntTypes.U64", "Lib.Sequence.lseq", "Hacl.Spec.Bignum.Definitions.limb", "FStar.Pervasives.Native.tuple2", "Lib.IntTypes.int_t", "Lib.IntTypes.SEC", "Hacl.Spec.Bignum.Definitions.lbignum", "Hacl.Spec.Curve25519.Field64.Core.add1", "FStar.Ghost.erased", "FStar.Monotonic.HyperStack.mem", "FStar.HyperStack.ST.get", "Hacl.Spec.Bignum.Base.carry", "Hacl.Bignum.bn_add1", "FStar.UInt32.__uint_to_t" ]
[]
module Hacl.Impl.Curve25519.Field64.Hacl open FStar.HyperStack open FStar.HyperStack.All open FStar.Mul open Lib.Sequence open Lib.IntTypes open Lib.Buffer module B = Lib.Buffer module ST = FStar.HyperStack.ST module BSeq = Lib.ByteSequence module LSeq = Lib.Sequence module CD = Hacl.Spec.Curve25519.Field64.Definition module CC = Hacl.Spec.Curve25519.Field64.Core module BN = Hacl.Bignum module BD = Hacl.Bignum.Definitions module SB = Hacl.Spec.Bignum module SD = Hacl.Spec.Bignum.Definitions #set-options "--z3rlimit 50 --fuel 0 --ifuel 0"
false
true
Hacl.Impl.Curve25519.Field64.Hacl.fst
{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 0, "initial_ifuel": 0, "max_fuel": 0, "max_ifuel": 0, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": false, "z3cliopt": [], "z3refresh": false, "z3rlimit": 50, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }
null
val add1_: add1_t True
[]
Hacl.Impl.Curve25519.Field64.Hacl.add1_
{ "file_name": "code/curve25519/Hacl.Impl.Curve25519.Field64.Hacl.fst", "git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e", "git_url": "https://github.com/hacl-star/hacl-star.git", "project_name": "hacl-star" }
Hacl.Impl.Curve25519.Fields.Core.add1_t Prims.l_True
{ "end_col": 3, "end_line": 35, "start_col": 21, "start_line": 28 }
Prims.Tot
val fsqr_: fsqr_t M64 True
[ { "abbrev": true, "full_module": "Hacl.Spec.Bignum.Definitions", "short_module": "SD" }, { "abbrev": true, "full_module": "Hacl.Spec.Bignum", "short_module": "SB" }, { "abbrev": true, "full_module": "Hacl.Bignum.Definitions", "short_module": "BD" }, { "abbrev": true, "full_module": "Hacl.Bignum", "short_module": "BN" }, { "abbrev": true, "full_module": "Hacl.Spec.Curve25519.Field64.Core", "short_module": "CC" }, { "abbrev": true, "full_module": "Hacl.Spec.Curve25519.Field64.Definition", "short_module": "CD" }, { "abbrev": true, "full_module": "Lib.Sequence", "short_module": "LSeq" }, { "abbrev": true, "full_module": "Lib.ByteSequence", "short_module": "BSeq" }, { "abbrev": true, "full_module": "FStar.HyperStack.ST", "short_module": "ST" }, { "abbrev": true, "full_module": "Lib.Buffer", "short_module": "B" }, { "abbrev": false, "full_module": "Lib.Buffer", "short_module": null }, { "abbrev": false, "full_module": "Lib.IntTypes", "short_module": null }, { "abbrev": false, "full_module": "Lib.Sequence", "short_module": null }, { "abbrev": false, "full_module": "FStar.Mul", "short_module": null }, { "abbrev": false, "full_module": "FStar.HyperStack.All", "short_module": null }, { "abbrev": false, "full_module": "FStar.HyperStack", "short_module": null }, { "abbrev": false, "full_module": "Hacl.Impl.Curve25519.Fields.Core", "short_module": null }, { "abbrev": false, "full_module": "Hacl.Impl.Curve25519.Field64", "short_module": null }, { "abbrev": false, "full_module": "Hacl.Impl.Curve25519.Field64", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]
false
let fsqr_ out f1 tmp = let h0 = ST.get () in BN.bn_sqr 4ul f1 tmp; SB.bn_sqr_lemma (as_seq h0 f1); let c0 = BN.bn_mul1_lshift_add_in_place 4ul (sub tmp 4ul 4ul) (u64 38) 4ul 0ul (sub tmp 0ul 4ul) in let c = BN.bn_add1 4ul (sub tmp 0ul 4ul) (c0 *. u64 38) out in out.(0ul) <- out.(0ul) +. c *. u64 38; let h1 = ST.get () in assert (as_seq h1 out == CC.fsqr4 (as_seq h0 f1)); CD.bn_v_is_as_nat (as_seq h0 f1); CD.bn_v_is_as_nat (as_seq h1 out)
val fsqr_: fsqr_t M64 True let fsqr_ out f1 tmp =
false
null
false
let h0 = ST.get () in BN.bn_sqr 4ul f1 tmp; SB.bn_sqr_lemma (as_seq h0 f1); let c0 = BN.bn_mul1_lshift_add_in_place 4ul (sub tmp 4ul 4ul) (u64 38) 4ul 0ul (sub tmp 0ul 4ul) in let c = BN.bn_add1 4ul (sub tmp 0ul 4ul) (c0 *. u64 38) out in out.(0ul) <- out.(0ul) +. c *. u64 38; let h1 = ST.get () in assert (as_seq h1 out == CC.fsqr4 (as_seq h0 f1)); CD.bn_v_is_as_nat (as_seq h0 f1); CD.bn_v_is_as_nat (as_seq h1 out)
{ "checked_file": "Hacl.Impl.Curve25519.Field64.Hacl.fst.checked", "dependencies": [ "prims.fst.checked", "Lib.Sequence.fsti.checked", "Lib.Loops.fsti.checked", "Lib.IntTypes.fsti.checked", "Lib.ByteSequence.fsti.checked", "Lib.Buffer.fsti.checked", "Hacl.Spec.Curve25519.Field64.Definition.fst.checked", "Hacl.Spec.Curve25519.Field64.Core.fst.checked", "Hacl.Spec.Bignum.Lib.fst.checked", "Hacl.Spec.Bignum.Definitions.fst.checked", "Hacl.Spec.Bignum.fsti.checked", "Hacl.Bignum.Definitions.fst.checked", "Hacl.Bignum.fsti.checked", "FStar.UInt32.fsti.checked", "FStar.Pervasives.fsti.checked", "FStar.Mul.fst.checked", "FStar.HyperStack.ST.fsti.checked", "FStar.HyperStack.All.fst.checked", "FStar.HyperStack.fst.checked" ], "interface_file": true, "source_file": "Hacl.Impl.Curve25519.Field64.Hacl.fst" }
[ "total" ]
[ "Hacl.Impl.Curve25519.Fields.Core.felem", "Hacl.Impl.Curve25519.Fields.Core.M64", "Hacl.Impl.Curve25519.Fields.Core.felem_wide", "Hacl.Spec.Curve25519.Field64.Definition.bn_v_is_as_nat", "Lib.Buffer.as_seq", "Lib.Buffer.MUT", "Hacl.Impl.Curve25519.Fields.Core.limb", "Hacl.Impl.Curve25519.Fields.Core.nlimb", "Prims.unit", "Prims._assert", "Prims.eq2", "Lib.Sequence.lseq", "Lib.IntTypes.v", "Lib.IntTypes.U32", "Lib.IntTypes.PUB", "Hacl.Spec.Curve25519.Field64.Core.fsqr4", "FStar.Monotonic.HyperStack.mem", "FStar.HyperStack.ST.get", "Lib.Buffer.op_Array_Assignment", "FStar.UInt32.__uint_to_t", "Lib.IntTypes.int_t", "Lib.IntTypes.U64", "Lib.IntTypes.SEC", "Lib.IntTypes.op_Plus_Dot", "Lib.IntTypes.op_Star_Dot", "Lib.IntTypes.u64", "Lib.Buffer.op_Array_Access", "Hacl.Spec.Bignum.Base.carry", "Hacl.Bignum.bn_add1", "Hacl.Bignum.Definitions.lbignum", "FStar.UInt32.uint_to_t", "FStar.UInt32.t", "Lib.Buffer.sub", "Hacl.Impl.Curve25519.Fields.Core.wide", "Hacl.Impl.Curve25519.Fields.Core.nwide", "Lib.Buffer.lbuffer_t", "Hacl.Bignum.Definitions.limb", "Hacl.Bignum.bn_mul1_lshift_add_in_place", "Hacl.Spec.Bignum.bn_sqr_lemma", "Hacl.Bignum.bn_sqr" ]
[]
module Hacl.Impl.Curve25519.Field64.Hacl open FStar.HyperStack open FStar.HyperStack.All open FStar.Mul open Lib.Sequence open Lib.IntTypes open Lib.Buffer module B = Lib.Buffer module ST = FStar.HyperStack.ST module BSeq = Lib.ByteSequence module LSeq = Lib.Sequence module CD = Hacl.Spec.Curve25519.Field64.Definition module CC = Hacl.Spec.Curve25519.Field64.Core module BN = Hacl.Bignum module BD = Hacl.Bignum.Definitions module SB = Hacl.Spec.Bignum module SD = Hacl.Spec.Bignum.Definitions #set-options "--z3rlimit 50 --fuel 0 --ifuel 0" [@CInline] let add1_ out f1 f2 = let h0 = ST.get () in let c = BN.bn_add1 4ul f1 f2 out in let h1 = ST.get () in assert (let c1, r1 = CC.add1 (as_seq h0 f1) f2 in c == c1 /\ as_seq h1 out == r1); CD.bn_v_is_as_nat (as_seq h0 f1); CD.bn_v_is_as_nat (as_seq h1 out); c [@CInline] let fadd_ out f1 f2 = let h0 = ST.get () in let c0 = BN.bn_add_eq_len 4ul f1 f2 out in let c = BN.bn_add1 4ul out (c0 *. u64 38) out in out.(0ul) <- out.(0ul) +. c *. u64 38; let h1 = ST.get () in assert (as_seq h1 out == CC.fadd4 (as_seq h0 f1) (as_seq h0 f2)); CD.bn_v_is_as_nat (as_seq h0 f1); CD.bn_v_is_as_nat (as_seq h0 f2); CD.bn_v_is_as_nat (as_seq h1 out) [@CInline] let fsub_ out f1 f2 = let h0 = ST.get () in let c0 = BN.bn_sub_eq_len 4ul f1 f2 out in let c = BN.bn_sub1 4ul out (c0 *! u64 38) out in out.(0ul) <- out.(0ul) -. c *. u64 38; let h1 = ST.get () in assert (as_seq h1 out == CC.fsub4 (as_seq h0 f1) (as_seq h0 f2)); CD.bn_v_is_as_nat (as_seq h0 f1); CD.bn_v_is_as_nat (as_seq h0 f2); CD.bn_v_is_as_nat (as_seq h1 out) [@CInline] let fmul_ out f1 f2 tmp = let h0 = ST.get () in let tmp0 = sub tmp 0ul 8ul in BN.bn_mul 4ul 4ul f1 f2 tmp0; let c0 = BN.bn_mul1_lshift_add_in_place 4ul (sub tmp0 4ul 4ul) (u64 38) 4ul 0ul (sub tmp0 0ul 4ul) in let c = BN.bn_add1 4ul (sub tmp0 0ul 4ul) (c0 *. u64 38) out in out.(0ul) <- out.(0ul) +. c *. u64 38; let h1 = ST.get () in assert (as_seq h1 out == CC.fmul4 (as_seq h0 f1) (as_seq h0 f2)); CD.bn_v_is_as_nat (as_seq h0 f1); CD.bn_v_is_as_nat (as_seq h0 f2); CD.bn_v_is_as_nat (as_seq h1 out) [@CInline] let fmul2_ out f1 f2 tmp = let out1 = B.sub out 0ul 4ul in let out2 = B.sub out 4ul 4ul in let f11 = B.sub f1 0ul 4ul in let f12 = B.sub f1 4ul 4ul in let f21 = B.sub f2 0ul 4ul in let f22 = B.sub f2 4ul 4ul in fmul_ out1 f11 f21 tmp; fmul_ out2 f12 f22 tmp [@CInline] let fmul1_ out f1 f2 = let h0 = ST.get () in let c0 = BN.bn_mul1 4ul f1 f2 out in let c = BN.bn_add1 4ul out (c0 *. u64 38) out in out.(0ul) <- out.(0ul) +. c *. u64 38; let h1 = ST.get () in assert (as_seq h1 out == CC.fmul14 (as_seq h0 f1) f2); CD.bn_v_is_as_nat (as_seq h0 f1); CD.bn_v_is_as_nat (as_seq h1 out)
false
true
Hacl.Impl.Curve25519.Field64.Hacl.fst
{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 0, "initial_ifuel": 0, "max_fuel": 0, "max_ifuel": 0, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": false, "z3cliopt": [], "z3refresh": false, "z3rlimit": 50, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }
null
val fsqr_: fsqr_t M64 True
[]
Hacl.Impl.Curve25519.Field64.Hacl.fsqr_
{ "file_name": "code/curve25519/Hacl.Impl.Curve25519.Field64.Hacl.fst", "git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e", "git_url": "https://github.com/hacl-star/hacl-star.git", "project_name": "hacl-star" }
Hacl.Impl.Curve25519.Fields.Core.fsqr_t Hacl.Impl.Curve25519.Fields.Core.M64 Prims.l_True
{ "end_col": 35, "end_line": 114, "start_col": 22, "start_line": 104 }
Prims.Tot
val fsqr2_: fsqr2_t M64 True
[ { "abbrev": true, "full_module": "Hacl.Spec.Bignum.Definitions", "short_module": "SD" }, { "abbrev": true, "full_module": "Hacl.Spec.Bignum", "short_module": "SB" }, { "abbrev": true, "full_module": "Hacl.Bignum.Definitions", "short_module": "BD" }, { "abbrev": true, "full_module": "Hacl.Bignum", "short_module": "BN" }, { "abbrev": true, "full_module": "Hacl.Spec.Curve25519.Field64.Core", "short_module": "CC" }, { "abbrev": true, "full_module": "Hacl.Spec.Curve25519.Field64.Definition", "short_module": "CD" }, { "abbrev": true, "full_module": "Lib.Sequence", "short_module": "LSeq" }, { "abbrev": true, "full_module": "Lib.ByteSequence", "short_module": "BSeq" }, { "abbrev": true, "full_module": "FStar.HyperStack.ST", "short_module": "ST" }, { "abbrev": true, "full_module": "Lib.Buffer", "short_module": "B" }, { "abbrev": false, "full_module": "Lib.Buffer", "short_module": null }, { "abbrev": false, "full_module": "Lib.IntTypes", "short_module": null }, { "abbrev": false, "full_module": "Lib.Sequence", "short_module": null }, { "abbrev": false, "full_module": "FStar.Mul", "short_module": null }, { "abbrev": false, "full_module": "FStar.HyperStack.All", "short_module": null }, { "abbrev": false, "full_module": "FStar.HyperStack", "short_module": null }, { "abbrev": false, "full_module": "Hacl.Impl.Curve25519.Fields.Core", "short_module": null }, { "abbrev": false, "full_module": "Hacl.Impl.Curve25519.Field64", "short_module": null }, { "abbrev": false, "full_module": "Hacl.Impl.Curve25519.Field64", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]
false
let fsqr2_ out f tmp = let out1 = B.sub out 0ul 4ul in let out2 = B.sub out 4ul 4ul in let f1 = B.sub f 0ul 4ul in let f2 = B.sub f 4ul 4ul in fmul_ out1 f1 f1 tmp; fmul_ out2 f2 f2 tmp
val fsqr2_: fsqr2_t M64 True let fsqr2_ out f tmp =
false
null
false
let out1 = B.sub out 0ul 4ul in let out2 = B.sub out 4ul 4ul in let f1 = B.sub f 0ul 4ul in let f2 = B.sub f 4ul 4ul in fmul_ out1 f1 f1 tmp; fmul_ out2 f2 f2 tmp
{ "checked_file": "Hacl.Impl.Curve25519.Field64.Hacl.fst.checked", "dependencies": [ "prims.fst.checked", "Lib.Sequence.fsti.checked", "Lib.Loops.fsti.checked", "Lib.IntTypes.fsti.checked", "Lib.ByteSequence.fsti.checked", "Lib.Buffer.fsti.checked", "Hacl.Spec.Curve25519.Field64.Definition.fst.checked", "Hacl.Spec.Curve25519.Field64.Core.fst.checked", "Hacl.Spec.Bignum.Lib.fst.checked", "Hacl.Spec.Bignum.Definitions.fst.checked", "Hacl.Spec.Bignum.fsti.checked", "Hacl.Bignum.Definitions.fst.checked", "Hacl.Bignum.fsti.checked", "FStar.UInt32.fsti.checked", "FStar.Pervasives.fsti.checked", "FStar.Mul.fst.checked", "FStar.HyperStack.ST.fsti.checked", "FStar.HyperStack.All.fst.checked", "FStar.HyperStack.fst.checked" ], "interface_file": true, "source_file": "Hacl.Impl.Curve25519.Field64.Hacl.fst" }
[ "total" ]
[ "Hacl.Impl.Curve25519.Fields.Core.felem2", "Hacl.Impl.Curve25519.Fields.Core.M64", "Hacl.Impl.Curve25519.Fields.Core.felem_wide2", "Hacl.Impl.Curve25519.Field64.Hacl.fmul_", "Prims.unit", "Lib.Buffer.lbuffer_t", "Lib.Buffer.MUT", "Lib.IntTypes.int_t", "Lib.IntTypes.U64", "Lib.IntTypes.SEC", "FStar.UInt32.uint_to_t", "FStar.UInt32.t", "Lib.Buffer.sub", "Hacl.Impl.Curve25519.Fields.Core.limb", "Lib.IntTypes.op_Plus_Dot", "Lib.IntTypes.U32", "Lib.IntTypes.PUB", "Hacl.Impl.Curve25519.Fields.Core.nlimb", "FStar.UInt32.__uint_to_t" ]
[]
module Hacl.Impl.Curve25519.Field64.Hacl open FStar.HyperStack open FStar.HyperStack.All open FStar.Mul open Lib.Sequence open Lib.IntTypes open Lib.Buffer module B = Lib.Buffer module ST = FStar.HyperStack.ST module BSeq = Lib.ByteSequence module LSeq = Lib.Sequence module CD = Hacl.Spec.Curve25519.Field64.Definition module CC = Hacl.Spec.Curve25519.Field64.Core module BN = Hacl.Bignum module BD = Hacl.Bignum.Definitions module SB = Hacl.Spec.Bignum module SD = Hacl.Spec.Bignum.Definitions #set-options "--z3rlimit 50 --fuel 0 --ifuel 0" [@CInline] let add1_ out f1 f2 = let h0 = ST.get () in let c = BN.bn_add1 4ul f1 f2 out in let h1 = ST.get () in assert (let c1, r1 = CC.add1 (as_seq h0 f1) f2 in c == c1 /\ as_seq h1 out == r1); CD.bn_v_is_as_nat (as_seq h0 f1); CD.bn_v_is_as_nat (as_seq h1 out); c [@CInline] let fadd_ out f1 f2 = let h0 = ST.get () in let c0 = BN.bn_add_eq_len 4ul f1 f2 out in let c = BN.bn_add1 4ul out (c0 *. u64 38) out in out.(0ul) <- out.(0ul) +. c *. u64 38; let h1 = ST.get () in assert (as_seq h1 out == CC.fadd4 (as_seq h0 f1) (as_seq h0 f2)); CD.bn_v_is_as_nat (as_seq h0 f1); CD.bn_v_is_as_nat (as_seq h0 f2); CD.bn_v_is_as_nat (as_seq h1 out) [@CInline] let fsub_ out f1 f2 = let h0 = ST.get () in let c0 = BN.bn_sub_eq_len 4ul f1 f2 out in let c = BN.bn_sub1 4ul out (c0 *! u64 38) out in out.(0ul) <- out.(0ul) -. c *. u64 38; let h1 = ST.get () in assert (as_seq h1 out == CC.fsub4 (as_seq h0 f1) (as_seq h0 f2)); CD.bn_v_is_as_nat (as_seq h0 f1); CD.bn_v_is_as_nat (as_seq h0 f2); CD.bn_v_is_as_nat (as_seq h1 out) [@CInline] let fmul_ out f1 f2 tmp = let h0 = ST.get () in let tmp0 = sub tmp 0ul 8ul in BN.bn_mul 4ul 4ul f1 f2 tmp0; let c0 = BN.bn_mul1_lshift_add_in_place 4ul (sub tmp0 4ul 4ul) (u64 38) 4ul 0ul (sub tmp0 0ul 4ul) in let c = BN.bn_add1 4ul (sub tmp0 0ul 4ul) (c0 *. u64 38) out in out.(0ul) <- out.(0ul) +. c *. u64 38; let h1 = ST.get () in assert (as_seq h1 out == CC.fmul4 (as_seq h0 f1) (as_seq h0 f2)); CD.bn_v_is_as_nat (as_seq h0 f1); CD.bn_v_is_as_nat (as_seq h0 f2); CD.bn_v_is_as_nat (as_seq h1 out) [@CInline] let fmul2_ out f1 f2 tmp = let out1 = B.sub out 0ul 4ul in let out2 = B.sub out 4ul 4ul in let f11 = B.sub f1 0ul 4ul in let f12 = B.sub f1 4ul 4ul in let f21 = B.sub f2 0ul 4ul in let f22 = B.sub f2 4ul 4ul in fmul_ out1 f11 f21 tmp; fmul_ out2 f12 f22 tmp [@CInline] let fmul1_ out f1 f2 = let h0 = ST.get () in let c0 = BN.bn_mul1 4ul f1 f2 out in let c = BN.bn_add1 4ul out (c0 *. u64 38) out in out.(0ul) <- out.(0ul) +. c *. u64 38; let h1 = ST.get () in assert (as_seq h1 out == CC.fmul14 (as_seq h0 f1) f2); CD.bn_v_is_as_nat (as_seq h0 f1); CD.bn_v_is_as_nat (as_seq h1 out) [@CInline] let fsqr_ out f1 tmp = let h0 = ST.get () in BN.bn_sqr 4ul f1 tmp; SB.bn_sqr_lemma (as_seq h0 f1); let c0 = BN.bn_mul1_lshift_add_in_place 4ul (sub tmp 4ul 4ul) (u64 38) 4ul 0ul (sub tmp 0ul 4ul) in let c = BN.bn_add1 4ul (sub tmp 0ul 4ul) (c0 *. u64 38) out in out.(0ul) <- out.(0ul) +. c *. u64 38; let h1 = ST.get () in assert (as_seq h1 out == CC.fsqr4 (as_seq h0 f1)); CD.bn_v_is_as_nat (as_seq h0 f1); CD.bn_v_is_as_nat (as_seq h1 out)
false
true
Hacl.Impl.Curve25519.Field64.Hacl.fst
{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 0, "initial_ifuel": 0, "max_fuel": 0, "max_ifuel": 0, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": false, "z3cliopt": [], "z3refresh": false, "z3rlimit": 50, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }
null
val fsqr2_: fsqr2_t M64 True
[]
Hacl.Impl.Curve25519.Field64.Hacl.fsqr2_
{ "file_name": "code/curve25519/Hacl.Impl.Curve25519.Field64.Hacl.fst", "git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e", "git_url": "https://github.com/hacl-star/hacl-star.git", "project_name": "hacl-star" }
Hacl.Impl.Curve25519.Fields.Core.fsqr2_t Hacl.Impl.Curve25519.Fields.Core.M64 Prims.l_True
{ "end_col": 22, "end_line": 124, "start_col": 22, "start_line": 118 }
Prims.Tot
val fmul1_: fmul1_t M64 True
[ { "abbrev": true, "full_module": "Hacl.Spec.Bignum.Definitions", "short_module": "SD" }, { "abbrev": true, "full_module": "Hacl.Spec.Bignum", "short_module": "SB" }, { "abbrev": true, "full_module": "Hacl.Bignum.Definitions", "short_module": "BD" }, { "abbrev": true, "full_module": "Hacl.Bignum", "short_module": "BN" }, { "abbrev": true, "full_module": "Hacl.Spec.Curve25519.Field64.Core", "short_module": "CC" }, { "abbrev": true, "full_module": "Hacl.Spec.Curve25519.Field64.Definition", "short_module": "CD" }, { "abbrev": true, "full_module": "Lib.Sequence", "short_module": "LSeq" }, { "abbrev": true, "full_module": "Lib.ByteSequence", "short_module": "BSeq" }, { "abbrev": true, "full_module": "FStar.HyperStack.ST", "short_module": "ST" }, { "abbrev": true, "full_module": "Lib.Buffer", "short_module": "B" }, { "abbrev": false, "full_module": "Lib.Buffer", "short_module": null }, { "abbrev": false, "full_module": "Lib.IntTypes", "short_module": null }, { "abbrev": false, "full_module": "Lib.Sequence", "short_module": null }, { "abbrev": false, "full_module": "FStar.Mul", "short_module": null }, { "abbrev": false, "full_module": "FStar.HyperStack.All", "short_module": null }, { "abbrev": false, "full_module": "FStar.HyperStack", "short_module": null }, { "abbrev": false, "full_module": "Hacl.Impl.Curve25519.Fields.Core", "short_module": null }, { "abbrev": false, "full_module": "Hacl.Impl.Curve25519.Field64", "short_module": null }, { "abbrev": false, "full_module": "Hacl.Impl.Curve25519.Field64", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]
false
let fmul1_ out f1 f2 = let h0 = ST.get () in let c0 = BN.bn_mul1 4ul f1 f2 out in let c = BN.bn_add1 4ul out (c0 *. u64 38) out in out.(0ul) <- out.(0ul) +. c *. u64 38; let h1 = ST.get () in assert (as_seq h1 out == CC.fmul14 (as_seq h0 f1) f2); CD.bn_v_is_as_nat (as_seq h0 f1); CD.bn_v_is_as_nat (as_seq h1 out)
val fmul1_: fmul1_t M64 True let fmul1_ out f1 f2 =
false
null
false
let h0 = ST.get () in let c0 = BN.bn_mul1 4ul f1 f2 out in let c = BN.bn_add1 4ul out (c0 *. u64 38) out in out.(0ul) <- out.(0ul) +. c *. u64 38; let h1 = ST.get () in assert (as_seq h1 out == CC.fmul14 (as_seq h0 f1) f2); CD.bn_v_is_as_nat (as_seq h0 f1); CD.bn_v_is_as_nat (as_seq h1 out)
{ "checked_file": "Hacl.Impl.Curve25519.Field64.Hacl.fst.checked", "dependencies": [ "prims.fst.checked", "Lib.Sequence.fsti.checked", "Lib.Loops.fsti.checked", "Lib.IntTypes.fsti.checked", "Lib.ByteSequence.fsti.checked", "Lib.Buffer.fsti.checked", "Hacl.Spec.Curve25519.Field64.Definition.fst.checked", "Hacl.Spec.Curve25519.Field64.Core.fst.checked", "Hacl.Spec.Bignum.Lib.fst.checked", "Hacl.Spec.Bignum.Definitions.fst.checked", "Hacl.Spec.Bignum.fsti.checked", "Hacl.Bignum.Definitions.fst.checked", "Hacl.Bignum.fsti.checked", "FStar.UInt32.fsti.checked", "FStar.Pervasives.fsti.checked", "FStar.Mul.fst.checked", "FStar.HyperStack.ST.fsti.checked", "FStar.HyperStack.All.fst.checked", "FStar.HyperStack.fst.checked" ], "interface_file": true, "source_file": "Hacl.Impl.Curve25519.Field64.Hacl.fst" }
[ "total" ]
[ "Hacl.Impl.Curve25519.Fields.Core.felem", "Hacl.Impl.Curve25519.Fields.Core.M64", "Lib.IntTypes.uint64", "Hacl.Spec.Curve25519.Field64.Definition.bn_v_is_as_nat", "Lib.Buffer.as_seq", "Lib.Buffer.MUT", "Hacl.Impl.Curve25519.Fields.Core.limb", "Hacl.Impl.Curve25519.Fields.Core.nlimb", "Prims.unit", "Prims._assert", "Prims.eq2", "Lib.Sequence.lseq", "Lib.IntTypes.v", "Lib.IntTypes.U32", "Lib.IntTypes.PUB", "Hacl.Spec.Curve25519.Field64.Core.fmul14", "FStar.Monotonic.HyperStack.mem", "FStar.HyperStack.ST.get", "Lib.Buffer.op_Array_Assignment", "FStar.UInt32.__uint_to_t", "Lib.IntTypes.int_t", "Lib.IntTypes.U64", "Lib.IntTypes.SEC", "Lib.IntTypes.op_Plus_Dot", "Lib.IntTypes.op_Star_Dot", "Lib.IntTypes.u64", "Lib.Buffer.op_Array_Access", "Hacl.Spec.Bignum.Base.carry", "Hacl.Bignum.bn_add1", "Hacl.Bignum.Definitions.limb", "Hacl.Bignum.bn_mul1" ]
[]
module Hacl.Impl.Curve25519.Field64.Hacl open FStar.HyperStack open FStar.HyperStack.All open FStar.Mul open Lib.Sequence open Lib.IntTypes open Lib.Buffer module B = Lib.Buffer module ST = FStar.HyperStack.ST module BSeq = Lib.ByteSequence module LSeq = Lib.Sequence module CD = Hacl.Spec.Curve25519.Field64.Definition module CC = Hacl.Spec.Curve25519.Field64.Core module BN = Hacl.Bignum module BD = Hacl.Bignum.Definitions module SB = Hacl.Spec.Bignum module SD = Hacl.Spec.Bignum.Definitions #set-options "--z3rlimit 50 --fuel 0 --ifuel 0" [@CInline] let add1_ out f1 f2 = let h0 = ST.get () in let c = BN.bn_add1 4ul f1 f2 out in let h1 = ST.get () in assert (let c1, r1 = CC.add1 (as_seq h0 f1) f2 in c == c1 /\ as_seq h1 out == r1); CD.bn_v_is_as_nat (as_seq h0 f1); CD.bn_v_is_as_nat (as_seq h1 out); c [@CInline] let fadd_ out f1 f2 = let h0 = ST.get () in let c0 = BN.bn_add_eq_len 4ul f1 f2 out in let c = BN.bn_add1 4ul out (c0 *. u64 38) out in out.(0ul) <- out.(0ul) +. c *. u64 38; let h1 = ST.get () in assert (as_seq h1 out == CC.fadd4 (as_seq h0 f1) (as_seq h0 f2)); CD.bn_v_is_as_nat (as_seq h0 f1); CD.bn_v_is_as_nat (as_seq h0 f2); CD.bn_v_is_as_nat (as_seq h1 out) [@CInline] let fsub_ out f1 f2 = let h0 = ST.get () in let c0 = BN.bn_sub_eq_len 4ul f1 f2 out in let c = BN.bn_sub1 4ul out (c0 *! u64 38) out in out.(0ul) <- out.(0ul) -. c *. u64 38; let h1 = ST.get () in assert (as_seq h1 out == CC.fsub4 (as_seq h0 f1) (as_seq h0 f2)); CD.bn_v_is_as_nat (as_seq h0 f1); CD.bn_v_is_as_nat (as_seq h0 f2); CD.bn_v_is_as_nat (as_seq h1 out) [@CInline] let fmul_ out f1 f2 tmp = let h0 = ST.get () in let tmp0 = sub tmp 0ul 8ul in BN.bn_mul 4ul 4ul f1 f2 tmp0; let c0 = BN.bn_mul1_lshift_add_in_place 4ul (sub tmp0 4ul 4ul) (u64 38) 4ul 0ul (sub tmp0 0ul 4ul) in let c = BN.bn_add1 4ul (sub tmp0 0ul 4ul) (c0 *. u64 38) out in out.(0ul) <- out.(0ul) +. c *. u64 38; let h1 = ST.get () in assert (as_seq h1 out == CC.fmul4 (as_seq h0 f1) (as_seq h0 f2)); CD.bn_v_is_as_nat (as_seq h0 f1); CD.bn_v_is_as_nat (as_seq h0 f2); CD.bn_v_is_as_nat (as_seq h1 out) [@CInline] let fmul2_ out f1 f2 tmp = let out1 = B.sub out 0ul 4ul in let out2 = B.sub out 4ul 4ul in let f11 = B.sub f1 0ul 4ul in let f12 = B.sub f1 4ul 4ul in let f21 = B.sub f2 0ul 4ul in let f22 = B.sub f2 4ul 4ul in fmul_ out1 f11 f21 tmp; fmul_ out2 f12 f22 tmp
false
true
Hacl.Impl.Curve25519.Field64.Hacl.fst
{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 0, "initial_ifuel": 0, "max_fuel": 0, "max_ifuel": 0, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": false, "z3cliopt": [], "z3refresh": false, "z3rlimit": 50, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }
null
val fmul1_: fmul1_t M64 True
[]
Hacl.Impl.Curve25519.Field64.Hacl.fmul1_
{ "file_name": "code/curve25519/Hacl.Impl.Curve25519.Field64.Hacl.fst", "git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e", "git_url": "https://github.com/hacl-star/hacl-star.git", "project_name": "hacl-star" }
Hacl.Impl.Curve25519.Fields.Core.fmul1_t Hacl.Impl.Curve25519.Fields.Core.M64 Prims.l_True
{ "end_col": 35, "end_line": 100, "start_col": 22, "start_line": 92 }
Prims.Tot
val fadd_: fadd_t M64 True
[ { "abbrev": true, "full_module": "Hacl.Spec.Bignum.Definitions", "short_module": "SD" }, { "abbrev": true, "full_module": "Hacl.Spec.Bignum", "short_module": "SB" }, { "abbrev": true, "full_module": "Hacl.Bignum.Definitions", "short_module": "BD" }, { "abbrev": true, "full_module": "Hacl.Bignum", "short_module": "BN" }, { "abbrev": true, "full_module": "Hacl.Spec.Curve25519.Field64.Core", "short_module": "CC" }, { "abbrev": true, "full_module": "Hacl.Spec.Curve25519.Field64.Definition", "short_module": "CD" }, { "abbrev": true, "full_module": "Lib.Sequence", "short_module": "LSeq" }, { "abbrev": true, "full_module": "Lib.ByteSequence", "short_module": "BSeq" }, { "abbrev": true, "full_module": "FStar.HyperStack.ST", "short_module": "ST" }, { "abbrev": true, "full_module": "Lib.Buffer", "short_module": "B" }, { "abbrev": false, "full_module": "Lib.Buffer", "short_module": null }, { "abbrev": false, "full_module": "Lib.IntTypes", "short_module": null }, { "abbrev": false, "full_module": "Lib.Sequence", "short_module": null }, { "abbrev": false, "full_module": "FStar.Mul", "short_module": null }, { "abbrev": false, "full_module": "FStar.HyperStack.All", "short_module": null }, { "abbrev": false, "full_module": "FStar.HyperStack", "short_module": null }, { "abbrev": false, "full_module": "Hacl.Impl.Curve25519.Fields.Core", "short_module": null }, { "abbrev": false, "full_module": "Hacl.Impl.Curve25519.Field64", "short_module": null }, { "abbrev": false, "full_module": "Hacl.Impl.Curve25519.Field64", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]
false
let fadd_ out f1 f2 = let h0 = ST.get () in let c0 = BN.bn_add_eq_len 4ul f1 f2 out in let c = BN.bn_add1 4ul out (c0 *. u64 38) out in out.(0ul) <- out.(0ul) +. c *. u64 38; let h1 = ST.get () in assert (as_seq h1 out == CC.fadd4 (as_seq h0 f1) (as_seq h0 f2)); CD.bn_v_is_as_nat (as_seq h0 f1); CD.bn_v_is_as_nat (as_seq h0 f2); CD.bn_v_is_as_nat (as_seq h1 out)
val fadd_: fadd_t M64 True let fadd_ out f1 f2 =
false
null
false
let h0 = ST.get () in let c0 = BN.bn_add_eq_len 4ul f1 f2 out in let c = BN.bn_add1 4ul out (c0 *. u64 38) out in out.(0ul) <- out.(0ul) +. c *. u64 38; let h1 = ST.get () in assert (as_seq h1 out == CC.fadd4 (as_seq h0 f1) (as_seq h0 f2)); CD.bn_v_is_as_nat (as_seq h0 f1); CD.bn_v_is_as_nat (as_seq h0 f2); CD.bn_v_is_as_nat (as_seq h1 out)
{ "checked_file": "Hacl.Impl.Curve25519.Field64.Hacl.fst.checked", "dependencies": [ "prims.fst.checked", "Lib.Sequence.fsti.checked", "Lib.Loops.fsti.checked", "Lib.IntTypes.fsti.checked", "Lib.ByteSequence.fsti.checked", "Lib.Buffer.fsti.checked", "Hacl.Spec.Curve25519.Field64.Definition.fst.checked", "Hacl.Spec.Curve25519.Field64.Core.fst.checked", "Hacl.Spec.Bignum.Lib.fst.checked", "Hacl.Spec.Bignum.Definitions.fst.checked", "Hacl.Spec.Bignum.fsti.checked", "Hacl.Bignum.Definitions.fst.checked", "Hacl.Bignum.fsti.checked", "FStar.UInt32.fsti.checked", "FStar.Pervasives.fsti.checked", "FStar.Mul.fst.checked", "FStar.HyperStack.ST.fsti.checked", "FStar.HyperStack.All.fst.checked", "FStar.HyperStack.fst.checked" ], "interface_file": true, "source_file": "Hacl.Impl.Curve25519.Field64.Hacl.fst" }
[ "total" ]
[ "Hacl.Impl.Curve25519.Fields.Core.felem", "Hacl.Impl.Curve25519.Fields.Core.M64", "Hacl.Spec.Curve25519.Field64.Definition.bn_v_is_as_nat", "Lib.Buffer.as_seq", "Lib.Buffer.MUT", "Hacl.Impl.Curve25519.Fields.Core.limb", "Hacl.Impl.Curve25519.Fields.Core.nlimb", "Prims.unit", "Prims._assert", "Prims.eq2", "Lib.Sequence.lseq", "Lib.IntTypes.v", "Lib.IntTypes.U32", "Lib.IntTypes.PUB", "Hacl.Spec.Curve25519.Field64.Core.fadd4", "FStar.Monotonic.HyperStack.mem", "FStar.HyperStack.ST.get", "Lib.Buffer.op_Array_Assignment", "FStar.UInt32.__uint_to_t", "Lib.IntTypes.int_t", "Lib.IntTypes.U64", "Lib.IntTypes.SEC", "Lib.IntTypes.op_Plus_Dot", "Lib.IntTypes.op_Star_Dot", "Lib.IntTypes.u64", "Lib.Buffer.op_Array_Access", "Hacl.Spec.Bignum.Base.carry", "Hacl.Bignum.bn_add1", "Hacl.Bignum.bn_add_eq_len" ]
[]
module Hacl.Impl.Curve25519.Field64.Hacl open FStar.HyperStack open FStar.HyperStack.All open FStar.Mul open Lib.Sequence open Lib.IntTypes open Lib.Buffer module B = Lib.Buffer module ST = FStar.HyperStack.ST module BSeq = Lib.ByteSequence module LSeq = Lib.Sequence module CD = Hacl.Spec.Curve25519.Field64.Definition module CC = Hacl.Spec.Curve25519.Field64.Core module BN = Hacl.Bignum module BD = Hacl.Bignum.Definitions module SB = Hacl.Spec.Bignum module SD = Hacl.Spec.Bignum.Definitions #set-options "--z3rlimit 50 --fuel 0 --ifuel 0" [@CInline] let add1_ out f1 f2 = let h0 = ST.get () in let c = BN.bn_add1 4ul f1 f2 out in let h1 = ST.get () in assert (let c1, r1 = CC.add1 (as_seq h0 f1) f2 in c == c1 /\ as_seq h1 out == r1); CD.bn_v_is_as_nat (as_seq h0 f1); CD.bn_v_is_as_nat (as_seq h1 out); c
false
true
Hacl.Impl.Curve25519.Field64.Hacl.fst
{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 0, "initial_ifuel": 0, "max_fuel": 0, "max_ifuel": 0, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": false, "z3cliopt": [], "z3refresh": false, "z3rlimit": 50, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }
null
val fadd_: fadd_t M64 True
[]
Hacl.Impl.Curve25519.Field64.Hacl.fadd_
{ "file_name": "code/curve25519/Hacl.Impl.Curve25519.Field64.Hacl.fst", "git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e", "git_url": "https://github.com/hacl-star/hacl-star.git", "project_name": "hacl-star" }
Hacl.Impl.Curve25519.Fields.Core.fadd_t Hacl.Impl.Curve25519.Fields.Core.M64 Prims.l_True
{ "end_col": 35, "end_line": 48, "start_col": 21, "start_line": 39 }
Prims.Tot
val fmul_: fmul_t M64 True
[ { "abbrev": true, "full_module": "Hacl.Spec.Bignum.Definitions", "short_module": "SD" }, { "abbrev": true, "full_module": "Hacl.Spec.Bignum", "short_module": "SB" }, { "abbrev": true, "full_module": "Hacl.Bignum.Definitions", "short_module": "BD" }, { "abbrev": true, "full_module": "Hacl.Bignum", "short_module": "BN" }, { "abbrev": true, "full_module": "Hacl.Spec.Curve25519.Field64.Core", "short_module": "CC" }, { "abbrev": true, "full_module": "Hacl.Spec.Curve25519.Field64.Definition", "short_module": "CD" }, { "abbrev": true, "full_module": "Lib.Sequence", "short_module": "LSeq" }, { "abbrev": true, "full_module": "Lib.ByteSequence", "short_module": "BSeq" }, { "abbrev": true, "full_module": "FStar.HyperStack.ST", "short_module": "ST" }, { "abbrev": true, "full_module": "Lib.Buffer", "short_module": "B" }, { "abbrev": false, "full_module": "Lib.Buffer", "short_module": null }, { "abbrev": false, "full_module": "Lib.IntTypes", "short_module": null }, { "abbrev": false, "full_module": "Lib.Sequence", "short_module": null }, { "abbrev": false, "full_module": "FStar.Mul", "short_module": null }, { "abbrev": false, "full_module": "FStar.HyperStack.All", "short_module": null }, { "abbrev": false, "full_module": "FStar.HyperStack", "short_module": null }, { "abbrev": false, "full_module": "Hacl.Impl.Curve25519.Fields.Core", "short_module": null }, { "abbrev": false, "full_module": "Hacl.Impl.Curve25519.Field64", "short_module": null }, { "abbrev": false, "full_module": "Hacl.Impl.Curve25519.Field64", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]
false
let fmul_ out f1 f2 tmp = let h0 = ST.get () in let tmp0 = sub tmp 0ul 8ul in BN.bn_mul 4ul 4ul f1 f2 tmp0; let c0 = BN.bn_mul1_lshift_add_in_place 4ul (sub tmp0 4ul 4ul) (u64 38) 4ul 0ul (sub tmp0 0ul 4ul) in let c = BN.bn_add1 4ul (sub tmp0 0ul 4ul) (c0 *. u64 38) out in out.(0ul) <- out.(0ul) +. c *. u64 38; let h1 = ST.get () in assert (as_seq h1 out == CC.fmul4 (as_seq h0 f1) (as_seq h0 f2)); CD.bn_v_is_as_nat (as_seq h0 f1); CD.bn_v_is_as_nat (as_seq h0 f2); CD.bn_v_is_as_nat (as_seq h1 out)
val fmul_: fmul_t M64 True let fmul_ out f1 f2 tmp =
false
null
false
let h0 = ST.get () in let tmp0 = sub tmp 0ul 8ul in BN.bn_mul 4ul 4ul f1 f2 tmp0; let c0 = BN.bn_mul1_lshift_add_in_place 4ul (sub tmp0 4ul 4ul) (u64 38) 4ul 0ul (sub tmp0 0ul 4ul) in let c = BN.bn_add1 4ul (sub tmp0 0ul 4ul) (c0 *. u64 38) out in out.(0ul) <- out.(0ul) +. c *. u64 38; let h1 = ST.get () in assert (as_seq h1 out == CC.fmul4 (as_seq h0 f1) (as_seq h0 f2)); CD.bn_v_is_as_nat (as_seq h0 f1); CD.bn_v_is_as_nat (as_seq h0 f2); CD.bn_v_is_as_nat (as_seq h1 out)
{ "checked_file": "Hacl.Impl.Curve25519.Field64.Hacl.fst.checked", "dependencies": [ "prims.fst.checked", "Lib.Sequence.fsti.checked", "Lib.Loops.fsti.checked", "Lib.IntTypes.fsti.checked", "Lib.ByteSequence.fsti.checked", "Lib.Buffer.fsti.checked", "Hacl.Spec.Curve25519.Field64.Definition.fst.checked", "Hacl.Spec.Curve25519.Field64.Core.fst.checked", "Hacl.Spec.Bignum.Lib.fst.checked", "Hacl.Spec.Bignum.Definitions.fst.checked", "Hacl.Spec.Bignum.fsti.checked", "Hacl.Bignum.Definitions.fst.checked", "Hacl.Bignum.fsti.checked", "FStar.UInt32.fsti.checked", "FStar.Pervasives.fsti.checked", "FStar.Mul.fst.checked", "FStar.HyperStack.ST.fsti.checked", "FStar.HyperStack.All.fst.checked", "FStar.HyperStack.fst.checked" ], "interface_file": true, "source_file": "Hacl.Impl.Curve25519.Field64.Hacl.fst" }
[ "total" ]
[ "Hacl.Impl.Curve25519.Fields.Core.felem", "Hacl.Impl.Curve25519.Fields.Core.M64", "Hacl.Impl.Curve25519.Fields.Core.felem_wide2", "Hacl.Spec.Curve25519.Field64.Definition.bn_v_is_as_nat", "Lib.Buffer.as_seq", "Lib.Buffer.MUT", "Hacl.Impl.Curve25519.Fields.Core.limb", "Hacl.Impl.Curve25519.Fields.Core.nlimb", "Prims.unit", "Prims._assert", "Prims.eq2", "Lib.Sequence.lseq", "Lib.IntTypes.v", "Lib.IntTypes.U32", "Lib.IntTypes.PUB", "Hacl.Spec.Curve25519.Field64.Core.fmul4", "FStar.Monotonic.HyperStack.mem", "FStar.HyperStack.ST.get", "Lib.Buffer.op_Array_Assignment", "FStar.UInt32.__uint_to_t", "Lib.IntTypes.int_t", "Lib.IntTypes.U64", "Lib.IntTypes.SEC", "Lib.IntTypes.op_Plus_Dot", "Lib.IntTypes.op_Star_Dot", "Lib.IntTypes.u64", "Lib.Buffer.op_Array_Access", "Hacl.Spec.Bignum.Base.carry", "Hacl.Bignum.bn_add1", "Hacl.Bignum.Definitions.lbignum", "FStar.UInt32.uint_to_t", "FStar.UInt32.t", "Lib.Buffer.sub", "Hacl.Impl.Curve25519.Fields.Core.wide", "Lib.Buffer.lbuffer_t", "Hacl.Bignum.Definitions.limb", "Hacl.Bignum.bn_mul1_lshift_add_in_place", "Hacl.Bignum.bn_mul", "Hacl.Impl.Curve25519.Fields.Core.nwide" ]
[]
module Hacl.Impl.Curve25519.Field64.Hacl open FStar.HyperStack open FStar.HyperStack.All open FStar.Mul open Lib.Sequence open Lib.IntTypes open Lib.Buffer module B = Lib.Buffer module ST = FStar.HyperStack.ST module BSeq = Lib.ByteSequence module LSeq = Lib.Sequence module CD = Hacl.Spec.Curve25519.Field64.Definition module CC = Hacl.Spec.Curve25519.Field64.Core module BN = Hacl.Bignum module BD = Hacl.Bignum.Definitions module SB = Hacl.Spec.Bignum module SD = Hacl.Spec.Bignum.Definitions #set-options "--z3rlimit 50 --fuel 0 --ifuel 0" [@CInline] let add1_ out f1 f2 = let h0 = ST.get () in let c = BN.bn_add1 4ul f1 f2 out in let h1 = ST.get () in assert (let c1, r1 = CC.add1 (as_seq h0 f1) f2 in c == c1 /\ as_seq h1 out == r1); CD.bn_v_is_as_nat (as_seq h0 f1); CD.bn_v_is_as_nat (as_seq h1 out); c [@CInline] let fadd_ out f1 f2 = let h0 = ST.get () in let c0 = BN.bn_add_eq_len 4ul f1 f2 out in let c = BN.bn_add1 4ul out (c0 *. u64 38) out in out.(0ul) <- out.(0ul) +. c *. u64 38; let h1 = ST.get () in assert (as_seq h1 out == CC.fadd4 (as_seq h0 f1) (as_seq h0 f2)); CD.bn_v_is_as_nat (as_seq h0 f1); CD.bn_v_is_as_nat (as_seq h0 f2); CD.bn_v_is_as_nat (as_seq h1 out) [@CInline] let fsub_ out f1 f2 = let h0 = ST.get () in let c0 = BN.bn_sub_eq_len 4ul f1 f2 out in let c = BN.bn_sub1 4ul out (c0 *! u64 38) out in out.(0ul) <- out.(0ul) -. c *. u64 38; let h1 = ST.get () in assert (as_seq h1 out == CC.fsub4 (as_seq h0 f1) (as_seq h0 f2)); CD.bn_v_is_as_nat (as_seq h0 f1); CD.bn_v_is_as_nat (as_seq h0 f2); CD.bn_v_is_as_nat (as_seq h1 out)
false
true
Hacl.Impl.Curve25519.Field64.Hacl.fst
{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 0, "initial_ifuel": 0, "max_fuel": 0, "max_ifuel": 0, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": false, "z3cliopt": [], "z3refresh": false, "z3rlimit": 50, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }
null
val fmul_: fmul_t M64 True
[]
Hacl.Impl.Curve25519.Field64.Hacl.fmul_
{ "file_name": "code/curve25519/Hacl.Impl.Curve25519.Field64.Hacl.fst", "git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e", "git_url": "https://github.com/hacl-star/hacl-star.git", "project_name": "hacl-star" }
Hacl.Impl.Curve25519.Fields.Core.fmul_t Hacl.Impl.Curve25519.Fields.Core.M64 Prims.l_True
{ "end_col": 35, "end_line": 76, "start_col": 25, "start_line": 65 }
Prims.Tot
val fsub_: fsub_t M64 True
[ { "abbrev": true, "full_module": "Hacl.Spec.Bignum.Definitions", "short_module": "SD" }, { "abbrev": true, "full_module": "Hacl.Spec.Bignum", "short_module": "SB" }, { "abbrev": true, "full_module": "Hacl.Bignum.Definitions", "short_module": "BD" }, { "abbrev": true, "full_module": "Hacl.Bignum", "short_module": "BN" }, { "abbrev": true, "full_module": "Hacl.Spec.Curve25519.Field64.Core", "short_module": "CC" }, { "abbrev": true, "full_module": "Hacl.Spec.Curve25519.Field64.Definition", "short_module": "CD" }, { "abbrev": true, "full_module": "Lib.Sequence", "short_module": "LSeq" }, { "abbrev": true, "full_module": "Lib.ByteSequence", "short_module": "BSeq" }, { "abbrev": true, "full_module": "FStar.HyperStack.ST", "short_module": "ST" }, { "abbrev": true, "full_module": "Lib.Buffer", "short_module": "B" }, { "abbrev": false, "full_module": "Lib.Buffer", "short_module": null }, { "abbrev": false, "full_module": "Lib.IntTypes", "short_module": null }, { "abbrev": false, "full_module": "Lib.Sequence", "short_module": null }, { "abbrev": false, "full_module": "FStar.Mul", "short_module": null }, { "abbrev": false, "full_module": "FStar.HyperStack.All", "short_module": null }, { "abbrev": false, "full_module": "FStar.HyperStack", "short_module": null }, { "abbrev": false, "full_module": "Hacl.Impl.Curve25519.Fields.Core", "short_module": null }, { "abbrev": false, "full_module": "Hacl.Impl.Curve25519.Field64", "short_module": null }, { "abbrev": false, "full_module": "Hacl.Impl.Curve25519.Field64", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]
false
let fsub_ out f1 f2 = let h0 = ST.get () in let c0 = BN.bn_sub_eq_len 4ul f1 f2 out in let c = BN.bn_sub1 4ul out (c0 *! u64 38) out in out.(0ul) <- out.(0ul) -. c *. u64 38; let h1 = ST.get () in assert (as_seq h1 out == CC.fsub4 (as_seq h0 f1) (as_seq h0 f2)); CD.bn_v_is_as_nat (as_seq h0 f1); CD.bn_v_is_as_nat (as_seq h0 f2); CD.bn_v_is_as_nat (as_seq h1 out)
val fsub_: fsub_t M64 True let fsub_ out f1 f2 =
false
null
false
let h0 = ST.get () in let c0 = BN.bn_sub_eq_len 4ul f1 f2 out in let c = BN.bn_sub1 4ul out (c0 *! u64 38) out in out.(0ul) <- out.(0ul) -. c *. u64 38; let h1 = ST.get () in assert (as_seq h1 out == CC.fsub4 (as_seq h0 f1) (as_seq h0 f2)); CD.bn_v_is_as_nat (as_seq h0 f1); CD.bn_v_is_as_nat (as_seq h0 f2); CD.bn_v_is_as_nat (as_seq h1 out)
{ "checked_file": "Hacl.Impl.Curve25519.Field64.Hacl.fst.checked", "dependencies": [ "prims.fst.checked", "Lib.Sequence.fsti.checked", "Lib.Loops.fsti.checked", "Lib.IntTypes.fsti.checked", "Lib.ByteSequence.fsti.checked", "Lib.Buffer.fsti.checked", "Hacl.Spec.Curve25519.Field64.Definition.fst.checked", "Hacl.Spec.Curve25519.Field64.Core.fst.checked", "Hacl.Spec.Bignum.Lib.fst.checked", "Hacl.Spec.Bignum.Definitions.fst.checked", "Hacl.Spec.Bignum.fsti.checked", "Hacl.Bignum.Definitions.fst.checked", "Hacl.Bignum.fsti.checked", "FStar.UInt32.fsti.checked", "FStar.Pervasives.fsti.checked", "FStar.Mul.fst.checked", "FStar.HyperStack.ST.fsti.checked", "FStar.HyperStack.All.fst.checked", "FStar.HyperStack.fst.checked" ], "interface_file": true, "source_file": "Hacl.Impl.Curve25519.Field64.Hacl.fst" }
[ "total" ]
[ "Hacl.Impl.Curve25519.Fields.Core.felem", "Hacl.Impl.Curve25519.Fields.Core.M64", "Hacl.Spec.Curve25519.Field64.Definition.bn_v_is_as_nat", "Lib.Buffer.as_seq", "Lib.Buffer.MUT", "Hacl.Impl.Curve25519.Fields.Core.limb", "Hacl.Impl.Curve25519.Fields.Core.nlimb", "Prims.unit", "Prims._assert", "Prims.eq2", "Lib.Sequence.lseq", "Lib.IntTypes.v", "Lib.IntTypes.U32", "Lib.IntTypes.PUB", "Hacl.Spec.Curve25519.Field64.Core.fsub4", "FStar.Monotonic.HyperStack.mem", "FStar.HyperStack.ST.get", "Lib.Buffer.op_Array_Assignment", "FStar.UInt32.__uint_to_t", "Lib.IntTypes.int_t", "Lib.IntTypes.U64", "Lib.IntTypes.SEC", "Lib.IntTypes.op_Subtraction_Dot", "Lib.IntTypes.op_Star_Dot", "Lib.IntTypes.u64", "Lib.Buffer.op_Array_Access", "Hacl.Spec.Bignum.Base.carry", "Hacl.Bignum.bn_sub1", "Lib.IntTypes.op_Star_Bang", "Hacl.Bignum.bn_sub_eq_len" ]
[]
module Hacl.Impl.Curve25519.Field64.Hacl open FStar.HyperStack open FStar.HyperStack.All open FStar.Mul open Lib.Sequence open Lib.IntTypes open Lib.Buffer module B = Lib.Buffer module ST = FStar.HyperStack.ST module BSeq = Lib.ByteSequence module LSeq = Lib.Sequence module CD = Hacl.Spec.Curve25519.Field64.Definition module CC = Hacl.Spec.Curve25519.Field64.Core module BN = Hacl.Bignum module BD = Hacl.Bignum.Definitions module SB = Hacl.Spec.Bignum module SD = Hacl.Spec.Bignum.Definitions #set-options "--z3rlimit 50 --fuel 0 --ifuel 0" [@CInline] let add1_ out f1 f2 = let h0 = ST.get () in let c = BN.bn_add1 4ul f1 f2 out in let h1 = ST.get () in assert (let c1, r1 = CC.add1 (as_seq h0 f1) f2 in c == c1 /\ as_seq h1 out == r1); CD.bn_v_is_as_nat (as_seq h0 f1); CD.bn_v_is_as_nat (as_seq h1 out); c [@CInline] let fadd_ out f1 f2 = let h0 = ST.get () in let c0 = BN.bn_add_eq_len 4ul f1 f2 out in let c = BN.bn_add1 4ul out (c0 *. u64 38) out in out.(0ul) <- out.(0ul) +. c *. u64 38; let h1 = ST.get () in assert (as_seq h1 out == CC.fadd4 (as_seq h0 f1) (as_seq h0 f2)); CD.bn_v_is_as_nat (as_seq h0 f1); CD.bn_v_is_as_nat (as_seq h0 f2); CD.bn_v_is_as_nat (as_seq h1 out)
false
true
Hacl.Impl.Curve25519.Field64.Hacl.fst
{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 0, "initial_ifuel": 0, "max_fuel": 0, "max_ifuel": 0, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": false, "z3cliopt": [], "z3refresh": false, "z3rlimit": 50, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }
null
val fsub_: fsub_t M64 True
[]
Hacl.Impl.Curve25519.Field64.Hacl.fsub_
{ "file_name": "code/curve25519/Hacl.Impl.Curve25519.Field64.Hacl.fst", "git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e", "git_url": "https://github.com/hacl-star/hacl-star.git", "project_name": "hacl-star" }
Hacl.Impl.Curve25519.Fields.Core.fsub_t Hacl.Impl.Curve25519.Fields.Core.M64 Prims.l_True
{ "end_col": 35, "end_line": 61, "start_col": 21, "start_line": 52 }
Prims.Tot
val fmul2_: fmul2_t M64 True
[ { "abbrev": true, "full_module": "Hacl.Spec.Bignum.Definitions", "short_module": "SD" }, { "abbrev": true, "full_module": "Hacl.Spec.Bignum", "short_module": "SB" }, { "abbrev": true, "full_module": "Hacl.Bignum.Definitions", "short_module": "BD" }, { "abbrev": true, "full_module": "Hacl.Bignum", "short_module": "BN" }, { "abbrev": true, "full_module": "Hacl.Spec.Curve25519.Field64.Core", "short_module": "CC" }, { "abbrev": true, "full_module": "Hacl.Spec.Curve25519.Field64.Definition", "short_module": "CD" }, { "abbrev": true, "full_module": "Lib.Sequence", "short_module": "LSeq" }, { "abbrev": true, "full_module": "Lib.ByteSequence", "short_module": "BSeq" }, { "abbrev": true, "full_module": "FStar.HyperStack.ST", "short_module": "ST" }, { "abbrev": true, "full_module": "Lib.Buffer", "short_module": "B" }, { "abbrev": false, "full_module": "Lib.Buffer", "short_module": null }, { "abbrev": false, "full_module": "Lib.IntTypes", "short_module": null }, { "abbrev": false, "full_module": "Lib.Sequence", "short_module": null }, { "abbrev": false, "full_module": "FStar.Mul", "short_module": null }, { "abbrev": false, "full_module": "FStar.HyperStack.All", "short_module": null }, { "abbrev": false, "full_module": "FStar.HyperStack", "short_module": null }, { "abbrev": false, "full_module": "Hacl.Impl.Curve25519.Fields.Core", "short_module": null }, { "abbrev": false, "full_module": "Hacl.Impl.Curve25519.Field64", "short_module": null }, { "abbrev": false, "full_module": "Hacl.Impl.Curve25519.Field64", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]
false
let fmul2_ out f1 f2 tmp = let out1 = B.sub out 0ul 4ul in let out2 = B.sub out 4ul 4ul in let f11 = B.sub f1 0ul 4ul in let f12 = B.sub f1 4ul 4ul in let f21 = B.sub f2 0ul 4ul in let f22 = B.sub f2 4ul 4ul in fmul_ out1 f11 f21 tmp; fmul_ out2 f12 f22 tmp
val fmul2_: fmul2_t M64 True let fmul2_ out f1 f2 tmp =
false
null
false
let out1 = B.sub out 0ul 4ul in let out2 = B.sub out 4ul 4ul in let f11 = B.sub f1 0ul 4ul in let f12 = B.sub f1 4ul 4ul in let f21 = B.sub f2 0ul 4ul in let f22 = B.sub f2 4ul 4ul in fmul_ out1 f11 f21 tmp; fmul_ out2 f12 f22 tmp
{ "checked_file": "Hacl.Impl.Curve25519.Field64.Hacl.fst.checked", "dependencies": [ "prims.fst.checked", "Lib.Sequence.fsti.checked", "Lib.Loops.fsti.checked", "Lib.IntTypes.fsti.checked", "Lib.ByteSequence.fsti.checked", "Lib.Buffer.fsti.checked", "Hacl.Spec.Curve25519.Field64.Definition.fst.checked", "Hacl.Spec.Curve25519.Field64.Core.fst.checked", "Hacl.Spec.Bignum.Lib.fst.checked", "Hacl.Spec.Bignum.Definitions.fst.checked", "Hacl.Spec.Bignum.fsti.checked", "Hacl.Bignum.Definitions.fst.checked", "Hacl.Bignum.fsti.checked", "FStar.UInt32.fsti.checked", "FStar.Pervasives.fsti.checked", "FStar.Mul.fst.checked", "FStar.HyperStack.ST.fsti.checked", "FStar.HyperStack.All.fst.checked", "FStar.HyperStack.fst.checked" ], "interface_file": true, "source_file": "Hacl.Impl.Curve25519.Field64.Hacl.fst" }
[ "total" ]
[ "Hacl.Impl.Curve25519.Fields.Core.felem2", "Hacl.Impl.Curve25519.Fields.Core.M64", "Hacl.Impl.Curve25519.Fields.Core.felem_wide2", "Hacl.Impl.Curve25519.Field64.Hacl.fmul_", "Prims.unit", "Lib.Buffer.lbuffer_t", "Lib.Buffer.MUT", "Lib.IntTypes.int_t", "Lib.IntTypes.U64", "Lib.IntTypes.SEC", "FStar.UInt32.uint_to_t", "FStar.UInt32.t", "Lib.Buffer.sub", "Hacl.Impl.Curve25519.Fields.Core.limb", "Lib.IntTypes.op_Plus_Dot", "Lib.IntTypes.U32", "Lib.IntTypes.PUB", "Hacl.Impl.Curve25519.Fields.Core.nlimb", "FStar.UInt32.__uint_to_t" ]
[]
module Hacl.Impl.Curve25519.Field64.Hacl open FStar.HyperStack open FStar.HyperStack.All open FStar.Mul open Lib.Sequence open Lib.IntTypes open Lib.Buffer module B = Lib.Buffer module ST = FStar.HyperStack.ST module BSeq = Lib.ByteSequence module LSeq = Lib.Sequence module CD = Hacl.Spec.Curve25519.Field64.Definition module CC = Hacl.Spec.Curve25519.Field64.Core module BN = Hacl.Bignum module BD = Hacl.Bignum.Definitions module SB = Hacl.Spec.Bignum module SD = Hacl.Spec.Bignum.Definitions #set-options "--z3rlimit 50 --fuel 0 --ifuel 0" [@CInline] let add1_ out f1 f2 = let h0 = ST.get () in let c = BN.bn_add1 4ul f1 f2 out in let h1 = ST.get () in assert (let c1, r1 = CC.add1 (as_seq h0 f1) f2 in c == c1 /\ as_seq h1 out == r1); CD.bn_v_is_as_nat (as_seq h0 f1); CD.bn_v_is_as_nat (as_seq h1 out); c [@CInline] let fadd_ out f1 f2 = let h0 = ST.get () in let c0 = BN.bn_add_eq_len 4ul f1 f2 out in let c = BN.bn_add1 4ul out (c0 *. u64 38) out in out.(0ul) <- out.(0ul) +. c *. u64 38; let h1 = ST.get () in assert (as_seq h1 out == CC.fadd4 (as_seq h0 f1) (as_seq h0 f2)); CD.bn_v_is_as_nat (as_seq h0 f1); CD.bn_v_is_as_nat (as_seq h0 f2); CD.bn_v_is_as_nat (as_seq h1 out) [@CInline] let fsub_ out f1 f2 = let h0 = ST.get () in let c0 = BN.bn_sub_eq_len 4ul f1 f2 out in let c = BN.bn_sub1 4ul out (c0 *! u64 38) out in out.(0ul) <- out.(0ul) -. c *. u64 38; let h1 = ST.get () in assert (as_seq h1 out == CC.fsub4 (as_seq h0 f1) (as_seq h0 f2)); CD.bn_v_is_as_nat (as_seq h0 f1); CD.bn_v_is_as_nat (as_seq h0 f2); CD.bn_v_is_as_nat (as_seq h1 out) [@CInline] let fmul_ out f1 f2 tmp = let h0 = ST.get () in let tmp0 = sub tmp 0ul 8ul in BN.bn_mul 4ul 4ul f1 f2 tmp0; let c0 = BN.bn_mul1_lshift_add_in_place 4ul (sub tmp0 4ul 4ul) (u64 38) 4ul 0ul (sub tmp0 0ul 4ul) in let c = BN.bn_add1 4ul (sub tmp0 0ul 4ul) (c0 *. u64 38) out in out.(0ul) <- out.(0ul) +. c *. u64 38; let h1 = ST.get () in assert (as_seq h1 out == CC.fmul4 (as_seq h0 f1) (as_seq h0 f2)); CD.bn_v_is_as_nat (as_seq h0 f1); CD.bn_v_is_as_nat (as_seq h0 f2); CD.bn_v_is_as_nat (as_seq h1 out)
false
true
Hacl.Impl.Curve25519.Field64.Hacl.fst
{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 0, "initial_ifuel": 0, "max_fuel": 0, "max_ifuel": 0, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": false, "z3cliopt": [], "z3refresh": false, "z3rlimit": 50, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }
null
val fmul2_: fmul2_t M64 True
[]
Hacl.Impl.Curve25519.Field64.Hacl.fmul2_
{ "file_name": "code/curve25519/Hacl.Impl.Curve25519.Field64.Hacl.fst", "git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e", "git_url": "https://github.com/hacl-star/hacl-star.git", "project_name": "hacl-star" }
Hacl.Impl.Curve25519.Fields.Core.fmul2_t Hacl.Impl.Curve25519.Fields.Core.M64 Prims.l_True
{ "end_col": 24, "end_line": 88, "start_col": 26, "start_line": 80 }
Prims.Tot
val cswap2_: cswap2_t M64 True
[ { "abbrev": true, "full_module": "Hacl.Spec.Bignum.Definitions", "short_module": "SD" }, { "abbrev": true, "full_module": "Hacl.Spec.Bignum", "short_module": "SB" }, { "abbrev": true, "full_module": "Hacl.Bignum.Definitions", "short_module": "BD" }, { "abbrev": true, "full_module": "Hacl.Bignum", "short_module": "BN" }, { "abbrev": true, "full_module": "Hacl.Spec.Curve25519.Field64.Core", "short_module": "CC" }, { "abbrev": true, "full_module": "Hacl.Spec.Curve25519.Field64.Definition", "short_module": "CD" }, { "abbrev": true, "full_module": "Lib.Sequence", "short_module": "LSeq" }, { "abbrev": true, "full_module": "Lib.ByteSequence", "short_module": "BSeq" }, { "abbrev": true, "full_module": "FStar.HyperStack.ST", "short_module": "ST" }, { "abbrev": true, "full_module": "Lib.Buffer", "short_module": "B" }, { "abbrev": false, "full_module": "Lib.Buffer", "short_module": null }, { "abbrev": false, "full_module": "Lib.IntTypes", "short_module": null }, { "abbrev": false, "full_module": "Lib.Sequence", "short_module": null }, { "abbrev": false, "full_module": "FStar.Mul", "short_module": null }, { "abbrev": false, "full_module": "FStar.HyperStack.All", "short_module": null }, { "abbrev": false, "full_module": "FStar.HyperStack", "short_module": null }, { "abbrev": false, "full_module": "Hacl.Impl.Curve25519.Fields.Core", "short_module": null }, { "abbrev": false, "full_module": "Hacl.Impl.Curve25519.Field64", "short_module": null }, { "abbrev": false, "full_module": "Hacl.Impl.Curve25519.Field64", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]
false
let cswap2_ bit p1 p2 = let h0 = ST.get () in let mask = u64 0 -. bit in [@ inline_let] let inv h1 (i:nat{i <= 8}) = (forall (k:nat{k < i}). if v bit = 1 then (as_seq h1 p1).[k] == (as_seq h0 p2).[k] /\ (as_seq h1 p2).[k] == (as_seq h0 p1).[k] else (as_seq h1 p1).[k] == (as_seq h0 p1).[k] /\ (as_seq h1 p2).[k] == (as_seq h0 p2).[k]) /\ (forall (k:nat{i <= k /\ k < 8}). (as_seq h1 p1).[k] == (as_seq h0 p1).[k] /\ (as_seq h1 p2).[k] == (as_seq h0 p2).[k]) /\ modifies (loc p1 |+| loc p2) h0 h1 in Lib.Loops.for 0ul 8ul inv (fun i -> let dummy = mask &. (p1.(i) ^. p2.(i)) in p1.(i) <- p1.(i) ^. dummy; p2.(i) <- p2.(i) ^. dummy; Hacl.Spec.Bignum.Lib.lemma_cswap2_step bit ((as_seq h0 p1).[v i]) ((as_seq h0 p2).[v i]) ); let h1 = ST.get () in assert (if v bit = 1 then (eq_intro (as_seq h1 p1) (as_seq h0 p2); as_seq h1 p1 == as_seq h0 p2) else (eq_intro (as_seq h1 p1) (as_seq h0 p1); as_seq h1 p1 == as_seq h0 p1)); assert (if v bit = 1 then (eq_intro (as_seq h1 p2) (as_seq h0 p1); as_seq h1 p2 == as_seq h0 p1) else (eq_intro (as_seq h1 p2) (as_seq h0 p2); as_seq h1 p2 == as_seq h0 p2))
val cswap2_: cswap2_t M64 True let cswap2_ bit p1 p2 =
false
null
false
let h0 = ST.get () in let mask = u64 0 -. bit in [@@ inline_let ]let inv h1 (i: nat{i <= 8}) = (forall (k: nat{k < i}). if v bit = 1 then (as_seq h1 p1).[ k ] == (as_seq h0 p2).[ k ] /\ (as_seq h1 p2).[ k ] == (as_seq h0 p1).[ k ] else (as_seq h1 p1).[ k ] == (as_seq h0 p1).[ k ] /\ (as_seq h1 p2).[ k ] == (as_seq h0 p2).[ k ] ) /\ (forall (k: nat{i <= k /\ k < 8}). (as_seq h1 p1).[ k ] == (as_seq h0 p1).[ k ] /\ (as_seq h1 p2).[ k ] == (as_seq h0 p2).[ k ]) /\ modifies (loc p1 |+| loc p2) h0 h1 in Lib.Loops.for 0ul 8ul inv (fun i -> let dummy = mask &. (p1.(i) ^. p2.(i)) in p1.(i) <- p1.(i) ^. dummy; p2.(i) <- p2.(i) ^. dummy; Hacl.Spec.Bignum.Lib.lemma_cswap2_step bit ((as_seq h0 p1).[ v i ]) ((as_seq h0 p2).[ v i ])); let h1 = ST.get () in assert (if v bit = 1 then (eq_intro (as_seq h1 p1) (as_seq h0 p2); as_seq h1 p1 == as_seq h0 p2) else (eq_intro (as_seq h1 p1) (as_seq h0 p1); as_seq h1 p1 == as_seq h0 p1)); assert (if v bit = 1 then (eq_intro (as_seq h1 p2) (as_seq h0 p1); as_seq h1 p2 == as_seq h0 p1) else (eq_intro (as_seq h1 p2) (as_seq h0 p2); as_seq h1 p2 == as_seq h0 p2))
{ "checked_file": "Hacl.Impl.Curve25519.Field64.Hacl.fst.checked", "dependencies": [ "prims.fst.checked", "Lib.Sequence.fsti.checked", "Lib.Loops.fsti.checked", "Lib.IntTypes.fsti.checked", "Lib.ByteSequence.fsti.checked", "Lib.Buffer.fsti.checked", "Hacl.Spec.Curve25519.Field64.Definition.fst.checked", "Hacl.Spec.Curve25519.Field64.Core.fst.checked", "Hacl.Spec.Bignum.Lib.fst.checked", "Hacl.Spec.Bignum.Definitions.fst.checked", "Hacl.Spec.Bignum.fsti.checked", "Hacl.Bignum.Definitions.fst.checked", "Hacl.Bignum.fsti.checked", "FStar.UInt32.fsti.checked", "FStar.Pervasives.fsti.checked", "FStar.Mul.fst.checked", "FStar.HyperStack.ST.fsti.checked", "FStar.HyperStack.All.fst.checked", "FStar.HyperStack.fst.checked" ], "interface_file": true, "source_file": "Hacl.Impl.Curve25519.Field64.Hacl.fst" }
[ "total" ]
[ "Lib.IntTypes.uint64", "Prims.b2t", "Prims.op_LessThanOrEqual", "Lib.IntTypes.v", "Lib.IntTypes.U64", "Lib.IntTypes.SEC", "Hacl.Impl.Curve25519.Fields.Core.felem2", "Hacl.Impl.Curve25519.Fields.Core.M64", "Prims._assert", "Prims.op_Equality", "Prims.int", "Prims.eq2", "Lib.Sequence.lseq", "Hacl.Impl.Curve25519.Fields.Core.limb", "Lib.IntTypes.U32", "Lib.IntTypes.PUB", "Lib.IntTypes.op_Plus_Dot", "Hacl.Impl.Curve25519.Fields.Core.nlimb", "Lib.Buffer.as_seq", "Lib.Buffer.MUT", "Prims.unit", "Lib.Sequence.eq_intro", "Prims.bool", "FStar.Monotonic.HyperStack.mem", "FStar.HyperStack.ST.get", "Lib.Loops.for", "FStar.UInt32.__uint_to_t", "Lib.IntTypes.size_t", "Prims.l_and", "Prims.op_LessThan", "Hacl.Spec.Bignum.Lib.lemma_cswap2_step", "Lib.Sequence.op_String_Access", "Lib.Buffer.op_Array_Assignment", "Lib.IntTypes.int_t", "Lib.IntTypes.op_Hat_Dot", "Lib.Buffer.op_Array_Access", "Lib.IntTypes.op_Amp_Dot", "Prims.nat", "Prims.logical", "Prims.l_Forall", "Prims.l_or", "FStar.Seq.Base.index", "Lib.Sequence.to_seq", "Lib.Buffer.modifies", "Lib.Buffer.op_Bar_Plus_Bar", "Lib.Buffer.loc", "Lib.IntTypes.op_Subtraction_Dot", "Lib.IntTypes.u64" ]
[]
module Hacl.Impl.Curve25519.Field64.Hacl open FStar.HyperStack open FStar.HyperStack.All open FStar.Mul open Lib.Sequence open Lib.IntTypes open Lib.Buffer module B = Lib.Buffer module ST = FStar.HyperStack.ST module BSeq = Lib.ByteSequence module LSeq = Lib.Sequence module CD = Hacl.Spec.Curve25519.Field64.Definition module CC = Hacl.Spec.Curve25519.Field64.Core module BN = Hacl.Bignum module BD = Hacl.Bignum.Definitions module SB = Hacl.Spec.Bignum module SD = Hacl.Spec.Bignum.Definitions #set-options "--z3rlimit 50 --fuel 0 --ifuel 0" [@CInline] let add1_ out f1 f2 = let h0 = ST.get () in let c = BN.bn_add1 4ul f1 f2 out in let h1 = ST.get () in assert (let c1, r1 = CC.add1 (as_seq h0 f1) f2 in c == c1 /\ as_seq h1 out == r1); CD.bn_v_is_as_nat (as_seq h0 f1); CD.bn_v_is_as_nat (as_seq h1 out); c [@CInline] let fadd_ out f1 f2 = let h0 = ST.get () in let c0 = BN.bn_add_eq_len 4ul f1 f2 out in let c = BN.bn_add1 4ul out (c0 *. u64 38) out in out.(0ul) <- out.(0ul) +. c *. u64 38; let h1 = ST.get () in assert (as_seq h1 out == CC.fadd4 (as_seq h0 f1) (as_seq h0 f2)); CD.bn_v_is_as_nat (as_seq h0 f1); CD.bn_v_is_as_nat (as_seq h0 f2); CD.bn_v_is_as_nat (as_seq h1 out) [@CInline] let fsub_ out f1 f2 = let h0 = ST.get () in let c0 = BN.bn_sub_eq_len 4ul f1 f2 out in let c = BN.bn_sub1 4ul out (c0 *! u64 38) out in out.(0ul) <- out.(0ul) -. c *. u64 38; let h1 = ST.get () in assert (as_seq h1 out == CC.fsub4 (as_seq h0 f1) (as_seq h0 f2)); CD.bn_v_is_as_nat (as_seq h0 f1); CD.bn_v_is_as_nat (as_seq h0 f2); CD.bn_v_is_as_nat (as_seq h1 out) [@CInline] let fmul_ out f1 f2 tmp = let h0 = ST.get () in let tmp0 = sub tmp 0ul 8ul in BN.bn_mul 4ul 4ul f1 f2 tmp0; let c0 = BN.bn_mul1_lshift_add_in_place 4ul (sub tmp0 4ul 4ul) (u64 38) 4ul 0ul (sub tmp0 0ul 4ul) in let c = BN.bn_add1 4ul (sub tmp0 0ul 4ul) (c0 *. u64 38) out in out.(0ul) <- out.(0ul) +. c *. u64 38; let h1 = ST.get () in assert (as_seq h1 out == CC.fmul4 (as_seq h0 f1) (as_seq h0 f2)); CD.bn_v_is_as_nat (as_seq h0 f1); CD.bn_v_is_as_nat (as_seq h0 f2); CD.bn_v_is_as_nat (as_seq h1 out) [@CInline] let fmul2_ out f1 f2 tmp = let out1 = B.sub out 0ul 4ul in let out2 = B.sub out 4ul 4ul in let f11 = B.sub f1 0ul 4ul in let f12 = B.sub f1 4ul 4ul in let f21 = B.sub f2 0ul 4ul in let f22 = B.sub f2 4ul 4ul in fmul_ out1 f11 f21 tmp; fmul_ out2 f12 f22 tmp [@CInline] let fmul1_ out f1 f2 = let h0 = ST.get () in let c0 = BN.bn_mul1 4ul f1 f2 out in let c = BN.bn_add1 4ul out (c0 *. u64 38) out in out.(0ul) <- out.(0ul) +. c *. u64 38; let h1 = ST.get () in assert (as_seq h1 out == CC.fmul14 (as_seq h0 f1) f2); CD.bn_v_is_as_nat (as_seq h0 f1); CD.bn_v_is_as_nat (as_seq h1 out) [@CInline] let fsqr_ out f1 tmp = let h0 = ST.get () in BN.bn_sqr 4ul f1 tmp; SB.bn_sqr_lemma (as_seq h0 f1); let c0 = BN.bn_mul1_lshift_add_in_place 4ul (sub tmp 4ul 4ul) (u64 38) 4ul 0ul (sub tmp 0ul 4ul) in let c = BN.bn_add1 4ul (sub tmp 0ul 4ul) (c0 *. u64 38) out in out.(0ul) <- out.(0ul) +. c *. u64 38; let h1 = ST.get () in assert (as_seq h1 out == CC.fsqr4 (as_seq h0 f1)); CD.bn_v_is_as_nat (as_seq h0 f1); CD.bn_v_is_as_nat (as_seq h1 out) [@CInline] let fsqr2_ out f tmp = let out1 = B.sub out 0ul 4ul in let out2 = B.sub out 4ul 4ul in let f1 = B.sub f 0ul 4ul in let f2 = B.sub f 4ul 4ul in fmul_ out1 f1 f1 tmp; fmul_ out2 f2 f2 tmp
false
true
Hacl.Impl.Curve25519.Field64.Hacl.fst
{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 0, "initial_ifuel": 0, "max_fuel": 0, "max_ifuel": 0, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": false, "z3cliopt": [], "z3refresh": false, "z3rlimit": 50, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }
null
val cswap2_: cswap2_t M64 True
[]
Hacl.Impl.Curve25519.Field64.Hacl.cswap2_
{ "file_name": "code/curve25519/Hacl.Impl.Curve25519.Field64.Hacl.fst", "git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e", "git_url": "https://github.com/hacl-star/hacl-star.git", "project_name": "hacl-star" }
Hacl.Impl.Curve25519.Fields.Core.cswap2_t Hacl.Impl.Curve25519.Fields.Core.M64 Prims.l_True
{ "end_col": 80, "end_line": 153, "start_col": 23, "start_line": 128 }
Prims.Tot
val tl: l:list 'a {Cons? l} -> Tot (list 'a)
[ { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]
false
let tl = tail
val tl: l:list 'a {Cons? l} -> Tot (list 'a) let tl =
false
null
false
tail
{ "checked_file": "FStar.List.Tot.Base.fst.checked", "dependencies": [ "prims.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Classical.fsti.checked" ], "interface_file": false, "source_file": "FStar.List.Tot.Base.fst" }
[ "total" ]
[ "FStar.List.Tot.Base.tail" ]
[]
(* Copyright 2008-2014 Nikhil Swamy and Microsoft Research Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License. *) (** This module defines all pure and total operations on lists that can be used in specifications. It is implemented by FStar_List_Tot_Base.ml, any functional change and/or the addition of new functions MUST be reflected there. @summary Pure total operations on lists *) module FStar.List.Tot.Base (** Base operations *) (** [isEmpty l] returns [true] if and only if [l] is empty *) val isEmpty: list 'a -> Tot bool let isEmpty l = match l with | [] -> true | _ -> false (** [hd l] returns the first element of [l]. Requires [l] to be nonempty, at type-checking time. Named as in: OCaml, F#, Coq *) val hd: l:list 'a{Cons? l} -> Tot 'a let hd = function | hd::_ -> hd (** [tail l] returns [l] without its first element. Requires, at type-checking time, that [l] be nonempty. Similar to: tl in OCaml, F#, Coq *) val tail: l:list 'a {Cons? l} -> Tot (list 'a) let tail = function | _::tl -> tl (** [tl l] returns [l] without its first element. Requires, at type-checking time, that [l] be nonempty. Named as in: OCaml, F#, Coq *)
false
false
FStar.List.Tot.Base.fst
{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 1, "max_fuel": 8, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": true, "z3cliopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }
null
val tl: l:list 'a {Cons? l} -> Tot (list 'a)
[]
FStar.List.Tot.Base.tl
{ "file_name": "ulib/FStar.List.Tot.Base.fst", "git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f", "git_url": "https://github.com/FStarLang/FStar.git", "project_name": "FStar" }
l: Prims.list 'a {Cons? l} -> Prims.list 'a
{ "end_col": 13, "end_line": 53, "start_col": 9, "start_line": 53 }
Prims.Tot
val isEmpty: list 'a -> Tot bool
[ { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]
false
let isEmpty l = match l with | [] -> true | _ -> false
val isEmpty: list 'a -> Tot bool let isEmpty l =
false
null
false
match l with | [] -> true | _ -> false
{ "checked_file": "FStar.List.Tot.Base.fst.checked", "dependencies": [ "prims.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Classical.fsti.checked" ], "interface_file": false, "source_file": "FStar.List.Tot.Base.fst" }
[ "total" ]
[ "Prims.list", "Prims.bool" ]
[]
(* Copyright 2008-2014 Nikhil Swamy and Microsoft Research Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License. *) (** This module defines all pure and total operations on lists that can be used in specifications. It is implemented by FStar_List_Tot_Base.ml, any functional change and/or the addition of new functions MUST be reflected there. @summary Pure total operations on lists *) module FStar.List.Tot.Base (** Base operations *) (** [isEmpty l] returns [true] if and only if [l] is empty *)
false
false
FStar.List.Tot.Base.fst
{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 1, "max_fuel": 8, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": true, "z3cliopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }
null
val isEmpty: list 'a -> Tot bool
[]
FStar.List.Tot.Base.isEmpty
{ "file_name": "ulib/FStar.List.Tot.Base.fst", "git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f", "git_url": "https://github.com/FStarLang/FStar.git", "project_name": "FStar" }
l: Prims.list 'a -> Prims.bool
{ "end_col": 14, "end_line": 34, "start_col": 16, "start_line": 32 }
Prims.Tot
[ { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]
false
let op_At x y = append x y
let op_At x y =
false
null
false
append x y
{ "checked_file": "FStar.List.Tot.Base.fst.checked", "dependencies": [ "prims.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Classical.fsti.checked" ], "interface_file": false, "source_file": "FStar.List.Tot.Base.fst" }
[ "total" ]
[ "Prims.list", "FStar.List.Tot.Base.append" ]
[]
(* Copyright 2008-2014 Nikhil Swamy and Microsoft Research Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License. *) (** This module defines all pure and total operations on lists that can be used in specifications. It is implemented by FStar_List_Tot_Base.ml, any functional change and/or the addition of new functions MUST be reflected there. @summary Pure total operations on lists *) module FStar.List.Tot.Base (** Base operations *) (** [isEmpty l] returns [true] if and only if [l] is empty *) val isEmpty: list 'a -> Tot bool let isEmpty l = match l with | [] -> true | _ -> false (** [hd l] returns the first element of [l]. Requires [l] to be nonempty, at type-checking time. Named as in: OCaml, F#, Coq *) val hd: l:list 'a{Cons? l} -> Tot 'a let hd = function | hd::_ -> hd (** [tail l] returns [l] without its first element. Requires, at type-checking time, that [l] be nonempty. Similar to: tl in OCaml, F#, Coq *) val tail: l:list 'a {Cons? l} -> Tot (list 'a) let tail = function | _::tl -> tl (** [tl l] returns [l] without its first element. Requires, at type-checking time, that [l] be nonempty. Named as in: OCaml, F#, Coq *) val tl: l:list 'a {Cons? l} -> Tot (list 'a) let tl = tail (** [last l] returns the last element of [l]. Requires, at type-checking time, that [l] be nonempty. Named as in: Haskell *) val last: l:list 'a {Cons? l} -> Tot 'a let rec last = function | [hd] -> hd | _::tl -> last tl (** [init l] returns [l] without its last element. Requires, at type-checking time, that [l] be nonempty. Named as in: Haskell *) val init: l:list 'a {Cons? l} -> Tot (list 'a) let rec init = function | [_] -> [] | hd::tl -> hd::(init tl) (** [length l] returns the total number of elements in [l]. Named as in: OCaml, F#, Coq *) val length: list 'a -> Tot nat let rec length = function | [] -> 0 | _::tl -> 1 + length tl (** [nth l n] returns the [n]-th element in list [l] (with the first element being the 0-th) if [l] is long enough, or [None] otherwise. Named as in: OCaml, F#, Coq *) val nth: list 'a -> nat -> Tot (option 'a) let rec nth l n = match l with | [] -> None | hd::tl -> if n = 0 then Some hd else nth tl (n - 1) (** [index l n] returns the [n]-th element in list [l] (with the first element being the 0-th). Requires, at type-checking time, that [l] be of length at least [n+1]. *) val index: #a:Type -> l:list a -> i:nat{i < length l} -> Tot a let rec index #a (l: list a) (i:nat{i < length l}): Tot a = if i = 0 then hd l else index (tl l) (i - 1) (** [count x l] returns the number of occurrences of [x] in [l]. Requires, at type-checking time, the type of [a] to have equality defined. Similar to: [List.count_occ] in Coq. *) val count: #a:eqtype -> a -> list a -> Tot nat let rec count #a x = function | [] -> 0 | hd::tl -> if x=hd then 1 + count x tl else count x tl (** [rev_acc l1 l2] appends the elements of [l1] to the beginning of [l2], in reverse order. It is equivalent to [append (rev l1) l2], but is tail-recursive. Similar to: [List.rev_append] in OCaml, Coq. *) val rev_acc: list 'a -> list 'a -> Tot (list 'a) let rec rev_acc l acc = match l with | [] -> acc | hd::tl -> rev_acc tl (hd::acc) (** [rev l] returns the list [l] in reverse order. Named as in: OCaml, F#, Coq. *) val rev: list 'a -> Tot (list 'a) let rev l = rev_acc l [] (** [append l1 l2] appends the elements of [l2] to the end of [l1]. Named as: OCaml, F#. Similar to: [List.app] in Coq. *) val append: list 'a -> list 'a -> Tot (list 'a) let rec append x y = match x with | [] -> y | a::tl -> a::append tl y
false
false
FStar.List.Tot.Base.fst
{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 1, "max_fuel": 8, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": true, "z3cliopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }
null
val op_At : x: Prims.list _ -> y: Prims.list _ -> Prims.list _
[]
FStar.List.Tot.Base.op_At
{ "file_name": "ulib/FStar.List.Tot.Base.fst", "git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f", "git_url": "https://github.com/FStarLang/FStar.git", "project_name": "FStar" }
x: Prims.list _ -> y: Prims.list _ -> Prims.list _
{ "end_col": 26, "end_line": 124, "start_col": 16, "start_line": 124 }
Prims.GTot
val map_gtot (#a #b: _) (f: (a -> GTot b)) (x: list a) : GTot (list b)
[ { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]
false
let map_gtot #a #b (f:a -> GTot b) (x:list a) : GTot (list b) = fold_right_gtot x (fun x tl -> f x :: tl) []
val map_gtot (#a #b: _) (f: (a -> GTot b)) (x: list a) : GTot (list b) let map_gtot #a #b (f: (a -> GTot b)) (x: list a) : GTot (list b) =
false
null
false
fold_right_gtot x (fun x tl -> f x :: tl) []
{ "checked_file": "FStar.List.Tot.Base.fst.checked", "dependencies": [ "prims.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Classical.fsti.checked" ], "interface_file": false, "source_file": "FStar.List.Tot.Base.fst" }
[ "sometrivial" ]
[ "Prims.list", "FStar.List.Tot.Base.fold_right_gtot", "Prims.Cons", "Prims.Nil" ]
[]
(* Copyright 2008-2014 Nikhil Swamy and Microsoft Research Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License. *) (** This module defines all pure and total operations on lists that can be used in specifications. It is implemented by FStar_List_Tot_Base.ml, any functional change and/or the addition of new functions MUST be reflected there. @summary Pure total operations on lists *) module FStar.List.Tot.Base (** Base operations *) (** [isEmpty l] returns [true] if and only if [l] is empty *) val isEmpty: list 'a -> Tot bool let isEmpty l = match l with | [] -> true | _ -> false (** [hd l] returns the first element of [l]. Requires [l] to be nonempty, at type-checking time. Named as in: OCaml, F#, Coq *) val hd: l:list 'a{Cons? l} -> Tot 'a let hd = function | hd::_ -> hd (** [tail l] returns [l] without its first element. Requires, at type-checking time, that [l] be nonempty. Similar to: tl in OCaml, F#, Coq *) val tail: l:list 'a {Cons? l} -> Tot (list 'a) let tail = function | _::tl -> tl (** [tl l] returns [l] without its first element. Requires, at type-checking time, that [l] be nonempty. Named as in: OCaml, F#, Coq *) val tl: l:list 'a {Cons? l} -> Tot (list 'a) let tl = tail (** [last l] returns the last element of [l]. Requires, at type-checking time, that [l] be nonempty. Named as in: Haskell *) val last: l:list 'a {Cons? l} -> Tot 'a let rec last = function | [hd] -> hd | _::tl -> last tl (** [init l] returns [l] without its last element. Requires, at type-checking time, that [l] be nonempty. Named as in: Haskell *) val init: l:list 'a {Cons? l} -> Tot (list 'a) let rec init = function | [_] -> [] | hd::tl -> hd::(init tl) (** [length l] returns the total number of elements in [l]. Named as in: OCaml, F#, Coq *) val length: list 'a -> Tot nat let rec length = function | [] -> 0 | _::tl -> 1 + length tl (** [nth l n] returns the [n]-th element in list [l] (with the first element being the 0-th) if [l] is long enough, or [None] otherwise. Named as in: OCaml, F#, Coq *) val nth: list 'a -> nat -> Tot (option 'a) let rec nth l n = match l with | [] -> None | hd::tl -> if n = 0 then Some hd else nth tl (n - 1) (** [index l n] returns the [n]-th element in list [l] (with the first element being the 0-th). Requires, at type-checking time, that [l] be of length at least [n+1]. *) val index: #a:Type -> l:list a -> i:nat{i < length l} -> Tot a let rec index #a (l: list a) (i:nat{i < length l}): Tot a = if i = 0 then hd l else index (tl l) (i - 1) (** [count x l] returns the number of occurrences of [x] in [l]. Requires, at type-checking time, the type of [a] to have equality defined. Similar to: [List.count_occ] in Coq. *) val count: #a:eqtype -> a -> list a -> Tot nat let rec count #a x = function | [] -> 0 | hd::tl -> if x=hd then 1 + count x tl else count x tl (** [rev_acc l1 l2] appends the elements of [l1] to the beginning of [l2], in reverse order. It is equivalent to [append (rev l1) l2], but is tail-recursive. Similar to: [List.rev_append] in OCaml, Coq. *) val rev_acc: list 'a -> list 'a -> Tot (list 'a) let rec rev_acc l acc = match l with | [] -> acc | hd::tl -> rev_acc tl (hd::acc) (** [rev l] returns the list [l] in reverse order. Named as in: OCaml, F#, Coq. *) val rev: list 'a -> Tot (list 'a) let rev l = rev_acc l [] (** [append l1 l2] appends the elements of [l2] to the end of [l1]. Named as: OCaml, F#. Similar to: [List.app] in Coq. *) val append: list 'a -> list 'a -> Tot (list 'a) let rec append x y = match x with | [] -> y | a::tl -> a::append tl y (** Defines notation [@@] for [append], as in OCaml, F# . *) let op_At x y = append x y (** [snoc (l, x)] adds [x] to the end of the list [l]. Note: We use an uncurried [snoc (l, x)] instead of the curried [snoc l x]. This is intentional. If [snoc] takes a pair instead of 2 arguments, it allows for a better pattern on [lemma_unsnoc_snoc], which connects [snoc] and [unsnoc]. In particular, if we had two arguments, then either the pattern would either be too restrictive or would lead to over-triggering. More context for this can be seen in the (collapsed and uncollapsed) comments at https://github.com/FStarLang/FStar/pull/1560 *) val snoc: (list 'a * 'a) -> Tot (list 'a) let snoc (l, x) = append l [x] (** [flatten l], where [l] is a list of lists, returns the list of the elements of the lists in [l], preserving their order. Named as in: OCaml, Coq. *) val flatten: list (list 'a) -> Tot (list 'a) let rec flatten l = match l with | [] -> [] | hd::tl -> append hd (flatten tl) (** [map f l] applies [f] to each element of [l] and returns the list of results, in the order of the original elements in [l]. Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml, Coq, F# *) val map: ('a -> Tot 'b) -> list 'a -> Tot (list 'b) let rec map f x = match x with | [] -> [] | a::tl -> f a::map f tl (** [mapi_init f l n] applies, for each [k], [f (n+k)] to the [k]-th element of [l] and returns the list of results, in the order of the original elements in [l]. Requires, at type-checking time, [f] to be a pure total function. *) val mapi_init: (int -> 'a -> Tot 'b) -> list 'a -> int -> Tot (list 'b) let rec mapi_init f l i = match l with | [] -> [] | hd::tl -> (f i hd)::(mapi_init f tl (i+1)) (** [mapi f l] applies, for each [k], [f k] to the [k]-th element of [l] and returns the list of results, in the order of the original elements in [l]. Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml *) val mapi: (int -> 'a -> Tot 'b) -> list 'a -> Tot (list 'b) let mapi f l = mapi_init f l 0 (** [concatMap f l] applies [f] to each element of [l] and returns the concatenation of the results, in the order of the original elements of [l]. This is equivalent to [flatten (map f l)]. Requires, at type-checking time, [f] to be a pure total function. *) val concatMap: ('a -> Tot (list 'b)) -> list 'a -> Tot (list 'b) let rec concatMap f = function | [] -> [] | a::tl -> let fa = f a in let ftl = concatMap f tl in append fa ftl (** [fold_left f x [y1; y2; ...; yn]] computes (f (... (f x y1) y2) ... yn). Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml, Coq. *) val fold_left: ('a -> 'b -> Tot 'a) -> 'a -> l:list 'b -> Tot 'a (decreases l) let rec fold_left f x l = match l with | [] -> x | hd::tl -> fold_left f (f x hd) tl (** [fold_right f [x1; x2; ...; xn] y] computes (f x1 (f x2 (... (f xn y)) ... )). Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml, Coq *) val fold_right: ('a -> 'b -> Tot 'b) -> list 'a -> 'b -> Tot 'b let rec fold_right f l x = match l with | [] -> x | hd::tl -> f hd (fold_right f tl x) (** [fold_right_gtot] is just like [fold_right], except `f` is a ghost function **) let rec fold_right_gtot (#a:Type) (#b:Type) (l:list a) (f:a -> b -> GTot b) (x:b) : GTot b = match l with | [] -> x | hd::tl -> f hd (fold_right_gtot tl f x) (* We define map in terms of fold, to share simple lemmas *) let map_gtot #a #b (f:a -> GTot b) (x:list a)
false
false
FStar.List.Tot.Base.fst
{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 1, "max_fuel": 8, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": true, "z3cliopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }
null
val map_gtot (#a #b: _) (f: (a -> GTot b)) (x: list a) : GTot (list b)
[]
FStar.List.Tot.Base.map_gtot
{ "file_name": "ulib/FStar.List.Tot.Base.fst", "git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f", "git_url": "https://github.com/FStarLang/FStar.git", "project_name": "FStar" }
f: (_: a -> Prims.GTot b) -> x: Prims.list a -> Prims.GTot (Prims.list b)
{ "end_col": 48, "end_line": 210, "start_col": 4, "start_line": 210 }
Prims.Tot
val contains: #a: eqtype -> a -> list a -> Tot bool
[ { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]
false
let contains : #a:eqtype -> a -> list a -> Tot bool = mem
val contains: #a: eqtype -> a -> list a -> Tot bool let contains: #a: eqtype -> a -> list a -> Tot bool =
false
null
false
mem
{ "checked_file": "FStar.List.Tot.Base.fst.checked", "dependencies": [ "prims.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Classical.fsti.checked" ], "interface_file": false, "source_file": "FStar.List.Tot.Base.fst" }
[ "total" ]
[ "FStar.List.Tot.Base.mem" ]
[]
