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coellscoells
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day 77
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‎day 77 - unification.ipynb‎

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{
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"cells": [
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## algorithm"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 1,
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"metadata": {
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"collapsed": false
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},
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"outputs": [],
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"source": [
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"class Unify:\n",
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" \n",
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" def __init__(self):\n",
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" self.reference = {} # variable bindings\n",
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" self.checkpoint = [] # unification checkpoints\n",
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" self.var_ctx = 0 # unique variable id\n",
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"\n",
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" def variable(self, *args):\n",
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" self.var_ctx += 1\n",
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" return ['%s_%d' % (var, self.var_ctx) for var in args]\n",
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"\n",
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" def __call__(self, var_x, var_y):\n",
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" # resolve variable X\n",
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" while isinstance(var_x, str) and var_x in self.reference:\n",
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" var_x = self.reference[var_x]\n",
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"\n",
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" # resolve variable Y\n",
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" while isinstance(var_y, str) and var_y in self.reference:\n",
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" var_y = self.reference[var_y]\n",
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"\n",
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" # unified to self?\n",
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" if isinstance(var_x, str) and isinstance(var_y, str):\n",
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" if var_x == var_y:\n",
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" return True\n",
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"\n",
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" # unify free variable X\n",
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" if isinstance(var_x, str):\n",
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" self.reference[var_x] = var_y\n",
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" self.checkpoint[-1].append(var_x)\n",
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" return True\n",
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"\n",
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" # unify free variable Y\n",
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" if isinstance(var_y, str):\n",
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" self.reference[var_y] = var_x\n",
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" self.checkpoint[-1].append(var_y)\n",
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" return True\n",
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"\n",
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" # tuple is unified element-wise\n",
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" if isinstance(var_x, tuple) and isinstance(var_y, tuple):\n",
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" if len(var_x) == len(var_y):\n",
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" return all(self(i, j) for i, j in zip(var_x, var_y))\n",
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"\n",
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" # atom is unified on equality\n",
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" if isinstance(var_x, int) and isinstance(var_y, int):\n",
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" if var_x == var_y:\n",
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" return True\n",
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"\n",
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" # not unifiable\n",
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" raise KeyError()\n",
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"\n",
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" def __getitem__(self, var):\n",
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" # resolve tuple by members\n",
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" if isinstance(var, tuple):\n",
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" return tuple(self[i] for i in var)\n",
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"\n",
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" # resolve variable recursively\n",
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" if isinstance(var, str):\n",
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" if var in self.reference:\n",
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" return self[self.reference[var]]\n",
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" return var\n",
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"\n",
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" # atomic value\n",
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" if isinstance(var, int):\n",
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" return var\n",
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"\n",
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" # invalid object\n",
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" raise TypeError()\n",
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"\n",
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" def __enter__(self):\n",
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" # store unification checkpoint\n",
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" self.checkpoint.append([])\n",
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"\n",
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" def __exit__(self, exc_type, *args):\n",
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" # remove checkpoint and unbind variables\n",
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" for var in self.checkpoint.pop():\n",
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" if var in self.reference:\n",
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" del self.reference[var]\n",
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"\n",
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" # suppress exception\n",
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" if exc_type is not GeneratorExit:\n",
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" return True"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 2,
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"metadata": {
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"collapsed": true
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},
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"outputs": [],
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"source": [
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"def conc(PREFIX, SUFFIX, RESULT):\n",
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" HEAD, TAIL, CONC = unify.variable('HEAD', 'TAIL', 'CONC')\n",
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"\n",
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" with unify:\n",
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" unify(PREFIX, EMPTY) and unify(SUFFIX, RESULT)\n",
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" yield\n",
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"\n",
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" with unify:\n",
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" unify(PREFIX, (HEAD, TAIL)) and unify(RESULT, (HEAD, CONC))\n",
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" yield from conc(TAIL, SUFFIX, CONC)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## run"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 3,
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"metadata": {
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"collapsed": false
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},
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"outputs": [],
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"source": [
