fall22_lec4_code_data.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "44f92d39-1cea-4854-9154-58551a2fc566",
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   "source": [
    "%%html\n",
    "<!--\n",
    "<style>\n",
    ".CodeMirror { width: 100vw; }\n",
    ".prompt  { visibility: hidden; width: 0px !important; }\n",
    ".prompt_container { visibility: hidden; width: 0px !important; }\n",
    ".container {  width: 95% !important; }\n",
    ".rendered_html { font-size:0.8em; }\n",
    ".rendered_html table, .rendered_html th, .rendered_html tr, .rendered_html td { font-size: 100%;}\n",
    "td { font-size: 16px }\n",
    "</style>\n",
    "-->"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "bb0ccb91-9809-4136-acc5-c465f1ecee6c",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "import schemdraw\n",
    "import schemdraw.logic as logic\n",
    "import schemdraw.elements as elm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "072634e3-8ee2-4feb-ac12-9310fd6a261a",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "%config InlineBackend.figure_format = 'svg'"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "818547ec-bf25-4c03-9498-d513c2fdd0df",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "![](https://i.imgur.com/xyqpqh0.png)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f5f2bff9",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "![](https://i.imgur.com/VVl1WOW.jpg)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "a5f94020-db85-4b4b-81ba-534fb9c4955f",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
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   "outputs": [],
   "source": [
    "# class Bit:\n",
    "#   counter = 0\n",
    "  \n",
    "#   @classmethod\n",
    "#   def uid(cls):\n",
    "#     cls.counter +=1\n",
    "#     return f\"t_{cls.counter}\"\n",
    "\n",
    "#   def __init__(self,label = None): \n",
    "#     self.label = self.uid() if label is None else label\n",
    "#     self.program = tuple([self.label])\n",
    "  \n",
    "#   def op(self,oper, *others):\n",
    "#     operands = [self, *others]\n",
    "#     out = Bit()\n",
    "#     out.program = tuple([oper, *[bit.program for bit in operands]])\n",
    "#     return out\n",
    "\n",
    "#   def __and__(self,other): return self.op(\"∧\", other)\n",
    "#   def __or__(self,other): return self.op(\"∨\", other)\n",
    "#   def __invert__(self): return self.op(\"¬\")\n",
    "  \n",
    "#   def __repr__(self): return f\"Bit{self.program}\"\n",
    "\n",
    "# def bits(n):\n",
    "#   return [Bit(f\"X[{i}]\") for i in range(n)]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8843dcbc-e05d-4484-972a-9c4242ff015f",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "# Some examples"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "a259bd4f",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "def lsb(x): return x & 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "e7e0938f",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = 1 \n",
    "b = 0\n",
    "c = a|b\n",
    "c"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "05512baf-dfee-45d0-89f2-66cd0cab01ef",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "class Bit:\n",
    "    \"\"\"Keeps track of operations that are done to it\"\"\"\n",
    " \n",
    "    def __init__(self, program):\n",
    "        self.program = program if isinstance(program,tuple) else (program,)\n",
    "  \n",
    "    def op(self,oper, other = None):\n",
    "        if other is None:\n",
    "            return Bit((oper,self.program))\n",
    "        return Bit((oper,self.program,other.program))\n",
    "        \n",
    "    def __and__(self,other): return self.op(\"∧\", other)\n",
    "    def __or__(self,other): return self.op(\"∨\", other)\n",
    "    def __invert__(self): return self.op(\"¬\")\n",
    "  \n",
    "    def __repr__(self): return f\"Bit{self.program}\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "dfd60d62",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "('∨', ('X[0]',), ('X[1]',))"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = Bit(\"X[0]\")\n",
    "b = Bit(\"X[1]\")\n",
    "(a|b).program"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c2a37394-70ac-4953-997c-0e01fdc04b1b",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "# Utilities\n",
    "\n",
    "Skip all of these in first reading"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "bf0515c3",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "def bits(n):\n",