(* Copyright 2008-2014 Nikhil Swamy and Microsoft Research Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License. *) (** This module defines all pure and total operations on lists that can be used in specifications. It is implemented by FStar_List_Tot_Base.ml, any functional change and/or the addition of new functions MUST be reflected there. @summary Pure total operations on lists *) module FStar.List.Tot.Base (** Base operations *) (** [isEmpty l] returns [true] if and only if [l] is empty *) val isEmpty: list 'a -> Tot bool let isEmpty l = match l with | [] -> true | _ -> false (** [hd l] returns the first element of [l]. Requires [l] to be nonempty, at type-checking time. Named as in: OCaml, F#, Coq *) val hd: l:list 'a{Cons? l} -> Tot 'a let hd = function | hd::_ -> hd (** [tail l] returns [l] without its first element. Requires, at type-checking time, that [l] be nonempty. Similar to: tl in OCaml, F#, Coq *) val tail: l:list 'a {Cons? l} -> Tot (list 'a) let tail = function | _::tl -> tl (** [tl l] returns [l] without its first element. Requires, at type-checking time, that [l] be nonempty. Named as in: OCaml, F#, Coq *) val tl: l:list 'a {Cons? l} -> Tot (list 'a) let tl = tail (** [last l] returns the last element of [l]. Requires, at type-checking time, that [l] be nonempty. Named as in: Haskell *) val last: l:list 'a {Cons? l} -> Tot 'a let rec last = function | [hd] -> hd | _::tl -> last tl (** [init l] returns [l] without its last element. Requires, at type-checking time, that [l] be nonempty. Named as in: Haskell *) val init: l:list 'a {Cons? l} -> Tot (list 'a) let rec init = function | [_] -> [] | hd::tl -> hd::(init tl) (** [length l] returns the total number of elements in [l]. Named as in: OCaml, F#, Coq *) val length: list 'a -> Tot nat let rec length = function | [] -> 0 | _::tl -> 1 + length tl (** [nth l n] returns the [n]-th element in list [l] (with the first element being the 0-th) if [l] is long enough, or [None] otherwise. Named as in: OCaml, F#, Coq *) val nth: list 'a -> nat -> Tot (option 'a) let rec nth l n = match l with | [] -> None | hd::tl -> if n = 0 then Some hd else nth tl (n - 1) (** [index l n] returns the [n]-th element in list [l] (with the first element being the 0-th). Requires, at type-checking time, that [l] be of length at least [n+1]. *) val index: #a:Type -> l:list a -> i:nat{i < length l} -> Tot a let rec index #a (l: list a) (i:nat{i < length l}): Tot a = if i = 0 then hd l else index (tl l) (i - 1) (** [count x l] returns the number of occurrences of [x] in [l]. Requires, at type-checking time, the type of [a] to have equality defined. Similar to: [List.count_occ] in Coq. *) val count: #a:eqtype -> a -> list a -> Tot nat let rec count #a x = function | [] -> 0 | hd::tl -> if x=hd then 1 + count x tl else count x tl (** [rev_acc l1 l2] appends the elements of [l1] to the beginning of [l2], in reverse order. It is equivalent to [append (rev l1) l2], but is tail-recursive. Similar to: [List.rev_append] in OCaml, Coq. *) val rev_acc: list 'a -> list 'a -> Tot (list 'a) let rec rev_acc l acc = match l with | [] -> acc | hd::tl -> rev_acc tl (hd::acc) (** [rev l] returns the list [l] in reverse order. Named as in: OCaml, F#, Coq. *) val rev: list 'a -> Tot (list 'a) let rev l = rev_acc l [] (** [append l1 l2] appends the elements of [l2] to the end of [l1]. Named as: OCaml, F#. Similar to: [List.app] in Coq. *) val append: list 'a -> list 'a -> Tot (list 'a) let rec append x y = match x with | [] -> y | a::tl -> a::append tl y (** Defines notation [@@] for [append], as in OCaml, F# . *) let op_At x y = append x y (** [snoc (l, x)] adds [x] to the end of the list [l]. Note: We use an uncurried [snoc (l, x)] instead of the curried [snoc l x]. This is intentional. If [snoc] takes a pair instead of 2 arguments, it allows for a better pattern on [lemma_unsnoc_snoc], which connects [snoc] and [unsnoc]. In particular, if we had two arguments, then either the pattern would either be too restrictive or would lead to over-triggering. More context for this can be seen in the (collapsed and uncollapsed) comments at https://github.com/FStarLang/FStar/pull/1560 *) val snoc: (list 'a * 'a) -> Tot (list 'a) let snoc (l, x) = append l [x] (** [flatten l], where [l] is a list of lists, returns the list of the elements of the lists in [l], preserving their order. Named as in: OCaml, Coq. *) val flatten: list (list 'a) -> Tot (list 'a) let rec flatten l = match l with | [] -> [] | hd::tl -> append hd (flatten tl) (** [map f l] applies [f] to each element of [l] and returns the list of results, in the order of the original elements in [l]. Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml, Coq, F# *) val map: ('a -> Tot 'b) -> list 'a -> Tot (list 'b) let rec map f x = match x with | [] -> [] | a::tl -> f a::map f tl (** [mapi_init f l n] applies, for each [k], [f (n+k)] to the [k]-th element of [l] and returns the list of results, in the order of the original elements in [l]. Requires, at type-checking time, [f] to be a pure total function. *) val mapi_init: (int -> 'a -> Tot 'b) -> list 'a -> int -> Tot (list 'b) let rec mapi_init f l i = match l with | [] -> [] | hd::tl -> (f i hd)::(mapi_init f tl (i+1)) (** [mapi f l] applies, for each [k], [f k] to the [k]-th element of [l] and returns the list of results, in the order of the original elements in [l]. Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml *) val mapi: (int -> 'a -> Tot 'b) -> list 'a -> Tot (list 'b) let mapi f l = mapi_init f l 0 (** [concatMap f l] applies [f] to each element of [l] and returns the concatenation of the results, in the order of the original elements of [l]. This is equivalent to [flatten (map f l)]. Requires, at type-checking time, [f] to be a pure total function. *) val concatMap: ('a -> Tot (list 'b)) -> list 'a -> Tot (list 'b) let rec concatMap f = function | [] -> [] | a::tl -> let fa = f a in let ftl = concatMap f tl in append fa ftl (** [fold_left f x [y1; y2; ...; yn]] computes (f (... (f x y1) y2) ... yn). Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml, Coq. *) val fold_left: ('a -> 'b -> Tot 'a) -> 'a -> l:list 'b -> Tot 'a (decreases l) let rec fold_left f x l = match l with | [] -> x | hd::tl -> fold_left f (f x hd) tl (** [fold_right f [x1; x2; ...; xn] y] computes (f x1 (f x2 (... (f xn y)) ... )). Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml, Coq *) val fold_right: ('a -> 'b -> Tot 'b) -> list 'a -> 'b -> Tot 'b let rec fold_right f l x = match l with | [] -> x | hd::tl -> f hd (fold_right f tl x) (** [fold_right_gtot] is just like [fold_right], except `f` is a ghost function **) let rec fold_right_gtot (#a:Type) (#b:Type) (l:list a) (f:a -> b -> GTot b) (x:b) : GTot b = match l with | [] -> x | hd::tl -> f hd (fold_right_gtot tl f x) (* We define map in terms of fold, to share simple lemmas *) let map_gtot #a #b (f:a -> GTot b) (x:list a) : GTot (list b) = fold_right_gtot x (fun x tl -> f x :: tl) [] (** [fold_left2 f x [y1; y2; ...; yn] [z1; z2; ...; zn]] computes (f (... (f x y1 z1) y2 z2) ... yn zn). Requires, at type-checking time, [f] to be a pure total function, and the lists [y1; y2; ...; yn] and [z1; z2; ...; zn] to have the same lengths. Named as in: OCaml *) val fold_left2 : f:('a -> 'b -> 'c -> Tot 'a) -> accu:'a -> l1:(list 'b) -> l2:(list 'c) -> Pure 'a (requires (length l1 == length l2)) (ensures (fun _ -> True)) (decreases l1) let rec fold_left2 f accu l1 l2 = match (l1, l2) with | ([], []) -> accu | (a1::l1, a2::l2) -> fold_left2 f (f accu a1 a2) l1 l2 (** Propositional membership (as in Coq). Does not require decidable equality. *) (** [memP x l] holds if, and only if, [x] appears as an element of [l]. Similar to: List.In in Coq. *) let rec memP (#a: Type) (x: a) (l: list a) : Tot Type0 = match l with | [] -> False | y :: q -> x == y \/ memP x q (** List searching **) (** [mem x l] returns [true] if, and only if, [x] appears as an element of [l]. Requires, at type-checking time, the type of elements of [l] to have decidable equality. Named as in: OCaml. See also: List.In in Coq, which is propositional. *) val mem: #a:eqtype -> a -> list a -> Tot bool let rec mem #a x = function | [] -> false | hd::tl -> if hd = x then true else mem x tl (** [contains x l] returns [true] if, and only if, [x] appears as an element of [l]. Requires, at type-checking time, the type of elements of [l] to have decidable equality. It is equivalent to: [mem x
false
false
FStar.List.Tot.Base.fst
{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 1, "max_fuel": 8, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": true, "z3cliopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }
null
val contains: #a: eqtype -> a -> list a -> Tot bool
[]
FStar.List.Tot.Base.contains
{ "file_name": "ulib/FStar.List.Tot.Base.fst", "git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f", "git_url": "https://github.com/FStarLang/FStar.git", "project_name": "FStar" }
_: a -> _: Prims.list a -> Prims.bool
{ "end_col": 57, "end_line": 248, "start_col": 54, "start_line": 248 }
Prims.Tot
val snoc: (list 'a * 'a) -> Tot (list 'a)
[ { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]
false
let snoc (l, x) = append l [x]
val snoc: (list 'a * 'a) -> Tot (list 'a) let snoc (l, x) =
false
null
false
append l [x]
{ "checked_file": "FStar.List.Tot.Base.fst.checked", "dependencies": [ "prims.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Classical.fsti.checked" ], "interface_file": false, "source_file": "FStar.List.Tot.Base.fst" }
[ "total" ]
[ "FStar.Pervasives.Native.tuple2", "Prims.list", "FStar.List.Tot.Base.append", "Prims.Cons", "Prims.Nil" ]
[]
(* Copyright 2008-2014 Nikhil Swamy and Microsoft Research Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License. *) (** This module defines all pure and total operations on lists that can be used in specifications. It is implemented by FStar_List_Tot_Base.ml, any functional change and/or the addition of new functions MUST be reflected there. @summary Pure total operations on lists *) module FStar.List.Tot.Base (** Base operations *) (** [isEmpty l] returns [true] if and only if [l] is empty *) val isEmpty: list 'a -> Tot bool let isEmpty l = match l with | [] -> true | _ -> false (** [hd l] returns the first element of [l]. Requires [l] to be nonempty, at type-checking time. Named as in: OCaml, F#, Coq *) val hd: l:list 'a{Cons? l} -> Tot 'a let hd = function | hd::_ -> hd (** [tail l] returns [l] without its first element. Requires, at type-checking time, that [l] be nonempty. Similar to: tl in OCaml, F#, Coq *) val tail: l:list 'a {Cons? l} -> Tot (list 'a) let tail = function | _::tl -> tl (** [tl l] returns [l] without its first element. Requires, at type-checking time, that [l] be nonempty. Named as in: OCaml, F#, Coq *) val tl: l:list 'a {Cons? l} -> Tot (list 'a) let tl = tail (** [last l] returns the last element of [l]. Requires, at type-checking time, that [l] be nonempty. Named as in: Haskell *) val last: l:list 'a {Cons? l} -> Tot 'a let rec last = function | [hd] -> hd | _::tl -> last tl (** [init l] returns [l] without its last element. Requires, at type-checking time, that [l] be nonempty. Named as in: Haskell *) val init: l:list 'a {Cons? l} -> Tot (list 'a) let rec init = function | [_] -> [] | hd::tl -> hd::(init tl) (** [length l] returns the total number of elements in [l]. Named as in: OCaml, F#, Coq *) val length: list 'a -> Tot nat let rec length = function | [] -> 0 | _::tl -> 1 + length tl (** [nth l n] returns the [n]-th element in list [l] (with the first element being the 0-th) if [l] is long enough, or [None] otherwise. Named as in: OCaml, F#, Coq *) val nth: list 'a -> nat -> Tot (option 'a) let rec nth l n = match l with | [] -> None | hd::tl -> if n = 0 then Some hd else nth tl (n - 1) (** [index l n] returns the [n]-th element in list [l] (with the first element being the 0-th). Requires, at type-checking time, that [l] be of length at least [n+1]. *) val index: #a:Type -> l:list a -> i:nat{i < length l} -> Tot a let rec index #a (l: list a) (i:nat{i < length l}): Tot a = if i = 0 then hd l else index (tl l) (i - 1) (** [count x l] returns the number of occurrences of [x] in [l]. Requires, at type-checking time, the type of [a] to have equality defined. Similar to: [List.count_occ] in Coq. *) val count: #a:eqtype -> a -> list a -> Tot nat let rec count #a x = function | [] -> 0 | hd::tl -> if x=hd then 1 + count x tl else count x tl (** [rev_acc l1 l2] appends the elements of [l1] to the beginning of [l2], in reverse order. It is equivalent to [append (rev l1) l2], but is tail-recursive. Similar to: [List.rev_append] in OCaml, Coq. *) val rev_acc: list 'a -> list 'a -> Tot (list 'a) let rec rev_acc l acc = match l with | [] -> acc | hd::tl -> rev_acc tl (hd::acc) (** [rev l] returns the list [l] in reverse order. Named as in: OCaml, F#, Coq. *) val rev: list 'a -> Tot (list 'a) let rev l = rev_acc l [] (** [append l1 l2] appends the elements of [l2] to the end of [l1]. Named as: OCaml, F#. Similar to: [List.app] in Coq. *) val append: list 'a -> list 'a -> Tot (list 'a) let rec append x y = match x with | [] -> y | a::tl -> a::append tl y (** Defines notation [@@] for [append], as in OCaml, F# . *) let op_At x y = append x y (** [snoc (l, x)] adds [x] to the end of the list [l]. Note: We use an uncurried [snoc (l, x)] instead of the curried [snoc l x]. This is intentional. If [snoc] takes a pair instead of 2 arguments, it allows for a better pattern on [lemma_unsnoc_snoc], which connects [snoc] and [unsnoc]. In particular, if we had two arguments, then either the pattern would either be too restrictive or would lead to over-triggering. More context for this can be seen in the (collapsed and uncollapsed) comments at https://github.com/FStarLang/FStar/pull/1560 *)
false
false
FStar.List.Tot.Base.fst
{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 1, "max_fuel": 8, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": true, "z3cliopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }
null
val snoc: (list 'a * 'a) -> Tot (list 'a)
[]
FStar.List.Tot.Base.snoc
{ "file_name": "ulib/FStar.List.Tot.Base.fst", "git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f", "git_url": "https://github.com/FStarLang/FStar.git", "project_name": "FStar" }
_: (Prims.list 'a * 'a) -> Prims.list 'a
{ "end_col": 30, "end_line": 137, "start_col": 18, "start_line": 137 }
Prims.Tot
val mapi: (int -> 'a -> Tot 'b) -> list 'a -> Tot (list 'b)
[ { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]
false
let mapi f l = mapi_init f l 0
val mapi: (int -> 'a -> Tot 'b) -> list 'a -> Tot (list 'b) let mapi f l =
false
null
false
mapi_init f l 0
{ "checked_file": "FStar.List.Tot.Base.fst.checked", "dependencies": [ "prims.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Classical.fsti.checked" ], "interface_file": false, "source_file": "FStar.List.Tot.Base.fst" }
[ "total" ]
[ "Prims.int", "Prims.list", "FStar.List.Tot.Base.mapi_init" ]
[]
(* Copyright 2008-2014 Nikhil Swamy and Microsoft Research Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License. *) (** This module defines all pure and total operations on lists that can be used in specifications. It is implemented by FStar_List_Tot_Base.ml, any functional change and/or the addition of new functions MUST be reflected there. @summary Pure total operations on lists *) module FStar.List.Tot.Base (** Base operations *) (** [isEmpty l] returns [true] if and only if [l] is empty *) val isEmpty: list 'a -> Tot bool let isEmpty l = match l with | [] -> true | _ -> false (** [hd l] returns the first element of [l]. Requires [l] to be nonempty, at type-checking time. Named as in: OCaml, F#, Coq *) val hd: l:list 'a{Cons? l} -> Tot 'a let hd = function | hd::_ -> hd (** [tail l] returns [l] without its first element. Requires, at type-checking time, that [l] be nonempty. Similar to: tl in OCaml, F#, Coq *) val tail: l:list 'a {Cons? l} -> Tot (list 'a) let tail = function | _::tl -> tl (** [tl l] returns [l] without its first element. Requires, at type-checking time, that [l] be nonempty. Named as in: OCaml, F#, Coq *) val tl: l:list 'a {Cons? l} -> Tot (list 'a) let tl = tail (** [last l] returns the last element of [l]. Requires, at type-checking time, that [l] be nonempty. Named as in: Haskell *) val last: l:list 'a {Cons? l} -> Tot 'a let rec last = function | [hd] -> hd | _::tl -> last tl (** [init l] returns [l] without its last element. Requires, at type-checking time, that [l] be nonempty. Named as in: Haskell *) val init: l:list 'a {Cons? l} -> Tot (list 'a) let rec init = function | [_] -> [] | hd::tl -> hd::(init tl) (** [length l] returns the total number of elements in [l]. Named as in: OCaml, F#, Coq *) val length: list 'a -> Tot nat let rec length = function | [] -> 0 | _::tl -> 1 + length tl (** [nth l n] returns the [n]-th element in list [l] (with the first element being the 0-th) if [l] is long enough, or [None] otherwise. Named as in: OCaml, F#, Coq *) val nth: list 'a -> nat -> Tot (option 'a) let rec nth l n = match l with | [] -> None | hd::tl -> if n = 0 then Some hd else nth tl (n - 1) (** [index l n] returns the [n]-th element in list [l] (with the first element being the 0-th). Requires, at type-checking time, that [l] be of length at least [n+1]. *) val index: #a:Type -> l:list a -> i:nat{i < length l} -> Tot a let rec index #a (l: list a) (i:nat{i < length l}): Tot a = if i = 0 then hd l else index (tl l) (i - 1) (** [count x l] returns the number of occurrences of [x] in [l]. Requires, at type-checking time, the type of [a] to have equality defined. Similar to: [List.count_occ] in Coq. *) val count: #a:eqtype -> a -> list a -> Tot nat let rec count #a x = function | [] -> 0 | hd::tl -> if x=hd then 1 + count x tl else count x tl (** [rev_acc l1 l2] appends the elements of [l1] to the beginning of [l2], in reverse order. It is equivalent to [append (rev l1) l2], but is tail-recursive. Similar to: [List.rev_append] in OCaml, Coq. *) val rev_acc: list 'a -> list 'a -> Tot (list 'a) let rec rev_acc l acc = match l with | [] -> acc | hd::tl -> rev_acc tl (hd::acc) (** [rev l] returns the list [l] in reverse order. Named as in: OCaml, F#, Coq. *) val rev: list 'a -> Tot (list 'a) let rev l = rev_acc l [] (** [append l1 l2] appends the elements of [l2] to the end of [l1]. Named as: OCaml, F#. Similar to: [List.app] in Coq. *) val append: list 'a -> list 'a -> Tot (list 'a) let rec append x y = match x with | [] -> y | a::tl -> a::append tl y (** Defines notation [@@] for [append], as in OCaml, F# . *) let op_At x y = append x y (** [snoc (l, x)] adds [x] to the end of the list [l]. Note: We use an uncurried [snoc (l, x)] instead of the curried [snoc l x]. This is intentional. If [snoc] takes a pair instead of 2 arguments, it allows for a better pattern on [lemma_unsnoc_snoc], which connects [snoc] and [unsnoc]. In particular, if we had two arguments, then either the pattern would either be too restrictive or would lead to over-triggering. More context for this can be seen in the (collapsed and uncollapsed) comments at https://github.com/FStarLang/FStar/pull/1560 *) val snoc: (list 'a * 'a) -> Tot (list 'a) let snoc (l, x) = append l [x] (** [flatten l], where [l] is a list of lists, returns the list of the elements of the lists in [l], preserving their order. Named as in: OCaml, Coq. *) val flatten: list (list 'a) -> Tot (list 'a) let rec flatten l = match l with | [] -> [] | hd::tl -> append hd (flatten tl) (** [map f l] applies [f] to each element of [l] and returns the list of results, in the order of the original elements in [l]. Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml, Coq, F# *) val map: ('a -> Tot 'b) -> list 'a -> Tot (list 'b) let rec map f x = match x with | [] -> [] | a::tl -> f a::map f tl (** [mapi_init f l n] applies, for each [k], [f (n+k)] to the [k]-th element of [l] and returns the list of results, in the order of the original elements in [l]. Requires, at type-checking time, [f] to be a pure total function. *) val mapi_init: (int -> 'a -> Tot 'b) -> list 'a -> int -> Tot (list 'b) let rec mapi_init f l i = match l with | [] -> [] | hd::tl -> (f i hd)::(mapi_init f tl (i+1)) (** [mapi f l] applies, for each [k], [f k] to the [k]-th element of [l] and returns the list of results, in the order of the original elements in [l]. Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml *)
false
false
FStar.List.Tot.Base.fst
{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 1, "max_fuel": 8, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": true, "z3cliopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }
null
val mapi: (int -> 'a -> Tot 'b) -> list 'a -> Tot (list 'b)
[]
FStar.List.Tot.Base.mapi
{ "file_name": "ulib/FStar.List.Tot.Base.fst", "git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f", "git_url": "https://github.com/FStarLang/FStar.git", "project_name": "FStar" }
f: (_: Prims.int -> _: 'a -> 'b) -> l: Prims.list 'a -> Prims.list 'b
{ "end_col": 30, "end_line": 169, "start_col": 15, "start_line": 169 }
Prims.Pure
[ { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]
false
let strict_prefix_of = strict_suffix_of
let strict_prefix_of =
false
null
false
strict_suffix_of
{ "checked_file": "FStar.List.Tot.Base.fst.checked", "dependencies": [ "prims.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Classical.fsti.checked" ], "interface_file": false, "source_file": "FStar.List.Tot.Base.fst" }
[ "" ]
[ "FStar.List.Tot.Base.strict_suffix_of", "Prims.list", "Prims.l_True" ]
[]
(* Copyright 2008-2014 Nikhil Swamy and Microsoft Research Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License. *) (** This module defines all pure and total operations on lists that can be used in specifications. It is implemented by FStar_List_Tot_Base.ml, any functional change and/or the addition of new functions MUST be reflected there. @summary Pure total operations on lists *) module FStar.List.Tot.Base (** Base operations *) (** [isEmpty l] returns [true] if and only if [l] is empty *) val isEmpty: list 'a -> Tot bool let isEmpty l = match l with | [] -> true | _ -> false (** [hd l] returns the first element of [l]. Requires [l] to be nonempty, at type-checking time. Named as in: OCaml, F#, Coq *) val hd: l:list 'a{Cons? l} -> Tot 'a let hd = function | hd::_ -> hd (** [tail l] returns [l] without its first element. Requires, at type-checking time, that [l] be nonempty. Similar to: tl in OCaml, F#, Coq *) val tail: l:list 'a {Cons? l} -> Tot (list 'a) let tail = function | _::tl -> tl (** [tl l] returns [l] without its first element. Requires, at type-checking time, that [l] be nonempty. Named as in: OCaml, F#, Coq *) val tl: l:list 'a {Cons? l} -> Tot (list 'a) let tl = tail (** [last l] returns the last element of [l]. Requires, at type-checking time, that [l] be nonempty. Named as in: Haskell *) val last: l:list 'a {Cons? l} -> Tot 'a let rec last = function | [hd] -> hd | _::tl -> last tl (** [init l] returns [l] without its last element. Requires, at type-checking time, that [l] be nonempty. Named as in: Haskell *) val init: l:list 'a {Cons? l} -> Tot (list 'a) let rec init = function | [_] -> [] | hd::tl -> hd::(init tl) (** [length l] returns the total number of elements in [l]. Named as in: OCaml, F#, Coq *) val length: list 'a -> Tot nat let rec length = function | [] -> 0 | _::tl -> 1 + length tl (** [nth l n] returns the [n]-th element in list [l] (with the first element being the 0-th) if [l] is long enough, or [None] otherwise. Named as in: OCaml, F#, Coq *) val nth: list 'a -> nat -> Tot (option 'a) let rec nth l n = match l with | [] -> None | hd::tl -> if n = 0 then Some hd else nth tl (n - 1) (** [index l n] returns the [n]-th element in list [l] (with the first element being the 0-th). Requires, at type-checking time, that [l] be of length at least [n+1]. *) val index: #a:Type -> l:list a -> i:nat{i < length l} -> Tot a let rec index #a (l: list a) (i:nat{i < length l}): Tot a = if i = 0 then hd l else index (tl l) (i - 1) (** [count x l] returns the number of occurrences of [x] in [l]. Requires, at type-checking time, the type of [a] to have equality defined. Similar to: [List.count_occ] in Coq. *) val count: #a:eqtype -> a -> list a -> Tot nat let rec count #a x = function | [] -> 0 | hd::tl -> if x=hd then 1 + count x tl else count x tl (** [rev_acc l1 l2] appends the elements of [l1] to the beginning of [l2], in reverse order. It is equivalent to [append (rev l1) l2], but is tail-recursive. Similar to: [List.rev_append] in OCaml, Coq. *) val rev_acc: list 'a -> list 'a -> Tot (list 'a) let rec rev_acc l acc = match l with | [] -> acc | hd::tl -> rev_acc tl (hd::acc) (** [rev l] returns the list [l] in reverse order. Named as in: OCaml, F#, Coq. *) val rev: list 'a -> Tot (list 'a) let rev l = rev_acc l [] (** [append l1 l2] appends the elements of [l2] to the end of [l1]. Named as: OCaml, F#. Similar to: [List.app] in Coq. *) val append: list 'a -> list 'a -> Tot (list 'a) let rec append x y = match x with | [] -> y | a::tl -> a::append tl y (** Defines notation [@@] for [append], as in OCaml, F# . *) let op_At x y = append x y (** [snoc (l, x)] adds [x] to the end of the list [l]. Note: We use an uncurried [snoc (l, x)] instead of the curried [snoc l x]. This is intentional. If [snoc] takes a pair instead of 2 arguments, it allows for a better pattern on [lemma_unsnoc_snoc], which connects [snoc] and [unsnoc]. In particular, if we had two arguments, then either the pattern would either be too restrictive or would lead to over-triggering. More context for this can be seen in the (collapsed and uncollapsed) comments at https://github.com/FStarLang/FStar/pull/1560 *) val snoc: (list 'a * 'a) -> Tot (list 'a) let snoc (l, x) = append l [x] (** [flatten l], where [l] is a list of lists, returns the list of the elements of the lists in [l], preserving their order. Named as in: OCaml, Coq. *) val flatten: list (list 'a) -> Tot (list 'a) let rec flatten l = match l with | [] -> [] | hd::tl -> append hd (flatten tl) (** [map f l] applies [f] to each element of [l] and returns the list of results, in the order of the original elements in [l]. Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml, Coq, F# *) val map: ('a -> Tot 'b) -> list 'a -> Tot (list 'b) let rec map f x = match x with | [] -> [] | a::tl -> f a::map f tl (** [mapi_init f l n] applies, for each [k], [f (n+k)] to the [k]-th element of [l] and returns the list of results, in the order of the original elements in [l]. Requires, at type-checking time, [f] to be a pure total function. *) val mapi_init: (int -> 'a -> Tot 'b) -> list 'a -> int -> Tot (list 'b) let rec mapi_init f l i = match l with | [] -> [] | hd::tl -> (f i hd)::(mapi_init f tl (i+1)) (** [mapi f l] applies, for each [k], [f k] to the [k]-th element of [l] and returns the list of results, in the order of the original elements in [l]. Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml *) val mapi: (int -> 'a -> Tot 'b) -> list 'a -> Tot (list 'b) let mapi f l = mapi_init f l 0 (** [concatMap f l] applies [f] to each element of [l] and returns the concatenation of the results, in the order of the original elements of [l]. This is equivalent to [flatten (map f l)]. Requires, at type-checking time, [f] to be a pure total function. *) val concatMap: ('a -> Tot (list 'b)) -> list 'a -> Tot (list 'b) let rec concatMap f = function | [] -> [] | a::tl -> let fa = f a in let ftl = concatMap f tl in append fa ftl (** [fold_left f x [y1; y2; ...; yn]] computes (f (... (f x y1) y2) ... yn). Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml, Coq. *) val fold_left: ('a -> 'b -> Tot 'a) -> 'a -> l:list 'b -> Tot 'a (decreases l) let rec fold_left f x l = match l with | [] -> x | hd::tl -> fold_left f (f x hd) tl (** [fold_right f [x1; x2; ...; xn] y] computes (f x1 (f x2 (... (f xn y)) ... )). Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml, Coq *) val fold_right: ('a -> 'b -> Tot 'b) -> list 'a -> 'b -> Tot 'b let rec fold_right f l x = match l with | [] -> x | hd::tl -> f hd (fold_right f tl x) (** [fold_right_gtot] is just like [fold_right], except `f` is a ghost function **) let rec fold_right_gtot (#a:Type) (#b:Type) (l:list a) (f:a -> b -> GTot b) (x:b) : GTot b = match l with | [] -> x | hd::tl -> f hd (fold_right_gtot tl f x) (* We define map in terms of fold, to share simple lemmas *) let map_gtot #a #b (f:a -> GTot b) (x:list a) : GTot (list b) = fold_right_gtot x (fun x tl -> f x :: tl) [] (** [fold_left2 f x [y1; y2; ...; yn] [z1; z2; ...; zn]] computes (f (... (f x y1 z1) y2 z2) ... yn zn). Requires, at type-checking time, [f] to be a pure total function, and the lists [y1; y2; ...; yn] and [z1; z2; ...; zn] to have the same lengths. Named as in: OCaml *) val fold_left2 : f:('a -> 'b -> 'c -> Tot 'a) -> accu:'a -> l1:(list 'b) -> l2:(list 'c) -> Pure 'a (requires (length l1 == length l2)) (ensures (fun _ -> True)) (decreases l1) let rec fold_left2 f accu l1 l2 = match (l1, l2) with | ([], []) -> accu | (a1::l1, a2::l2) -> fold_left2 f (f accu a1 a2) l1 l2 (** Propositional membership (as in Coq). Does not require decidable equality. *) (** [memP x l] holds if, and only if, [x] appears as an element of [l]. Similar to: List.In in Coq. *) let rec memP (#a: Type) (x: a) (l: list a) : Tot Type0 = match l with | [] -> False | y :: q -> x == y \/ memP x q (** List searching **) (** [mem x l] returns [true] if, and only if, [x] appears as an element of [l]. Requires, at type-checking time, the type of elements of [l] to have decidable equality. Named as in: OCaml. See also: List.In in Coq, which is propositional. *) val mem: #a:eqtype -> a -> list a -> Tot bool let rec mem #a x = function | [] -> false | hd::tl -> if hd = x then true else mem x tl (** [contains x l] returns [true] if, and only if, [x] appears as an element of [l]. Requires, at type-checking time, the type of elements of [l] to have decidable equality. It is equivalent to: [mem x l]. TODO: should we rather swap the order of arguments? *) let contains : #a:eqtype -> a -> list a -> Tot bool = mem (** [existsb f l] returns [true] if, and only if, there exists some element [x] in [l] such that [f x] holds. *) val existsb: #a:Type -> f:(a -> Tot bool) -> list a -> Tot bool let rec existsb #a f l = match l with | [] -> false | hd::tl -> if f hd then true else existsb f tl (** [find f l] returns [Some x] for some element [x] appearing in [l] such that [f x] holds, or [None] only if no such [x] exists. *) val find: #a:Type -> f:(a -> Tot bool) -> list a -> Tot (option (x:a{f x})) let rec find #a f l = match l with | [] -> None #(x:a{f x}) //These type annotations are only present because it makes bootstrapping go much faster | hd::tl -> if f hd then Some #(x:a{f x}) hd else find f tl (** Filtering elements of a list [l] through a Boolean pure total predicate [f] *) (** [filter f l] returns [l] with all elements [x] such that [f x] does not hold removed. Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml, Coq *) val filter : #a: Type -> f:(a -> Tot bool) -> l: list a -> Tot (m:list a{forall x. memP x m ==> f x}) let rec filter #a f = function | [] -> [] | hd::tl -> if f hd then hd::filter f tl else filter f tl (** Postcondition on [filter f l]: for any element [x] of [filter f l], [f x] holds. Requires, at type-checking time, [f] to be a pure total function.*) val mem_filter (#a:Type) (f: (a -> Tot bool)) (l: list a) (x: a) : Lemma (requires (memP x (filter f l))) (ensures (f x)) let mem_filter f l x = () (** Postcondition on [filter f l]: stated with [forall]: for any element [x] of [filter f l], [f x] holds. Requires, at type-checking time, [f] to be a pure total function. *) val mem_filter_forall (#a:Type) (f: (a -> Tot bool)) (l: list a) : Lemma (requires True) (ensures (forall x . memP x (filter f l) ==> f x)) [SMTPat (filter f l)] let mem_filter_forall f l = FStar.Classical.ghost_lemma (mem_filter f l) (** [for_all f l] returns [true] if, and only if, for all elements [x] appearing in [l], [f x] holds. Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml. Similar to: List.forallb in Coq *) val for_all: ('a -> Tot bool) -> list 'a -> Tot bool let rec for_all f l = match l with | [] -> true | hd::tl -> if f hd then for_all f tl else false (** Specification for [for_all f l] vs. mem *) let rec for_all_mem (#a: Type) (f: (a -> Tot bool)) (l: list a) : Lemma (for_all f l <==> (forall x . memP x l ==> f x)) = match l with | [] -> () | _ :: q -> for_all_mem f q (** [collect f l] applies [f] to each element of [l] and returns the concatenation of the results, in the order of the original elements of [l]. It is equivalent to [flatten (map f l)]. Requires, at type-checking time, [f] to be a pure total function. TODO: what is the difference with [concatMap]? *) val collect: ('a -> Tot (list 'b)) -> list 'a -> Tot (list 'b) let rec collect f l = match l with | [] -> [] | hd::tl -> append (f hd) (collect f tl) (** [tryFind f l] returns [Some x] for some element [x] appearing in [l] such that [f x] holds, or [None] only if no such [x] exists. Requires, at type-checking time, [f] to be a pure total function. Contrary to [find], [tryFind] provides no postcondition on its result. *) val tryFind: ('a -> Tot bool) -> list 'a -> Tot (option 'a) let rec tryFind p l = match l with | [] -> None | hd::tl -> if p hd then Some hd else tryFind p tl (** [tryPick f l] returns [y] for some element [x] appearing in [l] such that [f x = Some y] for some y, or [None] only if [f x = None] for all elements [x] of [l]. Requires, at type-checking time, [f] to be a pure total function. *) val tryPick: ('a -> Tot (option 'b)) -> list 'a -> Tot (option 'b) let rec tryPick f l = match l with | [] -> None | hd::tl -> match f hd with | Some x -> Some x | None -> tryPick f tl (** [choose f l] returns the list of [y] for all elements [x] appearing in [l] such that [f x = Some y] for some [y]. Requires, at type-checking time, [f] to be a pure total function. *) val choose: ('a -> Tot (option 'b)) -> list 'a -> Tot (list 'b) let rec choose f l = match l with | [] -> [] | hd::tl -> match f hd with | Some x -> x::(choose f tl) | None -> choose f tl (** [partition f l] returns the pair of lists [(l1, l2)] where all elements [x] of [l] are in [l1] if [f x] holds, and in [l2] otherwise. Both [l1] and [l2] retain the original order of [l]. Requires, at type-checking time, [f] to be a pure total function. *) val partition: f:('a -> Tot bool) -> list 'a -> Tot (list 'a * list 'a) let rec partition f = function | [] -> [], [] | hd::tl -> let l1, l2 = partition f tl in if f hd then hd::l1, l2 else l1, hd::l2 (** [subset la lb] is true if and only if all the elements from [la] are also in [lb]. Requires, at type-checking time, the type of elements of [la] and [lb] to have decidable equality. *) val subset: #a:eqtype -> list a -> list a -> Tot bool let rec subset #a la lb = match la with | [] -> true | h :: tl -> mem h lb && subset tl lb (** [noRepeats l] returns [true] if, and only if, no element of [l] appears in [l] more than once. Requires, at type-checking time, the type of elements of [la] and [lb] to have decidable equality. *) val noRepeats : #a:eqtype -> list a -> Tot bool let rec noRepeats #a la = match la with | [] -> true | h :: tl -> not(mem h tl) && noRepeats tl (** [no_repeats_p l] valid if, and only if, no element of [l] appears in [l] more than once. *) val no_repeats_p : #a:Type -> list a -> Tot prop let rec no_repeats_p #a la = match la with | [] -> True | h :: tl -> ~(memP h tl) /\ no_repeats_p tl (** List of tuples **) (** [assoc x l] returns [Some y] where [(x, y)] is the first element of [l] whose first element is [x], or [None] only if no such element exists. Requires, at type-checking time, the type of [x] to have decidable equality. Named as in: OCaml. *) val assoc: #a:eqtype -> #b:Type -> a -> list (a * b) -> Tot (option b) let rec assoc #a #b x = function | [] -> None | (x', y)::tl -> if x=x' then Some y else assoc x tl (** [split] takes a list of pairs [(x1, y1), ..., (xn, yn)] and returns the pair of lists ([x1, ..., xn], [y1, ..., yn]). Named as in: OCaml *) val split: list ('a * 'b) -> Tot (list 'a * list 'b) let rec split l = match l with | [] -> ([],[]) | (hd1,hd2)::tl -> let (tl1,tl2) = split tl in (hd1::tl1,hd2::tl2) (** [unzip] takes a list of pairs [(x1, y1), ..., (xn, yn)] and returns the pair of lists ([x1, ..., xn], [y1, ..., yn]). Named as in: Haskell *) let unzip l = split l (** [unzip3] takes a list of triples [(x1, y1, z1), ..., (xn, yn, zn)] and returns the triple of lists ([x1, ..., xn], [y1, ..., yn], [z1, ..., zn]). Named as in: Haskell *) val unzip3: list ('a * 'b * 'c) -> Tot (list 'a * list 'b * list 'c) let rec unzip3 l = match l with | [] -> ([],[],[]) | (hd1,hd2,hd3)::tl -> let (tl1,tl2,tl3) = unzip3 tl in (hd1::tl1,hd2::tl2,hd3::tl3) (** Splitting a list at some index **) (** [splitAt] takes a natural number n and a list and returns a pair of the maximal prefix of l of size smaller than n and the rest of the list *) let rec splitAt (#a:Type) (n:nat) (l:list a) : Tot (list a * list a) = if n = 0 then [], l else match l with | [] -> [], l | x :: xs -> let l1, l2 = splitAt (n-1) xs in x :: l1, l2 let rec lemma_splitAt_snd_length (#a:Type) (n:nat) (l:list a) : Lemma (requires (n <= length l)) (ensures (length (snd (splitAt n l)) = length l - n)) = match n, l with | 0, _ -> () | _, [] -> () | _, _ :: l' -> lemma_splitAt_snd_length (n - 1) l' (** [unsnoc] is an inverse of [snoc]. It splits a list into all-elements-except-last and last element. *) val unsnoc: #a:Type -> l:list a{length l > 0} -> Tot (list a * a) let unsnoc #a l = let l1, l2 = splitAt (length l - 1) l in lemma_splitAt_snd_length (length l - 1) l; l1, hd l2 (** [split3] splits a list into 3 parts. This allows easy access to the part of the list before and after the element, as well as the element itself. *) val split3: #a:Type -> l:list a -> i:nat{i < length l} -> Tot (list a * a * list a) let split3 #a l i = let a, rest = splitAt i l in lemma_splitAt_snd_length i l; let b :: c = rest in a, b, c (** Sorting (implemented as quicksort) **) (** [partition] splits a list [l] into two lists, the sum of whose lengths is the length of [l]. *) val partition_length: f:('a -> Tot bool) -> l:list 'a -> Lemma (requires True) (ensures (length (fst (partition f l)) + length (snd (partition f l)) = length l)) let rec partition_length f l = match l with | [] -> () | hd::tl -> partition_length f tl (** [bool_of_compare] turns a comparison function into a strict order. More precisely, [bool_of_compare compare x y] returns true if, and only if, [compare x y] is negative, meaning [x] precedes [y] in the ordering defined by compare. This is used in sorting, and is defined to be consistent with OCaml and F#, where sorting is performed in ascending order. *) val bool_of_compare : #a:Type -> (a -> a -> Tot int) -> a -> a -> Tot bool let bool_of_compare #a f x y = f x y < 0 (** [compare_of_bool] turns a strict order into a comparison function. More precisely, [compare_of_bool rel x y] returns a positive number if, and only if, x `rel` y holds. Inspired from OCaml, where polymorphic comparison using both the [compare] function and the (>) infix operator are such that [compare x y] is positive if, and only if, x > y. Requires, at type-checking time, [rel] to be a pure total function. *) val compare_of_bool : #a:eqtype -> (a -> a -> Tot bool) -> a -> a -> Tot int let compare_of_bool #a rel x y = if x `rel` y then -1 else if x = y then 0 else 1 let compare_of_bool_of_compare (#a:eqtype) (f:a -> a -> Tot bool) : Lemma (forall x y. bool_of_compare (compare_of_bool f) x y == f x y) = () (** [sortWith compare l] returns the list [l'] containing the elements of [l] sorted along the comparison function [compare], in such a way that if [compare x y > 0], then [x] appears before [y] in [l']. Sorts in ascending order *) val sortWith: ('a -> 'a -> Tot int) -> l:list 'a -> Tot (list 'a) (decreases (length l)) let rec sortWith f = function | [] -> [] | pivot::tl -> let hi, lo = partition (bool_of_compare f pivot) tl in partition_length (bool_of_compare f pivot) tl; append (sortWith f lo) (pivot::sortWith f hi) (** A l1 is a strict suffix of l2. *) let rec strict_suffix_of (#a: Type) (l1 l2: list a) : Pure Type0 (requires True) (ensures (fun _ -> True)) (decreases l2) = match l2 with | [] -> False | _ :: q -> l1 == q \/ l1 `strict_suffix_of` q
false
false
FStar.List.Tot.Base.fst
{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 1, "max_fuel": 8, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": true, "z3cliopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }
null
val strict_prefix_of : l1: Prims.list _ -> l2: Prims.list _ -> Prims.Pure Type0
[]
FStar.List.Tot.Base.strict_prefix_of
{ "file_name": "ulib/FStar.List.Tot.Base.fst", "git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f", "git_url": "https://github.com/FStarLang/FStar.git", "project_name": "FStar" }
l1: Prims.list _ -> l2: Prims.list _ -> Prims.Pure Type0
{ "end_col": 39, "end_line": 541, "start_col": 23, "start_line": 541 }
Prims.Tot
val bool_of_compare : #a:Type -> (a -> a -> Tot int) -> a -> a -> Tot bool
[ { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]
false
let bool_of_compare #a f x y = f x y < 0
val bool_of_compare : #a:Type -> (a -> a -> Tot int) -> a -> a -> Tot bool let bool_of_compare #a f x y =
false
null
false
f x y < 0
{ "checked_file": "FStar.List.Tot.Base.fst.checked", "dependencies": [ "prims.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Classical.fsti.checked" ], "interface_file": false, "source_file": "FStar.List.Tot.Base.fst" }
[ "total" ]
[ "Prims.int", "Prims.op_LessThan", "Prims.bool" ]
[]
(* Copyright 2008-2014 Nikhil Swamy and Microsoft Research Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License. *) (** This module defines all pure and total operations on lists that can be used in specifications. It is implemented by FStar_List_Tot_Base.ml, any functional change and/or the addition of new functions MUST be reflected there. @summary Pure total operations on lists *) module FStar.List.Tot.Base (** Base operations *) (** [isEmpty l] returns [true] if and only if [l] is empty *) val isEmpty: list 'a -> Tot bool let isEmpty l = match l with | [] -> true | _ -> false (** [hd l] returns the first element of [l]. Requires [l] to be nonempty, at type-checking time. Named as in: OCaml, F#, Coq *) val hd: l:list 'a{Cons? l} -> Tot 'a let hd = function | hd::_ -> hd (** [tail l] returns [l] without its first element. Requires, at type-checking time, that [l] be nonempty. Similar to: tl in OCaml, F#, Coq *) val tail: l:list 'a {Cons? l} -> Tot (list 'a) let tail = function | _::tl -> tl (** [tl l] returns [l] without its first element. Requires, at type-checking time, that [l] be nonempty. Named as in: OCaml, F#, Coq *) val tl: l:list 'a {Cons? l} -> Tot (list 'a) let tl = tail (** [last l] returns the last element of [l]. Requires, at type-checking time, that [l] be nonempty. Named as in: Haskell *) val last: l:list 'a {Cons? l} -> Tot 'a let rec last = function | [hd] -> hd | _::tl -> last tl (** [init l] returns [l] without its last element. Requires, at type-checking time, that [l] be nonempty. Named as in: Haskell *) val init: l:list 'a {Cons? l} -> Tot (list 'a) let rec init = function | [_] -> [] | hd::tl -> hd::(init tl) (** [length l] returns the total number of elements in [l]. Named as in: OCaml, F#, Coq *) val length: list 'a -> Tot nat let rec length = function | [] -> 0 | _::tl -> 1 + length tl (** [nth l n] returns the [n]-th element in list [l] (with the first element being the 0-th) if [l] is long enough, or [None] otherwise. Named as in: OCaml, F#, Coq *) val nth: list 'a -> nat -> Tot (option 'a) let rec nth l n = match l with | [] -> None | hd::tl -> if n = 0 then Some hd else nth tl (n - 1) (** [index l n] returns the [n]-th element in list [l] (with the first element being the 0-th). Requires, at type-checking time, that [l] be of length at least [n+1]. *) val index: #a:Type -> l:list a -> i:nat{i < length l} -> Tot a let rec index #a (l: list a) (i:nat{i < length l}): Tot a = if i = 0 then hd l else index (tl l) (i - 1) (** [count x l] returns the number of occurrences of [x] in [l]. Requires, at type-checking time, the type of [a] to have equality defined. Similar to: [List.count_occ] in Coq. *) val count: #a:eqtype -> a -> list a -> Tot nat let rec count #a x = function | [] -> 0 | hd::tl -> if x=hd then 1 + count x tl else count x tl (** [rev_acc l1 l2] appends the elements of [l1] to the beginning of [l2], in reverse order. It is equivalent to [append (rev l1) l2], but is tail-recursive. Similar to: [List.rev_append] in OCaml, Coq. *) val rev_acc: list 'a -> list 'a -> Tot (list 'a) let rec rev_acc l acc = match l with | [] -> acc | hd::tl -> rev_acc tl (hd::acc) (** [rev l] returns the list [l] in reverse order. Named as in: OCaml, F#, Coq. *) val rev: list 'a -> Tot (list 'a) let rev l = rev_acc l [] (** [append l1 l2] appends the elements of [l2] to the end of [l1]. Named as: OCaml, F#. Similar to: [List.app] in Coq. *) val append: list 'a -> list 'a -> Tot (list 'a) let rec append x y = match x with | [] -> y | a::tl -> a::append tl y (** Defines notation [@@] for [append], as in OCaml, F# . *) let op_At x y = append x y (** [snoc (l, x)] adds [x] to the end of the list [l]. Note: We use an uncurried [snoc (l, x)] instead of the curried [snoc l x]. This is intentional. If [snoc] takes a pair instead of 2 arguments, it allows for a better pattern on [lemma_unsnoc_snoc], which connects [snoc] and [unsnoc]. In particular, if we had two arguments, then either the pattern would either be too restrictive or would lead to over-triggering. More context for this can be seen in the (collapsed and uncollapsed) comments at https://github.com/FStarLang/FStar/pull/1560 *) val snoc: (list 'a * 'a) -> Tot (list 'a) let snoc (l, x) = append l [x] (** [flatten l], where [l] is a list of lists, returns the list of the elements of the lists in [l], preserving their order. Named as in: OCaml, Coq. *) val flatten: list (list 'a) -> Tot (list 'a) let rec flatten l = match l with | [] -> [] | hd::tl -> append hd (flatten tl) (** [map f l] applies [f] to each element of [l] and returns the list of results, in the order of the original elements in [l]. Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml, Coq, F# *) val map: ('a -> Tot 'b) -> list 'a -> Tot (list 'b) let rec map f x = match x with | [] -> [] | a::tl -> f a::map f tl (** [mapi_init f l n] applies, for each [k], [f (n+k)] to the [k]-th element of [l] and returns the list of results, in the order of the original elements in [l]. Requires, at type-checking time, [f] to be a pure total function. *) val mapi_init: (int -> 'a -> Tot 'b) -> list 'a -> int -> Tot (list 'b) let rec mapi_init f l i = match l with | [] -> [] | hd::tl -> (f i hd)::(mapi_init f tl (i+1)) (** [mapi f l] applies, for each [k], [f k] to the [k]-th element of [l] and returns the list of results, in the order of the original elements in [l]. Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml *) val mapi: (int -> 'a -> Tot 'b) -> list 'a -> Tot (list 'b) let mapi f l = mapi_init f l 0 (** [concatMap f l] applies [f] to each element of [l] and returns the concatenation of the results, in the order of the original elements of [l]. This is equivalent to [flatten (map f l)]. Requires, at type-checking time, [f] to be a pure total function. *) val concatMap: ('a -> Tot (list 'b)) -> list 'a -> Tot (list 'b) let rec concatMap f = function | [] -> [] | a::tl -> let fa = f a in let ftl = concatMap f tl in append fa ftl (** [fold_left f x [y1; y2; ...; yn]] computes (f (... (f x y1) y2) ... yn). Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml, Coq. *) val fold_left: ('a -> 'b -> Tot 'a) -> 'a -> l:list 'b -> Tot 'a (decreases l) let rec fold_left f x l = match l with | [] -> x | hd::tl -> fold_left f (f x hd) tl (** [fold_right f [x1; x2; ...; xn] y] computes (f x1 (f x2 (... (f xn y)) ... )). Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml, Coq *) val fold_right: ('a -> 'b -> Tot 'b) -> list 'a -> 'b -> Tot 'b let rec fold_right f l x = match l with | [] -> x | hd::tl -> f hd (fold_right f tl x) (** [fold_right_gtot] is just like [fold_right], except `f` is a ghost function **) let rec fold_right_gtot (#a:Type) (#b:Type) (l:list a) (f:a -> b -> GTot b) (x:b) : GTot b = match l with | [] -> x | hd::tl -> f hd (fold_right_gtot tl f x) (* We define map in terms of fold, to share simple lemmas *) let map_gtot #a #b (f:a -> GTot b) (x:list a) : GTot (list b) = fold_right_gtot x (fun x tl -> f x :: tl) [] (** [fold_left2 f x [y1; y2; ...; yn] [z1; z2; ...; zn]] computes (f (... (f x y1 z1) y2 z2) ... yn zn). Requires, at type-checking time, [f] to be a pure total function, and the lists [y1; y2; ...; yn] and [z1; z2; ...; zn] to have the same lengths. Named as in: OCaml *) val fold_left2 : f:('a -> 'b -> 'c -> Tot 'a) -> accu:'a -> l1:(list 'b) -> l2:(list 'c) -> Pure 'a (requires (length l1 == length l2)) (ensures (fun _ -> True)) (decreases l1) let rec fold_left2 f accu l1 l2 = match (l1, l2) with | ([], []) -> accu | (a1::l1, a2::l2) -> fold_left2 f (f accu a1 a2) l1 l2 (** Propositional membership (as in Coq). Does not require decidable equality. *) (** [memP x l] holds if, and only if, [x] appears as an element of [l]. Similar to: List.In in Coq. *) let rec memP (#a: Type) (x: a) (l: list a) : Tot Type0 = match l with | [] -> False | y :: q -> x == y \/ memP x q (** List searching **) (** [mem x l] returns [true] if, and only if, [x] appears as an element of [l]. Requires, at type-checking time, the type of elements of [l] to have decidable equality. Named as in: OCaml. See also: List.In in Coq, which is propositional. *) val mem: #a:eqtype -> a -> list a -> Tot bool let rec mem #a x = function | [] -> false | hd::tl -> if hd = x then true else mem x tl (** [contains x l] returns [true] if, and only if, [x] appears as an element of [l]. Requires, at type-checking time, the type of elements of [l] to have decidable equality. It is equivalent to: [mem x l]. TODO: should we rather swap the order of arguments? *) let contains : #a:eqtype -> a -> list a -> Tot bool = mem (** [existsb f l] returns [true] if, and only if, there exists some element [x] in [l] such that [f x] holds. *) val existsb: #a:Type -> f:(a -> Tot bool) -> list a -> Tot bool let rec existsb #a f l = match l with | [] -> false | hd::tl -> if f hd then true else existsb f tl (** [find f l] returns [Some x] for some element [x] appearing in [l] such that [f x] holds, or [None] only if no such [x] exists. *) val find: #a:Type -> f:(a -> Tot bool) -> list a -> Tot (option (x:a{f x})) let rec find #a f l = match l with | [] -> None #(x:a{f x}) //These type annotations are only present because it makes bootstrapping go much faster | hd::tl -> if f hd then Some #(x:a{f x}) hd else find f tl (** Filtering elements of a list [l] through a Boolean pure total predicate [f] *) (** [filter f l] returns [l] with all elements [x] such that [f x] does not hold removed. Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml, Coq *) val filter : #a: Type -> f:(a -> Tot bool) -> l: list a -> Tot (m:list a{forall x. memP x m ==> f x}) let rec filter #a f = function | [] -> [] | hd::tl -> if f hd then hd::filter f tl else filter f tl (** Postcondition on [filter f l]: for any element [x] of [filter f l], [f x] holds. Requires, at type-checking time, [f] to be a pure total function.*) val mem_filter (#a:Type) (f: (a -> Tot bool)) (l: list a) (x: a) : Lemma (requires (memP x (filter f l))) (ensures (f x)) let mem_filter f l x = () (** Postcondition on [filter f l]: stated with [forall]: for any element [x] of [filter f l], [f x] holds. Requires, at type-checking time, [f] to be a pure total function. *) val mem_filter_forall (#a:Type) (f: (a -> Tot bool)) (l: list a) : Lemma (requires True) (ensures (forall x . memP x (filter f l) ==> f x)) [SMTPat (filter f l)] let mem_filter_forall f l = FStar.Classical.ghost_lemma (mem_filter f l) (** [for_all f l] returns [true] if, and only if, for all elements [x] appearing in [l], [f x] holds. Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml. Similar to: List.forallb in Coq *) val for_all: ('a -> Tot bool) -> list 'a -> Tot bool let rec for_all f l = match l with | [] -> true | hd::tl -> if f hd then for_all f tl else false (** Specification for [for_all f l] vs. mem *) let rec for_all_mem (#a: Type) (f: (a -> Tot bool)) (l: list a) : Lemma (for_all f l <==> (forall x . memP x l ==> f x)) = match l with | [] -> () | _ :: q -> for_all_mem f q (** [collect f l] applies [f] to each element of [l] and returns the concatenation of the results, in the order of the original elements of [l]. It is equivalent to [flatten (map f l)]. Requires, at type-checking time, [f] to be a pure total function. TODO: what is the difference with [concatMap]? *) val collect: ('a -> Tot (list 'b)) -> list 'a -> Tot (list 'b) let rec collect f l = match l with | [] -> [] | hd::tl -> append (f hd) (collect f tl) (** [tryFind f l] returns [Some x] for some element [x] appearing in [l] such that [f x] holds, or [None] only if no such [x] exists. Requires, at type-checking time, [f] to be a pure total function. Contrary to [find], [tryFind] provides no postcondition on its result. *) val tryFind: ('a -> Tot bool) -> list 'a -> Tot (option 'a) let rec tryFind p l = match l with | [] -> None | hd::tl -> if p hd then Some hd else tryFind p tl (** [tryPick f l] returns [y] for some element [x] appearing in [l] such that [f x = Some y] for some y, or [None] only if [f x = None] for all elements [x] of [l]. Requires, at type-checking time, [f] to be a pure total function. *) val tryPick: ('a -> Tot (option 'b)) -> list 'a -> Tot (option 'b) let rec tryPick f l = match l with | [] -> None | hd::tl -> match f hd with | Some x -> Some x | None -> tryPick f tl (** [choose f l] returns the list of [y] for all elements [x] appearing in [l] such that [f x = Some y] for some [y]. Requires, at type-checking time, [f] to be a pure total function. *) val choose: ('a -> Tot (option 'b)) -> list 'a -> Tot (list 'b) let rec choose f l = match l with | [] -> [] | hd::tl -> match f hd with | Some x -> x::(choose f tl) | None -> choose f tl (** [partition f l] returns the pair of lists [(l1, l2)] where all elements [x] of [l] are in [l1] if [f x] holds, and in [l2] otherwise. Both [l1] and [l2] retain the original order of [l]. Requires, at type-checking time, [f] to be a pure total function. *) val partition: f:('a -> Tot bool) -> list 'a -> Tot (list 'a * list 'a) let rec partition f = function | [] -> [], [] | hd::tl -> let l1, l2 = partition f tl in if f hd then hd::l1, l2 else l1, hd::l2 (** [subset la lb] is true if and only if all the elements from [la] are also in [lb]. Requires, at type-checking time, the type of elements of [la] and [lb] to have decidable equality. *) val subset: #a:eqtype -> list a -> list a -> Tot bool let rec subset #a la lb = match la with | [] -> true | h :: tl -> mem h lb && subset tl lb (** [noRepeats l] returns [true] if, and only if, no element of [l] appears in [l] more than once. Requires, at type-checking time, the type of elements of [la] and [lb] to have decidable equality. *) val noRepeats : #a:eqtype -> list a -> Tot bool let rec noRepeats #a la = match la with | [] -> true | h :: tl -> not(mem h tl) && noRepeats tl (** [no_repeats_p l] valid if, and only if, no element of [l] appears in [l] more than once. *) val no_repeats_p : #a:Type -> list a -> Tot prop let rec no_repeats_p #a la = match la with | [] -> True | h :: tl -> ~(memP h tl) /\ no_repeats_p tl (** List of tuples **) (** [assoc x l] returns [Some y] where [(x, y)] is the first element of [l] whose first element is [x], or [None] only if no such element exists. Requires, at type-checking time, the type of [x] to have decidable equality. Named as in: OCaml. *) val assoc: #a:eqtype -> #b:Type -> a -> list (a * b) -> Tot (option b) let rec assoc #a #b x = function | [] -> None | (x', y)::tl -> if x=x' then Some y else assoc x tl (** [split] takes a list of pairs [(x1, y1), ..., (xn, yn)] and returns the pair of lists ([x1, ..., xn], [y1, ..., yn]). Named as in: OCaml *) val split: list ('a * 'b) -> Tot (list 'a * list 'b) let rec split l = match l with | [] -> ([],[]) | (hd1,hd2)::tl -> let (tl1,tl2) = split tl in (hd1::tl1,hd2::tl2) (** [unzip] takes a list of pairs [(x1, y1), ..., (xn, yn)] and returns the pair of lists ([x1, ..., xn], [y1, ..., yn]). Named as in: Haskell *) let unzip l = split l (** [unzip3] takes a list of triples [(x1, y1, z1), ..., (xn, yn, zn)] and returns the triple of lists ([x1, ..., xn], [y1, ..., yn], [z1, ..., zn]). Named as in: Haskell *) val unzip3: list ('a * 'b * 'c) -> Tot (list 'a * list 'b * list 'c) let rec unzip3 l = match l with | [] -> ([],[],[]) | (hd1,hd2,hd3)::tl -> let (tl1,tl2,tl3) = unzip3 tl in (hd1::tl1,hd2::tl2,hd3::tl3) (** Splitting a list at some index **) (** [splitAt] takes a natural number n and a list and returns a pair of the maximal prefix of l of size smaller than n and the rest of the list *) let rec splitAt (#a:Type) (n:nat) (l:list a) : Tot (list a * list a) = if n = 0 then [], l else match l with | [] -> [], l | x :: xs -> let l1, l2 = splitAt (n-1) xs in x :: l1, l2 let rec lemma_splitAt_snd_length (#a:Type) (n:nat) (l:list a) : Lemma (requires (n <= length l)) (ensures (length (snd (splitAt n l)) = length l - n)) = match n, l with | 0, _ -> () | _, [] -> () | _, _ :: l' -> lemma_splitAt_snd_length (n - 1) l' (** [unsnoc] is an inverse of [snoc]. It splits a list into all-elements-except-last and last element. *) val unsnoc: #a:Type -> l:list a{length l > 0} -> Tot (list a * a) let unsnoc #a l = let l1, l2 = splitAt (length l - 1) l in lemma_splitAt_snd_length (length l - 1) l; l1, hd l2 (** [split3] splits a list into 3 parts. This allows easy access to the part of the list before and after the element, as well as the element itself. *) val split3: #a:Type -> l:list a -> i:nat{i < length l} -> Tot (list a * a * list a) let split3 #a l i = let a, rest = splitAt i l in lemma_splitAt_snd_length i l; let b :: c = rest in a, b, c (** Sorting (implemented as quicksort) **) (** [partition] splits a list [l] into two lists, the sum of whose lengths is the length of [l]. *) val partition_length: f:('a -> Tot bool) -> l:list 'a -> Lemma (requires True) (ensures (length (fst (partition f l)) + length (snd (partition f l)) = length l)) let rec partition_length f l = match l with | [] -> () | hd::tl -> partition_length f tl (** [bool_of_compare] turns a comparison function into a strict order. More precisely, [bool_of_compare compare x y] returns true if, and only if, [compare x y] is negative, meaning [x] precedes [y] in the ordering defined by compare. This is used in sorting, and is defined to be consistent with OCaml and F#, where sorting is performed in ascending order. *)
false
false
FStar.List.Tot.Base.fst
{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 1, "max_fuel": 8, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": true, "z3cliopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }
null
val bool_of_compare : #a:Type -> (a -> a -> Tot int) -> a -> a -> Tot bool
[]
FStar.List.Tot.Base.bool_of_compare
{ "file_name": "ulib/FStar.List.Tot.Base.fst", "git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f", "git_url": "https://github.com/FStarLang/FStar.git", "project_name": "FStar" }
f: (_: a -> _: a -> Prims.int) -> x: a -> y: a -> Prims.bool
{ "end_col": 40, "end_line": 499, "start_col": 31, "start_line": 499 }
Prims.Tot
[ { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]
false
let unzip l = split l
let unzip l =
false
null
false
split l
{ "checked_file": "FStar.List.Tot.Base.fst.checked", "dependencies": [ "prims.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Classical.fsti.checked" ], "interface_file": false, "source_file": "FStar.List.Tot.Base.fst" }
[ "total" ]
[ "Prims.list", "FStar.Pervasives.Native.tuple2", "FStar.List.Tot.Base.split" ]
[]
(* Copyright 2008-2014 Nikhil Swamy and Microsoft Research Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License. *) (** This module defines all pure and total operations on lists that can be used in specifications. It is implemented by FStar_List_Tot_Base.ml, any functional change and/or the addition of new functions MUST be reflected there. @summary Pure total operations on lists *) module FStar.List.Tot.Base (** Base operations *) (** [isEmpty l] returns [true] if and only if [l] is empty *) val isEmpty: list 'a -> Tot bool let isEmpty l = match l with | [] -> true | _ -> false (** [hd l] returns the first element of [l]. Requires [l] to be nonempty, at type-checking time. Named as in: OCaml, F#, Coq *) val hd: l:list 'a{Cons? l} -> Tot 'a let hd = function | hd::_ -> hd (** [tail l] returns [l] without its first element. Requires, at type-checking time, that [l] be nonempty. Similar to: tl in OCaml, F#, Coq *) val tail: l:list 'a {Cons? l} -> Tot (list 'a) let tail = function | _::tl -> tl (** [tl l] returns [l] without its first element. Requires, at type-checking time, that [l] be nonempty. Named as in: OCaml, F#, Coq *) val tl: l:list 'a {Cons? l} -> Tot (list 'a) let tl = tail (** [last l] returns the last element of [l]. Requires, at type-checking time, that [l] be nonempty. Named as in: Haskell *) val last: l:list 'a {Cons? l} -> Tot 'a let rec last = function | [hd] -> hd | _::tl -> last tl (** [init l] returns [l] without its last element. Requires, at type-checking time, that [l] be nonempty. Named as in: Haskell *) val init: l:list 'a {Cons? l} -> Tot (list 'a) let rec init = function | [_] -> [] | hd::tl -> hd::(init tl) (** [length l] returns the total number of elements in [l]. Named as in: OCaml, F#, Coq *) val length: list 'a -> Tot nat let rec length = function | [] -> 0 | _::tl -> 1 + length tl (** [nth l n] returns the [n]-th element in list [l] (with the first element being the 0-th) if [l] is long enough, or [None] otherwise. Named as in: OCaml, F#, Coq *) val nth: list 'a -> nat -> Tot (option 'a) let rec nth l n = match l with | [] -> None | hd::tl -> if n = 0 then Some hd else nth tl (n - 1) (** [index l n] returns the [n]-th element in list [l] (with the first element being the 0-th). Requires, at type-checking time, that [l] be of length at least [n+1]. *) val index: #a:Type -> l:list a -> i:nat{i < length l} -> Tot a let rec index #a (l: list a) (i:nat{i < length l}): Tot a = if i = 0 then hd l else index (tl l) (i - 1) (** [count x l] returns the number of occurrences of [x] in [l]. Requires, at type-checking time, the type of [a] to have equality defined. Similar to: [List.count_occ] in Coq. *) val count: #a:eqtype -> a -> list a -> Tot nat let rec count #a x = function | [] -> 0 | hd::tl -> if x=hd then 1 + count x tl else count x tl (** [rev_acc l1 l2] appends the elements of [l1] to the beginning of [l2], in reverse order. It is equivalent to [append (rev l1) l2], but is tail-recursive. Similar to: [List.rev_append] in OCaml, Coq. *) val rev_acc: list 'a -> list 'a -> Tot (list 'a) let rec rev_acc l acc = match l with | [] -> acc | hd::tl -> rev_acc tl (hd::acc) (** [rev l] returns the list [l] in reverse order. Named as in: OCaml, F#, Coq. *) val rev: list 'a -> Tot (list 'a) let rev l = rev_acc l [] (** [append l1 l2] appends the elements of [l2] to the end of [l1]. Named as: OCaml, F#. Similar to: [List.app] in Coq. *) val append: list 'a -> list 'a -> Tot (list 'a) let rec append x y = match x with | [] -> y | a::tl -> a::append tl y (** Defines notation [@@] for [append], as in OCaml, F# . *) let op_At x y = append x y (** [snoc (l, x)] adds [x] to the end of the list [l]. Note: We use an uncurried [snoc (l, x)] instead of the curried [snoc l x]. This is intentional. If [snoc] takes a pair instead of 2 arguments, it allows for a better pattern on [lemma_unsnoc_snoc], which connects [snoc] and [unsnoc]. In particular, if we had two arguments, then either the pattern would either be too restrictive or would lead to over-triggering. More context for this can be seen in the (collapsed and uncollapsed) comments at https://github.com/FStarLang/FStar/pull/1560 *) val snoc: (list 'a * 'a) -> Tot (list 'a) let snoc (l, x) = append l [x] (** [flatten l], where [l] is a list of lists, returns the list of the elements of the lists in [l], preserving their order. Named as in: OCaml, Coq. *) val flatten: list (list 'a) -> Tot (list 'a) let rec flatten l = match l with | [] -> [] | hd::tl -> append hd (flatten tl) (** [map f l] applies [f] to each element of [l] and returns the list of results, in the order of the original elements in [l]. Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml, Coq, F# *) val map: ('a -> Tot 'b) -> list 'a -> Tot (list 'b) let rec map f x = match x with | [] -> [] | a::tl -> f a::map f tl (** [mapi_init f l n] applies, for each [k], [f (n+k)] to the [k]-th element of [l] and returns the list of results, in the order of the original elements in [l]. Requires, at type-checking time, [f] to be a pure total function. *) val mapi_init: (int -> 'a -> Tot 'b) -> list 'a -> int -> Tot (list 'b) let rec mapi_init f l i = match l with | [] -> [] | hd::tl -> (f i hd)::(mapi_init f tl (i+1)) (** [mapi f l] applies, for each [k], [f k] to the [k]-th element of [l] and returns the list of results, in the order of the original elements in [l]. Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml *) val mapi: (int -> 'a -> Tot 'b) -> list 'a -> Tot (list 'b) let mapi f l = mapi_init f l 0 (** [concatMap f l] applies [f] to each element of [l] and returns the concatenation of the results, in the order of the original elements of [l]. This is equivalent to [flatten (map f l)]. Requires, at type-checking time, [f] to be a pure total function. *) val concatMap: ('a -> Tot (list 'b)) -> list 'a -> Tot (list 'b) let rec concatMap f = function | [] -> [] | a::tl -> let fa = f a in let ftl = concatMap f tl in append fa ftl (** [fold_left f x [y1; y2; ...; yn]] computes (f (... (f x y1) y2) ... yn). Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml, Coq. *) val fold_left: ('a -> 'b -> Tot 'a) -> 'a -> l:list 'b -> Tot 'a (decreases l) let rec fold_left f x l = match l with | [] -> x | hd::tl -> fold_left f (f x hd) tl (** [fold_right f [x1; x2; ...; xn] y] computes (f x1 (f x2 (... (f xn y)) ... )). Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml, Coq *) val fold_right: ('a -> 'b -> Tot 'b) -> list 'a -> 'b -> Tot 'b let rec fold_right f l x = match l with | [] -> x | hd::tl -> f hd (fold_right f tl x) (** [fold_right_gtot] is just like [fold_right], except `f` is a ghost function **) let rec fold_right_gtot (#a:Type) (#b:Type) (l:list a) (f:a -> b -> GTot b) (x:b) : GTot b = match l with | [] -> x | hd::tl -> f hd (fold_right_gtot tl f x) (* We define map in terms of fold, to share simple lemmas *) let map_gtot #a #b (f:a -> GTot b) (x:list a) : GTot (list b) = fold_right_gtot x (fun x tl -> f x :: tl) [] (** [fold_left2 f x [y1; y2; ...; yn] [z1; z2; ...; zn]] computes (f (... (f x y1 z1) y2 z2) ... yn zn). Requires, at type-checking time, [f] to be a pure total function, and the lists [y1; y2; ...; yn] and [z1; z2; ...; zn] to have the same lengths. Named as in: OCaml *) val fold_left2 : f:('a -> 'b -> 'c -> Tot 'a) -> accu:'a -> l1:(list 'b) -> l2:(list 'c) -> Pure 'a (requires (length l1 == length l2)) (ensures (fun _ -> True)) (decreases l1) let rec fold_left2 f accu l1 l2 = match (l1, l2) with | ([], []) -> accu | (a1::l1, a2::l2) -> fold_left2 f (f accu a1 a2) l1 l2 (** Propositional membership (as in Coq). Does not require decidable equality. *) (** [memP x l] holds if, and only if, [x] appears as an element of [l]. Similar to: List.In in Coq. *) let rec memP (#a: Type) (x: a) (l: list a) : Tot Type0 = match l with | [] -> False | y :: q -> x == y \/ memP x q (** List searching **) (** [mem x l] returns [true] if, and only if, [x] appears as an element of [l]. Requires, at type-checking time, the type of elements of [l] to have decidable equality. Named as in: OCaml. See also: List.In in Coq, which is propositional. *) val mem: #a:eqtype -> a -> list a -> Tot bool let rec mem #a x = function | [] -> false | hd::tl -> if hd = x then true else mem x tl (** [contains x l] returns [true] if, and only if, [x] appears as an element of [l]. Requires, at type-checking time, the type of elements of [l] to have decidable equality. It is equivalent to: [mem x l]. TODO: should we rather swap the order of arguments? *) let contains : #a:eqtype -> a -> list a -> Tot bool = mem (** [existsb f l] returns [true] if, and only if, there exists some element [x] in [l] such that [f x] holds. *) val existsb: #a:Type -> f:(a -> Tot bool) -> list a -> Tot bool let rec existsb #a f l = match l with | [] -> false | hd::tl -> if f hd then true else existsb f tl (** [find f l] returns [Some x] for some element [x] appearing in [l] such that [f x] holds, or [None] only if no such [x] exists. *) val find: #a:Type -> f:(a -> Tot bool) -> list a -> Tot (option (x:a{f x})) let rec find #a f l = match l with | [] -> None #(x:a{f x}) //These type annotations are only present because it makes bootstrapping go much faster | hd::tl -> if f hd then Some #(x:a{f x}) hd else find f tl (** Filtering elements of a list [l] through a Boolean pure total predicate [f] *) (** [filter f l] returns [l] with all elements [x] such that [f x] does not hold removed. Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml, Coq *) val filter : #a: Type -> f:(a -> Tot bool) -> l: list a -> Tot (m:list a{forall x. memP x m ==> f x}) let rec filter #a f = function | [] -> [] | hd::tl -> if f hd then hd::filter f tl else filter f tl (** Postcondition on [filter f l]: for any element [x] of [filter f l], [f x] holds. Requires, at type-checking time, [f] to be a pure total function.*) val mem_filter (#a:Type) (f: (a -> Tot bool)) (l: list a) (x: a) : Lemma (requires (memP x (filter f l))) (ensures (f x)) let mem_filter f l x = () (** Postcondition on [filter f l]: stated with [forall]: for any element [x] of [filter f l], [f x] holds. Requires, at type-checking time, [f] to be a pure total function. *) val mem_filter_forall (#a:Type) (f: (a -> Tot bool)) (l: list a) : Lemma (requires True) (ensures (forall x . memP x (filter f l) ==> f x)) [SMTPat (filter f l)] let mem_filter_forall f l = FStar.Classical.ghost_lemma (mem_filter f l) (** [for_all f l] returns [true] if, and only if, for all elements [x] appearing in [l], [f x] holds. Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml. Similar to: List.forallb in Coq *) val for_all: ('a -> Tot bool) -> list 'a -> Tot bool let rec for_all f l = match l with | [] -> true | hd::tl -> if f hd then for_all f tl else false (** Specification for [for_all f l] vs. mem *) let rec for_all_mem (#a: Type) (f: (a -> Tot bool)) (l: list a) : Lemma (for_all f l <==> (forall x . memP x l ==> f x)) = match l with | [] -> () | _ :: q -> for_all_mem f q (** [collect f l] applies [f] to each element of [l] and returns the concatenation of the results, in the order of the original elements of [l]. It is equivalent to [flatten (map f l)]. Requires, at type-checking time, [f] to be a pure total function. TODO: what is the difference with [concatMap]? *) val collect: ('a -> Tot (list 'b)) -> list 'a -> Tot (list 'b) let rec collect f l = match l with | [] -> [] | hd::tl -> append (f hd) (collect f tl) (** [tryFind f l] returns [Some x] for some element [x] appearing in [l] such that [f x] holds, or [None] only if no such [x] exists. Requires, at type-checking time, [f] to be a pure total function. Contrary to [find], [tryFind] provides no postcondition on its result. *) val tryFind: ('a -> Tot bool) -> list 'a -> Tot (option 'a) let rec tryFind p l = match l with | [] -> None | hd::tl -> if p hd then Some hd else tryFind p tl (** [tryPick f l] returns [y] for some element [x] appearing in [l] such that [f x = Some y] for some y, or [None] only if [f x = None] for all elements [x] of [l]. Requires, at type-checking time, [f] to be a pure total function. *) val tryPick: ('a -> Tot (option 'b)) -> list 'a -> Tot (option 'b) let rec tryPick f l = match l with | [] -> None | hd::tl -> match f hd with | Some x -> Some x | None -> tryPick f tl (** [choose f l] returns the list of [y] for all elements [x] appearing in [l] such that [f x = Some y] for some [y]. Requires, at type-checking time, [f] to be a pure total function. *) val choose: ('a -> Tot (option 'b)) -> list 'a -> Tot (list 'b) let rec choose f l = match l with | [] -> [] | hd::tl -> match f hd with | Some x -> x::(choose f tl) | None -> choose f tl (** [partition f l] returns the pair of lists [(l1, l2)] where all elements [x] of [l] are in [l1] if [f x] holds, and in [l2] otherwise. Both [l1] and [l2] retain the original order of [l]. Requires, at type-checking time, [f] to be a pure total function. *) val partition: f:('a -> Tot bool) -> list 'a -> Tot (list 'a * list 'a) let rec partition f = function | [] -> [], [] | hd::tl -> let l1, l2 = partition f tl in if f hd then hd::l1, l2 else l1, hd::l2 (** [subset la lb] is true if and only if all the elements from [la] are also in [lb]. Requires, at type-checking time, the type of elements of [la] and [lb] to have decidable equality. *) val subset: #a:eqtype -> list a -> list a -> Tot bool let rec subset #a la lb = match la with | [] -> true | h :: tl -> mem h lb && subset tl lb (** [noRepeats l] returns [true] if, and only if, no element of [l] appears in [l] more than once. Requires, at type-checking time, the type of elements of [la] and [lb] to have decidable equality. *) val noRepeats : #a:eqtype -> list a -> Tot bool let rec noRepeats #a la = match la with | [] -> true | h :: tl -> not(mem h tl) && noRepeats tl (** [no_repeats_p l] valid if, and only if, no element of [l] appears in [l] more than once. *) val no_repeats_p : #a:Type -> list a -> Tot prop let rec no_repeats_p #a la = match la with | [] -> True | h :: tl -> ~(memP h tl) /\ no_repeats_p tl (** List of tuples **) (** [assoc x l] returns [Some y] where [(x, y)] is the first element of [l] whose first element is [x], or [None] only if no such element exists. Requires, at type-checking time, the type of [x] to have decidable equality. Named as in: OCaml. *) val assoc: #a:eqtype -> #b:Type -> a -> list (a * b) -> Tot (option b) let rec assoc #a #b x = function | [] -> None | (x', y)::tl -> if x=x' then Some y else assoc x tl (** [split] takes a list of pairs [(x1, y1), ..., (xn, yn)] and returns the pair of lists ([x1, ..., xn], [y1, ..., yn]). Named as in: OCaml *) val split: list ('a * 'b) -> Tot (list 'a * list 'b) let rec split l = match l with | [] -> ([],[]) | (hd1,hd2)::tl -> let (tl1,tl2) = split tl in (hd1::tl1,hd2::tl2) (** [unzip] takes a list of pairs [(x1, y1), ..., (xn, yn)] and returns the pair of lists ([x1, ..., xn], [y1, ..., yn]). Named as in:
false
false
FStar.List.Tot.Base.fst
{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 1, "max_fuel": 8, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": true, "z3cliopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }
null
val unzip : l: Prims.list (_ * _) -> Prims.list _ * Prims.list _
[]
FStar.List.Tot.Base.unzip
{ "file_name": "ulib/FStar.List.Tot.Base.fst", "git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f", "git_url": "https://github.com/FStarLang/FStar.git", "project_name": "FStar" }
l: Prims.list (_ * _) -> Prims.list _ * Prims.list _
{ "end_col": 21, "end_line": 426, "start_col": 14, "start_line": 426 }
FStar.Pervasives.Lemma
val mem_filter_forall (#a:Type) (f: (a -> Tot bool)) (l: list a) : Lemma (requires True) (ensures (forall x . memP x (filter f l) ==> f x)) [SMTPat (filter f l)]
[ { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]
false
let mem_filter_forall f l = FStar.Classical.ghost_lemma (mem_filter f l)
val mem_filter_forall (#a:Type) (f: (a -> Tot bool)) (l: list a) : Lemma (requires True) (ensures (forall x . memP x (filter f l) ==> f x)) [SMTPat (filter f l)] let mem_filter_forall f l =
false
null
true
FStar.Classical.ghost_lemma (mem_filter f l)
{ "checked_file": "FStar.List.Tot.Base.fst.checked", "dependencies": [ "prims.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Classical.fsti.checked" ], "interface_file": false, "source_file": "FStar.List.Tot.Base.fst" }
[ "lemma" ]
[ "Prims.bool", "Prims.list", "FStar.Classical.ghost_lemma", "FStar.List.Tot.Base.memP", "FStar.List.Tot.Base.filter", "Prims.unit", "Prims.b2t", "FStar.List.Tot.Base.mem_filter" ]
[]
