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   "source": [
    "# PSET 1: Bottom-Up Synthesis\n",
    "\n",
    "I follow Algorithm 1 in the BUSTLE paper:\n",
    "\n",
    "> Odena, A. *et al.* BUSTLE: Bottom-Up Program Synthesis Through Learning-Guided Exploration. in *9th International Conference on Learning Representations*; 2021 May 3-7; Austria.\n",
    "\n",
    "First, I import the required libraries."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import itertools\n",
    "\n",
    "# argument parser for command line arguments\n",
    "import argparse\n",
    "\n",
    "# import arithmetic module\n",
    "# from arithmetic import *\n",
    "from examples import examples\n",
    "\n",
    "# import project config file\n",
    "import sys\n",
    "sys.path.append('..')\n",
    "import project_config"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First, I define variables as proxies for command-line arguments provided to the synthesizer."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "domain = \"arithmetic\"\n",
    "examples_key = \"addition\"\n",
    "examples = examples[examples_key]\n",
    "max_level = 3"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I provide examples of arithmetic operations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "'''\n",
    "ARTHIMETIC OPERATORS\n",
    "This file contains Python classes that define the arithmetic operators for program synthesis.\n",
    "'''\n",
    "\n",
    "'''\n",
    "CLASS DEFINITIONS\n",
    "''' \n",
    "\n",
    "class IntegerValue:\n",
    "    '''\n",
    "    Class to represent an arithmetic value.\n",
    "    '''\n",
    "    def __init__(self, value):\n",
    "        self.value = value\n",
    "        self.type = int\n",
    "\n",
    "class Add:\n",
    "    '''\n",
    "    Operator to add two numerical values.\n",
    "    '''\n",
    "    def __init__(self):\n",
    "        self.arity = 2          # number of arguments of function\n",
    "        self.weight = 1         # weight of function\n",
    "        self.return_type = int  # return type of function\n",
    "\n",
    "    def __call__(self, x, y):\n",
    "        return x + y\n",
    "    \n",
    "    def str(x, y):\n",
    "        return f\"{x} + {y}\"\n",
    "\n",
    "class Subtract:\n",
    "    '''\n",
    "    Operator to subtract two numerical values.\n",
    "    '''\n",
    "    def __init__(self):\n",
    "        self.arity = 2          # number of arguments of function\n",
    "        self.weight = 1         # weight of function\n",
    "        self.return_type = int  # return type of function\n",
    "\n",
    "    def __call__(self, x, y):\n",
    "        return x - y\n",
    "    \n",
    "    def str(x, y):\n",
    "        return f\"{x} - {y}\"\n",
    "    \n",
    "class Multiply:\n",
    "    '''\n",
    "    Operator to multiply two numerical values.\n",
    "    '''\n",
    "    def __init__(self):\n",
    "        self.arity = 2          # number of arguments of function\n",
    "        self.weight = 1         # weight of function\n",
    "        self.return_type = int  # return type of function\n",
    "\n",
    "    def __call__(self, x, y):\n",
    "        return x * y\n",
    "    \n",
    "    def str(x, y):\n",
    "        return f\"{x} * {y}\" \n",
    "\n",
    "class Divide:\n",
    "    '''\n",
    "    Operator to divide two numerical values.\n",
    "    '''\n",
    "    def __init__(self):\n",
    "        self.arity = 2          # number of arguments of function\n",
    "        self.weight = 1         # weight of function\n",
    "        self.return_type = int  # return type of function\n",
    "\n",
    "    def __call__(self, x, y):\n",
    "        try: # check for division by zero error\n",
    "            return x / y\n",
    "        except ZeroDivisionError:\n",
    "            return None\n",
    "    \n",
    "    def str(x, y):\n",
    "        return f\"{x} / {y}\"\n",
    "\n",
    "\n",
    "'''\n",
    "FUNCTION DEFINITIONS\n",
    "''' \n",
    "\n",
    "\n",
    "'''\n",
    "GLOBAL CONSTANTS\n",
    "''' \n",
    "\n",
    "# define operators\n",
    "arithmetic_operators = [Add(), Subtract(), Multiply(), Divide()]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I define input-output examples."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I define a function to determine observational equivalence."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def observationally_equivalent(a, b):\n",
    "    \"\"\"\n",
    "    Returns True if a and b are observationally equivalent, False otherwise.\n",
    "    \"\"\"\n",
    "\n",
    "    pass"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, I define the bottom-up synthesis algorithm."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# initialize program bank\n",
    "program_bank = []\n",
    "\n",
    "# iterate over each level\n",
    "for i in range(1, max_level):\n",
    "\n",
    "    # define level program bank\n",
    "    level_program_bank = []\n",
    "\n",
    "    for op in arithmetic_operators():\n",
    "\n",
    "        break"
   ]
  }
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