    "    return [Bit(f\"X[{i}]\") for i in range(n)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "85ef6a6b-bcfd-4db6-9624-d195a5f05147",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "def p2f(P):\n",
    "  \"\"\"Recursive function to transform a program of a Bit into a formula\"\"\"\n",
    "  if len(P)==1:\n",
    "    return P[0]\n",
    "  if len(P)==2:\n",
    "    return P[0] + p2f(P[1])\n",
    "  if len(P)==3:\n",
    "    return f\"({p2f(P[1])} {P[0]} {p2f(P[2])})\"\n",
    "  return f\"{P[0]}(\"+\",\".join([p2f(P[i]) for i in range(1,len(P))])+\")\"\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "fd90c957-2011-4090-ab54-753ef8297e18",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "counter = 0\n",
    "def AON_(P):\n",
    "    \"\"\"Recursive function to transform a program of a bit into an AON straightline program\"\"\"\n",
    "    def uid():\n",
    "        global counter\n",
    "        counter +=1\n",
    "        return f\"z_{counter}\"\n",
    "    funcs = {\"∧\": \"AND\", \"∨\": \"OR\", \"¬\": \"NOT\" }\n",
    "    if len(P)==1:\n",
    "        return \"\",P[0]\n",
    "    op = funcs[P[0]]  \n",
    "    if len(P)==2:\n",
    "        prog, out_ = AON_(P[1])\n",
    "        out = uid() \n",
    "        return prog+f\"{out} = {op}({out_})\\n\", out\n",
    "    if len(P)==3:\n",
    "        prog1,out1 = AON_(P[1])\n",
    "        prog2,out2 = AON_(P[2])\n",
    "        out = uid()\n",
    "        return prog1+prog2+f\"{out} = {op}({out1},{out2})\\n\", out"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "cb7bb679-e7bd-4eab-92de-0b7fecfcf739",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "def AON(f):\n",
    "    \"\"\"Take either a function or a bit and return the AON program\"\"\"\n",
    "    global counter\n",
    "    counter = 0\n",
    "    if isinstance(f,Bit):\n",
    "        P = f.program\n",
    "    else:\n",
    "        n = len(signature(f).parameters)\n",
    "        P = f(*bits(n)).program\n",
    "    prog, out = AON_(P)\n",
    "    return prog.replace(out,\"Y[0]\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "6b0e7ffd-c37f-4320-a525-53ec6ad110b8",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "def formula(f):\n",
    "    \"\"\"Take either a function or a bit and return the AON program\"\"\"\n",
    "    if isinstance(f,Bit):\n",
    "        return Math(p2f(f.program))\n",
    "    n = len(signature(f).parameters)\n",
    "    F = p2f(f(*bits(n)).program)\n",
    "    return Math(F)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "2535f4a2-e1c2-4ee6-add5-b10405741906",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "def circuit_(P, d : schemdraw.Drawing , dx=0, dy=0, drawn = {}):\n",
    "  \"\"\"Recursive function to draw a circuit. Gets the Bit bit and outputs the circuit used to compute it\"\"\"\n",
    "  if P in drawn:\n",
    "    return drawn[P]\n",
    "  maxx = dx\n",
    "  maxy = dy\n",
    "  outs = []\n",
    "  gates = { \"∧\" : logic.And, \"∨\" : logic.Or, \"¬\": logic.Not } \n",
    "  for c in P[1:]:\n",
    "    dx_ , dy_ , out = circuit_(c,d,dx,dy ,drawn)\n",
    "    outs.append(out)\n",
    "    maxx = max(dx_,maxx)\n",
    "    maxy = max(dy_,maxy)\n",
    "    dy = dy_ + 1\n",
    "  maxx += 2\n",
    "  x,y = maxx,maxy\n",
    "  gate = gates[P[0]] if P[0] in gates else logic.Dot\n",
    "  g = gate(at = (x,y))\n",
    "  if isinstance(g, logic.Dot):\n",
    "    g.label(f\"{P[0]}\")\n",
    "  d += g\n",
    "  for i,out in enumerate(outs):\n",
    "    loc = getattr(g,f\"in{i+1}\") \n",
    "    d += logic.Wire().at(out).to(loc)  \n",
    "  drawn[P] =  x,y, g.out if hasattr(g,\"out\") else (x,y)\n",
    "  return drawn[P]\n",
    "\n",
    "def draw_circ(*Ys):\n",
    "  drawn = {}\n",
    "  dx,dy = 0,0\n",
    "  with schemdraw.Drawing() as d:\n",
    "    d.config(unit=0.5)\n",
    "    for i,y in enumerate(Ys):\n",
    "      label= f\"$Y[{i}]$\"\n",
    "      x,dy_, out = circuit_(y.program,d,dx,dy, drawn)\n",
    "      d += logic.Dot().at(out).label(label)\n",
    "      dy = dy_+2\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "f89391fa-2e7c-422b-8b69-0c943dcef73d",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "import itertools\n",
    "from IPython.display import Markdown, display, Math\n",
    "from inspect import signature\n",
    "\n",
    "def table(f,n=None):\n",
    "  \"\"\"Generate truth table of a function\"\"\"\n",
    "  if n is None:\n",