(* Copyright 2008-2014 Nikhil Swamy and Microsoft Research Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License. *) (** This module defines all pure and total operations on lists that can be used in specifications. It is implemented by FStar_List_Tot_Base.ml, any functional change and/or the addition of new functions MUST be reflected there. @summary Pure total operations on lists *) module FStar.List.Tot.Base (** Base operations *) (** [isEmpty l] returns [true] if and only if [l] is empty *) val isEmpty: list 'a -> Tot bool let isEmpty l = match l with | [] -> true | _ -> false (** [hd l] returns the first element of [l]. Requires [l] to be nonempty, at type-checking time. Named as in: OCaml, F#, Coq *) val hd: l:list 'a{Cons? l} -> Tot 'a let hd = function | hd::_ -> hd (** [tail l] returns [l] without its first element. Requires, at type-checking time, that [l] be nonempty. Similar to: tl in OCaml, F#, Coq *) val tail: l:list 'a {Cons? l} -> Tot (list 'a) let tail = function | _::tl -> tl (** [tl l] returns [l] without its first element. Requires, at type-checking time, that [l] be nonempty. Named as in: OCaml, F#, Coq *) val tl: l:list 'a {Cons? l} -> Tot (list 'a) let tl = tail (** [last l] returns the last element of [l]. Requires, at type-checking time, that [l] be nonempty. Named as in: Haskell *) val last: l:list 'a {Cons? l} -> Tot 'a let rec last = function | [hd] -> hd | _::tl -> last tl (** [init l] returns [l] without its last element. Requires, at type-checking time, that [l] be nonempty. Named as in: Haskell *) val init: l:list 'a {Cons? l} -> Tot (list 'a) let rec init = function | [_] -> [] | hd::tl -> hd::(init tl) (** [length l] returns the total number of elements in [l]. Named as in: OCaml, F#, Coq *) val length: list 'a -> Tot nat let rec length = function | [] -> 0 | _::tl -> 1 + length tl (** [nth l n] returns the [n]-th element in list [l] (with the first element being the 0-th) if [l] is long enough, or [None] otherwise. Named as in: OCaml, F#, Coq *) val nth: list 'a -> nat -> Tot (option 'a) let rec nth l n = match l with | [] -> None | hd::tl -> if n = 0 then Some hd else nth tl (n - 1) (** [index l n] returns the [n]-th element in list [l] (with the first element being the 0-th). Requires, at type-checking time, that [l] be of length at least [n+1]. *) val index: #a:Type -> l:list a -> i:nat{i < length l} -> Tot a let rec index #a (l: list a) (i:nat{i < length l}): Tot a = if i = 0 then hd l else index (tl l) (i - 1) (** [count x l] returns the number of occurrences of [x] in [l]. Requires, at type-checking time, the type of [a] to have equality defined. Similar to: [List.count_occ] in Coq. *) val count: #a:eqtype -> a -> list a -> Tot nat let rec count #a x = function | [] -> 0 | hd::tl -> if x=hd then 1 + count x tl else count x tl (** [rev_acc l1 l2] appends the elements of [l1] to the beginning of [l2], in reverse order. It is equivalent to [append (rev l1) l2], but is tail-recursive. Similar to: [List.rev_append] in OCaml, Coq. *) val rev_acc: list 'a -> list 'a -> Tot (list 'a) let rec rev_acc l acc = match l with | [] -> acc | hd::tl -> rev_acc tl (hd::acc) (** [rev l] returns the list [l] in reverse order. Named as in: OCaml, F#, Coq. *) val rev: list 'a -> Tot (list 'a) let rev l = rev_acc l [] (** [append l1 l2] appends the elements of [l2] to the end of [l1]. Named as: OCaml, F#. Similar to: [List.app] in Coq. *) val append: list 'a -> list 'a -> Tot (list 'a) let rec append x y = match x with | [] -> y | a::tl -> a::append tl y (** Defines notation [@@] for [append], as in OCaml, F# . *) let op_At x y = append x y (** [snoc (l, x)] adds [x] to the end of the list [l]. Note: We use an uncurried [snoc (l, x)] instead of the curried [snoc l x]. This is intentional. If [snoc] takes a pair instead of 2 arguments, it allows for a better pattern on [lemma_unsnoc_snoc], which connects [snoc] and [unsnoc]. In particular, if we had two arguments, then either the pattern would either be too restrictive or would lead to over-triggering. More context for this can be seen in the (collapsed and uncollapsed) comments at https://github.com/FStarLang/FStar/pull/1560 *) val snoc: (list 'a * 'a) -> Tot (list 'a) let snoc (l, x) = append l [x] (** [flatten l], where [l] is a list of lists, returns the list of the elements of the lists in [l], preserving their order. Named as in: OCaml, Coq. *) val flatten: list (list 'a) -> Tot (list 'a) let rec flatten l = match l with | [] -> [] | hd::tl -> append hd (flatten tl) (** [map f l] applies [f] to each element of [l] and returns the list of results, in the order of the original elements in [l]. Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml, Coq, F# *) val map: ('a -> Tot 'b) -> list 'a -> Tot (list 'b) let rec map f x = match x with | [] -> [] | a::tl -> f a::map f tl (** [mapi_init f l n] applies, for each [k], [f (n+k)] to the [k]-th element of [l] and returns the list of results, in the order of the original elements in [l]. Requires, at type-checking time, [f] to be a pure total function. *) val mapi_init: (int -> 'a -> Tot 'b) -> list 'a -> int -> Tot (list 'b) let rec mapi_init f l i = match l with | [] -> [] | hd::tl -> (f i hd)::(mapi_init f tl (i+1)) (** [mapi f l] applies, for each [k], [f k] to the [k]-th element of [l] and returns the list of results, in the order of the original elements in [l]. Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml *) val mapi: (int -> 'a -> Tot 'b) -> list 'a -> Tot (list 'b) let mapi f l = mapi_init f l 0 (** [concatMap f l] applies [f] to each element of [l] and returns the concatenation of the results, in the order of the original elements of [l]. This is equivalent to [flatten (map f l)]. Requires, at type-checking time, [f] to be a pure total function. *) val concatMap: ('a -> Tot (list 'b)) -> list 'a -> Tot (list 'b) let rec concatMap f = function | [] -> [] | a::tl -> let fa = f a in let ftl = concatMap f tl in append fa ftl (** [fold_left f x [y1; y2; ...; yn]] computes (f (... (f x y1) y2) ... yn). Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml, Coq. *) val fold_left: ('a -> 'b -> Tot 'a) -> 'a -> l:list 'b -> Tot 'a (decreases l) let rec fold_left f x l = match l with | [] -> x | hd::tl -> fold_left f (f x hd) tl (** [fold_right f [x1; x2; ...; xn] y] computes (f x1 (f x2 (... (f xn y)) ... )). Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml, Coq *) val fold_right: ('a -> 'b -> Tot 'b) -> list 'a -> 'b -> Tot 'b let rec fold_right f l x = match l with | [] -> x | hd::tl -> f hd (fold_right f tl x) (** [fold_right_gtot] is just like [fold_right], except `f` is a ghost function **) let rec fold_right_gtot (#a:Type) (#b:Type) (l:list a) (f:a -> b -> GTot b) (x:b) : GTot b = match l with | [] -> x | hd::tl -> f hd (fold_right_gtot tl f x) (* We define map in terms of fold, to share simple lemmas *) let map_gtot #a #b (f:a -> GTot b) (x:list a) : GTot (list b) = fold_right_gtot x (fun x tl -> f x :: tl) [] (** [fold_left2 f x [y1; y2; ...; yn] [z1; z2; ...; zn]] computes (f (... (f x y1 z1) y2 z2) ... yn zn). Requires, at type-checking time, [f] to be a pure total function, and the lists [y1; y2; ...; yn] and [z1; z2; ...; zn] to have the same lengths. Named as in: OCaml *) val fold_left2 : f:('a -> 'b -> 'c -> Tot 'a) -> accu:'a -> l1:(list 'b) -> l2:(list 'c) -> Pure 'a (requires (length l1 == length l2)) (ensures (fun _ -> True)) (decreases l1) let rec fold_left2 f accu l1 l2 = match (l1, l2) with | ([], []) -> accu | (a1::l1, a2::l2) -> fold_left2 f (f accu a1 a2) l1 l2 (** Propositional membership (as in Coq). Does not require decidable equality. *) (** [memP x l] holds if, and only if, [x] appears as an element of [l]. Similar to: List.In in Coq. *) let rec memP (#a: Type) (x: a) (l: list a) : Tot Type0 = match l with | [] -> False | y :: q -> x == y \/ memP x q (** List searching **) (** [mem x l] returns [true] if, and only if, [x] appears as an element of [l]. Requires, at type-checking time, the type of elements of [l] to have decidable equality. Named as in: OCaml. See also: List.In in Coq, which is propositional. *) val mem: #a:eqtype -> a -> list a -> Tot bool let rec mem #a x = function | [] -> false | hd::tl -> if hd = x then true else mem x tl (** [contains x l] returns [true] if, and only if, [x] appears as an element of [l]. Requires, at type-checking time, the type of elements of [l] to have decidable equality. It is equivalent to: [mem x l]. TODO: should we rather swap the order of arguments? *) let contains : #a:eqtype -> a -> list a -> Tot bool = mem (** [existsb f l] returns [true] if, and only if, there exists some element [x] in [l] such that [f x] holds. *) val existsb: #a:Type -> f:(a -> Tot bool) -> list a -> Tot bool let rec existsb #a f l = match l with | [] -> false | hd::tl -> if f hd then true else existsb f tl (** [find f l] returns [Some x] for some element [x] appearing in [l] such that [f x] holds, or [None] only if no such [x] exists. *) val find: #a:Type -> f:(a -> Tot bool) -> list a -> Tot (option (x:a{f x})) let rec find #a f l = match l with | [] -> None #(x:a{f x}) //These type annotations are only present because it makes bootstrapping go much faster | hd::tl -> if f hd then Some #(x:a{f x}) hd else find f tl (** Filtering elements of a list [l] through a Boolean pure total predicate [f] *) (** [filter f l] returns [l] with all elements [x] such that [f x] does not hold removed. Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml, Coq *) val filter : #a: Type -> f:(a -> Tot bool) -> l: list a -> Tot (m:list a{forall x. memP x m ==> f x}) let rec filter #a f = function | [] -> [] | hd::tl -> if f hd then hd::filter f tl else filter f tl (** Postcondition on [filter f l]: for any element [x] of [filter f l], [f x] holds. Requires, at type-checking time, [f] to be a pure total function.*) val mem_filter (#a:Type) (f: (a -> Tot bool)) (l: list a) (x: a) : Lemma (requires (memP x (filter f l))) (ensures (f x)) let mem_filter f l x = () (** Postcondition on [filter f l]: stated with [forall]: for any element [x] of [filter f l], [f x] holds. Requires, at type-checking time, [f] to be a pure total function. *) val mem_filter_forall (#a:Type) (f: (a -> Tot bool)) (l: list a) : Lemma (requires True) (ensures (forall x . memP x (filter f l) ==> f x))
false
false
FStar.List.Tot.Base.fst
{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 1, "max_fuel": 8, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": true, "z3cliopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }
null
val mem_filter_forall (#a:Type) (f: (a -> Tot bool)) (l: list a) : Lemma (requires True) (ensures (forall x . memP x (filter f l) ==> f x)) [SMTPat (filter f l)]
[]
FStar.List.Tot.Base.mem_filter_forall
{ "file_name": "ulib/FStar.List.Tot.Base.fst", "git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f", "git_url": "https://github.com/FStarLang/FStar.git", "project_name": "FStar" }
f: (_: a -> Prims.bool) -> l: Prims.list a -> FStar.Pervasives.Lemma (ensures forall (x: a). FStar.List.Tot.Base.memP x (FStar.List.Tot.Base.filter f l) ==> f x) [SMTPat (FStar.List.Tot.Base.filter f l)]
{ "end_col": 72, "end_line": 296, "start_col": 28, "start_line": 296 }
Prims.Tot
val compare_of_bool : #a:eqtype -> (a -> a -> Tot bool) -> a -> a -> Tot int
[ { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]
false
let compare_of_bool #a rel x y = if x `rel` y then -1 else if x = y then 0 else 1
val compare_of_bool : #a:eqtype -> (a -> a -> Tot bool) -> a -> a -> Tot int let compare_of_bool #a rel x y =
false
null
false
if x `rel` y then - 1 else if x = y then 0 else 1
{ "checked_file": "FStar.List.Tot.Base.fst.checked", "dependencies": [ "prims.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Classical.fsti.checked" ], "interface_file": false, "source_file": "FStar.List.Tot.Base.fst" }
[ "total" ]
[ "Prims.eqtype", "Prims.bool", "Prims.op_Minus", "Prims.op_Equality", "Prims.int" ]
[]
(* Copyright 2008-2014 Nikhil Swamy and Microsoft Research Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License. *) (** This module defines all pure and total operations on lists that can be used in specifications. It is implemented by FStar_List_Tot_Base.ml, any functional change and/or the addition of new functions MUST be reflected there. @summary Pure total operations on lists *) module FStar.List.Tot.Base (** Base operations *) (** [isEmpty l] returns [true] if and only if [l] is empty *) val isEmpty: list 'a -> Tot bool let isEmpty l = match l with | [] -> true | _ -> false (** [hd l] returns the first element of [l]. Requires [l] to be nonempty, at type-checking time. Named as in: OCaml, F#, Coq *) val hd: l:list 'a{Cons? l} -> Tot 'a let hd = function | hd::_ -> hd (** [tail l] returns [l] without its first element. Requires, at type-checking time, that [l] be nonempty. Similar to: tl in OCaml, F#, Coq *) val tail: l:list 'a {Cons? l} -> Tot (list 'a) let tail = function | _::tl -> tl (** [tl l] returns [l] without its first element. Requires, at type-checking time, that [l] be nonempty. Named as in: OCaml, F#, Coq *) val tl: l:list 'a {Cons? l} -> Tot (list 'a) let tl = tail (** [last l] returns the last element of [l]. Requires, at type-checking time, that [l] be nonempty. Named as in: Haskell *) val last: l:list 'a {Cons? l} -> Tot 'a let rec last = function | [hd] -> hd | _::tl -> last tl (** [init l] returns [l] without its last element. Requires, at type-checking time, that [l] be nonempty. Named as in: Haskell *) val init: l:list 'a {Cons? l} -> Tot (list 'a) let rec init = function | [_] -> [] | hd::tl -> hd::(init tl) (** [length l] returns the total number of elements in [l]. Named as in: OCaml, F#, Coq *) val length: list 'a -> Tot nat let rec length = function | [] -> 0 | _::tl -> 1 + length tl (** [nth l n] returns the [n]-th element in list [l] (with the first element being the 0-th) if [l] is long enough, or [None] otherwise. Named as in: OCaml, F#, Coq *) val nth: list 'a -> nat -> Tot (option 'a) let rec nth l n = match l with | [] -> None | hd::tl -> if n = 0 then Some hd else nth tl (n - 1) (** [index l n] returns the [n]-th element in list [l] (with the first element being the 0-th). Requires, at type-checking time, that [l] be of length at least [n+1]. *) val index: #a:Type -> l:list a -> i:nat{i < length l} -> Tot a let rec index #a (l: list a) (i:nat{i < length l}): Tot a = if i = 0 then hd l else index (tl l) (i - 1) (** [count x l] returns the number of occurrences of [x] in [l]. Requires, at type-checking time, the type of [a] to have equality defined. Similar to: [List.count_occ] in Coq. *) val count: #a:eqtype -> a -> list a -> Tot nat let rec count #a x = function | [] -> 0 | hd::tl -> if x=hd then 1 + count x tl else count x tl (** [rev_acc l1 l2] appends the elements of [l1] to the beginning of [l2], in reverse order. It is equivalent to [append (rev l1) l2], but is tail-recursive. Similar to: [List.rev_append] in OCaml, Coq. *) val rev_acc: list 'a -> list 'a -> Tot (list 'a) let rec rev_acc l acc = match l with | [] -> acc | hd::tl -> rev_acc tl (hd::acc) (** [rev l] returns the list [l] in reverse order. Named as in: OCaml, F#, Coq. *) val rev: list 'a -> Tot (list 'a) let rev l = rev_acc l [] (** [append l1 l2] appends the elements of [l2] to the end of [l1]. Named as: OCaml, F#. Similar to: [List.app] in Coq. *) val append: list 'a -> list 'a -> Tot (list 'a) let rec append x y = match x with | [] -> y | a::tl -> a::append tl y (** Defines notation [@@] for [append], as in OCaml, F# . *) let op_At x y = append x y (** [snoc (l, x)] adds [x] to the end of the list [l]. Note: We use an uncurried [snoc (l, x)] instead of the curried [snoc l x]. This is intentional. If [snoc] takes a pair instead of 2 arguments, it allows for a better pattern on [lemma_unsnoc_snoc], which connects [snoc] and [unsnoc]. In particular, if we had two arguments, then either the pattern would either be too restrictive or would lead to over-triggering. More context for this can be seen in the (collapsed and uncollapsed) comments at https://github.com/FStarLang/FStar/pull/1560 *) val snoc: (list 'a * 'a) -> Tot (list 'a) let snoc (l, x) = append l [x] (** [flatten l], where [l] is a list of lists, returns the list of the elements of the lists in [l], preserving their order. Named as in: OCaml, Coq. *) val flatten: list (list 'a) -> Tot (list 'a) let rec flatten l = match l with | [] -> [] | hd::tl -> append hd (flatten tl) (** [map f l] applies [f] to each element of [l] and returns the list of results, in the order of the original elements in [l]. Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml, Coq, F# *) val map: ('a -> Tot 'b) -> list 'a -> Tot (list 'b) let rec map f x = match x with | [] -> [] | a::tl -> f a::map f tl (** [mapi_init f l n] applies, for each [k], [f (n+k)] to the [k]-th element of [l] and returns the list of results, in the order of the original elements in [l]. Requires, at type-checking time, [f] to be a pure total function. *) val mapi_init: (int -> 'a -> Tot 'b) -> list 'a -> int -> Tot (list 'b) let rec mapi_init f l i = match l with | [] -> [] | hd::tl -> (f i hd)::(mapi_init f tl (i+1)) (** [mapi f l] applies, for each [k], [f k] to the [k]-th element of [l] and returns the list of results, in the order of the original elements in [l]. Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml *) val mapi: (int -> 'a -> Tot 'b) -> list 'a -> Tot (list 'b) let mapi f l = mapi_init f l 0 (** [concatMap f l] applies [f] to each element of [l] and returns the concatenation of the results, in the order of the original elements of [l]. This is equivalent to [flatten (map f l)]. Requires, at type-checking time, [f] to be a pure total function. *) val concatMap: ('a -> Tot (list 'b)) -> list 'a -> Tot (list 'b) let rec concatMap f = function | [] -> [] | a::tl -> let fa = f a in let ftl = concatMap f tl in append fa ftl (** [fold_left f x [y1; y2; ...; yn]] computes (f (... (f x y1) y2) ... yn). Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml, Coq. *) val fold_left: ('a -> 'b -> Tot 'a) -> 'a -> l:list 'b -> Tot 'a (decreases l) let rec fold_left f x l = match l with | [] -> x | hd::tl -> fold_left f (f x hd) tl (** [fold_right f [x1; x2; ...; xn] y] computes (f x1 (f x2 (... (f xn y)) ... )). Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml, Coq *) val fold_right: ('a -> 'b -> Tot 'b) -> list 'a -> 'b -> Tot 'b let rec fold_right f l x = match l with | [] -> x | hd::tl -> f hd (fold_right f tl x) (** [fold_right_gtot] is just like [fold_right], except `f` is a ghost function **) let rec fold_right_gtot (#a:Type) (#b:Type) (l:list a) (f:a -> b -> GTot b) (x:b) : GTot b = match l with | [] -> x | hd::tl -> f hd (fold_right_gtot tl f x) (* We define map in terms of fold, to share simple lemmas *) let map_gtot #a #b (f:a -> GTot b) (x:list a) : GTot (list b) = fold_right_gtot x (fun x tl -> f x :: tl) [] (** [fold_left2 f x [y1; y2; ...; yn] [z1; z2; ...; zn]] computes (f (... (f x y1 z1) y2 z2) ... yn zn). Requires, at type-checking time, [f] to be a pure total function, and the lists [y1; y2; ...; yn] and [z1; z2; ...; zn] to have the same lengths. Named as in: OCaml *) val fold_left2 : f:('a -> 'b -> 'c -> Tot 'a) -> accu:'a -> l1:(list 'b) -> l2:(list 'c) -> Pure 'a (requires (length l1 == length l2)) (ensures (fun _ -> True)) (decreases l1) let rec fold_left2 f accu l1 l2 = match (l1, l2) with | ([], []) -> accu | (a1::l1, a2::l2) -> fold_left2 f (f accu a1 a2) l1 l2 (** Propositional membership (as in Coq). Does not require decidable equality. *) (** [memP x l] holds if, and only if, [x] appears as an element of [l]. Similar to: List.In in Coq. *) let rec memP (#a: Type) (x: a) (l: list a) : Tot Type0 = match l with | [] -> False | y :: q -> x == y \/ memP x q (** List searching **) (** [mem x l] returns [true] if, and only if, [x] appears as an element of [l]. Requires, at type-checking time, the type of elements of [l] to have decidable equality. Named as in: OCaml. See also: List.In in Coq, which is propositional. *) val mem: #a:eqtype -> a -> list a -> Tot bool let rec mem #a x = function | [] -> false | hd::tl -> if hd = x then true else mem x tl (** [contains x l] returns [true] if, and only if, [x] appears as an element of [l]. Requires, at type-checking time, the type of elements of [l] to have decidable equality. It is equivalent to: [mem x l]. TODO: should we rather swap the order of arguments? *) let contains : #a:eqtype -> a -> list a -> Tot bool = mem (** [existsb f l] returns [true] if, and only if, there exists some element [x] in [l] such that [f x] holds. *) val existsb: #a:Type -> f:(a -> Tot bool) -> list a -> Tot bool let rec existsb #a f l = match l with | [] -> false | hd::tl -> if f hd then true else existsb f tl (** [find f l] returns [Some x] for some element [x] appearing in [l] such that [f x] holds, or [None] only if no such [x] exists. *) val find: #a:Type -> f:(a -> Tot bool) -> list a -> Tot (option (x:a{f x})) let rec find #a f l = match l with | [] -> None #(x:a{f x}) //These type annotations are only present because it makes bootstrapping go much faster | hd::tl -> if f hd then Some #(x:a{f x}) hd else find f tl (** Filtering elements of a list [l] through a Boolean pure total predicate [f] *) (** [filter f l] returns [l] with all elements [x] such that [f x] does not hold removed. Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml, Coq *) val filter : #a: Type -> f:(a -> Tot bool) -> l: list a -> Tot (m:list a{forall x. memP x m ==> f x}) let rec filter #a f = function | [] -> [] | hd::tl -> if f hd then hd::filter f tl else filter f tl (** Postcondition on [filter f l]: for any element [x] of [filter f l], [f x] holds. Requires, at type-checking time, [f] to be a pure total function.*) val mem_filter (#a:Type) (f: (a -> Tot bool)) (l: list a) (x: a) : Lemma (requires (memP x (filter f l))) (ensures (f x)) let mem_filter f l x = () (** Postcondition on [filter f l]: stated with [forall]: for any element [x] of [filter f l], [f x] holds. Requires, at type-checking time, [f] to be a pure total function. *) val mem_filter_forall (#a:Type) (f: (a -> Tot bool)) (l: list a) : Lemma (requires True) (ensures (forall x . memP x (filter f l) ==> f x)) [SMTPat (filter f l)] let mem_filter_forall f l = FStar.Classical.ghost_lemma (mem_filter f l) (** [for_all f l] returns [true] if, and only if, for all elements [x] appearing in [l], [f x] holds. Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml. Similar to: List.forallb in Coq *) val for_all: ('a -> Tot bool) -> list 'a -> Tot bool let rec for_all f l = match l with | [] -> true | hd::tl -> if f hd then for_all f tl else false (** Specification for [for_all f l] vs. mem *) let rec for_all_mem (#a: Type) (f: (a -> Tot bool)) (l: list a) : Lemma (for_all f l <==> (forall x . memP x l ==> f x)) = match l with | [] -> () | _ :: q -> for_all_mem f q (** [collect f l] applies [f] to each element of [l] and returns the concatenation of the results, in the order of the original elements of [l]. It is equivalent to [flatten (map f l)]. Requires, at type-checking time, [f] to be a pure total function. TODO: what is the difference with [concatMap]? *) val collect: ('a -> Tot (list 'b)) -> list 'a -> Tot (list 'b) let rec collect f l = match l with | [] -> [] | hd::tl -> append (f hd) (collect f tl) (** [tryFind f l] returns [Some x] for some element [x] appearing in [l] such that [f x] holds, or [None] only if no such [x] exists. Requires, at type-checking time, [f] to be a pure total function. Contrary to [find], [tryFind] provides no postcondition on its result. *) val tryFind: ('a -> Tot bool) -> list 'a -> Tot (option 'a) let rec tryFind p l = match l with | [] -> None | hd::tl -> if p hd then Some hd else tryFind p tl (** [tryPick f l] returns [y] for some element [x] appearing in [l] such that [f x = Some y] for some y, or [None] only if [f x = None] for all elements [x] of [l]. Requires, at type-checking time, [f] to be a pure total function. *) val tryPick: ('a -> Tot (option 'b)) -> list 'a -> Tot (option 'b) let rec tryPick f l = match l with | [] -> None | hd::tl -> match f hd with | Some x -> Some x | None -> tryPick f tl (** [choose f l] returns the list of [y] for all elements [x] appearing in [l] such that [f x = Some y] for some [y]. Requires, at type-checking time, [f] to be a pure total function. *) val choose: ('a -> Tot (option 'b)) -> list 'a -> Tot (list 'b) let rec choose f l = match l with | [] -> [] | hd::tl -> match f hd with | Some x -> x::(choose f tl) | None -> choose f tl (** [partition f l] returns the pair of lists [(l1, l2)] where all elements [x] of [l] are in [l1] if [f x] holds, and in [l2] otherwise. Both [l1] and [l2] retain the original order of [l]. Requires, at type-checking time, [f] to be a pure total function. *) val partition: f:('a -> Tot bool) -> list 'a -> Tot (list 'a * list 'a) let rec partition f = function | [] -> [], [] | hd::tl -> let l1, l2 = partition f tl in if f hd then hd::l1, l2 else l1, hd::l2 (** [subset la lb] is true if and only if all the elements from [la] are also in [lb]. Requires, at type-checking time, the type of elements of [la] and [lb] to have decidable equality. *) val subset: #a:eqtype -> list a -> list a -> Tot bool let rec subset #a la lb = match la with | [] -> true | h :: tl -> mem h lb && subset tl lb (** [noRepeats l] returns [true] if, and only if, no element of [l] appears in [l] more than once. Requires, at type-checking time, the type of elements of [la] and [lb] to have decidable equality. *) val noRepeats : #a:eqtype -> list a -> Tot bool let rec noRepeats #a la = match la with | [] -> true | h :: tl -> not(mem h tl) && noRepeats tl (** [no_repeats_p l] valid if, and only if, no element of [l] appears in [l] more than once. *) val no_repeats_p : #a:Type -> list a -> Tot prop let rec no_repeats_p #a la = match la with | [] -> True | h :: tl -> ~(memP h tl) /\ no_repeats_p tl (** List of tuples **) (** [assoc x l] returns [Some y] where [(x, y)] is the first element of [l] whose first element is [x], or [None] only if no such element exists. Requires, at type-checking time, the type of [x] to have decidable equality. Named as in: OCaml. *) val assoc: #a:eqtype -> #b:Type -> a -> list (a * b) -> Tot (option b) let rec assoc #a #b x = function | [] -> None | (x', y)::tl -> if x=x' then Some y else assoc x tl (** [split] takes a list of pairs [(x1, y1), ..., (xn, yn)] and returns the pair of lists ([x1, ..., xn], [y1, ..., yn]). Named as in: OCaml *) val split: list ('a * 'b) -> Tot (list 'a * list 'b) let rec split l = match l with | [] -> ([],[]) | (hd1,hd2)::tl -> let (tl1,tl2) = split tl in (hd1::tl1,hd2::tl2) (** [unzip] takes a list of pairs [(x1, y1), ..., (xn, yn)] and returns the pair of lists ([x1, ..., xn], [y1, ..., yn]). Named as in: Haskell *) let unzip l = split l (** [unzip3] takes a list of triples [(x1, y1, z1), ..., (xn, yn, zn)] and returns the triple of lists ([x1, ..., xn], [y1, ..., yn], [z1, ..., zn]). Named as in: Haskell *) val unzip3: list ('a * 'b * 'c) -> Tot (list 'a * list 'b * list 'c) let rec unzip3 l = match l with | [] -> ([],[],[]) | (hd1,hd2,hd3)::tl -> let (tl1,tl2,tl3) = unzip3 tl in (hd1::tl1,hd2::tl2,hd3::tl3) (** Splitting a list at some index **) (** [splitAt] takes a natural number n and a list and returns a pair of the maximal prefix of l of size smaller than n and the rest of the list *) let rec splitAt (#a:Type) (n:nat) (l:list a) : Tot (list a * list a) = if n = 0 then [], l else match l with | [] -> [], l | x :: xs -> let l1, l2 = splitAt (n-1) xs in x :: l1, l2 let rec lemma_splitAt_snd_length (#a:Type) (n:nat) (l:list a) : Lemma (requires (n <= length l)) (ensures (length (snd (splitAt n l)) = length l - n)) = match n, l with | 0, _ -> () | _, [] -> () | _, _ :: l' -> lemma_splitAt_snd_length (n - 1) l' (** [unsnoc] is an inverse of [snoc]. It splits a list into all-elements-except-last and last element. *) val unsnoc: #a:Type -> l:list a{length l > 0} -> Tot (list a * a) let unsnoc #a l = let l1, l2 = splitAt (length l - 1) l in lemma_splitAt_snd_length (length l - 1) l; l1, hd l2 (** [split3] splits a list into 3 parts. This allows easy access to the part of the list before and after the element, as well as the element itself. *) val split3: #a:Type -> l:list a -> i:nat{i < length l} -> Tot (list a * a * list a) let split3 #a l i = let a, rest = splitAt i l in lemma_splitAt_snd_length i l; let b :: c = rest in a, b, c (** Sorting (implemented as quicksort) **) (** [partition] splits a list [l] into two lists, the sum of whose lengths is the length of [l]. *) val partition_length: f:('a -> Tot bool) -> l:list 'a -> Lemma (requires True) (ensures (length (fst (partition f l)) + length (snd (partition f l)) = length l)) let rec partition_length f l = match l with | [] -> () | hd::tl -> partition_length f tl (** [bool_of_compare] turns a comparison function into a strict order. More precisely, [bool_of_compare compare x y] returns true if, and only if, [compare x y] is negative, meaning [x] precedes [y] in the ordering defined by compare. This is used in sorting, and is defined to be consistent with OCaml and F#, where sorting is performed in ascending order. *) val bool_of_compare : #a:Type -> (a -> a -> Tot int) -> a -> a -> Tot bool let bool_of_compare #a f x y = f x y < 0 (** [compare_of_bool] turns a strict order into a comparison function. More precisely, [compare_of_bool rel x y] returns a positive number if, and only if, x `rel` y holds. Inspired from OCaml, where polymorphic comparison using both the [compare] function and the (>) infix operator are such that [compare x y] is positive if, and only if, x > y. Requires, at type-checking time, [rel] to be a pure total function. *) val compare_of_bool : #a:eqtype -> (a -> a -> Tot bool) -> a -> a -> Tot int
false
false
FStar.List.Tot.Base.fst
{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 1, "max_fuel": 8, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": true, "z3cliopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }
null
val compare_of_bool : #a:eqtype -> (a -> a -> Tot bool) -> a -> a -> Tot int
[]
FStar.List.Tot.Base.compare_of_bool
{ "file_name": "ulib/FStar.List.Tot.Base.fst", "git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f", "git_url": "https://github.com/FStarLang/FStar.git", "project_name": "FStar" }
rel: (_: a -> _: a -> Prims.bool) -> x: a -> y: a -> Prims.int
{ "end_col": 10, "end_line": 512, "start_col": 4, "start_line": 510 }
Prims.Tot
val rev: list 'a -> Tot (list 'a)
[ { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]
false
let rev l = rev_acc l []
val rev: list 'a -> Tot (list 'a) let rev l =
false
null
false
rev_acc l []
{ "checked_file": "FStar.List.Tot.Base.fst.checked", "dependencies": [ "prims.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Classical.fsti.checked" ], "interface_file": false, "source_file": "FStar.List.Tot.Base.fst" }
[ "total" ]
[ "Prims.list", "FStar.List.Tot.Base.rev_acc", "Prims.Nil" ]
[]
(* Copyright 2008-2014 Nikhil Swamy and Microsoft Research Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License. *) (** This module defines all pure and total operations on lists that can be used in specifications. It is implemented by FStar_List_Tot_Base.ml, any functional change and/or the addition of new functions MUST be reflected there. @summary Pure total operations on lists *) module FStar.List.Tot.Base (** Base operations *) (** [isEmpty l] returns [true] if and only if [l] is empty *) val isEmpty: list 'a -> Tot bool let isEmpty l = match l with | [] -> true | _ -> false (** [hd l] returns the first element of [l]. Requires [l] to be nonempty, at type-checking time. Named as in: OCaml, F#, Coq *) val hd: l:list 'a{Cons? l} -> Tot 'a let hd = function | hd::_ -> hd (** [tail l] returns [l] without its first element. Requires, at type-checking time, that [l] be nonempty. Similar to: tl in OCaml, F#, Coq *) val tail: l:list 'a {Cons? l} -> Tot (list 'a) let tail = function | _::tl -> tl (** [tl l] returns [l] without its first element. Requires, at type-checking time, that [l] be nonempty. Named as in: OCaml, F#, Coq *) val tl: l:list 'a {Cons? l} -> Tot (list 'a) let tl = tail (** [last l] returns the last element of [l]. Requires, at type-checking time, that [l] be nonempty. Named as in: Haskell *) val last: l:list 'a {Cons? l} -> Tot 'a let rec last = function | [hd] -> hd | _::tl -> last tl (** [init l] returns [l] without its last element. Requires, at type-checking time, that [l] be nonempty. Named as in: Haskell *) val init: l:list 'a {Cons? l} -> Tot (list 'a) let rec init = function | [_] -> [] | hd::tl -> hd::(init tl) (** [length l] returns the total number of elements in [l]. Named as in: OCaml, F#, Coq *) val length: list 'a -> Tot nat let rec length = function | [] -> 0 | _::tl -> 1 + length tl (** [nth l n] returns the [n]-th element in list [l] (with the first element being the 0-th) if [l] is long enough, or [None] otherwise. Named as in: OCaml, F#, Coq *) val nth: list 'a -> nat -> Tot (option 'a) let rec nth l n = match l with | [] -> None | hd::tl -> if n = 0 then Some hd else nth tl (n - 1) (** [index l n] returns the [n]-th element in list [l] (with the first element being the 0-th). Requires, at type-checking time, that [l] be of length at least [n+1]. *) val index: #a:Type -> l:list a -> i:nat{i < length l} -> Tot a let rec index #a (l: list a) (i:nat{i < length l}): Tot a = if i = 0 then hd l else index (tl l) (i - 1) (** [count x l] returns the number of occurrences of [x] in [l]. Requires, at type-checking time, the type of [a] to have equality defined. Similar to: [List.count_occ] in Coq. *) val count: #a:eqtype -> a -> list a -> Tot nat let rec count #a x = function | [] -> 0 | hd::tl -> if x=hd then 1 + count x tl else count x tl (** [rev_acc l1 l2] appends the elements of [l1] to the beginning of [l2], in reverse order. It is equivalent to [append (rev l1) l2], but is tail-recursive. Similar to: [List.rev_append] in OCaml, Coq. *) val rev_acc: list 'a -> list 'a -> Tot (list 'a) let rec rev_acc l acc = match l with | [] -> acc | hd::tl -> rev_acc tl (hd::acc) (** [rev l] returns the list [l] in reverse order. Named as in: OCaml, F#, Coq. *)
false
false
FStar.List.Tot.Base.fst
{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 1, "max_fuel": 8, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": true, "z3cliopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }
null
val rev: list 'a -> Tot (list 'a)
[]
FStar.List.Tot.Base.rev
{ "file_name": "ulib/FStar.List.Tot.Base.fst", "git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f", "git_url": "https://github.com/FStarLang/FStar.git", "project_name": "FStar" }
l: Prims.list 'a -> Prims.list 'a
{ "end_col": 24, "end_line": 115, "start_col": 12, "start_line": 115 }
Prims.Tot
val length: list 'a -> Tot nat
[ { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]
false
let rec length = function | [] -> 0 | _::tl -> 1 + length tl
val length: list 'a -> Tot nat let rec length =
false
null
false
function | [] -> 0 | _ :: tl -> 1 + length tl
{ "checked_file": "FStar.List.Tot.Base.fst.checked", "dependencies": [ "prims.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Classical.fsti.checked" ], "interface_file": false, "source_file": "FStar.List.Tot.Base.fst" }
[ "total" ]
[ "Prims.list", "Prims.op_Addition", "FStar.List.Tot.Base.length", "Prims.nat" ]
[]
(* Copyright 2008-2014 Nikhil Swamy and Microsoft Research Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License. *) (** This module defines all pure and total operations on lists that can be used in specifications. It is implemented by FStar_List_Tot_Base.ml, any functional change and/or the addition of new functions MUST be reflected there. @summary Pure total operations on lists *) module FStar.List.Tot.Base (** Base operations *) (** [isEmpty l] returns [true] if and only if [l] is empty *) val isEmpty: list 'a -> Tot bool let isEmpty l = match l with | [] -> true | _ -> false (** [hd l] returns the first element of [l]. Requires [l] to be nonempty, at type-checking time. Named as in: OCaml, F#, Coq *) val hd: l:list 'a{Cons? l} -> Tot 'a let hd = function | hd::_ -> hd (** [tail l] returns [l] without its first element. Requires, at type-checking time, that [l] be nonempty. Similar to: tl in OCaml, F#, Coq *) val tail: l:list 'a {Cons? l} -> Tot (list 'a) let tail = function | _::tl -> tl (** [tl l] returns [l] without its first element. Requires, at type-checking time, that [l] be nonempty. Named as in: OCaml, F#, Coq *) val tl: l:list 'a {Cons? l} -> Tot (list 'a) let tl = tail (** [last l] returns the last element of [l]. Requires, at type-checking time, that [l] be nonempty. Named as in: Haskell *) val last: l:list 'a {Cons? l} -> Tot 'a let rec last = function | [hd] -> hd | _::tl -> last tl (** [init l] returns [l] without its last element. Requires, at type-checking time, that [l] be nonempty. Named as in: Haskell *) val init: l:list 'a {Cons? l} -> Tot (list 'a) let rec init = function | [_] -> [] | hd::tl -> hd::(init tl) (** [length l] returns the total number of elements in [l]. Named as in: OCaml, F#, Coq *)
false
false
FStar.List.Tot.Base.fst
{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 1, "max_fuel": 8, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": true, "z3cliopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }
null
val length: list 'a -> Tot nat
[ "recursion" ]
FStar.List.Tot.Base.length
{ "file_name": "ulib/FStar.List.Tot.Base.fst", "git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f", "git_url": "https://github.com/FStarLang/FStar.git", "project_name": "FStar" }
_: Prims.list 'a -> Prims.nat
{ "end_col": 26, "end_line": 76, "start_col": 17, "start_line": 74 }
Prims.Tot
val index: #a:Type -> l:list a -> i:nat{i < length l} -> Tot a
[ { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]
false
let rec index #a (l: list a) (i:nat{i < length l}): Tot a = if i = 0 then hd l else index (tl l) (i - 1)
val index: #a:Type -> l:list a -> i:nat{i < length l} -> Tot a let rec index #a (l: list a) (i: nat{i < length l}) : Tot a =
false
null
false
if i = 0 then hd l else index (tl l) (i - 1)
{ "checked_file": "FStar.List.Tot.Base.fst.checked", "dependencies": [ "prims.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Classical.fsti.checked" ], "interface_file": false, "source_file": "FStar.List.Tot.Base.fst" }
[ "total" ]
[ "Prims.list", "Prims.nat", "Prims.b2t", "Prims.op_LessThan", "FStar.List.Tot.Base.length", "Prims.op_Equality", "Prims.int", "FStar.List.Tot.Base.hd", "Prims.bool", "FStar.List.Tot.Base.index", "FStar.List.Tot.Base.tl", "Prims.op_Subtraction" ]
[]
(* Copyright 2008-2014 Nikhil Swamy and Microsoft Research Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License. *) (** This module defines all pure and total operations on lists that can be used in specifications. It is implemented by FStar_List_Tot_Base.ml, any functional change and/or the addition of new functions MUST be reflected there. @summary Pure total operations on lists *) module FStar.List.Tot.Base (** Base operations *) (** [isEmpty l] returns [true] if and only if [l] is empty *) val isEmpty: list 'a -> Tot bool let isEmpty l = match l with | [] -> true | _ -> false (** [hd l] returns the first element of [l]. Requires [l] to be nonempty, at type-checking time. Named as in: OCaml, F#, Coq *) val hd: l:list 'a{Cons? l} -> Tot 'a let hd = function | hd::_ -> hd (** [tail l] returns [l] without its first element. Requires, at type-checking time, that [l] be nonempty. Similar to: tl in OCaml, F#, Coq *) val tail: l:list 'a {Cons? l} -> Tot (list 'a) let tail = function | _::tl -> tl (** [tl l] returns [l] without its first element. Requires, at type-checking time, that [l] be nonempty. Named as in: OCaml, F#, Coq *) val tl: l:list 'a {Cons? l} -> Tot (list 'a) let tl = tail (** [last l] returns the last element of [l]. Requires, at type-checking time, that [l] be nonempty. Named as in: Haskell *) val last: l:list 'a {Cons? l} -> Tot 'a let rec last = function | [hd] -> hd | _::tl -> last tl (** [init l] returns [l] without its last element. Requires, at type-checking time, that [l] be nonempty. Named as in: Haskell *) val init: l:list 'a {Cons? l} -> Tot (list 'a) let rec init = function | [_] -> [] | hd::tl -> hd::(init tl) (** [length l] returns the total number of elements in [l]. Named as in: OCaml, F#, Coq *) val length: list 'a -> Tot nat let rec length = function | [] -> 0 | _::tl -> 1 + length tl (** [nth l n] returns the [n]-th element in list [l] (with the first element being the 0-th) if [l] is long enough, or [None] otherwise. Named as in: OCaml, F#, Coq *) val nth: list 'a -> nat -> Tot (option 'a) let rec nth l n = match l with | [] -> None | hd::tl -> if n = 0 then Some hd else nth tl (n - 1) (** [index l n] returns the [n]-th element in list [l] (with the first element being the 0-th). Requires, at type-checking time, that [l] be of length at least [n+1]. *) val index: #a:Type -> l:list a -> i:nat{i < length l} -> Tot a
false
false
FStar.List.Tot.Base.fst
{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 1, "max_fuel": 8, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": true, "z3cliopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }
null
val index: #a:Type -> l:list a -> i:nat{i < length l} -> Tot a
[ "recursion" ]
FStar.List.Tot.Base.index
{ "file_name": "ulib/FStar.List.Tot.Base.fst", "git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f", "git_url": "https://github.com/FStarLang/FStar.git", "project_name": "FStar" }
l: Prims.list a -> i: Prims.nat{i < FStar.List.Tot.Base.length l} -> a
{ "end_col": 24, "end_line": 94, "start_col": 2, "start_line": 91 }
Prims.Tot
val tail: l:list 'a {Cons? l} -> Tot (list 'a)
[ { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]
false
let tail = function | _::tl -> tl
val tail: l:list 'a {Cons? l} -> Tot (list 'a) let tail =
false
null
false
function | _ :: tl -> tl
{ "checked_file": "FStar.List.Tot.Base.fst.checked", "dependencies": [ "prims.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Classical.fsti.checked" ], "interface_file": false, "source_file": "FStar.List.Tot.Base.fst" }
[ "total" ]
[ "Prims.list", "Prims.b2t", "Prims.uu___is_Cons" ]
[]
(* Copyright 2008-2014 Nikhil Swamy and Microsoft Research Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License. *) (** This module defines all pure and total operations on lists that can be used in specifications. It is implemented by FStar_List_Tot_Base.ml, any functional change and/or the addition of new functions MUST be reflected there. @summary Pure total operations on lists *) module FStar.List.Tot.Base (** Base operations *) (** [isEmpty l] returns [true] if and only if [l] is empty *) val isEmpty: list 'a -> Tot bool let isEmpty l = match l with | [] -> true | _ -> false (** [hd l] returns the first element of [l]. Requires [l] to be nonempty, at type-checking time. Named as in: OCaml, F#, Coq *) val hd: l:list 'a{Cons? l} -> Tot 'a let hd = function | hd::_ -> hd (** [tail l] returns [l] without its first element. Requires, at type-checking time, that [l] be nonempty. Similar to: tl in OCaml, F#, Coq *)
false
false
FStar.List.Tot.Base.fst
{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 1, "max_fuel": 8, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": true, "z3cliopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }
null
val tail: l:list 'a {Cons? l} -> Tot (list 'a)
[]
FStar.List.Tot.Base.tail
{ "file_name": "ulib/FStar.List.Tot.Base.fst", "git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f", "git_url": "https://github.com/FStarLang/FStar.git", "project_name": "FStar" }
l: Prims.list 'a {Cons? l} -> Prims.list 'a
{ "end_col": 15, "end_line": 47, "start_col": 11, "start_line": 46 }
Prims.Tot
val collect: ('a -> Tot (list 'b)) -> list 'a -> Tot (list 'b)
[ { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]
false
let rec collect f l = match l with | [] -> [] | hd::tl -> append (f hd) (collect f tl)
val collect: ('a -> Tot (list 'b)) -> list 'a -> Tot (list 'b) let rec collect f l =
false
null
false
match l with | [] -> [] | hd :: tl -> append (f hd) (collect f tl)
{ "checked_file": "FStar.List.Tot.Base.fst.checked", "dependencies": [ "prims.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Classical.fsti.checked" ], "interface_file": false, "source_file": "FStar.List.Tot.Base.fst" }
[ "total" ]
[ "Prims.list", "Prims.Nil", "FStar.List.Tot.Base.append", "FStar.List.Tot.Base.collect" ]
[]
(* Copyright 2008-2014 Nikhil Swamy and Microsoft Research Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License. *) (** This module defines all pure and total operations on lists that can be used in specifications. It is implemented by FStar_List_Tot_Base.ml, any functional change and/or the addition of new functions MUST be reflected there. @summary Pure total operations on lists *) module FStar.List.Tot.Base (** Base operations *) (** [isEmpty l] returns [true] if and only if [l] is empty *) val isEmpty: list 'a -> Tot bool let isEmpty l = match l with | [] -> true | _ -> false (** [hd l] returns the first element of [l]. Requires [l] to be nonempty, at type-checking time. Named as in: OCaml, F#, Coq *) val hd: l:list 'a{Cons? l} -> Tot 'a let hd = function | hd::_ -> hd (** [tail l] returns [l] without its first element. Requires, at type-checking time, that [l] be nonempty. Similar to: tl in OCaml, F#, Coq *) val tail: l:list 'a {Cons? l} -> Tot (list 'a) let tail = function | _::tl -> tl (** [tl l] returns [l] without its first element. Requires, at type-checking time, that [l] be nonempty. Named as in: OCaml, F#, Coq *) val tl: l:list 'a {Cons? l} -> Tot (list 'a) let tl = tail (** [last l] returns the last element of [l]. Requires, at type-checking time, that [l] be nonempty. Named as in: Haskell *) val last: l:list 'a {Cons? l} -> Tot 'a let rec last = function | [hd] -> hd | _::tl -> last tl (** [init l] returns [l] without its last element. Requires, at type-checking time, that [l] be nonempty. Named as in: Haskell *) val init: l:list 'a {Cons? l} -> Tot (list 'a) let rec init = function | [_] -> [] | hd::tl -> hd::(init tl) (** [length l] returns the total number of elements in [l]. Named as in: OCaml, F#, Coq *) val length: list 'a -> Tot nat let rec length = function | [] -> 0 | _::tl -> 1 + length tl (** [nth l n] returns the [n]-th element in list [l] (with the first element being the 0-th) if [l] is long enough, or [None] otherwise. Named as in: OCaml, F#, Coq *) val nth: list 'a -> nat -> Tot (option 'a) let rec nth l n = match l with | [] -> None | hd::tl -> if n = 0 then Some hd else nth tl (n - 1) (** [index l n] returns the [n]-th element in list [l] (with the first element being the 0-th). Requires, at type-checking time, that [l] be of length at least [n+1]. *) val index: #a:Type -> l:list a -> i:nat{i < length l} -> Tot a let rec index #a (l: list a) (i:nat{i < length l}): Tot a = if i = 0 then hd l else index (tl l) (i - 1) (** [count x l] returns the number of occurrences of [x] in [l]. Requires, at type-checking time, the type of [a] to have equality defined. Similar to: [List.count_occ] in Coq. *) val count: #a:eqtype -> a -> list a -> Tot nat let rec count #a x = function | [] -> 0 | hd::tl -> if x=hd then 1 + count x tl else count x tl (** [rev_acc l1 l2] appends the elements of [l1] to the beginning of [l2], in reverse order. It is equivalent to [append (rev l1) l2], but is tail-recursive. Similar to: [List.rev_append] in OCaml, Coq. *) val rev_acc: list 'a -> list 'a -> Tot (list 'a) let rec rev_acc l acc = match l with | [] -> acc | hd::tl -> rev_acc tl (hd::acc) (** [rev l] returns the list [l] in reverse order. Named as in: OCaml, F#, Coq. *) val rev: list 'a -> Tot (list 'a) let rev l = rev_acc l [] (** [append l1 l2] appends the elements of [l2] to the end of [l1]. Named as: OCaml, F#. Similar to: [List.app] in Coq. *) val append: list 'a -> list 'a -> Tot (list 'a) let rec append x y = match x with | [] -> y | a::tl -> a::append tl y (** Defines notation [@@] for [append], as in OCaml, F# . *) let op_At x y = append x y (** [snoc (l, x)] adds [x] to the end of the list [l]. Note: We use an uncurried [snoc (l, x)] instead of the curried [snoc l x]. This is intentional. If [snoc] takes a pair instead of 2 arguments, it allows for a better pattern on [lemma_unsnoc_snoc], which connects [snoc] and [unsnoc]. In particular, if we had two arguments, then either the pattern would either be too restrictive or would lead to over-triggering. More context for this can be seen in the (collapsed and uncollapsed) comments at https://github.com/FStarLang/FStar/pull/1560 *) val snoc: (list 'a * 'a) -> Tot (list 'a) let snoc (l, x) = append l [x] (** [flatten l], where [l] is a list of lists, returns the list of the elements of the lists in [l], preserving their order. Named as in: OCaml, Coq. *) val flatten: list (list 'a) -> Tot (list 'a) let rec flatten l = match l with | [] -> [] | hd::tl -> append hd (flatten tl) (** [map f l] applies [f] to each element of [l] and returns the list of results, in the order of the original elements in [l]. Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml, Coq, F# *) val map: ('a -> Tot 'b) -> list 'a -> Tot (list 'b) let rec map f x = match x with | [] -> [] | a::tl -> f a::map f tl (** [mapi_init f l n] applies, for each [k], [f (n+k)] to the [k]-th element of [l] and returns the list of results, in the order of the original elements in [l]. Requires, at type-checking time, [f] to be a pure total function. *) val mapi_init: (int -> 'a -> Tot 'b) -> list 'a -> int -> Tot (list 'b) let rec mapi_init f l i = match l with | [] -> [] | hd::tl -> (f i hd)::(mapi_init f tl (i+1)) (** [mapi f l] applies, for each [k], [f k] to the [k]-th element of [l] and returns the list of results, in the order of the original elements in [l]. Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml *) val mapi: (int -> 'a -> Tot 'b) -> list 'a -> Tot (list 'b) let mapi f l = mapi_init f l 0 (** [concatMap f l] applies [f] to each element of [l] and returns the concatenation of the results, in the order of the original elements of [l]. This is equivalent to [flatten (map f l)]. Requires, at type-checking time, [f] to be a pure total function. *) val concatMap: ('a -> Tot (list 'b)) -> list 'a -> Tot (list 'b) let rec concatMap f = function | [] -> [] | a::tl -> let fa = f a in let ftl = concatMap f tl in append fa ftl (** [fold_left f x [y1; y2; ...; yn]] computes (f (... (f x y1) y2) ... yn). Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml, Coq. *) val fold_left: ('a -> 'b -> Tot 'a) -> 'a -> l:list 'b -> Tot 'a (decreases l) let rec fold_left f x l = match l with | [] -> x | hd::tl -> fold_left f (f x hd) tl (** [fold_right f [x1; x2; ...; xn] y] computes (f x1 (f x2 (... (f xn y)) ... )). Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml, Coq *) val fold_right: ('a -> 'b -> Tot 'b) -> list 'a -> 'b -> Tot 'b let rec fold_right f l x = match l with | [] -> x | hd::tl -> f hd (fold_right f tl x) (** [fold_right_gtot] is just like [fold_right], except `f` is a ghost function **) let rec fold_right_gtot (#a:Type) (#b:Type) (l:list a) (f:a -> b -> GTot b) (x:b) : GTot b = match l with | [] -> x | hd::tl -> f hd (fold_right_gtot tl f x) (* We define map in terms of fold, to share simple lemmas *) let map_gtot #a #b (f:a -> GTot b) (x:list a) : GTot (list b) = fold_right_gtot x (fun x tl -> f x :: tl) [] (** [fold_left2 f x [y1; y2; ...; yn] [z1; z2; ...; zn]] computes (f (... (f x y1 z1) y2 z2) ... yn zn). Requires, at type-checking time, [f] to be a pure total function, and the lists [y1; y2; ...; yn] and [z1; z2; ...; zn] to have the same lengths. Named as in: OCaml *) val fold_left2 : f:('a -> 'b -> 'c -> Tot 'a) -> accu:'a -> l1:(list 'b) -> l2:(list 'c) -> Pure 'a (requires (length l1 == length l2)) (ensures (fun _ -> True)) (decreases l1) let rec fold_left2 f accu l1 l2 = match (l1, l2) with | ([], []) -> accu | (a1::l1, a2::l2) -> fold_left2 f (f accu a1 a2) l1 l2 (** Propositional membership (as in Coq). Does not require decidable equality. *) (** [memP x l] holds if, and only if, [x] appears as an element of [l]. Similar to: List.In in Coq. *) let rec memP (#a: Type) (x: a) (l: list a) : Tot Type0 = match l with | [] -> False | y :: q -> x == y \/ memP x q (** List searching **) (** [mem x l] returns [true] if, and only if, [x] appears as an element of [l]. Requires, at type-checking time, the type of elements of [l] to have decidable equality. Named as in: OCaml. See also: List.In in Coq, which is propositional. *) val mem: #a:eqtype -> a -> list a -> Tot bool let rec mem #a x = function | [] -> false | hd::tl -> if hd = x then true else mem x tl (** [contains x l] returns [true] if, and only if, [x] appears as an element of [l]. Requires, at type-checking time, the type of elements of [l] to have decidable equality. It is equivalent to: [mem x l]. TODO: should we rather swap the order of arguments? *) let contains : #a:eqtype -> a -> list a -> Tot bool = mem (** [existsb f l] returns [true] if, and only if, there exists some element [x] in [l] such that [f x] holds. *) val existsb: #a:Type -> f:(a -> Tot bool) -> list a -> Tot bool let rec existsb #a f l = match l with | [] -> false | hd::tl -> if f hd then true else existsb f tl (** [find f l] returns [Some x] for some element [x] appearing in [l] such that [f x] holds, or [None] only if no such [x] exists. *) val find: #a:Type -> f:(a -> Tot bool) -> list a -> Tot (option (x:a{f x})) let rec find #a f l = match l with | [] -> None #(x:a{f x}) //These type annotations are only present because it makes bootstrapping go much faster | hd::tl -> if f hd then Some #(x:a{f x}) hd else find f tl (** Filtering elements of a list [l] through a Boolean pure total predicate [f] *) (** [filter f l] returns [l] with all elements [x] such that [f x] does not hold removed. Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml, Coq *) val filter : #a: Type -> f:(a -> Tot bool) -> l: list a -> Tot (m:list a{forall x. memP x m ==> f x}) let rec filter #a f = function | [] -> [] | hd::tl -> if f hd then hd::filter f tl else filter f tl (** Postcondition on [filter f l]: for any element [x] of [filter f l], [f x] holds. Requires, at type-checking time, [f] to be a pure total function.*) val mem_filter (#a:Type) (f: (a -> Tot bool)) (l: list a) (x: a) : Lemma (requires (memP x (filter f l))) (ensures (f x)) let mem_filter f l x = () (** Postcondition on [filter f l]: stated with [forall]: for any element [x] of [filter f l], [f x] holds. Requires, at type-checking time, [f] to be a pure total function. *) val mem_filter_forall (#a:Type) (f: (a -> Tot bool)) (l: list a) : Lemma (requires True) (ensures (forall x . memP x (filter f l) ==> f x)) [SMTPat (filter f l)] let mem_filter_forall f l = FStar.Classical.ghost_lemma (mem_filter f l) (** [for_all f l] returns [true] if, and only if, for all elements [x] appearing in [l], [f x] holds. Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml. Similar to: List.forallb in Coq *) val for_all: ('a -> Tot bool) -> list 'a -> Tot bool let rec for_all f l = match l with | [] -> true | hd::tl -> if f hd then for_all f tl else false (** Specification for [for_all f l] vs. mem *) let rec for_all_mem (#a: Type) (f: (a -> Tot bool)) (l: list a) : Lemma (for_all f l <==> (forall x . memP x l ==> f x)) = match l with | [] -> () | _ :: q -> for_all_mem f q (** [collect f l] applies [f] to each element of [l] and returns the concatenation of the results, in the order of the original elements of [l]. It is equivalent to [flatten (map f l)]. Requires, at type-checking time, [f] to be a pure total function. TODO: what is the difference with [concatMap]? *)
false
false
FStar.List.Tot.Base.fst
{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 1, "max_fuel": 8, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": true, "z3cliopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }
null
val collect: ('a -> Tot (list 'b)) -> list 'a -> Tot (list 'b)
[ "recursion" ]
FStar.List.Tot.Base.collect
{ "file_name": "ulib/FStar.List.Tot.Base.fst", "git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f", "git_url": "https://github.com/FStarLang/FStar.git", "project_name": "FStar" }
f: (_: 'a -> Prims.list 'b) -> l: Prims.list 'a -> Prims.list 'b
{ "end_col": 44, "end_line": 326, "start_col": 22, "start_line": 324 }
Prims.Tot
val flatten: list (list 'a) -> Tot (list 'a)
[ { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]
false
let rec flatten l = match l with | [] -> [] | hd::tl -> append hd (flatten tl)
val flatten: list (list 'a) -> Tot (list 'a) let rec flatten l =
false
null
false
match l with | [] -> [] | hd :: tl -> append hd (flatten tl)
{ "checked_file": "FStar.List.Tot.Base.fst.checked", "dependencies": [ "prims.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Classical.fsti.checked" ], "interface_file": false, "source_file": "FStar.List.Tot.Base.fst" }
[ "total" ]
[ "Prims.list", "Prims.Nil", "FStar.List.Tot.Base.append", "FStar.List.Tot.Base.flatten" ]
[]
(* Copyright 2008-2014 Nikhil Swamy and Microsoft Research Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License. *) (** This module defines all pure and total operations on lists that can be used in specifications. It is implemented by FStar_List_Tot_Base.ml, any functional change and/or the addition of new functions MUST be reflected there. @summary Pure total operations on lists *) module FStar.List.Tot.Base (** Base operations *) (** [isEmpty l] returns [true] if and only if [l] is empty *) val isEmpty: list 'a -> Tot bool let isEmpty l = match l with | [] -> true | _ -> false (** [hd l] returns the first element of [l]. Requires [l] to be nonempty, at type-checking time. Named as in: OCaml, F#, Coq *) val hd: l:list 'a{Cons? l} -> Tot 'a let hd = function | hd::_ -> hd (** [tail l] returns [l] without its first element. Requires, at type-checking time, that [l] be nonempty. Similar to: tl in OCaml, F#, Coq *) val tail: l:list 'a {Cons? l} -> Tot (list 'a) let tail = function | _::tl -> tl (** [tl l] returns [l] without its first element. Requires, at type-checking time, that [l] be nonempty. Named as in: OCaml, F#, Coq *) val tl: l:list 'a {Cons? l} -> Tot (list 'a) let tl = tail (** [last l] returns the last element of [l]. Requires, at type-checking time, that [l] be nonempty. Named as in: Haskell *) val last: l:list 'a {Cons? l} -> Tot 'a let rec last = function | [hd] -> hd | _::tl -> last tl (** [init l] returns [l] without its last element. Requires, at type-checking time, that [l] be nonempty. Named as in: Haskell *) val init: l:list 'a {Cons? l} -> Tot (list 'a) let rec init = function | [_] -> [] | hd::tl -> hd::(init tl) (** [length l] returns the total number of elements in [l]. Named as in: OCaml, F#, Coq *) val length: list 'a -> Tot nat let rec length = function | [] -> 0 | _::tl -> 1 + length tl (** [nth l n] returns the [n]-th element in list [l] (with the first element being the 0-th) if [l] is long enough, or [None] otherwise. Named as in: OCaml, F#, Coq *) val nth: list 'a -> nat -> Tot (option 'a) let rec nth l n = match l with | [] -> None | hd::tl -> if n = 0 then Some hd else nth tl (n - 1) (** [index l n] returns the [n]-th element in list [l] (with the first element being the 0-th). Requires, at type-checking time, that [l] be of length at least [n+1]. *) val index: #a:Type -> l:list a -> i:nat{i < length l} -> Tot a let rec index #a (l: list a) (i:nat{i < length l}): Tot a = if i = 0 then hd l else index (tl l) (i - 1) (** [count x l] returns the number of occurrences of [x] in [l]. Requires, at type-checking time, the type of [a] to have equality defined. Similar to: [List.count_occ] in Coq. *) val count: #a:eqtype -> a -> list a -> Tot nat let rec count #a x = function | [] -> 0 | hd::tl -> if x=hd then 1 + count x tl else count x tl (** [rev_acc l1 l2] appends the elements of [l1] to the beginning of [l2], in reverse order. It is equivalent to [append (rev l1) l2], but is tail-recursive. Similar to: [List.rev_append] in OCaml, Coq. *) val rev_acc: list 'a -> list 'a -> Tot (list 'a) let rec rev_acc l acc = match l with | [] -> acc | hd::tl -> rev_acc tl (hd::acc) (** [rev l] returns the list [l] in reverse order. Named as in: OCaml, F#, Coq. *) val rev: list 'a -> Tot (list 'a) let rev l = rev_acc l [] (** [append l1 l2] appends the elements of [l2] to the end of [l1]. Named as: OCaml, F#. Similar to: [List.app] in Coq. *) val append: list 'a -> list 'a -> Tot (list 'a) let rec append x y = match x with | [] -> y | a::tl -> a::append tl y (** Defines notation [@@] for [append], as in OCaml, F# . *) let op_At x y = append x y (** [snoc (l, x)] adds [x] to the end of the list [l]. Note: We use an uncurried [snoc (l, x)] instead of the curried [snoc l x]. This is intentional. If [snoc] takes a pair instead of 2 arguments, it allows for a better pattern on [lemma_unsnoc_snoc], which connects [snoc] and [unsnoc]. In particular, if we had two arguments, then either the pattern would either be too restrictive or would lead to over-triggering. More context for this can be seen in the (collapsed and uncollapsed) comments at https://github.com/FStarLang/FStar/pull/1560 *) val snoc: (list 'a * 'a) -> Tot (list 'a) let snoc (l, x) = append l [x] (** [flatten l], where [l] is a list of lists, returns the list of the elements of the lists in [l], preserving their order. Named as in: OCaml, Coq. *)
false
false
FStar.List.Tot.Base.fst
{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 1, "max_fuel": 8, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": true, "z3cliopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }
null
val flatten: list (list 'a) -> Tot (list 'a)
[ "recursion" ]
FStar.List.Tot.Base.flatten
{ "file_name": "ulib/FStar.List.Tot.Base.fst", "git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f", "git_url": "https://github.com/FStarLang/FStar.git", "project_name": "FStar" }
l: Prims.list (Prims.list 'a) -> Prims.list 'a
{ "end_col": 38, "end_line": 145, "start_col": 20, "start_line": 143 }
Prims.Tot
val last: l:list 'a {Cons? l} -> Tot 'a
[ { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]
false
let rec last = function | [hd] -> hd | _::tl -> last tl
val last: l:list 'a {Cons? l} -> Tot 'a let rec last =
false
null
false
function | [hd] -> hd | _ :: tl -> last tl
{ "checked_file": "FStar.List.Tot.Base.fst.checked", "dependencies": [ "prims.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Classical.fsti.checked" ], "interface_file": false, "source_file": "FStar.List.Tot.Base.fst" }
[ "total" ]
[ "Prims.list", "Prims.b2t", "Prims.uu___is_Cons", "FStar.List.Tot.Base.last" ]
[]
(* Copyright 2008-2014 Nikhil Swamy and Microsoft Research Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License. *) (** This module defines all pure and total operations on lists that can be used in specifications. It is implemented by FStar_List_Tot_Base.ml, any functional change and/or the addition of new functions MUST be reflected there. @summary Pure total operations on lists *) module FStar.List.Tot.Base (** Base operations *) (** [isEmpty l] returns [true] if and only if [l] is empty *) val isEmpty: list 'a -> Tot bool let isEmpty l = match l with | [] -> true | _ -> false (** [hd l] returns the first element of [l]. Requires [l] to be nonempty, at type-checking time. Named as in: OCaml, F#, Coq *) val hd: l:list 'a{Cons? l} -> Tot 'a let hd = function | hd::_ -> hd (** [tail l] returns [l] without its first element. Requires, at type-checking time, that [l] be nonempty. Similar to: tl in OCaml, F#, Coq *) val tail: l:list 'a {Cons? l} -> Tot (list 'a) let tail = function | _::tl -> tl (** [tl l] returns [l] without its first element. Requires, at type-checking time, that [l] be nonempty. Named as in: OCaml, F#, Coq *) val tl: l:list 'a {Cons? l} -> Tot (list 'a) let tl = tail (** [last l] returns the last element of [l]. Requires, at type-checking time, that [l] be nonempty. Named as in: Haskell *)
false
false
FStar.List.Tot.Base.fst
{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 1, "max_fuel": 8, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": true, "z3cliopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }
null
val last: l:list 'a {Cons? l} -> Tot 'a
[ "recursion" ]
FStar.List.Tot.Base.last
{ "file_name": "ulib/FStar.List.Tot.Base.fst", "git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f", "git_url": "https://github.com/FStarLang/FStar.git", "project_name": "FStar" }
l: Prims.list 'a {Cons? l} -> 'a
{ "end_col": 20, "end_line": 61, "start_col": 15, "start_line": 59 }
Prims.Tot
val hd: l:list 'a{Cons? l} -> Tot 'a
[ { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]
false
let hd = function | hd::_ -> hd
val hd: l:list 'a{Cons? l} -> Tot 'a let hd =
false
null
false
function | hd :: _ -> hd
{ "checked_file": "FStar.List.Tot.Base.fst.checked", "dependencies": [ "prims.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Classical.fsti.checked" ], "interface_file": false, "source_file": "FStar.List.Tot.Base.fst" }
[ "total" ]
[ "Prims.list", "Prims.b2t", "Prims.uu___is_Cons" ]
[]
(* Copyright 2008-2014 Nikhil Swamy and Microsoft Research Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License. *) (** This module defines all pure and total operations on lists that can be used in specifications. It is implemented by FStar_List_Tot_Base.ml, any functional change and/or the addition of new functions MUST be reflected there. @summary Pure total operations on lists *) module FStar.List.Tot.Base (** Base operations *) (** [isEmpty l] returns [true] if and only if [l] is empty *) val isEmpty: list 'a -> Tot bool let isEmpty l = match l with | [] -> true | _ -> false (** [hd l] returns the first element of [l]. Requires [l] to be nonempty, at type-checking time. Named as in: OCaml, F#, Coq *)
false
false
FStar.List.Tot.Base.fst
{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 1, "max_fuel": 8, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": true, "z3cliopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }
null
val hd: l:list 'a{Cons? l} -> Tot 'a
[]
FStar.List.Tot.Base.hd
{ "file_name": "ulib/FStar.List.Tot.Base.fst", "git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f", "git_url": "https://github.com/FStarLang/FStar.git", "project_name": "FStar" }
l: Prims.list 'a {Cons? l} -> 'a
{ "end_col": 15, "end_line": 40, "start_col": 9, "start_line": 39 }
Prims.Tot
val count: #a:eqtype -> a -> list a -> Tot nat
[ { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]
false
let rec count #a x = function | [] -> 0 | hd::tl -> if x=hd then 1 + count x tl else count x tl
val count: #a:eqtype -> a -> list a -> Tot nat let rec count #a x =
false
null
false
function | [] -> 0 | hd :: tl -> if x = hd then 1 + count x tl else count x tl
{ "checked_file": "FStar.List.Tot.Base.fst.checked", "dependencies": [ "prims.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Classical.fsti.checked" ], "interface_file": false, "source_file": "FStar.List.Tot.Base.fst" }
[ "total" ]
[ "Prims.eqtype", "Prims.list", "Prims.op_Equality", "Prims.op_Addition", "FStar.List.Tot.Base.count", "Prims.bool", "Prims.nat" ]
[]
(* Copyright 2008-2014 Nikhil Swamy and Microsoft Research Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License. *) (** This module defines all pure and total operations on lists that can be used in specifications. It is implemented by FStar_List_Tot_Base.ml, any functional change and/or the addition of new functions MUST be reflected there. @summary Pure total operations on lists *) module FStar.List.Tot.Base (** Base operations *) (** [isEmpty l] returns [true] if and only if [l] is empty *) val isEmpty: list 'a -> Tot bool let isEmpty l = match l with | [] -> true | _ -> false (** [hd l] returns the first element of [l]. Requires [l] to be nonempty, at type-checking time. Named as in: OCaml, F#, Coq *) val hd: l:list 'a{Cons? l} -> Tot 'a let hd = function | hd::_ -> hd (** [tail l] returns [l] without its first element. Requires, at type-checking time, that [l] be nonempty. Similar to: tl in OCaml, F#, Coq *) val tail: l:list 'a {Cons? l} -> Tot (list 'a) let tail = function | _::tl -> tl (** [tl l] returns [l] without its first element. Requires, at type-checking time, that [l] be nonempty. Named as in: OCaml, F#, Coq *) val tl: l:list 'a {Cons? l} -> Tot (list 'a) let tl = tail (** [last l] returns the last element of [l]. Requires, at type-checking time, that [l] be nonempty. Named as in: Haskell *) val last: l:list 'a {Cons? l} -> Tot 'a let rec last = function | [hd] -> hd | _::tl -> last tl (** [init l] returns [l] without its last element. Requires, at type-checking time, that [l] be nonempty. Named as in: Haskell *) val init: l:list 'a {Cons? l} -> Tot (list 'a) let rec init = function | [_] -> [] | hd::tl -> hd::(init tl) (** [length l] returns the total number of elements in [l]. Named as in: OCaml, F#, Coq *) val length: list 'a -> Tot nat let rec length = function | [] -> 0 | _::tl -> 1 + length tl (** [nth l n] returns the [n]-th element in list [l] (with the first element being the 0-th) if [l] is long enough, or [None] otherwise. Named as in: OCaml, F#, Coq *) val nth: list 'a -> nat -> Tot (option 'a) let rec nth l n = match l with | [] -> None | hd::tl -> if n = 0 then Some hd else nth tl (n - 1) (** [index l n] returns the [n]-th element in list [l] (with the first element being the 0-th). Requires, at type-checking time, that [l] be of length at least [n+1]. *) val index: #a:Type -> l:list a -> i:nat{i < length l} -> Tot a let rec index #a (l: list a) (i:nat{i < length l}): Tot a = if i = 0 then hd l else index (tl l) (i - 1) (** [count x l] returns the number of occurrences of [x] in [l]. Requires, at type-checking time, the type of [a] to have equality defined. Similar to: [List.count_occ] in Coq. *)
false
false
FStar.List.Tot.Base.fst
{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 1, "max_fuel": 8, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": true, "z3cliopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }
null
val count: #a:eqtype -> a -> list a -> Tot nat
[ "recursion" ]
FStar.List.Tot.Base.count
{ "file_name": "ulib/FStar.List.Tot.Base.fst", "git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f", "git_url": "https://github.com/FStarLang/FStar.git", "project_name": "FStar" }
x: a -> _: Prims.list a -> Prims.nat
{ "end_col": 57, "end_line": 102, "start_col": 21, "start_line": 100 }
Prims.Tot
val find: #a:Type -> f:(a -> Tot bool) -> list a -> Tot (option (x:a{f x}))
[ { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]
false
let rec find #a f l = match l with | [] -> None #(x:a{f x}) //These type annotations are only present because it makes bootstrapping go much faster | hd::tl -> if f hd then Some #(x:a{f x}) hd else find f tl
val find: #a:Type -> f:(a -> Tot bool) -> list a -> Tot (option (x:a{f x})) let rec find #a f l =
false
null
false
match l with | [] -> None #(x: a{f x}) | hd :: tl -> if f hd then Some #(x: a{f x}) hd else find f tl
{ "checked_file": "FStar.List.Tot.Base.fst.checked", "dependencies": [ "prims.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Classical.fsti.checked" ], "interface_file": false, "source_file": "FStar.List.Tot.Base.fst" }
[ "total" ]
[ "Prims.bool", "Prims.list", "FStar.Pervasives.Native.None", "Prims.b2t", "FStar.Pervasives.Native.Some", "FStar.List.Tot.Base.find", "FStar.Pervasives.Native.option" ]
[]
(* Copyright 2008-2014 Nikhil Swamy and Microsoft Research Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License. *) (** This module defines all pure and total operations on lists that can be used in specifications. It is implemented by FStar_List_Tot_Base.ml, any functional change and/or the addition of new functions MUST be reflected there. @summary Pure total operations on lists *) module FStar.List.Tot.Base (** Base operations *) (** [isEmpty l] returns [true] if and only if [l] is empty *) val isEmpty: list 'a -> Tot bool let isEmpty l = match l with | [] -> true | _ -> false (** [hd l] returns the first element of [l]. Requires [l] to be nonempty, at type-checking time. Named as in: OCaml, F#, Coq *) val hd: l:list 'a{Cons? l} -> Tot 'a let hd = function | hd::_ -> hd (** [tail l] returns [l] without its first element. Requires, at type-checking time, that [l] be nonempty. Similar to: tl in OCaml, F#, Coq *) val tail: l:list 'a {Cons? l} -> Tot (list 'a) let tail = function | _::tl -> tl (** [tl l] returns [l] without its first element. Requires, at type-checking time, that [l] be nonempty. Named as in: OCaml, F#, Coq *) val tl: l:list 'a {Cons? l} -> Tot (list 'a) let tl = tail (** [last l] returns the last element of [l]. Requires, at type-checking time, that [l] be nonempty. Named as in: Haskell *) val last: l:list 'a {Cons? l} -> Tot 'a let rec last = function | [hd] -> hd | _::tl -> last tl (** [init l] returns [l] without its last element. Requires, at type-checking time, that [l] be nonempty. Named as in: Haskell *) val init: l:list 'a {Cons? l} -> Tot (list 'a) let rec init = function | [_] -> [] | hd::tl -> hd::(init tl) (** [length l] returns the total number of elements in [l]. Named as in: OCaml, F#, Coq *) val length: list 'a -> Tot nat let rec length = function | [] -> 0 | _::tl -> 1 + length tl (** [nth l n] returns the [n]-th element in list [l] (with the first element being the 0-th) if [l] is long enough, or [None] otherwise. Named as in: OCaml, F#, Coq *) val nth: list 'a -> nat -> Tot (option 'a) let rec nth l n = match l with | [] -> None | hd::tl -> if n = 0 then Some hd else nth tl (n - 1) (** [index l n] returns the [n]-th element in list [l] (with the first element being the 0-th). Requires, at type-checking time, that [l] be of length at least [n+1]. *) val index: #a:Type -> l:list a -> i:nat{i < length l} -> Tot a let rec index #a (l: list a) (i:nat{i < length l}): Tot a = if i = 0 then hd l else index (tl l) (i - 1) (** [count x l] returns the number of occurrences of [x] in [l]. Requires, at type-checking time, the type of [a] to have equality defined. Similar to: [List.count_occ] in Coq. *) val count: #a:eqtype -> a -> list a -> Tot nat let rec count #a x = function | [] -> 0 | hd::tl -> if x=hd then 1 + count x tl else count x tl (** [rev_acc l1 l2] appends the elements of [l1] to the beginning of [l2], in reverse order. It is equivalent to [append (rev l1) l2], but is tail-recursive. Similar to: [List.rev_append] in OCaml, Coq. *) val rev_acc: list 'a -> list 'a -> Tot (list 'a) let rec rev_acc l acc = match l with | [] -> acc | hd::tl -> rev_acc tl (hd::acc) (** [rev l] returns the list [l] in reverse order. Named as in: OCaml, F#, Coq. *) val rev: list 'a -> Tot (list 'a) let rev l = rev_acc l [] (** [append l1 l2] appends the elements of [l2] to the end of [l1]. Named as: OCaml, F#. Similar to: [List.app] in Coq. *) val append: list 'a -> list 'a -> Tot (list 'a) let rec append x y = match x with | [] -> y | a::tl -> a::append tl y (** Defines notation [@@] for [append], as in OCaml, F# . *) let op_At x y = append x y (** [snoc (l, x)] adds [x] to the end of the list [l]. Note: We use an uncurried [snoc (l, x)] instead of the curried [snoc l x]. This is intentional. If [snoc] takes a pair instead of 2 arguments, it allows for a better pattern on [lemma_unsnoc_snoc], which connects [snoc] and [unsnoc]. In particular, if we had two arguments, then either the pattern would either be too restrictive or would lead to over-triggering. More context for this can be seen in the (collapsed and uncollapsed) comments at https://github.com/FStarLang/FStar/pull/1560 *) val snoc: (list 'a * 'a) -> Tot (list 'a) let snoc (l, x) = append l [x] (** [flatten l], where [l] is a list of lists, returns the list of the elements of the lists in [l], preserving their order. Named as in: OCaml, Coq. *) val flatten: list (list 'a) -> Tot (list 'a) let rec flatten l = match l with | [] -> [] | hd::tl -> append hd (flatten tl) (** [map f l] applies [f] to each element of [l] and returns the list of results, in the order of the original elements in [l]. Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml, Coq, F# *) val map: ('a -> Tot 'b) -> list 'a -> Tot (list 'b) let rec map f x = match x with | [] -> [] | a::tl -> f a::map f tl (** [mapi_init f l n] applies, for each [k], [f (n+k)] to the [k]-th element of [l] and returns the list of results, in the order of the original elements in [l]. Requires, at type-checking time, [f] to be a pure total function. *) val mapi_init: (int -> 'a -> Tot 'b) -> list 'a -> int -> Tot (list 'b) let rec mapi_init f l i = match l with | [] -> [] | hd::tl -> (f i hd)::(mapi_init f tl (i+1)) (** [mapi f l] applies, for each [k], [f k] to the [k]-th element of [l] and returns the list of results, in the order of the original elements in [l]. Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml *) val mapi: (int -> 'a -> Tot 'b) -> list 'a -> Tot (list 'b) let mapi f l = mapi_init f l 0 (** [concatMap f l] applies [f] to each element of [l] and returns the concatenation of the results, in the order of the original elements of [l]. This is equivalent to [flatten (map f l)]. Requires, at type-checking time, [f] to be a pure total function. *) val concatMap: ('a -> Tot (list 'b)) -> list 'a -> Tot (list 'b) let rec concatMap f = function | [] -> [] | a::tl -> let fa = f a in let ftl = concatMap f tl in append fa ftl (** [fold_left f x [y1; y2; ...; yn]] computes (f (... (f x y1) y2) ... yn). Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml, Coq. *) val fold_left: ('a -> 'b -> Tot 'a) -> 'a -> l:list 'b -> Tot 'a (decreases l) let rec fold_left f x l = match l with | [] -> x | hd::tl -> fold_left f (f x hd) tl (** [fold_right f [x1; x2; ...; xn] y] computes (f x1 (f x2 (... (f xn y)) ... )). Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml, Coq *) val fold_right: ('a -> 'b -> Tot 'b) -> list 'a -> 'b -> Tot 'b let rec fold_right f l x = match l with | [] -> x | hd::tl -> f hd (fold_right f tl x) (** [fold_right_gtot] is just like [fold_right], except `f` is a ghost function **) let rec fold_right_gtot (#a:Type) (#b:Type) (l:list a) (f:a -> b -> GTot b) (x:b) : GTot b = match l with | [] -> x | hd::tl -> f hd (fold_right_gtot tl f x) (* We define map in terms of fold, to share simple lemmas *) let map_gtot #a #b (f:a -> GTot b) (x:list a) : GTot (list b) = fold_right_gtot x (fun x tl -> f x :: tl) [] (** [fold_left2 f x [y1; y2; ...; yn] [z1; z2; ...; zn]] computes (f (... (f x y1 z1) y2 z2) ... yn zn). Requires, at type-checking time, [f] to be a pure total function, and the lists [y1; y2; ...; yn] and [z1; z2; ...; zn] to have the same lengths. Named as in: OCaml *) val fold_left2 : f:('a -> 'b -> 'c -> Tot 'a) -> accu:'a -> l1:(list 'b) -> l2:(list 'c) -> Pure 'a (requires (length l1 == length l2)) (ensures (fun _ -> True)) (decreases l1) let rec fold_left2 f accu l1 l2 = match (l1, l2) with | ([], []) -> accu | (a1::l1, a2::l2) -> fold_left2 f (f accu a1 a2) l1 l2 (** Propositional membership (as in Coq). Does not require decidable equality. *) (** [memP x l] holds if, and only if, [x] appears as an element of [l]. Similar to: List.In in Coq. *) let rec memP (#a: Type) (x: a) (l: list a) : Tot Type0 = match l with | [] -> False | y :: q -> x == y \/ memP x q (** List searching **) (** [mem x l] returns [true] if, and only if, [x] appears as an element of [l]. Requires, at type-checking time, the type of elements of [l] to have decidable equality. Named as in: OCaml. See also: List.In in Coq, which is propositional. *) val mem: #a:eqtype -> a -> list a -> Tot bool let rec mem #a x = function | [] -> false | hd::tl -> if hd = x then true else mem x tl (** [contains x l] returns [true] if, and only if, [x] appears as an element of [l]. Requires, at type-checking time, the type of elements of [l] to have decidable equality. It is equivalent to: [mem x l]. TODO: should we rather swap the order of arguments? *) let contains : #a:eqtype -> a -> list a -> Tot bool = mem (** [existsb f l] returns [true] if, and only if, there exists some element [x] in [l] such that [f x] holds. *) val existsb: #a:Type -> f:(a -> Tot bool) -> list a -> Tot bool let rec existsb #a f l = match l with | [] -> false | hd::tl -> if f hd then true else existsb f tl (** [find f l] returns [Some x] for some element [x] appearing in [l] such that [f x] holds, or [None] only if no such [x] exists. *) val find: #a:Type -> f:(a -> Tot bool) -> list a
false
false
FStar.List.Tot.Base.fst
{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 1, "max_fuel": 8, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": true, "z3cliopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }
null
val find: #a:Type -> f:(a -> Tot bool) -> list a -> Tot (option (x:a{f x}))
[ "recursion" ]
FStar.List.Tot.Base.find
{ "file_name": "ulib/FStar.List.Tot.Base.fst", "git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f", "git_url": "https://github.com/FStarLang/FStar.git", "project_name": "FStar" }
f: (_: a -> Prims.bool) -> l: Prims.list a -> FStar.Pervasives.Native.option (x: a{f x})
{ "end_col": 61, "end_line": 268, "start_col": 22, "start_line": 266 }
Prims.Tot
val nth: list 'a -> nat -> Tot (option 'a)
[ { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]
false
let rec nth l n = match l with | [] -> None | hd::tl -> if n = 0 then Some hd else nth tl (n - 1)
val nth: list 'a -> nat -> Tot (option 'a) let rec nth l n =
false
null
false
match l with | [] -> None | hd :: tl -> if n = 0 then Some hd else nth tl (n - 1)
{ "checked_file": "FStar.List.Tot.Base.fst.checked", "dependencies": [ "prims.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Classical.fsti.checked" ], "interface_file": false, "source_file": "FStar.List.Tot.Base.fst" }
[ "total" ]
[ "Prims.list", "Prims.nat", "FStar.Pervasives.Native.None", "Prims.op_Equality", "Prims.int", "FStar.Pervasives.Native.Some", "Prims.bool", "FStar.List.Tot.Base.nth", "Prims.op_Subtraction", "FStar.Pervasives.Native.option" ]
[]