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"unify = Unify()"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 4,
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"metadata": {
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"collapsed": true
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},
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"outputs": [],
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"source": [
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"EMPTY = tuple()\n",
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"prefix = (1, (2, EMPTY))\n",
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"suffix = (3, (4, EMPTY))\n",
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"result = (1, (2, (3, (4, EMPTY))))"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"#### concatenate PREFIX and SUFFIX"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 5,
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"metadata": {
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"collapsed": false
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},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"(1, (2, (3, (4, ()))))\n"
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]
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}
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],
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"source": [
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"for _ in conc(prefix, suffix, 'RESULT'):\n",
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" print(unify['RESULT'])"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"#### what was concatenated to PREFIX if RESULT is this?"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 6,
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"metadata": {
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"collapsed": false
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},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"(3, (4, ()))\n"
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]
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}
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],
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"source": [
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"for _ in conc(prefix, 'SUFFIX', result):\n",
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" print(unify['SUFFIX'])"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"#### this is super cool! if RESULT is this, what was PREFIX and SUFFIX?"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 7,
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"metadata": {
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"collapsed": false
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},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"possible answer is () and (1, (2, (3, (4, ()))))\n",
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"possible answer is (1, ()) and (2, (3, (4, ())))\n",
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"possible answer is (1, (2, ())) and (3, (4, ()))\n",
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"possible answer is (1, (2, (3, ()))) and (4, ())\n",
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"possible answer is (1, (2, (3, (4, ())))) and ()\n"
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]
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}
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],
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"source": [
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"for _ in conc('PREFIX', 'SUFFIX', result):\n",
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" print('possible answer is', unify['PREFIX'], 'and', unify['SUFFIX'])"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"#### if PREFIX and SUFFIX are concatenated, would this be RESULT?"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 8,
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"metadata": {
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"collapsed": false
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},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"yes\n"
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]
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}
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],
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"source": [
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"for _ in conc(prefix, suffix, result):\n",
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" print('yes')\n",
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" break\n",
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"else:\n",
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" print('no')"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 9,
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"metadata": {
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"collapsed": false
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},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"yes\n"
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]
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}
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],
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"source": [
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"for _ in conc(prefix, suffix, result):\n",
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" print('yes')\n",
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" break\n",
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"else:\n",
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" print('no')"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## most people won't solve this one"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 10,
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"metadata": {
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"collapsed": false
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},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"PREFIX = ()\n",
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"SUFFIX = RESULT\n",
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"RESULT = RESULT\n",
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"\n",
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"PREFIX = ('HEAD_18', ())\n",
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"SUFFIX = CONC_18\n",
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"RESULT = ('HEAD_18', 'CONC_18')\n",
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"\n",
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"PREFIX = ('HEAD_18', ('HEAD_19', ()))\n",
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"SUFFIX = CONC_19\n",
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"RESULT = ('HEAD_18', ('HEAD_19', 'CONC_19'))\n",
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"\n",
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"PREFIX = ('HEAD_18', ('HEAD_19', ('HEAD_20', ())))\n",
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"SUFFIX = CONC_20\n",
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"RESULT = ('HEAD_18', ('HEAD_19', ('HEAD_20', 'CONC_20')))\n",
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"\n",
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"PREFIX = ('HEAD_18', ('HEAD_19', ('HEAD_20', ('HEAD_21', ()))))\n",
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"SUFFIX = CONC_21\n",
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"RESULT = ('HEAD_18', ('HEAD_19', ('HEAD_20', ('HEAD_21', 'CONC_21'))))\n",
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"\n"
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]
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}
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],
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"source": [
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"for _ in zip(range(5), conc('PREFIX', 'SUFFIX', 'RESULT')):\n",
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" print('PREFIX =', unify['PREFIX'])\n",
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" print('SUFFIX =', unify['SUFFIX'])\n",
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" print('RESULT =', unify['RESULT'])\n",
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" print()"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"collapsed": true
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},
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"outputs": [],
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"source": []
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "Python 3",
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"language": "python",
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"name": "python3"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.6.0"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 2
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}

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