    "    n = len(signature(f).parameters)\n",
    "  m = max(n+2,len(f.__name__)+4)\n",
    "  res = \"x\".ljust(m) + \" | \" + f\"{f.__name__}(x)\".ljust(m) \n",
    "  res += \"\\n\" + \"-\"*m+\"-|-\"+ \"-\"*m \n",
    "  \n",
    "  for x in itertools.product([0,1],repeat=n):\n",
    "    s = \"\".join([str(c) for c in x])\n",
    "    res += \"\\n\"+ s.ljust(m) + \" | \" + str(f(*x)).ljust(m)\n",
    "  res +=\"\\n\"\n",
    "  return Markdown(res)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "8228f0d7-0c0f-463c-9aa7-e055edec25b3",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "def circuit(f,n=None):\n",
    "    \"\"\"Take a function or a bit and output circuit\"\"\"\n",
    "    if isinstance(f,Bit):\n",
    "        res = f\n",
    "    else:\n",
    "        if n is None:\n",
    "            n = len(signature(f).parameters)\n",
    "        res = f(*bits(n))\n",
    "    return draw_circ(*res) if isinstance(res,(tuple,list)) else draw_circ(res)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7bc78cb5",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "# End of utilities"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "b099a461-088e-4e12-ae6c-54c73400e058",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Bit('¬', ('∧', ('X[0]',), ('X[1]',)))"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = Bit(\"X[0]\")\n",
    "b = Bit(\"X[1]\")\n",
    "c = a & b\n",
    "~c "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "3b180695-bf3b-42ad-a1ca-7f561254221f",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Bit('¬', ('∨', ('X[2]',), ('∧', ('X[0]',), ('X[1]',))))"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d = Bit(\"X[2]\")\n",
    "e = ~(d | c)\n",
    "e"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "310faa96",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle ¬(X[2] ∨ (X[0] ∧ X[1]))$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "formula(e)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "c0488e95-5954-4e65-9b2c-d3dc25a79f1f",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
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   "outputs": [
    {
     "data": {
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   "source": [
    "### XOR"
   ]
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  {
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   "execution_count": 197,
   "id": "c8b2472b-2230-4813-bbac-aa0ce0b93925",
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   "source": [
    "def XOR(a,b):\n",
    "    return (a & ~b) | (~a & b)"
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     "execution_count": 199,
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   "source": [
    "XOR(1,1)"
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  },
  {
   "cell_type": "code",
   "execution_count": 200,
   "id": "f677be24-fd38-4dae-b2d1-81e847edb2dc",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/markdown": [
       "x       | XOR(x) \n",
       "--------|--------\n",
       "00      | 0      \n",
       "01      | 1      \n",
       "10      | 1      \n",
       "11      | 0      \n"
      ],
      "text/plain": [
       "<IPython.core.display.Markdown object>"
      ]
     },
     "execution_count": 200,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "table(XOR)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 201,
   "id": "8ab6d399",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Bit('∨', ('∧', ('X[0]',), ('¬', ('X[1]',))), ('∧', ('¬', ('X[0]',)), ('X[1]',)))"
      ]
     },
     "execution_count": 201,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "XOR(Bit(\"X[0]\"),Bit(\"X[1]\"))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 202,
   "id": "0fa50196-825c-43ba-b809-40343519c158",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle ((X[0] ∧ ¬X[1]) ∨ (¬X[0] ∧ X[1]))$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "execution_count": 202,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "formula(XOR)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 203,
   "id": "d0542ae5-a902-4b67-b00e-79cf079f01b0",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'z_1 = NOT(X[1])\\nz_2 = AND(X[0],z_1)\\nz_3 = NOT(X[0])\\nz_4 = AND(z_3,X[1])\\nY[0] = OR(z_2,z_4)\\n'"
      ]
     },
     "execution_count": 203,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "AON(XOR)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 204,
   "id": "a3088a07",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "z_1 = NOT(X[1])\n",