(* Copyright 2008-2014 Nikhil Swamy and Microsoft Research Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License. *) (** This module defines all pure and total operations on lists that can be used in specifications. It is implemented by FStar_List_Tot_Base.ml, any functional change and/or the addition of new functions MUST be reflected there. @summary Pure total operations on lists *) module FStar.List.Tot.Base (** Base operations *) (** [isEmpty l] returns [true] if and only if [l] is empty *) val isEmpty: list 'a -> Tot bool let isEmpty l = match l with | [] -> true | _ -> false (** [hd l] returns the first element of [l]. Requires [l] to be nonempty, at type-checking time. Named as in: OCaml, F#, Coq *) val hd: l:list 'a{Cons? l} -> Tot 'a let hd = function | hd::_ -> hd (** [tail l] returns [l] without its first element. Requires, at type-checking time, that [l] be nonempty. Similar to: tl in OCaml, F#, Coq *) val tail: l:list 'a {Cons? l} -> Tot (list 'a) let tail = function | _::tl -> tl (** [tl l] returns [l] without its first element. Requires, at type-checking time, that [l] be nonempty. Named as in: OCaml, F#, Coq *) val tl: l:list 'a {Cons? l} -> Tot (list 'a) let tl = tail (** [last l] returns the last element of [l]. Requires, at type-checking time, that [l] be nonempty. Named as in: Haskell *) val last: l:list 'a {Cons? l} -> Tot 'a let rec last = function | [hd] -> hd | _::tl -> last tl (** [init l] returns [l] without its last element. Requires, at type-checking time, that [l] be nonempty. Named as in: Haskell *) val init: l:list 'a {Cons? l} -> Tot (list 'a) let rec init = function | [_] -> [] | hd::tl -> hd::(init tl) (** [length l] returns the total number of elements in [l]. Named as in: OCaml, F#, Coq *) val length: list 'a -> Tot nat let rec length = function | [] -> 0 | _::tl -> 1 + length tl (** [nth l n] returns the [n]-th element in list [l] (with the first element being the 0-th) if [l] is long enough, or [None] otherwise. Named as in: OCaml, F#, Coq *)
false
false
FStar.List.Tot.Base.fst
{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 1, "max_fuel": 8, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": true, "z3cliopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }
null
val nth: list 'a -> nat -> Tot (option 'a)
[ "recursion" ]
FStar.List.Tot.Base.nth
{ "file_name": "ulib/FStar.List.Tot.Base.fst", "git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f", "git_url": "https://github.com/FStarLang/FStar.git", "project_name": "FStar" }
l: Prims.list 'a -> n: Prims.nat -> FStar.Pervasives.Native.option 'a
{ "end_col": 55, "end_line": 84, "start_col": 18, "start_line": 82 }
Prims.GTot
val fold_right_gtot (#a #b: Type) (l: list a) (f: (a -> b -> GTot b)) (x: b) : GTot b
[ { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]
false
let rec fold_right_gtot (#a:Type) (#b:Type) (l:list a) (f:a -> b -> GTot b) (x:b) : GTot b = match l with | [] -> x | hd::tl -> f hd (fold_right_gtot tl f x)
val fold_right_gtot (#a #b: Type) (l: list a) (f: (a -> b -> GTot b)) (x: b) : GTot b let rec fold_right_gtot (#a #b: Type) (l: list a) (f: (a -> b -> GTot b)) (x: b) : GTot b =
false
null
false
match l with | [] -> x | hd :: tl -> f hd (fold_right_gtot tl f x)
{ "checked_file": "FStar.List.Tot.Base.fst.checked", "dependencies": [ "prims.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Classical.fsti.checked" ], "interface_file": false, "source_file": "FStar.List.Tot.Base.fst" }
[ "sometrivial" ]
[ "Prims.list", "FStar.List.Tot.Base.fold_right_gtot" ]
[]
(* Copyright 2008-2014 Nikhil Swamy and Microsoft Research Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License. *) (** This module defines all pure and total operations on lists that can be used in specifications. It is implemented by FStar_List_Tot_Base.ml, any functional change and/or the addition of new functions MUST be reflected there. @summary Pure total operations on lists *) module FStar.List.Tot.Base (** Base operations *) (** [isEmpty l] returns [true] if and only if [l] is empty *) val isEmpty: list 'a -> Tot bool let isEmpty l = match l with | [] -> true | _ -> false (** [hd l] returns the first element of [l]. Requires [l] to be nonempty, at type-checking time. Named as in: OCaml, F#, Coq *) val hd: l:list 'a{Cons? l} -> Tot 'a let hd = function | hd::_ -> hd (** [tail l] returns [l] without its first element. Requires, at type-checking time, that [l] be nonempty. Similar to: tl in OCaml, F#, Coq *) val tail: l:list 'a {Cons? l} -> Tot (list 'a) let tail = function | _::tl -> tl (** [tl l] returns [l] without its first element. Requires, at type-checking time, that [l] be nonempty. Named as in: OCaml, F#, Coq *) val tl: l:list 'a {Cons? l} -> Tot (list 'a) let tl = tail (** [last l] returns the last element of [l]. Requires, at type-checking time, that [l] be nonempty. Named as in: Haskell *) val last: l:list 'a {Cons? l} -> Tot 'a let rec last = function | [hd] -> hd | _::tl -> last tl (** [init l] returns [l] without its last element. Requires, at type-checking time, that [l] be nonempty. Named as in: Haskell *) val init: l:list 'a {Cons? l} -> Tot (list 'a) let rec init = function | [_] -> [] | hd::tl -> hd::(init tl) (** [length l] returns the total number of elements in [l]. Named as in: OCaml, F#, Coq *) val length: list 'a -> Tot nat let rec length = function | [] -> 0 | _::tl -> 1 + length tl (** [nth l n] returns the [n]-th element in list [l] (with the first element being the 0-th) if [l] is long enough, or [None] otherwise. Named as in: OCaml, F#, Coq *) val nth: list 'a -> nat -> Tot (option 'a) let rec nth l n = match l with | [] -> None | hd::tl -> if n = 0 then Some hd else nth tl (n - 1) (** [index l n] returns the [n]-th element in list [l] (with the first element being the 0-th). Requires, at type-checking time, that [l] be of length at least [n+1]. *) val index: #a:Type -> l:list a -> i:nat{i < length l} -> Tot a let rec index #a (l: list a) (i:nat{i < length l}): Tot a = if i = 0 then hd l else index (tl l) (i - 1) (** [count x l] returns the number of occurrences of [x] in [l]. Requires, at type-checking time, the type of [a] to have equality defined. Similar to: [List.count_occ] in Coq. *) val count: #a:eqtype -> a -> list a -> Tot nat let rec count #a x = function | [] -> 0 | hd::tl -> if x=hd then 1 + count x tl else count x tl (** [rev_acc l1 l2] appends the elements of [l1] to the beginning of [l2], in reverse order. It is equivalent to [append (rev l1) l2], but is tail-recursive. Similar to: [List.rev_append] in OCaml, Coq. *) val rev_acc: list 'a -> list 'a -> Tot (list 'a) let rec rev_acc l acc = match l with | [] -> acc | hd::tl -> rev_acc tl (hd::acc) (** [rev l] returns the list [l] in reverse order. Named as in: OCaml, F#, Coq. *) val rev: list 'a -> Tot (list 'a) let rev l = rev_acc l [] (** [append l1 l2] appends the elements of [l2] to the end of [l1]. Named as: OCaml, F#. Similar to: [List.app] in Coq. *) val append: list 'a -> list 'a -> Tot (list 'a) let rec append x y = match x with | [] -> y | a::tl -> a::append tl y (** Defines notation [@@] for [append], as in OCaml, F# . *) let op_At x y = append x y (** [snoc (l, x)] adds [x] to the end of the list [l]. Note: We use an uncurried [snoc (l, x)] instead of the curried [snoc l x]. This is intentional. If [snoc] takes a pair instead of 2 arguments, it allows for a better pattern on [lemma_unsnoc_snoc], which connects [snoc] and [unsnoc]. In particular, if we had two arguments, then either the pattern would either be too restrictive or would lead to over-triggering. More context for this can be seen in the (collapsed and uncollapsed) comments at https://github.com/FStarLang/FStar/pull/1560 *) val snoc: (list 'a * 'a) -> Tot (list 'a) let snoc (l, x) = append l [x] (** [flatten l], where [l] is a list of lists, returns the list of the elements of the lists in [l], preserving their order. Named as in: OCaml, Coq. *) val flatten: list (list 'a) -> Tot (list 'a) let rec flatten l = match l with | [] -> [] | hd::tl -> append hd (flatten tl) (** [map f l] applies [f] to each element of [l] and returns the list of results, in the order of the original elements in [l]. Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml, Coq, F# *) val map: ('a -> Tot 'b) -> list 'a -> Tot (list 'b) let rec map f x = match x with | [] -> [] | a::tl -> f a::map f tl (** [mapi_init f l n] applies, for each [k], [f (n+k)] to the [k]-th element of [l] and returns the list of results, in the order of the original elements in [l]. Requires, at type-checking time, [f] to be a pure total function. *) val mapi_init: (int -> 'a -> Tot 'b) -> list 'a -> int -> Tot (list 'b) let rec mapi_init f l i = match l with | [] -> [] | hd::tl -> (f i hd)::(mapi_init f tl (i+1)) (** [mapi f l] applies, for each [k], [f k] to the [k]-th element of [l] and returns the list of results, in the order of the original elements in [l]. Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml *) val mapi: (int -> 'a -> Tot 'b) -> list 'a -> Tot (list 'b) let mapi f l = mapi_init f l 0 (** [concatMap f l] applies [f] to each element of [l] and returns the concatenation of the results, in the order of the original elements of [l]. This is equivalent to [flatten (map f l)]. Requires, at type-checking time, [f] to be a pure total function. *) val concatMap: ('a -> Tot (list 'b)) -> list 'a -> Tot (list 'b) let rec concatMap f = function | [] -> [] | a::tl -> let fa = f a in let ftl = concatMap f tl in append fa ftl (** [fold_left f x [y1; y2; ...; yn]] computes (f (... (f x y1) y2) ... yn). Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml, Coq. *) val fold_left: ('a -> 'b -> Tot 'a) -> 'a -> l:list 'b -> Tot 'a (decreases l) let rec fold_left f x l = match l with | [] -> x | hd::tl -> fold_left f (f x hd) tl (** [fold_right f [x1; x2; ...; xn] y] computes (f x1 (f x2 (... (f xn y)) ... )). Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml, Coq *) val fold_right: ('a -> 'b -> Tot 'b) -> list 'a -> 'b -> Tot 'b let rec fold_right f l x = match l with | [] -> x | hd::tl -> f hd (fold_right f tl x) (** [fold_right_gtot] is just like [fold_right], except `f` is a ghost function **) let rec fold_right_gtot (#a:Type) (#b:Type) (l:list a) (f:a -> b -> GTot b) (x:b)
false
false
FStar.List.Tot.Base.fst
{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 1, "max_fuel": 8, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": true, "z3cliopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }
null
val fold_right_gtot (#a #b: Type) (l: list a) (f: (a -> b -> GTot b)) (x: b) : GTot b
[ "recursion" ]
FStar.List.Tot.Base.fold_right_gtot
{ "file_name": "ulib/FStar.List.Tot.Base.fst", "git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f", "git_url": "https://github.com/FStarLang/FStar.git", "project_name": "FStar" }
l: Prims.list a -> f: (_: a -> _: b -> Prims.GTot b) -> x: b -> Prims.GTot b
{ "end_col": 45, "end_line": 205, "start_col": 4, "start_line": 203 }
Prims.Tot
val mapi_init: (int -> 'a -> Tot 'b) -> list 'a -> int -> Tot (list 'b)
[ { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]
false
let rec mapi_init f l i = match l with | [] -> [] | hd::tl -> (f i hd)::(mapi_init f tl (i+1))
val mapi_init: (int -> 'a -> Tot 'b) -> list 'a -> int -> Tot (list 'b) let rec mapi_init f l i =
false
null
false
match l with | [] -> [] | hd :: tl -> (f i hd) :: (mapi_init f tl (i + 1))
{ "checked_file": "FStar.List.Tot.Base.fst.checked", "dependencies": [ "prims.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Classical.fsti.checked" ], "interface_file": false, "source_file": "FStar.List.Tot.Base.fst" }
[ "total" ]
[ "Prims.int", "Prims.list", "Prims.Nil", "Prims.Cons", "FStar.List.Tot.Base.mapi_init", "Prims.op_Addition" ]
[]
(* Copyright 2008-2014 Nikhil Swamy and Microsoft Research Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License. *) (** This module defines all pure and total operations on lists that can be used in specifications. It is implemented by FStar_List_Tot_Base.ml, any functional change and/or the addition of new functions MUST be reflected there. @summary Pure total operations on lists *) module FStar.List.Tot.Base (** Base operations *) (** [isEmpty l] returns [true] if and only if [l] is empty *) val isEmpty: list 'a -> Tot bool let isEmpty l = match l with | [] -> true | _ -> false (** [hd l] returns the first element of [l]. Requires [l] to be nonempty, at type-checking time. Named as in: OCaml, F#, Coq *) val hd: l:list 'a{Cons? l} -> Tot 'a let hd = function | hd::_ -> hd (** [tail l] returns [l] without its first element. Requires, at type-checking time, that [l] be nonempty. Similar to: tl in OCaml, F#, Coq *) val tail: l:list 'a {Cons? l} -> Tot (list 'a) let tail = function | _::tl -> tl (** [tl l] returns [l] without its first element. Requires, at type-checking time, that [l] be nonempty. Named as in: OCaml, F#, Coq *) val tl: l:list 'a {Cons? l} -> Tot (list 'a) let tl = tail (** [last l] returns the last element of [l]. Requires, at type-checking time, that [l] be nonempty. Named as in: Haskell *) val last: l:list 'a {Cons? l} -> Tot 'a let rec last = function | [hd] -> hd | _::tl -> last tl (** [init l] returns [l] without its last element. Requires, at type-checking time, that [l] be nonempty. Named as in: Haskell *) val init: l:list 'a {Cons? l} -> Tot (list 'a) let rec init = function | [_] -> [] | hd::tl -> hd::(init tl) (** [length l] returns the total number of elements in [l]. Named as in: OCaml, F#, Coq *) val length: list 'a -> Tot nat let rec length = function | [] -> 0 | _::tl -> 1 + length tl (** [nth l n] returns the [n]-th element in list [l] (with the first element being the 0-th) if [l] is long enough, or [None] otherwise. Named as in: OCaml, F#, Coq *) val nth: list 'a -> nat -> Tot (option 'a) let rec nth l n = match l with | [] -> None | hd::tl -> if n = 0 then Some hd else nth tl (n - 1) (** [index l n] returns the [n]-th element in list [l] (with the first element being the 0-th). Requires, at type-checking time, that [l] be of length at least [n+1]. *) val index: #a:Type -> l:list a -> i:nat{i < length l} -> Tot a let rec index #a (l: list a) (i:nat{i < length l}): Tot a = if i = 0 then hd l else index (tl l) (i - 1) (** [count x l] returns the number of occurrences of [x] in [l]. Requires, at type-checking time, the type of [a] to have equality defined. Similar to: [List.count_occ] in Coq. *) val count: #a:eqtype -> a -> list a -> Tot nat let rec count #a x = function | [] -> 0 | hd::tl -> if x=hd then 1 + count x tl else count x tl (** [rev_acc l1 l2] appends the elements of [l1] to the beginning of [l2], in reverse order. It is equivalent to [append (rev l1) l2], but is tail-recursive. Similar to: [List.rev_append] in OCaml, Coq. *) val rev_acc: list 'a -> list 'a -> Tot (list 'a) let rec rev_acc l acc = match l with | [] -> acc | hd::tl -> rev_acc tl (hd::acc) (** [rev l] returns the list [l] in reverse order. Named as in: OCaml, F#, Coq. *) val rev: list 'a -> Tot (list 'a) let rev l = rev_acc l [] (** [append l1 l2] appends the elements of [l2] to the end of [l1]. Named as: OCaml, F#. Similar to: [List.app] in Coq. *) val append: list 'a -> list 'a -> Tot (list 'a) let rec append x y = match x with | [] -> y | a::tl -> a::append tl y (** Defines notation [@@] for [append], as in OCaml, F# . *) let op_At x y = append x y (** [snoc (l, x)] adds [x] to the end of the list [l]. Note: We use an uncurried [snoc (l, x)] instead of the curried [snoc l x]. This is intentional. If [snoc] takes a pair instead of 2 arguments, it allows for a better pattern on [lemma_unsnoc_snoc], which connects [snoc] and [unsnoc]. In particular, if we had two arguments, then either the pattern would either be too restrictive or would lead to over-triggering. More context for this can be seen in the (collapsed and uncollapsed) comments at https://github.com/FStarLang/FStar/pull/1560 *) val snoc: (list 'a * 'a) -> Tot (list 'a) let snoc (l, x) = append l [x] (** [flatten l], where [l] is a list of lists, returns the list of the elements of the lists in [l], preserving their order. Named as in: OCaml, Coq. *) val flatten: list (list 'a) -> Tot (list 'a) let rec flatten l = match l with | [] -> [] | hd::tl -> append hd (flatten tl) (** [map f l] applies [f] to each element of [l] and returns the list of results, in the order of the original elements in [l]. Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml, Coq, F# *) val map: ('a -> Tot 'b) -> list 'a -> Tot (list 'b) let rec map f x = match x with | [] -> [] | a::tl -> f a::map f tl (** [mapi_init f l n] applies, for each [k], [f (n+k)] to the [k]-th element of [l] and returns the list of results, in the order of the original elements in [l]. Requires, at type-checking time, [f] to be a pure total function. *)
false
false
FStar.List.Tot.Base.fst
{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 1, "max_fuel": 8, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": true, "z3cliopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }
null
val mapi_init: (int -> 'a -> Tot 'b) -> list 'a -> int -> Tot (list 'b)
[ "recursion" ]
FStar.List.Tot.Base.mapi_init
{ "file_name": "ulib/FStar.List.Tot.Base.fst", "git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f", "git_url": "https://github.com/FStarLang/FStar.git", "project_name": "FStar" }
f: (_: Prims.int -> _: 'a -> 'b) -> l: Prims.list 'a -> i: Prims.int -> Prims.list 'b
{ "end_col": 48, "end_line": 162, "start_col": 26, "start_line": 160 }
Prims.Tot
val append: list 'a -> list 'a -> Tot (list 'a)
[ { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]
false
let rec append x y = match x with | [] -> y | a::tl -> a::append tl y
val append: list 'a -> list 'a -> Tot (list 'a) let rec append x y =
false
null
false
match x with | [] -> y | a :: tl -> a :: append tl y
{ "checked_file": "FStar.List.Tot.Base.fst.checked", "dependencies": [ "prims.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Classical.fsti.checked" ], "interface_file": false, "source_file": "FStar.List.Tot.Base.fst" }
[ "total" ]
[ "Prims.list", "Prims.Cons", "FStar.List.Tot.Base.append" ]
[]
(* Copyright 2008-2014 Nikhil Swamy and Microsoft Research Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License. *) (** This module defines all pure and total operations on lists that can be used in specifications. It is implemented by FStar_List_Tot_Base.ml, any functional change and/or the addition of new functions MUST be reflected there. @summary Pure total operations on lists *) module FStar.List.Tot.Base (** Base operations *) (** [isEmpty l] returns [true] if and only if [l] is empty *) val isEmpty: list 'a -> Tot bool let isEmpty l = match l with | [] -> true | _ -> false (** [hd l] returns the first element of [l]. Requires [l] to be nonempty, at type-checking time. Named as in: OCaml, F#, Coq *) val hd: l:list 'a{Cons? l} -> Tot 'a let hd = function | hd::_ -> hd (** [tail l] returns [l] without its first element. Requires, at type-checking time, that [l] be nonempty. Similar to: tl in OCaml, F#, Coq *) val tail: l:list 'a {Cons? l} -> Tot (list 'a) let tail = function | _::tl -> tl (** [tl l] returns [l] without its first element. Requires, at type-checking time, that [l] be nonempty. Named as in: OCaml, F#, Coq *) val tl: l:list 'a {Cons? l} -> Tot (list 'a) let tl = tail (** [last l] returns the last element of [l]. Requires, at type-checking time, that [l] be nonempty. Named as in: Haskell *) val last: l:list 'a {Cons? l} -> Tot 'a let rec last = function | [hd] -> hd | _::tl -> last tl (** [init l] returns [l] without its last element. Requires, at type-checking time, that [l] be nonempty. Named as in: Haskell *) val init: l:list 'a {Cons? l} -> Tot (list 'a) let rec init = function | [_] -> [] | hd::tl -> hd::(init tl) (** [length l] returns the total number of elements in [l]. Named as in: OCaml, F#, Coq *) val length: list 'a -> Tot nat let rec length = function | [] -> 0 | _::tl -> 1 + length tl (** [nth l n] returns the [n]-th element in list [l] (with the first element being the 0-th) if [l] is long enough, or [None] otherwise. Named as in: OCaml, F#, Coq *) val nth: list 'a -> nat -> Tot (option 'a) let rec nth l n = match l with | [] -> None | hd::tl -> if n = 0 then Some hd else nth tl (n - 1) (** [index l n] returns the [n]-th element in list [l] (with the first element being the 0-th). Requires, at type-checking time, that [l] be of length at least [n+1]. *) val index: #a:Type -> l:list a -> i:nat{i < length l} -> Tot a let rec index #a (l: list a) (i:nat{i < length l}): Tot a = if i = 0 then hd l else index (tl l) (i - 1) (** [count x l] returns the number of occurrences of [x] in [l]. Requires, at type-checking time, the type of [a] to have equality defined. Similar to: [List.count_occ] in Coq. *) val count: #a:eqtype -> a -> list a -> Tot nat let rec count #a x = function | [] -> 0 | hd::tl -> if x=hd then 1 + count x tl else count x tl (** [rev_acc l1 l2] appends the elements of [l1] to the beginning of [l2], in reverse order. It is equivalent to [append (rev l1) l2], but is tail-recursive. Similar to: [List.rev_append] in OCaml, Coq. *) val rev_acc: list 'a -> list 'a -> Tot (list 'a) let rec rev_acc l acc = match l with | [] -> acc | hd::tl -> rev_acc tl (hd::acc) (** [rev l] returns the list [l] in reverse order. Named as in: OCaml, F#, Coq. *) val rev: list 'a -> Tot (list 'a) let rev l = rev_acc l [] (** [append l1 l2] appends the elements of [l2] to the end of [l1]. Named as: OCaml, F#. Similar to: [List.app] in Coq. *)
false
false
FStar.List.Tot.Base.fst
{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 1, "max_fuel": 8, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": true, "z3cliopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }
null
val append: list 'a -> list 'a -> Tot (list 'a)
[ "recursion" ]
FStar.List.Tot.Base.append
{ "file_name": "ulib/FStar.List.Tot.Base.fst", "git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f", "git_url": "https://github.com/FStarLang/FStar.git", "project_name": "FStar" }
x: Prims.list 'a -> y: Prims.list 'a -> Prims.list 'a
{ "end_col": 27, "end_line": 121, "start_col": 21, "start_line": 119 }
Prims.Tot
val map: ('a -> Tot 'b) -> list 'a -> Tot (list 'b)
[ { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]
false
let rec map f x = match x with | [] -> [] | a::tl -> f a::map f tl
val map: ('a -> Tot 'b) -> list 'a -> Tot (list 'b) let rec map f x =
false
null
false
match x with | [] -> [] | a :: tl -> f a :: map f tl
{ "checked_file": "FStar.List.Tot.Base.fst.checked", "dependencies": [ "prims.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Classical.fsti.checked" ], "interface_file": false, "source_file": "FStar.List.Tot.Base.fst" }
[ "total" ]
[ "Prims.list", "Prims.Nil", "Prims.Cons", "FStar.List.Tot.Base.map" ]
[]
(* Copyright 2008-2014 Nikhil Swamy and Microsoft Research Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License. *) (** This module defines all pure and total operations on lists that can be used in specifications. It is implemented by FStar_List_Tot_Base.ml, any functional change and/or the addition of new functions MUST be reflected there. @summary Pure total operations on lists *) module FStar.List.Tot.Base (** Base operations *) (** [isEmpty l] returns [true] if and only if [l] is empty *) val isEmpty: list 'a -> Tot bool let isEmpty l = match l with | [] -> true | _ -> false (** [hd l] returns the first element of [l]. Requires [l] to be nonempty, at type-checking time. Named as in: OCaml, F#, Coq *) val hd: l:list 'a{Cons? l} -> Tot 'a let hd = function | hd::_ -> hd (** [tail l] returns [l] without its first element. Requires, at type-checking time, that [l] be nonempty. Similar to: tl in OCaml, F#, Coq *) val tail: l:list 'a {Cons? l} -> Tot (list 'a) let tail = function | _::tl -> tl (** [tl l] returns [l] without its first element. Requires, at type-checking time, that [l] be nonempty. Named as in: OCaml, F#, Coq *) val tl: l:list 'a {Cons? l} -> Tot (list 'a) let tl = tail (** [last l] returns the last element of [l]. Requires, at type-checking time, that [l] be nonempty. Named as in: Haskell *) val last: l:list 'a {Cons? l} -> Tot 'a let rec last = function | [hd] -> hd | _::tl -> last tl (** [init l] returns [l] without its last element. Requires, at type-checking time, that [l] be nonempty. Named as in: Haskell *) val init: l:list 'a {Cons? l} -> Tot (list 'a) let rec init = function | [_] -> [] | hd::tl -> hd::(init tl) (** [length l] returns the total number of elements in [l]. Named as in: OCaml, F#, Coq *) val length: list 'a -> Tot nat let rec length = function | [] -> 0 | _::tl -> 1 + length tl (** [nth l n] returns the [n]-th element in list [l] (with the first element being the 0-th) if [l] is long enough, or [None] otherwise. Named as in: OCaml, F#, Coq *) val nth: list 'a -> nat -> Tot (option 'a) let rec nth l n = match l with | [] -> None | hd::tl -> if n = 0 then Some hd else nth tl (n - 1) (** [index l n] returns the [n]-th element in list [l] (with the first element being the 0-th). Requires, at type-checking time, that [l] be of length at least [n+1]. *) val index: #a:Type -> l:list a -> i:nat{i < length l} -> Tot a let rec index #a (l: list a) (i:nat{i < length l}): Tot a = if i = 0 then hd l else index (tl l) (i - 1) (** [count x l] returns the number of occurrences of [x] in [l]. Requires, at type-checking time, the type of [a] to have equality defined. Similar to: [List.count_occ] in Coq. *) val count: #a:eqtype -> a -> list a -> Tot nat let rec count #a x = function | [] -> 0 | hd::tl -> if x=hd then 1 + count x tl else count x tl (** [rev_acc l1 l2] appends the elements of [l1] to the beginning of [l2], in reverse order. It is equivalent to [append (rev l1) l2], but is tail-recursive. Similar to: [List.rev_append] in OCaml, Coq. *) val rev_acc: list 'a -> list 'a -> Tot (list 'a) let rec rev_acc l acc = match l with | [] -> acc | hd::tl -> rev_acc tl (hd::acc) (** [rev l] returns the list [l] in reverse order. Named as in: OCaml, F#, Coq. *) val rev: list 'a -> Tot (list 'a) let rev l = rev_acc l [] (** [append l1 l2] appends the elements of [l2] to the end of [l1]. Named as: OCaml, F#. Similar to: [List.app] in Coq. *) val append: list 'a -> list 'a -> Tot (list 'a) let rec append x y = match x with | [] -> y | a::tl -> a::append tl y (** Defines notation [@@] for [append], as in OCaml, F# . *) let op_At x y = append x y (** [snoc (l, x)] adds [x] to the end of the list [l]. Note: We use an uncurried [snoc (l, x)] instead of the curried [snoc l x]. This is intentional. If [snoc] takes a pair instead of 2 arguments, it allows for a better pattern on [lemma_unsnoc_snoc], which connects [snoc] and [unsnoc]. In particular, if we had two arguments, then either the pattern would either be too restrictive or would lead to over-triggering. More context for this can be seen in the (collapsed and uncollapsed) comments at https://github.com/FStarLang/FStar/pull/1560 *) val snoc: (list 'a * 'a) -> Tot (list 'a) let snoc (l, x) = append l [x] (** [flatten l], where [l] is a list of lists, returns the list of the elements of the lists in [l], preserving their order. Named as in: OCaml, Coq. *) val flatten: list (list 'a) -> Tot (list 'a) let rec flatten l = match l with | [] -> [] | hd::tl -> append hd (flatten tl) (** [map f l] applies [f] to each element of [l] and returns the list of results, in the order of the original elements in [l]. Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml, Coq, F# *)
false
false
FStar.List.Tot.Base.fst
{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 1, "max_fuel": 8, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": true, "z3cliopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }
null
val map: ('a -> Tot 'b) -> list 'a -> Tot (list 'b)
[ "recursion" ]
FStar.List.Tot.Base.map
{ "file_name": "ulib/FStar.List.Tot.Base.fst", "git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f", "git_url": "https://github.com/FStarLang/FStar.git", "project_name": "FStar" }
f: (_: 'a -> 'b) -> x: Prims.list 'a -> Prims.list 'b
{ "end_col": 26, "end_line": 153, "start_col": 18, "start_line": 151 }
Prims.Tot
val init: l:list 'a {Cons? l} -> Tot (list 'a)
[ { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]
false
let rec init = function | [_] -> [] | hd::tl -> hd::(init tl)
val init: l:list 'a {Cons? l} -> Tot (list 'a) let rec init =
false
null
false
function | [_] -> [] | hd :: tl -> hd :: (init tl)
{ "checked_file": "FStar.List.Tot.Base.fst.checked", "dependencies": [ "prims.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Classical.fsti.checked" ], "interface_file": false, "source_file": "FStar.List.Tot.Base.fst" }
[ "total" ]
[ "Prims.list", "Prims.b2t", "Prims.uu___is_Cons", "Prims.Nil", "Prims.Cons", "FStar.List.Tot.Base.init" ]
[]
(* Copyright 2008-2014 Nikhil Swamy and Microsoft Research Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License. *) (** This module defines all pure and total operations on lists that can be used in specifications. It is implemented by FStar_List_Tot_Base.ml, any functional change and/or the addition of new functions MUST be reflected there. @summary Pure total operations on lists *) module FStar.List.Tot.Base (** Base operations *) (** [isEmpty l] returns [true] if and only if [l] is empty *) val isEmpty: list 'a -> Tot bool let isEmpty l = match l with | [] -> true | _ -> false (** [hd l] returns the first element of [l]. Requires [l] to be nonempty, at type-checking time. Named as in: OCaml, F#, Coq *) val hd: l:list 'a{Cons? l} -> Tot 'a let hd = function | hd::_ -> hd (** [tail l] returns [l] without its first element. Requires, at type-checking time, that [l] be nonempty. Similar to: tl in OCaml, F#, Coq *) val tail: l:list 'a {Cons? l} -> Tot (list 'a) let tail = function | _::tl -> tl (** [tl l] returns [l] without its first element. Requires, at type-checking time, that [l] be nonempty. Named as in: OCaml, F#, Coq *) val tl: l:list 'a {Cons? l} -> Tot (list 'a) let tl = tail (** [last l] returns the last element of [l]. Requires, at type-checking time, that [l] be nonempty. Named as in: Haskell *) val last: l:list 'a {Cons? l} -> Tot 'a let rec last = function | [hd] -> hd | _::tl -> last tl (** [init l] returns [l] without its last element. Requires, at type-checking time, that [l] be nonempty. Named as in: Haskell *)
false
false
FStar.List.Tot.Base.fst
{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 1, "max_fuel": 8, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": true, "z3cliopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }
null
val init: l:list 'a {Cons? l} -> Tot (list 'a)
[ "recursion" ]
FStar.List.Tot.Base.init
{ "file_name": "ulib/FStar.List.Tot.Base.fst", "git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f", "git_url": "https://github.com/FStarLang/FStar.git", "project_name": "FStar" }
l: Prims.list 'a {Cons? l} -> Prims.list 'a
{ "end_col": 27, "end_line": 69, "start_col": 15, "start_line": 67 }
Prims.Tot
val concatMap: ('a -> Tot (list 'b)) -> list 'a -> Tot (list 'b)
[ { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]
false
let rec concatMap f = function | [] -> [] | a::tl -> let fa = f a in let ftl = concatMap f tl in append fa ftl
val concatMap: ('a -> Tot (list 'b)) -> list 'a -> Tot (list 'b) let rec concatMap f =
false
null
false
function | [] -> [] | a :: tl -> let fa = f a in let ftl = concatMap f tl in append fa ftl
{ "checked_file": "FStar.List.Tot.Base.fst.checked", "dependencies": [ "prims.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Classical.fsti.checked" ], "interface_file": false, "source_file": "FStar.List.Tot.Base.fst" }
[ "total" ]
[ "Prims.list", "Prims.Nil", "FStar.List.Tot.Base.append", "FStar.List.Tot.Base.concatMap" ]
[]
(* Copyright 2008-2014 Nikhil Swamy and Microsoft Research Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License. *) (** This module defines all pure and total operations on lists that can be used in specifications. It is implemented by FStar_List_Tot_Base.ml, any functional change and/or the addition of new functions MUST be reflected there. @summary Pure total operations on lists *) module FStar.List.Tot.Base (** Base operations *) (** [isEmpty l] returns [true] if and only if [l] is empty *) val isEmpty: list 'a -> Tot bool let isEmpty l = match l with | [] -> true | _ -> false (** [hd l] returns the first element of [l]. Requires [l] to be nonempty, at type-checking time. Named as in: OCaml, F#, Coq *) val hd: l:list 'a{Cons? l} -> Tot 'a let hd = function | hd::_ -> hd (** [tail l] returns [l] without its first element. Requires, at type-checking time, that [l] be nonempty. Similar to: tl in OCaml, F#, Coq *) val tail: l:list 'a {Cons? l} -> Tot (list 'a) let tail = function | _::tl -> tl (** [tl l] returns [l] without its first element. Requires, at type-checking time, that [l] be nonempty. Named as in: OCaml, F#, Coq *) val tl: l:list 'a {Cons? l} -> Tot (list 'a) let tl = tail (** [last l] returns the last element of [l]. Requires, at type-checking time, that [l] be nonempty. Named as in: Haskell *) val last: l:list 'a {Cons? l} -> Tot 'a let rec last = function | [hd] -> hd | _::tl -> last tl (** [init l] returns [l] without its last element. Requires, at type-checking time, that [l] be nonempty. Named as in: Haskell *) val init: l:list 'a {Cons? l} -> Tot (list 'a) let rec init = function | [_] -> [] | hd::tl -> hd::(init tl) (** [length l] returns the total number of elements in [l]. Named as in: OCaml, F#, Coq *) val length: list 'a -> Tot nat let rec length = function | [] -> 0 | _::tl -> 1 + length tl (** [nth l n] returns the [n]-th element in list [l] (with the first element being the 0-th) if [l] is long enough, or [None] otherwise. Named as in: OCaml, F#, Coq *) val nth: list 'a -> nat -> Tot (option 'a) let rec nth l n = match l with | [] -> None | hd::tl -> if n = 0 then Some hd else nth tl (n - 1) (** [index l n] returns the [n]-th element in list [l] (with the first element being the 0-th). Requires, at type-checking time, that [l] be of length at least [n+1]. *) val index: #a:Type -> l:list a -> i:nat{i < length l} -> Tot a let rec index #a (l: list a) (i:nat{i < length l}): Tot a = if i = 0 then hd l else index (tl l) (i - 1) (** [count x l] returns the number of occurrences of [x] in [l]. Requires, at type-checking time, the type of [a] to have equality defined. Similar to: [List.count_occ] in Coq. *) val count: #a:eqtype -> a -> list a -> Tot nat let rec count #a x = function | [] -> 0 | hd::tl -> if x=hd then 1 + count x tl else count x tl (** [rev_acc l1 l2] appends the elements of [l1] to the beginning of [l2], in reverse order. It is equivalent to [append (rev l1) l2], but is tail-recursive. Similar to: [List.rev_append] in OCaml, Coq. *) val rev_acc: list 'a -> list 'a -> Tot (list 'a) let rec rev_acc l acc = match l with | [] -> acc | hd::tl -> rev_acc tl (hd::acc) (** [rev l] returns the list [l] in reverse order. Named as in: OCaml, F#, Coq. *) val rev: list 'a -> Tot (list 'a) let rev l = rev_acc l [] (** [append l1 l2] appends the elements of [l2] to the end of [l1]. Named as: OCaml, F#. Similar to: [List.app] in Coq. *) val append: list 'a -> list 'a -> Tot (list 'a) let rec append x y = match x with | [] -> y | a::tl -> a::append tl y (** Defines notation [@@] for [append], as in OCaml, F# . *) let op_At x y = append x y (** [snoc (l, x)] adds [x] to the end of the list [l]. Note: We use an uncurried [snoc (l, x)] instead of the curried [snoc l x]. This is intentional. If [snoc] takes a pair instead of 2 arguments, it allows for a better pattern on [lemma_unsnoc_snoc], which connects [snoc] and [unsnoc]. In particular, if we had two arguments, then either the pattern would either be too restrictive or would lead to over-triggering. More context for this can be seen in the (collapsed and uncollapsed) comments at https://github.com/FStarLang/FStar/pull/1560 *) val snoc: (list 'a * 'a) -> Tot (list 'a) let snoc (l, x) = append l [x] (** [flatten l], where [l] is a list of lists, returns the list of the elements of the lists in [l], preserving their order. Named as in: OCaml, Coq. *) val flatten: list (list 'a) -> Tot (list 'a) let rec flatten l = match l with | [] -> [] | hd::tl -> append hd (flatten tl) (** [map f l] applies [f] to each element of [l] and returns the list of results, in the order of the original elements in [l]. Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml, Coq, F# *) val map: ('a -> Tot 'b) -> list 'a -> Tot (list 'b) let rec map f x = match x with | [] -> [] | a::tl -> f a::map f tl (** [mapi_init f l n] applies, for each [k], [f (n+k)] to the [k]-th element of [l] and returns the list of results, in the order of the original elements in [l]. Requires, at type-checking time, [f] to be a pure total function. *) val mapi_init: (int -> 'a -> Tot 'b) -> list 'a -> int -> Tot (list 'b) let rec mapi_init f l i = match l with | [] -> [] | hd::tl -> (f i hd)::(mapi_init f tl (i+1)) (** [mapi f l] applies, for each [k], [f k] to the [k]-th element of [l] and returns the list of results, in the order of the original elements in [l]. Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml *) val mapi: (int -> 'a -> Tot 'b) -> list 'a -> Tot (list 'b) let mapi f l = mapi_init f l 0 (** [concatMap f l] applies [f] to each element of [l] and returns the concatenation of the results, in the order of the original elements of [l]. This is equivalent to [flatten (map f l)]. Requires, at type-checking time, [f] to be a pure total function. *)
false
false
FStar.List.Tot.Base.fst
{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 1, "max_fuel": 8, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": true, "z3cliopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }
null
val concatMap: ('a -> Tot (list 'b)) -> list 'a -> Tot (list 'b)
[ "recursion" ]
FStar.List.Tot.Base.concatMap
{ "file_name": "ulib/FStar.List.Tot.Base.fst", "git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f", "git_url": "https://github.com/FStarLang/FStar.git", "project_name": "FStar" }
f: (_: 'a -> Prims.list 'b) -> _: Prims.list 'a -> Prims.list 'b
{ "end_col": 17, "end_line": 181, "start_col": 22, "start_line": 176 }
Prims.Tot
val split3: #a:Type -> l:list a -> i:nat{i < length l} -> Tot (list a * a * list a)
[ { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]
false
let split3 #a l i = let a, rest = splitAt i l in lemma_splitAt_snd_length i l; let b :: c = rest in a, b, c
val split3: #a:Type -> l:list a -> i:nat{i < length l} -> Tot (list a * a * list a) let split3 #a l i =
false
null
false
let a, rest = splitAt i l in lemma_splitAt_snd_length i l; let b :: c = rest in a, b, c
{ "checked_file": "FStar.List.Tot.Base.fst.checked", "dependencies": [ "prims.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Classical.fsti.checked" ], "interface_file": false, "source_file": "FStar.List.Tot.Base.fst" }
[ "total" ]
[ "Prims.list", "Prims.nat", "Prims.b2t", "Prims.op_LessThan", "FStar.List.Tot.Base.length", "FStar.Pervasives.Native.Mktuple3", "FStar.Pervasives.Native.tuple3", "Prims.unit", "FStar.List.Tot.Base.lemma_splitAt_snd_length", "FStar.Pervasives.Native.tuple2", "FStar.List.Tot.Base.splitAt" ]
[]
(* Copyright 2008-2014 Nikhil Swamy and Microsoft Research Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License. *) (** This module defines all pure and total operations on lists that can be used in specifications. It is implemented by FStar_List_Tot_Base.ml, any functional change and/or the addition of new functions MUST be reflected there. @summary Pure total operations on lists *) module FStar.List.Tot.Base (** Base operations *) (** [isEmpty l] returns [true] if and only if [l] is empty *) val isEmpty: list 'a -> Tot bool let isEmpty l = match l with | [] -> true | _ -> false (** [hd l] returns the first element of [l]. Requires [l] to be nonempty, at type-checking time. Named as in: OCaml, F#, Coq *) val hd: l:list 'a{Cons? l} -> Tot 'a let hd = function | hd::_ -> hd (** [tail l] returns [l] without its first element. Requires, at type-checking time, that [l] be nonempty. Similar to: tl in OCaml, F#, Coq *) val tail: l:list 'a {Cons? l} -> Tot (list 'a) let tail = function | _::tl -> tl (** [tl l] returns [l] without its first element. Requires, at type-checking time, that [l] be nonempty. Named as in: OCaml, F#, Coq *) val tl: l:list 'a {Cons? l} -> Tot (list 'a) let tl = tail (** [last l] returns the last element of [l]. Requires, at type-checking time, that [l] be nonempty. Named as in: Haskell *) val last: l:list 'a {Cons? l} -> Tot 'a let rec last = function | [hd] -> hd | _::tl -> last tl (** [init l] returns [l] without its last element. Requires, at type-checking time, that [l] be nonempty. Named as in: Haskell *) val init: l:list 'a {Cons? l} -> Tot (list 'a) let rec init = function | [_] -> [] | hd::tl -> hd::(init tl) (** [length l] returns the total number of elements in [l]. Named as in: OCaml, F#, Coq *) val length: list 'a -> Tot nat let rec length = function | [] -> 0 | _::tl -> 1 + length tl (** [nth l n] returns the [n]-th element in list [l] (with the first element being the 0-th) if [l] is long enough, or [None] otherwise. Named as in: OCaml, F#, Coq *) val nth: list 'a -> nat -> Tot (option 'a) let rec nth l n = match l with | [] -> None | hd::tl -> if n = 0 then Some hd else nth tl (n - 1) (** [index l n] returns the [n]-th element in list [l] (with the first element being the 0-th). Requires, at type-checking time, that [l] be of length at least [n+1]. *) val index: #a:Type -> l:list a -> i:nat{i < length l} -> Tot a let rec index #a (l: list a) (i:nat{i < length l}): Tot a = if i = 0 then hd l else index (tl l) (i - 1) (** [count x l] returns the number of occurrences of [x] in [l]. Requires, at type-checking time, the type of [a] to have equality defined. Similar to: [List.count_occ] in Coq. *) val count: #a:eqtype -> a -> list a -> Tot nat let rec count #a x = function | [] -> 0 | hd::tl -> if x=hd then 1 + count x tl else count x tl (** [rev_acc l1 l2] appends the elements of [l1] to the beginning of [l2], in reverse order. It is equivalent to [append (rev l1) l2], but is tail-recursive. Similar to: [List.rev_append] in OCaml, Coq. *) val rev_acc: list 'a -> list 'a -> Tot (list 'a) let rec rev_acc l acc = match l with | [] -> acc | hd::tl -> rev_acc tl (hd::acc) (** [rev l] returns the list [l] in reverse order. Named as in: OCaml, F#, Coq. *) val rev: list 'a -> Tot (list 'a) let rev l = rev_acc l [] (** [append l1 l2] appends the elements of [l2] to the end of [l1]. Named as: OCaml, F#. Similar to: [List.app] in Coq. *) val append: list 'a -> list 'a -> Tot (list 'a) let rec append x y = match x with | [] -> y | a::tl -> a::append tl y (** Defines notation [@@] for [append], as in OCaml, F# . *) let op_At x y = append x y (** [snoc (l, x)] adds [x] to the end of the list [l]. Note: We use an uncurried [snoc (l, x)] instead of the curried [snoc l x]. This is intentional. If [snoc] takes a pair instead of 2 arguments, it allows for a better pattern on [lemma_unsnoc_snoc], which connects [snoc] and [unsnoc]. In particular, if we had two arguments, then either the pattern would either be too restrictive or would lead to over-triggering. More context for this can be seen in the (collapsed and uncollapsed) comments at https://github.com/FStarLang/FStar/pull/1560 *) val snoc: (list 'a * 'a) -> Tot (list 'a) let snoc (l, x) = append l [x] (** [flatten l], where [l] is a list of lists, returns the list of the elements of the lists in [l], preserving their order. Named as in: OCaml, Coq. *) val flatten: list (list 'a) -> Tot (list 'a) let rec flatten l = match l with | [] -> [] | hd::tl -> append hd (flatten tl) (** [map f l] applies [f] to each element of [l] and returns the list of results, in the order of the original elements in [l]. Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml, Coq, F# *) val map: ('a -> Tot 'b) -> list 'a -> Tot (list 'b) let rec map f x = match x with | [] -> [] | a::tl -> f a::map f tl (** [mapi_init f l n] applies, for each [k], [f (n+k)] to the [k]-th element of [l] and returns the list of results, in the order of the original elements in [l]. Requires, at type-checking time, [f] to be a pure total function. *) val mapi_init: (int -> 'a -> Tot 'b) -> list 'a -> int -> Tot (list 'b) let rec mapi_init f l i = match l with | [] -> [] | hd::tl -> (f i hd)::(mapi_init f tl (i+1)) (** [mapi f l] applies, for each [k], [f k] to the [k]-th element of [l] and returns the list of results, in the order of the original elements in [l]. Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml *) val mapi: (int -> 'a -> Tot 'b) -> list 'a -> Tot (list 'b) let mapi f l = mapi_init f l 0 (** [concatMap f l] applies [f] to each element of [l] and returns the concatenation of the results, in the order of the original elements of [l]. This is equivalent to [flatten (map f l)]. Requires, at type-checking time, [f] to be a pure total function. *) val concatMap: ('a -> Tot (list 'b)) -> list 'a -> Tot (list 'b) let rec concatMap f = function | [] -> [] | a::tl -> let fa = f a in let ftl = concatMap f tl in append fa ftl (** [fold_left f x [y1; y2; ...; yn]] computes (f (... (f x y1) y2) ... yn). Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml, Coq. *) val fold_left: ('a -> 'b -> Tot 'a) -> 'a -> l:list 'b -> Tot 'a (decreases l) let rec fold_left f x l = match l with | [] -> x | hd::tl -> fold_left f (f x hd) tl (** [fold_right f [x1; x2; ...; xn] y] computes (f x1 (f x2 (... (f xn y)) ... )). Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml, Coq *) val fold_right: ('a -> 'b -> Tot 'b) -> list 'a -> 'b -> Tot 'b let rec fold_right f l x = match l with | [] -> x | hd::tl -> f hd (fold_right f tl x) (** [fold_right_gtot] is just like [fold_right], except `f` is a ghost function **) let rec fold_right_gtot (#a:Type) (#b:Type) (l:list a) (f:a -> b -> GTot b) (x:b) : GTot b = match l with | [] -> x | hd::tl -> f hd (fold_right_gtot tl f x) (* We define map in terms of fold, to share simple lemmas *) let map_gtot #a #b (f:a -> GTot b) (x:list a) : GTot (list b) = fold_right_gtot x (fun x tl -> f x :: tl) [] (** [fold_left2 f x [y1; y2; ...; yn] [z1; z2; ...; zn]] computes (f (... (f x y1 z1) y2 z2) ... yn zn). Requires, at type-checking time, [f] to be a pure total function, and the lists [y1; y2; ...; yn] and [z1; z2; ...; zn] to have the same lengths. Named as in: OCaml *) val fold_left2 : f:('a -> 'b -> 'c -> Tot 'a) -> accu:'a -> l1:(list 'b) -> l2:(list 'c) -> Pure 'a (requires (length l1 == length l2)) (ensures (fun _ -> True)) (decreases l1) let rec fold_left2 f accu l1 l2 = match (l1, l2) with | ([], []) -> accu | (a1::l1, a2::l2) -> fold_left2 f (f accu a1 a2) l1 l2 (** Propositional membership (as in Coq). Does not require decidable equality. *) (** [memP x l] holds if, and only if, [x] appears as an element of [l]. Similar to: List.In in Coq. *) let rec memP (#a: Type) (x: a) (l: list a) : Tot Type0 = match l with | [] -> False | y :: q -> x == y \/ memP x q (** List searching **) (** [mem x l] returns [true] if, and only if, [x] appears as an element of [l]. Requires, at type-checking time, the type of elements of [l] to have decidable equality. Named as in: OCaml. See also: List.In in Coq, which is propositional. *) val mem: #a:eqtype -> a -> list a -> Tot bool let rec mem #a x = function | [] -> false | hd::tl -> if hd = x then true else mem x tl (** [contains x l] returns [true] if, and only if, [x] appears as an element of [l]. Requires, at type-checking time, the type of elements of [l] to have decidable equality. It is equivalent to: [mem x l]. TODO: should we rather swap the order of arguments? *) let contains : #a:eqtype -> a -> list a -> Tot bool = mem (** [existsb f l] returns [true] if, and only if, there exists some element [x] in [l] such that [f x] holds. *) val existsb: #a:Type -> f:(a -> Tot bool) -> list a -> Tot bool let rec existsb #a f l = match l with | [] -> false | hd::tl -> if f hd then true else existsb f tl (** [find f l] returns [Some x] for some element [x] appearing in [l] such that [f x] holds, or [None] only if no such [x] exists. *) val find: #a:Type -> f:(a -> Tot bool) -> list a -> Tot (option (x:a{f x})) let rec find #a f l = match l with | [] -> None #(x:a{f x}) //These type annotations are only present because it makes bootstrapping go much faster | hd::tl -> if f hd then Some #(x:a{f x}) hd else find f tl (** Filtering elements of a list [l] through a Boolean pure total predicate [f] *) (** [filter f l] returns [l] with all elements [x] such that [f x] does not hold removed. Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml, Coq *) val filter : #a: Type -> f:(a -> Tot bool) -> l: list a -> Tot (m:list a{forall x. memP x m ==> f x}) let rec filter #a f = function | [] -> [] | hd::tl -> if f hd then hd::filter f tl else filter f tl (** Postcondition on [filter f l]: for any element [x] of [filter f l], [f x] holds. Requires, at type-checking time, [f] to be a pure total function.*) val mem_filter (#a:Type) (f: (a -> Tot bool)) (l: list a) (x: a) : Lemma (requires (memP x (filter f l))) (ensures (f x)) let mem_filter f l x = () (** Postcondition on [filter f l]: stated with [forall]: for any element [x] of [filter f l], [f x] holds. Requires, at type-checking time, [f] to be a pure total function. *) val mem_filter_forall (#a:Type) (f: (a -> Tot bool)) (l: list a) : Lemma (requires True) (ensures (forall x . memP x (filter f l) ==> f x)) [SMTPat (filter f l)] let mem_filter_forall f l = FStar.Classical.ghost_lemma (mem_filter f l) (** [for_all f l] returns [true] if, and only if, for all elements [x] appearing in [l], [f x] holds. Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml. Similar to: List.forallb in Coq *) val for_all: ('a -> Tot bool) -> list 'a -> Tot bool let rec for_all f l = match l with | [] -> true | hd::tl -> if f hd then for_all f tl else false (** Specification for [for_all f l] vs. mem *) let rec for_all_mem (#a: Type) (f: (a -> Tot bool)) (l: list a) : Lemma (for_all f l <==> (forall x . memP x l ==> f x)) = match l with | [] -> () | _ :: q -> for_all_mem f q (** [collect f l] applies [f] to each element of [l] and returns the concatenation of the results, in the order of the original elements of [l]. It is equivalent to [flatten (map f l)]. Requires, at type-checking time, [f] to be a pure total function. TODO: what is the difference with [concatMap]? *) val collect: ('a -> Tot (list 'b)) -> list 'a -> Tot (list 'b) let rec collect f l = match l with | [] -> [] | hd::tl -> append (f hd) (collect f tl) (** [tryFind f l] returns [Some x] for some element [x] appearing in [l] such that [f x] holds, or [None] only if no such [x] exists. Requires, at type-checking time, [f] to be a pure total function. Contrary to [find], [tryFind] provides no postcondition on its result. *) val tryFind: ('a -> Tot bool) -> list 'a -> Tot (option 'a) let rec tryFind p l = match l with | [] -> None | hd::tl -> if p hd then Some hd else tryFind p tl (** [tryPick f l] returns [y] for some element [x] appearing in [l] such that [f x = Some y] for some y, or [None] only if [f x = None] for all elements [x] of [l]. Requires, at type-checking time, [f] to be a pure total function. *) val tryPick: ('a -> Tot (option 'b)) -> list 'a -> Tot (option 'b) let rec tryPick f l = match l with | [] -> None | hd::tl -> match f hd with | Some x -> Some x | None -> tryPick f tl (** [choose f l] returns the list of [y] for all elements [x] appearing in [l] such that [f x = Some y] for some [y]. Requires, at type-checking time, [f] to be a pure total function. *) val choose: ('a -> Tot (option 'b)) -> list 'a -> Tot (list 'b) let rec choose f l = match l with | [] -> [] | hd::tl -> match f hd with | Some x -> x::(choose f tl) | None -> choose f tl (** [partition f l] returns the pair of lists [(l1, l2)] where all elements [x] of [l] are in [l1] if [f x] holds, and in [l2] otherwise. Both [l1] and [l2] retain the original order of [l]. Requires, at type-checking time, [f] to be a pure total function. *) val partition: f:('a -> Tot bool) -> list 'a -> Tot (list 'a * list 'a) let rec partition f = function | [] -> [], [] | hd::tl -> let l1, l2 = partition f tl in if f hd then hd::l1, l2 else l1, hd::l2 (** [subset la lb] is true if and only if all the elements from [la] are also in [lb]. Requires, at type-checking time, the type of elements of [la] and [lb] to have decidable equality. *) val subset: #a:eqtype -> list a -> list a -> Tot bool let rec subset #a la lb = match la with | [] -> true | h :: tl -> mem h lb && subset tl lb (** [noRepeats l] returns [true] if, and only if, no element of [l] appears in [l] more than once. Requires, at type-checking time, the type of elements of [la] and [lb] to have decidable equality. *) val noRepeats : #a:eqtype -> list a -> Tot bool let rec noRepeats #a la = match la with | [] -> true | h :: tl -> not(mem h tl) && noRepeats tl (** [no_repeats_p l] valid if, and only if, no element of [l] appears in [l] more than once. *) val no_repeats_p : #a:Type -> list a -> Tot prop let rec no_repeats_p #a la = match la with | [] -> True | h :: tl -> ~(memP h tl) /\ no_repeats_p tl (** List of tuples **) (** [assoc x l] returns [Some y] where [(x, y)] is the first element of [l] whose first element is [x], or [None] only if no such element exists. Requires, at type-checking time, the type of [x] to have decidable equality. Named as in: OCaml. *) val assoc: #a:eqtype -> #b:Type -> a -> list (a * b) -> Tot (option b) let rec assoc #a #b x = function | [] -> None | (x', y)::tl -> if x=x' then Some y else assoc x tl (** [split] takes a list of pairs [(x1, y1), ..., (xn, yn)] and returns the pair of lists ([x1, ..., xn], [y1, ..., yn]). Named as in: OCaml *) val split: list ('a * 'b) -> Tot (list 'a * list 'b) let rec split l = match l with | [] -> ([],[]) | (hd1,hd2)::tl -> let (tl1,tl2) = split tl in (hd1::tl1,hd2::tl2) (** [unzip] takes a list of pairs [(x1, y1), ..., (xn, yn)] and returns the pair of lists ([x1, ..., xn], [y1, ..., yn]). Named as in: Haskell *) let unzip l = split l (** [unzip3] takes a list of triples [(x1, y1, z1), ..., (xn, yn, zn)] and returns the triple of lists ([x1, ..., xn], [y1, ..., yn], [z1, ..., zn]). Named as in: Haskell *) val unzip3: list ('a * 'b * 'c) -> Tot (list 'a * list 'b * list 'c) let rec unzip3 l = match l with | [] -> ([],[],[]) | (hd1,hd2,hd3)::tl -> let (tl1,tl2,tl3) = unzip3 tl in (hd1::tl1,hd2::tl2,hd3::tl3) (** Splitting a list at some index **) (** [splitAt] takes a natural number n and a list and returns a pair of the maximal prefix of l of size smaller than n and the rest of the list *) let rec splitAt (#a:Type) (n:nat) (l:list a) : Tot (list a * list a) = if n = 0 then [], l else match l with | [] -> [], l | x :: xs -> let l1, l2 = splitAt (n-1) xs in x :: l1, l2 let rec lemma_splitAt_snd_length (#a:Type) (n:nat) (l:list a) : Lemma (requires (n <= length l)) (ensures (length (snd (splitAt n l)) = length l - n)) = match n, l with | 0, _ -> () | _, [] -> () | _, _ :: l' -> lemma_splitAt_snd_length (n - 1) l' (** [unsnoc] is an inverse of [snoc]. It splits a list into all-elements-except-last and last element. *) val unsnoc: #a:Type -> l:list a{length l > 0} -> Tot (list a * a) let unsnoc #a l = let l1, l2 = splitAt (length l - 1) l in lemma_splitAt_snd_length (length l - 1) l; l1, hd l2 (** [split3] splits a list into 3 parts. This allows easy access to the part of the list before and after the element, as well as the element itself. *)
false
false
FStar.List.Tot.Base.fst
{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 1, "max_fuel": 8, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": true, "z3cliopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }
null
val split3: #a:Type -> l:list a -> i:nat{i < length l} -> Tot (list a * a * list a)
[]
FStar.List.Tot.Base.split3
{ "file_name": "ulib/FStar.List.Tot.Base.fst", "git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f", "git_url": "https://github.com/FStarLang/FStar.git", "project_name": "FStar" }
l: Prims.list a -> i: Prims.nat{i < FStar.List.Tot.Base.length l} -> (Prims.list a * a) * Prims.list a
{ "end_col": 9, "end_line": 475, "start_col": 19, "start_line": 471 }
Prims.Tot
val mem: #a:eqtype -> a -> list a -> Tot bool
[ { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]
false
let rec mem #a x = function | [] -> false | hd::tl -> if hd = x then true else mem x tl
val mem: #a:eqtype -> a -> list a -> Tot bool let rec mem #a x =
false
null
false
function | [] -> false | hd :: tl -> if hd = x then true else mem x tl
{ "checked_file": "FStar.List.Tot.Base.fst.checked", "dependencies": [ "prims.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Classical.fsti.checked" ], "interface_file": false, "source_file": "FStar.List.Tot.Base.fst" }
[ "total" ]
[ "Prims.eqtype", "Prims.list", "Prims.op_Equality", "Prims.bool", "FStar.List.Tot.Base.mem" ]
[]
(* Copyright 2008-2014 Nikhil Swamy and Microsoft Research Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License. *) (** This module defines all pure and total operations on lists that can be used in specifications. It is implemented by FStar_List_Tot_Base.ml, any functional change and/or the addition of new functions MUST be reflected there. @summary Pure total operations on lists *) module FStar.List.Tot.Base (** Base operations *) (** [isEmpty l] returns [true] if and only if [l] is empty *) val isEmpty: list 'a -> Tot bool let isEmpty l = match l with | [] -> true | _ -> false (** [hd l] returns the first element of [l]. Requires [l] to be nonempty, at type-checking time. Named as in: OCaml, F#, Coq *) val hd: l:list 'a{Cons? l} -> Tot 'a let hd = function | hd::_ -> hd (** [tail l] returns [l] without its first element. Requires, at type-checking time, that [l] be nonempty. Similar to: tl in OCaml, F#, Coq *) val tail: l:list 'a {Cons? l} -> Tot (list 'a) let tail = function | _::tl -> tl (** [tl l] returns [l] without its first element. Requires, at type-checking time, that [l] be nonempty. Named as in: OCaml, F#, Coq *) val tl: l:list 'a {Cons? l} -> Tot (list 'a) let tl = tail (** [last l] returns the last element of [l]. Requires, at type-checking time, that [l] be nonempty. Named as in: Haskell *) val last: l:list 'a {Cons? l} -> Tot 'a let rec last = function | [hd] -> hd | _::tl -> last tl (** [init l] returns [l] without its last element. Requires, at type-checking time, that [l] be nonempty. Named as in: Haskell *) val init: l:list 'a {Cons? l} -> Tot (list 'a) let rec init = function | [_] -> [] | hd::tl -> hd::(init tl) (** [length l] returns the total number of elements in [l]. Named as in: OCaml, F#, Coq *) val length: list 'a -> Tot nat let rec length = function | [] -> 0 | _::tl -> 1 + length tl (** [nth l n] returns the [n]-th element in list [l] (with the first element being the 0-th) if [l] is long enough, or [None] otherwise. Named as in: OCaml, F#, Coq *) val nth: list 'a -> nat -> Tot (option 'a) let rec nth l n = match l with | [] -> None | hd::tl -> if n = 0 then Some hd else nth tl (n - 1) (** [index l n] returns the [n]-th element in list [l] (with the first element being the 0-th). Requires, at type-checking time, that [l] be of length at least [n+1]. *) val index: #a:Type -> l:list a -> i:nat{i < length l} -> Tot a let rec index #a (l: list a) (i:nat{i < length l}): Tot a = if i = 0 then hd l else index (tl l) (i - 1) (** [count x l] returns the number of occurrences of [x] in [l]. Requires, at type-checking time, the type of [a] to have equality defined. Similar to: [List.count_occ] in Coq. *) val count: #a:eqtype -> a -> list a -> Tot nat let rec count #a x = function | [] -> 0 | hd::tl -> if x=hd then 1 + count x tl else count x tl (** [rev_acc l1 l2] appends the elements of [l1] to the beginning of [l2], in reverse order. It is equivalent to [append (rev l1) l2], but is tail-recursive. Similar to: [List.rev_append] in OCaml, Coq. *) val rev_acc: list 'a -> list 'a -> Tot (list 'a) let rec rev_acc l acc = match l with | [] -> acc | hd::tl -> rev_acc tl (hd::acc) (** [rev l] returns the list [l] in reverse order. Named as in: OCaml, F#, Coq. *) val rev: list 'a -> Tot (list 'a) let rev l = rev_acc l [] (** [append l1 l2] appends the elements of [l2] to the end of [l1]. Named as: OCaml, F#. Similar to: [List.app] in Coq. *) val append: list 'a -> list 'a -> Tot (list 'a) let rec append x y = match x with | [] -> y | a::tl -> a::append tl y (** Defines notation [@@] for [append], as in OCaml, F# . *) let op_At x y = append x y (** [snoc (l, x)] adds [x] to the end of the list [l]. Note: We use an uncurried [snoc (l, x)] instead of the curried [snoc l x]. This is intentional. If [snoc] takes a pair instead of 2 arguments, it allows for a better pattern on [lemma_unsnoc_snoc], which connects [snoc] and [unsnoc]. In particular, if we had two arguments, then either the pattern would either be too restrictive or would lead to over-triggering. More context for this can be seen in the (collapsed and uncollapsed) comments at https://github.com/FStarLang/FStar/pull/1560 *) val snoc: (list 'a * 'a) -> Tot (list 'a) let snoc (l, x) = append l [x] (** [flatten l], where [l] is a list of lists, returns the list of the elements of the lists in [l], preserving their order. Named as in: OCaml, Coq. *) val flatten: list (list 'a) -> Tot (list 'a) let rec flatten l = match l with | [] -> [] | hd::tl -> append hd (flatten tl) (** [map f l] applies [f] to each element of [l] and returns the list of results, in the order of the original elements in [l]. Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml, Coq, F# *) val map: ('a -> Tot 'b) -> list 'a -> Tot (list 'b) let rec map f x = match x with | [] -> [] | a::tl -> f a::map f tl (** [mapi_init f l n] applies, for each [k], [f (n+k)] to the [k]-th element of [l] and returns the list of results, in the order of the original elements in [l]. Requires, at type-checking time, [f] to be a pure total function. *) val mapi_init: (int -> 'a -> Tot 'b) -> list 'a -> int -> Tot (list 'b) let rec mapi_init f l i = match l with | [] -> [] | hd::tl -> (f i hd)::(mapi_init f tl (i+1)) (** [mapi f l] applies, for each [k], [f k] to the [k]-th element of [l] and returns the list of results, in the order of the original elements in [l]. Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml *) val mapi: (int -> 'a -> Tot 'b) -> list 'a -> Tot (list 'b) let mapi f l = mapi_init f l 0 (** [concatMap f l] applies [f] to each element of [l] and returns the concatenation of the results, in the order of the original elements of [l]. This is equivalent to [flatten (map f l)]. Requires, at type-checking time, [f] to be a pure total function. *) val concatMap: ('a -> Tot (list 'b)) -> list 'a -> Tot (list 'b) let rec concatMap f = function | [] -> [] | a::tl -> let fa = f a in let ftl = concatMap f tl in append fa ftl (** [fold_left f x [y1; y2; ...; yn]] computes (f (... (f x y1) y2) ... yn). Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml, Coq. *) val fold_left: ('a -> 'b -> Tot 'a) -> 'a -> l:list 'b -> Tot 'a (decreases l) let rec fold_left f x l = match l with | [] -> x | hd::tl -> fold_left f (f x hd) tl (** [fold_right f [x1; x2; ...; xn] y] computes (f x1 (f x2 (... (f xn y)) ... )). Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml, Coq *) val fold_right: ('a -> 'b -> Tot 'b) -> list 'a -> 'b -> Tot 'b let rec fold_right f l x = match l with | [] -> x | hd::tl -> f hd (fold_right f tl x) (** [fold_right_gtot] is just like [fold_right], except `f` is a ghost function **) let rec fold_right_gtot (#a:Type) (#b:Type) (l:list a) (f:a -> b -> GTot b) (x:b) : GTot b = match l with | [] -> x | hd::tl -> f hd (fold_right_gtot tl f x) (* We define map in terms of fold, to share simple lemmas *) let map_gtot #a #b (f:a -> GTot b) (x:list a) : GTot (list b) = fold_right_gtot x (fun x tl -> f x :: tl) [] (** [fold_left2 f x [y1; y2; ...; yn] [z1; z2; ...; zn]] computes (f (... (f x y1 z1) y2 z2) ... yn zn). Requires, at type-checking time, [f] to be a pure total function, and the lists [y1; y2; ...; yn] and [z1; z2; ...; zn] to have the same lengths. Named as in: OCaml *) val fold_left2 : f:('a -> 'b -> 'c -> Tot 'a) -> accu:'a -> l1:(list 'b) -> l2:(list 'c) -> Pure 'a (requires (length l1 == length l2)) (ensures (fun _ -> True)) (decreases l1) let rec fold_left2 f accu l1 l2 = match (l1, l2) with | ([], []) -> accu | (a1::l1, a2::l2) -> fold_left2 f (f accu a1 a2) l1 l2 (** Propositional membership (as in Coq). Does not require decidable equality. *) (** [memP x l] holds if, and only if, [x] appears as an element of [l]. Similar to: List.In in Coq. *) let rec memP (#a: Type) (x: a) (l: list a) : Tot Type0 = match l with | [] -> False | y :: q -> x == y \/ memP x q (** List searching **) (** [mem x l] returns [true] if, and only if, [x] appears as an element of [l]. Requires, at type-checking time, the type of elements of [l] to have decidable equality. Named as in: OCaml. See also: List.In in Coq, which is propositional. *)
false
false
FStar.List.Tot.Base.fst
{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 1, "max_fuel": 8, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": true, "z3cliopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }
null
val mem: #a:eqtype -> a -> list a -> Tot bool
[ "recursion" ]
FStar.List.Tot.Base.mem
{ "file_name": "ulib/FStar.List.Tot.Base.fst", "git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f", "git_url": "https://github.com/FStarLang/FStar.git", "project_name": "FStar" }
x: a -> _: Prims.list a -> Prims.bool
{ "end_col": 47, "end_line": 242, "start_col": 19, "start_line": 240 }
Prims.Tot
val noRepeats : #a:eqtype -> list a -> Tot bool
[ { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]
false
let rec noRepeats #a la = match la with | [] -> true | h :: tl -> not(mem h tl) && noRepeats tl
val noRepeats : #a:eqtype -> list a -> Tot bool let rec noRepeats #a la =
false
null
false
match la with | [] -> true | h :: tl -> not (mem h tl) && noRepeats tl
{ "checked_file": "FStar.List.Tot.Base.fst.checked", "dependencies": [ "prims.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Classical.fsti.checked" ], "interface_file": false, "source_file": "FStar.List.Tot.Base.fst" }
[ "total" ]
[ "Prims.eqtype", "Prims.list", "Prims.op_AmpAmp", "Prims.op_Negation", "FStar.List.Tot.Base.mem", "FStar.List.Tot.Base.noRepeats", "Prims.bool" ]
[]
(* Copyright 2008-2014 Nikhil Swamy and Microsoft Research Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License. *) (** This module defines all pure and total operations on lists that can be used in specifications. It is implemented by FStar_List_Tot_Base.ml, any functional change and/or the addition of new functions MUST be reflected there. @summary Pure total operations on lists *) module FStar.List.Tot.Base (** Base operations *) (** [isEmpty l] returns [true] if and only if [l] is empty *) val isEmpty: list 'a -> Tot bool let isEmpty l = match l with | [] -> true | _ -> false (** [hd l] returns the first element of [l]. Requires [l] to be nonempty, at type-checking time. Named as in: OCaml, F#, Coq *) val hd: l:list 'a{Cons? l} -> Tot 'a let hd = function | hd::_ -> hd (** [tail l] returns [l] without its first element. Requires, at type-checking time, that [l] be nonempty. Similar to: tl in OCaml, F#, Coq *) val tail: l:list 'a {Cons? l} -> Tot (list 'a) let tail = function | _::tl -> tl (** [tl l] returns [l] without its first element. Requires, at type-checking time, that [l] be nonempty. Named as in: OCaml, F#, Coq *) val tl: l:list 'a {Cons? l} -> Tot (list 'a) let tl = tail (** [last l] returns the last element of [l]. Requires, at type-checking time, that [l] be nonempty. Named as in: Haskell *) val last: l:list 'a {Cons? l} -> Tot 'a let rec last = function | [hd] -> hd | _::tl -> last tl (** [init l] returns [l] without its last element. Requires, at type-checking time, that [l] be nonempty. Named as in: Haskell *) val init: l:list 'a {Cons? l} -> Tot (list 'a) let rec init = function | [_] -> [] | hd::tl -> hd::(init tl) (** [length l] returns the total number of elements in [l]. Named as in: OCaml, F#, Coq *) val length: list 'a -> Tot nat let rec length = function | [] -> 0 | _::tl -> 1 + length tl (** [nth l n] returns the [n]-th element in list [l] (with the first element being the 0-th) if [l] is long enough, or [None] otherwise. Named as in: OCaml, F#, Coq *) val nth: list 'a -> nat -> Tot (option 'a) let rec nth l n = match l with | [] -> None | hd::tl -> if n = 0 then Some hd else nth tl (n - 1) (** [index l n] returns the [n]-th element in list [l] (with the first element being the 0-th). Requires, at type-checking time, that [l] be of length at least [n+1]. *) val index: #a:Type -> l:list a -> i:nat{i < length l} -> Tot a let rec index #a (l: list a) (i:nat{i < length l}): Tot a = if i = 0 then hd l else index (tl l) (i - 1) (** [count x l] returns the number of occurrences of [x] in [l]. Requires, at type-checking time, the type of [a] to have equality defined. Similar to: [List.count_occ] in Coq. *) val count: #a:eqtype -> a -> list a -> Tot nat let rec count #a x = function | [] -> 0 | hd::tl -> if x=hd then 1 + count x tl else count x tl (** [rev_acc l1 l2] appends the elements of [l1] to the beginning of [l2], in reverse order. It is equivalent to [append (rev l1) l2], but is tail-recursive. Similar to: [List.rev_append] in OCaml, Coq. *) val rev_acc: list 'a -> list 'a -> Tot (list 'a) let rec rev_acc l acc = match l with | [] -> acc | hd::tl -> rev_acc tl (hd::acc) (** [rev l] returns the list [l] in reverse order. Named as in: OCaml, F#, Coq. *) val rev: list 'a -> Tot (list 'a) let rev l = rev_acc l [] (** [append l1 l2] appends the elements of [l2] to the end of [l1]. Named as: OCaml, F#. Similar to: [List.app] in Coq. *) val append: list 'a -> list 'a -> Tot (list 'a) let rec append x y = match x with | [] -> y | a::tl -> a::append tl y (** Defines notation [@@] for [append], as in OCaml, F# . *) let op_At x y = append x y (** [snoc (l, x)] adds [x] to the end of the list [l]. Note: We use an uncurried [snoc (l, x)] instead of the curried [snoc l x]. This is intentional. If [snoc] takes a pair instead of 2 arguments, it allows for a better pattern on [lemma_unsnoc_snoc], which connects [snoc] and [unsnoc]. In particular, if we had two arguments, then either the pattern would either be too restrictive or would lead to over-triggering. More context for this can be seen in the (collapsed and uncollapsed) comments at https://github.com/FStarLang/FStar/pull/1560 *) val snoc: (list 'a * 'a) -> Tot (list 'a) let snoc (l, x) = append l [x] (** [flatten l], where [l] is a list of lists, returns the list of the elements of the lists in [l], preserving their order. Named as in: OCaml, Coq. *) val flatten: list (list 'a) -> Tot (list 'a) let rec flatten l = match l with | [] -> [] | hd::tl -> append hd (flatten tl) (** [map f l] applies [f] to each element of [l] and returns the list of results, in the order of the original elements in [l]. Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml, Coq, F# *) val map: ('a -> Tot 'b) -> list 'a -> Tot (list 'b) let rec map f x = match x with | [] -> [] | a::tl -> f a::map f tl (** [mapi_init f l n] applies, for each [k], [f (n+k)] to the [k]-th element of [l] and returns the list of results, in the order of the original elements in [l]. Requires, at type-checking time, [f] to be a pure total function. *) val mapi_init: (int -> 'a -> Tot 'b) -> list 'a -> int -> Tot (list 'b) let rec mapi_init f l i = match l with | [] -> [] | hd::tl -> (f i hd)::(mapi_init f tl (i+1)) (** [mapi f l] applies, for each [k], [f k] to the [k]-th element of [l] and returns the list of results, in the order of the original elements in [l]. Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml *) val mapi: (int -> 'a -> Tot 'b) -> list 'a -> Tot (list 'b) let mapi f l = mapi_init f l 0 (** [concatMap f l] applies [f] to each element of [l] and returns the concatenation of the results, in the order of the original elements of [l]. This is equivalent to [flatten (map f l)]. Requires, at type-checking time, [f] to be a pure total function. *) val concatMap: ('a -> Tot (list 'b)) -> list 'a -> Tot (list 'b) let rec concatMap f = function | [] -> [] | a::tl -> let fa = f a in let ftl = concatMap f tl in append fa ftl (** [fold_left f x [y1; y2; ...; yn]] computes (f (... (f x y1) y2) ... yn). Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml, Coq. *) val fold_left: ('a -> 'b -> Tot 'a) -> 'a -> l:list 'b -> Tot 'a (decreases l) let rec fold_left f x l = match l with | [] -> x | hd::tl -> fold_left f (f x hd) tl (** [fold_right f [x1; x2; ...; xn] y] computes (f x1 (f x2 (... (f xn y)) ... )). Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml, Coq *) val fold_right: ('a -> 'b -> Tot 'b) -> list 'a -> 'b -> Tot 'b let rec fold_right f l x = match l with | [] -> x | hd::tl -> f hd (fold_right f tl x) (** [fold_right_gtot] is just like [fold_right], except `f` is a ghost function **) let rec fold_right_gtot (#a:Type) (#b:Type) (l:list a) (f:a -> b -> GTot b) (x:b) : GTot b = match l with | [] -> x | hd::tl -> f hd (fold_right_gtot tl f x) (* We define map in terms of fold, to share simple lemmas *) let map_gtot #a #b (f:a -> GTot b) (x:list a) : GTot (list b) = fold_right_gtot x (fun x tl -> f x :: tl) [] (** [fold_left2 f x [y1; y2; ...; yn] [z1; z2; ...; zn]] computes (f (... (f x y1 z1) y2 z2) ... yn zn). Requires, at type-checking time, [f] to be a pure total function, and the lists [y1; y2; ...; yn] and [z1; z2; ...; zn] to have the same lengths. Named as in: OCaml *) val fold_left2 : f:('a -> 'b -> 'c -> Tot 'a) -> accu:'a -> l1:(list 'b) -> l2:(list 'c) -> Pure 'a (requires (length l1 == length l2)) (ensures (fun _ -> True)) (decreases l1) let rec fold_left2 f accu l1 l2 = match (l1, l2) with | ([], []) -> accu | (a1::l1, a2::l2) -> fold_left2 f (f accu a1 a2) l1 l2 (** Propositional membership (as in Coq). Does not require decidable equality. *) (** [memP x l] holds if, and only if, [x] appears as an element of [l]. Similar to: List.In in Coq. *) let rec memP (#a: Type) (x: a) (l: list a) : Tot Type0 = match l with | [] -> False | y :: q -> x == y \/ memP x q (** List searching **) (** [mem x l] returns [true] if, and only if, [x] appears as an element of [l]. Requires, at type-checking time, the type of elements of [l] to have decidable equality. Named as in: OCaml. See also: List.In in Coq, which is propositional. *) val mem: #a:eqtype -> a -> list a -> Tot bool let rec mem #a x = function | [] -> false | hd::tl -> if hd = x then true else mem x tl (** [contains x l] returns [true] if, and only if, [x] appears as an element of [l]. Requires, at type-checking time, the type of elements of [l] to have decidable equality. It is equivalent to: [mem x l]. TODO: should we rather swap the order of arguments? *) let contains : #a:eqtype -> a -> list a -> Tot bool = mem (** [existsb f l] returns [true] if, and only if, there exists some element [x] in [l] such that [f x] holds. *) val existsb: #a:Type -> f:(a -> Tot bool) -> list a -> Tot bool let rec existsb #a f l = match l with | [] -> false | hd::tl -> if f hd then true else existsb f tl (** [find f l] returns [Some x] for some element [x] appearing in [l] such that [f x] holds, or [None] only if no such [x] exists. *) val find: #a:Type -> f:(a -> Tot bool) -> list a -> Tot (option (x:a{f x})) let rec find #a f l = match l with | [] -> None #(x:a{f x}) //These type annotations are only present because it makes bootstrapping go much faster | hd::tl -> if f hd then Some #(x:a{f x}) hd else find f tl (** Filtering elements of a list [l] through a Boolean pure total predicate [f] *) (** [filter f l] returns [l] with all elements [x] such that [f x] does not hold removed. Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml, Coq *) val filter : #a: Type -> f:(a -> Tot bool) -> l: list a -> Tot (m:list a{forall x. memP x m ==> f x}) let rec filter #a f = function | [] -> [] | hd::tl -> if f hd then hd::filter f tl else filter f tl (** Postcondition on [filter f l]: for any element [x] of [filter f l], [f x] holds. Requires, at type-checking time, [f] to be a pure total function.*) val mem_filter (#a:Type) (f: (a -> Tot bool)) (l: list a) (x: a) : Lemma (requires (memP x (filter f l))) (ensures (f x)) let mem_filter f l x = () (** Postcondition on [filter f l]: stated with [forall]: for any element [x] of [filter f l], [f x] holds. Requires, at type-checking time, [f] to be a pure total function. *) val mem_filter_forall (#a:Type) (f: (a -> Tot bool)) (l: list a) : Lemma (requires True) (ensures (forall x . memP x (filter f l) ==> f x)) [SMTPat (filter f l)] let mem_filter_forall f l = FStar.Classical.ghost_lemma (mem_filter f l) (** [for_all f l] returns [true] if, and only if, for all elements [x] appearing in [l], [f x] holds. Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml. Similar to: List.forallb in Coq *) val for_all: ('a -> Tot bool) -> list 'a -> Tot bool let rec for_all f l = match l with | [] -> true | hd::tl -> if f hd then for_all f tl else false (** Specification for [for_all f l] vs. mem *) let rec for_all_mem (#a: Type) (f: (a -> Tot bool)) (l: list a) : Lemma (for_all f l <==> (forall x . memP x l ==> f x)) = match l with | [] -> () | _ :: q -> for_all_mem f q (** [collect f l] applies [f] to each element of [l] and returns the concatenation of the results, in the order of the original elements of [l]. It is equivalent to [flatten (map f l)]. Requires, at type-checking time, [f] to be a pure total function. TODO: what is the difference with [concatMap]? *) val collect: ('a -> Tot (list 'b)) -> list 'a -> Tot (list 'b) let rec collect f l = match l with | [] -> [] | hd::tl -> append (f hd) (collect f tl) (** [tryFind f l] returns [Some x] for some element [x] appearing in [l] such that [f x] holds, or [None] only if no such [x] exists. Requires, at type-checking time, [f] to be a pure total function. Contrary to [find], [tryFind] provides no postcondition on its result. *) val tryFind: ('a -> Tot bool) -> list 'a -> Tot (option 'a) let rec tryFind p l = match l with | [] -> None | hd::tl -> if p hd then Some hd else tryFind p tl (** [tryPick f l] returns [y] for some element [x] appearing in [l] such that [f x = Some y] for some y, or [None] only if [f x = None] for all elements [x] of [l]. Requires, at type-checking time, [f] to be a pure total function. *) val tryPick: ('a -> Tot (option 'b)) -> list 'a -> Tot (option 'b) let rec tryPick f l = match l with | [] -> None | hd::tl -> match f hd with | Some x -> Some x | None -> tryPick f tl (** [choose f l] returns the list of [y] for all elements [x] appearing in [l] such that [f x = Some y] for some [y]. Requires, at type-checking time, [f] to be a pure total function. *) val choose: ('a -> Tot (option 'b)) -> list 'a -> Tot (list 'b) let rec choose f l = match l with | [] -> [] | hd::tl -> match f hd with | Some x -> x::(choose f tl) | None -> choose f tl (** [partition f l] returns the pair of lists [(l1, l2)] where all elements [x] of [l] are in [l1] if [f x] holds, and in [l2] otherwise. Both [l1] and [l2] retain the original order of [l]. Requires, at type-checking time, [f] to be a pure total function. *) val partition: f:('a -> Tot bool) -> list 'a -> Tot (list 'a * list 'a) let rec partition f = function | [] -> [], [] | hd::tl -> let l1, l2 = partition f tl in if f hd then hd::l1, l2 else l1, hd::l2 (** [subset la lb] is true if and only if all the elements from [la] are also in [lb]. Requires, at type-checking time, the type of elements of [la] and [lb] to have decidable equality. *) val subset: #a:eqtype -> list a -> list a -> Tot bool let rec subset #a la lb = match la with | [] -> true | h :: tl -> mem h lb && subset tl lb (** [noRepeats l] returns [true] if, and only if, no element of [l] appears in [l] more than once. Requires, at type-checking time, the type of elements of [la] and [lb] to have decidable equality. *) val noRepeats : #a:eqtype -> list a -> Tot bool
