Lec_9_universailty.ipynb

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 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Lecture 9: Universility and uncomputability"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# utility code \n",
    "%run \"Utilities.ipynb\"\n",
    "from IPython.display import clear_output\n",
    "clear_output()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Universal TM"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def EVAL(δ,x):\n",
    "    Tape = [\"▷\"] + [a for a in x]\n",
    "    i = 0; s = 0 \n",
    "    while True:\n",
    "        s, Tape[i], d = δ[(s,Tape[i])] \n",
    "        if d == \"H\": break\n",
    "        if d == \"L\": i = max(i-1,0)\n",
    "        if d == \"R\": i += 1\n",
    "        if i>= len(Tape): Tape.append('Φ')\n",
    "    return Tape[1]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Hardwiring"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "def hardwire(code,m):\n",
    "    return code.replace(\"f(n):\\n\",f\"g():\\n    n={m}\\n\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "import inspect"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "def f(n):\n",
    "    res = 1\n",
    "    for i in range(n):\n",
    "        res *= 2\n",
    "    return res"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "def g():\n",
    "    n=10\n",
    "    res = 1\n",
    "    for i in range(n):\n",
    "        res *= 2\n",
    "    return res"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "def g():\n",
      "    n=10\n",
      "    res = 1\n",
      "    for i in range(n):\n",
      "        res *= 2\n",
      "    return res\n",
      "\n"
     ]
    }
   ],
   "source": [
    "code = hardwire(inspect.getsource(f),10)\n",
    "print(code)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "exec(code)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1024"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1024"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "g()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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