      "z_2 = AND(X[0],z_1)\n",
      "z_3 = NOT(X[0])\n",
      "z_4 = AND(z_3,X[1])\n",
      "Y[0] = OR(z_2,z_4)\n",
      "\n"
     ]
    }
   ],
   "source": [
    "print(AON(XOR))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 205,
   "id": "315a7567-1419-4549-8090-afd1199bf9a0",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<schemdraw.backends.mpl.Figure object at 0x7fa1703e1b40>"
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     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "circuit(XOR)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8b25df7e-6518-4de1-8eb2-961744f0e91b",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Composition"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 206,
   "id": "29f9a187-7d52-4b51-94b1-0b9089b19972",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "def XOR4(a,b,c,d):\n",
    "    return XOR(XOR(a,b),XOR(c,d))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 207,
   "id": "fb8849e2-4bdc-4a23-b9dc-47273d407f06",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle ((((X[0] ∧ ¬X[1]) ∨ (¬X[0] ∧ X[1])) ∧ ¬((X[2] ∧ ¬X[3]) ∨ (¬X[2] ∧ X[3]))) ∨ (¬((X[0] ∧ ¬X[1]) ∨ (¬X[0] ∧ X[1])) ∧ ((X[2] ∧ ¬X[3]) ∨ (¬X[2] ∧ X[3]))))$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "execution_count": 207,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "formula(XOR4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 208,
   "id": "1a7ba167-5f97-4952-9f85-118df1d437b0",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "z_1 = NOT(X[1])\n",
      "z_2 = AND(X[0],z_1)\n",
      "z_3 = NOT(X[0])\n",
      "z_4 = AND(z_3,X[1])\n",
      "z_5 = OR(z_2,z_4)\n",
      "z_6 = NOT(X[3])\n",
      "z_7 = AND(X[2],z_6)\n",
      "z_8 = NOT(X[2])\n",
      "z_9 = AND(z_8,X[3])\n",
      "z_10 = OR(z_7,z_9)\n",
      "z_11 = NOT(z_10)\n",
      "z_12 = AND(z_5,z_11)\n",
      "z_13 = NOT(X[1])\n",
      "z_14 = AND(X[0],z_13)\n",
      "z_15 = NOT(X[0])\n",
      "z_16 = AND(z_15,X[1])\n",
      "z_17 = OR(z_14,z_16)\n",
      "z_18 = NOT(z_17)\n",
      "z_19 = NOT(X[3])\n",
      "z_20 = AND(X[2],z_19)\n",
      "z_21 = NOT(X[2])\n",
      "z_22 = AND(z_21,X[3])\n",
      "z_23 = OR(z_20,z_22)\n",
      "z_24 = AND(z_18,z_23)\n",
      "Y[0] = OR(z_12,z_24)\n",
      "\n"
     ]
    }
   ],
   "source": [
    "print(AON(XOR4))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 209,
   "id": "90241783-dd39-466a-a8f5-9355ead5b820",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
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   "source": [
    "circuit(XOR4)"
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   "source": [
    "def MAJ(a,b,c):\n",
    "    return (a&b) | (b&c) | (a&c)"
   ]
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    "table(MAJ)"
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    "formula(MAJ)"
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  {
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    "circuit(MAJ)"
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  {
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   "source": [
    "def add(a,b):\n",
    "    return XOR(a,b), a&b"
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  {
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   "id": "9651424a-e634-48cb-be68-e314ab5485f9",
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   "source": [
    "# Parsing programs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "3baf7f08-340b-4b1a-a470-3e16ab71728c",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "import re\n",
    "def parse(P):\n",
    "    \"\"\"Take an AON program and split each line into components\"\"\"\n",
    "    result  = []\n",
    "    for line in P.split('\\n'):\n",
    "        split = re.split(\"=|\\(|\\)|,| \",line) \n",
    "        split = [x for x in split if x != \"\"]\n",
    "        if split:\n",
    "            result.append(split)\n",
    "    return result\n",
    " "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 210,
   "id": "a32de32c-b02e-4ff4-9572-a203f525f617",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[['z_1', 'NOT', 'X[1]'],\n",
       " ['z_2', 'AND', 'X[0]', 'z_1'],\n",
       " ['z_3', 'NOT', 'X[0]'],\n",
       " ['z_4', 'AND', 'z_3', 'X[1]'],\n",
       " ['Y[0]', 'OR', 'z_2', 'z_4']]"
      ]
     },
     "execution_count": 210,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "parse(AON(XOR))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 211,