false
false
FStar.List.Tot.Base.fst
{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 1, "max_fuel": 8, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": true, "z3cliopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }
null
val noRepeats : #a:eqtype -> list a -> Tot bool
[ "recursion" ]
FStar.List.Tot.Base.noRepeats
{ "file_name": "ulib/FStar.List.Tot.Base.fst", "git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f", "git_url": "https://github.com/FStarLang/FStar.git", "project_name": "FStar" }
la: Prims.list a -> Prims.bool
{ "end_col": 44, "end_line": 391, "start_col": 2, "start_line": 389 }
Prims.Tot
val fold_left: ('a -> 'b -> Tot 'a) -> 'a -> l:list 'b -> Tot 'a (decreases l)
[ { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]
false
let rec fold_left f x l = match l with | [] -> x | hd::tl -> fold_left f (f x hd) tl
val fold_left: ('a -> 'b -> Tot 'a) -> 'a -> l:list 'b -> Tot 'a (decreases l) let rec fold_left f x l =
false
null
false
match l with | [] -> x | hd :: tl -> fold_left f (f x hd) tl
{ "checked_file": "FStar.List.Tot.Base.fst.checked", "dependencies": [ "prims.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Classical.fsti.checked" ], "interface_file": false, "source_file": "FStar.List.Tot.Base.fst" }
[ "total", "" ]
[ "Prims.list", "FStar.List.Tot.Base.fold_left" ]
[]
(* Copyright 2008-2014 Nikhil Swamy and Microsoft Research Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License. *) (** This module defines all pure and total operations on lists that can be used in specifications. It is implemented by FStar_List_Tot_Base.ml, any functional change and/or the addition of new functions MUST be reflected there. @summary Pure total operations on lists *) module FStar.List.Tot.Base (** Base operations *) (** [isEmpty l] returns [true] if and only if [l] is empty *) val isEmpty: list 'a -> Tot bool let isEmpty l = match l with | [] -> true | _ -> false (** [hd l] returns the first element of [l]. Requires [l] to be nonempty, at type-checking time. Named as in: OCaml, F#, Coq *) val hd: l:list 'a{Cons? l} -> Tot 'a let hd = function | hd::_ -> hd (** [tail l] returns [l] without its first element. Requires, at type-checking time, that [l] be nonempty. Similar to: tl in OCaml, F#, Coq *) val tail: l:list 'a {Cons? l} -> Tot (list 'a) let tail = function | _::tl -> tl (** [tl l] returns [l] without its first element. Requires, at type-checking time, that [l] be nonempty. Named as in: OCaml, F#, Coq *) val tl: l:list 'a {Cons? l} -> Tot (list 'a) let tl = tail (** [last l] returns the last element of [l]. Requires, at type-checking time, that [l] be nonempty. Named as in: Haskell *) val last: l:list 'a {Cons? l} -> Tot 'a let rec last = function | [hd] -> hd | _::tl -> last tl (** [init l] returns [l] without its last element. Requires, at type-checking time, that [l] be nonempty. Named as in: Haskell *) val init: l:list 'a {Cons? l} -> Tot (list 'a) let rec init = function | [_] -> [] | hd::tl -> hd::(init tl) (** [length l] returns the total number of elements in [l]. Named as in: OCaml, F#, Coq *) val length: list 'a -> Tot nat let rec length = function | [] -> 0 | _::tl -> 1 + length tl (** [nth l n] returns the [n]-th element in list [l] (with the first element being the 0-th) if [l] is long enough, or [None] otherwise. Named as in: OCaml, F#, Coq *) val nth: list 'a -> nat -> Tot (option 'a) let rec nth l n = match l with | [] -> None | hd::tl -> if n = 0 then Some hd else nth tl (n - 1) (** [index l n] returns the [n]-th element in list [l] (with the first element being the 0-th). Requires, at type-checking time, that [l] be of length at least [n+1]. *) val index: #a:Type -> l:list a -> i:nat{i < length l} -> Tot a let rec index #a (l: list a) (i:nat{i < length l}): Tot a = if i = 0 then hd l else index (tl l) (i - 1) (** [count x l] returns the number of occurrences of [x] in [l]. Requires, at type-checking time, the type of [a] to have equality defined. Similar to: [List.count_occ] in Coq. *) val count: #a:eqtype -> a -> list a -> Tot nat let rec count #a x = function | [] -> 0 | hd::tl -> if x=hd then 1 + count x tl else count x tl (** [rev_acc l1 l2] appends the elements of [l1] to the beginning of [l2], in reverse order. It is equivalent to [append (rev l1) l2], but is tail-recursive. Similar to: [List.rev_append] in OCaml, Coq. *) val rev_acc: list 'a -> list 'a -> Tot (list 'a) let rec rev_acc l acc = match l with | [] -> acc | hd::tl -> rev_acc tl (hd::acc) (** [rev l] returns the list [l] in reverse order. Named as in: OCaml, F#, Coq. *) val rev: list 'a -> Tot (list 'a) let rev l = rev_acc l [] (** [append l1 l2] appends the elements of [l2] to the end of [l1]. Named as: OCaml, F#. Similar to: [List.app] in Coq. *) val append: list 'a -> list 'a -> Tot (list 'a) let rec append x y = match x with | [] -> y | a::tl -> a::append tl y (** Defines notation [@@] for [append], as in OCaml, F# . *) let op_At x y = append x y (** [snoc (l, x)] adds [x] to the end of the list [l]. Note: We use an uncurried [snoc (l, x)] instead of the curried [snoc l x]. This is intentional. If [snoc] takes a pair instead of 2 arguments, it allows for a better pattern on [lemma_unsnoc_snoc], which connects [snoc] and [unsnoc]. In particular, if we had two arguments, then either the pattern would either be too restrictive or would lead to over-triggering. More context for this can be seen in the (collapsed and uncollapsed) comments at https://github.com/FStarLang/FStar/pull/1560 *) val snoc: (list 'a * 'a) -> Tot (list 'a) let snoc (l, x) = append l [x] (** [flatten l], where [l] is a list of lists, returns the list of the elements of the lists in [l], preserving their order. Named as in: OCaml, Coq. *) val flatten: list (list 'a) -> Tot (list 'a) let rec flatten l = match l with | [] -> [] | hd::tl -> append hd (flatten tl) (** [map f l] applies [f] to each element of [l] and returns the list of results, in the order of the original elements in [l]. Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml, Coq, F# *) val map: ('a -> Tot 'b) -> list 'a -> Tot (list 'b) let rec map f x = match x with | [] -> [] | a::tl -> f a::map f tl (** [mapi_init f l n] applies, for each [k], [f (n+k)] to the [k]-th element of [l] and returns the list of results, in the order of the original elements in [l]. Requires, at type-checking time, [f] to be a pure total function. *) val mapi_init: (int -> 'a -> Tot 'b) -> list 'a -> int -> Tot (list 'b) let rec mapi_init f l i = match l with | [] -> [] | hd::tl -> (f i hd)::(mapi_init f tl (i+1)) (** [mapi f l] applies, for each [k], [f k] to the [k]-th element of [l] and returns the list of results, in the order of the original elements in [l]. Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml *) val mapi: (int -> 'a -> Tot 'b) -> list 'a -> Tot (list 'b) let mapi f l = mapi_init f l 0 (** [concatMap f l] applies [f] to each element of [l] and returns the concatenation of the results, in the order of the original elements of [l]. This is equivalent to [flatten (map f l)]. Requires, at type-checking time, [f] to be a pure total function. *) val concatMap: ('a -> Tot (list 'b)) -> list 'a -> Tot (list 'b) let rec concatMap f = function | [] -> [] | a::tl -> let fa = f a in let ftl = concatMap f tl in append fa ftl (** [fold_left f x [y1; y2; ...; yn]] computes (f (... (f x y1) y2) ... yn). Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml, Coq. *)
false
false
FStar.List.Tot.Base.fst
{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 1, "max_fuel": 8, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": true, "z3cliopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }
null
val fold_left: ('a -> 'b -> Tot 'a) -> 'a -> l:list 'b -> Tot 'a (decreases l)
[ "recursion" ]
FStar.List.Tot.Base.fold_left
{ "file_name": "ulib/FStar.List.Tot.Base.fst", "git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f", "git_url": "https://github.com/FStarLang/FStar.git", "project_name": "FStar" }
f: (_: 'a -> _: 'b -> 'a) -> x: 'a -> l: Prims.list 'b -> Prims.Tot 'a
{ "end_col": 37, "end_line": 189, "start_col": 26, "start_line": 187 }
Prims.Tot
val for_all: ('a -> Tot bool) -> list 'a -> Tot bool
[ { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]
false
let rec for_all f l = match l with | [] -> true | hd::tl -> if f hd then for_all f tl else false
val for_all: ('a -> Tot bool) -> list 'a -> Tot bool let rec for_all f l =
false
null
false
match l with | [] -> true | hd :: tl -> if f hd then for_all f tl else false
{ "checked_file": "FStar.List.Tot.Base.fst.checked", "dependencies": [ "prims.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Classical.fsti.checked" ], "interface_file": false, "source_file": "FStar.List.Tot.Base.fst" }
[ "total" ]
[ "Prims.bool", "Prims.list", "FStar.List.Tot.Base.for_all" ]
[]
(* Copyright 2008-2014 Nikhil Swamy and Microsoft Research Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License. *) (** This module defines all pure and total operations on lists that can be used in specifications. It is implemented by FStar_List_Tot_Base.ml, any functional change and/or the addition of new functions MUST be reflected there. @summary Pure total operations on lists *) module FStar.List.Tot.Base (** Base operations *) (** [isEmpty l] returns [true] if and only if [l] is empty *) val isEmpty: list 'a -> Tot bool let isEmpty l = match l with | [] -> true | _ -> false (** [hd l] returns the first element of [l]. Requires [l] to be nonempty, at type-checking time. Named as in: OCaml, F#, Coq *) val hd: l:list 'a{Cons? l} -> Tot 'a let hd = function | hd::_ -> hd (** [tail l] returns [l] without its first element. Requires, at type-checking time, that [l] be nonempty. Similar to: tl in OCaml, F#, Coq *) val tail: l:list 'a {Cons? l} -> Tot (list 'a) let tail = function | _::tl -> tl (** [tl l] returns [l] without its first element. Requires, at type-checking time, that [l] be nonempty. Named as in: OCaml, F#, Coq *) val tl: l:list 'a {Cons? l} -> Tot (list 'a) let tl = tail (** [last l] returns the last element of [l]. Requires, at type-checking time, that [l] be nonempty. Named as in: Haskell *) val last: l:list 'a {Cons? l} -> Tot 'a let rec last = function | [hd] -> hd | _::tl -> last tl (** [init l] returns [l] without its last element. Requires, at type-checking time, that [l] be nonempty. Named as in: Haskell *) val init: l:list 'a {Cons? l} -> Tot (list 'a) let rec init = function | [_] -> [] | hd::tl -> hd::(init tl) (** [length l] returns the total number of elements in [l]. Named as in: OCaml, F#, Coq *) val length: list 'a -> Tot nat let rec length = function | [] -> 0 | _::tl -> 1 + length tl (** [nth l n] returns the [n]-th element in list [l] (with the first element being the 0-th) if [l] is long enough, or [None] otherwise. Named as in: OCaml, F#, Coq *) val nth: list 'a -> nat -> Tot (option 'a) let rec nth l n = match l with | [] -> None | hd::tl -> if n = 0 then Some hd else nth tl (n - 1) (** [index l n] returns the [n]-th element in list [l] (with the first element being the 0-th). Requires, at type-checking time, that [l] be of length at least [n+1]. *) val index: #a:Type -> l:list a -> i:nat{i < length l} -> Tot a let rec index #a (l: list a) (i:nat{i < length l}): Tot a = if i = 0 then hd l else index (tl l) (i - 1) (** [count x l] returns the number of occurrences of [x] in [l]. Requires, at type-checking time, the type of [a] to have equality defined. Similar to: [List.count_occ] in Coq. *) val count: #a:eqtype -> a -> list a -> Tot nat let rec count #a x = function | [] -> 0 | hd::tl -> if x=hd then 1 + count x tl else count x tl (** [rev_acc l1 l2] appends the elements of [l1] to the beginning of [l2], in reverse order. It is equivalent to [append (rev l1) l2], but is tail-recursive. Similar to: [List.rev_append] in OCaml, Coq. *) val rev_acc: list 'a -> list 'a -> Tot (list 'a) let rec rev_acc l acc = match l with | [] -> acc | hd::tl -> rev_acc tl (hd::acc) (** [rev l] returns the list [l] in reverse order. Named as in: OCaml, F#, Coq. *) val rev: list 'a -> Tot (list 'a) let rev l = rev_acc l [] (** [append l1 l2] appends the elements of [l2] to the end of [l1]. Named as: OCaml, F#. Similar to: [List.app] in Coq. *) val append: list 'a -> list 'a -> Tot (list 'a) let rec append x y = match x with | [] -> y | a::tl -> a::append tl y (** Defines notation [@@] for [append], as in OCaml, F# . *) let op_At x y = append x y (** [snoc (l, x)] adds [x] to the end of the list [l]. Note: We use an uncurried [snoc (l, x)] instead of the curried [snoc l x]. This is intentional. If [snoc] takes a pair instead of 2 arguments, it allows for a better pattern on [lemma_unsnoc_snoc], which connects [snoc] and [unsnoc]. In particular, if we had two arguments, then either the pattern would either be too restrictive or would lead to over-triggering. More context for this can be seen in the (collapsed and uncollapsed) comments at https://github.com/FStarLang/FStar/pull/1560 *) val snoc: (list 'a * 'a) -> Tot (list 'a) let snoc (l, x) = append l [x] (** [flatten l], where [l] is a list of lists, returns the list of the elements of the lists in [l], preserving their order. Named as in: OCaml, Coq. *) val flatten: list (list 'a) -> Tot (list 'a) let rec flatten l = match l with | [] -> [] | hd::tl -> append hd (flatten tl) (** [map f l] applies [f] to each element of [l] and returns the list of results, in the order of the original elements in [l]. Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml, Coq, F# *) val map: ('a -> Tot 'b) -> list 'a -> Tot (list 'b) let rec map f x = match x with | [] -> [] | a::tl -> f a::map f tl (** [mapi_init f l n] applies, for each [k], [f (n+k)] to the [k]-th element of [l] and returns the list of results, in the order of the original elements in [l]. Requires, at type-checking time, [f] to be a pure total function. *) val mapi_init: (int -> 'a -> Tot 'b) -> list 'a -> int -> Tot (list 'b) let rec mapi_init f l i = match l with | [] -> [] | hd::tl -> (f i hd)::(mapi_init f tl (i+1)) (** [mapi f l] applies, for each [k], [f k] to the [k]-th element of [l] and returns the list of results, in the order of the original elements in [l]. Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml *) val mapi: (int -> 'a -> Tot 'b) -> list 'a -> Tot (list 'b) let mapi f l = mapi_init f l 0 (** [concatMap f l] applies [f] to each element of [l] and returns the concatenation of the results, in the order of the original elements of [l]. This is equivalent to [flatten (map f l)]. Requires, at type-checking time, [f] to be a pure total function. *) val concatMap: ('a -> Tot (list 'b)) -> list 'a -> Tot (list 'b) let rec concatMap f = function | [] -> [] | a::tl -> let fa = f a in let ftl = concatMap f tl in append fa ftl (** [fold_left f x [y1; y2; ...; yn]] computes (f (... (f x y1) y2) ... yn). Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml, Coq. *) val fold_left: ('a -> 'b -> Tot 'a) -> 'a -> l:list 'b -> Tot 'a (decreases l) let rec fold_left f x l = match l with | [] -> x | hd::tl -> fold_left f (f x hd) tl (** [fold_right f [x1; x2; ...; xn] y] computes (f x1 (f x2 (... (f xn y)) ... )). Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml, Coq *) val fold_right: ('a -> 'b -> Tot 'b) -> list 'a -> 'b -> Tot 'b let rec fold_right f l x = match l with | [] -> x | hd::tl -> f hd (fold_right f tl x) (** [fold_right_gtot] is just like [fold_right], except `f` is a ghost function **) let rec fold_right_gtot (#a:Type) (#b:Type) (l:list a) (f:a -> b -> GTot b) (x:b) : GTot b = match l with | [] -> x | hd::tl -> f hd (fold_right_gtot tl f x) (* We define map in terms of fold, to share simple lemmas *) let map_gtot #a #b (f:a -> GTot b) (x:list a) : GTot (list b) = fold_right_gtot x (fun x tl -> f x :: tl) [] (** [fold_left2 f x [y1; y2; ...; yn] [z1; z2; ...; zn]] computes (f (... (f x y1 z1) y2 z2) ... yn zn). Requires, at type-checking time, [f] to be a pure total function, and the lists [y1; y2; ...; yn] and [z1; z2; ...; zn] to have the same lengths. Named as in: OCaml *) val fold_left2 : f:('a -> 'b -> 'c -> Tot 'a) -> accu:'a -> l1:(list 'b) -> l2:(list 'c) -> Pure 'a (requires (length l1 == length l2)) (ensures (fun _ -> True)) (decreases l1) let rec fold_left2 f accu l1 l2 = match (l1, l2) with | ([], []) -> accu | (a1::l1, a2::l2) -> fold_left2 f (f accu a1 a2) l1 l2 (** Propositional membership (as in Coq). Does not require decidable equality. *) (** [memP x l] holds if, and only if, [x] appears as an element of [l]. Similar to: List.In in Coq. *) let rec memP (#a: Type) (x: a) (l: list a) : Tot Type0 = match l with | [] -> False | y :: q -> x == y \/ memP x q (** List searching **) (** [mem x l] returns [true] if, and only if, [x] appears as an element of [l]. Requires, at type-checking time, the type of elements of [l] to have decidable equality. Named as in: OCaml. See also: List.In in Coq, which is propositional. *) val mem: #a:eqtype -> a -> list a -> Tot bool let rec mem #a x = function | [] -> false | hd::tl -> if hd = x then true else mem x tl (** [contains x l] returns [true] if, and only if, [x] appears as an element of [l]. Requires, at type-checking time, the type of elements of [l] to have decidable equality. It is equivalent to: [mem x l]. TODO: should we rather swap the order of arguments? *) let contains : #a:eqtype -> a -> list a -> Tot bool = mem (** [existsb f l] returns [true] if, and only if, there exists some element [x] in [l] such that [f x] holds. *) val existsb: #a:Type -> f:(a -> Tot bool) -> list a -> Tot bool let rec existsb #a f l = match l with | [] -> false | hd::tl -> if f hd then true else existsb f tl (** [find f l] returns [Some x] for some element [x] appearing in [l] such that [f x] holds, or [None] only if no such [x] exists. *) val find: #a:Type -> f:(a -> Tot bool) -> list a -> Tot (option (x:a{f x})) let rec find #a f l = match l with | [] -> None #(x:a{f x}) //These type annotations are only present because it makes bootstrapping go much faster | hd::tl -> if f hd then Some #(x:a{f x}) hd else find f tl (** Filtering elements of a list [l] through a Boolean pure total predicate [f] *) (** [filter f l] returns [l] with all elements [x] such that [f x] does not hold removed. Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml, Coq *) val filter : #a: Type -> f:(a -> Tot bool) -> l: list a -> Tot (m:list a{forall x. memP x m ==> f x}) let rec filter #a f = function | [] -> [] | hd::tl -> if f hd then hd::filter f tl else filter f tl (** Postcondition on [filter f l]: for any element [x] of [filter f l], [f x] holds. Requires, at type-checking time, [f] to be a pure total function.*) val mem_filter (#a:Type) (f: (a -> Tot bool)) (l: list a) (x: a) : Lemma (requires (memP x (filter f l))) (ensures (f x)) let mem_filter f l x = () (** Postcondition on [filter f l]: stated with [forall]: for any element [x] of [filter f l], [f x] holds. Requires, at type-checking time, [f] to be a pure total function. *) val mem_filter_forall (#a:Type) (f: (a -> Tot bool)) (l: list a) : Lemma (requires True) (ensures (forall x . memP x (filter f l) ==> f x)) [SMTPat (filter f l)] let mem_filter_forall f l = FStar.Classical.ghost_lemma (mem_filter f l) (** [for_all f l] returns [true] if, and only if, for all elements [x] appearing in [l], [f x] holds. Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml. Similar to: List.forallb in Coq *)
false
false
FStar.List.Tot.Base.fst
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null
val for_all: ('a -> Tot bool) -> list 'a -> Tot bool
[ "recursion" ]
FStar.List.Tot.Base.for_all
{ "file_name": "ulib/FStar.List.Tot.Base.fst", "git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f", "git_url": "https://github.com/FStarLang/FStar.git", "project_name": "FStar" }
f: (_: 'a -> Prims.bool) -> l: Prims.list 'a -> Prims.bool
{ "end_col": 52, "end_line": 305, "start_col": 22, "start_line": 303 }
Prims.Tot
val splitAt (#a: Type) (n: nat) (l: list a) : Tot (list a * list a)
[ { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]
false
let rec splitAt (#a:Type) (n:nat) (l:list a) : Tot (list a * list a) = if n = 0 then [], l else match l with | [] -> [], l | x :: xs -> let l1, l2 = splitAt (n-1) xs in x :: l1, l2
val splitAt (#a: Type) (n: nat) (l: list a) : Tot (list a * list a) let rec splitAt (#a: Type) (n: nat) (l: list a) : Tot (list a * list a) =
false
null
false
if n = 0 then [], l else match l with | [] -> [], l | x :: xs -> let l1, l2 = splitAt (n - 1) xs in x :: l1, l2
{ "checked_file": "FStar.List.Tot.Base.fst.checked", "dependencies": [ "prims.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Classical.fsti.checked" ], "interface_file": false, "source_file": "FStar.List.Tot.Base.fst" }
[ "total" ]
[ "Prims.nat", "Prims.list", "Prims.op_Equality", "Prims.int", "FStar.Pervasives.Native.Mktuple2", "Prims.Nil", "Prims.bool", "Prims.Cons", "FStar.Pervasives.Native.tuple2", "FStar.List.Tot.Base.splitAt", "Prims.op_Subtraction" ]
[]
(* Copyright 2008-2014 Nikhil Swamy and Microsoft Research Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License. *) (** This module defines all pure and total operations on lists that can be used in specifications. It is implemented by FStar_List_Tot_Base.ml, any functional change and/or the addition of new functions MUST be reflected there. @summary Pure total operations on lists *) module FStar.List.Tot.Base (** Base operations *) (** [isEmpty l] returns [true] if and only if [l] is empty *) val isEmpty: list 'a -> Tot bool let isEmpty l = match l with | [] -> true | _ -> false (** [hd l] returns the first element of [l]. Requires [l] to be nonempty, at type-checking time. Named as in: OCaml, F#, Coq *) val hd: l:list 'a{Cons? l} -> Tot 'a let hd = function | hd::_ -> hd (** [tail l] returns [l] without its first element. Requires, at type-checking time, that [l] be nonempty. Similar to: tl in OCaml, F#, Coq *) val tail: l:list 'a {Cons? l} -> Tot (list 'a) let tail = function | _::tl -> tl (** [tl l] returns [l] without its first element. Requires, at type-checking time, that [l] be nonempty. Named as in: OCaml, F#, Coq *) val tl: l:list 'a {Cons? l} -> Tot (list 'a) let tl = tail (** [last l] returns the last element of [l]. Requires, at type-checking time, that [l] be nonempty. Named as in: Haskell *) val last: l:list 'a {Cons? l} -> Tot 'a let rec last = function | [hd] -> hd | _::tl -> last tl (** [init l] returns [l] without its last element. Requires, at type-checking time, that [l] be nonempty. Named as in: Haskell *) val init: l:list 'a {Cons? l} -> Tot (list 'a) let rec init = function | [_] -> [] | hd::tl -> hd::(init tl) (** [length l] returns the total number of elements in [l]. Named as in: OCaml, F#, Coq *) val length: list 'a -> Tot nat let rec length = function | [] -> 0 | _::tl -> 1 + length tl (** [nth l n] returns the [n]-th element in list [l] (with the first element being the 0-th) if [l] is long enough, or [None] otherwise. Named as in: OCaml, F#, Coq *) val nth: list 'a -> nat -> Tot (option 'a) let rec nth l n = match l with | [] -> None | hd::tl -> if n = 0 then Some hd else nth tl (n - 1) (** [index l n] returns the [n]-th element in list [l] (with the first element being the 0-th). Requires, at type-checking time, that [l] be of length at least [n+1]. *) val index: #a:Type -> l:list a -> i:nat{i < length l} -> Tot a let rec index #a (l: list a) (i:nat{i < length l}): Tot a = if i = 0 then hd l else index (tl l) (i - 1) (** [count x l] returns the number of occurrences of [x] in [l]. Requires, at type-checking time, the type of [a] to have equality defined. Similar to: [List.count_occ] in Coq. *) val count: #a:eqtype -> a -> list a -> Tot nat let rec count #a x = function | [] -> 0 | hd::tl -> if x=hd then 1 + count x tl else count x tl (** [rev_acc l1 l2] appends the elements of [l1] to the beginning of [l2], in reverse order. It is equivalent to [append (rev l1) l2], but is tail-recursive. Similar to: [List.rev_append] in OCaml, Coq. *) val rev_acc: list 'a -> list 'a -> Tot (list 'a) let rec rev_acc l acc = match l with | [] -> acc | hd::tl -> rev_acc tl (hd::acc) (** [rev l] returns the list [l] in reverse order. Named as in: OCaml, F#, Coq. *) val rev: list 'a -> Tot (list 'a) let rev l = rev_acc l [] (** [append l1 l2] appends the elements of [l2] to the end of [l1]. Named as: OCaml, F#. Similar to: [List.app] in Coq. *) val append: list 'a -> list 'a -> Tot (list 'a) let rec append x y = match x with | [] -> y | a::tl -> a::append tl y (** Defines notation [@@] for [append], as in OCaml, F# . *) let op_At x y = append x y (** [snoc (l, x)] adds [x] to the end of the list [l]. Note: We use an uncurried [snoc (l, x)] instead of the curried [snoc l x]. This is intentional. If [snoc] takes a pair instead of 2 arguments, it allows for a better pattern on [lemma_unsnoc_snoc], which connects [snoc] and [unsnoc]. In particular, if we had two arguments, then either the pattern would either be too restrictive or would lead to over-triggering. More context for this can be seen in the (collapsed and uncollapsed) comments at https://github.com/FStarLang/FStar/pull/1560 *) val snoc: (list 'a * 'a) -> Tot (list 'a) let snoc (l, x) = append l [x] (** [flatten l], where [l] is a list of lists, returns the list of the elements of the lists in [l], preserving their order. Named as in: OCaml, Coq. *) val flatten: list (list 'a) -> Tot (list 'a) let rec flatten l = match l with | [] -> [] | hd::tl -> append hd (flatten tl) (** [map f l] applies [f] to each element of [l] and returns the list of results, in the order of the original elements in [l]. Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml, Coq, F# *) val map: ('a -> Tot 'b) -> list 'a -> Tot (list 'b) let rec map f x = match x with | [] -> [] | a::tl -> f a::map f tl (** [mapi_init f l n] applies, for each [k], [f (n+k)] to the [k]-th element of [l] and returns the list of results, in the order of the original elements in [l]. Requires, at type-checking time, [f] to be a pure total function. *) val mapi_init: (int -> 'a -> Tot 'b) -> list 'a -> int -> Tot (list 'b) let rec mapi_init f l i = match l with | [] -> [] | hd::tl -> (f i hd)::(mapi_init f tl (i+1)) (** [mapi f l] applies, for each [k], [f k] to the [k]-th element of [l] and returns the list of results, in the order of the original elements in [l]. Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml *) val mapi: (int -> 'a -> Tot 'b) -> list 'a -> Tot (list 'b) let mapi f l = mapi_init f l 0 (** [concatMap f l] applies [f] to each element of [l] and returns the concatenation of the results, in the order of the original elements of [l]. This is equivalent to [flatten (map f l)]. Requires, at type-checking time, [f] to be a pure total function. *) val concatMap: ('a -> Tot (list 'b)) -> list 'a -> Tot (list 'b) let rec concatMap f = function | [] -> [] | a::tl -> let fa = f a in let ftl = concatMap f tl in append fa ftl (** [fold_left f x [y1; y2; ...; yn]] computes (f (... (f x y1) y2) ... yn). Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml, Coq. *) val fold_left: ('a -> 'b -> Tot 'a) -> 'a -> l:list 'b -> Tot 'a (decreases l) let rec fold_left f x l = match l with | [] -> x | hd::tl -> fold_left f (f x hd) tl (** [fold_right f [x1; x2; ...; xn] y] computes (f x1 (f x2 (... (f xn y)) ... )). Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml, Coq *) val fold_right: ('a -> 'b -> Tot 'b) -> list 'a -> 'b -> Tot 'b let rec fold_right f l x = match l with | [] -> x | hd::tl -> f hd (fold_right f tl x) (** [fold_right_gtot] is just like [fold_right], except `f` is a ghost function **) let rec fold_right_gtot (#a:Type) (#b:Type) (l:list a) (f:a -> b -> GTot b) (x:b) : GTot b = match l with | [] -> x | hd::tl -> f hd (fold_right_gtot tl f x) (* We define map in terms of fold, to share simple lemmas *) let map_gtot #a #b (f:a -> GTot b) (x:list a) : GTot (list b) = fold_right_gtot x (fun x tl -> f x :: tl) [] (** [fold_left2 f x [y1; y2; ...; yn] [z1; z2; ...; zn]] computes (f (... (f x y1 z1) y2 z2) ... yn zn). Requires, at type-checking time, [f] to be a pure total function, and the lists [y1; y2; ...; yn] and [z1; z2; ...; zn] to have the same lengths. Named as in: OCaml *) val fold_left2 : f:('a -> 'b -> 'c -> Tot 'a) -> accu:'a -> l1:(list 'b) -> l2:(list 'c) -> Pure 'a (requires (length l1 == length l2)) (ensures (fun _ -> True)) (decreases l1) let rec fold_left2 f accu l1 l2 = match (l1, l2) with | ([], []) -> accu | (a1::l1, a2::l2) -> fold_left2 f (f accu a1 a2) l1 l2 (** Propositional membership (as in Coq). Does not require decidable equality. *) (** [memP x l] holds if, and only if, [x] appears as an element of [l]. Similar to: List.In in Coq. *) let rec memP (#a: Type) (x: a) (l: list a) : Tot Type0 = match l with | [] -> False | y :: q -> x == y \/ memP x q (** List searching **) (** [mem x l] returns [true] if, and only if, [x] appears as an element of [l]. Requires, at type-checking time, the type of elements of [l] to have decidable equality. Named as in: OCaml. See also: List.In in Coq, which is propositional. *) val mem: #a:eqtype -> a -> list a -> Tot bool let rec mem #a x = function | [] -> false | hd::tl -> if hd = x then true else mem x tl (** [contains x l] returns [true] if, and only if, [x] appears as an element of [l]. Requires, at type-checking time, the type of elements of [l] to have decidable equality. It is equivalent to: [mem x l]. TODO: should we rather swap the order of arguments? *) let contains : #a:eqtype -> a -> list a -> Tot bool = mem (** [existsb f l] returns [true] if, and only if, there exists some element [x] in [l] such that [f x] holds. *) val existsb: #a:Type -> f:(a -> Tot bool) -> list a -> Tot bool let rec existsb #a f l = match l with | [] -> false | hd::tl -> if f hd then true else existsb f tl (** [find f l] returns [Some x] for some element [x] appearing in [l] such that [f x] holds, or [None] only if no such [x] exists. *) val find: #a:Type -> f:(a -> Tot bool) -> list a -> Tot (option (x:a{f x})) let rec find #a f l = match l with | [] -> None #(x:a{f x}) //These type annotations are only present because it makes bootstrapping go much faster | hd::tl -> if f hd then Some #(x:a{f x}) hd else find f tl (** Filtering elements of a list [l] through a Boolean pure total predicate [f] *) (** [filter f l] returns [l] with all elements [x] such that [f x] does not hold removed. Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml, Coq *) val filter : #a: Type -> f:(a -> Tot bool) -> l: list a -> Tot (m:list a{forall x. memP x m ==> f x}) let rec filter #a f = function | [] -> [] | hd::tl -> if f hd then hd::filter f tl else filter f tl (** Postcondition on [filter f l]: for any element [x] of [filter f l], [f x] holds. Requires, at type-checking time, [f] to be a pure total function.*) val mem_filter (#a:Type) (f: (a -> Tot bool)) (l: list a) (x: a) : Lemma (requires (memP x (filter f l))) (ensures (f x)) let mem_filter f l x = () (** Postcondition on [filter f l]: stated with [forall]: for any element [x] of [filter f l], [f x] holds. Requires, at type-checking time, [f] to be a pure total function. *) val mem_filter_forall (#a:Type) (f: (a -> Tot bool)) (l: list a) : Lemma (requires True) (ensures (forall x . memP x (filter f l) ==> f x)) [SMTPat (filter f l)] let mem_filter_forall f l = FStar.Classical.ghost_lemma (mem_filter f l) (** [for_all f l] returns [true] if, and only if, for all elements [x] appearing in [l], [f x] holds. Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml. Similar to: List.forallb in Coq *) val for_all: ('a -> Tot bool) -> list 'a -> Tot bool let rec for_all f l = match l with | [] -> true | hd::tl -> if f hd then for_all f tl else false (** Specification for [for_all f l] vs. mem *) let rec for_all_mem (#a: Type) (f: (a -> Tot bool)) (l: list a) : Lemma (for_all f l <==> (forall x . memP x l ==> f x)) = match l with | [] -> () | _ :: q -> for_all_mem f q (** [collect f l] applies [f] to each element of [l] and returns the concatenation of the results, in the order of the original elements of [l]. It is equivalent to [flatten (map f l)]. Requires, at type-checking time, [f] to be a pure total function. TODO: what is the difference with [concatMap]? *) val collect: ('a -> Tot (list 'b)) -> list 'a -> Tot (list 'b) let rec collect f l = match l with | [] -> [] | hd::tl -> append (f hd) (collect f tl) (** [tryFind f l] returns [Some x] for some element [x] appearing in [l] such that [f x] holds, or [None] only if no such [x] exists. Requires, at type-checking time, [f] to be a pure total function. Contrary to [find], [tryFind] provides no postcondition on its result. *) val tryFind: ('a -> Tot bool) -> list 'a -> Tot (option 'a) let rec tryFind p l = match l with | [] -> None | hd::tl -> if p hd then Some hd else tryFind p tl (** [tryPick f l] returns [y] for some element [x] appearing in [l] such that [f x = Some y] for some y, or [None] only if [f x = None] for all elements [x] of [l]. Requires, at type-checking time, [f] to be a pure total function. *) val tryPick: ('a -> Tot (option 'b)) -> list 'a -> Tot (option 'b) let rec tryPick f l = match l with | [] -> None | hd::tl -> match f hd with | Some x -> Some x | None -> tryPick f tl (** [choose f l] returns the list of [y] for all elements [x] appearing in [l] such that [f x = Some y] for some [y]. Requires, at type-checking time, [f] to be a pure total function. *) val choose: ('a -> Tot (option 'b)) -> list 'a -> Tot (list 'b) let rec choose f l = match l with | [] -> [] | hd::tl -> match f hd with | Some x -> x::(choose f tl) | None -> choose f tl (** [partition f l] returns the pair of lists [(l1, l2)] where all elements [x] of [l] are in [l1] if [f x] holds, and in [l2] otherwise. Both [l1] and [l2] retain the original order of [l]. Requires, at type-checking time, [f] to be a pure total function. *) val partition: f:('a -> Tot bool) -> list 'a -> Tot (list 'a * list 'a) let rec partition f = function | [] -> [], [] | hd::tl -> let l1, l2 = partition f tl in if f hd then hd::l1, l2 else l1, hd::l2 (** [subset la lb] is true if and only if all the elements from [la] are also in [lb]. Requires, at type-checking time, the type of elements of [la] and [lb] to have decidable equality. *) val subset: #a:eqtype -> list a -> list a -> Tot bool let rec subset #a la lb = match la with | [] -> true | h :: tl -> mem h lb && subset tl lb (** [noRepeats l] returns [true] if, and only if, no element of [l] appears in [l] more than once. Requires, at type-checking time, the type of elements of [la] and [lb] to have decidable equality. *) val noRepeats : #a:eqtype -> list a -> Tot bool let rec noRepeats #a la = match la with | [] -> true | h :: tl -> not(mem h tl) && noRepeats tl (** [no_repeats_p l] valid if, and only if, no element of [l] appears in [l] more than once. *) val no_repeats_p : #a:Type -> list a -> Tot prop let rec no_repeats_p #a la = match la with | [] -> True | h :: tl -> ~(memP h tl) /\ no_repeats_p tl (** List of tuples **) (** [assoc x l] returns [Some y] where [(x, y)] is the first element of [l] whose first element is [x], or [None] only if no such element exists. Requires, at type-checking time, the type of [x] to have decidable equality. Named as in: OCaml. *) val assoc: #a:eqtype -> #b:Type -> a -> list (a * b) -> Tot (option b) let rec assoc #a #b x = function | [] -> None | (x', y)::tl -> if x=x' then Some y else assoc x tl (** [split] takes a list of pairs [(x1, y1), ..., (xn, yn)] and returns the pair of lists ([x1, ..., xn], [y1, ..., yn]). Named as in: OCaml *) val split: list ('a * 'b) -> Tot (list 'a * list 'b) let rec split l = match l with | [] -> ([],[]) | (hd1,hd2)::tl -> let (tl1,tl2) = split tl in (hd1::tl1,hd2::tl2) (** [unzip] takes a list of pairs [(x1, y1), ..., (xn, yn)] and returns the pair of lists ([x1, ..., xn], [y1, ..., yn]). Named as in: Haskell *) let unzip l = split l (** [unzip3] takes a list of triples [(x1, y1, z1), ..., (xn, yn, zn)] and returns the triple of lists ([x1, ..., xn], [y1, ..., yn], [z1, ..., zn]). Named as in: Haskell *) val unzip3: list ('a * 'b * 'c) -> Tot (list 'a * list 'b * list 'c) let rec unzip3 l = match l with | [] -> ([],[],[]) | (hd1,hd2,hd3)::tl -> let (tl1,tl2,tl3) = unzip3 tl in (hd1::tl1,hd2::tl2,hd3::tl3) (** Splitting a list at some index **) (** [splitAt] takes a natural number n and a list and returns a pair of the maximal prefix of l of size smaller than n and the rest of the list *)
false
false
FStar.List.Tot.Base.fst
{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 1, "max_fuel": 8, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": true, "z3cliopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }
null
val splitAt (#a: Type) (n: nat) (l: list a) : Tot (list a * list a)
[ "recursion" ]
FStar.List.Tot.Base.splitAt
{ "file_name": "ulib/FStar.List.Tot.Base.fst", "git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f", "git_url": "https://github.com/FStarLang/FStar.git", "project_name": "FStar" }
n: Prims.nat -> l: Prims.list a -> Prims.list a * Prims.list a
{ "end_col": 61, "end_line": 448, "start_col": 2, "start_line": 444 }
Prims.Tot
val assoc: #a:eqtype -> #b:Type -> a -> list (a * b) -> Tot (option b)
[ { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]
false
let rec assoc #a #b x = function | [] -> None | (x', y)::tl -> if x=x' then Some y else assoc x tl
val assoc: #a:eqtype -> #b:Type -> a -> list (a * b) -> Tot (option b) let rec assoc #a #b x =
false
null
false
function | [] -> None | (x', y) :: tl -> if x = x' then Some y else assoc x tl
{ "checked_file": "FStar.List.Tot.Base.fst.checked", "dependencies": [ "prims.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Classical.fsti.checked" ], "interface_file": false, "source_file": "FStar.List.Tot.Base.fst" }
[ "total" ]
[ "Prims.eqtype", "Prims.list", "FStar.Pervasives.Native.tuple2", "FStar.Pervasives.Native.None", "Prims.op_Equality", "FStar.Pervasives.Native.Some", "Prims.bool", "FStar.List.Tot.Base.assoc", "FStar.Pervasives.Native.option" ]
[]
(* Copyright 2008-2014 Nikhil Swamy and Microsoft Research Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License. *) (** This module defines all pure and total operations on lists that can be used in specifications. It is implemented by FStar_List_Tot_Base.ml, any functional change and/or the addition of new functions MUST be reflected there. @summary Pure total operations on lists *) module FStar.List.Tot.Base (** Base operations *) (** [isEmpty l] returns [true] if and only if [l] is empty *) val isEmpty: list 'a -> Tot bool let isEmpty l = match l with | [] -> true | _ -> false (** [hd l] returns the first element of [l]. Requires [l] to be nonempty, at type-checking time. Named as in: OCaml, F#, Coq *) val hd: l:list 'a{Cons? l} -> Tot 'a let hd = function | hd::_ -> hd (** [tail l] returns [l] without its first element. Requires, at type-checking time, that [l] be nonempty. Similar to: tl in OCaml, F#, Coq *) val tail: l:list 'a {Cons? l} -> Tot (list 'a) let tail = function | _::tl -> tl (** [tl l] returns [l] without its first element. Requires, at type-checking time, that [l] be nonempty. Named as in: OCaml, F#, Coq *) val tl: l:list 'a {Cons? l} -> Tot (list 'a) let tl = tail (** [last l] returns the last element of [l]. Requires, at type-checking time, that [l] be nonempty. Named as in: Haskell *) val last: l:list 'a {Cons? l} -> Tot 'a let rec last = function | [hd] -> hd | _::tl -> last tl (** [init l] returns [l] without its last element. Requires, at type-checking time, that [l] be nonempty. Named as in: Haskell *) val init: l:list 'a {Cons? l} -> Tot (list 'a) let rec init = function | [_] -> [] | hd::tl -> hd::(init tl) (** [length l] returns the total number of elements in [l]. Named as in: OCaml, F#, Coq *) val length: list 'a -> Tot nat let rec length = function | [] -> 0 | _::tl -> 1 + length tl (** [nth l n] returns the [n]-th element in list [l] (with the first element being the 0-th) if [l] is long enough, or [None] otherwise. Named as in: OCaml, F#, Coq *) val nth: list 'a -> nat -> Tot (option 'a) let rec nth l n = match l with | [] -> None | hd::tl -> if n = 0 then Some hd else nth tl (n - 1) (** [index l n] returns the [n]-th element in list [l] (with the first element being the 0-th). Requires, at type-checking time, that [l] be of length at least [n+1]. *) val index: #a:Type -> l:list a -> i:nat{i < length l} -> Tot a let rec index #a (l: list a) (i:nat{i < length l}): Tot a = if i = 0 then hd l else index (tl l) (i - 1) (** [count x l] returns the number of occurrences of [x] in [l]. Requires, at type-checking time, the type of [a] to have equality defined. Similar to: [List.count_occ] in Coq. *) val count: #a:eqtype -> a -> list a -> Tot nat let rec count #a x = function | [] -> 0 | hd::tl -> if x=hd then 1 + count x tl else count x tl (** [rev_acc l1 l2] appends the elements of [l1] to the beginning of [l2], in reverse order. It is equivalent to [append (rev l1) l2], but is tail-recursive. Similar to: [List.rev_append] in OCaml, Coq. *) val rev_acc: list 'a -> list 'a -> Tot (list 'a) let rec rev_acc l acc = match l with | [] -> acc | hd::tl -> rev_acc tl (hd::acc) (** [rev l] returns the list [l] in reverse order. Named as in: OCaml, F#, Coq. *) val rev: list 'a -> Tot (list 'a) let rev l = rev_acc l [] (** [append l1 l2] appends the elements of [l2] to the end of [l1]. Named as: OCaml, F#. Similar to: [List.app] in Coq. *) val append: list 'a -> list 'a -> Tot (list 'a) let rec append x y = match x with | [] -> y | a::tl -> a::append tl y (** Defines notation [@@] for [append], as in OCaml, F# . *) let op_At x y = append x y (** [snoc (l, x)] adds [x] to the end of the list [l]. Note: We use an uncurried [snoc (l, x)] instead of the curried [snoc l x]. This is intentional. If [snoc] takes a pair instead of 2 arguments, it allows for a better pattern on [lemma_unsnoc_snoc], which connects [snoc] and [unsnoc]. In particular, if we had two arguments, then either the pattern would either be too restrictive or would lead to over-triggering. More context for this can be seen in the (collapsed and uncollapsed) comments at https://github.com/FStarLang/FStar/pull/1560 *) val snoc: (list 'a * 'a) -> Tot (list 'a) let snoc (l, x) = append l [x] (** [flatten l], where [l] is a list of lists, returns the list of the elements of the lists in [l], preserving their order. Named as in: OCaml, Coq. *) val flatten: list (list 'a) -> Tot (list 'a) let rec flatten l = match l with | [] -> [] | hd::tl -> append hd (flatten tl) (** [map f l] applies [f] to each element of [l] and returns the list of results, in the order of the original elements in [l]. Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml, Coq, F# *) val map: ('a -> Tot 'b) -> list 'a -> Tot (list 'b) let rec map f x = match x with | [] -> [] | a::tl -> f a::map f tl (** [mapi_init f l n] applies, for each [k], [f (n+k)] to the [k]-th element of [l] and returns the list of results, in the order of the original elements in [l]. Requires, at type-checking time, [f] to be a pure total function. *) val mapi_init: (int -> 'a -> Tot 'b) -> list 'a -> int -> Tot (list 'b) let rec mapi_init f l i = match l with | [] -> [] | hd::tl -> (f i hd)::(mapi_init f tl (i+1)) (** [mapi f l] applies, for each [k], [f k] to the [k]-th element of [l] and returns the list of results, in the order of the original elements in [l]. Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml *) val mapi: (int -> 'a -> Tot 'b) -> list 'a -> Tot (list 'b) let mapi f l = mapi_init f l 0 (** [concatMap f l] applies [f] to each element of [l] and returns the concatenation of the results, in the order of the original elements of [l]. This is equivalent to [flatten (map f l)]. Requires, at type-checking time, [f] to be a pure total function. *) val concatMap: ('a -> Tot (list 'b)) -> list 'a -> Tot (list 'b) let rec concatMap f = function | [] -> [] | a::tl -> let fa = f a in let ftl = concatMap f tl in append fa ftl (** [fold_left f x [y1; y2; ...; yn]] computes (f (... (f x y1) y2) ... yn). Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml, Coq. *) val fold_left: ('a -> 'b -> Tot 'a) -> 'a -> l:list 'b -> Tot 'a (decreases l) let rec fold_left f x l = match l with | [] -> x | hd::tl -> fold_left f (f x hd) tl (** [fold_right f [x1; x2; ...; xn] y] computes (f x1 (f x2 (... (f xn y)) ... )). Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml, Coq *) val fold_right: ('a -> 'b -> Tot 'b) -> list 'a -> 'b -> Tot 'b let rec fold_right f l x = match l with | [] -> x | hd::tl -> f hd (fold_right f tl x) (** [fold_right_gtot] is just like [fold_right], except `f` is a ghost function **) let rec fold_right_gtot (#a:Type) (#b:Type) (l:list a) (f:a -> b -> GTot b) (x:b) : GTot b = match l with | [] -> x | hd::tl -> f hd (fold_right_gtot tl f x) (* We define map in terms of fold, to share simple lemmas *) let map_gtot #a #b (f:a -> GTot b) (x:list a) : GTot (list b) = fold_right_gtot x (fun x tl -> f x :: tl) [] (** [fold_left2 f x [y1; y2; ...; yn] [z1; z2; ...; zn]] computes (f (... (f x y1 z1) y2 z2) ... yn zn). Requires, at type-checking time, [f] to be a pure total function, and the lists [y1; y2; ...; yn] and [z1; z2; ...; zn] to have the same lengths. Named as in: OCaml *) val fold_left2 : f:('a -> 'b -> 'c -> Tot 'a) -> accu:'a -> l1:(list 'b) -> l2:(list 'c) -> Pure 'a (requires (length l1 == length l2)) (ensures (fun _ -> True)) (decreases l1) let rec fold_left2 f accu l1 l2 = match (l1, l2) with | ([], []) -> accu | (a1::l1, a2::l2) -> fold_left2 f (f accu a1 a2) l1 l2 (** Propositional membership (as in Coq). Does not require decidable equality. *) (** [memP x l] holds if, and only if, [x] appears as an element of [l]. Similar to: List.In in Coq. *) let rec memP (#a: Type) (x: a) (l: list a) : Tot Type0 = match l with | [] -> False | y :: q -> x == y \/ memP x q (** List searching **) (** [mem x l] returns [true] if, and only if, [x] appears as an element of [l]. Requires, at type-checking time, the type of elements of [l] to have decidable equality. Named as in: OCaml. See also: List.In in Coq, which is propositional. *) val mem: #a:eqtype -> a -> list a -> Tot bool let rec mem #a x = function | [] -> false | hd::tl -> if hd = x then true else mem x tl (** [contains x l] returns [true] if, and only if, [x] appears as an element of [l]. Requires, at type-checking time, the type of elements of [l] to have decidable equality. It is equivalent to: [mem x l]. TODO: should we rather swap the order of arguments? *) let contains : #a:eqtype -> a -> list a -> Tot bool = mem (** [existsb f l] returns [true] if, and only if, there exists some element [x] in [l] such that [f x] holds. *) val existsb: #a:Type -> f:(a -> Tot bool) -> list a -> Tot bool let rec existsb #a f l = match l with | [] -> false | hd::tl -> if f hd then true else existsb f tl (** [find f l] returns [Some x] for some element [x] appearing in [l] such that [f x] holds, or [None] only if no such [x] exists. *) val find: #a:Type -> f:(a -> Tot bool) -> list a -> Tot (option (x:a{f x})) let rec find #a f l = match l with | [] -> None #(x:a{f x}) //These type annotations are only present because it makes bootstrapping go much faster | hd::tl -> if f hd then Some #(x:a{f x}) hd else find f tl (** Filtering elements of a list [l] through a Boolean pure total predicate [f] *) (** [filter f l] returns [l] with all elements [x] such that [f x] does not hold removed. Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml, Coq *) val filter : #a: Type -> f:(a -> Tot bool) -> l: list a -> Tot (m:list a{forall x. memP x m ==> f x}) let rec filter #a f = function | [] -> [] | hd::tl -> if f hd then hd::filter f tl else filter f tl (** Postcondition on [filter f l]: for any element [x] of [filter f l], [f x] holds. Requires, at type-checking time, [f] to be a pure total function.*) val mem_filter (#a:Type) (f: (a -> Tot bool)) (l: list a) (x: a) : Lemma (requires (memP x (filter f l))) (ensures (f x)) let mem_filter f l x = () (** Postcondition on [filter f l]: stated with [forall]: for any element [x] of [filter f l], [f x] holds. Requires, at type-checking time, [f] to be a pure total function. *) val mem_filter_forall (#a:Type) (f: (a -> Tot bool)) (l: list a) : Lemma (requires True) (ensures (forall x . memP x (filter f l) ==> f x)) [SMTPat (filter f l)] let mem_filter_forall f l = FStar.Classical.ghost_lemma (mem_filter f l) (** [for_all f l] returns [true] if, and only if, for all elements [x] appearing in [l], [f x] holds. Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml. Similar to: List.forallb in Coq *) val for_all: ('a -> Tot bool) -> list 'a -> Tot bool let rec for_all f l = match l with | [] -> true | hd::tl -> if f hd then for_all f tl else false (** Specification for [for_all f l] vs. mem *) let rec for_all_mem (#a: Type) (f: (a -> Tot bool)) (l: list a) : Lemma (for_all f l <==> (forall x . memP x l ==> f x)) = match l with | [] -> () | _ :: q -> for_all_mem f q (** [collect f l] applies [f] to each element of [l] and returns the concatenation of the results, in the order of the original elements of [l]. It is equivalent to [flatten (map f l)]. Requires, at type-checking time, [f] to be a pure total function. TODO: what is the difference with [concatMap]? *) val collect: ('a -> Tot (list 'b)) -> list 'a -> Tot (list 'b) let rec collect f l = match l with | [] -> [] | hd::tl -> append (f hd) (collect f tl) (** [tryFind f l] returns [Some x] for some element [x] appearing in [l] such that [f x] holds, or [None] only if no such [x] exists. Requires, at type-checking time, [f] to be a pure total function. Contrary to [find], [tryFind] provides no postcondition on its result. *) val tryFind: ('a -> Tot bool) -> list 'a -> Tot (option 'a) let rec tryFind p l = match l with | [] -> None | hd::tl -> if p hd then Some hd else tryFind p tl (** [tryPick f l] returns [y] for some element [x] appearing in [l] such that [f x = Some y] for some y, or [None] only if [f x = None] for all elements [x] of [l]. Requires, at type-checking time, [f] to be a pure total function. *) val tryPick: ('a -> Tot (option 'b)) -> list 'a -> Tot (option 'b) let rec tryPick f l = match l with | [] -> None | hd::tl -> match f hd with | Some x -> Some x | None -> tryPick f tl (** [choose f l] returns the list of [y] for all elements [x] appearing in [l] such that [f x = Some y] for some [y]. Requires, at type-checking time, [f] to be a pure total function. *) val choose: ('a -> Tot (option 'b)) -> list 'a -> Tot (list 'b) let rec choose f l = match l with | [] -> [] | hd::tl -> match f hd with | Some x -> x::(choose f tl) | None -> choose f tl (** [partition f l] returns the pair of lists [(l1, l2)] where all elements [x] of [l] are in [l1] if [f x] holds, and in [l2] otherwise. Both [l1] and [l2] retain the original order of [l]. Requires, at type-checking time, [f] to be a pure total function. *) val partition: f:('a -> Tot bool) -> list 'a -> Tot (list 'a * list 'a) let rec partition f = function | [] -> [], [] | hd::tl -> let l1, l2 = partition f tl in if f hd then hd::l1, l2 else l1, hd::l2 (** [subset la lb] is true if and only if all the elements from [la] are also in [lb]. Requires, at type-checking time, the type of elements of [la] and [lb] to have decidable equality. *) val subset: #a:eqtype -> list a -> list a -> Tot bool let rec subset #a la lb = match la with | [] -> true | h :: tl -> mem h lb && subset tl lb (** [noRepeats l] returns [true] if, and only if, no element of [l] appears in [l] more than once. Requires, at type-checking time, the type of elements of [la] and [lb] to have decidable equality. *) val noRepeats : #a:eqtype -> list a -> Tot bool let rec noRepeats #a la = match la with | [] -> true | h :: tl -> not(mem h tl) && noRepeats tl (** [no_repeats_p l] valid if, and only if, no element of [l] appears in [l] more than once. *) val no_repeats_p : #a:Type -> list a -> Tot prop let rec no_repeats_p #a la = match la with | [] -> True | h :: tl -> ~(memP h tl) /\ no_repeats_p tl (** List of tuples **) (** [assoc x l] returns [Some y] where [(x, y)] is the first element of [l] whose first element is [x], or [None] only if no such element exists. Requires, at type-checking time, the type of [x] to have decidable equality. Named as in: OCaml. *)
false
false
FStar.List.Tot.Base.fst
{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 1, "max_fuel": 8, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": true, "z3cliopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }
null
val assoc: #a:eqtype -> #b:Type -> a -> list (a * b) -> Tot (option b)
[ "recursion" ]
FStar.List.Tot.Base.assoc
{ "file_name": "ulib/FStar.List.Tot.Base.fst", "git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f", "git_url": "https://github.com/FStarLang/FStar.git", "project_name": "FStar" }
x: a -> _: Prims.list (a * b) -> FStar.Pervasives.Native.option b
{ "end_col": 54, "end_line": 411, "start_col": 24, "start_line": 409 }
Prims.Tot
val unsnoc: #a:Type -> l:list a{length l > 0} -> Tot (list a * a)
[ { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]
false
let unsnoc #a l = let l1, l2 = splitAt (length l - 1) l in lemma_splitAt_snd_length (length l - 1) l; l1, hd l2
val unsnoc: #a:Type -> l:list a{length l > 0} -> Tot (list a * a) let unsnoc #a l =
false
null
false
let l1, l2 = splitAt (length l - 1) l in lemma_splitAt_snd_length (length l - 1) l; l1, hd l2
{ "checked_file": "FStar.List.Tot.Base.fst.checked", "dependencies": [ "prims.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Classical.fsti.checked" ], "interface_file": false, "source_file": "FStar.List.Tot.Base.fst" }
[ "total" ]
[ "Prims.list", "Prims.b2t", "Prims.op_GreaterThan", "FStar.List.Tot.Base.length", "FStar.Pervasives.Native.Mktuple2", "FStar.List.Tot.Base.hd", "Prims.unit", "FStar.List.Tot.Base.lemma_splitAt_snd_length", "Prims.op_Subtraction", "FStar.Pervasives.Native.tuple2", "FStar.List.Tot.Base.splitAt" ]
[]
(* Copyright 2008-2014 Nikhil Swamy and Microsoft Research Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License. *) (** This module defines all pure and total operations on lists that can be used in specifications. It is implemented by FStar_List_Tot_Base.ml, any functional change and/or the addition of new functions MUST be reflected there. @summary Pure total operations on lists *) module FStar.List.Tot.Base (** Base operations *) (** [isEmpty l] returns [true] if and only if [l] is empty *) val isEmpty: list 'a -> Tot bool let isEmpty l = match l with | [] -> true | _ -> false (** [hd l] returns the first element of [l]. Requires [l] to be nonempty, at type-checking time. Named as in: OCaml, F#, Coq *) val hd: l:list 'a{Cons? l} -> Tot 'a let hd = function | hd::_ -> hd (** [tail l] returns [l] without its first element. Requires, at type-checking time, that [l] be nonempty. Similar to: tl in OCaml, F#, Coq *) val tail: l:list 'a {Cons? l} -> Tot (list 'a) let tail = function | _::tl -> tl (** [tl l] returns [l] without its first element. Requires, at type-checking time, that [l] be nonempty. Named as in: OCaml, F#, Coq *) val tl: l:list 'a {Cons? l} -> Tot (list 'a) let tl = tail (** [last l] returns the last element of [l]. Requires, at type-checking time, that [l] be nonempty. Named as in: Haskell *) val last: l:list 'a {Cons? l} -> Tot 'a let rec last = function | [hd] -> hd | _::tl -> last tl (** [init l] returns [l] without its last element. Requires, at type-checking time, that [l] be nonempty. Named as in: Haskell *) val init: l:list 'a {Cons? l} -> Tot (list 'a) let rec init = function | [_] -> [] | hd::tl -> hd::(init tl) (** [length l] returns the total number of elements in [l]. Named as in: OCaml, F#, Coq *) val length: list 'a -> Tot nat let rec length = function | [] -> 0 | _::tl -> 1 + length tl (** [nth l n] returns the [n]-th element in list [l] (with the first element being the 0-th) if [l] is long enough, or [None] otherwise. Named as in: OCaml, F#, Coq *) val nth: list 'a -> nat -> Tot (option 'a) let rec nth l n = match l with | [] -> None | hd::tl -> if n = 0 then Some hd else nth tl (n - 1) (** [index l n] returns the [n]-th element in list [l] (with the first element being the 0-th). Requires, at type-checking time, that [l] be of length at least [n+1]. *) val index: #a:Type -> l:list a -> i:nat{i < length l} -> Tot a let rec index #a (l: list a) (i:nat{i < length l}): Tot a = if i = 0 then hd l else index (tl l) (i - 1) (** [count x l] returns the number of occurrences of [x] in [l]. Requires, at type-checking time, the type of [a] to have equality defined. Similar to: [List.count_occ] in Coq. *) val count: #a:eqtype -> a -> list a -> Tot nat let rec count #a x = function | [] -> 0 | hd::tl -> if x=hd then 1 + count x tl else count x tl (** [rev_acc l1 l2] appends the elements of [l1] to the beginning of [l2], in reverse order. It is equivalent to [append (rev l1) l2], but is tail-recursive. Similar to: [List.rev_append] in OCaml, Coq. *) val rev_acc: list 'a -> list 'a -> Tot (list 'a) let rec rev_acc l acc = match l with | [] -> acc | hd::tl -> rev_acc tl (hd::acc) (** [rev l] returns the list [l] in reverse order. Named as in: OCaml, F#, Coq. *) val rev: list 'a -> Tot (list 'a) let rev l = rev_acc l [] (** [append l1 l2] appends the elements of [l2] to the end of [l1]. Named as: OCaml, F#. Similar to: [List.app] in Coq. *) val append: list 'a -> list 'a -> Tot (list 'a) let rec append x y = match x with | [] -> y | a::tl -> a::append tl y (** Defines notation [@@] for [append], as in OCaml, F# . *) let op_At x y = append x y (** [snoc (l, x)] adds [x] to the end of the list [l]. Note: We use an uncurried [snoc (l, x)] instead of the curried [snoc l x]. This is intentional. If [snoc] takes a pair instead of 2 arguments, it allows for a better pattern on [lemma_unsnoc_snoc], which connects [snoc] and [unsnoc]. In particular, if we had two arguments, then either the pattern would either be too restrictive or would lead to over-triggering. More context for this can be seen in the (collapsed and uncollapsed) comments at https://github.com/FStarLang/FStar/pull/1560 *) val snoc: (list 'a * 'a) -> Tot (list 'a) let snoc (l, x) = append l [x] (** [flatten l], where [l] is a list of lists, returns the list of the elements of the lists in [l], preserving their order. Named as in: OCaml, Coq. *) val flatten: list (list 'a) -> Tot (list 'a) let rec flatten l = match l with | [] -> [] | hd::tl -> append hd (flatten tl) (** [map f l] applies [f] to each element of [l] and returns the list of results, in the order of the original elements in [l]. Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml, Coq, F# *) val map: ('a -> Tot 'b) -> list 'a -> Tot (list 'b) let rec map f x = match x with | [] -> [] | a::tl -> f a::map f tl (** [mapi_init f l n] applies, for each [k], [f (n+k)] to the [k]-th element of [l] and returns the list of results, in the order of the original elements in [l]. Requires, at type-checking time, [f] to be a pure total function. *) val mapi_init: (int -> 'a -> Tot 'b) -> list 'a -> int -> Tot (list 'b) let rec mapi_init f l i = match l with | [] -> [] | hd::tl -> (f i hd)::(mapi_init f tl (i+1)) (** [mapi f l] applies, for each [k], [f k] to the [k]-th element of [l] and returns the list of results, in the order of the original elements in [l]. Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml *) val mapi: (int -> 'a -> Tot 'b) -> list 'a -> Tot (list 'b) let mapi f l = mapi_init f l 0 (** [concatMap f l] applies [f] to each element of [l] and returns the concatenation of the results, in the order of the original elements of [l]. This is equivalent to [flatten (map f l)]. Requires, at type-checking time, [f] to be a pure total function. *) val concatMap: ('a -> Tot (list 'b)) -> list 'a -> Tot (list 'b) let rec concatMap f = function | [] -> [] | a::tl -> let fa = f a in let ftl = concatMap f tl in append fa ftl (** [fold_left f x [y1; y2; ...; yn]] computes (f (... (f x y1) y2) ... yn). Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml, Coq. *) val fold_left: ('a -> 'b -> Tot 'a) -> 'a -> l:list 'b -> Tot 'a (decreases l) let rec fold_left f x l = match l with | [] -> x | hd::tl -> fold_left f (f x hd) tl (** [fold_right f [x1; x2; ...; xn] y] computes (f x1 (f x2 (... (f xn y)) ... )). Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml, Coq *) val fold_right: ('a -> 'b -> Tot 'b) -> list 'a -> 'b -> Tot 'b let rec fold_right f l x = match l with | [] -> x | hd::tl -> f hd (fold_right f tl x) (** [fold_right_gtot] is just like [fold_right], except `f` is a ghost function **) let rec fold_right_gtot (#a:Type) (#b:Type) (l:list a) (f:a -> b -> GTot b) (x:b) : GTot b = match l with | [] -> x | hd::tl -> f hd (fold_right_gtot tl f x) (* We define map in terms of fold, to share simple lemmas *) let map_gtot #a #b (f:a -> GTot b) (x:list a) : GTot (list b) = fold_right_gtot x (fun x tl -> f x :: tl) [] (** [fold_left2 f x [y1; y2; ...; yn] [z1; z2; ...; zn]] computes (f (... (f x y1 z1) y2 z2) ... yn zn). Requires, at type-checking time, [f] to be a pure total function, and the lists [y1; y2; ...; yn] and [z1; z2; ...; zn] to have the same lengths. Named as in: OCaml *) val fold_left2 : f:('a -> 'b -> 'c -> Tot 'a) -> accu:'a -> l1:(list 'b) -> l2:(list 'c) -> Pure 'a (requires (length l1 == length l2)) (ensures (fun _ -> True)) (decreases l1) let rec fold_left2 f accu l1 l2 = match (l1, l2) with | ([], []) -> accu | (a1::l1, a2::l2) -> fold_left2 f (f accu a1 a2) l1 l2 (** Propositional membership (as in Coq). Does not require decidable equality. *) (** [memP x l] holds if, and only if, [x] appears as an element of [l]. Similar to: List.In in Coq. *) let rec memP (#a: Type) (x: a) (l: list a) : Tot Type0 = match l with | [] -> False | y :: q -> x == y \/ memP x q (** List searching **) (** [mem x l] returns [true] if, and only if, [x] appears as an element of [l]. Requires, at type-checking time, the type of elements of [l] to have decidable equality. Named as in: OCaml. See also: List.In in Coq, which is propositional. *) val mem: #a:eqtype -> a -> list a -> Tot bool let rec mem #a x = function | [] -> false | hd::tl -> if hd = x then true else mem x tl (** [contains x l] returns [true] if, and only if, [x] appears as an element of [l]. Requires, at type-checking time, the type of elements of [l] to have decidable equality. It is equivalent to: [mem x l]. TODO: should we rather swap the order of arguments? *) let contains : #a:eqtype -> a -> list a -> Tot bool = mem (** [existsb f l] returns [true] if, and only if, there exists some element [x] in [l] such that [f x] holds. *) val existsb: #a:Type -> f:(a -> Tot bool) -> list a -> Tot bool let rec existsb #a f l = match l with | [] -> false | hd::tl -> if f hd then true else existsb f tl (** [find f l] returns [Some x] for some element [x] appearing in [l] such that [f x] holds, or [None] only if no such [x] exists. *) val find: #a:Type -> f:(a -> Tot bool) -> list a -> Tot (option (x:a{f x})) let rec find #a f l = match l with | [] -> None #(x:a{f x}) //These type annotations are only present because it makes bootstrapping go much faster | hd::tl -> if f hd then Some #(x:a{f x}) hd else find f tl (** Filtering elements of a list [l] through a Boolean pure total predicate [f] *) (** [filter f l] returns [l] with all elements [x] such that [f x] does not hold removed. Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml, Coq *) val filter : #a: Type -> f:(a -> Tot bool) -> l: list a -> Tot (m:list a{forall x. memP x m ==> f x}) let rec filter #a f = function | [] -> [] | hd::tl -> if f hd then hd::filter f tl else filter f tl (** Postcondition on [filter f l]: for any element [x] of [filter f l], [f x] holds. Requires, at type-checking time, [f] to be a pure total function.*) val mem_filter (#a:Type) (f: (a -> Tot bool)) (l: list a) (x: a) : Lemma (requires (memP x (filter f l))) (ensures (f x)) let mem_filter f l x = () (** Postcondition on [filter f l]: stated with [forall]: for any element [x] of [filter f l], [f x] holds. Requires, at type-checking time, [f] to be a pure total function. *) val mem_filter_forall (#a:Type) (f: (a -> Tot bool)) (l: list a) : Lemma (requires True) (ensures (forall x . memP x (filter f l) ==> f x)) [SMTPat (filter f l)] let mem_filter_forall f l = FStar.Classical.ghost_lemma (mem_filter f l) (** [for_all f l] returns [true] if, and only if, for all elements [x] appearing in [l], [f x] holds. Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml. Similar to: List.forallb in Coq *) val for_all: ('a -> Tot bool) -> list 'a -> Tot bool let rec for_all f l = match l with | [] -> true | hd::tl -> if f hd then for_all f tl else false (** Specification for [for_all f l] vs. mem *) let rec for_all_mem (#a: Type) (f: (a -> Tot bool)) (l: list a) : Lemma (for_all f l <==> (forall x . memP x l ==> f x)) = match l with | [] -> () | _ :: q -> for_all_mem f q (** [collect f l] applies [f] to each element of [l] and returns the concatenation of the results, in the order of the original elements of [l]. It is equivalent to [flatten (map f l)]. Requires, at type-checking time, [f] to be a pure total function. TODO: what is the difference with [concatMap]? *) val collect: ('a -> Tot (list 'b)) -> list 'a -> Tot (list 'b) let rec collect f l = match l with | [] -> [] | hd::tl -> append (f hd) (collect f tl) (** [tryFind f l] returns [Some x] for some element [x] appearing in [l] such that [f x] holds, or [None] only if no such [x] exists. Requires, at type-checking time, [f] to be a pure total function. Contrary to [find], [tryFind] provides no postcondition on its result. *) val tryFind: ('a -> Tot bool) -> list 'a -> Tot (option 'a) let rec tryFind p l = match l with | [] -> None | hd::tl -> if p hd then Some hd else tryFind p tl (** [tryPick f l] returns [y] for some element [x] appearing in [l] such that [f x = Some y] for some y, or [None] only if [f x = None] for all elements [x] of [l]. Requires, at type-checking time, [f] to be a pure total function. *) val tryPick: ('a -> Tot (option 'b)) -> list 'a -> Tot (option 'b) let rec tryPick f l = match l with | [] -> None | hd::tl -> match f hd with | Some x -> Some x | None -> tryPick f tl (** [choose f l] returns the list of [y] for all elements [x] appearing in [l] such that [f x = Some y] for some [y]. Requires, at type-checking time, [f] to be a pure total function. *) val choose: ('a -> Tot (option 'b)) -> list 'a -> Tot (list 'b) let rec choose f l = match l with | [] -> [] | hd::tl -> match f hd with | Some x -> x::(choose f tl) | None -> choose f tl (** [partition f l] returns the pair of lists [(l1, l2)] where all elements [x] of [l] are in [l1] if [f x] holds, and in [l2] otherwise. Both [l1] and [l2] retain the original order of [l]. Requires, at type-checking time, [f] to be a pure total function. *) val partition: f:('a -> Tot bool) -> list 'a -> Tot (list 'a * list 'a) let rec partition f = function | [] -> [], [] | hd::tl -> let l1, l2 = partition f tl in if f hd then hd::l1, l2 else l1, hd::l2 (** [subset la lb] is true if and only if all the elements from [la] are also in [lb]. Requires, at type-checking time, the type of elements of [la] and [lb] to have decidable equality. *) val subset: #a:eqtype -> list a -> list a -> Tot bool let rec subset #a la lb = match la with | [] -> true | h :: tl -> mem h lb && subset tl lb (** [noRepeats l] returns [true] if, and only if, no element of [l] appears in [l] more than once. Requires, at type-checking time, the type of elements of [la] and [lb] to have decidable equality. *) val noRepeats : #a:eqtype -> list a -> Tot bool let rec noRepeats #a la = match la with | [] -> true | h :: tl -> not(mem h tl) && noRepeats tl (** [no_repeats_p l] valid if, and only if, no element of [l] appears in [l] more than once. *) val no_repeats_p : #a:Type -> list a -> Tot prop let rec no_repeats_p #a la = match la with | [] -> True | h :: tl -> ~(memP h tl) /\ no_repeats_p tl (** List of tuples **) (** [assoc x l] returns [Some y] where [(x, y)] is the first element of [l] whose first element is [x], or [None] only if no such element exists. Requires, at type-checking time, the type of [x] to have decidable equality. Named as in: OCaml. *) val assoc: #a:eqtype -> #b:Type -> a -> list (a * b) -> Tot (option b) let rec assoc #a #b x = function | [] -> None | (x', y)::tl -> if x=x' then Some y else assoc x tl (** [split] takes a list of pairs [(x1, y1), ..., (xn, yn)] and returns the pair of lists ([x1, ..., xn], [y1, ..., yn]). Named as in: OCaml *) val split: list ('a * 'b) -> Tot (list 'a * list 'b) let rec split l = match l with | [] -> ([],[]) | (hd1,hd2)::tl -> let (tl1,tl2) = split tl in (hd1::tl1,hd2::tl2) (** [unzip] takes a list of pairs [(x1, y1), ..., (xn, yn)] and returns the pair of lists ([x1, ..., xn], [y1, ..., yn]). Named as in: Haskell *) let unzip l = split l (** [unzip3] takes a list of triples [(x1, y1, z1), ..., (xn, yn, zn)] and returns the triple of lists ([x1, ..., xn], [y1, ..., yn], [z1, ..., zn]). Named as in: Haskell *) val unzip3: list ('a * 'b * 'c) -> Tot (list 'a * list 'b * list 'c) let rec unzip3 l = match l with | [] -> ([],[],[]) | (hd1,hd2,hd3)::tl -> let (tl1,tl2,tl3) = unzip3 tl in (hd1::tl1,hd2::tl2,hd3::tl3) (** Splitting a list at some index **) (** [splitAt] takes a natural number n and a list and returns a pair of the maximal prefix of l of size smaller than n and the rest of the list *) let rec splitAt (#a:Type) (n:nat) (l:list a) : Tot (list a * list a) = if n = 0 then [], l else match l with | [] -> [], l | x :: xs -> let l1, l2 = splitAt (n-1) xs in x :: l1, l2 let rec lemma_splitAt_snd_length (#a:Type) (n:nat) (l:list a) : Lemma (requires (n <= length l)) (ensures (length (snd (splitAt n l)) = length l - n)) = match n, l with | 0, _ -> () | _, [] -> () | _, _ :: l' -> lemma_splitAt_snd_length (n - 1) l' (** [unsnoc] is an inverse of [snoc]. It splits a list into all-elements-except-last and last element. *)
false
false
FStar.List.Tot.Base.fst
{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 1, "max_fuel": 8, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": true, "z3cliopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }
null
val unsnoc: #a:Type -> l:list a{length l > 0} -> Tot (list a * a)
[]
FStar.List.Tot.Base.unsnoc
{ "file_name": "ulib/FStar.List.Tot.Base.fst", "git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f", "git_url": "https://github.com/FStarLang/FStar.git", "project_name": "FStar" }
l: Prims.list a {FStar.List.Tot.Base.length l > 0} -> Prims.list a * a
{ "end_col": 11, "end_line": 465, "start_col": 17, "start_line": 462 }
Prims.Tot
val unzip3: list ('a * 'b * 'c) -> Tot (list 'a * list 'b * list 'c)
[ { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]
false
let rec unzip3 l = match l with | [] -> ([],[],[]) | (hd1,hd2,hd3)::tl -> let (tl1,tl2,tl3) = unzip3 tl in (hd1::tl1,hd2::tl2,hd3::tl3)
val unzip3: list ('a * 'b * 'c) -> Tot (list 'a * list 'b * list 'c) let rec unzip3 l =
false
null
false
match l with | [] -> ([], [], []) | (hd1, hd2, hd3) :: tl -> let tl1, tl2, tl3 = unzip3 tl in (hd1 :: tl1, hd2 :: tl2, hd3 :: tl3)
{ "checked_file": "FStar.List.Tot.Base.fst.checked", "dependencies": [ "prims.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Classical.fsti.checked" ], "interface_file": false, "source_file": "FStar.List.Tot.Base.fst" }
[ "total" ]
[ "Prims.list", "FStar.Pervasives.Native.tuple3", "FStar.Pervasives.Native.Mktuple3", "Prims.Nil", "Prims.Cons", "FStar.List.Tot.Base.unzip3" ]
[]
