File size: 6,779 Bytes
f4224d0 |
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 |
# Copyright 2023 DeepMind Technologies Limited
#
# 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.
# ==============================================================================
"""Unit tests for ar.py."""
import unittest
from absl.testing import absltest
import ar
import graph as gh
import problem as pr
class ARTest(unittest.TestCase):
@classmethod
def setUpClass(cls):
super().setUpClass()
cls.defs = pr.Definition.from_txt_file('defs.txt', to_dict=True)
cls.rules = pr.Theorem.from_txt_file('rules.txt', to_dict=True)
def test_update_groups(self):
"""Test for update_groups."""
groups1 = [{1, 2}, {3, 4, 5}, {6, 7}]
groups2 = [{2, 3, 8}, {9, 10, 11}]
_, links, history = ar.update_groups(groups1, groups2)
self.assertEqual(
history,
[
[{1, 2, 3, 4, 5, 8}, {6, 7}],
[{1, 2, 3, 4, 5, 8}, {6, 7}, {9, 10, 11}],
],
)
self.assertEqual(links, [(2, 3), (3, 8), (9, 10), (10, 11)])
groups1 = [{1, 2}, {3, 4}, {5, 6}, {7, 8}]
groups2 = [{2, 3, 8, 9, 10}, {3, 6, 11}]
_, links, history = ar.update_groups(groups1, groups2)
self.assertEqual(
history,
[
[{1, 2, 3, 4, 7, 8, 9, 10}, {5, 6}],
[{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11}],
],
)
self.assertEqual(links, [(2, 3), (3, 8), (8, 9), (9, 10), (3, 6), (6, 11)])
groups1 = []
groups2 = [{1, 2}, {3, 4}, {5, 6}, {2, 3}]
_, links, history = ar.update_groups(groups1, groups2)
self.assertEqual(
history,
[
[{1, 2}],
[{1, 2}, {3, 4}],
[{1, 2}, {3, 4}, {5, 6}],
[{1, 2, 3, 4}, {5, 6}],
],
)
self.assertEqual(links, [(1, 2), (3, 4), (5, 6), (2, 3)])
def test_generic_table_simple(self):
tb = ar.Table()
# If a-b = b-c & d-a = c-d
tb.add_eq4('a', 'b', 'b', 'c', 'fact1')
tb.add_eq4('d', 'a', 'c', 'd', 'fact2')
tb.add_eq4('x', 'y', 'z', 't', 'fact3') # distractor fact
# Then b=d, because {fact1, fact2} but not fact3.
result = list(tb.get_all_eqs_and_why())
self.assertIn(('b', 'd', ['fact1', 'fact2']), result)
def test_angle_table_inbisector_exbisector(self):
"""Test that AR can figure out bisector & ex-bisector are perpendicular."""
# Load the scenario that we have cd is bisector of acb and
# ce is the ex-bisector of acb.
p = pr.Problem.from_txt(
'a b c = triangle a b c; d = incenter d a b c; e = excenter e a b c ?'
' perp d c c e'
)
g, _ = gh.Graph.build_problem(p, ARTest.defs)
# Create an external angle table:
tb = ar.AngleTable('pi')
# Add bisector & ex-bisector facts into the table:
ca, cd, cb, ce = g.names2nodes(['d(ac)', 'd(cd)', 'd(bc)', 'd(ce)'])
tb.add_eqangle(ca, cd, cd, cb, 'fact1')
tb.add_eqangle(ce, ca, cb, ce, 'fact2')
# Add a distractor fact to make sure traceback does not include this fact
ab = g.names2nodes(['d(ab)'])[0]
tb.add_eqangle(ab, cb, cb, ca, 'fact3')
# Check for all new equalities
result = list(tb.get_all_eqs_and_why())
# halfpi is represented as a tuple (1, 2)
halfpi = (1, 2)
# check that cd-ce == halfpi and this is because fact1 & fact2, not fact3
self.assertCountEqual(
result,
[
(cd, ce, halfpi, ['fact1', 'fact2']),
(ce, cd, halfpi, ['fact1', 'fact2']),
],
)
def test_angle_table_equilateral_triangle(self):
"""Test that AR can figure out triangles with 3 equal angles => each is pi/3."""
# Load an equaliteral scenario
p = pr.Problem.from_txt('a b c = ieq_triangle ? cong a b a c')
g, _ = gh.Graph.build_problem(p, ARTest.defs)
# Add two eqangles facts because ieq_triangle only add congruent sides
a, b, c = g.names2nodes('abc')
g.add_eqangle([a, b, b, c, b, c, c, a], pr.EmptyDependency(0, None))
g.add_eqangle([b, c, c, a, c, a, a, b], pr.EmptyDependency(0, None))
# Create an external angle table:
tb = ar.AngleTable('pi')
# Add the fact that there are three equal angles
ab, bc, ca = g.names2nodes(['d(ab)', 'd(bc)', 'd(ac)'])
tb.add_eqangle(ab, bc, bc, ca, 'fact1')
tb.add_eqangle(bc, ca, ca, ab, 'fact2')
# Now check for all new equalities
result = list(tb.get_all_eqs_and_why())
result = [(x.name, y.name, z, t) for x, y, z, t in result]
# 1/3 pi is represented as a tuple angle_60
angle_60 = (1, 3)
angle_120 = (2, 3)
# check that angles constants are created and figured out:
self.assertCountEqual(
result,
[
('d(bc)', 'd(ac)', angle_120, ['fact1', 'fact2']),
('d(ab)', 'd(bc)', angle_120, ['fact1', 'fact2']),
('d(ac)', 'd(ab)', angle_120, ['fact1', 'fact2']),
('d(ac)', 'd(bc)', angle_60, ['fact1', 'fact2']),
('d(bc)', 'd(ab)', angle_60, ['fact1', 'fact2']),
('d(ab)', 'd(ac)', angle_60, ['fact1', 'fact2']),
],
)
def test_incenter_excenter_touchpoints(self):
"""Test that AR can figure out incenter/excenter touchpoints are equidistant to midpoint."""
p = pr.Problem.from_txt(
'a b c = triangle a b c; d1 d2 d3 d = incenter2 a b c; e1 e2 e3 e ='
' excenter2 a b c ? perp d c c e',
translate=False,
)
g, _ = gh.Graph.build_problem(p, ARTest.defs)
a, b, c, ab, bc, ca, d1, d2, d3, e1, e2, e3 = g.names2nodes(
['a', 'b', 'c', 'ab', 'bc', 'ac', 'd1', 'd2', 'd3', 'e1', 'e2', 'e3']
)
# Create an external distance table:
tb = ar.DistanceTable()
# DD can figure out the following facts,
# we manually add them to AR.
tb.add_cong(ab, ca, a, d3, a, d2, 'fact1')
tb.add_cong(ab, ca, a, e3, a, e2, 'fact2')
tb.add_cong(ca, bc, c, d2, c, d1, 'fact5')
tb.add_cong(ca, bc, c, e2, c, e1, 'fact6')
tb.add_cong(bc, ab, b, d1, b, d3, 'fact3')
tb.add_cong(bc, ab, b, e1, b, e3, 'fact4')
# Now we check whether tb has figured out that
# distance(b, d1) == distance(e1, c)
# linear comb exprssion of each variables:
b = tb.v2e['bc:b']
c = tb.v2e['bc:c']
d1 = tb.v2e['bc:d1']
e1 = tb.v2e['bc:e1']
self.assertEqual(ar.minus(d1, b), ar.minus(c, e1))
if __name__ == '__main__':
absltest.main()
|