   "id": "01f11112-dc63-49af-95d5-d9cb2510028f",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "def evalp(tuples,x):\n",
    "    \"\"\"Evaluate a parsed program on an input\"\"\"\n",
    "    variables = { f\"X[{i}]\":x[i] for i in range(len(x)) }\n",
    "    for rhs,op,*oper in tuples:\n",
    "        print(f\"Evaluating {rhs} = {op}({','.join(oper)}):\\t variables = {variables}\")\n",
    "        oper = [variables[o] for o in oper]\n",
    "        if op==\"NOT\":\n",
    "            variables[rhs] = 1 - oper[0]\n",
    "        elif op==\"AND\":\n",
    "            variables[rhs] = oper[0]*oper[1]\n",
    "        elif op==\"OR\":\n",
    "            variables[rhs] = 1 - (1-oper[0])*(1-oper[1])\n",
    "    return variables[\"Y[0]\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 212,
   "id": "949c8d9a-6d56-4b10-95c4-684850848337",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "z_1 = NOT(X[1])\n",
      "z_2 = AND(X[0],z_1)\n",
      "z_3 = NOT(X[0])\n",
      "z_4 = AND(z_3,X[1])\n",
      "Y[0] = OR(z_2,z_4)\n",
      "\n"
     ]
    }
   ],
   "source": [
    "aon = parse(AON(XOR))\n",
    "print(AON(XOR))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 214,
   "id": "517dfcd9-b6e9-4899-a9b1-31658507018a",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Evaluating z_1 = NOT(X[1]):\t variables = {'X[0]': 1, 'X[1]': 1}\n",
      "Evaluating z_2 = AND(X[0],z_1):\t variables = {'X[0]': 1, 'X[1]': 1, 'z_1': 0}\n",
      "Evaluating z_3 = NOT(X[0]):\t variables = {'X[0]': 1, 'X[1]': 1, 'z_1': 0, 'z_2': 0}\n",
      "Evaluating z_4 = AND(z_3,X[1]):\t variables = {'X[0]': 1, 'X[1]': 1, 'z_1': 0, 'z_2': 0, 'z_3': 0}\n",
      "Evaluating Y[0] = OR(z_2,z_4):\t variables = {'X[0]': 1, 'X[1]': 1, 'z_1': 0, 'z_2': 0, 'z_3': 0, 'z_4': 0}\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 214,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "evalp(aon,[1,1])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f41ef8b9",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "[tiny.cc/areyouhere](https://tiny.cc/areyouhere)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f86686d2",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Digression: Neural networks and pytorch\n",
    "\n",
    "\n",
    "![](https://i.imgur.com/JbPlJlM.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ca7863ca",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "![](https://i.imgur.com/pG0RixM.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9a10b977",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "![](https://i.imgur.com/DXAO5vi.png)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "2b41b38d",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "import torch"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 215,
   "id": "b7ead96f",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([1.], grad_fn=<MulBackward0>)"
      ]
     },
     "execution_count": 215,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import torch\n",
    "a = torch.tensor([0.5], requires_grad=True)\n",
    "b = torch.tensor([2.0], requires_grad=True)\n",
    "a*b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "a09604f9",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "def t2f(fn):\n",
    "    if isinstance(fn,torch.Tensor):\n",
    "        fn = fn._grad_fn\n",
    "    ops = [t2f(x) for x,_ in fn.next_functions]\n",
    "    name = str(fn.__class__)\n",
    "    i = name.find(\"'\")\n",
    "    j = name[i+1:].find(\"'\")+i+1\n",
    "    name = name[i+1:j]\n",
    "    if not ops:\n",
    "        return name\n",
    "    return name+\"(\"+ \",\".join(ops) +\")\"\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 216,
   "id": "3ddda0cb",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'MulBackward0(AddBackward0(AccumulateGrad,AccumulateGrad),AddBackward0(AccumulateGrad,AccumulateGrad))'"
      ]
     },
     "execution_count": 216,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "t2f( (a+b)*(a+b))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 217,
   "id": "26ce624d",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'LogBackward0(MulBackward0(AccumulateGrad,AccumulateGrad))'"
      ]
     },
     "execution_count": 217,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c = torch.log(a*b)\n",
    "t2f(c)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "120259b8",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "# Adaptation of gist https://gist.github.com/OniDaito/f5bfb83b6677835219feeb95ddb1e4ad \n",