(* Copyright 2008-2014 Nikhil Swamy and Microsoft Research Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License. *) (** This module defines all pure and total operations on lists that can be used in specifications. It is implemented by FStar_List_Tot_Base.ml, any functional change and/or the addition of new functions MUST be reflected there. @summary Pure total operations on lists *) module FStar.List.Tot.Base (** Base operations *) (** [isEmpty l] returns [true] if and only if [l] is empty *) val isEmpty: list 'a -> Tot bool let isEmpty l = match l with | [] -> true | _ -> false (** [hd l] returns the first element of [l]. Requires [l] to be nonempty, at type-checking time. Named as in: OCaml, F#, Coq *) val hd: l:list 'a{Cons? l} -> Tot 'a let hd = function | hd::_ -> hd (** [tail l] returns [l] without its first element. Requires, at type-checking time, that [l] be nonempty. Similar to: tl in OCaml, F#, Coq *) val tail: l:list 'a {Cons? l} -> Tot (list 'a) let tail = function | _::tl -> tl (** [tl l] returns [l] without its first element. Requires, at type-checking time, that [l] be nonempty. Named as in: OCaml, F#, Coq *) val tl: l:list 'a {Cons? l} -> Tot (list 'a) let tl = tail (** [last l] returns the last element of [l]. Requires, at type-checking time, that [l] be nonempty. Named as in: Haskell *) val last: l:list 'a {Cons? l} -> Tot 'a let rec last = function | [hd] -> hd | _::tl -> last tl (** [init l] returns [l] without its last element. Requires, at type-checking time, that [l] be nonempty. Named as in: Haskell *) val init: l:list 'a {Cons? l} -> Tot (list 'a) let rec init = function | [_] -> [] | hd::tl -> hd::(init tl) (** [length l] returns the total number of elements in [l]. Named as in: OCaml, F#, Coq *) val length: list 'a -> Tot nat let rec length = function | [] -> 0 | _::tl -> 1 + length tl (** [nth l n] returns the [n]-th element in list [l] (with the first element being the 0-th) if [l] is long enough, or [None] otherwise. Named as in: OCaml, F#, Coq *) val nth: list 'a -> nat -> Tot (option 'a) let rec nth l n = match l with | [] -> None | hd::tl -> if n = 0 then Some hd else nth tl (n - 1) (** [index l n] returns the [n]-th element in list [l] (with the first element being the 0-th). Requires, at type-checking time, that [l] be of length at least [n+1]. *) val index: #a:Type -> l:list a -> i:nat{i < length l} -> Tot a let rec index #a (l: list a) (i:nat{i < length l}): Tot a = if i = 0 then hd l else index (tl l) (i - 1) (** [count x l] returns the number of occurrences of [x] in [l]. Requires, at type-checking time, the type of [a] to have equality defined. Similar to: [List.count_occ] in Coq. *) val count: #a:eqtype -> a -> list a -> Tot nat let rec count #a x = function | [] -> 0 | hd::tl -> if x=hd then 1 + count x tl else count x tl (** [rev_acc l1 l2] appends the elements of [l1] to the beginning of [l2], in reverse order. It is equivalent to [append (rev l1) l2], but is tail-recursive. Similar to: [List.rev_append] in OCaml, Coq. *) val rev_acc: list 'a -> list 'a -> Tot (list 'a) let rec rev_acc l acc = match l with | [] -> acc | hd::tl -> rev_acc tl (hd::acc) (** [rev l] returns the list [l] in reverse order. Named as in: OCaml, F#, Coq. *) val rev: list 'a -> Tot (list 'a) let rev l = rev_acc l [] (** [append l1 l2] appends the elements of [l2] to the end of [l1]. Named as: OCaml, F#. Similar to: [List.app] in Coq. *) val append: list 'a -> list 'a -> Tot (list 'a) let rec append x y = match x with | [] -> y | a::tl -> a::append tl y (** Defines notation [@@] for [append], as in OCaml, F# . *) let op_At x y = append x y (** [snoc (l, x)] adds [x] to the end of the list [l]. Note: We use an uncurried [snoc (l, x)] instead of the curried [snoc l x]. This is intentional. If [snoc] takes a pair instead of 2 arguments, it allows for a better pattern on [lemma_unsnoc_snoc], which connects [snoc] and [unsnoc]. In particular, if we had two arguments, then either the pattern would either be too restrictive or would lead to over-triggering. More context for this can be seen in the (collapsed and uncollapsed) comments at https://github.com/FStarLang/FStar/pull/1560 *) val snoc: (list 'a * 'a) -> Tot (list 'a) let snoc (l, x) = append l [x] (** [flatten l], where [l] is a list of lists, returns the list of the elements of the lists in [l], preserving their order. Named as in: OCaml, Coq. *) val flatten: list (list 'a) -> Tot (list 'a) let rec flatten l = match l with | [] -> [] | hd::tl -> append hd (flatten tl) (** [map f l] applies [f] to each element of [l] and returns the list of results, in the order of the original elements in [l]. Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml, Coq, F# *) val map: ('a -> Tot 'b) -> list 'a -> Tot (list 'b) let rec map f x = match x with | [] -> [] | a::tl -> f a::map f tl (** [mapi_init f l n] applies, for each [k], [f (n+k)] to the [k]-th element of [l] and returns the list of results, in the order of the original elements in [l]. Requires, at type-checking time, [f] to be a pure total function. *) val mapi_init: (int -> 'a -> Tot 'b) -> list 'a -> int -> Tot (list 'b) let rec mapi_init f l i = match l with | [] -> [] | hd::tl -> (f i hd)::(mapi_init f tl (i+1)) (** [mapi f l] applies, for each [k], [f k] to the [k]-th element of [l] and returns the list of results, in the order of the original elements in [l]. Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml *) val mapi: (int -> 'a -> Tot 'b) -> list 'a -> Tot (list 'b) let mapi f l = mapi_init f l 0 (** [concatMap f l] applies [f] to each element of [l] and returns the concatenation of the results, in the order of the original elements of [l]. This is equivalent to [flatten (map f l)]. Requires, at type-checking time, [f] to be a pure total function. *) val concatMap: ('a -> Tot (list 'b)) -> list 'a -> Tot (list 'b) let rec concatMap f = function | [] -> [] | a::tl -> let fa = f a in let ftl = concatMap f tl in append fa ftl (** [fold_left f x [y1; y2; ...; yn]] computes (f (... (f x y1) y2) ... yn). Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml, Coq. *) val fold_left: ('a -> 'b -> Tot 'a) -> 'a -> l:list 'b -> Tot 'a (decreases l) let rec fold_left f x l = match l with | [] -> x | hd::tl -> fold_left f (f x hd) tl (** [fold_right f [x1; x2; ...; xn] y] computes (f x1 (f x2 (... (f xn y)) ... )). Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml, Coq *) val fold_right: ('a -> 'b -> Tot 'b) -> list 'a -> 'b -> Tot 'b let rec fold_right f l x = match l with | [] -> x | hd::tl -> f hd (fold_right f tl x) (** [fold_right_gtot] is just like [fold_right], except `f` is a ghost function **) let rec fold_right_gtot (#a:Type) (#b:Type) (l:list a) (f:a -> b -> GTot b) (x:b) : GTot b = match l with | [] -> x | hd::tl -> f hd (fold_right_gtot tl f x) (* We define map in terms of fold, to share simple lemmas *) let map_gtot #a #b (f:a -> GTot b) (x:list a) : GTot (list b) = fold_right_gtot x (fun x tl -> f x :: tl) [] (** [fold_left2 f x [y1; y2; ...; yn] [z1; z2; ...; zn]] computes (f (... (f x y1 z1) y2 z2) ... yn zn). Requires, at type-checking time, [f] to be a pure total function, and the lists [y1; y2; ...; yn] and [z1; z2; ...; zn] to have the same lengths. Named as in: OCaml *) val fold_left2 : f:('a -> 'b -> 'c -> Tot 'a) -> accu:'a -> l1:(list 'b) -> l2:(list 'c) -> Pure 'a (requires (length l1 == length l2)) (ensures (fun _ -> True)) (decreases l1) let rec fold_left2 f accu l1 l2 = match (l1, l2) with | ([], []) -> accu | (a1::l1, a2::l2) -> fold_left2 f (f accu a1 a2) l1 l2 (** Propositional membership (as in Coq). Does not require decidable equality. *) (** [memP x l] holds if, and only if, [x] appears as an element of [l]. Similar to: List.In in Coq. *) let rec memP (#a: Type) (x: a) (l: list a) : Tot Type0 = match l with | [] -> False | y :: q -> x == y \/ memP x q (** List searching **) (** [mem x l] returns [true] if, and only if, [x] appears as an element of [l]. Requires, at type-checking time, the type of elements of [l] to have decidable equality. Named as in: OCaml. See also: List.In in Coq, which is propositional. *) val mem: #a:eqtype -> a -> list a -> Tot bool let rec mem #a x = function | [] -> false | hd::tl -> if hd = x then true else mem x tl (** [contains x l] returns [true] if, and only if, [x] appears as an element of [l]. Requires, at type-checking time, the type of elements of [l] to have decidable equality. It is equivalent to: [mem x l]. TODO: should we rather swap the order of arguments? *) let contains : #a:eqtype -> a -> list a -> Tot bool = mem (** [existsb f l] returns [true] if, and only if, there exists some element [x] in [l] such that [f x] holds. *) val existsb: #a:Type -> f:(a -> Tot bool) -> list a -> Tot bool let rec existsb #a f l = match l with | [] -> false | hd::tl -> if f hd then true else existsb f tl (** [find f l] returns [Some x] for some element [x] appearing in [l] such that [f x] holds, or [None] only if no such [x] exists. *) val find: #a:Type -> f:(a -> Tot bool) -> list a -> Tot (option (x:a{f x})) let rec find #a f l = match l with | [] -> None #(x:a{f x}) //These type annotations are only present because it makes bootstrapping go much faster | hd::tl -> if f hd then Some #(x:a{f x}) hd else find f tl (** Filtering elements of a list [l] through a Boolean pure total predicate [f] *) (** [filter f l] returns [l] with all elements [x] such that [f x] does not hold removed. Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml, Coq *) val filter : #a: Type -> f:(a -> Tot bool) -> l: list a -> Tot (m:list a{forall x. memP x m ==> f x}) let rec filter #a f = function | [] -> [] | hd::tl -> if f hd then hd::filter f tl else filter f tl (** Postcondition on [filter f l]: for any element [x] of [filter f l], [f x] holds. Requires, at type-checking time, [f] to be a pure total function.*) val mem_filter (#a:Type) (f: (a -> Tot bool)) (l: list a) (x: a) : Lemma (requires (memP x (filter f l))) (ensures (f x)) let mem_filter f l x = () (** Postcondition on [filter f l]: stated with [forall]: for any element [x] of [filter f l], [f x] holds. Requires, at type-checking time, [f] to be a pure total function. *) val mem_filter_forall (#a:Type) (f: (a -> Tot bool)) (l: list a) : Lemma (requires True) (ensures (forall x . memP x (filter f l) ==> f x)) [SMTPat (filter f l)] let mem_filter_forall f l = FStar.Classical.ghost_lemma (mem_filter f l) (** [for_all f l] returns [true] if, and only if, for all elements [x] appearing in [l], [f x] holds. Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml. Similar to: List.forallb in Coq *) val for_all: ('a -> Tot bool) -> list 'a -> Tot bool let rec for_all f l = match l with | [] -> true | hd::tl -> if f hd then for_all f tl else false (** Specification for [for_all f l] vs. mem *) let rec for_all_mem (#a: Type) (f: (a -> Tot bool)) (l: list a) : Lemma (for_all f l <==> (forall x . memP x l ==> f x)) = match l with | [] -> () | _ :: q -> for_all_mem f q (** [collect f l] applies [f] to each element of [l] and returns the concatenation of the results, in the order of the original elements of [l]. It is equivalent to [flatten (map f l)]. Requires, at type-checking time, [f] to be a pure total function. TODO: what is the difference with [concatMap]? *) val collect: ('a -> Tot (list 'b)) -> list 'a -> Tot (list 'b) let rec collect f l = match l with | [] -> [] | hd::tl -> append (f hd) (collect f tl) (** [tryFind f l] returns [Some x] for some element [x] appearing in [l] such that [f x] holds, or [None] only if no such [x] exists. Requires, at type-checking time, [f] to be a pure total function. Contrary to [find], [tryFind] provides no postcondition on its result. *) val tryFind: ('a -> Tot bool) -> list 'a -> Tot (option 'a) let rec tryFind p l = match l with | [] -> None | hd::tl -> if p hd then Some hd else tryFind p tl (** [tryPick f l] returns [y] for some element [x] appearing in [l] such that [f x = Some y] for some y, or [None] only if [f x = None] for all elements [x] of [l]. Requires, at type-checking time, [f] to be a pure total function. *) val tryPick: ('a -> Tot (option 'b)) -> list 'a -> Tot (option 'b) let rec tryPick f l = match l with | [] -> None | hd::tl -> match f hd with | Some x -> Some x | None -> tryPick f tl (** [choose f l] returns the list of [y] for all elements [x] appearing in [l] such that [f x = Some y] for some [y]. Requires, at type-checking time, [f] to be a pure total function. *) val choose: ('a -> Tot (option 'b)) -> list 'a -> Tot (list 'b) let rec choose f l = match l with | [] -> [] | hd::tl -> match f hd with | Some x -> x::(choose f tl) | None -> choose f tl (** [partition f l] returns the pair of lists [(l1, l2)] where all elements [x] of [l] are in [l1] if [f x] holds, and in [l2] otherwise. Both [l1] and [l2] retain the original order of [l]. Requires, at type-checking time, [f] to be a pure total function. *) val partition: f:('a -> Tot bool) -> list 'a -> Tot (list 'a * list 'a) let rec partition f = function | [] -> [], [] | hd::tl -> let l1, l2 = partition f tl in if f hd then hd::l1, l2 else l1, hd::l2 (** [subset la lb] is true if and only if all the elements from [la] are also in [lb]. Requires, at type-checking time, the type of elements of [la] and [lb] to have decidable equality. *) val subset: #a:eqtype -> list a -> list a -> Tot bool let rec subset #a la lb = match la with | [] -> true | h :: tl -> mem h lb && subset tl lb (** [noRepeats l] returns [true] if, and only if, no element of [l] appears in [l] more than once. Requires, at type-checking time, the type of elements of [la] and [lb] to have decidable equality. *) val noRepeats : #a:eqtype -> list a -> Tot bool let rec noRepeats #a la = match la with | [] -> true | h :: tl -> not(mem h tl) && noRepeats tl (** [no_repeats_p l] valid if, and only if, no element of [l] appears in [l] more than once. *) val no_repeats_p : #a:Type -> list a -> Tot prop let rec no_repeats_p #a la = match la with | [] -> True | h :: tl -> ~(memP h tl) /\ no_repeats_p tl (** List of tuples **) (** [assoc x l] returns [Some y] where [(x, y)] is the first element of [l] whose first element is [x], or [None] only if no such element exists. Requires, at type-checking time, the type of [x] to have decidable equality. Named as in: OCaml. *) val assoc: #a:eqtype -> #b:Type -> a -> list (a * b) -> Tot (option b) let rec assoc #a #b x = function | [] -> None | (x', y)::tl -> if x=x' then Some y else assoc x tl (** [split] takes a list of pairs [(x1, y1), ..., (xn, yn)] and returns the pair of lists ([x1, ..., xn], [y1, ..., yn]). Named as in: OCaml *) val split: list ('a * 'b) -> Tot (list 'a * list 'b) let rec split l = match l with | [] -> ([],[]) | (hd1,hd2)::tl -> let (tl1,tl2) = split tl in (hd1::tl1,hd2::tl2) (** [unzip] takes a list of pairs [(x1, y1), ..., (xn, yn)] and returns the pair of lists ([x1, ..., xn], [y1, ..., yn]). Named as in: Haskell *) let unzip l = split l (** [unzip3] takes a list of triples [(x1, y1, z1), ..., (xn, yn, zn)] and returns the triple of lists ([x1, ..., xn], [y1, ..., yn], [z1, ..., zn]). Named as in: Haskell *)
false
false
FStar.List.Tot.Base.fst
{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 1, "max_fuel": 8, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": true, "z3cliopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }
null
val unzip3: list ('a * 'b * 'c) -> Tot (list 'a * list 'b * list 'c)
[ "recursion" ]
FStar.List.Tot.Base.unzip3
{ "file_name": "ulib/FStar.List.Tot.Base.fst", "git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f", "git_url": "https://github.com/FStarLang/FStar.git", "project_name": "FStar" }
l: Prims.list (('a * 'b) * 'c) -> (Prims.list 'a * Prims.list 'b) * Prims.list 'c
{ "end_col": 35, "end_line": 436, "start_col": 19, "start_line": 432 }
Prims.Pure
val fold_left2 : f:('a -> 'b -> 'c -> Tot 'a) -> accu:'a -> l1:(list 'b) -> l2:(list 'c) -> Pure 'a (requires (length l1 == length l2)) (ensures (fun _ -> True)) (decreases l1)
[ { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]
false
let rec fold_left2 f accu l1 l2 = match (l1, l2) with | ([], []) -> accu | (a1::l1, a2::l2) -> fold_left2 f (f accu a1 a2) l1 l2
val fold_left2 : f:('a -> 'b -> 'c -> Tot 'a) -> accu:'a -> l1:(list 'b) -> l2:(list 'c) -> Pure 'a (requires (length l1 == length l2)) (ensures (fun _ -> True)) (decreases l1) let rec fold_left2 f accu l1 l2 =
false
null
false
match (l1, l2) with | [], [] -> accu | a1 :: l1, a2 :: l2 -> fold_left2 f (f accu a1 a2) l1 l2
{ "checked_file": "FStar.List.Tot.Base.fst.checked", "dependencies": [ "prims.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Classical.fsti.checked" ], "interface_file": false, "source_file": "FStar.List.Tot.Base.fst" }
[ "" ]
[ "Prims.list", "FStar.Pervasives.Native.Mktuple2", "FStar.List.Tot.Base.fold_left2" ]
[]
(* Copyright 2008-2014 Nikhil Swamy and Microsoft Research Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License. *) (** This module defines all pure and total operations on lists that can be used in specifications. It is implemented by FStar_List_Tot_Base.ml, any functional change and/or the addition of new functions MUST be reflected there. @summary Pure total operations on lists *) module FStar.List.Tot.Base (** Base operations *) (** [isEmpty l] returns [true] if and only if [l] is empty *) val isEmpty: list 'a -> Tot bool let isEmpty l = match l with | [] -> true | _ -> false (** [hd l] returns the first element of [l]. Requires [l] to be nonempty, at type-checking time. Named as in: OCaml, F#, Coq *) val hd: l:list 'a{Cons? l} -> Tot 'a let hd = function | hd::_ -> hd (** [tail l] returns [l] without its first element. Requires, at type-checking time, that [l] be nonempty. Similar to: tl in OCaml, F#, Coq *) val tail: l:list 'a {Cons? l} -> Tot (list 'a) let tail = function | _::tl -> tl (** [tl l] returns [l] without its first element. Requires, at type-checking time, that [l] be nonempty. Named as in: OCaml, F#, Coq *) val tl: l:list 'a {Cons? l} -> Tot (list 'a) let tl = tail (** [last l] returns the last element of [l]. Requires, at type-checking time, that [l] be nonempty. Named as in: Haskell *) val last: l:list 'a {Cons? l} -> Tot 'a let rec last = function | [hd] -> hd | _::tl -> last tl (** [init l] returns [l] without its last element. Requires, at type-checking time, that [l] be nonempty. Named as in: Haskell *) val init: l:list 'a {Cons? l} -> Tot (list 'a) let rec init = function | [_] -> [] | hd::tl -> hd::(init tl) (** [length l] returns the total number of elements in [l]. Named as in: OCaml, F#, Coq *) val length: list 'a -> Tot nat let rec length = function | [] -> 0 | _::tl -> 1 + length tl (** [nth l n] returns the [n]-th element in list [l] (with the first element being the 0-th) if [l] is long enough, or [None] otherwise. Named as in: OCaml, F#, Coq *) val nth: list 'a -> nat -> Tot (option 'a) let rec nth l n = match l with | [] -> None | hd::tl -> if n = 0 then Some hd else nth tl (n - 1) (** [index l n] returns the [n]-th element in list [l] (with the first element being the 0-th). Requires, at type-checking time, that [l] be of length at least [n+1]. *) val index: #a:Type -> l:list a -> i:nat{i < length l} -> Tot a let rec index #a (l: list a) (i:nat{i < length l}): Tot a = if i = 0 then hd l else index (tl l) (i - 1) (** [count x l] returns the number of occurrences of [x] in [l]. Requires, at type-checking time, the type of [a] to have equality defined. Similar to: [List.count_occ] in Coq. *) val count: #a:eqtype -> a -> list a -> Tot nat let rec count #a x = function | [] -> 0 | hd::tl -> if x=hd then 1 + count x tl else count x tl (** [rev_acc l1 l2] appends the elements of [l1] to the beginning of [l2], in reverse order. It is equivalent to [append (rev l1) l2], but is tail-recursive. Similar to: [List.rev_append] in OCaml, Coq. *) val rev_acc: list 'a -> list 'a -> Tot (list 'a) let rec rev_acc l acc = match l with | [] -> acc | hd::tl -> rev_acc tl (hd::acc) (** [rev l] returns the list [l] in reverse order. Named as in: OCaml, F#, Coq. *) val rev: list 'a -> Tot (list 'a) let rev l = rev_acc l [] (** [append l1 l2] appends the elements of [l2] to the end of [l1]. Named as: OCaml, F#. Similar to: [List.app] in Coq. *) val append: list 'a -> list 'a -> Tot (list 'a) let rec append x y = match x with | [] -> y | a::tl -> a::append tl y (** Defines notation [@@] for [append], as in OCaml, F# . *) let op_At x y = append x y (** [snoc (l, x)] adds [x] to the end of the list [l]. Note: We use an uncurried [snoc (l, x)] instead of the curried [snoc l x]. This is intentional. If [snoc] takes a pair instead of 2 arguments, it allows for a better pattern on [lemma_unsnoc_snoc], which connects [snoc] and [unsnoc]. In particular, if we had two arguments, then either the pattern would either be too restrictive or would lead to over-triggering. More context for this can be seen in the (collapsed and uncollapsed) comments at https://github.com/FStarLang/FStar/pull/1560 *) val snoc: (list 'a * 'a) -> Tot (list 'a) let snoc (l, x) = append l [x] (** [flatten l], where [l] is a list of lists, returns the list of the elements of the lists in [l], preserving their order. Named as in: OCaml, Coq. *) val flatten: list (list 'a) -> Tot (list 'a) let rec flatten l = match l with | [] -> [] | hd::tl -> append hd (flatten tl) (** [map f l] applies [f] to each element of [l] and returns the list of results, in the order of the original elements in [l]. Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml, Coq, F# *) val map: ('a -> Tot 'b) -> list 'a -> Tot (list 'b) let rec map f x = match x with | [] -> [] | a::tl -> f a::map f tl (** [mapi_init f l n] applies, for each [k], [f (n+k)] to the [k]-th element of [l] and returns the list of results, in the order of the original elements in [l]. Requires, at type-checking time, [f] to be a pure total function. *) val mapi_init: (int -> 'a -> Tot 'b) -> list 'a -> int -> Tot (list 'b) let rec mapi_init f l i = match l with | [] -> [] | hd::tl -> (f i hd)::(mapi_init f tl (i+1)) (** [mapi f l] applies, for each [k], [f k] to the [k]-th element of [l] and returns the list of results, in the order of the original elements in [l]. Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml *) val mapi: (int -> 'a -> Tot 'b) -> list 'a -> Tot (list 'b) let mapi f l = mapi_init f l 0 (** [concatMap f l] applies [f] to each element of [l] and returns the concatenation of the results, in the order of the original elements of [l]. This is equivalent to [flatten (map f l)]. Requires, at type-checking time, [f] to be a pure total function. *) val concatMap: ('a -> Tot (list 'b)) -> list 'a -> Tot (list 'b) let rec concatMap f = function | [] -> [] | a::tl -> let fa = f a in let ftl = concatMap f tl in append fa ftl (** [fold_left f x [y1; y2; ...; yn]] computes (f (... (f x y1) y2) ... yn). Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml, Coq. *) val fold_left: ('a -> 'b -> Tot 'a) -> 'a -> l:list 'b -> Tot 'a (decreases l) let rec fold_left f x l = match l with | [] -> x | hd::tl -> fold_left f (f x hd) tl (** [fold_right f [x1; x2; ...; xn] y] computes (f x1 (f x2 (... (f xn y)) ... )). Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml, Coq *) val fold_right: ('a -> 'b -> Tot 'b) -> list 'a -> 'b -> Tot 'b let rec fold_right f l x = match l with | [] -> x | hd::tl -> f hd (fold_right f tl x) (** [fold_right_gtot] is just like [fold_right], except `f` is a ghost function **) let rec fold_right_gtot (#a:Type) (#b:Type) (l:list a) (f:a -> b -> GTot b) (x:b) : GTot b = match l with | [] -> x | hd::tl -> f hd (fold_right_gtot tl f x) (* We define map in terms of fold, to share simple lemmas *) let map_gtot #a #b (f:a -> GTot b) (x:list a) : GTot (list b) = fold_right_gtot x (fun x tl -> f x :: tl) [] (** [fold_left2 f x [y1; y2; ...; yn] [z1; z2; ...; zn]] computes (f (... (f x y1 z1) y2 z2) ... yn zn). Requires, at type-checking time, [f] to be a pure total function, and the lists [y1; y2; ...; yn] and [z1; z2; ...; zn] to have the same lengths. Named as in: OCaml *) val fold_left2 : f:('a -> 'b -> 'c -> Tot 'a) -> accu:'a -> l1:(list 'b) -> l2:(list 'c) -> Pure 'a (requires (length l1 == length l2)) (ensures (fun _ -> True)) (decreases l1)
false
false
FStar.List.Tot.Base.fst
{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 1, "max_fuel": 8, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": true, "z3cliopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }
null
val fold_left2 : f:('a -> 'b -> 'c -> Tot 'a) -> accu:'a -> l1:(list 'b) -> l2:(list 'c) -> Pure 'a (requires (length l1 == length l2)) (ensures (fun _ -> True)) (decreases l1)
[ "recursion" ]
FStar.List.Tot.Base.fold_left2
{ "file_name": "ulib/FStar.List.Tot.Base.fst", "git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f", "git_url": "https://github.com/FStarLang/FStar.git", "project_name": "FStar" }
f: (_: 'a -> _: 'b -> _: 'c -> 'a) -> accu: 'a -> l1: Prims.list 'b -> l2: Prims.list 'c -> Prims.Pure 'a
{ "end_col": 57, "end_line": 221, "start_col": 2, "start_line": 219 }
Prims.Tot
val sortWith: ('a -> 'a -> Tot int) -> l:list 'a -> Tot (list 'a) (decreases (length l))
[ { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]
false
let rec sortWith f = function | [] -> [] | pivot::tl -> let hi, lo = partition (bool_of_compare f pivot) tl in partition_length (bool_of_compare f pivot) tl; append (sortWith f lo) (pivot::sortWith f hi)
val sortWith: ('a -> 'a -> Tot int) -> l:list 'a -> Tot (list 'a) (decreases (length l)) let rec sortWith f =
false
null
false
function | [] -> [] | pivot :: tl -> let hi, lo = partition (bool_of_compare f pivot) tl in partition_length (bool_of_compare f pivot) tl; append (sortWith f lo) (pivot :: sortWith f hi)
{ "checked_file": "FStar.List.Tot.Base.fst.checked", "dependencies": [ "prims.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Classical.fsti.checked" ], "interface_file": false, "source_file": "FStar.List.Tot.Base.fst" }
[ "total", "" ]
[ "Prims.int", "Prims.list", "Prims.Nil", "FStar.List.Tot.Base.append", "FStar.List.Tot.Base.sortWith", "Prims.Cons", "Prims.unit", "FStar.List.Tot.Base.partition_length", "FStar.List.Tot.Base.bool_of_compare", "FStar.Pervasives.Native.tuple2", "FStar.List.Tot.Base.partition" ]
[]
(* Copyright 2008-2014 Nikhil Swamy and Microsoft Research Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License. *) (** This module defines all pure and total operations on lists that can be used in specifications. It is implemented by FStar_List_Tot_Base.ml, any functional change and/or the addition of new functions MUST be reflected there. @summary Pure total operations on lists *) module FStar.List.Tot.Base (** Base operations *) (** [isEmpty l] returns [true] if and only if [l] is empty *) val isEmpty: list 'a -> Tot bool let isEmpty l = match l with | [] -> true | _ -> false (** [hd l] returns the first element of [l]. Requires [l] to be nonempty, at type-checking time. Named as in: OCaml, F#, Coq *) val hd: l:list 'a{Cons? l} -> Tot 'a let hd = function | hd::_ -> hd (** [tail l] returns [l] without its first element. Requires, at type-checking time, that [l] be nonempty. Similar to: tl in OCaml, F#, Coq *) val tail: l:list 'a {Cons? l} -> Tot (list 'a) let tail = function | _::tl -> tl (** [tl l] returns [l] without its first element. Requires, at type-checking time, that [l] be nonempty. Named as in: OCaml, F#, Coq *) val tl: l:list 'a {Cons? l} -> Tot (list 'a) let tl = tail (** [last l] returns the last element of [l]. Requires, at type-checking time, that [l] be nonempty. Named as in: Haskell *) val last: l:list 'a {Cons? l} -> Tot 'a let rec last = function | [hd] -> hd | _::tl -> last tl (** [init l] returns [l] without its last element. Requires, at type-checking time, that [l] be nonempty. Named as in: Haskell *) val init: l:list 'a {Cons? l} -> Tot (list 'a) let rec init = function | [_] -> [] | hd::tl -> hd::(init tl) (** [length l] returns the total number of elements in [l]. Named as in: OCaml, F#, Coq *) val length: list 'a -> Tot nat let rec length = function | [] -> 0 | _::tl -> 1 + length tl (** [nth l n] returns the [n]-th element in list [l] (with the first element being the 0-th) if [l] is long enough, or [None] otherwise. Named as in: OCaml, F#, Coq *) val nth: list 'a -> nat -> Tot (option 'a) let rec nth l n = match l with | [] -> None | hd::tl -> if n = 0 then Some hd else nth tl (n - 1) (** [index l n] returns the [n]-th element in list [l] (with the first element being the 0-th). Requires, at type-checking time, that [l] be of length at least [n+1]. *) val index: #a:Type -> l:list a -> i:nat{i < length l} -> Tot a let rec index #a (l: list a) (i:nat{i < length l}): Tot a = if i = 0 then hd l else index (tl l) (i - 1) (** [count x l] returns the number of occurrences of [x] in [l]. Requires, at type-checking time, the type of [a] to have equality defined. Similar to: [List.count_occ] in Coq. *) val count: #a:eqtype -> a -> list a -> Tot nat let rec count #a x = function | [] -> 0 | hd::tl -> if x=hd then 1 + count x tl else count x tl (** [rev_acc l1 l2] appends the elements of [l1] to the beginning of [l2], in reverse order. It is equivalent to [append (rev l1) l2], but is tail-recursive. Similar to: [List.rev_append] in OCaml, Coq. *) val rev_acc: list 'a -> list 'a -> Tot (list 'a) let rec rev_acc l acc = match l with | [] -> acc | hd::tl -> rev_acc tl (hd::acc) (** [rev l] returns the list [l] in reverse order. Named as in: OCaml, F#, Coq. *) val rev: list 'a -> Tot (list 'a) let rev l = rev_acc l [] (** [append l1 l2] appends the elements of [l2] to the end of [l1]. Named as: OCaml, F#. Similar to: [List.app] in Coq. *) val append: list 'a -> list 'a -> Tot (list 'a) let rec append x y = match x with | [] -> y | a::tl -> a::append tl y (** Defines notation [@@] for [append], as in OCaml, F# . *) let op_At x y = append x y (** [snoc (l, x)] adds [x] to the end of the list [l]. Note: We use an uncurried [snoc (l, x)] instead of the curried [snoc l x]. This is intentional. If [snoc] takes a pair instead of 2 arguments, it allows for a better pattern on [lemma_unsnoc_snoc], which connects [snoc] and [unsnoc]. In particular, if we had two arguments, then either the pattern would either be too restrictive or would lead to over-triggering. More context for this can be seen in the (collapsed and uncollapsed) comments at https://github.com/FStarLang/FStar/pull/1560 *) val snoc: (list 'a * 'a) -> Tot (list 'a) let snoc (l, x) = append l [x] (** [flatten l], where [l] is a list of lists, returns the list of the elements of the lists in [l], preserving their order. Named as in: OCaml, Coq. *) val flatten: list (list 'a) -> Tot (list 'a) let rec flatten l = match l with | [] -> [] | hd::tl -> append hd (flatten tl) (** [map f l] applies [f] to each element of [l] and returns the list of results, in the order of the original elements in [l]. Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml, Coq, F# *) val map: ('a -> Tot 'b) -> list 'a -> Tot (list 'b) let rec map f x = match x with | [] -> [] | a::tl -> f a::map f tl (** [mapi_init f l n] applies, for each [k], [f (n+k)] to the [k]-th element of [l] and returns the list of results, in the order of the original elements in [l]. Requires, at type-checking time, [f] to be a pure total function. *) val mapi_init: (int -> 'a -> Tot 'b) -> list 'a -> int -> Tot (list 'b) let rec mapi_init f l i = match l with | [] -> [] | hd::tl -> (f i hd)::(mapi_init f tl (i+1)) (** [mapi f l] applies, for each [k], [f k] to the [k]-th element of [l] and returns the list of results, in the order of the original elements in [l]. Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml *) val mapi: (int -> 'a -> Tot 'b) -> list 'a -> Tot (list 'b) let mapi f l = mapi_init f l 0 (** [concatMap f l] applies [f] to each element of [l] and returns the concatenation of the results, in the order of the original elements of [l]. This is equivalent to [flatten (map f l)]. Requires, at type-checking time, [f] to be a pure total function. *) val concatMap: ('a -> Tot (list 'b)) -> list 'a -> Tot (list 'b) let rec concatMap f = function | [] -> [] | a::tl -> let fa = f a in let ftl = concatMap f tl in append fa ftl (** [fold_left f x [y1; y2; ...; yn]] computes (f (... (f x y1) y2) ... yn). Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml, Coq. *) val fold_left: ('a -> 'b -> Tot 'a) -> 'a -> l:list 'b -> Tot 'a (decreases l) let rec fold_left f x l = match l with | [] -> x | hd::tl -> fold_left f (f x hd) tl (** [fold_right f [x1; x2; ...; xn] y] computes (f x1 (f x2 (... (f xn y)) ... )). Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml, Coq *) val fold_right: ('a -> 'b -> Tot 'b) -> list 'a -> 'b -> Tot 'b let rec fold_right f l x = match l with | [] -> x | hd::tl -> f hd (fold_right f tl x) (** [fold_right_gtot] is just like [fold_right], except `f` is a ghost function **) let rec fold_right_gtot (#a:Type) (#b:Type) (l:list a) (f:a -> b -> GTot b) (x:b) : GTot b = match l with | [] -> x | hd::tl -> f hd (fold_right_gtot tl f x) (* We define map in terms of fold, to share simple lemmas *) let map_gtot #a #b (f:a -> GTot b) (x:list a) : GTot (list b) = fold_right_gtot x (fun x tl -> f x :: tl) [] (** [fold_left2 f x [y1; y2; ...; yn] [z1; z2; ...; zn]] computes (f (... (f x y1 z1) y2 z2) ... yn zn). Requires, at type-checking time, [f] to be a pure total function, and the lists [y1; y2; ...; yn] and [z1; z2; ...; zn] to have the same lengths. Named as in: OCaml *) val fold_left2 : f:('a -> 'b -> 'c -> Tot 'a) -> accu:'a -> l1:(list 'b) -> l2:(list 'c) -> Pure 'a (requires (length l1 == length l2)) (ensures (fun _ -> True)) (decreases l1) let rec fold_left2 f accu l1 l2 = match (l1, l2) with | ([], []) -> accu | (a1::l1, a2::l2) -> fold_left2 f (f accu a1 a2) l1 l2 (** Propositional membership (as in Coq). Does not require decidable equality. *) (** [memP x l] holds if, and only if, [x] appears as an element of [l]. Similar to: List.In in Coq. *) let rec memP (#a: Type) (x: a) (l: list a) : Tot Type0 = match l with | [] -> False | y :: q -> x == y \/ memP x q (** List searching **) (** [mem x l] returns [true] if, and only if, [x] appears as an element of [l]. Requires, at type-checking time, the type of elements of [l] to have decidable equality. Named as in: OCaml. See also: List.In in Coq, which is propositional. *) val mem: #a:eqtype -> a -> list a -> Tot bool let rec mem #a x = function | [] -> false | hd::tl -> if hd = x then true else mem x tl (** [contains x l] returns [true] if, and only if, [x] appears as an element of [l]. Requires, at type-checking time, the type of elements of [l] to have decidable equality. It is equivalent to: [mem x l]. TODO: should we rather swap the order of arguments? *) let contains : #a:eqtype -> a -> list a -> Tot bool = mem (** [existsb f l] returns [true] if, and only if, there exists some element [x] in [l] such that [f x] holds. *) val existsb: #a:Type -> f:(a -> Tot bool) -> list a -> Tot bool let rec existsb #a f l = match l with | [] -> false | hd::tl -> if f hd then true else existsb f tl (** [find f l] returns [Some x] for some element [x] appearing in [l] such that [f x] holds, or [None] only if no such [x] exists. *) val find: #a:Type -> f:(a -> Tot bool) -> list a -> Tot (option (x:a{f x})) let rec find #a f l = match l with | [] -> None #(x:a{f x}) //These type annotations are only present because it makes bootstrapping go much faster | hd::tl -> if f hd then Some #(x:a{f x}) hd else find f tl (** Filtering elements of a list [l] through a Boolean pure total predicate [f] *) (** [filter f l] returns [l] with all elements [x] such that [f x] does not hold removed. Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml, Coq *) val filter : #a: Type -> f:(a -> Tot bool) -> l: list a -> Tot (m:list a{forall x. memP x m ==> f x}) let rec filter #a f = function | [] -> [] | hd::tl -> if f hd then hd::filter f tl else filter f tl (** Postcondition on [filter f l]: for any element [x] of [filter f l], [f x] holds. Requires, at type-checking time, [f] to be a pure total function.*) val mem_filter (#a:Type) (f: (a -> Tot bool)) (l: list a) (x: a) : Lemma (requires (memP x (filter f l))) (ensures (f x)) let mem_filter f l x = () (** Postcondition on [filter f l]: stated with [forall]: for any element [x] of [filter f l], [f x] holds. Requires, at type-checking time, [f] to be a pure total function. *) val mem_filter_forall (#a:Type) (f: (a -> Tot bool)) (l: list a) : Lemma (requires True) (ensures (forall x . memP x (filter f l) ==> f x)) [SMTPat (filter f l)] let mem_filter_forall f l = FStar.Classical.ghost_lemma (mem_filter f l) (** [for_all f l] returns [true] if, and only if, for all elements [x] appearing in [l], [f x] holds. Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml. Similar to: List.forallb in Coq *) val for_all: ('a -> Tot bool) -> list 'a -> Tot bool let rec for_all f l = match l with | [] -> true | hd::tl -> if f hd then for_all f tl else false (** Specification for [for_all f l] vs. mem *) let rec for_all_mem (#a: Type) (f: (a -> Tot bool)) (l: list a) : Lemma (for_all f l <==> (forall x . memP x l ==> f x)) = match l with | [] -> () | _ :: q -> for_all_mem f q (** [collect f l] applies [f] to each element of [l] and returns the concatenation of the results, in the order of the original elements of [l]. It is equivalent to [flatten (map f l)]. Requires, at type-checking time, [f] to be a pure total function. TODO: what is the difference with [concatMap]? *) val collect: ('a -> Tot (list 'b)) -> list 'a -> Tot (list 'b) let rec collect f l = match l with | [] -> [] | hd::tl -> append (f hd) (collect f tl) (** [tryFind f l] returns [Some x] for some element [x] appearing in [l] such that [f x] holds, or [None] only if no such [x] exists. Requires, at type-checking time, [f] to be a pure total function. Contrary to [find], [tryFind] provides no postcondition on its result. *) val tryFind: ('a -> Tot bool) -> list 'a -> Tot (option 'a) let rec tryFind p l = match l with | [] -> None | hd::tl -> if p hd then Some hd else tryFind p tl (** [tryPick f l] returns [y] for some element [x] appearing in [l] such that [f x = Some y] for some y, or [None] only if [f x = None] for all elements [x] of [l]. Requires, at type-checking time, [f] to be a pure total function. *) val tryPick: ('a -> Tot (option 'b)) -> list 'a -> Tot (option 'b) let rec tryPick f l = match l with | [] -> None | hd::tl -> match f hd with | Some x -> Some x | None -> tryPick f tl (** [choose f l] returns the list of [y] for all elements [x] appearing in [l] such that [f x = Some y] for some [y]. Requires, at type-checking time, [f] to be a pure total function. *) val choose: ('a -> Tot (option 'b)) -> list 'a -> Tot (list 'b) let rec choose f l = match l with | [] -> [] | hd::tl -> match f hd with | Some x -> x::(choose f tl) | None -> choose f tl (** [partition f l] returns the pair of lists [(l1, l2)] where all elements [x] of [l] are in [l1] if [f x] holds, and in [l2] otherwise. Both [l1] and [l2] retain the original order of [l]. Requires, at type-checking time, [f] to be a pure total function. *) val partition: f:('a -> Tot bool) -> list 'a -> Tot (list 'a * list 'a) let rec partition f = function | [] -> [], [] | hd::tl -> let l1, l2 = partition f tl in if f hd then hd::l1, l2 else l1, hd::l2 (** [subset la lb] is true if and only if all the elements from [la] are also in [lb]. Requires, at type-checking time, the type of elements of [la] and [lb] to have decidable equality. *) val subset: #a:eqtype -> list a -> list a -> Tot bool let rec subset #a la lb = match la with | [] -> true | h :: tl -> mem h lb && subset tl lb (** [noRepeats l] returns [true] if, and only if, no element of [l] appears in [l] more than once. Requires, at type-checking time, the type of elements of [la] and [lb] to have decidable equality. *) val noRepeats : #a:eqtype -> list a -> Tot bool let rec noRepeats #a la = match la with | [] -> true | h :: tl -> not(mem h tl) && noRepeats tl (** [no_repeats_p l] valid if, and only if, no element of [l] appears in [l] more than once. *) val no_repeats_p : #a:Type -> list a -> Tot prop let rec no_repeats_p #a la = match la with | [] -> True | h :: tl -> ~(memP h tl) /\ no_repeats_p tl (** List of tuples **) (** [assoc x l] returns [Some y] where [(x, y)] is the first element of [l] whose first element is [x], or [None] only if no such element exists. Requires, at type-checking time, the type of [x] to have decidable equality. Named as in: OCaml. *) val assoc: #a:eqtype -> #b:Type -> a -> list (a * b) -> Tot (option b) let rec assoc #a #b x = function | [] -> None | (x', y)::tl -> if x=x' then Some y else assoc x tl (** [split] takes a list of pairs [(x1, y1), ..., (xn, yn)] and returns the pair of lists ([x1, ..., xn], [y1, ..., yn]). Named as in: OCaml *) val split: list ('a * 'b) -> Tot (list 'a * list 'b) let rec split l = match l with | [] -> ([],[]) | (hd1,hd2)::tl -> let (tl1,tl2) = split tl in (hd1::tl1,hd2::tl2) (** [unzip] takes a list of pairs [(x1, y1), ..., (xn, yn)] and returns the pair of lists ([x1, ..., xn], [y1, ..., yn]). Named as in: Haskell *) let unzip l = split l (** [unzip3] takes a list of triples [(x1, y1, z1), ..., (xn, yn, zn)] and returns the triple of lists ([x1, ..., xn], [y1, ..., yn], [z1, ..., zn]). Named as in: Haskell *) val unzip3: list ('a * 'b * 'c) -> Tot (list 'a * list 'b * list 'c) let rec unzip3 l = match l with | [] -> ([],[],[]) | (hd1,hd2,hd3)::tl -> let (tl1,tl2,tl3) = unzip3 tl in (hd1::tl1,hd2::tl2,hd3::tl3) (** Splitting a list at some index **) (** [splitAt] takes a natural number n and a list and returns a pair of the maximal prefix of l of size smaller than n and the rest of the list *) let rec splitAt (#a:Type) (n:nat) (l:list a) : Tot (list a * list a) = if n = 0 then [], l else match l with | [] -> [], l | x :: xs -> let l1, l2 = splitAt (n-1) xs in x :: l1, l2 let rec lemma_splitAt_snd_length (#a:Type) (n:nat) (l:list a) : Lemma (requires (n <= length l)) (ensures (length (snd (splitAt n l)) = length l - n)) = match n, l with | 0, _ -> () | _, [] -> () | _, _ :: l' -> lemma_splitAt_snd_length (n - 1) l' (** [unsnoc] is an inverse of [snoc]. It splits a list into all-elements-except-last and last element. *) val unsnoc: #a:Type -> l:list a{length l > 0} -> Tot (list a * a) let unsnoc #a l = let l1, l2 = splitAt (length l - 1) l in lemma_splitAt_snd_length (length l - 1) l; l1, hd l2 (** [split3] splits a list into 3 parts. This allows easy access to the part of the list before and after the element, as well as the element itself. *) val split3: #a:Type -> l:list a -> i:nat{i < length l} -> Tot (list a * a * list a) let split3 #a l i = let a, rest = splitAt i l in lemma_splitAt_snd_length i l; let b :: c = rest in a, b, c (** Sorting (implemented as quicksort) **) (** [partition] splits a list [l] into two lists, the sum of whose lengths is the length of [l]. *) val partition_length: f:('a -> Tot bool) -> l:list 'a -> Lemma (requires True) (ensures (length (fst (partition f l)) + length (snd (partition f l)) = length l)) let rec partition_length f l = match l with | [] -> () | hd::tl -> partition_length f tl (** [bool_of_compare] turns a comparison function into a strict order. More precisely, [bool_of_compare compare x y] returns true if, and only if, [compare x y] is negative, meaning [x] precedes [y] in the ordering defined by compare. This is used in sorting, and is defined to be consistent with OCaml and F#, where sorting is performed in ascending order. *) val bool_of_compare : #a:Type -> (a -> a -> Tot int) -> a -> a -> Tot bool let bool_of_compare #a f x y = f x y < 0 (** [compare_of_bool] turns a strict order into a comparison function. More precisely, [compare_of_bool rel x y] returns a positive number if, and only if, x `rel` y holds. Inspired from OCaml, where polymorphic comparison using both the [compare] function and the (>) infix operator are such that [compare x y] is positive if, and only if, x > y. Requires, at type-checking time, [rel] to be a pure total function. *) val compare_of_bool : #a:eqtype -> (a -> a -> Tot bool) -> a -> a -> Tot int let compare_of_bool #a rel x y = if x `rel` y then -1 else if x = y then 0 else 1 let compare_of_bool_of_compare (#a:eqtype) (f:a -> a -> Tot bool) : Lemma (forall x y. bool_of_compare (compare_of_bool f) x y == f x y) = () (** [sortWith compare l] returns the list [l'] containing the elements of [l] sorted along the comparison function [compare], in such a way that if [compare x y > 0], then [x] appears before [y] in [l']. Sorts in ascending order *)
false
false
FStar.List.Tot.Base.fst
{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 1, "max_fuel": 8, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": true, "z3cliopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }
null
val sortWith: ('a -> 'a -> Tot int) -> l:list 'a -> Tot (list 'a) (decreases (length l))
[ "recursion" ]
FStar.List.Tot.Base.sortWith
{ "file_name": "ulib/FStar.List.Tot.Base.fst", "git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f", "git_url": "https://github.com/FStarLang/FStar.git", "project_name": "FStar" }
f: (_: 'a -> _: 'a -> Prims.int) -> l: Prims.list 'a -> Prims.Tot (Prims.list 'a)
{ "end_col": 50, "end_line": 528, "start_col": 21, "start_line": 523 }
Prims.Tot
val split: list ('a * 'b) -> Tot (list 'a * list 'b)
[ { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]
false
let rec split l = match l with | [] -> ([],[]) | (hd1,hd2)::tl -> let (tl1,tl2) = split tl in (hd1::tl1,hd2::tl2)
val split: list ('a * 'b) -> Tot (list 'a * list 'b) let rec split l =
false
null
false
match l with | [] -> ([], []) | (hd1, hd2) :: tl -> let tl1, tl2 = split tl in (hd1 :: tl1, hd2 :: tl2)
{ "checked_file": "FStar.List.Tot.Base.fst.checked", "dependencies": [ "prims.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Classical.fsti.checked" ], "interface_file": false, "source_file": "FStar.List.Tot.Base.fst" }
[ "total" ]
[ "Prims.list", "FStar.Pervasives.Native.tuple2", "FStar.Pervasives.Native.Mktuple2", "Prims.Nil", "Prims.Cons", "FStar.List.Tot.Base.split" ]
[]
(* Copyright 2008-2014 Nikhil Swamy and Microsoft Research Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License. *) (** This module defines all pure and total operations on lists that can be used in specifications. It is implemented by FStar_List_Tot_Base.ml, any functional change and/or the addition of new functions MUST be reflected there. @summary Pure total operations on lists *) module FStar.List.Tot.Base (** Base operations *) (** [isEmpty l] returns [true] if and only if [l] is empty *) val isEmpty: list 'a -> Tot bool let isEmpty l = match l with | [] -> true | _ -> false (** [hd l] returns the first element of [l]. Requires [l] to be nonempty, at type-checking time. Named as in: OCaml, F#, Coq *) val hd: l:list 'a{Cons? l} -> Tot 'a let hd = function | hd::_ -> hd (** [tail l] returns [l] without its first element. Requires, at type-checking time, that [l] be nonempty. Similar to: tl in OCaml, F#, Coq *) val tail: l:list 'a {Cons? l} -> Tot (list 'a) let tail = function | _::tl -> tl (** [tl l] returns [l] without its first element. Requires, at type-checking time, that [l] be nonempty. Named as in: OCaml, F#, Coq *) val tl: l:list 'a {Cons? l} -> Tot (list 'a) let tl = tail (** [last l] returns the last element of [l]. Requires, at type-checking time, that [l] be nonempty. Named as in: Haskell *) val last: l:list 'a {Cons? l} -> Tot 'a let rec last = function | [hd] -> hd | _::tl -> last tl (** [init l] returns [l] without its last element. Requires, at type-checking time, that [l] be nonempty. Named as in: Haskell *) val init: l:list 'a {Cons? l} -> Tot (list 'a) let rec init = function | [_] -> [] | hd::tl -> hd::(init tl) (** [length l] returns the total number of elements in [l]. Named as in: OCaml, F#, Coq *) val length: list 'a -> Tot nat let rec length = function | [] -> 0 | _::tl -> 1 + length tl (** [nth l n] returns the [n]-th element in list [l] (with the first element being the 0-th) if [l] is long enough, or [None] otherwise. Named as in: OCaml, F#, Coq *) val nth: list 'a -> nat -> Tot (option 'a) let rec nth l n = match l with | [] -> None | hd::tl -> if n = 0 then Some hd else nth tl (n - 1) (** [index l n] returns the [n]-th element in list [l] (with the first element being the 0-th). Requires, at type-checking time, that [l] be of length at least [n+1]. *) val index: #a:Type -> l:list a -> i:nat{i < length l} -> Tot a let rec index #a (l: list a) (i:nat{i < length l}): Tot a = if i = 0 then hd l else index (tl l) (i - 1) (** [count x l] returns the number of occurrences of [x] in [l]. Requires, at type-checking time, the type of [a] to have equality defined. Similar to: [List.count_occ] in Coq. *) val count: #a:eqtype -> a -> list a -> Tot nat let rec count #a x = function | [] -> 0 | hd::tl -> if x=hd then 1 + count x tl else count x tl (** [rev_acc l1 l2] appends the elements of [l1] to the beginning of [l2], in reverse order. It is equivalent to [append (rev l1) l2], but is tail-recursive. Similar to: [List.rev_append] in OCaml, Coq. *) val rev_acc: list 'a -> list 'a -> Tot (list 'a) let rec rev_acc l acc = match l with | [] -> acc | hd::tl -> rev_acc tl (hd::acc) (** [rev l] returns the list [l] in reverse order. Named as in: OCaml, F#, Coq. *) val rev: list 'a -> Tot (list 'a) let rev l = rev_acc l [] (** [append l1 l2] appends the elements of [l2] to the end of [l1]. Named as: OCaml, F#. Similar to: [List.app] in Coq. *) val append: list 'a -> list 'a -> Tot (list 'a) let rec append x y = match x with | [] -> y | a::tl -> a::append tl y (** Defines notation [@@] for [append], as in OCaml, F# . *) let op_At x y = append x y (** [snoc (l, x)] adds [x] to the end of the list [l]. Note: We use an uncurried [snoc (l, x)] instead of the curried [snoc l x]. This is intentional. If [snoc] takes a pair instead of 2 arguments, it allows for a better pattern on [lemma_unsnoc_snoc], which connects [snoc] and [unsnoc]. In particular, if we had two arguments, then either the pattern would either be too restrictive or would lead to over-triggering. More context for this can be seen in the (collapsed and uncollapsed) comments at https://github.com/FStarLang/FStar/pull/1560 *) val snoc: (list 'a * 'a) -> Tot (list 'a) let snoc (l, x) = append l [x] (** [flatten l], where [l] is a list of lists, returns the list of the elements of the lists in [l], preserving their order. Named as in: OCaml, Coq. *) val flatten: list (list 'a) -> Tot (list 'a) let rec flatten l = match l with | [] -> [] | hd::tl -> append hd (flatten tl) (** [map f l] applies [f] to each element of [l] and returns the list of results, in the order of the original elements in [l]. Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml, Coq, F# *) val map: ('a -> Tot 'b) -> list 'a -> Tot (list 'b) let rec map f x = match x with | [] -> [] | a::tl -> f a::map f tl (** [mapi_init f l n] applies, for each [k], [f (n+k)] to the [k]-th element of [l] and returns the list of results, in the order of the original elements in [l]. Requires, at type-checking time, [f] to be a pure total function. *) val mapi_init: (int -> 'a -> Tot 'b) -> list 'a -> int -> Tot (list 'b) let rec mapi_init f l i = match l with | [] -> [] | hd::tl -> (f i hd)::(mapi_init f tl (i+1)) (** [mapi f l] applies, for each [k], [f k] to the [k]-th element of [l] and returns the list of results, in the order of the original elements in [l]. Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml *) val mapi: (int -> 'a -> Tot 'b) -> list 'a -> Tot (list 'b) let mapi f l = mapi_init f l 0 (** [concatMap f l] applies [f] to each element of [l] and returns the concatenation of the results, in the order of the original elements of [l]. This is equivalent to [flatten (map f l)]. Requires, at type-checking time, [f] to be a pure total function. *) val concatMap: ('a -> Tot (list 'b)) -> list 'a -> Tot (list 'b) let rec concatMap f = function | [] -> [] | a::tl -> let fa = f a in let ftl = concatMap f tl in append fa ftl (** [fold_left f x [y1; y2; ...; yn]] computes (f (... (f x y1) y2) ... yn). Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml, Coq. *) val fold_left: ('a -> 'b -> Tot 'a) -> 'a -> l:list 'b -> Tot 'a (decreases l) let rec fold_left f x l = match l with | [] -> x | hd::tl -> fold_left f (f x hd) tl (** [fold_right f [x1; x2; ...; xn] y] computes (f x1 (f x2 (... (f xn y)) ... )). Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml, Coq *) val fold_right: ('a -> 'b -> Tot 'b) -> list 'a -> 'b -> Tot 'b let rec fold_right f l x = match l with | [] -> x | hd::tl -> f hd (fold_right f tl x) (** [fold_right_gtot] is just like [fold_right], except `f` is a ghost function **) let rec fold_right_gtot (#a:Type) (#b:Type) (l:list a) (f:a -> b -> GTot b) (x:b) : GTot b = match l with | [] -> x | hd::tl -> f hd (fold_right_gtot tl f x) (* We define map in terms of fold, to share simple lemmas *) let map_gtot #a #b (f:a -> GTot b) (x:list a) : GTot (list b) = fold_right_gtot x (fun x tl -> f x :: tl) [] (** [fold_left2 f x [y1; y2; ...; yn] [z1; z2; ...; zn]] computes (f (... (f x y1 z1) y2 z2) ... yn zn). Requires, at type-checking time, [f] to be a pure total function, and the lists [y1; y2; ...; yn] and [z1; z2; ...; zn] to have the same lengths. Named as in: OCaml *) val fold_left2 : f:('a -> 'b -> 'c -> Tot 'a) -> accu:'a -> l1:(list 'b) -> l2:(list 'c) -> Pure 'a (requires (length l1 == length l2)) (ensures (fun _ -> True)) (decreases l1) let rec fold_left2 f accu l1 l2 = match (l1, l2) with | ([], []) -> accu | (a1::l1, a2::l2) -> fold_left2 f (f accu a1 a2) l1 l2 (** Propositional membership (as in Coq). Does not require decidable equality. *) (** [memP x l] holds if, and only if, [x] appears as an element of [l]. Similar to: List.In in Coq. *) let rec memP (#a: Type) (x: a) (l: list a) : Tot Type0 = match l with | [] -> False | y :: q -> x == y \/ memP x q (** List searching **) (** [mem x l] returns [true] if, and only if, [x] appears as an element of [l]. Requires, at type-checking time, the type of elements of [l] to have decidable equality. Named as in: OCaml. See also: List.In in Coq, which is propositional. *) val mem: #a:eqtype -> a -> list a -> Tot bool let rec mem #a x = function | [] -> false | hd::tl -> if hd = x then true else mem x tl (** [contains x l] returns [true] if, and only if, [x] appears as an element of [l]. Requires, at type-checking time, the type of elements of [l] to have decidable equality. It is equivalent to: [mem x l]. TODO: should we rather swap the order of arguments? *) let contains : #a:eqtype -> a -> list a -> Tot bool = mem (** [existsb f l] returns [true] if, and only if, there exists some element [x] in [l] such that [f x] holds. *) val existsb: #a:Type -> f:(a -> Tot bool) -> list a -> Tot bool let rec existsb #a f l = match l with | [] -> false | hd::tl -> if f hd then true else existsb f tl (** [find f l] returns [Some x] for some element [x] appearing in [l] such that [f x] holds, or [None] only if no such [x] exists. *) val find: #a:Type -> f:(a -> Tot bool) -> list a -> Tot (option (x:a{f x})) let rec find #a f l = match l with | [] -> None #(x:a{f x}) //These type annotations are only present because it makes bootstrapping go much faster | hd::tl -> if f hd then Some #(x:a{f x}) hd else find f tl (** Filtering elements of a list [l] through a Boolean pure total predicate [f] *) (** [filter f l] returns [l] with all elements [x] such that [f x] does not hold removed. Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml, Coq *) val filter : #a: Type -> f:(a -> Tot bool) -> l: list a -> Tot (m:list a{forall x. memP x m ==> f x}) let rec filter #a f = function | [] -> [] | hd::tl -> if f hd then hd::filter f tl else filter f tl (** Postcondition on [filter f l]: for any element [x] of [filter f l], [f x] holds. Requires, at type-checking time, [f] to be a pure total function.*) val mem_filter (#a:Type) (f: (a -> Tot bool)) (l: list a) (x: a) : Lemma (requires (memP x (filter f l))) (ensures (f x)) let mem_filter f l x = () (** Postcondition on [filter f l]: stated with [forall]: for any element [x] of [filter f l], [f x] holds. Requires, at type-checking time, [f] to be a pure total function. *) val mem_filter_forall (#a:Type) (f: (a -> Tot bool)) (l: list a) : Lemma (requires True) (ensures (forall x . memP x (filter f l) ==> f x)) [SMTPat (filter f l)] let mem_filter_forall f l = FStar.Classical.ghost_lemma (mem_filter f l) (** [for_all f l] returns [true] if, and only if, for all elements [x] appearing in [l], [f x] holds. Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml. Similar to: List.forallb in Coq *) val for_all: ('a -> Tot bool) -> list 'a -> Tot bool let rec for_all f l = match l with | [] -> true | hd::tl -> if f hd then for_all f tl else false (** Specification for [for_all f l] vs. mem *) let rec for_all_mem (#a: Type) (f: (a -> Tot bool)) (l: list a) : Lemma (for_all f l <==> (forall x . memP x l ==> f x)) = match l with | [] -> () | _ :: q -> for_all_mem f q (** [collect f l] applies [f] to each element of [l] and returns the concatenation of the results, in the order of the original elements of [l]. It is equivalent to [flatten (map f l)]. Requires, at type-checking time, [f] to be a pure total function. TODO: what is the difference with [concatMap]? *) val collect: ('a -> Tot (list 'b)) -> list 'a -> Tot (list 'b) let rec collect f l = match l with | [] -> [] | hd::tl -> append (f hd) (collect f tl) (** [tryFind f l] returns [Some x] for some element [x] appearing in [l] such that [f x] holds, or [None] only if no such [x] exists. Requires, at type-checking time, [f] to be a pure total function. Contrary to [find], [tryFind] provides no postcondition on its result. *) val tryFind: ('a -> Tot bool) -> list 'a -> Tot (option 'a) let rec tryFind p l = match l with | [] -> None | hd::tl -> if p hd then Some hd else tryFind p tl (** [tryPick f l] returns [y] for some element [x] appearing in [l] such that [f x = Some y] for some y, or [None] only if [f x = None] for all elements [x] of [l]. Requires, at type-checking time, [f] to be a pure total function. *) val tryPick: ('a -> Tot (option 'b)) -> list 'a -> Tot (option 'b) let rec tryPick f l = match l with | [] -> None | hd::tl -> match f hd with | Some x -> Some x | None -> tryPick f tl (** [choose f l] returns the list of [y] for all elements [x] appearing in [l] such that [f x = Some y] for some [y]. Requires, at type-checking time, [f] to be a pure total function. *) val choose: ('a -> Tot (option 'b)) -> list 'a -> Tot (list 'b) let rec choose f l = match l with | [] -> [] | hd::tl -> match f hd with | Some x -> x::(choose f tl) | None -> choose f tl (** [partition f l] returns the pair of lists [(l1, l2)] where all elements [x] of [l] are in [l1] if [f x] holds, and in [l2] otherwise. Both [l1] and [l2] retain the original order of [l]. Requires, at type-checking time, [f] to be a pure total function. *) val partition: f:('a -> Tot bool) -> list 'a -> Tot (list 'a * list 'a) let rec partition f = function | [] -> [], [] | hd::tl -> let l1, l2 = partition f tl in if f hd then hd::l1, l2 else l1, hd::l2 (** [subset la lb] is true if and only if all the elements from [la] are also in [lb]. Requires, at type-checking time, the type of elements of [la] and [lb] to have decidable equality. *) val subset: #a:eqtype -> list a -> list a -> Tot bool let rec subset #a la lb = match la with | [] -> true | h :: tl -> mem h lb && subset tl lb (** [noRepeats l] returns [true] if, and only if, no element of [l] appears in [l] more than once. Requires, at type-checking time, the type of elements of [la] and [lb] to have decidable equality. *) val noRepeats : #a:eqtype -> list a -> Tot bool let rec noRepeats #a la = match la with | [] -> true | h :: tl -> not(mem h tl) && noRepeats tl (** [no_repeats_p l] valid if, and only if, no element of [l] appears in [l] more than once. *) val no_repeats_p : #a:Type -> list a -> Tot prop let rec no_repeats_p #a la = match la with | [] -> True | h :: tl -> ~(memP h tl) /\ no_repeats_p tl (** List of tuples **) (** [assoc x l] returns [Some y] where [(x, y)] is the first element of [l] whose first element is [x], or [None] only if no such element exists. Requires, at type-checking time, the type of [x] to have decidable equality. Named as in: OCaml. *) val assoc: #a:eqtype -> #b:Type -> a -> list (a * b) -> Tot (option b) let rec assoc #a #b x = function | [] -> None | (x', y)::tl -> if x=x' then Some y else assoc x tl (** [split] takes a list of pairs [(x1, y1), ..., (xn, yn)] and returns the pair of lists ([x1, ..., xn], [y1, ..., yn]). Named as in: OCaml *)
false
false
FStar.List.Tot.Base.fst
{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 1, "max_fuel": 8, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": true, "z3cliopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }
null
val split: list ('a * 'b) -> Tot (list 'a * list 'b)
[ "recursion" ]
FStar.List.Tot.Base.split
{ "file_name": "ulib/FStar.List.Tot.Base.fst", "git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f", "git_url": "https://github.com/FStarLang/FStar.git", "project_name": "FStar" }
l: Prims.list ('a * 'b) -> Prims.list 'a * Prims.list 'b
{ "end_col": 26, "end_line": 421, "start_col": 18, "start_line": 417 }
Prims.Tot
val tryFind: ('a -> Tot bool) -> list 'a -> Tot (option 'a)
[ { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]
false
let rec tryFind p l = match l with | [] -> None | hd::tl -> if p hd then Some hd else tryFind p tl
val tryFind: ('a -> Tot bool) -> list 'a -> Tot (option 'a) let rec tryFind p l =
false
null
false
match l with | [] -> None | hd :: tl -> if p hd then Some hd else tryFind p tl
{ "checked_file": "FStar.List.Tot.Base.fst.checked", "dependencies": [ "prims.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Classical.fsti.checked" ], "interface_file": false, "source_file": "FStar.List.Tot.Base.fst" }
[ "total" ]
[ "Prims.bool", "Prims.list", "FStar.Pervasives.Native.None", "FStar.Pervasives.Native.Some", "FStar.List.Tot.Base.tryFind", "FStar.Pervasives.Native.option" ]
[]
(* Copyright 2008-2014 Nikhil Swamy and Microsoft Research Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License. *) (** This module defines all pure and total operations on lists that can be used in specifications. It is implemented by FStar_List_Tot_Base.ml, any functional change and/or the addition of new functions MUST be reflected there. @summary Pure total operations on lists *) module FStar.List.Tot.Base (** Base operations *) (** [isEmpty l] returns [true] if and only if [l] is empty *) val isEmpty: list 'a -> Tot bool let isEmpty l = match l with | [] -> true | _ -> false (** [hd l] returns the first element of [l]. Requires [l] to be nonempty, at type-checking time. Named as in: OCaml, F#, Coq *) val hd: l:list 'a{Cons? l} -> Tot 'a let hd = function | hd::_ -> hd (** [tail l] returns [l] without its first element. Requires, at type-checking time, that [l] be nonempty. Similar to: tl in OCaml, F#, Coq *) val tail: l:list 'a {Cons? l} -> Tot (list 'a) let tail = function | _::tl -> tl (** [tl l] returns [l] without its first element. Requires, at type-checking time, that [l] be nonempty. Named as in: OCaml, F#, Coq *) val tl: l:list 'a {Cons? l} -> Tot (list 'a) let tl = tail (** [last l] returns the last element of [l]. Requires, at type-checking time, that [l] be nonempty. Named as in: Haskell *) val last: l:list 'a {Cons? l} -> Tot 'a let rec last = function | [hd] -> hd | _::tl -> last tl (** [init l] returns [l] without its last element. Requires, at type-checking time, that [l] be nonempty. Named as in: Haskell *) val init: l:list 'a {Cons? l} -> Tot (list 'a) let rec init = function | [_] -> [] | hd::tl -> hd::(init tl) (** [length l] returns the total number of elements in [l]. Named as in: OCaml, F#, Coq *) val length: list 'a -> Tot nat let rec length = function | [] -> 0 | _::tl -> 1 + length tl (** [nth l n] returns the [n]-th element in list [l] (with the first element being the 0-th) if [l] is long enough, or [None] otherwise. Named as in: OCaml, F#, Coq *) val nth: list 'a -> nat -> Tot (option 'a) let rec nth l n = match l with | [] -> None | hd::tl -> if n = 0 then Some hd else nth tl (n - 1) (** [index l n] returns the [n]-th element in list [l] (with the first element being the 0-th). Requires, at type-checking time, that [l] be of length at least [n+1]. *) val index: #a:Type -> l:list a -> i:nat{i < length l} -> Tot a let rec index #a (l: list a) (i:nat{i < length l}): Tot a = if i = 0 then hd l else index (tl l) (i - 1) (** [count x l] returns the number of occurrences of [x] in [l]. Requires, at type-checking time, the type of [a] to have equality defined. Similar to: [List.count_occ] in Coq. *) val count: #a:eqtype -> a -> list a -> Tot nat let rec count #a x = function | [] -> 0 | hd::tl -> if x=hd then 1 + count x tl else count x tl (** [rev_acc l1 l2] appends the elements of [l1] to the beginning of [l2], in reverse order. It is equivalent to [append (rev l1) l2], but is tail-recursive. Similar to: [List.rev_append] in OCaml, Coq. *) val rev_acc: list 'a -> list 'a -> Tot (list 'a) let rec rev_acc l acc = match l with | [] -> acc | hd::tl -> rev_acc tl (hd::acc) (** [rev l] returns the list [l] in reverse order. Named as in: OCaml, F#, Coq. *) val rev: list 'a -> Tot (list 'a) let rev l = rev_acc l [] (** [append l1 l2] appends the elements of [l2] to the end of [l1]. Named as: OCaml, F#. Similar to: [List.app] in Coq. *) val append: list 'a -> list 'a -> Tot (list 'a) let rec append x y = match x with | [] -> y | a::tl -> a::append tl y (** Defines notation [@@] for [append], as in OCaml, F# . *) let op_At x y = append x y (** [snoc (l, x)] adds [x] to the end of the list [l]. Note: We use an uncurried [snoc (l, x)] instead of the curried [snoc l x]. This is intentional. If [snoc] takes a pair instead of 2 arguments, it allows for a better pattern on [lemma_unsnoc_snoc], which connects [snoc] and [unsnoc]. In particular, if we had two arguments, then either the pattern would either be too restrictive or would lead to over-triggering. More context for this can be seen in the (collapsed and uncollapsed) comments at https://github.com/FStarLang/FStar/pull/1560 *) val snoc: (list 'a * 'a) -> Tot (list 'a) let snoc (l, x) = append l [x] (** [flatten l], where [l] is a list of lists, returns the list of the elements of the lists in [l], preserving their order. Named as in: OCaml, Coq. *) val flatten: list (list 'a) -> Tot (list 'a) let rec flatten l = match l with | [] -> [] | hd::tl -> append hd (flatten tl) (** [map f l] applies [f] to each element of [l] and returns the list of results, in the order of the original elements in [l]. Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml, Coq, F# *) val map: ('a -> Tot 'b) -> list 'a -> Tot (list 'b) let rec map f x = match x with | [] -> [] | a::tl -> f a::map f tl (** [mapi_init f l n] applies, for each [k], [f (n+k)] to the [k]-th element of [l] and returns the list of results, in the order of the original elements in [l]. Requires, at type-checking time, [f] to be a pure total function. *) val mapi_init: (int -> 'a -> Tot 'b) -> list 'a -> int -> Tot (list 'b) let rec mapi_init f l i = match l with | [] -> [] | hd::tl -> (f i hd)::(mapi_init f tl (i+1)) (** [mapi f l] applies, for each [k], [f k] to the [k]-th element of [l] and returns the list of results, in the order of the original elements in [l]. Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml *) val mapi: (int -> 'a -> Tot 'b) -> list 'a -> Tot (list 'b) let mapi f l = mapi_init f l 0 (** [concatMap f l] applies [f] to each element of [l] and returns the concatenation of the results, in the order of the original elements of [l]. This is equivalent to [flatten (map f l)]. Requires, at type-checking time, [f] to be a pure total function. *) val concatMap: ('a -> Tot (list 'b)) -> list 'a -> Tot (list 'b) let rec concatMap f = function | [] -> [] | a::tl -> let fa = f a in let ftl = concatMap f tl in append fa ftl (** [fold_left f x [y1; y2; ...; yn]] computes (f (... (f x y1) y2) ... yn). Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml, Coq. *) val fold_left: ('a -> 'b -> Tot 'a) -> 'a -> l:list 'b -> Tot 'a (decreases l) let rec fold_left f x l = match l with | [] -> x | hd::tl -> fold_left f (f x hd) tl (** [fold_right f [x1; x2; ...; xn] y] computes (f x1 (f x2 (... (f xn y)) ... )). Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml, Coq *) val fold_right: ('a -> 'b -> Tot 'b) -> list 'a -> 'b -> Tot 'b let rec fold_right f l x = match l with | [] -> x | hd::tl -> f hd (fold_right f tl x) (** [fold_right_gtot] is just like [fold_right], except `f` is a ghost function **) let rec fold_right_gtot (#a:Type) (#b:Type) (l:list a) (f:a -> b -> GTot b) (x:b) : GTot b = match l with | [] -> x | hd::tl -> f hd (fold_right_gtot tl f x) (* We define map in terms of fold, to share simple lemmas *) let map_gtot #a #b (f:a -> GTot b) (x:list a) : GTot (list b) = fold_right_gtot x (fun x tl -> f x :: tl) [] (** [fold_left2 f x [y1; y2; ...; yn] [z1; z2; ...; zn]] computes (f (... (f x y1 z1) y2 z2) ... yn zn). Requires, at type-checking time, [f] to be a pure total function, and the lists [y1; y2; ...; yn] and [z1; z2; ...; zn] to have the same lengths. Named as in: OCaml *) val fold_left2 : f:('a -> 'b -> 'c -> Tot 'a) -> accu:'a -> l1:(list 'b) -> l2:(list 'c) -> Pure 'a (requires (length l1 == length l2)) (ensures (fun _ -> True)) (decreases l1) let rec fold_left2 f accu l1 l2 = match (l1, l2) with | ([], []) -> accu | (a1::l1, a2::l2) -> fold_left2 f (f accu a1 a2) l1 l2 (** Propositional membership (as in Coq). Does not require decidable equality. *) (** [memP x l] holds if, and only if, [x] appears as an element of [l]. Similar to: List.In in Coq. *) let rec memP (#a: Type) (x: a) (l: list a) : Tot Type0 = match l with | [] -> False | y :: q -> x == y \/ memP x q (** List searching **) (** [mem x l] returns [true] if, and only if, [x] appears as an element of [l]. Requires, at type-checking time, the type of elements of [l] to have decidable equality. Named as in: OCaml. See also: List.In in Coq, which is propositional. *) val mem: #a:eqtype -> a -> list a -> Tot bool let rec mem #a x = function | [] -> false | hd::tl -> if hd = x then true else mem x tl (** [contains x l] returns [true] if, and only if, [x] appears as an element of [l]. Requires, at type-checking time, the type of elements of [l] to have decidable equality. It is equivalent to: [mem x l]. TODO: should we rather swap the order of arguments? *) let contains : #a:eqtype -> a -> list a -> Tot bool = mem (** [existsb f l] returns [true] if, and only if, there exists some element [x] in [l] such that [f x] holds. *) val existsb: #a:Type -> f:(a -> Tot bool) -> list a -> Tot bool let rec existsb #a f l = match l with | [] -> false | hd::tl -> if f hd then true else existsb f tl (** [find f l] returns [Some x] for some element [x] appearing in [l] such that [f x] holds, or [None] only if no such [x] exists. *) val find: #a:Type -> f:(a -> Tot bool) -> list a -> Tot (option (x:a{f x})) let rec find #a f l = match l with | [] -> None #(x:a{f x}) //These type annotations are only present because it makes bootstrapping go much faster | hd::tl -> if f hd then Some #(x:a{f x}) hd else find f tl (** Filtering elements of a list [l] through a Boolean pure total predicate [f] *) (** [filter f l] returns [l] with all elements [x] such that [f x] does not hold removed. Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml, Coq *) val filter : #a: Type -> f:(a -> Tot bool) -> l: list a -> Tot (m:list a{forall x. memP x m ==> f x}) let rec filter #a f = function | [] -> [] | hd::tl -> if f hd then hd::filter f tl else filter f tl (** Postcondition on [filter f l]: for any element [x] of [filter f l], [f x] holds. Requires, at type-checking time, [f] to be a pure total function.*) val mem_filter (#a:Type) (f: (a -> Tot bool)) (l: list a) (x: a) : Lemma (requires (memP x (filter f l))) (ensures (f x)) let mem_filter f l x = () (** Postcondition on [filter f l]: stated with [forall]: for any element [x] of [filter f l], [f x] holds. Requires, at type-checking time, [f] to be a pure total function. *) val mem_filter_forall (#a:Type) (f: (a -> Tot bool)) (l: list a) : Lemma (requires True) (ensures (forall x . memP x (filter f l) ==> f x)) [SMTPat (filter f l)] let mem_filter_forall f l = FStar.Classical.ghost_lemma (mem_filter f l) (** [for_all f l] returns [true] if, and only if, for all elements [x] appearing in [l], [f x] holds. Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml. Similar to: List.forallb in Coq *) val for_all: ('a -> Tot bool) -> list 'a -> Tot bool let rec for_all f l = match l with | [] -> true | hd::tl -> if f hd then for_all f tl else false (** Specification for [for_all f l] vs. mem *) let rec for_all_mem (#a: Type) (f: (a -> Tot bool)) (l: list a) : Lemma (for_all f l <==> (forall x . memP x l ==> f x)) = match l with | [] -> () | _ :: q -> for_all_mem f q (** [collect f l] applies [f] to each element of [l] and returns the concatenation of the results, in the order of the original elements of [l]. It is equivalent to [flatten (map f l)]. Requires, at type-checking time, [f] to be a pure total function. TODO: what is the difference with [concatMap]? *) val collect: ('a -> Tot (list 'b)) -> list 'a -> Tot (list 'b) let rec collect f l = match l with | [] -> [] | hd::tl -> append (f hd) (collect f tl) (** [tryFind f l] returns [Some x] for some element [x] appearing in [l] such that [f x] holds, or [None] only if no such [x] exists. Requires, at type-checking time, [f] to be a pure total function. Contrary to [find], [tryFind] provides no postcondition on its result. *)
false
false
FStar.List.Tot.Base.fst
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null
val tryFind: ('a -> Tot bool) -> list 'a -> Tot (option 'a)
[ "recursion" ]
FStar.List.Tot.Base.tryFind
{ "file_name": "ulib/FStar.List.Tot.Base.fst", "git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f", "git_url": "https://github.com/FStarLang/FStar.git", "project_name": "FStar" }
p: (_: 'a -> Prims.bool) -> l: Prims.list 'a -> FStar.Pervasives.Native.option 'a
{ "end_col": 54, "end_line": 336, "start_col": 22, "start_line": 334 }
Prims.Tot
val tryPick: ('a -> Tot (option 'b)) -> list 'a -> Tot (option 'b)
[ { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]
false
let rec tryPick f l = match l with | [] -> None | hd::tl -> match f hd with | Some x -> Some x | None -> tryPick f tl
val tryPick: ('a -> Tot (option 'b)) -> list 'a -> Tot (option 'b) let rec tryPick f l =
false
null
false
match l with | [] -> None | hd :: tl -> match f hd with | Some x -> Some x | None -> tryPick f tl
{ "checked_file": "FStar.List.Tot.Base.fst.checked", "dependencies": [ "prims.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Classical.fsti.checked" ], "interface_file": false, "source_file": "FStar.List.Tot.Base.fst" }
[ "total" ]
[ "FStar.Pervasives.Native.option", "Prims.list", "FStar.Pervasives.Native.None", "FStar.Pervasives.Native.Some", "FStar.List.Tot.Base.tryPick" ]
[]
(* Copyright 2008-2014 Nikhil Swamy and Microsoft Research Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License. *) (** This module defines all pure and total operations on lists that can be used in specifications. It is implemented by FStar_List_Tot_Base.ml, any functional change and/or the addition of new functions MUST be reflected there. @summary Pure total operations on lists *) module FStar.List.Tot.Base (** Base operations *) (** [isEmpty l] returns [true] if and only if [l] is empty *) val isEmpty: list 'a -> Tot bool let isEmpty l = match l with | [] -> true | _ -> false (** [hd l] returns the first element of [l]. Requires [l] to be nonempty, at type-checking time. Named as in: OCaml, F#, Coq *) val hd: l:list 'a{Cons? l} -> Tot 'a let hd = function | hd::_ -> hd (** [tail l] returns [l] without its first element. Requires, at type-checking time, that [l] be nonempty. Similar to: tl in OCaml, F#, Coq *) val tail: l:list 'a {Cons? l} -> Tot (list 'a) let tail = function | _::tl -> tl (** [tl l] returns [l] without its first element. Requires, at type-checking time, that [l] be nonempty. Named as in: OCaml, F#, Coq *) val tl: l:list 'a {Cons? l} -> Tot (list 'a) let tl = tail (** [last l] returns the last element of [l]. Requires, at type-checking time, that [l] be nonempty. Named as in: Haskell *) val last: l:list 'a {Cons? l} -> Tot 'a let rec last = function | [hd] -> hd | _::tl -> last tl (** [init l] returns [l] without its last element. Requires, at type-checking time, that [l] be nonempty. Named as in: Haskell *) val init: l:list 'a {Cons? l} -> Tot (list 'a) let rec init = function | [_] -> [] | hd::tl -> hd::(init tl) (** [length l] returns the total number of elements in [l]. Named as in: OCaml, F#, Coq *) val length: list 'a -> Tot nat let rec length = function | [] -> 0 | _::tl -> 1 + length tl (** [nth l n] returns the [n]-th element in list [l] (with the first element being the 0-th) if [l] is long enough, or [None] otherwise. Named as in: OCaml, F#, Coq *) val nth: list 'a -> nat -> Tot (option 'a) let rec nth l n = match l with | [] -> None | hd::tl -> if n = 0 then Some hd else nth tl (n - 1) (** [index l n] returns the [n]-th element in list [l] (with the first element being the 0-th). Requires, at type-checking time, that [l] be of length at least [n+1]. *) val index: #a:Type -> l:list a -> i:nat{i < length l} -> Tot a let rec index #a (l: list a) (i:nat{i < length l}): Tot a = if i = 0 then hd l else index (tl l) (i - 1) (** [count x l] returns the number of occurrences of [x] in [l]. Requires, at type-checking time, the type of [a] to have equality defined. Similar to: [List.count_occ] in Coq. *) val count: #a:eqtype -> a -> list a -> Tot nat let rec count #a x = function | [] -> 0 | hd::tl -> if x=hd then 1 + count x tl else count x tl (** [rev_acc l1 l2] appends the elements of [l1] to the beginning of [l2], in reverse order. It is equivalent to [append (rev l1) l2], but is tail-recursive. Similar to: [List.rev_append] in OCaml, Coq. *) val rev_acc: list 'a -> list 'a -> Tot (list 'a) let rec rev_acc l acc = match l with | [] -> acc | hd::tl -> rev_acc tl (hd::acc) (** [rev l] returns the list [l] in reverse order. Named as in: OCaml, F#, Coq. *) val rev: list 'a -> Tot (list 'a) let rev l = rev_acc l [] (** [append l1 l2] appends the elements of [l2] to the end of [l1]. Named as: OCaml, F#. Similar to: [List.app] in Coq. *) val append: list 'a -> list 'a -> Tot (list 'a) let rec append x y = match x with | [] -> y | a::tl -> a::append tl y (** Defines notation [@@] for [append], as in OCaml, F# . *) let op_At x y = append x y (** [snoc (l, x)] adds [x] to the end of the list [l]. Note: We use an uncurried [snoc (l, x)] instead of the curried [snoc l x]. This is intentional. If [snoc] takes a pair instead of 2 arguments, it allows for a better pattern on [lemma_unsnoc_snoc], which connects [snoc] and [unsnoc]. In particular, if we had two arguments, then either the pattern would either be too restrictive or would lead to over-triggering. More context for this can be seen in the (collapsed and uncollapsed) comments at https://github.com/FStarLang/FStar/pull/1560 *) val snoc: (list 'a * 'a) -> Tot (list 'a) let snoc (l, x) = append l [x] (** [flatten l], where [l] is a list of lists, returns the list of the elements of the lists in [l], preserving their order. Named as in: OCaml, Coq. *) val flatten: list (list 'a) -> Tot (list 'a) let rec flatten l = match l with | [] -> [] | hd::tl -> append hd (flatten tl) (** [map f l] applies [f] to each element of [l] and returns the list of results, in the order of the original elements in [l]. Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml, Coq, F# *) val map: ('a -> Tot 'b) -> list 'a -> Tot (list 'b) let rec map f x = match x with | [] -> [] | a::tl -> f a::map f tl (** [mapi_init f l n] applies, for each [k], [f (n+k)] to the [k]-th element of [l] and returns the list of results, in the order of the original elements in [l]. Requires, at type-checking time, [f] to be a pure total function. *) val mapi_init: (int -> 'a -> Tot 'b) -> list 'a -> int -> Tot (list 'b) let rec mapi_init f l i = match l with | [] -> [] | hd::tl -> (f i hd)::(mapi_init f tl (i+1)) (** [mapi f l] applies, for each [k], [f k] to the [k]-th element of [l] and returns the list of results, in the order of the original elements in [l]. Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml *) val mapi: (int -> 'a -> Tot 'b) -> list 'a -> Tot (list 'b) let mapi f l = mapi_init f l 0 (** [concatMap f l] applies [f] to each element of [l] and returns the concatenation of the results, in the order of the original elements of [l]. This is equivalent to [flatten (map f l)]. Requires, at type-checking time, [f] to be a pure total function. *) val concatMap: ('a -> Tot (list 'b)) -> list 'a -> Tot (list 'b) let rec concatMap f = function | [] -> [] | a::tl -> let fa = f a in let ftl = concatMap f tl in append fa ftl (** [fold_left f x [y1; y2; ...; yn]] computes (f (... (f x y1) y2) ... yn). Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml, Coq. *) val fold_left: ('a -> 'b -> Tot 'a) -> 'a -> l:list 'b -> Tot 'a (decreases l) let rec fold_left f x l = match l with | [] -> x | hd::tl -> fold_left f (f x hd) tl (** [fold_right f [x1; x2; ...; xn] y] computes (f x1 (f x2 (... (f xn y)) ... )). Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml, Coq *) val fold_right: ('a -> 'b -> Tot 'b) -> list 'a -> 'b -> Tot 'b let rec fold_right f l x = match l with | [] -> x | hd::tl -> f hd (fold_right f tl x) (** [fold_right_gtot] is just like [fold_right], except `f` is a ghost function **) let rec fold_right_gtot (#a:Type) (#b:Type) (l:list a) (f:a -> b -> GTot b) (x:b) : GTot b = match l with | [] -> x | hd::tl -> f hd (fold_right_gtot tl f x) (* We define map in terms of fold, to share simple lemmas *) let map_gtot #a #b (f:a -> GTot b) (x:list a) : GTot (list b) = fold_right_gtot x (fun x tl -> f x :: tl) [] (** [fold_left2 f x [y1; y2; ...; yn] [z1; z2; ...; zn]] computes (f (... (f x y1 z1) y2 z2) ... yn zn). Requires, at type-checking time, [f] to be a pure total function, and the lists [y1; y2; ...; yn] and [z1; z2; ...; zn] to have the same lengths. Named as in: OCaml *) val fold_left2 : f:('a -> 'b -> 'c -> Tot 'a) -> accu:'a -> l1:(list 'b) -> l2:(list 'c) -> Pure 'a (requires (length l1 == length l2)) (ensures (fun _ -> True)) (decreases l1) let rec fold_left2 f accu l1 l2 = match (l1, l2) with | ([], []) -> accu | (a1::l1, a2::l2) -> fold_left2 f (f accu a1 a2) l1 l2 (** Propositional membership (as in Coq). Does not require decidable equality. *) (** [memP x l] holds if, and only if, [x] appears as an element of [l]. Similar to: List.In in Coq. *) let rec memP (#a: Type) (x: a) (l: list a) : Tot Type0 = match l with | [] -> False | y :: q -> x == y \/ memP x q (** List searching **) (** [mem x l] returns [true] if, and only if, [x] appears as an element of [l]. Requires, at type-checking time, the type of elements of [l] to have decidable equality. Named as in: OCaml. See also: List.In in Coq, which is propositional. *) val mem: #a:eqtype -> a -> list a -> Tot bool let rec mem #a x = function | [] -> false | hd::tl -> if hd = x then true else mem x tl (** [contains x l] returns [true] if, and only if, [x] appears as an element of [l]. Requires, at type-checking time, the type of elements of [l] to have decidable equality. It is equivalent to: [mem x l]. TODO: should we rather swap the order of arguments? *) let contains : #a:eqtype -> a -> list a -> Tot bool = mem (** [existsb f l] returns [true] if, and only if, there exists some element [x] in [l] such that [f x] holds. *) val existsb: #a:Type -> f:(a -> Tot bool) -> list a -> Tot bool let rec existsb #a f l = match l with | [] -> false | hd::tl -> if f hd then true else existsb f tl (** [find f l] returns [Some x] for some element [x] appearing in [l] such that [f x] holds, or [None] only if no such [x] exists. *) val find: #a:Type -> f:(a -> Tot bool) -> list a -> Tot (option (x:a{f x})) let rec find #a f l = match l with | [] -> None #(x:a{f x}) //These type annotations are only present because it makes bootstrapping go much faster | hd::tl -> if f hd then Some #(x:a{f x}) hd else find f tl (** Filtering elements of a list [l] through a Boolean pure total predicate [f] *) (** [filter f l] returns [l] with all elements [x] such that [f x] does not hold removed. Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml, Coq *) val filter : #a: Type -> f:(a -> Tot bool) -> l: list a -> Tot (m:list a{forall x. memP x m ==> f x}) let rec filter #a f = function | [] -> [] | hd::tl -> if f hd then hd::filter f tl else filter f tl (** Postcondition on [filter f l]: for any element [x] of [filter f l], [f x] holds. Requires, at type-checking time, [f] to be a pure total function.*) val mem_filter (#a:Type) (f: (a -> Tot bool)) (l: list a) (x: a) : Lemma (requires (memP x (filter f l))) (ensures (f x)) let mem_filter f l x = () (** Postcondition on [filter f l]: stated with [forall]: for any element [x] of [filter f l], [f x] holds. Requires, at type-checking time, [f] to be a pure total function. *) val mem_filter_forall (#a:Type) (f: (a -> Tot bool)) (l: list a) : Lemma (requires True) (ensures (forall x . memP x (filter f l) ==> f x)) [SMTPat (filter f l)] let mem_filter_forall f l = FStar.Classical.ghost_lemma (mem_filter f l) (** [for_all f l] returns [true] if, and only if, for all elements [x] appearing in [l], [f x] holds. Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml. Similar to: List.forallb in Coq *) val for_all: ('a -> Tot bool) -> list 'a -> Tot bool let rec for_all f l = match l with | [] -> true | hd::tl -> if f hd then for_all f tl else false (** Specification for [for_all f l] vs. mem *) let rec for_all_mem (#a: Type) (f: (a -> Tot bool)) (l: list a) : Lemma (for_all f l <==> (forall x . memP x l ==> f x)) = match l with | [] -> () | _ :: q -> for_all_mem f q (** [collect f l] applies [f] to each element of [l] and returns the concatenation of the results, in the order of the original elements of [l]. It is equivalent to [flatten (map f l)]. Requires, at type-checking time, [f] to be a pure total function. TODO: what is the difference with [concatMap]? *) val collect: ('a -> Tot (list 'b)) -> list 'a -> Tot (list 'b) let rec collect f l = match l with | [] -> [] | hd::tl -> append (f hd) (collect f tl) (** [tryFind f l] returns [Some x] for some element [x] appearing in [l] such that [f x] holds, or [None] only if no such [x] exists. Requires, at type-checking time, [f] to be a pure total function. Contrary to [find], [tryFind] provides no postcondition on its result. *) val tryFind: ('a -> Tot bool) -> list 'a -> Tot (option 'a) let rec tryFind p l = match l with | [] -> None | hd::tl -> if p hd then Some hd else tryFind p tl (** [tryPick f l] returns [y] for some element [x] appearing in [l] such that [f x = Some y] for some y, or [None] only if [f x = None] for all elements [x] of [l]. Requires, at type-checking time, [f] to be a pure total function. *)
false
false
FStar.List.Tot.Base.fst
{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 1, "max_fuel": 8, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": true, "z3cliopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }
null
val tryPick: ('a -> Tot (option 'b)) -> list 'a -> Tot (option 'b)
[ "recursion" ]
FStar.List.Tot.Base.tryPick
{ "file_name": "ulib/FStar.List.Tot.Base.fst", "git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f", "git_url": "https://github.com/FStarLang/FStar.git", "project_name": "FStar" }
f: (_: 'a -> FStar.Pervasives.Native.option 'b) -> l: Prims.list 'a -> FStar.Pervasives.Native.option 'b
{ "end_col": 31, "end_line": 348, "start_col": 22, "start_line": 343 }
FStar.Pervasives.Lemma
val lemma_splitAt_snd_length (#a: Type) (n: nat) (l: list a) : Lemma (requires (n <= length l)) (ensures (length (snd (splitAt n l)) = length l - n))
[ { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]
false
let rec lemma_splitAt_snd_length (#a:Type) (n:nat) (l:list a) : Lemma (requires (n <= length l)) (ensures (length (snd (splitAt n l)) = length l - n)) = match n, l with | 0, _ -> () | _, [] -> () | _, _ :: l' -> lemma_splitAt_snd_length (n - 1) l'
val lemma_splitAt_snd_length (#a: Type) (n: nat) (l: list a) : Lemma (requires (n <= length l)) (ensures (length (snd (splitAt n l)) = length l - n)) let rec lemma_splitAt_snd_length (#a: Type) (n: nat) (l: list a) : Lemma (requires (n <= length l)) (ensures (length (snd (splitAt n l)) = length l - n)) =
false
null
true
match n, l with | 0, _ -> () | _, [] -> () | _, _ :: l' -> lemma_splitAt_snd_length (n - 1) l'
{ "checked_file": "FStar.List.Tot.Base.fst.checked", "dependencies": [ "prims.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Classical.fsti.checked" ], "interface_file": false, "source_file": "FStar.List.Tot.Base.fst" }
[ "lemma" ]
[ "Prims.nat", "Prims.list", "FStar.Pervasives.Native.Mktuple2", "Prims.int", "FStar.List.Tot.Base.lemma_splitAt_snd_length", "Prims.op_Subtraction", "Prims.unit", "Prims.b2t", "Prims.op_LessThanOrEqual", "FStar.List.Tot.Base.length", "Prims.squash", "Prims.op_Equality", "FStar.Pervasives.Native.snd", "FStar.List.Tot.Base.splitAt", "Prims.Nil", "FStar.Pervasives.pattern" ]
[]
(* Copyright 2008-2014 Nikhil Swamy and Microsoft Research Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License. *) (** This module defines all pure and total operations on lists that can be used in specifications. It is implemented by FStar_List_Tot_Base.ml, any functional change and/or the addition of new functions MUST be reflected there. @summary Pure total operations on lists *) module FStar.List.Tot.Base (** Base operations *) (** [isEmpty l] returns [true] if and only if [l] is empty *) val isEmpty: list 'a -> Tot bool let isEmpty l = match l with | [] -> true | _ -> false (** [hd l] returns the first element of [l]. Requires [l] to be nonempty, at type-checking time. Named as in: OCaml, F#, Coq *) val hd: l:list 'a{Cons? l} -> Tot 'a let hd = function | hd::_ -> hd (** [tail l] returns [l] without its first element. Requires, at type-checking time, that [l] be nonempty. Similar to: tl in OCaml, F#, Coq *) val tail: l:list 'a {Cons? l} -> Tot (list 'a) let tail = function | _::tl -> tl (** [tl l] returns [l] without its first element. Requires, at type-checking time, that [l] be nonempty. Named as in: OCaml, F#, Coq *) val tl: l:list 'a {Cons? l} -> Tot (list 'a) let tl = tail (** [last l] returns the last element of [l]. Requires, at type-checking time, that [l] be nonempty. Named as in: Haskell *) val last: l:list 'a {Cons? l} -> Tot 'a let rec last = function | [hd] -> hd | _::tl -> last tl (** [init l] returns [l] without its last element. Requires, at type-checking time, that [l] be nonempty. Named as in: Haskell *) val init: l:list 'a {Cons? l} -> Tot (list 'a) let rec init = function | [_] -> [] | hd::tl -> hd::(init tl) (** [length l] returns the total number of elements in [l]. Named as in: OCaml, F#, Coq *) val length: list 'a -> Tot nat let rec length = function | [] -> 0 | _::tl -> 1 + length tl (** [nth l n] returns the [n]-th element in list [l] (with the first element being the 0-th) if [l] is long enough, or [None] otherwise. Named as in: OCaml, F#, Coq *) val nth: list 'a -> nat -> Tot (option 'a) let rec nth l n = match l with | [] -> None | hd::tl -> if n = 0 then Some hd else nth tl (n - 1) (** [index l n] returns the [n]-th element in list [l] (with the first element being the 0-th). Requires, at type-checking time, that [l] be of length at least [n+1]. *) val index: #a:Type -> l:list a -> i:nat{i < length l} -> Tot a let rec index #a (l: list a) (i:nat{i < length l}): Tot a = if i = 0 then hd l else index (tl l) (i - 1) (** [count x l] returns the number of occurrences of [x] in [l]. Requires, at type-checking time, the type of [a] to have equality defined. Similar to: [List.count_occ] in Coq. *) val count: #a:eqtype -> a -> list a -> Tot nat let rec count #a x = function | [] -> 0 | hd::tl -> if x=hd then 1 + count x tl else count x tl (** [rev_acc l1 l2] appends the elements of [l1] to the beginning of [l2], in reverse order. It is equivalent to [append (rev l1) l2], but is tail-recursive. Similar to: [List.rev_append] in OCaml, Coq. *) val rev_acc: list 'a -> list 'a -> Tot (list 'a) let rec rev_acc l acc = match l with | [] -> acc | hd::tl -> rev_acc tl (hd::acc) (** [rev l] returns the list [l] in reverse order. Named as in: OCaml, F#, Coq. *) val rev: list 'a -> Tot (list 'a) let rev l = rev_acc l [] (** [append l1 l2] appends the elements of [l2] to the end of [l1]. Named as: OCaml, F#. Similar to: [List.app] in Coq. *) val append: list 'a -> list 'a -> Tot (list 'a) let rec append x y = match x with | [] -> y | a::tl -> a::append tl y (** Defines notation [@@] for [append], as in OCaml, F# . *) let op_At x y = append x y (** [snoc (l, x)] adds [x] to the end of the list [l]. Note: We use an uncurried [snoc (l, x)] instead of the curried [snoc l x]. This is intentional. If [snoc] takes a pair instead of 2 arguments, it allows for a better pattern on [lemma_unsnoc_snoc], which connects [snoc] and [unsnoc]. In particular, if we had two arguments, then either the pattern would either be too restrictive or would lead to over-triggering. More context for this can be seen in the (collapsed and uncollapsed) comments at https://github.com/FStarLang/FStar/pull/1560 *) val snoc: (list 'a * 'a) -> Tot (list 'a) let snoc (l, x) = append l [x] (** [flatten l], where [l] is a list of lists, returns the list of the elements of the lists in [l], preserving their order. Named as in: OCaml, Coq. *) val flatten: list (list 'a) -> Tot (list 'a) let rec flatten l = match l with | [] -> [] | hd::tl -> append hd (flatten tl) (** [map f l] applies [f] to each element of [l] and returns the list of results, in the order of the original elements in [l]. Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml, Coq, F# *) val map: ('a -> Tot 'b) -> list 'a -> Tot (list 'b) let rec map f x = match x with | [] -> [] | a::tl -> f a::map f tl (** [mapi_init f l n] applies, for each [k], [f (n+k)] to the [k]-th element of [l] and returns the list of results, in the order of the original elements in [l]. Requires, at type-checking time, [f] to be a pure total function. *) val mapi_init: (int -> 'a -> Tot 'b) -> list 'a -> int -> Tot (list 'b) let rec mapi_init f l i = match l with | [] -> [] | hd::tl -> (f i hd)::(mapi_init f tl (i+1)) (** [mapi f l] applies, for each [k], [f k] to the [k]-th element of [l] and returns the list of results, in the order of the original elements in [l]. Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml *) val mapi: (int -> 'a -> Tot 'b) -> list 'a -> Tot (list 'b) let mapi f l = mapi_init f l 0 (** [concatMap f l] applies [f] to each element of [l] and returns the concatenation of the results, in the order of the original elements of [l]. This is equivalent to [flatten (map f l)]. Requires, at type-checking time, [f] to be a pure total function. *) val concatMap: ('a -> Tot (list 'b)) -> list 'a -> Tot (list 'b) let rec concatMap f = function | [] -> [] | a::tl -> let fa = f a in let ftl = concatMap f tl in append fa ftl (** [fold_left f x [y1; y2; ...; yn]] computes (f (... (f x y1) y2) ... yn). Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml, Coq. *) val fold_left: ('a -> 'b -> Tot 'a) -> 'a -> l:list 'b -> Tot 'a (decreases l) let rec fold_left f x l = match l with | [] -> x | hd::tl -> fold_left f (f x hd) tl (** [fold_right f [x1; x2; ...; xn] y] computes (f x1 (f x2 (... (f xn y)) ... )). Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml, Coq *) val fold_right: ('a -> 'b -> Tot 'b) -> list 'a -> 'b -> Tot 'b let rec fold_right f l x = match l with | [] -> x | hd::tl -> f hd (fold_right f tl x) (** [fold_right_gtot] is just like [fold_right], except `f` is a ghost function **) let rec fold_right_gtot (#a:Type) (#b:Type) (l:list a) (f:a -> b -> GTot b) (x:b) : GTot b = match l with | [] -> x | hd::tl -> f hd (fold_right_gtot tl f x) (* We define map in terms of fold, to share simple lemmas *) let map_gtot #a #b (f:a -> GTot b) (x:list a) : GTot (list b) = fold_right_gtot x (fun x tl -> f x :: tl) [] (** [fold_left2 f x [y1; y2; ...; yn] [z1; z2; ...; zn]] computes (f (... (f x y1 z1) y2 z2) ... yn zn). Requires, at type-checking time, [f] to be a pure total function, and the lists [y1; y2; ...; yn] and [z1; z2; ...; zn] to have the same lengths. Named as in: OCaml *) val fold_left2 : f:('a -> 'b -> 'c -> Tot 'a) -> accu:'a -> l1:(list 'b) -> l2:(list 'c) -> Pure 'a (requires (length l1 == length l2)) (ensures (fun _ -> True)) (decreases l1) let rec fold_left2 f accu l1 l2 = match (l1, l2) with | ([], []) -> accu | (a1::l1, a2::l2) -> fold_left2 f (f accu a1 a2) l1 l2 (** Propositional membership (as in Coq). Does not require decidable equality. *) (** [memP x l] holds if, and only if, [x] appears as an element of [l]. Similar to: List.In in Coq. *) let rec memP (#a: Type) (x: a) (l: list a) : Tot Type0 = match l with | [] -> False | y :: q -> x == y \/ memP x q (** List searching **) (** [mem x l] returns [true] if, and only if, [x] appears as an element of [l]. Requires, at type-checking time, the type of elements of [l] to have decidable equality. Named as in: OCaml. See also: List.In in Coq, which is propositional. *) val mem: #a:eqtype -> a -> list a -> Tot bool let rec mem #a x = function | [] -> false | hd::tl -> if hd = x then true else mem x tl (** [contains x l] returns [true] if, and only if, [x] appears as an element of [l]. Requires, at type-checking time, the type of elements of [l] to have decidable equality. It is equivalent to: [mem x l]. TODO: should we rather swap the order of arguments? *) let contains : #a:eqtype -> a -> list a -> Tot bool = mem (** [existsb f l] returns [true] if, and only if, there exists some element [x] in [l] such that [f x] holds. *) val existsb: #a:Type -> f:(a -> Tot bool) -> list a -> Tot bool let rec existsb #a f l = match l with | [] -> false | hd::tl -> if f hd then true else existsb f tl (** [find f l] returns [Some x] for some element [x] appearing in [l] such that [f x] holds, or [None] only if no such [x] exists. *) val find: #a:Type -> f:(a -> Tot bool) -> list a -> Tot (option (x:a{f x})) let rec find #a f l = match l with | [] -> None #(x:a{f x}) //These type annotations are only present because it makes bootstrapping go much faster | hd::tl -> if f hd then Some #(x:a{f x}) hd else find f tl (** Filtering elements of a list [l] through a Boolean pure total predicate [f] *) (** [filter f l] returns [l] with all elements [x] such that [f x] does not hold removed. Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml, Coq *) val filter : #a: Type -> f:(a -> Tot bool) -> l: list a -> Tot (m:list a{forall x. memP x m ==> f x}) let rec filter #a f = function | [] -> [] | hd::tl -> if f hd then hd::filter f tl else filter f tl (** Postcondition on [filter f l]: for any element [x] of [filter f l], [f x] holds. Requires, at type-checking time, [f] to be a pure total function.*) val mem_filter (#a:Type) (f: (a -> Tot bool)) (l: list a) (x: a) : Lemma (requires (memP x (filter f l))) (ensures (f x)) let mem_filter f l x = () (** Postcondition on [filter f l]: stated with [forall]: for any element [x] of [filter f l], [f x] holds. Requires, at type-checking time, [f] to be a pure total function. *) val mem_filter_forall (#a:Type) (f: (a -> Tot bool)) (l: list a) : Lemma (requires True) (ensures (forall x . memP x (filter f l) ==> f x)) [SMTPat (filter f l)] let mem_filter_forall f l = FStar.Classical.ghost_lemma (mem_filter f l) (** [for_all f l] returns [true] if, and only if, for all elements [x] appearing in [l], [f x] holds. Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml. Similar to: List.forallb in Coq *) val for_all: ('a -> Tot bool) -> list 'a -> Tot bool let rec for_all f l = match l with | [] -> true | hd::tl -> if f hd then for_all f tl else false (** Specification for [for_all f l] vs. mem *) let rec for_all_mem (#a: Type) (f: (a -> Tot bool)) (l: list a) : Lemma (for_all f l <==> (forall x . memP x l ==> f x)) = match l with | [] -> () | _ :: q -> for_all_mem f q (** [collect f l] applies [f] to each element of [l] and returns the concatenation of the results, in the order of the original elements of [l]. It is equivalent to [flatten (map f l)]. Requires, at type-checking time, [f] to be a pure total function. TODO: what is the difference with [concatMap]? *) val collect: ('a -> Tot (list 'b)) -> list 'a -> Tot (list 'b) let rec collect f l = match l with | [] -> [] | hd::tl -> append (f hd) (collect f tl) (** [tryFind f l] returns [Some x] for some element [x] appearing in [l] such that [f x] holds, or [None] only if no such [x] exists. Requires, at type-checking time, [f] to be a pure total function. Contrary to [find], [tryFind] provides no postcondition on its result. *) val tryFind: ('a -> Tot bool) -> list 'a -> Tot (option 'a) let rec tryFind p l = match l with | [] -> None | hd::tl -> if p hd then Some hd else tryFind p tl (** [tryPick f l] returns [y] for some element [x] appearing in [l] such that [f x = Some y] for some y, or [None] only if [f x = None] for all elements [x] of [l]. Requires, at type-checking time, [f] to be a pure total function. *) val tryPick: ('a -> Tot (option 'b)) -> list 'a -> Tot (option 'b) let rec tryPick f l = match l with | [] -> None | hd::tl -> match f hd with | Some x -> Some x | None -> tryPick f tl (** [choose f l] returns the list of [y] for all elements [x] appearing in [l] such that [f x = Some y] for some [y]. Requires, at type-checking time, [f] to be a pure total function. *) val choose: ('a -> Tot (option 'b)) -> list 'a -> Tot (list 'b) let rec choose f l = match l with | [] -> [] | hd::tl -> match f hd with | Some x -> x::(choose f tl) | None -> choose f tl (** [partition f l] returns the pair of lists [(l1, l2)] where all elements [x] of [l] are in [l1] if [f x] holds, and in [l2] otherwise. Both [l1] and [l2] retain the original order of [l]. Requires, at type-checking time, [f] to be a pure total function. *) val partition: f:('a -> Tot bool) -> list 'a -> Tot (list 'a * list 'a) let rec partition f = function | [] -> [], [] | hd::tl -> let l1, l2 = partition f tl in if f hd then hd::l1, l2 else l1, hd::l2 (** [subset la lb] is true if and only if all the elements from [la] are also in [lb]. Requires, at type-checking time, the type of elements of [la] and [lb] to have decidable equality. *) val subset: #a:eqtype -> list a -> list a -> Tot bool let rec subset #a la lb = match la with | [] -> true | h :: tl -> mem h lb && subset tl lb (** [noRepeats l] returns [true] if, and only if, no element of [l] appears in [l] more than once. Requires, at type-checking time, the type of elements of [la] and [lb] to have decidable equality. *) val noRepeats : #a:eqtype -> list a -> Tot bool let rec noRepeats #a la = match la with | [] -> true | h :: tl -> not(mem h tl) && noRepeats tl (** [no_repeats_p l] valid if, and only if, no element of [l] appears in [l] more than once. *) val no_repeats_p : #a:Type -> list a -> Tot prop let rec no_repeats_p #a la = match la with | [] -> True | h :: tl -> ~(memP h tl) /\ no_repeats_p tl (** List of tuples **) (** [assoc x l] returns [Some y] where [(x, y)] is the first element of [l] whose first element is [x], or [None] only if no such element exists. Requires, at type-checking time, the type of [x] to have decidable equality. Named as in: OCaml. *) val assoc: #a:eqtype -> #b:Type -> a -> list (a * b) -> Tot (option b) let rec assoc #a #b x = function | [] -> None | (x', y)::tl -> if x=x' then Some y else assoc x tl (** [split] takes a list of pairs [(x1, y1), ..., (xn, yn)] and returns the pair of lists ([x1, ..., xn], [y1, ..., yn]). Named as in: OCaml *) val split: list ('a * 'b) -> Tot (list 'a * list 'b) let rec split l = match l with | [] -> ([],[]) | (hd1,hd2)::tl -> let (tl1,tl2) = split tl in (hd1::tl1,hd2::tl2) (** [unzip] takes a list of pairs [(x1, y1), ..., (xn, yn)] and returns the pair of lists ([x1, ..., xn], [y1, ..., yn]). Named as in: Haskell *) let unzip l = split l (** [unzip3] takes a list of triples [(x1, y1, z1), ..., (xn, yn, zn)] and returns the triple of lists ([x1, ..., xn], [y1, ..., yn], [z1, ..., zn]). Named as in: Haskell *) val unzip3: list ('a * 'b * 'c) -> Tot (list 'a * list 'b * list 'c) let rec unzip3 l = match l with | [] -> ([],[],[]) | (hd1,hd2,hd3)::tl -> let (tl1,tl2,tl3) = unzip3 tl in (hd1::tl1,hd2::tl2,hd3::tl3) (** Splitting a list at some index **) (** [splitAt] takes a natural number n and a list and returns a pair of the maximal prefix of l of size smaller than n and the rest of the list *) let rec splitAt (#a:Type) (n:nat) (l:list a) : Tot (list a * list a) = if n = 0 then [], l else match l with | [] -> [], l | x :: xs -> let l1, l2 = splitAt (n-1) xs in x :: l1, l2 let rec lemma_splitAt_snd_length (#a:Type) (n:nat) (l:list a) : Lemma (requires (n <= length l))
false
false
FStar.List.Tot.Base.fst
{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 1, "max_fuel": 8, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": true, "z3cliopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }
null
val lemma_splitAt_snd_length (#a: Type) (n: nat) (l: list a) : Lemma (requires (n <= length l)) (ensures (length (snd (splitAt n l)) = length l - n))
[ "recursion" ]
FStar.List.Tot.Base.lemma_splitAt_snd_length
{ "file_name": "ulib/FStar.List.Tot.Base.fst", "git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f", "git_url": "https://github.com/FStarLang/FStar.git", "project_name": "FStar" }
n: Prims.nat -> l: Prims.list a -> FStar.Pervasives.Lemma (requires n <= FStar.List.Tot.Base.length l) (ensures FStar.List.Tot.Base.length (FStar.Pervasives.Native.snd (FStar.List.Tot.Base.splitAt n l)) = FStar.List.Tot.Base.length l - n)
{ "end_col": 53, "end_line": 457, "start_col": 2, "start_line": 454 }
Prims.Tot
val list_unref : #a:Type -> #p:(a -> Type0) -> list (x:a{p x}) -> Tot (list a)
[ { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]
false
let rec list_unref #a #p l = match l with | [] -> [] | x::xs -> x :: list_unref xs
val list_unref : #a:Type -> #p:(a -> Type0) -> list (x:a{p x}) -> Tot (list a) let rec list_unref #a #p l =
false
null
false
match l with | [] -> [] | x :: xs -> x :: list_unref xs
{ "checked_file": "FStar.List.Tot.Base.fst.checked", "dependencies": [ "prims.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Classical.fsti.checked" ], "interface_file": false, "source_file": "FStar.List.Tot.Base.fst" }
[ "total" ]
[ "Prims.list", "Prims.Nil", "Prims.Cons", "FStar.List.Tot.Base.list_unref" ]
[]
(* Copyright 2008-2014 Nikhil Swamy and Microsoft Research Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License. *) (** This module defines all pure and total operations on lists that can be used in specifications. It is implemented by FStar_List_Tot_Base.ml, any functional change and/or the addition of new functions MUST be reflected there. @summary Pure total operations on lists *) module FStar.List.Tot.Base (** Base operations *) (** [isEmpty l] returns [true] if and only if [l] is empty *) val isEmpty: list 'a -> Tot bool let isEmpty l = match l with | [] -> true | _ -> false (** [hd l] returns the first element of [l]. Requires [l] to be nonempty, at type-checking time. Named as in: OCaml, F#, Coq *) val hd: l:list 'a{Cons? l} -> Tot 'a let hd = function | hd::_ -> hd (** [tail l] returns [l] without its first element. Requires, at type-checking time, that [l] be nonempty. Similar to: tl in OCaml, F#, Coq *) val tail: l:list 'a {Cons? l} -> Tot (list 'a) let tail = function | _::tl -> tl (** [tl l] returns [l] without its first element. Requires, at type-checking time, that [l] be nonempty. Named as in: OCaml, F#, Coq *) val tl: l:list 'a {Cons? l} -> Tot (list 'a) let tl = tail (** [last l] returns the last element of [l]. Requires, at type-checking time, that [l] be nonempty. Named as in: Haskell *) val last: l:list 'a {Cons? l} -> Tot 'a let rec last = function | [hd] -> hd | _::tl -> last tl (** [init l] returns [l] without its last element. Requires, at type-checking time, that [l] be nonempty. Named as in: Haskell *) val init: l:list 'a {Cons? l} -> Tot (list 'a) let rec init = function | [_] -> [] | hd::tl -> hd::(init tl) (** [length l] returns the total number of elements in [l]. Named as in: OCaml, F#, Coq *) val length: list 'a -> Tot nat let rec length = function | [] -> 0 | _::tl -> 1 + length tl (** [nth l n] returns the [n]-th element in list [l] (with the first element being the 0-th) if [l] is long enough, or [None] otherwise. Named as in: OCaml, F#, Coq *) val nth: list 'a -> nat -> Tot (option 'a) let rec nth l n = match l with | [] -> None | hd::tl -> if n = 0 then Some hd else nth tl (n - 1) (** [index l n] returns the [n]-th element in list [l] (with the first element being the 0-th). Requires, at type-checking time, that [l] be of length at least [n+1]. *) val index: #a:Type -> l:list a -> i:nat{i < length l} -> Tot a let rec index #a (l: list a) (i:nat{i < length l}): Tot a = if i = 0 then hd l else index (tl l) (i - 1) (** [count x l] returns the number of occurrences of [x] in [l]. Requires, at type-checking time, the type of [a] to have equality defined. Similar to: [List.count_occ] in Coq. *) val count: #a:eqtype -> a -> list a -> Tot nat let rec count #a x = function | [] -> 0 | hd::tl -> if x=hd then 1 + count x tl else count x tl (** [rev_acc l1 l2] appends the elements of [l1] to the beginning of [l2], in reverse order. It is equivalent to [append (rev l1) l2], but is tail-recursive. Similar to: [List.rev_append] in OCaml, Coq. *) val rev_acc: list 'a -> list 'a -> Tot (list 'a) let rec rev_acc l acc = match l with | [] -> acc | hd::tl -> rev_acc tl (hd::acc) (** [rev l] returns the list [l] in reverse order. Named as in: OCaml, F#, Coq. *) val rev: list 'a -> Tot (list 'a) let rev l = rev_acc l [] (** [append l1 l2] appends the elements of [l2] to the end of [l1]. Named as: OCaml, F#. Similar to: [List.app] in Coq. *) val append: list 'a -> list 'a -> Tot (list 'a) let rec append x y = match x with | [] -> y | a::tl -> a::append tl y (** Defines notation [@@] for [append], as in OCaml, F# . *) let op_At x y = append x y (** [snoc (l, x)] adds [x] to the end of the list [l]. Note: We use an uncurried [snoc (l, x)] instead of the curried [snoc l x]. This is intentional. If [snoc] takes a pair instead of 2 arguments, it allows for a better pattern on [lemma_unsnoc_snoc], which connects [snoc] and [unsnoc]. In particular, if we had two arguments, then either the pattern would either be too restrictive or would lead to over-triggering. More context for this can be seen in the (collapsed and uncollapsed) comments at https://github.com/FStarLang/FStar/pull/1560 *) val snoc: (list 'a * 'a) -> Tot (list 'a) let snoc (l, x) = append l [x] (** [flatten l], where [l] is a list of lists, returns the list of the elements of the lists in [l], preserving their order. Named as in: OCaml, Coq. *) val flatten: list (list 'a) -> Tot (list 'a) let rec flatten l = match l with | [] -> [] | hd::tl -> append hd (flatten tl) (** [map f l] applies [f] to each element of [l] and returns the list of results, in the order of the original elements in [l]. Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml, Coq, F# *) val map: ('a -> Tot 'b) -> list 'a -> Tot (list 'b) let rec map f x = match x with | [] -> [] | a::tl -> f a::map f tl (** [mapi_init f l n] applies, for each [k], [f (n+k)] to the [k]-th element of [l] and returns the list of results, in the order of the original elements in [l]. Requires, at type-checking time, [f] to be a pure total function. *) val mapi_init: (int -> 'a -> Tot 'b) -> list 'a -> int -> Tot (list 'b) let rec mapi_init f l i = match l with | [] -> [] | hd::tl -> (f i hd)::(mapi_init f tl (i+1)) (** [mapi f l] applies, for each [k], [f k] to the [k]-th element of [l] and returns the list of results, in the order of the original elements in [l]. Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml *) val mapi: (int -> 'a -> Tot 'b) -> list 'a -> Tot (list 'b) let mapi f l = mapi_init f l 0 (** [concatMap f l] applies [f] to each element of [l] and returns the concatenation of the results, in the order of the original elements of [l]. This is equivalent to [flatten (map f l)]. Requires, at type-checking time, [f] to be a pure total function. *) val concatMap: ('a -> Tot (list 'b)) -> list 'a -> Tot (list 'b) let rec concatMap f = function | [] -> [] | a::tl -> let fa = f a in let ftl = concatMap f tl in append fa ftl (** [fold_left f x [y1; y2; ...; yn]] computes (f (... (f x y1) y2) ... yn). Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml, Coq. *) val fold_left: ('a -> 'b -> Tot 'a) -> 'a -> l:list 'b -> Tot 'a (decreases l) let rec fold_left f x l = match l with | [] -> x | hd::tl -> fold_left f (f x hd) tl (** [fold_right f [x1; x2; ...; xn] y] computes (f x1 (f x2 (... (f xn y)) ... )). Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml, Coq *) val fold_right: ('a -> 'b -> Tot 'b) -> list 'a -> 'b -> Tot 'b let rec fold_right f l x = match l with | [] -> x | hd::tl -> f hd (fold_right f tl x) (** [fold_right_gtot] is just like [fold_right], except `f` is a ghost function **) let rec fold_right_gtot (#a:Type) (#b:Type) (l:list a) (f:a -> b -> GTot b) (x:b) : GTot b = match l with | [] -> x | hd::tl -> f hd (fold_right_gtot tl f x) (* We define map in terms of fold, to share simple lemmas *) let map_gtot #a #b (f:a -> GTot b) (x:list a) : GTot (list b) = fold_right_gtot x (fun x tl -> f x :: tl) [] (** [fold_left2 f x [y1; y2; ...; yn] [z1; z2; ...; zn]] computes (f (... (f x y1 z1) y2 z2) ... yn zn). Requires, at type-checking time, [f] to be a pure total function, and the lists [y1; y2; ...; yn] and [z1; z2; ...; zn] to have the same lengths. Named as in: OCaml *) val fold_left2 : f:('a -> 'b -> 'c -> Tot 'a) -> accu:'a -> l1:(list 'b) -> l2:(list 'c) -> Pure 'a (requires (length l1 == length l2)) (ensures (fun _ -> True)) (decreases l1) let rec fold_left2 f accu l1 l2 = match (l1, l2) with | ([], []) -> accu | (a1::l1, a2::l2) -> fold_left2 f (f accu a1 a2) l1 l2 (** Propositional membership (as in Coq). Does not require decidable equality. *) (** [memP x l] holds if, and only if, [x] appears as an element of [l]. Similar to: List.In in Coq. *) let rec memP (#a: Type) (x: a) (l: list a) : Tot Type0 = match l with | [] -> False | y :: q -> x == y \/ memP x q (** List searching **) (** [mem x l] returns [true] if, and only if, [x] appears as an element of [l]. Requires, at type-checking time, the type of elements of [l] to have decidable equality. Named as in: OCaml. See also: List.In in Coq, which is propositional. *) val mem: #a:eqtype -> a -> list a -> Tot bool let rec mem #a x = function | [] -> false | hd::tl -> if hd = x then true else mem x tl (** [contains x l] returns [true] if, and only if, [x] appears as an element of [l]. Requires, at type-checking time, the type of elements of [l] to have decidable equality. It is equivalent to: [mem x l]. TODO: should we rather swap the order of arguments? *) let contains : #a:eqtype -> a -> list a -> Tot bool = mem (** [existsb f l] returns [true] if, and only if, there exists some element [x] in [l] such that [f x] holds. *) val existsb: #a:Type -> f:(a -> Tot bool) -> list a -> Tot bool let rec existsb #a f l = match l with | [] -> false | hd::tl -> if f hd then true else existsb f tl (** [find f l] returns [Some x] for some element [x] appearing in [l] such that [f x] holds, or [None] only if no such [x] exists. *) val find: #a:Type -> f:(a -> Tot bool) -> list a -> Tot (option (x:a{f x})) let rec find #a f l = match l with | [] -> None #(x:a{f x}) //These type annotations are only present because it makes bootstrapping go much faster | hd::tl -> if f hd then Some #(x:a{f x}) hd else find f tl (** Filtering elements of a list [l] through a Boolean pure total predicate [f] *) (** [filter f l] returns [l] with all elements [x] such that [f x] does not hold removed. Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml, Coq *) val filter : #a: Type -> f:(a -> Tot bool) -> l: list a -> Tot (m:list a{forall x. memP x m ==> f x}) let rec filter #a f = function | [] -> [] | hd::tl -> if f hd then hd::filter f tl else filter f tl (** Postcondition on [filter f l]: for any element [x] of [filter f l], [f x] holds. Requires, at type-checking time, [f] to be a pure total function.*) val mem_filter (#a:Type) (f: (a -> Tot bool)) (l: list a) (x: a) : Lemma (requires (memP x (filter f l))) (ensures (f x)) let mem_filter f l x = () (** Postcondition on [filter f l]: stated with [forall]: for any element [x] of [filter f l], [f x] holds. Requires, at type-checking time, [f] to be a pure total function. *) val mem_filter_forall (#a:Type) (f: (a -> Tot bool)) (l: list a) : Lemma (requires True) (ensures (forall x . memP x (filter f l) ==> f x)) [SMTPat (filter f l)] let mem_filter_forall f l = FStar.Classical.ghost_lemma (mem_filter f l) (** [for_all f l] returns [true] if, and only if, for all elements [x] appearing in [l], [f x] holds. Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml. Similar to: List.forallb in Coq *) val for_all: ('a -> Tot bool) -> list 'a -> Tot bool let rec for_all f l = match l with | [] -> true | hd::tl -> if f hd then for_all f tl else false (** Specification for [for_all f l] vs. mem *) let rec for_all_mem (#a: Type) (f: (a -> Tot bool)) (l: list a) : Lemma (for_all f l <==> (forall x . memP x l ==> f x)) = match l with | [] -> () | _ :: q -> for_all_mem f q (** [collect f l] applies [f] to each element of [l] and returns the concatenation of the results, in the order of the original elements of [l]. It is equivalent to [flatten (map f l)]. Requires, at type-checking time, [f] to be a pure total function. TODO: what is the difference with [concatMap]? *) val collect: ('a -> Tot (list 'b)) -> list 'a -> Tot (list 'b) let rec collect f l = match l with | [] -> [] | hd::tl -> append (f hd) (collect f tl) (** [tryFind f l] returns [Some x] for some element [x] appearing in [l] such that [f x] holds, or [None] only if no such [x] exists. Requires, at type-checking time, [f] to be a pure total function. Contrary to [find], [tryFind] provides no postcondition on its result. *) val tryFind: ('a -> Tot bool) -> list 'a -> Tot (option 'a) let rec tryFind p l = match l with | [] -> None | hd::tl -> if p hd then Some hd else tryFind p tl (** [tryPick f l] returns [y] for some element [x] appearing in [l] such that [f x = Some y] for some y, or [None] only if [f x = None] for all elements [x] of [l]. Requires, at type-checking time, [f] to be a pure total function. *) val tryPick: ('a -> Tot (option 'b)) -> list 'a -> Tot (option 'b) let rec tryPick f l = match l with | [] -> None | hd::tl -> match f hd with | Some x -> Some x | None -> tryPick f tl (** [choose f l] returns the list of [y] for all elements [x] appearing in [l] such that [f x = Some y] for some [y]. Requires, at type-checking time, [f] to be a pure total function. *) val choose: ('a -> Tot (option 'b)) -> list 'a -> Tot (list 'b) let rec choose f l = match l with | [] -> [] | hd::tl -> match f hd with | Some x -> x::(choose f tl) | None -> choose f tl (** [partition f l] returns the pair of lists [(l1, l2)] where all elements [x] of [l] are in [l1] if [f x] holds, and in [l2] otherwise. Both [l1] and [l2] retain the original order of [l]. Requires, at type-checking time, [f] to be a pure total function. *) val partition: f:('a -> Tot bool) -> list 'a -> Tot (list 'a * list 'a) let rec partition f = function | [] -> [], [] | hd::tl -> let l1, l2 = partition f tl in if f hd then hd::l1, l2 else l1, hd::l2 (** [subset la lb] is true if and only if all the elements from [la] are also in [lb]. Requires, at type-checking time, the type of elements of [la] and [lb] to have decidable equality. *) val subset: #a:eqtype -> list a -> list a -> Tot bool let rec subset #a la lb = match la with | [] -> true | h :: tl -> mem h lb && subset tl lb (** [noRepeats l] returns [true] if, and only if, no element of [l] appears in [l] more than once. Requires, at type-checking time, the type of elements of [la] and [lb] to have decidable equality. *) val noRepeats : #a:eqtype -> list a -> Tot bool let rec noRepeats #a la = match la with | [] -> true | h :: tl -> not(mem h tl) && noRepeats tl (** [no_repeats_p l] valid if, and only if, no element of [l] appears in [l] more than once. *) val no_repeats_p : #a:Type -> list a -> Tot prop let rec no_repeats_p #a la = match la with | [] -> True | h :: tl -> ~(memP h tl) /\ no_repeats_p tl (** List of tuples **) (** [assoc x l] returns [Some y] where [(x, y)] is the first element of [l] whose first element is [x], or [None] only if no such element exists. Requires, at type-checking time, the type of [x] to have decidable equality. Named as in: OCaml. *) val assoc: #a:eqtype -> #b:Type -> a -> list (a * b) -> Tot (option b) let rec assoc #a #b x = function | [] -> None | (x', y)::tl -> if x=x' then Some y else assoc x tl (** [split] takes a list of pairs [(x1, y1), ..., (xn, yn)] and returns the pair of lists ([x1, ..., xn], [y1, ..., yn]). Named as in: OCaml *) val split: list ('a * 'b) -> Tot (list 'a * list 'b) let rec split l = match l with | [] -> ([],[]) | (hd1,hd2)::tl -> let (tl1,tl2) = split tl in (hd1::tl1,hd2::tl2) (** [unzip] takes a list of pairs [(x1, y1), ..., (xn, yn)] and returns the pair of lists ([x1, ..., xn], [y1, ..., yn]). Named as in: Haskell *) let unzip l = split l (** [unzip3] takes a list of triples [(x1, y1, z1), ..., (xn, yn, zn)] and returns the triple of lists ([x1, ..., xn], [y1, ..., yn], [z1, ..., zn]). Named as in: Haskell *) val unzip3: list ('a * 'b * 'c) -> Tot (list 'a * list 'b * list 'c) let rec unzip3 l = match l with | [] -> ([],[],[]) | (hd1,hd2,hd3)::tl -> let (tl1,tl2,tl3) = unzip3 tl in (hd1::tl1,hd2::tl2,hd3::tl3) (** Splitting a list at some index **) (** [splitAt] takes a natural number n and a list and returns a pair of the maximal prefix of l of size smaller than n and the rest of the list *) let rec splitAt (#a:Type) (n:nat) (l:list a) : Tot (list a * list a) = if n = 0 then [], l else match l with | [] -> [], l | x :: xs -> let l1, l2 = splitAt (n-1) xs in x :: l1, l2 let rec lemma_splitAt_snd_length (#a:Type) (n:nat) (l:list a) : Lemma (requires (n <= length l)) (ensures (length (snd (splitAt n l)) = length l - n)) = match n, l with | 0, _ -> () | _, [] -> () | _, _ :: l' -> lemma_splitAt_snd_length (n - 1) l' (** [unsnoc] is an inverse of [snoc]. It splits a list into all-elements-except-last and last element. *) val unsnoc: #a:Type -> l:list a{length l > 0} -> Tot (list a * a) let unsnoc #a l = let l1, l2 = splitAt (length l - 1) l in lemma_splitAt_snd_length (length l - 1) l; l1, hd l2 (** [split3] splits a list into 3 parts. This allows easy access to the part of the list before and after the element, as well as the element itself. *) val split3: #a:Type -> l:list a -> i:nat{i < length l} -> Tot (list a * a * list a) let split3 #a l i = let a, rest = splitAt i l in lemma_splitAt_snd_length i l; let b :: c = rest in a, b, c (** Sorting (implemented as quicksort) **) (** [partition] splits a list [l] into two lists, the sum of whose lengths is the length of [l]. *) val partition_length: f:('a -> Tot bool) -> l:list 'a -> Lemma (requires True) (ensures (length (fst (partition f l)) + length (snd (partition f l)) = length l)) let rec partition_length f l = match l with | [] -> () | hd::tl -> partition_length f tl (** [bool_of_compare] turns a comparison function into a strict order. More precisely, [bool_of_compare compare x y] returns true if, and only if, [compare x y] is negative, meaning [x] precedes [y] in the ordering defined by compare. This is used in sorting, and is defined to be consistent with OCaml and F#, where sorting is performed in ascending order. *) val bool_of_compare : #a:Type -> (a -> a -> Tot int) -> a -> a -> Tot bool let bool_of_compare #a f x y = f x y < 0 (** [compare_of_bool] turns a strict order into a comparison function. More precisely, [compare_of_bool rel x y] returns a positive number if, and only if, x `rel` y holds. Inspired from OCaml, where polymorphic comparison using both the [compare] function and the (>) infix operator are such that [compare x y] is positive if, and only if, x > y. Requires, at type-checking time, [rel] to be a pure total function. *) val compare_of_bool : #a:eqtype -> (a -> a -> Tot bool) -> a -> a -> Tot int let compare_of_bool #a rel x y = if x `rel` y then -1 else if x = y then 0 else 1 let compare_of_bool_of_compare (#a:eqtype) (f:a -> a -> Tot bool) : Lemma (forall x y. bool_of_compare (compare_of_bool f) x y == f x y) = () (** [sortWith compare l] returns the list [l'] containing the elements of [l] sorted along the comparison function [compare], in such a way that if [compare x y > 0], then [x] appears before [y] in [l']. Sorts in ascending order *) val sortWith: ('a -> 'a -> Tot int) -> l:list 'a -> Tot (list 'a) (decreases (length l)) let rec sortWith f = function | [] -> [] | pivot::tl -> let hi, lo = partition (bool_of_compare f pivot) tl in partition_length (bool_of_compare f pivot) tl; append (sortWith f lo) (pivot::sortWith f hi) (** A l1 is a strict suffix of l2. *) let rec strict_suffix_of (#a: Type) (l1 l2: list a) : Pure Type0 (requires True) (ensures (fun _ -> True)) (decreases l2) = match l2 with | [] -> False | _ :: q -> l1 == q \/ l1 `strict_suffix_of` q [@@deprecated "This function was misnamed: Please use 'strict_suffix_of'"] let strict_prefix_of = strict_suffix_of val list_unref : #a:Type -> #p:(a -> Type0) -> list (x:a{p x}) -> Tot (list a)
false
false
FStar.List.Tot.Base.fst
{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 1, "max_fuel": 8, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": true, "z3cliopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }
null
val list_unref : #a:Type -> #p:(a -> Type0) -> list (x:a{p x}) -> Tot (list a)
[ "recursion" ]
FStar.List.Tot.Base.list_unref
{ "file_name": "ulib/FStar.List.Tot.Base.fst", "git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f", "git_url": "https://github.com/FStarLang/FStar.git", "project_name": "FStar" }
l: Prims.list (x: a{p x}) -> Prims.list a
{ "end_col": 33, "end_line": 547, "start_col": 4, "start_line": 545 }
Prims.Tot
val partition: f:('a -> Tot bool) -> list 'a -> Tot (list 'a * list 'a)
[ { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]
false
let rec partition f = function | [] -> [], [] | hd::tl -> let l1, l2 = partition f tl in if f hd then hd::l1, l2 else l1, hd::l2
val partition: f:('a -> Tot bool) -> list 'a -> Tot (list 'a * list 'a) let rec partition f =
false
null
false
function | [] -> [], [] | hd :: tl -> let l1, l2 = partition f tl in if f hd then hd :: l1, l2 else l1, hd :: l2
{ "checked_file": "FStar.List.Tot.Base.fst.checked", "dependencies": [ "prims.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Classical.fsti.checked" ], "interface_file": false, "source_file": "FStar.List.Tot.Base.fst" }
[ "total" ]
[ "Prims.bool", "Prims.list", "FStar.Pervasives.Native.Mktuple2", "Prims.Nil", "Prims.Cons", "FStar.Pervasives.Native.tuple2", "FStar.List.Tot.Base.partition" ]
[]
(* Copyright 2008-2014 Nikhil Swamy and Microsoft Research Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License. *) (** This module defines all pure and total operations on lists that can be used in specifications. It is implemented by FStar_List_Tot_Base.ml, any functional change and/or the addition of new functions MUST be reflected there. @summary Pure total operations on lists *) module FStar.List.Tot.Base (** Base operations *) (** [isEmpty l] returns [true] if and only if [l] is empty *) val isEmpty: list 'a -> Tot bool let isEmpty l = match l with | [] -> true | _ -> false (** [hd l] returns the first element of [l]. Requires [l] to be nonempty, at type-checking time. Named as in: OCaml, F#, Coq *) val hd: l:list 'a{Cons? l} -> Tot 'a let hd = function | hd::_ -> hd (** [tail l] returns [l] without its first element. Requires, at type-checking time, that [l] be nonempty. Similar to: tl in OCaml, F#, Coq *) val tail: l:list 'a {Cons? l} -> Tot (list 'a) let tail = function | _::tl -> tl (** [tl l] returns [l] without its first element. Requires, at type-checking time, that [l] be nonempty. Named as in: OCaml, F#, Coq *) val tl: l:list 'a {Cons? l} -> Tot (list 'a) let tl = tail (** [last l] returns the last element of [l]. Requires, at type-checking time, that [l] be nonempty. Named as in: Haskell *) val last: l:list 'a {Cons? l} -> Tot 'a let rec last = function | [hd] -> hd | _::tl -> last tl (** [init l] returns [l] without its last element. Requires, at type-checking time, that [l] be nonempty. Named as in: Haskell *) val init: l:list 'a {Cons? l} -> Tot (list 'a) let rec init = function | [_] -> [] | hd::tl -> hd::(init tl) (** [length l] returns the total number of elements in [l]. Named as in: OCaml, F#, Coq *) val length: list 'a -> Tot nat let rec length = function | [] -> 0 | _::tl -> 1 + length tl (** [nth l n] returns the [n]-th element in list [l] (with the first element being the 0-th) if [l] is long enough, or [None] otherwise. Named as in: OCaml, F#, Coq *) val nth: list 'a -> nat -> Tot (option 'a) let rec nth l n = match l with | [] -> None | hd::tl -> if n = 0 then Some hd else nth tl (n - 1) (** [index l n] returns the [n]-th element in list [l] (with the first element being the 0-th). Requires, at type-checking time, that [l] be of length at least [n+1]. *) val index: #a:Type -> l:list a -> i:nat{i < length l} -> Tot a let rec index #a (l: list a) (i:nat{i < length l}): Tot a = if i = 0 then hd l else index (tl l) (i - 1) (** [count x l] returns the number of occurrences of [x] in [l]. Requires, at type-checking time, the type of [a] to have equality defined. Similar to: [List.count_occ] in Coq. *) val count: #a:eqtype -> a -> list a -> Tot nat let rec count #a x = function | [] -> 0 | hd::tl -> if x=hd then 1 + count x tl else count x tl (** [rev_acc l1 l2] appends the elements of [l1] to the beginning of [l2], in reverse order. It is equivalent to [append (rev l1) l2], but is tail-recursive. Similar to: [List.rev_append] in OCaml, Coq. *) val rev_acc: list 'a -> list 'a -> Tot (list 'a) let rec rev_acc l acc = match l with | [] -> acc | hd::tl -> rev_acc tl (hd::acc) (** [rev l] returns the list [l] in reverse order. Named as in: OCaml, F#, Coq. *) val rev: list 'a -> Tot (list 'a) let rev l = rev_acc l [] (** [append l1 l2] appends the elements of [l2] to the end of [l1]. Named as: OCaml, F#. Similar to: [List.app] in Coq. *) val append: list 'a -> list 'a -> Tot (list 'a) let rec append x y = match x with | [] -> y | a::tl -> a::append tl y (** Defines notation [@@] for [append], as in OCaml, F# . *) let op_At x y = append x y (** [snoc (l, x)] adds [x] to the end of the list [l]. Note: We use an uncurried [snoc (l, x)] instead of the curried [snoc l x]. This is intentional. If [snoc] takes a pair instead of 2 arguments, it allows for a better pattern on [lemma_unsnoc_snoc], which connects [snoc] and [unsnoc]. In particular, if we had two arguments, then either the pattern would either be too restrictive or would lead to over-triggering. More context for this can be seen in the (collapsed and uncollapsed) comments at https://github.com/FStarLang/FStar/pull/1560 *) val snoc: (list 'a * 'a) -> Tot (list 'a) let snoc (l, x) = append l [x] (** [flatten l], where [l] is a list of lists, returns the list of the elements of the lists in [l], preserving their order. Named as in: OCaml, Coq. *) val flatten: list (list 'a) -> Tot (list 'a) let rec flatten l = match l with | [] -> [] | hd::tl -> append hd (flatten tl) (** [map f l] applies [f] to each element of [l] and returns the list of results, in the order of the original elements in [l]. Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml, Coq, F# *) val map: ('a -> Tot 'b) -> list 'a -> Tot (list 'b) let rec map f x = match x with | [] -> [] | a::tl -> f a::map f tl (** [mapi_init f l n] applies, for each [k], [f (n+k)] to the [k]-th element of [l] and returns the list of results, in the order of the original elements in [l]. Requires, at type-checking time, [f] to be a pure total function. *) val mapi_init: (int -> 'a -> Tot 'b) -> list 'a -> int -> Tot (list 'b) let rec mapi_init f l i = match l with | [] -> [] | hd::tl -> (f i hd)::(mapi_init f tl (i+1)) (** [mapi f l] applies, for each [k], [f k] to the [k]-th element of [l] and returns the list of results, in the order of the original elements in [l]. Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml *) val mapi: (int -> 'a -> Tot 'b) -> list 'a -> Tot (list 'b) let mapi f l = mapi_init f l 0 (** [concatMap f l] applies [f] to each element of [l] and returns the concatenation of the results, in the order of the original elements of [l]. This is equivalent to [flatten (map f l)]. Requires, at type-checking time, [f] to be a pure total function. *) val concatMap: ('a -> Tot (list 'b)) -> list 'a -> Tot (list 'b) let rec concatMap f = function | [] -> [] | a::tl -> let fa = f a in let ftl = concatMap f tl in append fa ftl (** [fold_left f x [y1; y2; ...; yn]] computes (f (... (f x y1) y2) ... yn). Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml, Coq. *) val fold_left: ('a -> 'b -> Tot 'a) -> 'a -> l:list 'b -> Tot 'a (decreases l) let rec fold_left f x l = match l with | [] -> x | hd::tl -> fold_left f (f x hd) tl (** [fold_right f [x1; x2; ...; xn] y] computes (f x1 (f x2 (... (f xn y)) ... )). Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml, Coq *) val fold_right: ('a -> 'b -> Tot 'b) -> list 'a -> 'b -> Tot 'b let rec fold_right f l x = match l with | [] -> x | hd::tl -> f hd (fold_right f tl x) (** [fold_right_gtot] is just like [fold_right], except `f` is a ghost function **) let rec fold_right_gtot (#a:Type) (#b:Type) (l:list a) (f:a -> b -> GTot b) (x:b) : GTot b = match l with | [] -> x | hd::tl -> f hd (fold_right_gtot tl f x) (* We define map in terms of fold, to share simple lemmas *) let map_gtot #a #b (f:a -> GTot b) (x:list a) : GTot (list b) = fold_right_gtot x (fun x tl -> f x :: tl) [] (** [fold_left2 f x [y1; y2; ...; yn] [z1; z2; ...; zn]] computes (f (... (f x y1 z1) y2 z2) ... yn zn). Requires, at type-checking time, [f] to be a pure total function, and the lists [y1; y2; ...; yn] and [z1; z2; ...; zn] to have the same lengths. Named as in: OCaml *) val fold_left2 : f:('a -> 'b -> 'c -> Tot 'a) -> accu:'a -> l1:(list 'b) -> l2:(list 'c) -> Pure 'a (requires (length l1 == length l2)) (ensures (fun _ -> True)) (decreases l1) let rec fold_left2 f accu l1 l2 = match (l1, l2) with | ([], []) -> accu | (a1::l1, a2::l2) -> fold_left2 f (f accu a1 a2) l1 l2 (** Propositional membership (as in Coq). Does not require decidable equality. *) (** [memP x l] holds if, and only if, [x] appears as an element of [l]. Similar to: List.In in Coq. *) let rec memP (#a: Type) (x: a) (l: list a) : Tot Type0 = match l with | [] -> False | y :: q -> x == y \/ memP x q (** List searching **) (** [mem x l] returns [true] if, and only if, [x] appears as an element of [l]. Requires, at type-checking time, the type of elements of [l] to have decidable equality. Named as in: OCaml. See also: List.In in Coq, which is propositional. *) val mem: #a:eqtype -> a -> list a -> Tot bool let rec mem #a x = function | [] -> false | hd::tl -> if hd = x then true else mem x tl (** [contains x l] returns [true] if, and only if, [x] appears as an element of [l]. Requires, at type-checking time, the type of elements of [l] to have decidable equality. It is equivalent to: [mem x l]. TODO: should we rather swap the order of arguments? *) let contains : #a:eqtype -> a -> list a -> Tot bool = mem (** [existsb f l] returns [true] if, and only if, there exists some element [x] in [l] such that [f x] holds. *) val existsb: #a:Type -> f:(a -> Tot bool) -> list a -> Tot bool let rec existsb #a f l = match l with | [] -> false | hd::tl -> if f hd then true else existsb f tl (** [find f l] returns [Some x] for some element [x] appearing in [l] such that [f x] holds, or [None] only if no such [x] exists. *) val find: #a:Type -> f:(a -> Tot bool) -> list a -> Tot (option (x:a{f x})) let rec find #a f l = match l with | [] -> None #(x:a{f x}) //These type annotations are only present because it makes bootstrapping go much faster | hd::tl -> if f hd then Some #(x:a{f x}) hd else find f tl (** Filtering elements of a list [l] through a Boolean pure total predicate [f] *) (** [filter f l] returns [l] with all elements [x] such that [f x] does not hold removed. Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml, Coq *) val filter : #a: Type -> f:(a -> Tot bool) -> l: list a -> Tot (m:list a{forall x. memP x m ==> f x}) let rec filter #a f = function | [] -> [] | hd::tl -> if f hd then hd::filter f tl else filter f tl (** Postcondition on [filter f l]: for any element [x] of [filter f l], [f x] holds. Requires, at type-checking time, [f] to be a pure total function.*) val mem_filter (#a:Type) (f: (a -> Tot bool)) (l: list a) (x: a) : Lemma (requires (memP x (filter f l))) (ensures (f x)) let mem_filter f l x = () (** Postcondition on [filter f l]: stated with [forall]: for any element [x] of [filter f l], [f x] holds. Requires, at type-checking time, [f] to be a pure total function. *) val mem_filter_forall (#a:Type) (f: (a -> Tot bool)) (l: list a) : Lemma (requires True) (ensures (forall x . memP x (filter f l) ==> f x)) [SMTPat (filter f l)] let mem_filter_forall f l = FStar.Classical.ghost_lemma (mem_filter f l) (** [for_all f l] returns [true] if, and only if, for all elements [x] appearing in [l], [f x] holds. Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml. Similar to: List.forallb in Coq *) val for_all: ('a -> Tot bool) -> list 'a -> Tot bool let rec for_all f l = match l with | [] -> true | hd::tl -> if f hd then for_all f tl else false (** Specification for [for_all f l] vs. mem *) let rec for_all_mem (#a: Type) (f: (a -> Tot bool)) (l: list a) : Lemma (for_all f l <==> (forall x . memP x l ==> f x)) = match l with | [] -> () | _ :: q -> for_all_mem f q (** [collect f l] applies [f] to each element of [l] and returns the concatenation of the results, in the order of the original elements of [l]. It is equivalent to [flatten (map f l)]. Requires, at type-checking time, [f] to be a pure total function. TODO: what is the difference with [concatMap]? *) val collect: ('a -> Tot (list 'b)) -> list 'a -> Tot (list 'b) let rec collect f l = match l with | [] -> [] | hd::tl -> append (f hd) (collect f tl) (** [tryFind f l] returns [Some x] for some element [x] appearing in [l] such that [f x] holds, or [None] only if no such [x] exists. Requires, at type-checking time, [f] to be a pure total function. Contrary to [find], [tryFind] provides no postcondition on its result. *) val tryFind: ('a -> Tot bool) -> list 'a -> Tot (option 'a) let rec tryFind p l = match l with | [] -> None | hd::tl -> if p hd then Some hd else tryFind p tl (** [tryPick f l] returns [y] for some element [x] appearing in [l] such that [f x = Some y] for some y, or [None] only if [f x = None] for all elements [x] of [l]. Requires, at type-checking time, [f] to be a pure total function. *) val tryPick: ('a -> Tot (option 'b)) -> list 'a -> Tot (option 'b) let rec tryPick f l = match l with | [] -> None | hd::tl -> match f hd with | Some x -> Some x | None -> tryPick f tl (** [choose f l] returns the list of [y] for all elements [x] appearing in [l] such that [f x = Some y] for some [y]. Requires, at type-checking time, [f] to be a pure total function. *) val choose: ('a -> Tot (option 'b)) -> list 'a -> Tot (list 'b) let rec choose f l = match l with | [] -> [] | hd::tl -> match f hd with | Some x -> x::(choose f tl) | None -> choose f tl (** [partition f l] returns the pair of lists [(l1, l2)] where all elements [x] of [l] are in [l1] if [f x] holds, and in [l2] otherwise. Both [l1] and [l2] retain the original order of [l]. Requires, at type-checking time, [f] to be a pure total function. *)
false
false
FStar.List.Tot.Base.fst
{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 1, "max_fuel": 8, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": true, "z3cliopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }
null
val partition: f:('a -> Tot bool) -> list 'a -> Tot (list 'a * list 'a)
[ "recursion" ]
FStar.List.Tot.Base.partition
{ "file_name": "ulib/FStar.List.Tot.Base.fst", "git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f", "git_url": "https://github.com/FStarLang/FStar.git", "project_name": "FStar" }
f: (_: 'a -> Prims.bool) -> _: Prims.list 'a -> Prims.list 'a * Prims.list 'a
{ "end_col": 20, "end_line": 373, "start_col": 22, "start_line": 367 }
FStar.Pervasives.Lemma
val for_all_mem (#a: Type) (f: (a -> Tot bool)) (l: list a) : Lemma (for_all f l <==> (forall x. memP x l ==> f x))
[ { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]
false
let rec for_all_mem (#a: Type) (f: (a -> Tot bool)) (l: list a) : Lemma (for_all f l <==> (forall x . memP x l ==> f x)) = match l with | [] -> () | _ :: q -> for_all_mem f q
val for_all_mem (#a: Type) (f: (a -> Tot bool)) (l: list a) : Lemma (for_all f l <==> (forall x. memP x l ==> f x)) let rec for_all_mem (#a: Type) (f: (a -> Tot bool)) (l: list a) : Lemma (for_all f l <==> (forall x. memP x l ==> f x)) =
false
null
true
match l with | [] -> () | _ :: q -> for_all_mem f q
{ "checked_file": "FStar.List.Tot.Base.fst.checked", "dependencies": [ "prims.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Classical.fsti.checked" ], "interface_file": false, "source_file": "FStar.List.Tot.Base.fst" }
[ "lemma" ]
[ "Prims.bool", "Prims.list", "FStar.List.Tot.Base.for_all_mem", "Prims.unit", "Prims.l_True", "Prims.squash", "Prims.l_iff", "Prims.b2t", "FStar.List.Tot.Base.for_all", "Prims.l_Forall", "Prims.l_imp", "FStar.List.Tot.Base.memP", "Prims.Nil", "FStar.Pervasives.pattern" ]
[]
(* Copyright 2008-2014 Nikhil Swamy and Microsoft Research Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License. *) (** This module defines all pure and total operations on lists that can be used in specifications. It is implemented by FStar_List_Tot_Base.ml, any functional change and/or the addition of new functions MUST be reflected there. @summary Pure total operations on lists *) module FStar.List.Tot.Base (** Base operations *) (** [isEmpty l] returns [true] if and only if [l] is empty *) val isEmpty: list 'a -> Tot bool let isEmpty l = match l with | [] -> true | _ -> false (** [hd l] returns the first element of [l]. Requires [l] to be nonempty, at type-checking time. Named as in: OCaml, F#, Coq *) val hd: l:list 'a{Cons? l} -> Tot 'a let hd = function | hd::_ -> hd (** [tail l] returns [l] without its first element. Requires, at type-checking time, that [l] be nonempty. Similar to: tl in OCaml, F#, Coq *) val tail: l:list 'a {Cons? l} -> Tot (list 'a) let tail = function | _::tl -> tl (** [tl l] returns [l] without its first element. Requires, at type-checking time, that [l] be nonempty. Named as in: OCaml, F#, Coq *) val tl: l:list 'a {Cons? l} -> Tot (list 'a) let tl = tail (** [last l] returns the last element of [l]. Requires, at type-checking time, that [l] be nonempty. Named as in: Haskell *) val last: l:list 'a {Cons? l} -> Tot 'a let rec last = function | [hd] -> hd | _::tl -> last tl (** [init l] returns [l] without its last element. Requires, at type-checking time, that [l] be nonempty. Named as in: Haskell *) val init: l:list 'a {Cons? l} -> Tot (list 'a) let rec init = function | [_] -> [] | hd::tl -> hd::(init tl) (** [length l] returns the total number of elements in [l]. Named as in: OCaml, F#, Coq *) val length: list 'a -> Tot nat let rec length = function | [] -> 0 | _::tl -> 1 + length tl (** [nth l n] returns the [n]-th element in list [l] (with the first element being the 0-th) if [l] is long enough, or [None] otherwise. Named as in: OCaml, F#, Coq *) val nth: list 'a -> nat -> Tot (option 'a) let rec nth l n = match l with | [] -> None | hd::tl -> if n = 0 then Some hd else nth tl (n - 1) (** [index l n] returns the [n]-th element in list [l] (with the first element being the 0-th). Requires, at type-checking time, that [l] be of length at least [n+1]. *) val index: #a:Type -> l:list a -> i:nat{i < length l} -> Tot a let rec index #a (l: list a) (i:nat{i < length l}): Tot a = if i = 0 then hd l else index (tl l) (i - 1) (** [count x l] returns the number of occurrences of [x] in [l]. Requires, at type-checking time, the type of [a] to have equality defined. Similar to: [List.count_occ] in Coq. *) val count: #a:eqtype -> a -> list a -> Tot nat let rec count #a x = function | [] -> 0 | hd::tl -> if x=hd then 1 + count x tl else count x tl (** [rev_acc l1 l2] appends the elements of [l1] to the beginning of [l2], in reverse order. It is equivalent to [append (rev l1) l2], but is tail-recursive. Similar to: [List.rev_append] in OCaml, Coq. *) val rev_acc: list 'a -> list 'a -> Tot (list 'a) let rec rev_acc l acc = match l with | [] -> acc | hd::tl -> rev_acc tl (hd::acc) (** [rev l] returns the list [l] in reverse order. Named as in: OCaml, F#, Coq. *) val rev: list 'a -> Tot (list 'a) let rev l = rev_acc l [] (** [append l1 l2] appends the elements of [l2] to the end of [l1]. Named as: OCaml, F#. Similar to: [List.app] in Coq. *) val append: list 'a -> list 'a -> Tot (list 'a) let rec append x y = match x with | [] -> y | a::tl -> a::append tl y (** Defines notation [@@] for [append], as in OCaml, F# . *) let op_At x y = append x y (** [snoc (l, x)] adds [x] to the end of the list [l]. Note: We use an uncurried [snoc (l, x)] instead of the curried [snoc l x]. This is intentional. If [snoc] takes a pair instead of 2 arguments, it allows for a better pattern on [lemma_unsnoc_snoc], which connects [snoc] and [unsnoc]. In particular, if we had two arguments, then either the pattern would either be too restrictive or would lead to over-triggering. More context for this can be seen in the (collapsed and uncollapsed) comments at https://github.com/FStarLang/FStar/pull/1560 *) val snoc: (list 'a * 'a) -> Tot (list 'a) let snoc (l, x) = append l [x] (** [flatten l], where [l] is a list of lists, returns the list of the elements of the lists in [l], preserving their order. Named as in: OCaml, Coq. *) val flatten: list (list 'a) -> Tot (list 'a) let rec flatten l = match l with | [] -> [] | hd::tl -> append hd (flatten tl) (** [map f l] applies [f] to each element of [l] and returns the list of results, in the order of the original elements in [l]. Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml, Coq, F# *) val map: ('a -> Tot 'b) -> list 'a -> Tot (list 'b) let rec map f x = match x with | [] -> [] | a::tl -> f a::map f tl (** [mapi_init f l n] applies, for each [k], [f (n+k)] to the [k]-th element of [l] and returns the list of results, in the order of the original elements in [l]. Requires, at type-checking time, [f] to be a pure total function. *) val mapi_init: (int -> 'a -> Tot 'b) -> list 'a -> int -> Tot (list 'b) let rec mapi_init f l i = match l with | [] -> [] | hd::tl -> (f i hd)::(mapi_init f tl (i+1)) (** [mapi f l] applies, for each [k], [f k] to the [k]-th element of [l] and returns the list of results, in the order of the original elements in [l]. Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml *) val mapi: (int -> 'a -> Tot 'b) -> list 'a -> Tot (list 'b) let mapi f l = mapi_init f l 0 (** [concatMap f l] applies [f] to each element of [l] and returns the concatenation of the results, in the order of the original elements of [l]. This is equivalent to [flatten (map f l)]. Requires, at type-checking time, [f] to be a pure total function. *) val concatMap: ('a -> Tot (list 'b)) -> list 'a -> Tot (list 'b) let rec concatMap f = function | [] -> [] | a::tl -> let fa = f a in let ftl = concatMap f tl in append fa ftl (** [fold_left f x [y1; y2; ...; yn]] computes (f (... (f x y1) y2) ... yn). Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml, Coq. *) val fold_left: ('a -> 'b -> Tot 'a) -> 'a -> l:list 'b -> Tot 'a (decreases l) let rec fold_left f x l = match l with | [] -> x | hd::tl -> fold_left f (f x hd) tl (** [fold_right f [x1; x2; ...; xn] y] computes (f x1 (f x2 (... (f xn y)) ... )). Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml, Coq *) val fold_right: ('a -> 'b -> Tot 'b) -> list 'a -> 'b -> Tot 'b let rec fold_right f l x = match l with | [] -> x | hd::tl -> f hd (fold_right f tl x) (** [fold_right_gtot] is just like [fold_right], except `f` is a ghost function **) let rec fold_right_gtot (#a:Type) (#b:Type) (l:list a) (f:a -> b -> GTot b) (x:b) : GTot b = match l with | [] -> x | hd::tl -> f hd (fold_right_gtot tl f x) (* We define map in terms of fold, to share simple lemmas *) let map_gtot #a #b (f:a -> GTot b) (x:list a) : GTot (list b) = fold_right_gtot x (fun x tl -> f x :: tl) [] (** [fold_left2 f x [y1; y2; ...; yn] [z1; z2; ...; zn]] computes (f (... (f x y1 z1) y2 z2) ... yn zn). Requires, at type-checking time, [f] to be a pure total function, and the lists [y1; y2; ...; yn] and [z1; z2; ...; zn] to have the same lengths. Named as in: OCaml *) val fold_left2 : f:('a -> 'b -> 'c -> Tot 'a) -> accu:'a -> l1:(list 'b) -> l2:(list 'c) -> Pure 'a (requires (length l1 == length l2)) (ensures (fun _ -> True)) (decreases l1) let rec fold_left2 f accu l1 l2 = match (l1, l2) with | ([], []) -> accu | (a1::l1, a2::l2) -> fold_left2 f (f accu a1 a2) l1 l2 (** Propositional membership (as in Coq). Does not require decidable equality. *) (** [memP x l] holds if, and only if, [x] appears as an element of [l]. Similar to: List.In in Coq. *) let rec memP (#a: Type) (x: a) (l: list a) : Tot Type0 = match l with | [] -> False | y :: q -> x == y \/ memP x q (** List searching **) (** [mem x l] returns [true] if, and only if, [x] appears as an element of [l]. Requires, at type-checking time, the type of elements of [l] to have decidable equality. Named as in: OCaml. See also: List.In in Coq, which is propositional. *) val mem: #a:eqtype -> a -> list a -> Tot bool let rec mem #a x = function | [] -> false | hd::tl -> if hd = x then true else mem x tl (** [contains x l] returns [true] if, and only if, [x] appears as an element of [l]. Requires, at type-checking time, the type of elements of [l] to have decidable equality. It is equivalent to: [mem x l]. TODO: should we rather swap the order of arguments? *) let contains : #a:eqtype -> a -> list a -> Tot bool = mem (** [existsb f l] returns [true] if, and only if, there exists some element [x] in [l] such that [f x] holds. *) val existsb: #a:Type -> f:(a -> Tot bool) -> list a -> Tot bool let rec existsb #a f l = match l with | [] -> false | hd::tl -> if f hd then true else existsb f tl (** [find f l] returns [Some x] for some element [x] appearing in [l] such that [f x] holds, or [None] only if no such [x] exists. *) val find: #a:Type -> f:(a -> Tot bool) -> list a -> Tot (option (x:a{f x})) let rec find #a f l = match l with | [] -> None #(x:a{f x}) //These type annotations are only present because it makes bootstrapping go much faster | hd::tl -> if f hd then Some #(x:a{f x}) hd else find f tl (** Filtering elements of a list [l] through a Boolean pure total predicate [f] *) (** [filter f l] returns [l] with all elements [x] such that [f x] does not hold removed. Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml, Coq *) val filter : #a: Type -> f:(a -> Tot bool) -> l: list a -> Tot (m:list a{forall x. memP x m ==> f x}) let rec filter #a f = function | [] -> [] | hd::tl -> if f hd then hd::filter f tl else filter f tl (** Postcondition on [filter f l]: for any element [x] of [filter f l], [f x] holds. Requires, at type-checking time, [f] to be a pure total function.*) val mem_filter (#a:Type) (f: (a -> Tot bool)) (l: list a) (x: a) : Lemma (requires (memP x (filter f l))) (ensures (f x)) let mem_filter f l x = () (** Postcondition on [filter f l]: stated with [forall]: for any element [x] of [filter f l], [f x] holds. Requires, at type-checking time, [f] to be a pure total function. *) val mem_filter_forall (#a:Type) (f: (a -> Tot bool)) (l: list a) : Lemma (requires True) (ensures (forall x . memP x (filter f l) ==> f x)) [SMTPat (filter f l)] let mem_filter_forall f l = FStar.Classical.ghost_lemma (mem_filter f l) (** [for_all f l] returns [true] if, and only if, for all elements [x] appearing in [l], [f x] holds. Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml. Similar to: List.forallb in Coq *) val for_all: ('a -> Tot bool) -> list 'a -> Tot bool let rec for_all f l = match l with | [] -> true | hd::tl -> if f hd then for_all f tl else false (** Specification for [for_all f l] vs. mem *) let rec for_all_mem (#a: Type) (f: (a -> Tot bool)) (l: list a) : Lemma
false
false
FStar.List.Tot.Base.fst
{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 1, "max_fuel": 8, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": true, "z3cliopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }
null
val for_all_mem (#a: Type) (f: (a -> Tot bool)) (l: list a) : Lemma (for_all f l <==> (forall x. memP x l ==> f x))
[ "recursion" ]
FStar.List.Tot.Base.for_all_mem
{ "file_name": "ulib/FStar.List.Tot.Base.fst", "git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f", "git_url": "https://github.com/FStarLang/FStar.git", "project_name": "FStar" }
f: (_: a -> Prims.bool) -> l: Prims.list a -> FStar.Pervasives.Lemma (ensures FStar.List.Tot.Base.for_all f l <==> (forall (x: a). FStar.List.Tot.Base.memP x l ==> f x))
{ "end_col": 29, "end_line": 316, "start_col": 2, "start_line": 314 }
Prims.Tot
val fold_right: ('a -> 'b -> Tot 'b) -> list 'a -> 'b -> Tot 'b
[ { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]
false
let rec fold_right f l x = match l with | [] -> x | hd::tl -> f hd (fold_right f tl x)
val fold_right: ('a -> 'b -> Tot 'b) -> list 'a -> 'b -> Tot 'b let rec fold_right f l x =
false
null
false
match l with | [] -> x | hd :: tl -> f hd (fold_right f tl x)
{ "checked_file": "FStar.List.Tot.Base.fst.checked", "dependencies": [ "prims.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Classical.fsti.checked" ], "interface_file": false, "source_file": "FStar.List.Tot.Base.fst" }
[ "total" ]
[ "Prims.list", "FStar.List.Tot.Base.fold_right" ]
[]
(* Copyright 2008-2014 Nikhil Swamy and Microsoft Research Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License. *) (** This module defines all pure and total operations on lists that can be used in specifications. It is implemented by FStar_List_Tot_Base.ml, any functional change and/or the addition of new functions MUST be reflected there. @summary Pure total operations on lists *) module FStar.List.Tot.Base (** Base operations *) (** [isEmpty l] returns [true] if and only if [l] is empty *) val isEmpty: list 'a -> Tot bool let isEmpty l = match l with | [] -> true | _ -> false (** [hd l] returns the first element of [l]. Requires [l] to be nonempty, at type-checking time. Named as in: OCaml, F#, Coq *) val hd: l:list 'a{Cons? l} -> Tot 'a let hd = function | hd::_ -> hd (** [tail l] returns [l] without its first element. Requires, at type-checking time, that [l] be nonempty. Similar to: tl in OCaml, F#, Coq *) val tail: l:list 'a {Cons? l} -> Tot (list 'a) let tail = function | _::tl -> tl (** [tl l] returns [l] without its first element. Requires, at type-checking time, that [l] be nonempty. Named as in: OCaml, F#, Coq *) val tl: l:list 'a {Cons? l} -> Tot (list 'a) let tl = tail (** [last l] returns the last element of [l]. Requires, at type-checking time, that [l] be nonempty. Named as in: Haskell *) val last: l:list 'a {Cons? l} -> Tot 'a let rec last = function | [hd] -> hd | _::tl -> last tl (** [init l] returns [l] without its last element. Requires, at type-checking time, that [l] be nonempty. Named as in: Haskell *) val init: l:list 'a {Cons? l} -> Tot (list 'a) let rec init = function | [_] -> [] | hd::tl -> hd::(init tl) (** [length l] returns the total number of elements in [l]. Named as in: OCaml, F#, Coq *) val length: list 'a -> Tot nat let rec length = function | [] -> 0 | _::tl -> 1 + length tl (** [nth l n] returns the [n]-th element in list [l] (with the first element being the 0-th) if [l] is long enough, or [None] otherwise. Named as in: OCaml, F#, Coq *) val nth: list 'a -> nat -> Tot (option 'a) let rec nth l n = match l with | [] -> None | hd::tl -> if n = 0 then Some hd else nth tl (n - 1) (** [index l n] returns the [n]-th element in list [l] (with the first element being the 0-th). Requires, at type-checking time, that [l] be of length at least [n+1]. *) val index: #a:Type -> l:list a -> i:nat{i < length l} -> Tot a let rec index #a (l: list a) (i:nat{i < length l}): Tot a = if i = 0 then hd l else index (tl l) (i - 1) (** [count x l] returns the number of occurrences of [x] in [l]. Requires, at type-checking time, the type of [a] to have equality defined. Similar to: [List.count_occ] in Coq. *) val count: #a:eqtype -> a -> list a -> Tot nat let rec count #a x = function | [] -> 0 | hd::tl -> if x=hd then 1 + count x tl else count x tl (** [rev_acc l1 l2] appends the elements of [l1] to the beginning of [l2], in reverse order. It is equivalent to [append (rev l1) l2], but is tail-recursive. Similar to: [List.rev_append] in OCaml, Coq. *) val rev_acc: list 'a -> list 'a -> Tot (list 'a) let rec rev_acc l acc = match l with | [] -> acc | hd::tl -> rev_acc tl (hd::acc) (** [rev l] returns the list [l] in reverse order. Named as in: OCaml, F#, Coq. *) val rev: list 'a -> Tot (list 'a) let rev l = rev_acc l [] (** [append l1 l2] appends the elements of [l2] to the end of [l1]. Named as: OCaml, F#. Similar to: [List.app] in Coq. *) val append: list 'a -> list 'a -> Tot (list 'a) let rec append x y = match x with | [] -> y | a::tl -> a::append tl y (** Defines notation [@@] for [append], as in OCaml, F# . *) let op_At x y = append x y (** [snoc (l, x)] adds [x] to the end of the list [l]. Note: We use an uncurried [snoc (l, x)] instead of the curried [snoc l x]. This is intentional. If [snoc] takes a pair instead of 2 arguments, it allows for a better pattern on [lemma_unsnoc_snoc], which connects [snoc] and [unsnoc]. In particular, if we had two arguments, then either the pattern would either be too restrictive or would lead to over-triggering. More context for this can be seen in the (collapsed and uncollapsed) comments at https://github.com/FStarLang/FStar/pull/1560 *) val snoc: (list 'a * 'a) -> Tot (list 'a) let snoc (l, x) = append l [x] (** [flatten l], where [l] is a list of lists, returns the list of the elements of the lists in [l], preserving their order. Named as in: OCaml, Coq. *) val flatten: list (list 'a) -> Tot (list 'a) let rec flatten l = match l with | [] -> [] | hd::tl -> append hd (flatten tl) (** [map f l] applies [f] to each element of [l] and returns the list of results, in the order of the original elements in [l]. Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml, Coq, F# *) val map: ('a -> Tot 'b) -> list 'a -> Tot (list 'b) let rec map f x = match x with | [] -> [] | a::tl -> f a::map f tl (** [mapi_init f l n] applies, for each [k], [f (n+k)] to the [k]-th element of [l] and returns the list of results, in the order of the original elements in [l]. Requires, at type-checking time, [f] to be a pure total function. *) val mapi_init: (int -> 'a -> Tot 'b) -> list 'a -> int -> Tot (list 'b) let rec mapi_init f l i = match l with | [] -> [] | hd::tl -> (f i hd)::(mapi_init f tl (i+1)) (** [mapi f l] applies, for each [k], [f k] to the [k]-th element of [l] and returns the list of results, in the order of the original elements in [l]. Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml *) val mapi: (int -> 'a -> Tot 'b) -> list 'a -> Tot (list 'b) let mapi f l = mapi_init f l 0 (** [concatMap f l] applies [f] to each element of [l] and returns the concatenation of the results, in the order of the original elements of [l]. This is equivalent to [flatten (map f l)]. Requires, at type-checking time, [f] to be a pure total function. *) val concatMap: ('a -> Tot (list 'b)) -> list 'a -> Tot (list 'b) let rec concatMap f = function | [] -> [] | a::tl -> let fa = f a in let ftl = concatMap f tl in append fa ftl (** [fold_left f x [y1; y2; ...; yn]] computes (f (... (f x y1) y2) ... yn). Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml, Coq. *) val fold_left: ('a -> 'b -> Tot 'a) -> 'a -> l:list 'b -> Tot 'a (decreases l) let rec fold_left f x l = match l with | [] -> x | hd::tl -> fold_left f (f x hd) tl (** [fold_right f [x1; x2; ...; xn] y] computes (f x1 (f x2 (... (f xn y)) ... )). Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml, Coq *)
false
false
FStar.List.Tot.Base.fst
{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 1, "max_fuel": 8, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": true, "z3cliopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }
null
val fold_right: ('a -> 'b -> Tot 'b) -> list 'a -> 'b -> Tot 'b
[ "recursion" ]
FStar.List.Tot.Base.fold_right
{ "file_name": "ulib/FStar.List.Tot.Base.fst", "git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f", "git_url": "https://github.com/FStarLang/FStar.git", "project_name": "FStar" }
f: (_: 'a -> _: 'b -> 'b) -> l: Prims.list 'a -> x: 'b -> 'b
{ "end_col": 38, "end_line": 197, "start_col": 27, "start_line": 195 }
Prims.Tot
val rev_acc: list 'a -> list 'a -> Tot (list 'a)
[ { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]
false
let rec rev_acc l acc = match l with | [] -> acc | hd::tl -> rev_acc tl (hd::acc)
val rev_acc: list 'a -> list 'a -> Tot (list 'a) let rec rev_acc l acc =
false
null
false
match l with | [] -> acc | hd :: tl -> rev_acc tl (hd :: acc)
{ "checked_file": "FStar.List.Tot.Base.fst.checked", "dependencies": [ "prims.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Classical.fsti.checked" ], "interface_file": false, "source_file": "FStar.List.Tot.Base.fst" }
[ "total" ]
[ "Prims.list", "FStar.List.Tot.Base.rev_acc", "Prims.Cons" ]
[]