    "\n",
    "\n",
    "# Our drawing graph functions. We rely / have borrowed from the following\n",
    "# python libraries:\n",
    "# https://github.com/szagoruyko/pytorchviz/blob/master/torchviz/dot.py\n",
    "# https://github.com/willmcgugan/rich\n",
    "# https://graphviz.readthedocs.io/en/stable/\n",
    "\n",
    "\n",
    "def draw_graph(start, watch=[]):\n",
    "    from graphviz import Digraph\n",
    "\n",
    "    node_attr = dict(style='filled',\n",
    "                     shape='box',\n",
    "                     align='left',\n",
    "                     fontsize='12',\n",
    "                     ranksep='0.1',\n",
    "                     height='0.2')\n",
    "    graph = Digraph(node_attr=node_attr, graph_attr=dict(size=\"12,12\"))\n",
    "\n",
    "    assert(hasattr(start, \"grad_fn\"))\n",
    "    if start.grad_fn is not None:\n",
    "        o = lambda a: None\n",
    "        o.next_functions = [(start.grad_fn,0)]\n",
    "        _draw_graph(o, graph, watch=watch)\n",
    "\n",
    "    size_per_element = 0.15\n",
    "    min_size = 12\n",
    "\n",
    "    # Get the approximate number of nodes and edges\n",
    "    num_rows = len(graph.body)\n",
    "    content_size = num_rows * size_per_element\n",
    "    size = max(min_size, content_size)\n",
    "    size_str = str(size) + \",\" + str(size)\n",
    "    graph.graph_attr.update(size=size_str)\n",
    "    graph.render(filename='net_graph.jpg')\n",
    "    return graph\n",
    "\n",
    "\n",
    "def _draw_graph(var, graph, watch=[], seen=[], indent=\"\", pobj=None):\n",
    "    ''' recursive function going through the hierarchical graph printing off\n",
    "    what we need to see what autograd is doing.'''\n",
    "    #from rich import print\n",
    "    \n",
    "    if hasattr(var, \"next_functions\"):\n",
    "        for fun in var.next_functions:\n",
    "            joy = fun[0]\n",
    "            if joy is not None:\n",
    "                if True or joy not in seen:\n",
    "                    label = str(type(joy)).replace(\n",
    "                        \"class\", \"\").replace(\"'\", \"\").replace(\" \", \"\")\n",
    "                    label_graph = label\n",
    "                    colour_graph = \"\"\n",
    "                    seen.append(joy)\n",
    "\n",
    "                    if hasattr(joy, 'variable'):\n",
    "                        happy = joy.variable\n",
    "                        if happy.is_leaf:\n",
    "                            label += \" \\U0001F343\"\n",
    "                            colour_graph = \"green\"\n",
    "\n",
    "                            for (name, obj) in watch:\n",
    "                                if obj is happy:\n",
    "                                    label += \" \\U000023E9 \" + \\\n",
    "                                        \"[b][u][color=#FF00FF]\" + name + \\\n",
    "                                        \"[/color][/u][/b]\"\n",
    "                                    label_graph += name\n",
    "                                    \n",
    "                                    colour_graph = \"blue\"\n",
    "                                    break\n",
    "\n",
    "                                vv = [str(obj.shape[x]) for x in range(len(obj.shape))]\n",
    "                                label += \" [[\"\n",
    "                                label += ', '.join(vv)\n",
    "                                label += \"]]\"\n",
    "                                label += \" \" + str(happy.var())\n",
    "\n",
    "                    graph.node(str(joy), label_graph, fillcolor=colour_graph)\n",
    "                    #print(indent + label)\n",
    "                    _draw_graph(joy, graph, watch, seen, indent + \".\", joy)\n",
    "                    if pobj is not None:\n",
    "                        graph.edge(str(pobj), str(joy))"
   ]
  },
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   "execution_count": 218,
   "id": "0d5105fd",
   "metadata": {
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   "source": [
    "draw_graph((a+b)*(a+b))"
   ]
  },
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   "execution_count": 220,
   "id": "2c989c5a",
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     "execution_count": 220,
     "metadata": {},
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    "draw_graph(c*(a+b))"
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