(* Copyright 2008-2014 Nikhil Swamy and Microsoft Research Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License. *) (** This module defines all pure and total operations on lists that can be used in specifications. It is implemented by FStar_List_Tot_Base.ml, any functional change and/or the addition of new functions MUST be reflected there. @summary Pure total operations on lists *) module FStar.List.Tot.Base (** Base operations *) (** [isEmpty l] returns [true] if and only if [l] is empty *) val isEmpty: list 'a -> Tot bool let isEmpty l = match l with | [] -> true | _ -> false (** [hd l] returns the first element of [l]. Requires [l] to be nonempty, at type-checking time. Named as in: OCaml, F#, Coq *) val hd: l:list 'a{Cons? l} -> Tot 'a let hd = function | hd::_ -> hd (** [tail l] returns [l] without its first element. Requires, at type-checking time, that [l] be nonempty. Similar to: tl in OCaml, F#, Coq *) val tail: l:list 'a {Cons? l} -> Tot (list 'a) let tail = function | _::tl -> tl (** [tl l] returns [l] without its first element. Requires, at type-checking time, that [l] be nonempty. Named as in: OCaml, F#, Coq *) val tl: l:list 'a {Cons? l} -> Tot (list 'a) let tl = tail (** [last l] returns the last element of [l]. Requires, at type-checking time, that [l] be nonempty. Named as in: Haskell *) val last: l:list 'a {Cons? l} -> Tot 'a let rec last = function | [hd] -> hd | _::tl -> last tl (** [init l] returns [l] without its last element. Requires, at type-checking time, that [l] be nonempty. Named as in: Haskell *) val init: l:list 'a {Cons? l} -> Tot (list 'a) let rec init = function | [_] -> [] | hd::tl -> hd::(init tl) (** [length l] returns the total number of elements in [l]. Named as in: OCaml, F#, Coq *) val length: list 'a -> Tot nat let rec length = function | [] -> 0 | _::tl -> 1 + length tl (** [nth l n] returns the [n]-th element in list [l] (with the first element being the 0-th) if [l] is long enough, or [None] otherwise. Named as in: OCaml, F#, Coq *) val nth: list 'a -> nat -> Tot (option 'a) let rec nth l n = match l with | [] -> None | hd::tl -> if n = 0 then Some hd else nth tl (n - 1) (** [index l n] returns the [n]-th element in list [l] (with the first element being the 0-th). Requires, at type-checking time, that [l] be of length at least [n+1]. *) val index: #a:Type -> l:list a -> i:nat{i < length l} -> Tot a let rec index #a (l: list a) (i:nat{i < length l}): Tot a = if i = 0 then hd l else index (tl l) (i - 1) (** [count x l] returns the number of occurrences of [x] in [l]. Requires, at type-checking time, the type of [a] to have equality defined. Similar to: [List.count_occ] in Coq. *) val count: #a:eqtype -> a -> list a -> Tot nat let rec count #a x = function | [] -> 0 | hd::tl -> if x=hd then 1 + count x tl else count x tl (** [rev_acc l1 l2] appends the elements of [l1] to the beginning of [l2], in reverse order. It is equivalent to [append (rev l1) l2], but is tail-recursive. Similar to: [List.rev_append] in OCaml, Coq. *)
false
false
FStar.List.Tot.Base.fst
{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 1, "max_fuel": 8, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": true, "z3cliopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }
null
val rev_acc: list 'a -> list 'a -> Tot (list 'a)
[ "recursion" ]
FStar.List.Tot.Base.rev_acc
{ "file_name": "ulib/FStar.List.Tot.Base.fst", "git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f", "git_url": "https://github.com/FStarLang/FStar.git", "project_name": "FStar" }
l: Prims.list 'a -> acc: Prims.list 'a -> Prims.list 'a
{ "end_col": 36, "end_line": 110, "start_col": 24, "start_line": 108 }
Prims.Tot
val existsb: #a:Type -> f:(a -> Tot bool) -> list a -> Tot bool
[ { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]
false
let rec existsb #a f l = match l with | [] -> false | hd::tl -> if f hd then true else existsb f tl
val existsb: #a:Type -> f:(a -> Tot bool) -> list a -> Tot bool let rec existsb #a f l =
false
null
false
match l with | [] -> false | hd :: tl -> if f hd then true else existsb f tl
{ "checked_file": "FStar.List.Tot.Base.fst.checked", "dependencies": [ "prims.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Classical.fsti.checked" ], "interface_file": false, "source_file": "FStar.List.Tot.Base.fst" }
[ "total" ]
[ "Prims.bool", "Prims.list", "FStar.List.Tot.Base.existsb" ]
[]
(* Copyright 2008-2014 Nikhil Swamy and Microsoft Research Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License. *) (** This module defines all pure and total operations on lists that can be used in specifications. It is implemented by FStar_List_Tot_Base.ml, any functional change and/or the addition of new functions MUST be reflected there. @summary Pure total operations on lists *) module FStar.List.Tot.Base (** Base operations *) (** [isEmpty l] returns [true] if and only if [l] is empty *) val isEmpty: list 'a -> Tot bool let isEmpty l = match l with | [] -> true | _ -> false (** [hd l] returns the first element of [l]. Requires [l] to be nonempty, at type-checking time. Named as in: OCaml, F#, Coq *) val hd: l:list 'a{Cons? l} -> Tot 'a let hd = function | hd::_ -> hd (** [tail l] returns [l] without its first element. Requires, at type-checking time, that [l] be nonempty. Similar to: tl in OCaml, F#, Coq *) val tail: l:list 'a {Cons? l} -> Tot (list 'a) let tail = function | _::tl -> tl (** [tl l] returns [l] without its first element. Requires, at type-checking time, that [l] be nonempty. Named as in: OCaml, F#, Coq *) val tl: l:list 'a {Cons? l} -> Tot (list 'a) let tl = tail (** [last l] returns the last element of [l]. Requires, at type-checking time, that [l] be nonempty. Named as in: Haskell *) val last: l:list 'a {Cons? l} -> Tot 'a let rec last = function | [hd] -> hd | _::tl -> last tl (** [init l] returns [l] without its last element. Requires, at type-checking time, that [l] be nonempty. Named as in: Haskell *) val init: l:list 'a {Cons? l} -> Tot (list 'a) let rec init = function | [_] -> [] | hd::tl -> hd::(init tl) (** [length l] returns the total number of elements in [l]. Named as in: OCaml, F#, Coq *) val length: list 'a -> Tot nat let rec length = function | [] -> 0 | _::tl -> 1 + length tl (** [nth l n] returns the [n]-th element in list [l] (with the first element being the 0-th) if [l] is long enough, or [None] otherwise. Named as in: OCaml, F#, Coq *) val nth: list 'a -> nat -> Tot (option 'a) let rec nth l n = match l with | [] -> None | hd::tl -> if n = 0 then Some hd else nth tl (n - 1) (** [index l n] returns the [n]-th element in list [l] (with the first element being the 0-th). Requires, at type-checking time, that [l] be of length at least [n+1]. *) val index: #a:Type -> l:list a -> i:nat{i < length l} -> Tot a let rec index #a (l: list a) (i:nat{i < length l}): Tot a = if i = 0 then hd l else index (tl l) (i - 1) (** [count x l] returns the number of occurrences of [x] in [l]. Requires, at type-checking time, the type of [a] to have equality defined. Similar to: [List.count_occ] in Coq. *) val count: #a:eqtype -> a -> list a -> Tot nat let rec count #a x = function | [] -> 0 | hd::tl -> if x=hd then 1 + count x tl else count x tl (** [rev_acc l1 l2] appends the elements of [l1] to the beginning of [l2], in reverse order. It is equivalent to [append (rev l1) l2], but is tail-recursive. Similar to: [List.rev_append] in OCaml, Coq. *) val rev_acc: list 'a -> list 'a -> Tot (list 'a) let rec rev_acc l acc = match l with | [] -> acc | hd::tl -> rev_acc tl (hd::acc) (** [rev l] returns the list [l] in reverse order. Named as in: OCaml, F#, Coq. *) val rev: list 'a -> Tot (list 'a) let rev l = rev_acc l [] (** [append l1 l2] appends the elements of [l2] to the end of [l1]. Named as: OCaml, F#. Similar to: [List.app] in Coq. *) val append: list 'a -> list 'a -> Tot (list 'a) let rec append x y = match x with | [] -> y | a::tl -> a::append tl y (** Defines notation [@@] for [append], as in OCaml, F# . *) let op_At x y = append x y (** [snoc (l, x)] adds [x] to the end of the list [l]. Note: We use an uncurried [snoc (l, x)] instead of the curried [snoc l x]. This is intentional. If [snoc] takes a pair instead of 2 arguments, it allows for a better pattern on [lemma_unsnoc_snoc], which connects [snoc] and [unsnoc]. In particular, if we had two arguments, then either the pattern would either be too restrictive or would lead to over-triggering. More context for this can be seen in the (collapsed and uncollapsed) comments at https://github.com/FStarLang/FStar/pull/1560 *) val snoc: (list 'a * 'a) -> Tot (list 'a) let snoc (l, x) = append l [x] (** [flatten l], where [l] is a list of lists, returns the list of the elements of the lists in [l], preserving their order. Named as in: OCaml, Coq. *) val flatten: list (list 'a) -> Tot (list 'a) let rec flatten l = match l with | [] -> [] | hd::tl -> append hd (flatten tl) (** [map f l] applies [f] to each element of [l] and returns the list of results, in the order of the original elements in [l]. Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml, Coq, F# *) val map: ('a -> Tot 'b) -> list 'a -> Tot (list 'b) let rec map f x = match x with | [] -> [] | a::tl -> f a::map f tl (** [mapi_init f l n] applies, for each [k], [f (n+k)] to the [k]-th element of [l] and returns the list of results, in the order of the original elements in [l]. Requires, at type-checking time, [f] to be a pure total function. *) val mapi_init: (int -> 'a -> Tot 'b) -> list 'a -> int -> Tot (list 'b) let rec mapi_init f l i = match l with | [] -> [] | hd::tl -> (f i hd)::(mapi_init f tl (i+1)) (** [mapi f l] applies, for each [k], [f k] to the [k]-th element of [l] and returns the list of results, in the order of the original elements in [l]. Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml *) val mapi: (int -> 'a -> Tot 'b) -> list 'a -> Tot (list 'b) let mapi f l = mapi_init f l 0 (** [concatMap f l] applies [f] to each element of [l] and returns the concatenation of the results, in the order of the original elements of [l]. This is equivalent to [flatten (map f l)]. Requires, at type-checking time, [f] to be a pure total function. *) val concatMap: ('a -> Tot (list 'b)) -> list 'a -> Tot (list 'b) let rec concatMap f = function | [] -> [] | a::tl -> let fa = f a in let ftl = concatMap f tl in append fa ftl (** [fold_left f x [y1; y2; ...; yn]] computes (f (... (f x y1) y2) ... yn). Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml, Coq. *) val fold_left: ('a -> 'b -> Tot 'a) -> 'a -> l:list 'b -> Tot 'a (decreases l) let rec fold_left f x l = match l with | [] -> x | hd::tl -> fold_left f (f x hd) tl (** [fold_right f [x1; x2; ...; xn] y] computes (f x1 (f x2 (... (f xn y)) ... )). Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml, Coq *) val fold_right: ('a -> 'b -> Tot 'b) -> list 'a -> 'b -> Tot 'b let rec fold_right f l x = match l with | [] -> x | hd::tl -> f hd (fold_right f tl x) (** [fold_right_gtot] is just like [fold_right], except `f` is a ghost function **) let rec fold_right_gtot (#a:Type) (#b:Type) (l:list a) (f:a -> b -> GTot b) (x:b) : GTot b = match l with | [] -> x | hd::tl -> f hd (fold_right_gtot tl f x) (* We define map in terms of fold, to share simple lemmas *) let map_gtot #a #b (f:a -> GTot b) (x:list a) : GTot (list b) = fold_right_gtot x (fun x tl -> f x :: tl) [] (** [fold_left2 f x [y1; y2; ...; yn] [z1; z2; ...; zn]] computes (f (... (f x y1 z1) y2 z2) ... yn zn). Requires, at type-checking time, [f] to be a pure total function, and the lists [y1; y2; ...; yn] and [z1; z2; ...; zn] to have the same lengths. Named as in: OCaml *) val fold_left2 : f:('a -> 'b -> 'c -> Tot 'a) -> accu:'a -> l1:(list 'b) -> l2:(list 'c) -> Pure 'a (requires (length l1 == length l2)) (ensures (fun _ -> True)) (decreases l1) let rec fold_left2 f accu l1 l2 = match (l1, l2) with | ([], []) -> accu | (a1::l1, a2::l2) -> fold_left2 f (f accu a1 a2) l1 l2 (** Propositional membership (as in Coq). Does not require decidable equality. *) (** [memP x l] holds if, and only if, [x] appears as an element of [l]. Similar to: List.In in Coq. *) let rec memP (#a: Type) (x: a) (l: list a) : Tot Type0 = match l with | [] -> False | y :: q -> x == y \/ memP x q (** List searching **) (** [mem x l] returns [true] if, and only if, [x] appears as an element of [l]. Requires, at type-checking time, the type of elements of [l] to have decidable equality. Named as in: OCaml. See also: List.In in Coq, which is propositional. *) val mem: #a:eqtype -> a -> list a -> Tot bool let rec mem #a x = function | [] -> false | hd::tl -> if hd = x then true else mem x tl (** [contains x l] returns [true] if, and only if, [x] appears as an element of [l]. Requires, at type-checking time, the type of elements of [l] to have decidable equality. It is equivalent to: [mem x l]. TODO: should we rather swap the order of arguments? *) let contains : #a:eqtype -> a -> list a -> Tot bool = mem (** [existsb f l] returns [true] if, and only if, there exists some element [x] in [l] such that [f x] holds. *) val existsb: #a:Type -> f:(a -> Tot bool) -> list a
false
false
FStar.List.Tot.Base.fst
{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 1, "max_fuel": 8, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": true, "z3cliopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }
null
val existsb: #a:Type -> f:(a -> Tot bool) -> list a -> Tot bool
[ "recursion" ]
FStar.List.Tot.Base.existsb
{ "file_name": "ulib/FStar.List.Tot.Base.fst", "git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f", "git_url": "https://github.com/FStarLang/FStar.git", "project_name": "FStar" }
f: (_: a -> Prims.bool) -> l: Prims.list a -> Prims.bool
{ "end_col": 48, "end_line": 258, "start_col": 25, "start_line": 256 }
Prims.Tot
val memP (#a: Type) (x: a) (l: list a) : Tot Type0
[ { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]
false
let rec memP (#a: Type) (x: a) (l: list a) : Tot Type0 = match l with | [] -> False | y :: q -> x == y \/ memP x q
val memP (#a: Type) (x: a) (l: list a) : Tot Type0 let rec memP (#a: Type) (x: a) (l: list a) : Tot Type0 =
false
null
false
match l with | [] -> False | y :: q -> x == y \/ memP x q
{ "checked_file": "FStar.List.Tot.Base.fst.checked", "dependencies": [ "prims.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Classical.fsti.checked" ], "interface_file": false, "source_file": "FStar.List.Tot.Base.fst" }
[ "total" ]
[ "Prims.list", "Prims.l_False", "Prims.l_or", "Prims.eq2", "FStar.List.Tot.Base.memP" ]
[]
(* Copyright 2008-2014 Nikhil Swamy and Microsoft Research Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License. *) (** This module defines all pure and total operations on lists that can be used in specifications. It is implemented by FStar_List_Tot_Base.ml, any functional change and/or the addition of new functions MUST be reflected there. @summary Pure total operations on lists *) module FStar.List.Tot.Base (** Base operations *) (** [isEmpty l] returns [true] if and only if [l] is empty *) val isEmpty: list 'a -> Tot bool let isEmpty l = match l with | [] -> true | _ -> false (** [hd l] returns the first element of [l]. Requires [l] to be nonempty, at type-checking time. Named as in: OCaml, F#, Coq *) val hd: l:list 'a{Cons? l} -> Tot 'a let hd = function | hd::_ -> hd (** [tail l] returns [l] without its first element. Requires, at type-checking time, that [l] be nonempty. Similar to: tl in OCaml, F#, Coq *) val tail: l:list 'a {Cons? l} -> Tot (list 'a) let tail = function | _::tl -> tl (** [tl l] returns [l] without its first element. Requires, at type-checking time, that [l] be nonempty. Named as in: OCaml, F#, Coq *) val tl: l:list 'a {Cons? l} -> Tot (list 'a) let tl = tail (** [last l] returns the last element of [l]. Requires, at type-checking time, that [l] be nonempty. Named as in: Haskell *) val last: l:list 'a {Cons? l} -> Tot 'a let rec last = function | [hd] -> hd | _::tl -> last tl (** [init l] returns [l] without its last element. Requires, at type-checking time, that [l] be nonempty. Named as in: Haskell *) val init: l:list 'a {Cons? l} -> Tot (list 'a) let rec init = function | [_] -> [] | hd::tl -> hd::(init tl) (** [length l] returns the total number of elements in [l]. Named as in: OCaml, F#, Coq *) val length: list 'a -> Tot nat let rec length = function | [] -> 0 | _::tl -> 1 + length tl (** [nth l n] returns the [n]-th element in list [l] (with the first element being the 0-th) if [l] is long enough, or [None] otherwise. Named as in: OCaml, F#, Coq *) val nth: list 'a -> nat -> Tot (option 'a) let rec nth l n = match l with | [] -> None | hd::tl -> if n = 0 then Some hd else nth tl (n - 1) (** [index l n] returns the [n]-th element in list [l] (with the first element being the 0-th). Requires, at type-checking time, that [l] be of length at least [n+1]. *) val index: #a:Type -> l:list a -> i:nat{i < length l} -> Tot a let rec index #a (l: list a) (i:nat{i < length l}): Tot a = if i = 0 then hd l else index (tl l) (i - 1) (** [count x l] returns the number of occurrences of [x] in [l]. Requires, at type-checking time, the type of [a] to have equality defined. Similar to: [List.count_occ] in Coq. *) val count: #a:eqtype -> a -> list a -> Tot nat let rec count #a x = function | [] -> 0 | hd::tl -> if x=hd then 1 + count x tl else count x tl (** [rev_acc l1 l2] appends the elements of [l1] to the beginning of [l2], in reverse order. It is equivalent to [append (rev l1) l2], but is tail-recursive. Similar to: [List.rev_append] in OCaml, Coq. *) val rev_acc: list 'a -> list 'a -> Tot (list 'a) let rec rev_acc l acc = match l with | [] -> acc | hd::tl -> rev_acc tl (hd::acc) (** [rev l] returns the list [l] in reverse order. Named as in: OCaml, F#, Coq. *) val rev: list 'a -> Tot (list 'a) let rev l = rev_acc l [] (** [append l1 l2] appends the elements of [l2] to the end of [l1]. Named as: OCaml, F#. Similar to: [List.app] in Coq. *) val append: list 'a -> list 'a -> Tot (list 'a) let rec append x y = match x with | [] -> y | a::tl -> a::append tl y (** Defines notation [@@] for [append], as in OCaml, F# . *) let op_At x y = append x y (** [snoc (l, x)] adds [x] to the end of the list [l]. Note: We use an uncurried [snoc (l, x)] instead of the curried [snoc l x]. This is intentional. If [snoc] takes a pair instead of 2 arguments, it allows for a better pattern on [lemma_unsnoc_snoc], which connects [snoc] and [unsnoc]. In particular, if we had two arguments, then either the pattern would either be too restrictive or would lead to over-triggering. More context for this can be seen in the (collapsed and uncollapsed) comments at https://github.com/FStarLang/FStar/pull/1560 *) val snoc: (list 'a * 'a) -> Tot (list 'a) let snoc (l, x) = append l [x] (** [flatten l], where [l] is a list of lists, returns the list of the elements of the lists in [l], preserving their order. Named as in: OCaml, Coq. *) val flatten: list (list 'a) -> Tot (list 'a) let rec flatten l = match l with | [] -> [] | hd::tl -> append hd (flatten tl) (** [map f l] applies [f] to each element of [l] and returns the list of results, in the order of the original elements in [l]. Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml, Coq, F# *) val map: ('a -> Tot 'b) -> list 'a -> Tot (list 'b) let rec map f x = match x with | [] -> [] | a::tl -> f a::map f tl (** [mapi_init f l n] applies, for each [k], [f (n+k)] to the [k]-th element of [l] and returns the list of results, in the order of the original elements in [l]. Requires, at type-checking time, [f] to be a pure total function. *) val mapi_init: (int -> 'a -> Tot 'b) -> list 'a -> int -> Tot (list 'b) let rec mapi_init f l i = match l with | [] -> [] | hd::tl -> (f i hd)::(mapi_init f tl (i+1)) (** [mapi f l] applies, for each [k], [f k] to the [k]-th element of [l] and returns the list of results, in the order of the original elements in [l]. Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml *) val mapi: (int -> 'a -> Tot 'b) -> list 'a -> Tot (list 'b) let mapi f l = mapi_init f l 0 (** [concatMap f l] applies [f] to each element of [l] and returns the concatenation of the results, in the order of the original elements of [l]. This is equivalent to [flatten (map f l)]. Requires, at type-checking time, [f] to be a pure total function. *) val concatMap: ('a -> Tot (list 'b)) -> list 'a -> Tot (list 'b) let rec concatMap f = function | [] -> [] | a::tl -> let fa = f a in let ftl = concatMap f tl in append fa ftl (** [fold_left f x [y1; y2; ...; yn]] computes (f (... (f x y1) y2) ... yn). Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml, Coq. *) val fold_left: ('a -> 'b -> Tot 'a) -> 'a -> l:list 'b -> Tot 'a (decreases l) let rec fold_left f x l = match l with | [] -> x | hd::tl -> fold_left f (f x hd) tl (** [fold_right f [x1; x2; ...; xn] y] computes (f x1 (f x2 (... (f xn y)) ... )). Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml, Coq *) val fold_right: ('a -> 'b -> Tot 'b) -> list 'a -> 'b -> Tot 'b let rec fold_right f l x = match l with | [] -> x | hd::tl -> f hd (fold_right f tl x) (** [fold_right_gtot] is just like [fold_right], except `f` is a ghost function **) let rec fold_right_gtot (#a:Type) (#b:Type) (l:list a) (f:a -> b -> GTot b) (x:b) : GTot b = match l with | [] -> x | hd::tl -> f hd (fold_right_gtot tl f x) (* We define map in terms of fold, to share simple lemmas *) let map_gtot #a #b (f:a -> GTot b) (x:list a) : GTot (list b) = fold_right_gtot x (fun x tl -> f x :: tl) [] (** [fold_left2 f x [y1; y2; ...; yn] [z1; z2; ...; zn]] computes (f (... (f x y1 z1) y2 z2) ... yn zn). Requires, at type-checking time, [f] to be a pure total function, and the lists [y1; y2; ...; yn] and [z1; z2; ...; zn] to have the same lengths. Named as in: OCaml *) val fold_left2 : f:('a -> 'b -> 'c -> Tot 'a) -> accu:'a -> l1:(list 'b) -> l2:(list 'c) -> Pure 'a (requires (length l1 == length l2)) (ensures (fun _ -> True)) (decreases l1) let rec fold_left2 f accu l1 l2 = match (l1, l2) with | ([], []) -> accu | (a1::l1, a2::l2) -> fold_left2 f (f accu a1 a2) l1 l2 (** Propositional membership (as in Coq). Does not require decidable equality. *) (** [memP x l] holds if, and only if, [x] appears as an element of [l]. Similar to: List.In in Coq. *)
false
false
FStar.List.Tot.Base.fst
{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 1, "max_fuel": 8, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": true, "z3cliopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }
null
val memP (#a: Type) (x: a) (l: list a) : Tot Type0
[ "recursion" ]
FStar.List.Tot.Base.memP
{ "file_name": "ulib/FStar.List.Tot.Base.fst", "git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f", "git_url": "https://github.com/FStarLang/FStar.git", "project_name": "FStar" }
x: a -> l: Prims.list a -> Type0
{ "end_col": 32, "end_line": 231, "start_col": 2, "start_line": 229 }
Prims.Tot
val filter : #a: Type -> f:(a -> Tot bool) -> l: list a -> Tot (m:list a{forall x. memP x m ==> f x})
[ { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]
false
let rec filter #a f = function | [] -> [] | hd::tl -> if f hd then hd::filter f tl else filter f tl
val filter : #a: Type -> f:(a -> Tot bool) -> l: list a -> Tot (m:list a{forall x. memP x m ==> f x}) let rec filter #a f =
false
null
false
function | [] -> [] | hd :: tl -> if f hd then hd :: filter f tl else filter f tl
{ "checked_file": "FStar.List.Tot.Base.fst.checked", "dependencies": [ "prims.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Classical.fsti.checked" ], "interface_file": false, "source_file": "FStar.List.Tot.Base.fst" }
[ "total" ]
[ "Prims.bool", "Prims.list", "Prims.Nil", "Prims.Cons", "FStar.List.Tot.Base.filter", "Prims.l_Forall", "Prims.l_imp", "FStar.List.Tot.Base.memP", "Prims.b2t" ]
[]
(* Copyright 2008-2014 Nikhil Swamy and Microsoft Research Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License. *) (** This module defines all pure and total operations on lists that can be used in specifications. It is implemented by FStar_List_Tot_Base.ml, any functional change and/or the addition of new functions MUST be reflected there. @summary Pure total operations on lists *) module FStar.List.Tot.Base (** Base operations *) (** [isEmpty l] returns [true] if and only if [l] is empty *) val isEmpty: list 'a -> Tot bool let isEmpty l = match l with | [] -> true | _ -> false (** [hd l] returns the first element of [l]. Requires [l] to be nonempty, at type-checking time. Named as in: OCaml, F#, Coq *) val hd: l:list 'a{Cons? l} -> Tot 'a let hd = function | hd::_ -> hd (** [tail l] returns [l] without its first element. Requires, at type-checking time, that [l] be nonempty. Similar to: tl in OCaml, F#, Coq *) val tail: l:list 'a {Cons? l} -> Tot (list 'a) let tail = function | _::tl -> tl (** [tl l] returns [l] without its first element. Requires, at type-checking time, that [l] be nonempty. Named as in: OCaml, F#, Coq *) val tl: l:list 'a {Cons? l} -> Tot (list 'a) let tl = tail (** [last l] returns the last element of [l]. Requires, at type-checking time, that [l] be nonempty. Named as in: Haskell *) val last: l:list 'a {Cons? l} -> Tot 'a let rec last = function | [hd] -> hd | _::tl -> last tl (** [init l] returns [l] without its last element. Requires, at type-checking time, that [l] be nonempty. Named as in: Haskell *) val init: l:list 'a {Cons? l} -> Tot (list 'a) let rec init = function | [_] -> [] | hd::tl -> hd::(init tl) (** [length l] returns the total number of elements in [l]. Named as in: OCaml, F#, Coq *) val length: list 'a -> Tot nat let rec length = function | [] -> 0 | _::tl -> 1 + length tl (** [nth l n] returns the [n]-th element in list [l] (with the first element being the 0-th) if [l] is long enough, or [None] otherwise. Named as in: OCaml, F#, Coq *) val nth: list 'a -> nat -> Tot (option 'a) let rec nth l n = match l with | [] -> None | hd::tl -> if n = 0 then Some hd else nth tl (n - 1) (** [index l n] returns the [n]-th element in list [l] (with the first element being the 0-th). Requires, at type-checking time, that [l] be of length at least [n+1]. *) val index: #a:Type -> l:list a -> i:nat{i < length l} -> Tot a let rec index #a (l: list a) (i:nat{i < length l}): Tot a = if i = 0 then hd l else index (tl l) (i - 1) (** [count x l] returns the number of occurrences of [x] in [l]. Requires, at type-checking time, the type of [a] to have equality defined. Similar to: [List.count_occ] in Coq. *) val count: #a:eqtype -> a -> list a -> Tot nat let rec count #a x = function | [] -> 0 | hd::tl -> if x=hd then 1 + count x tl else count x tl (** [rev_acc l1 l2] appends the elements of [l1] to the beginning of [l2], in reverse order. It is equivalent to [append (rev l1) l2], but is tail-recursive. Similar to: [List.rev_append] in OCaml, Coq. *) val rev_acc: list 'a -> list 'a -> Tot (list 'a) let rec rev_acc l acc = match l with | [] -> acc | hd::tl -> rev_acc tl (hd::acc) (** [rev l] returns the list [l] in reverse order. Named as in: OCaml, F#, Coq. *) val rev: list 'a -> Tot (list 'a) let rev l = rev_acc l [] (** [append l1 l2] appends the elements of [l2] to the end of [l1]. Named as: OCaml, F#. Similar to: [List.app] in Coq. *) val append: list 'a -> list 'a -> Tot (list 'a) let rec append x y = match x with | [] -> y | a::tl -> a::append tl y (** Defines notation [@@] for [append], as in OCaml, F# . *) let op_At x y = append x y (** [snoc (l, x)] adds [x] to the end of the list [l]. Note: We use an uncurried [snoc (l, x)] instead of the curried [snoc l x]. This is intentional. If [snoc] takes a pair instead of 2 arguments, it allows for a better pattern on [lemma_unsnoc_snoc], which connects [snoc] and [unsnoc]. In particular, if we had two arguments, then either the pattern would either be too restrictive or would lead to over-triggering. More context for this can be seen in the (collapsed and uncollapsed) comments at https://github.com/FStarLang/FStar/pull/1560 *) val snoc: (list 'a * 'a) -> Tot (list 'a) let snoc (l, x) = append l [x] (** [flatten l], where [l] is a list of lists, returns the list of the elements of the lists in [l], preserving their order. Named as in: OCaml, Coq. *) val flatten: list (list 'a) -> Tot (list 'a) let rec flatten l = match l with | [] -> [] | hd::tl -> append hd (flatten tl) (** [map f l] applies [f] to each element of [l] and returns the list of results, in the order of the original elements in [l]. Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml, Coq, F# *) val map: ('a -> Tot 'b) -> list 'a -> Tot (list 'b) let rec map f x = match x with | [] -> [] | a::tl -> f a::map f tl (** [mapi_init f l n] applies, for each [k], [f (n+k)] to the [k]-th element of [l] and returns the list of results, in the order of the original elements in [l]. Requires, at type-checking time, [f] to be a pure total function. *) val mapi_init: (int -> 'a -> Tot 'b) -> list 'a -> int -> Tot (list 'b) let rec mapi_init f l i = match l with | [] -> [] | hd::tl -> (f i hd)::(mapi_init f tl (i+1)) (** [mapi f l] applies, for each [k], [f k] to the [k]-th element of [l] and returns the list of results, in the order of the original elements in [l]. Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml *) val mapi: (int -> 'a -> Tot 'b) -> list 'a -> Tot (list 'b) let mapi f l = mapi_init f l 0 (** [concatMap f l] applies [f] to each element of [l] and returns the concatenation of the results, in the order of the original elements of [l]. This is equivalent to [flatten (map f l)]. Requires, at type-checking time, [f] to be a pure total function. *) val concatMap: ('a -> Tot (list 'b)) -> list 'a -> Tot (list 'b) let rec concatMap f = function | [] -> [] | a::tl -> let fa = f a in let ftl = concatMap f tl in append fa ftl (** [fold_left f x [y1; y2; ...; yn]] computes (f (... (f x y1) y2) ... yn). Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml, Coq. *) val fold_left: ('a -> 'b -> Tot 'a) -> 'a -> l:list 'b -> Tot 'a (decreases l) let rec fold_left f x l = match l with | [] -> x | hd::tl -> fold_left f (f x hd) tl (** [fold_right f [x1; x2; ...; xn] y] computes (f x1 (f x2 (... (f xn y)) ... )). Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml, Coq *) val fold_right: ('a -> 'b -> Tot 'b) -> list 'a -> 'b -> Tot 'b let rec fold_right f l x = match l with | [] -> x | hd::tl -> f hd (fold_right f tl x) (** [fold_right_gtot] is just like [fold_right], except `f` is a ghost function **) let rec fold_right_gtot (#a:Type) (#b:Type) (l:list a) (f:a -> b -> GTot b) (x:b) : GTot b = match l with | [] -> x | hd::tl -> f hd (fold_right_gtot tl f x) (* We define map in terms of fold, to share simple lemmas *) let map_gtot #a #b (f:a -> GTot b) (x:list a) : GTot (list b) = fold_right_gtot x (fun x tl -> f x :: tl) [] (** [fold_left2 f x [y1; y2; ...; yn] [z1; z2; ...; zn]] computes (f (... (f x y1 z1) y2 z2) ... yn zn). Requires, at type-checking time, [f] to be a pure total function, and the lists [y1; y2; ...; yn] and [z1; z2; ...; zn] to have the same lengths. Named as in: OCaml *) val fold_left2 : f:('a -> 'b -> 'c -> Tot 'a) -> accu:'a -> l1:(list 'b) -> l2:(list 'c) -> Pure 'a (requires (length l1 == length l2)) (ensures (fun _ -> True)) (decreases l1) let rec fold_left2 f accu l1 l2 = match (l1, l2) with | ([], []) -> accu | (a1::l1, a2::l2) -> fold_left2 f (f accu a1 a2) l1 l2 (** Propositional membership (as in Coq). Does not require decidable equality. *) (** [memP x l] holds if, and only if, [x] appears as an element of [l]. Similar to: List.In in Coq. *) let rec memP (#a: Type) (x: a) (l: list a) : Tot Type0 = match l with | [] -> False | y :: q -> x == y \/ memP x q (** List searching **) (** [mem x l] returns [true] if, and only if, [x] appears as an element of [l]. Requires, at type-checking time, the type of elements of [l] to have decidable equality. Named as in: OCaml. See also: List.In in Coq, which is propositional. *) val mem: #a:eqtype -> a -> list a -> Tot bool let rec mem #a x = function | [] -> false | hd::tl -> if hd = x then true else mem x tl (** [contains x l] returns [true] if, and only if, [x] appears as an element of [l]. Requires, at type-checking time, the type of elements of [l] to have decidable equality. It is equivalent to: [mem x l]. TODO: should we rather swap the order of arguments? *) let contains : #a:eqtype -> a -> list a -> Tot bool = mem (** [existsb f l] returns [true] if, and only if, there exists some element [x] in [l] such that [f x] holds. *) val existsb: #a:Type -> f:(a -> Tot bool) -> list a -> Tot bool let rec existsb #a f l = match l with | [] -> false | hd::tl -> if f hd then true else existsb f tl (** [find f l] returns [Some x] for some element [x] appearing in [l] such that [f x] holds, or [None] only if no such [x] exists. *) val find: #a:Type -> f:(a -> Tot bool) -> list a -> Tot (option (x:a{f x})) let rec find #a f l = match l with | [] -> None #(x:a{f x}) //These type annotations are only present because it makes bootstrapping go much faster | hd::tl -> if f hd then Some #(x:a{f x}) hd else find f tl (** Filtering elements of a list [l] through a Boolean pure total predicate [f] *) (** [filter f l] returns [l] with all elements [x] such that [f x] does not hold removed. Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml, Coq *)
false
false
FStar.List.Tot.Base.fst
{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 1, "max_fuel": 8, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": true, "z3cliopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }
null
val filter : #a: Type -> f:(a -> Tot bool) -> l: list a -> Tot (m:list a{forall x. memP x m ==> f x})
[ "recursion" ]
FStar.List.Tot.Base.filter
{ "file_name": "ulib/FStar.List.Tot.Base.fst", "git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f", "git_url": "https://github.com/FStarLang/FStar.git", "project_name": "FStar" }
f: (_: a -> Prims.bool) -> l: Prims.list a -> m: Prims.list a {forall (x: a). FStar.List.Tot.Base.memP x m ==> f x}
{ "end_col": 59, "end_line": 279, "start_col": 22, "start_line": 277 }
Prims.Tot
val list_refb: #a:eqtype -> #p:(a -> Tot bool) -> l:list a { for_all p l } -> Tot (l':list (x:a{ p x }) { length l = length l' /\ (forall i. {:pattern (index l i) } index l i = index l' i) })
[ { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]
false
let rec list_refb #a #p l = match l with | hd :: tl -> hd :: list_refb #a #p tl | [] -> []
val list_refb: #a:eqtype -> #p:(a -> Tot bool) -> l:list a { for_all p l } -> Tot (l':list (x:a{ p x }) { length l = length l' /\ (forall i. {:pattern (index l i) } index l i = index l' i) }) let rec list_refb #a #p l =
false
null
false
match l with | hd :: tl -> hd :: list_refb #a #p tl | [] -> []
{ "checked_file": "FStar.List.Tot.Base.fst.checked", "dependencies": [ "prims.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Classical.fsti.checked" ], "interface_file": false, "source_file": "FStar.List.Tot.Base.fst" }
[ "total" ]
[ "Prims.eqtype", "Prims.bool", "Prims.list", "Prims.b2t", "FStar.List.Tot.Base.for_all", "Prims.Cons", "FStar.List.Tot.Base.list_refb", "Prims.Nil", "Prims.l_and", "Prims.op_Equality", "Prims.nat", "FStar.List.Tot.Base.length", "Prims.l_Forall", "Prims.op_LessThan", "FStar.List.Tot.Base.index" ]
[]
(* Copyright 2008-2014 Nikhil Swamy and Microsoft Research Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License. *) (** This module defines all pure and total operations on lists that can be used in specifications. It is implemented by FStar_List_Tot_Base.ml, any functional change and/or the addition of new functions MUST be reflected there. @summary Pure total operations on lists *) module FStar.List.Tot.Base (** Base operations *) (** [isEmpty l] returns [true] if and only if [l] is empty *) val isEmpty: list 'a -> Tot bool let isEmpty l = match l with | [] -> true | _ -> false (** [hd l] returns the first element of [l]. Requires [l] to be nonempty, at type-checking time. Named as in: OCaml, F#, Coq *) val hd: l:list 'a{Cons? l} -> Tot 'a let hd = function | hd::_ -> hd (** [tail l] returns [l] without its first element. Requires, at type-checking time, that [l] be nonempty. Similar to: tl in OCaml, F#, Coq *) val tail: l:list 'a {Cons? l} -> Tot (list 'a) let tail = function | _::tl -> tl (** [tl l] returns [l] without its first element. Requires, at type-checking time, that [l] be nonempty. Named as in: OCaml, F#, Coq *) val tl: l:list 'a {Cons? l} -> Tot (list 'a) let tl = tail (** [last l] returns the last element of [l]. Requires, at type-checking time, that [l] be nonempty. Named as in: Haskell *) val last: l:list 'a {Cons? l} -> Tot 'a let rec last = function | [hd] -> hd | _::tl -> last tl (** [init l] returns [l] without its last element. Requires, at type-checking time, that [l] be nonempty. Named as in: Haskell *) val init: l:list 'a {Cons? l} -> Tot (list 'a) let rec init = function | [_] -> [] | hd::tl -> hd::(init tl) (** [length l] returns the total number of elements in [l]. Named as in: OCaml, F#, Coq *) val length: list 'a -> Tot nat let rec length = function | [] -> 0 | _::tl -> 1 + length tl (** [nth l n] returns the [n]-th element in list [l] (with the first element being the 0-th) if [l] is long enough, or [None] otherwise. Named as in: OCaml, F#, Coq *) val nth: list 'a -> nat -> Tot (option 'a) let rec nth l n = match l with | [] -> None | hd::tl -> if n = 0 then Some hd else nth tl (n - 1) (** [index l n] returns the [n]-th element in list [l] (with the first element being the 0-th). Requires, at type-checking time, that [l] be of length at least [n+1]. *) val index: #a:Type -> l:list a -> i:nat{i < length l} -> Tot a let rec index #a (l: list a) (i:nat{i < length l}): Tot a = if i = 0 then hd l else index (tl l) (i - 1) (** [count x l] returns the number of occurrences of [x] in [l]. Requires, at type-checking time, the type of [a] to have equality defined. Similar to: [List.count_occ] in Coq. *) val count: #a:eqtype -> a -> list a -> Tot nat let rec count #a x = function | [] -> 0 | hd::tl -> if x=hd then 1 + count x tl else count x tl (** [rev_acc l1 l2] appends the elements of [l1] to the beginning of [l2], in reverse order. It is equivalent to [append (rev l1) l2], but is tail-recursive. Similar to: [List.rev_append] in OCaml, Coq. *) val rev_acc: list 'a -> list 'a -> Tot (list 'a) let rec rev_acc l acc = match l with | [] -> acc | hd::tl -> rev_acc tl (hd::acc) (** [rev l] returns the list [l] in reverse order. Named as in: OCaml, F#, Coq. *) val rev: list 'a -> Tot (list 'a) let rev l = rev_acc l [] (** [append l1 l2] appends the elements of [l2] to the end of [l1]. Named as: OCaml, F#. Similar to: [List.app] in Coq. *) val append: list 'a -> list 'a -> Tot (list 'a) let rec append x y = match x with | [] -> y | a::tl -> a::append tl y (** Defines notation [@@] for [append], as in OCaml, F# . *) let op_At x y = append x y (** [snoc (l, x)] adds [x] to the end of the list [l]. Note: We use an uncurried [snoc (l, x)] instead of the curried [snoc l x]. This is intentional. If [snoc] takes a pair instead of 2 arguments, it allows for a better pattern on [lemma_unsnoc_snoc], which connects [snoc] and [unsnoc]. In particular, if we had two arguments, then either the pattern would either be too restrictive or would lead to over-triggering. More context for this can be seen in the (collapsed and uncollapsed) comments at https://github.com/FStarLang/FStar/pull/1560 *) val snoc: (list 'a * 'a) -> Tot (list 'a) let snoc (l, x) = append l [x] (** [flatten l], where [l] is a list of lists, returns the list of the elements of the lists in [l], preserving their order. Named as in: OCaml, Coq. *) val flatten: list (list 'a) -> Tot (list 'a) let rec flatten l = match l with | [] -> [] | hd::tl -> append hd (flatten tl) (** [map f l] applies [f] to each element of [l] and returns the list of results, in the order of the original elements in [l]. Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml, Coq, F# *) val map: ('a -> Tot 'b) -> list 'a -> Tot (list 'b) let rec map f x = match x with | [] -> [] | a::tl -> f a::map f tl (** [mapi_init f l n] applies, for each [k], [f (n+k)] to the [k]-th element of [l] and returns the list of results, in the order of the original elements in [l]. Requires, at type-checking time, [f] to be a pure total function. *) val mapi_init: (int -> 'a -> Tot 'b) -> list 'a -> int -> Tot (list 'b) let rec mapi_init f l i = match l with | [] -> [] | hd::tl -> (f i hd)::(mapi_init f tl (i+1)) (** [mapi f l] applies, for each [k], [f k] to the [k]-th element of [l] and returns the list of results, in the order of the original elements in [l]. Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml *) val mapi: (int -> 'a -> Tot 'b) -> list 'a -> Tot (list 'b) let mapi f l = mapi_init f l 0 (** [concatMap f l] applies [f] to each element of [l] and returns the concatenation of the results, in the order of the original elements of [l]. This is equivalent to [flatten (map f l)]. Requires, at type-checking time, [f] to be a pure total function. *) val concatMap: ('a -> Tot (list 'b)) -> list 'a -> Tot (list 'b) let rec concatMap f = function | [] -> [] | a::tl -> let fa = f a in let ftl = concatMap f tl in append fa ftl (** [fold_left f x [y1; y2; ...; yn]] computes (f (... (f x y1) y2) ... yn). Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml, Coq. *) val fold_left: ('a -> 'b -> Tot 'a) -> 'a -> l:list 'b -> Tot 'a (decreases l) let rec fold_left f x l = match l with | [] -> x | hd::tl -> fold_left f (f x hd) tl (** [fold_right f [x1; x2; ...; xn] y] computes (f x1 (f x2 (... (f xn y)) ... )). Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml, Coq *) val fold_right: ('a -> 'b -> Tot 'b) -> list 'a -> 'b -> Tot 'b let rec fold_right f l x = match l with | [] -> x | hd::tl -> f hd (fold_right f tl x) (** [fold_right_gtot] is just like [fold_right], except `f` is a ghost function **) let rec fold_right_gtot (#a:Type) (#b:Type) (l:list a) (f:a -> b -> GTot b) (x:b) : GTot b = match l with | [] -> x | hd::tl -> f hd (fold_right_gtot tl f x) (* We define map in terms of fold, to share simple lemmas *) let map_gtot #a #b (f:a -> GTot b) (x:list a) : GTot (list b) = fold_right_gtot x (fun x tl -> f x :: tl) [] (** [fold_left2 f x [y1; y2; ...; yn] [z1; z2; ...; zn]] computes (f (... (f x y1 z1) y2 z2) ... yn zn). Requires, at type-checking time, [f] to be a pure total function, and the lists [y1; y2; ...; yn] and [z1; z2; ...; zn] to have the same lengths. Named as in: OCaml *) val fold_left2 : f:('a -> 'b -> 'c -> Tot 'a) -> accu:'a -> l1:(list 'b) -> l2:(list 'c) -> Pure 'a (requires (length l1 == length l2)) (ensures (fun _ -> True)) (decreases l1) let rec fold_left2 f accu l1 l2 = match (l1, l2) with | ([], []) -> accu | (a1::l1, a2::l2) -> fold_left2 f (f accu a1 a2) l1 l2 (** Propositional membership (as in Coq). Does not require decidable equality. *) (** [memP x l] holds if, and only if, [x] appears as an element of [l]. Similar to: List.In in Coq. *) let rec memP (#a: Type) (x: a) (l: list a) : Tot Type0 = match l with | [] -> False | y :: q -> x == y \/ memP x q (** List searching **) (** [mem x l] returns [true] if, and only if, [x] appears as an element of [l]. Requires, at type-checking time, the type of elements of [l] to have decidable equality. Named as in: OCaml. See also: List.In in Coq, which is propositional. *) val mem: #a:eqtype -> a -> list a -> Tot bool let rec mem #a x = function | [] -> false | hd::tl -> if hd = x then true else mem x tl (** [contains x l] returns [true] if, and only if, [x] appears as an element of [l]. Requires, at type-checking time, the type of elements of [l] to have decidable equality. It is equivalent to: [mem x l]. TODO: should we rather swap the order of arguments? *) let contains : #a:eqtype -> a -> list a -> Tot bool = mem (** [existsb f l] returns [true] if, and only if, there exists some element [x] in [l] such that [f x] holds. *) val existsb: #a:Type -> f:(a -> Tot bool) -> list a -> Tot bool let rec existsb #a f l = match l with | [] -> false | hd::tl -> if f hd then true else existsb f tl (** [find f l] returns [Some x] for some element [x] appearing in [l] such that [f x] holds, or [None] only if no such [x] exists. *) val find: #a:Type -> f:(a -> Tot bool) -> list a -> Tot (option (x:a{f x})) let rec find #a f l = match l with | [] -> None #(x:a{f x}) //These type annotations are only present because it makes bootstrapping go much faster | hd::tl -> if f hd then Some #(x:a{f x}) hd else find f tl (** Filtering elements of a list [l] through a Boolean pure total predicate [f] *) (** [filter f l] returns [l] with all elements [x] such that [f x] does not hold removed. Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml, Coq *) val filter : #a: Type -> f:(a -> Tot bool) -> l: list a -> Tot (m:list a{forall x. memP x m ==> f x}) let rec filter #a f = function | [] -> [] | hd::tl -> if f hd then hd::filter f tl else filter f tl (** Postcondition on [filter f l]: for any element [x] of [filter f l], [f x] holds. Requires, at type-checking time, [f] to be a pure total function.*) val mem_filter (#a:Type) (f: (a -> Tot bool)) (l: list a) (x: a) : Lemma (requires (memP x (filter f l))) (ensures (f x)) let mem_filter f l x = () (** Postcondition on [filter f l]: stated with [forall]: for any element [x] of [filter f l], [f x] holds. Requires, at type-checking time, [f] to be a pure total function. *) val mem_filter_forall (#a:Type) (f: (a -> Tot bool)) (l: list a) : Lemma (requires True) (ensures (forall x . memP x (filter f l) ==> f x)) [SMTPat (filter f l)] let mem_filter_forall f l = FStar.Classical.ghost_lemma (mem_filter f l) (** [for_all f l] returns [true] if, and only if, for all elements [x] appearing in [l], [f x] holds. Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml. Similar to: List.forallb in Coq *) val for_all: ('a -> Tot bool) -> list 'a -> Tot bool let rec for_all f l = match l with | [] -> true | hd::tl -> if f hd then for_all f tl else false (** Specification for [for_all f l] vs. mem *) let rec for_all_mem (#a: Type) (f: (a -> Tot bool)) (l: list a) : Lemma (for_all f l <==> (forall x . memP x l ==> f x)) = match l with | [] -> () | _ :: q -> for_all_mem f q (** [collect f l] applies [f] to each element of [l] and returns the concatenation of the results, in the order of the original elements of [l]. It is equivalent to [flatten (map f l)]. Requires, at type-checking time, [f] to be a pure total function. TODO: what is the difference with [concatMap]? *) val collect: ('a -> Tot (list 'b)) -> list 'a -> Tot (list 'b) let rec collect f l = match l with | [] -> [] | hd::tl -> append (f hd) (collect f tl) (** [tryFind f l] returns [Some x] for some element [x] appearing in [l] such that [f x] holds, or [None] only if no such [x] exists. Requires, at type-checking time, [f] to be a pure total function. Contrary to [find], [tryFind] provides no postcondition on its result. *) val tryFind: ('a -> Tot bool) -> list 'a -> Tot (option 'a) let rec tryFind p l = match l with | [] -> None | hd::tl -> if p hd then Some hd else tryFind p tl (** [tryPick f l] returns [y] for some element [x] appearing in [l] such that [f x = Some y] for some y, or [None] only if [f x = None] for all elements [x] of [l]. Requires, at type-checking time, [f] to be a pure total function. *) val tryPick: ('a -> Tot (option 'b)) -> list 'a -> Tot (option 'b) let rec tryPick f l = match l with | [] -> None | hd::tl -> match f hd with | Some x -> Some x | None -> tryPick f tl (** [choose f l] returns the list of [y] for all elements [x] appearing in [l] such that [f x = Some y] for some [y]. Requires, at type-checking time, [f] to be a pure total function. *) val choose: ('a -> Tot (option 'b)) -> list 'a -> Tot (list 'b) let rec choose f l = match l with | [] -> [] | hd::tl -> match f hd with | Some x -> x::(choose f tl) | None -> choose f tl (** [partition f l] returns the pair of lists [(l1, l2)] where all elements [x] of [l] are in [l1] if [f x] holds, and in [l2] otherwise. Both [l1] and [l2] retain the original order of [l]. Requires, at type-checking time, [f] to be a pure total function. *) val partition: f:('a -> Tot bool) -> list 'a -> Tot (list 'a * list 'a) let rec partition f = function | [] -> [], [] | hd::tl -> let l1, l2 = partition f tl in if f hd then hd::l1, l2 else l1, hd::l2 (** [subset la lb] is true if and only if all the elements from [la] are also in [lb]. Requires, at type-checking time, the type of elements of [la] and [lb] to have decidable equality. *) val subset: #a:eqtype -> list a -> list a -> Tot bool let rec subset #a la lb = match la with | [] -> true | h :: tl -> mem h lb && subset tl lb (** [noRepeats l] returns [true] if, and only if, no element of [l] appears in [l] more than once. Requires, at type-checking time, the type of elements of [la] and [lb] to have decidable equality. *) val noRepeats : #a:eqtype -> list a -> Tot bool let rec noRepeats #a la = match la with | [] -> true | h :: tl -> not(mem h tl) && noRepeats tl (** [no_repeats_p l] valid if, and only if, no element of [l] appears in [l] more than once. *) val no_repeats_p : #a:Type -> list a -> Tot prop let rec no_repeats_p #a la = match la with | [] -> True | h :: tl -> ~(memP h tl) /\ no_repeats_p tl (** List of tuples **) (** [assoc x l] returns [Some y] where [(x, y)] is the first element of [l] whose first element is [x], or [None] only if no such element exists. Requires, at type-checking time, the type of [x] to have decidable equality. Named as in: OCaml. *) val assoc: #a:eqtype -> #b:Type -> a -> list (a * b) -> Tot (option b) let rec assoc #a #b x = function | [] -> None | (x', y)::tl -> if x=x' then Some y else assoc x tl (** [split] takes a list of pairs [(x1, y1), ..., (xn, yn)] and returns the pair of lists ([x1, ..., xn], [y1, ..., yn]). Named as in: OCaml *) val split: list ('a * 'b) -> Tot (list 'a * list 'b) let rec split l = match l with | [] -> ([],[]) | (hd1,hd2)::tl -> let (tl1,tl2) = split tl in (hd1::tl1,hd2::tl2) (** [unzip] takes a list of pairs [(x1, y1), ..., (xn, yn)] and returns the pair of lists ([x1, ..., xn], [y1, ..., yn]). Named as in: Haskell *) let unzip l = split l (** [unzip3] takes a list of triples [(x1, y1, z1), ..., (xn, yn, zn)] and returns the triple of lists ([x1, ..., xn], [y1, ..., yn], [z1, ..., zn]). Named as in: Haskell *) val unzip3: list ('a * 'b * 'c) -> Tot (list 'a * list 'b * list 'c) let rec unzip3 l = match l with | [] -> ([],[],[]) | (hd1,hd2,hd3)::tl -> let (tl1,tl2,tl3) = unzip3 tl in (hd1::tl1,hd2::tl2,hd3::tl3) (** Splitting a list at some index **) (** [splitAt] takes a natural number n and a list and returns a pair of the maximal prefix of l of size smaller than n and the rest of the list *) let rec splitAt (#a:Type) (n:nat) (l:list a) : Tot (list a * list a) = if n = 0 then [], l else match l with | [] -> [], l | x :: xs -> let l1, l2 = splitAt (n-1) xs in x :: l1, l2 let rec lemma_splitAt_snd_length (#a:Type) (n:nat) (l:list a) : Lemma (requires (n <= length l)) (ensures (length (snd (splitAt n l)) = length l - n)) = match n, l with | 0, _ -> () | _, [] -> () | _, _ :: l' -> lemma_splitAt_snd_length (n - 1) l' (** [unsnoc] is an inverse of [snoc]. It splits a list into all-elements-except-last and last element. *) val unsnoc: #a:Type -> l:list a{length l > 0} -> Tot (list a * a) let unsnoc #a l = let l1, l2 = splitAt (length l - 1) l in lemma_splitAt_snd_length (length l - 1) l; l1, hd l2 (** [split3] splits a list into 3 parts. This allows easy access to the part of the list before and after the element, as well as the element itself. *) val split3: #a:Type -> l:list a -> i:nat{i < length l} -> Tot (list a * a * list a) let split3 #a l i = let a, rest = splitAt i l in lemma_splitAt_snd_length i l; let b :: c = rest in a, b, c (** Sorting (implemented as quicksort) **) (** [partition] splits a list [l] into two lists, the sum of whose lengths is the length of [l]. *) val partition_length: f:('a -> Tot bool) -> l:list 'a -> Lemma (requires True) (ensures (length (fst (partition f l)) + length (snd (partition f l)) = length l)) let rec partition_length f l = match l with | [] -> () | hd::tl -> partition_length f tl (** [bool_of_compare] turns a comparison function into a strict order. More precisely, [bool_of_compare compare x y] returns true if, and only if, [compare x y] is negative, meaning [x] precedes [y] in the ordering defined by compare. This is used in sorting, and is defined to be consistent with OCaml and F#, where sorting is performed in ascending order. *) val bool_of_compare : #a:Type -> (a -> a -> Tot int) -> a -> a -> Tot bool let bool_of_compare #a f x y = f x y < 0 (** [compare_of_bool] turns a strict order into a comparison function. More precisely, [compare_of_bool rel x y] returns a positive number if, and only if, x `rel` y holds. Inspired from OCaml, where polymorphic comparison using both the [compare] function and the (>) infix operator are such that [compare x y] is positive if, and only if, x > y. Requires, at type-checking time, [rel] to be a pure total function. *) val compare_of_bool : #a:eqtype -> (a -> a -> Tot bool) -> a -> a -> Tot int let compare_of_bool #a rel x y = if x `rel` y then -1 else if x = y then 0 else 1 let compare_of_bool_of_compare (#a:eqtype) (f:a -> a -> Tot bool) : Lemma (forall x y. bool_of_compare (compare_of_bool f) x y == f x y) = () (** [sortWith compare l] returns the list [l'] containing the elements of [l] sorted along the comparison function [compare], in such a way that if [compare x y > 0], then [x] appears before [y] in [l']. Sorts in ascending order *) val sortWith: ('a -> 'a -> Tot int) -> l:list 'a -> Tot (list 'a) (decreases (length l)) let rec sortWith f = function | [] -> [] | pivot::tl -> let hi, lo = partition (bool_of_compare f pivot) tl in partition_length (bool_of_compare f pivot) tl; append (sortWith f lo) (pivot::sortWith f hi) (** A l1 is a strict suffix of l2. *) let rec strict_suffix_of (#a: Type) (l1 l2: list a) : Pure Type0 (requires True) (ensures (fun _ -> True)) (decreases l2) = match l2 with | [] -> False | _ :: q -> l1 == q \/ l1 `strict_suffix_of` q [@@deprecated "This function was misnamed: Please use 'strict_suffix_of'"] let strict_prefix_of = strict_suffix_of val list_unref : #a:Type -> #p:(a -> Type0) -> list (x:a{p x}) -> Tot (list a) let rec list_unref #a #p l = match l with | [] -> [] | x::xs -> x :: list_unref xs val list_refb: #a:eqtype -> #p:(a -> Tot bool) -> l:list a { for_all p l } -> Tot (l':list (x:a{ p x }) { length l = length l' /\ (forall i. {:pattern (index l i) } index l i = index l' i) })
false
false
FStar.List.Tot.Base.fst
{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 1, "max_fuel": 8, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": true, "z3cliopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }
null
val list_refb: #a:eqtype -> #p:(a -> Tot bool) -> l:list a { for_all p l } -> Tot (l':list (x:a{ p x }) { length l = length l' /\ (forall i. {:pattern (index l i) } index l i = index l' i) })
[ "recursion" ]
FStar.List.Tot.Base.list_refb
{ "file_name": "ulib/FStar.List.Tot.Base.fst", "git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f", "git_url": "https://github.com/FStarLang/FStar.git", "project_name": "FStar" }
l: Prims.list a {FStar.List.Tot.Base.for_all p l} -> l': Prims.list (x: a{p x}) { FStar.List.Tot.Base.length l = FStar.List.Tot.Base.length l' /\ (forall (i: Prims.nat{i < FStar.List.Tot.Base.length l /\ i < FStar.List.Tot.Base.length l'}). {:pattern FStar.List.Tot.Base.index l i} FStar.List.Tot.Base.index l i = FStar.List.Tot.Base.index l' i) }
{ "end_col": 12, "end_line": 557, "start_col": 2, "start_line": 555 }
Prims.Tot
val list_ref: #a:eqtype -> #p:(a -> Tot prop) -> l:list a { forall x. {:pattern mem x l} mem x l ==> p x } -> Tot (l':list (x:a{ p x }) { length l = length l' /\ (forall i. {:pattern (index l i) } index l i = index l' i) })
[ { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.List.Tot", "short_module": null }, { "abbrev": false, "full_module": "FStar.Pervasives", "short_module": null }, { "abbrev": false, "full_module": "Prims", "short_module": null }, { "abbrev": false, "full_module": "FStar", "short_module": null } ]
false
let rec list_ref #a #p l = match l with | hd :: tl -> assert (mem hd l); assert (p hd); assert (forall x. {:pattern mem x tl} mem x tl ==> mem x l); hd :: list_ref #a #p tl | [] -> []
val list_ref: #a:eqtype -> #p:(a -> Tot prop) -> l:list a { forall x. {:pattern mem x l} mem x l ==> p x } -> Tot (l':list (x:a{ p x }) { length l = length l' /\ (forall i. {:pattern (index l i) } index l i = index l' i) }) let rec list_ref #a #p l =
false
null
false
match l with | hd :: tl -> assert (mem hd l); assert (p hd); assert (forall x. {:pattern mem x tl} mem x tl ==> mem x l); hd :: list_ref #a #p tl | [] -> []
{ "checked_file": "FStar.List.Tot.Base.fst.checked", "dependencies": [ "prims.fst.checked", "FStar.Pervasives.Native.fst.checked", "FStar.Pervasives.fsti.checked", "FStar.Classical.fsti.checked" ], "interface_file": false, "source_file": "FStar.List.Tot.Base.fst" }
[ "total" ]
[ "Prims.eqtype", "Prims.prop", "Prims.list", "Prims.l_Forall", "Prims.l_imp", "Prims.b2t", "FStar.List.Tot.Base.mem", "Prims.Cons", "FStar.List.Tot.Base.list_ref", "Prims.unit", "Prims._assert", "Prims.Nil", "Prims.l_and", "Prims.op_Equality", "Prims.nat", "FStar.List.Tot.Base.length", "Prims.op_LessThan", "FStar.List.Tot.Base.index" ]
[]
(* Copyright 2008-2014 Nikhil Swamy and Microsoft Research Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License. *) (** This module defines all pure and total operations on lists that can be used in specifications. It is implemented by FStar_List_Tot_Base.ml, any functional change and/or the addition of new functions MUST be reflected there. @summary Pure total operations on lists *) module FStar.List.Tot.Base (** Base operations *) (** [isEmpty l] returns [true] if and only if [l] is empty *) val isEmpty: list 'a -> Tot bool let isEmpty l = match l with | [] -> true | _ -> false (** [hd l] returns the first element of [l]. Requires [l] to be nonempty, at type-checking time. Named as in: OCaml, F#, Coq *) val hd: l:list 'a{Cons? l} -> Tot 'a let hd = function | hd::_ -> hd (** [tail l] returns [l] without its first element. Requires, at type-checking time, that [l] be nonempty. Similar to: tl in OCaml, F#, Coq *) val tail: l:list 'a {Cons? l} -> Tot (list 'a) let tail = function | _::tl -> tl (** [tl l] returns [l] without its first element. Requires, at type-checking time, that [l] be nonempty. Named as in: OCaml, F#, Coq *) val tl: l:list 'a {Cons? l} -> Tot (list 'a) let tl = tail (** [last l] returns the last element of [l]. Requires, at type-checking time, that [l] be nonempty. Named as in: Haskell *) val last: l:list 'a {Cons? l} -> Tot 'a let rec last = function | [hd] -> hd | _::tl -> last tl (** [init l] returns [l] without its last element. Requires, at type-checking time, that [l] be nonempty. Named as in: Haskell *) val init: l:list 'a {Cons? l} -> Tot (list 'a) let rec init = function | [_] -> [] | hd::tl -> hd::(init tl) (** [length l] returns the total number of elements in [l]. Named as in: OCaml, F#, Coq *) val length: list 'a -> Tot nat let rec length = function | [] -> 0 | _::tl -> 1 + length tl (** [nth l n] returns the [n]-th element in list [l] (with the first element being the 0-th) if [l] is long enough, or [None] otherwise. Named as in: OCaml, F#, Coq *) val nth: list 'a -> nat -> Tot (option 'a) let rec nth l n = match l with | [] -> None | hd::tl -> if n = 0 then Some hd else nth tl (n - 1) (** [index l n] returns the [n]-th element in list [l] (with the first element being the 0-th). Requires, at type-checking time, that [l] be of length at least [n+1]. *) val index: #a:Type -> l:list a -> i:nat{i < length l} -> Tot a let rec index #a (l: list a) (i:nat{i < length l}): Tot a = if i = 0 then hd l else index (tl l) (i - 1) (** [count x l] returns the number of occurrences of [x] in [l]. Requires, at type-checking time, the type of [a] to have equality defined. Similar to: [List.count_occ] in Coq. *) val count: #a:eqtype -> a -> list a -> Tot nat let rec count #a x = function | [] -> 0 | hd::tl -> if x=hd then 1 + count x tl else count x tl (** [rev_acc l1 l2] appends the elements of [l1] to the beginning of [l2], in reverse order. It is equivalent to [append (rev l1) l2], but is tail-recursive. Similar to: [List.rev_append] in OCaml, Coq. *) val rev_acc: list 'a -> list 'a -> Tot (list 'a) let rec rev_acc l acc = match l with | [] -> acc | hd::tl -> rev_acc tl (hd::acc) (** [rev l] returns the list [l] in reverse order. Named as in: OCaml, F#, Coq. *) val rev: list 'a -> Tot (list 'a) let rev l = rev_acc l [] (** [append l1 l2] appends the elements of [l2] to the end of [l1]. Named as: OCaml, F#. Similar to: [List.app] in Coq. *) val append: list 'a -> list 'a -> Tot (list 'a) let rec append x y = match x with | [] -> y | a::tl -> a::append tl y (** Defines notation [@@] for [append], as in OCaml, F# . *) let op_At x y = append x y (** [snoc (l, x)] adds [x] to the end of the list [l]. Note: We use an uncurried [snoc (l, x)] instead of the curried [snoc l x]. This is intentional. If [snoc] takes a pair instead of 2 arguments, it allows for a better pattern on [lemma_unsnoc_snoc], which connects [snoc] and [unsnoc]. In particular, if we had two arguments, then either the pattern would either be too restrictive or would lead to over-triggering. More context for this can be seen in the (collapsed and uncollapsed) comments at https://github.com/FStarLang/FStar/pull/1560 *) val snoc: (list 'a * 'a) -> Tot (list 'a) let snoc (l, x) = append l [x] (** [flatten l], where [l] is a list of lists, returns the list of the elements of the lists in [l], preserving their order. Named as in: OCaml, Coq. *) val flatten: list (list 'a) -> Tot (list 'a) let rec flatten l = match l with | [] -> [] | hd::tl -> append hd (flatten tl) (** [map f l] applies [f] to each element of [l] and returns the list of results, in the order of the original elements in [l]. Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml, Coq, F# *) val map: ('a -> Tot 'b) -> list 'a -> Tot (list 'b) let rec map f x = match x with | [] -> [] | a::tl -> f a::map f tl (** [mapi_init f l n] applies, for each [k], [f (n+k)] to the [k]-th element of [l] and returns the list of results, in the order of the original elements in [l]. Requires, at type-checking time, [f] to be a pure total function. *) val mapi_init: (int -> 'a -> Tot 'b) -> list 'a -> int -> Tot (list 'b) let rec mapi_init f l i = match l with | [] -> [] | hd::tl -> (f i hd)::(mapi_init f tl (i+1)) (** [mapi f l] applies, for each [k], [f k] to the [k]-th element of [l] and returns the list of results, in the order of the original elements in [l]. Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml *) val mapi: (int -> 'a -> Tot 'b) -> list 'a -> Tot (list 'b) let mapi f l = mapi_init f l 0 (** [concatMap f l] applies [f] to each element of [l] and returns the concatenation of the results, in the order of the original elements of [l]. This is equivalent to [flatten (map f l)]. Requires, at type-checking time, [f] to be a pure total function. *) val concatMap: ('a -> Tot (list 'b)) -> list 'a -> Tot (list 'b) let rec concatMap f = function | [] -> [] | a::tl -> let fa = f a in let ftl = concatMap f tl in append fa ftl (** [fold_left f x [y1; y2; ...; yn]] computes (f (... (f x y1) y2) ... yn). Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml, Coq. *) val fold_left: ('a -> 'b -> Tot 'a) -> 'a -> l:list 'b -> Tot 'a (decreases l) let rec fold_left f x l = match l with | [] -> x | hd::tl -> fold_left f (f x hd) tl (** [fold_right f [x1; x2; ...; xn] y] computes (f x1 (f x2 (... (f xn y)) ... )). Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml, Coq *) val fold_right: ('a -> 'b -> Tot 'b) -> list 'a -> 'b -> Tot 'b let rec fold_right f l x = match l with | [] -> x | hd::tl -> f hd (fold_right f tl x) (** [fold_right_gtot] is just like [fold_right], except `f` is a ghost function **) let rec fold_right_gtot (#a:Type) (#b:Type) (l:list a) (f:a -> b -> GTot b) (x:b) : GTot b = match l with | [] -> x | hd::tl -> f hd (fold_right_gtot tl f x) (* We define map in terms of fold, to share simple lemmas *) let map_gtot #a #b (f:a -> GTot b) (x:list a) : GTot (list b) = fold_right_gtot x (fun x tl -> f x :: tl) [] (** [fold_left2 f x [y1; y2; ...; yn] [z1; z2; ...; zn]] computes (f (... (f x y1 z1) y2 z2) ... yn zn). Requires, at type-checking time, [f] to be a pure total function, and the lists [y1; y2; ...; yn] and [z1; z2; ...; zn] to have the same lengths. Named as in: OCaml *) val fold_left2 : f:('a -> 'b -> 'c -> Tot 'a) -> accu:'a -> l1:(list 'b) -> l2:(list 'c) -> Pure 'a (requires (length l1 == length l2)) (ensures (fun _ -> True)) (decreases l1) let rec fold_left2 f accu l1 l2 = match (l1, l2) with | ([], []) -> accu | (a1::l1, a2::l2) -> fold_left2 f (f accu a1 a2) l1 l2 (** Propositional membership (as in Coq). Does not require decidable equality. *) (** [memP x l] holds if, and only if, [x] appears as an element of [l]. Similar to: List.In in Coq. *) let rec memP (#a: Type) (x: a) (l: list a) : Tot Type0 = match l with | [] -> False | y :: q -> x == y \/ memP x q (** List searching **) (** [mem x l] returns [true] if, and only if, [x] appears as an element of [l]. Requires, at type-checking time, the type of elements of [l] to have decidable equality. Named as in: OCaml. See also: List.In in Coq, which is propositional. *) val mem: #a:eqtype -> a -> list a -> Tot bool let rec mem #a x = function | [] -> false | hd::tl -> if hd = x then true else mem x tl (** [contains x l] returns [true] if, and only if, [x] appears as an element of [l]. Requires, at type-checking time, the type of elements of [l] to have decidable equality. It is equivalent to: [mem x l]. TODO: should we rather swap the order of arguments? *) let contains : #a:eqtype -> a -> list a -> Tot bool = mem (** [existsb f l] returns [true] if, and only if, there exists some element [x] in [l] such that [f x] holds. *) val existsb: #a:Type -> f:(a -> Tot bool) -> list a -> Tot bool let rec existsb #a f l = match l with | [] -> false | hd::tl -> if f hd then true else existsb f tl (** [find f l] returns [Some x] for some element [x] appearing in [l] such that [f x] holds, or [None] only if no such [x] exists. *) val find: #a:Type -> f:(a -> Tot bool) -> list a -> Tot (option (x:a{f x})) let rec find #a f l = match l with | [] -> None #(x:a{f x}) //These type annotations are only present because it makes bootstrapping go much faster | hd::tl -> if f hd then Some #(x:a{f x}) hd else find f tl (** Filtering elements of a list [l] through a Boolean pure total predicate [f] *) (** [filter f l] returns [l] with all elements [x] such that [f x] does not hold removed. Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml, Coq *) val filter : #a: Type -> f:(a -> Tot bool) -> l: list a -> Tot (m:list a{forall x. memP x m ==> f x}) let rec filter #a f = function | [] -> [] | hd::tl -> if f hd then hd::filter f tl else filter f tl (** Postcondition on [filter f l]: for any element [x] of [filter f l], [f x] holds. Requires, at type-checking time, [f] to be a pure total function.*) val mem_filter (#a:Type) (f: (a -> Tot bool)) (l: list a) (x: a) : Lemma (requires (memP x (filter f l))) (ensures (f x)) let mem_filter f l x = () (** Postcondition on [filter f l]: stated with [forall]: for any element [x] of [filter f l], [f x] holds. Requires, at type-checking time, [f] to be a pure total function. *) val mem_filter_forall (#a:Type) (f: (a -> Tot bool)) (l: list a) : Lemma (requires True) (ensures (forall x . memP x (filter f l) ==> f x)) [SMTPat (filter f l)] let mem_filter_forall f l = FStar.Classical.ghost_lemma (mem_filter f l) (** [for_all f l] returns [true] if, and only if, for all elements [x] appearing in [l], [f x] holds. Requires, at type-checking time, [f] to be a pure total function. Named as in: OCaml. Similar to: List.forallb in Coq *) val for_all: ('a -> Tot bool) -> list 'a -> Tot bool let rec for_all f l = match l with | [] -> true | hd::tl -> if f hd then for_all f tl else false (** Specification for [for_all f l] vs. mem *) let rec for_all_mem (#a: Type) (f: (a -> Tot bool)) (l: list a) : Lemma (for_all f l <==> (forall x . memP x l ==> f x)) = match l with | [] -> () | _ :: q -> for_all_mem f q (** [collect f l] applies [f] to each element of [l] and returns the concatenation of the results, in the order of the original elements of [l]. It is equivalent to [flatten (map f l)]. Requires, at type-checking time, [f] to be a pure total function. TODO: what is the difference with [concatMap]? *) val collect: ('a -> Tot (list 'b)) -> list 'a -> Tot (list 'b) let rec collect f l = match l with | [] -> [] | hd::tl -> append (f hd) (collect f tl) (** [tryFind f l] returns [Some x] for some element [x] appearing in [l] such that [f x] holds, or [None] only if no such [x] exists. Requires, at type-checking time, [f] to be a pure total function. Contrary to [find], [tryFind] provides no postcondition on its result. *) val tryFind: ('a -> Tot bool) -> list 'a -> Tot (option 'a) let rec tryFind p l = match l with | [] -> None | hd::tl -> if p hd then Some hd else tryFind p tl (** [tryPick f l] returns [y] for some element [x] appearing in [l] such that [f x = Some y] for some y, or [None] only if [f x = None] for all elements [x] of [l]. Requires, at type-checking time, [f] to be a pure total function. *) val tryPick: ('a -> Tot (option 'b)) -> list 'a -> Tot (option 'b) let rec tryPick f l = match l with | [] -> None | hd::tl -> match f hd with | Some x -> Some x | None -> tryPick f tl (** [choose f l] returns the list of [y] for all elements [x] appearing in [l] such that [f x = Some y] for some [y]. Requires, at type-checking time, [f] to be a pure total function. *) val choose: ('a -> Tot (option 'b)) -> list 'a -> Tot (list 'b) let rec choose f l = match l with | [] -> [] | hd::tl -> match f hd with | Some x -> x::(choose f tl) | None -> choose f tl (** [partition f l] returns the pair of lists [(l1, l2)] where all elements [x] of [l] are in [l1] if [f x] holds, and in [l2] otherwise. Both [l1] and [l2] retain the original order of [l]. Requires, at type-checking time, [f] to be a pure total function. *) val partition: f:('a -> Tot bool) -> list 'a -> Tot (list 'a * list 'a) let rec partition f = function | [] -> [], [] | hd::tl -> let l1, l2 = partition f tl in if f hd then hd::l1, l2 else l1, hd::l2 (** [subset la lb] is true if and only if all the elements from [la] are also in [lb]. Requires, at type-checking time, the type of elements of [la] and [lb] to have decidable equality. *) val subset: #a:eqtype -> list a -> list a -> Tot bool let rec subset #a la lb = match la with | [] -> true | h :: tl -> mem h lb && subset tl lb (** [noRepeats l] returns [true] if, and only if, no element of [l] appears in [l] more than once. Requires, at type-checking time, the type of elements of [la] and [lb] to have decidable equality. *) val noRepeats : #a:eqtype -> list a -> Tot bool let rec noRepeats #a la = match la with | [] -> true | h :: tl -> not(mem h tl) && noRepeats tl (** [no_repeats_p l] valid if, and only if, no element of [l] appears in [l] more than once. *) val no_repeats_p : #a:Type -> list a -> Tot prop let rec no_repeats_p #a la = match la with | [] -> True | h :: tl -> ~(memP h tl) /\ no_repeats_p tl (** List of tuples **) (** [assoc x l] returns [Some y] where [(x, y)] is the first element of [l] whose first element is [x], or [None] only if no such element exists. Requires, at type-checking time, the type of [x] to have decidable equality. Named as in: OCaml. *) val assoc: #a:eqtype -> #b:Type -> a -> list (a * b) -> Tot (option b) let rec assoc #a #b x = function | [] -> None | (x', y)::tl -> if x=x' then Some y else assoc x tl (** [split] takes a list of pairs [(x1, y1), ..., (xn, yn)] and returns the pair of lists ([x1, ..., xn], [y1, ..., yn]). Named as in: OCaml *) val split: list ('a * 'b) -> Tot (list 'a * list 'b) let rec split l = match l with | [] -> ([],[]) | (hd1,hd2)::tl -> let (tl1,tl2) = split tl in (hd1::tl1,hd2::tl2) (** [unzip] takes a list of pairs [(x1, y1), ..., (xn, yn)] and returns the pair of lists ([x1, ..., xn], [y1, ..., yn]). Named as in: Haskell *) let unzip l = split l (** [unzip3] takes a list of triples [(x1, y1, z1), ..., (xn, yn, zn)] and returns the triple of lists ([x1, ..., xn], [y1, ..., yn], [z1, ..., zn]). Named as in: Haskell *) val unzip3: list ('a * 'b * 'c) -> Tot (list 'a * list 'b * list 'c) let rec unzip3 l = match l with | [] -> ([],[],[]) | (hd1,hd2,hd3)::tl -> let (tl1,tl2,tl3) = unzip3 tl in (hd1::tl1,hd2::tl2,hd3::tl3) (** Splitting a list at some index **) (** [splitAt] takes a natural number n and a list and returns a pair of the maximal prefix of l of size smaller than n and the rest of the list *) let rec splitAt (#a:Type) (n:nat) (l:list a) : Tot (list a * list a) = if n = 0 then [], l else match l with | [] -> [], l | x :: xs -> let l1, l2 = splitAt (n-1) xs in x :: l1, l2 let rec lemma_splitAt_snd_length (#a:Type) (n:nat) (l:list a) : Lemma (requires (n <= length l)) (ensures (length (snd (splitAt n l)) = length l - n)) = match n, l with | 0, _ -> () | _, [] -> () | _, _ :: l' -> lemma_splitAt_snd_length (n - 1) l' (** [unsnoc] is an inverse of [snoc]. It splits a list into all-elements-except-last and last element. *) val unsnoc: #a:Type -> l:list a{length l > 0} -> Tot (list a * a) let unsnoc #a l = let l1, l2 = splitAt (length l - 1) l in lemma_splitAt_snd_length (length l - 1) l; l1, hd l2 (** [split3] splits a list into 3 parts. This allows easy access to the part of the list before and after the element, as well as the element itself. *) val split3: #a:Type -> l:list a -> i:nat{i < length l} -> Tot (list a * a * list a) let split3 #a l i = let a, rest = splitAt i l in lemma_splitAt_snd_length i l; let b :: c = rest in a, b, c (** Sorting (implemented as quicksort) **) (** [partition] splits a list [l] into two lists, the sum of whose lengths is the length of [l]. *) val partition_length: f:('a -> Tot bool) -> l:list 'a -> Lemma (requires True) (ensures (length (fst (partition f l)) + length (snd (partition f l)) = length l)) let rec partition_length f l = match l with | [] -> () | hd::tl -> partition_length f tl (** [bool_of_compare] turns a comparison function into a strict order. More precisely, [bool_of_compare compare x y] returns true if, and only if, [compare x y] is negative, meaning [x] precedes [y] in the ordering defined by compare. This is used in sorting, and is defined to be consistent with OCaml and F#, where sorting is performed in ascending order. *) val bool_of_compare : #a:Type -> (a -> a -> Tot int) -> a -> a -> Tot bool let bool_of_compare #a f x y = f x y < 0 (** [compare_of_bool] turns a strict order into a comparison function. More precisely, [compare_of_bool rel x y] returns a positive number if, and only if, x `rel` y holds. Inspired from OCaml, where polymorphic comparison using both the [compare] function and the (>) infix operator are such that [compare x y] is positive if, and only if, x > y. Requires, at type-checking time, [rel] to be a pure total function. *) val compare_of_bool : #a:eqtype -> (a -> a -> Tot bool) -> a -> a -> Tot int let compare_of_bool #a rel x y = if x `rel` y then -1 else if x = y then 0 else 1 let compare_of_bool_of_compare (#a:eqtype) (f:a -> a -> Tot bool) : Lemma (forall x y. bool_of_compare (compare_of_bool f) x y == f x y) = () (** [sortWith compare l] returns the list [l'] containing the elements of [l] sorted along the comparison function [compare], in such a way that if [compare x y > 0], then [x] appears before [y] in [l']. Sorts in ascending order *) val sortWith: ('a -> 'a -> Tot int) -> l:list 'a -> Tot (list 'a) (decreases (length l)) let rec sortWith f = function | [] -> [] | pivot::tl -> let hi, lo = partition (bool_of_compare f pivot) tl in partition_length (bool_of_compare f pivot) tl; append (sortWith f lo) (pivot::sortWith f hi) (** A l1 is a strict suffix of l2. *) let rec strict_suffix_of (#a: Type) (l1 l2: list a) : Pure Type0 (requires True) (ensures (fun _ -> True)) (decreases l2) = match l2 with | [] -> False | _ :: q -> l1 == q \/ l1 `strict_suffix_of` q [@@deprecated "This function was misnamed: Please use 'strict_suffix_of'"] let strict_prefix_of = strict_suffix_of val list_unref : #a:Type -> #p:(a -> Type0) -> list (x:a{p x}) -> Tot (list a) let rec list_unref #a #p l = match l with | [] -> [] | x::xs -> x :: list_unref xs val list_refb: #a:eqtype -> #p:(a -> Tot bool) -> l:list a { for_all p l } -> Tot (l':list (x:a{ p x }) { length l = length l' /\ (forall i. {:pattern (index l i) } index l i = index l' i) }) let rec list_refb #a #p l = match l with | hd :: tl -> hd :: list_refb #a #p tl | [] -> [] val list_ref: #a:eqtype -> #p:(a -> Tot prop) -> l:list a { forall x. {:pattern mem x l} mem x l ==> p x } -> Tot (l':list (x:a{ p x }) { length l = length l' /\ (forall i. {:pattern (index l i) } index l i = index l' i) })
false
false
FStar.List.Tot.Base.fst
{ "detail_errors": false, "detail_hint_replay": false, "initial_fuel": 2, "initial_ifuel": 1, "max_fuel": 8, "max_ifuel": 2, "no_plugins": false, "no_smt": false, "no_tactics": false, "quake_hi": 1, "quake_keep": false, "quake_lo": 1, "retry": false, "reuse_hint_for": null, "smtencoding_elim_box": false, "smtencoding_l_arith_repr": "boxwrap", "smtencoding_nl_arith_repr": "boxwrap", "smtencoding_valid_elim": false, "smtencoding_valid_intro": true, "tcnorm": true, "trivial_pre_for_unannotated_effectful_fns": true, "z3cliopt": [], "z3refresh": false, "z3rlimit": 5, "z3rlimit_factor": 1, "z3seed": 0, "z3smtopt": [], "z3version": "4.8.5" }
null
val list_ref: #a:eqtype -> #p:(a -> Tot prop) -> l:list a { forall x. {:pattern mem x l} mem x l ==> p x } -> Tot (l':list (x:a{ p x }) { length l = length l' /\ (forall i. {:pattern (index l i) } index l i = index l' i) })
[ "recursion" ]
FStar.List.Tot.Base.list_ref
{ "file_name": "ulib/FStar.List.Tot.Base.fst", "git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f", "git_url": "https://github.com/FStarLang/FStar.git", "project_name": "FStar" }
l: Prims.list a {forall (x: a). {:pattern FStar.List.Tot.Base.mem x l} FStar.List.Tot.Base.mem x l ==> p x} -> l': Prims.list (x: a{p x}) { FStar.List.Tot.Base.length l = FStar.List.Tot.Base.length l' /\ (forall (i: Prims.nat{i < FStar.List.Tot.Base.length l /\ i < FStar.List.Tot.Base.length l'}). {:pattern FStar.List.Tot.Base.index l i} FStar.List.Tot.Base.index l i = FStar.List.Tot.Base.index l' i) }
{ "end_col": 12, "end_line": 571, "start_col": 2, "start_line": 565 }