4. Metaprogramming.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Non-standard string literals"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Example: Write rationals using standard syntax (1/3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "@rat_str (macro with 1 method)"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "macro rat_str(s)\n",
    "    @show s\n",
    "    return nothing\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "s = \"1/3\"\n"
     ]
    }
   ],
   "source": [
    "rat\"1/3\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "@rat_str (macro with 1 method)"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "macro rat_str(s)\n",
    "    # @show s\n",
    "    \n",
    "    !contains(s, \"/\") && throw(ArgumentError(\"Must contain /\"))\n",
    "    \n",
    "    num, den = split(s, \"/\")\n",
    "    \n",
    "    # @show num, den\n",
    "    \n",
    "    n, d = parse.((num, den))\n",
    "    \n",
    "    return Rational(n, d)\n",
    "    \n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1//3"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rat\"1 / 3\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Metaprogramming: Access to structure of code expressions\n",
    "- Macros\n",
    "- MacroTools.jl"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Expressions and syntax trees"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A Julia expression is an unevaluated tree of symbols. We can create an expression object using `:(...)` or `quote`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       ":(x ^ 2 + y ^ 2)"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ex = :(x^2 + y^2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "quote  # In[30], line 2:\n",
       "    x ^ 2 + y ^ 2\n",
       "end"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ex = quote\n",
    "        x^2 + y^2\n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see the internal structure with `dump` or `Meta.show_sexpr`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Expr\n",
      "  head: Symbol call\n",
      "  args: Array{Any}((3,))\n",
      "    1: Symbol +\n",
      "    2: Expr\n",
      "      head: Symbol call\n",
      "      args: Array{Any}((3,))\n",
      "        1: Symbol ^\n",
      "        2: Symbol x\n",
      "        3: Int64 2\n",
      "      typ: Any\n",
      "    3: Expr\n",
      "      head: Symbol call\n",
      "      args: Array{Any}((3,))\n",
      "        1: Symbol ^\n",
      "        2: Symbol y\n",
      "        3: Int64 2\n",
      "      typ: Any\n",
      "  typ: Any\n"
     ]
    }
   ],
   "source": [
    "dump(ex)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(:call, :+, (:call, :^, :x, 2), (:call, :^, :y, 2))"
     ]
    }
   ],
   "source": [
    "Meta.show_sexpr(ex)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can also see it visually with the `TreeView` package I wrote:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\u001b[1m\u001b[36mINFO: \u001b[39m\u001b[22m\u001b[36mPackage TreeView is already installed\n",
      "\u001b[39m\u001b[1m\u001b[36mINFO: \u001b[39m\u001b[22m\u001b[36mMETADATA is out-of-date — you may not have the latest version of TreeView\n",
      "\u001b[39m\u001b[1m\u001b[36mINFO: \u001b[39m\u001b[22m\u001b[36mUse `Pkg.update()` to get the latest versions of your packages\n",
      "\u001b[39m"
     ]
    }
   ],
   "source": [
    "Pkg.add(\"TreeView\")  # needs LaTeX installed on your system"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
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       "\n"
      ],
      "text/plain": [
       "TreeView.LabelledTree({7, 6} directed simple Int64 graph, Any[:+, :^, :x, 2, :^, :y, 2])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "using TreeView\n",
    "\n",
    "@tree x^2 + y^2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Walking a tree"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "We can walk through a tree recursively:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "traverse (generic function with 2 methods)"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function traverse(ex)\n",
    "    println(\"Found $ex\")\n",
    "end\n",
    "        \n",
    "\n",
    "function traverse(ex::Expr)\n",
    "    println(\"Processing expression with head $(ex.head)\")\n",
    "    \n",
    "    for arg in ex.args\n",
    "        println(\"Processing argument $arg\")\n",
    "        \n",
    "        traverse(arg)  # recursive\n",
    "    end\n",
    "end\n",
    "   "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Processing expression with head call\n",
      "Processing argument +\n",
      "Found +\n",
      "Processing argument x ^ 2\n",
      "Processing expression with head call\n",
      "Processing argument ^\n",
      "Found ^\n",
      "Processing argument x\n",
      "Found x\n",
      "Processing argument 2\n",
      "Found 2\n",
      "Processing argument y ^ 2\n",
      "Processing expression with head call\n",
      "Processing argument ^\n",
      "Found ^\n",
      "Processing argument y\n",
      "Found y\n",
      "Processing argument 2\n",
      "Found 2\n"
     ]
    }
   ],
   "source": [
    "traverse(:(x^2 + y^2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercise"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Return a list of all the (non-numeric) symbols in the expression. Hint: you will need to keep track of all the symbols seen so far. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Solution to the exercise "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "traverse (generic function with 1 method)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function traverse!(ex, symbols)\n",
    "    # nothing here!\n",
    "end\n",
    "\n",
    "function traverse!(ex::Symbol, symbols)\n",
    "    push!(symbols, ex)\n",
    "end\n",
    "        \n",
    "\n",
    "function traverse!(ex::Expr, symbols)\n",
    "    \n",
    "    if ex.head == :call  # function call\n",
    "        \n",
    "        for arg in ex.args[2:end]\n",
    "            traverse!(arg, symbols)  # recursive\n",
    "        end\n",
    "        \n",
    "    else\n",
    "    \n",
    "        for arg in ex.args\n",
    "            traverse!(arg, symbols)  # recursive\n",
    "        end\n",
    "    end\n",
    "end\n",
    "\n",
    "function traverse(ex::Expr) \n",
    "    symbols = Symbol[]\n",
    "    traverse!(ex, symbols)\n",
    "    \n",
    "    return symbols\n",
    "end\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(:call, :+, 3, 4)"
     ]
    }
   ],
   "source": [
    "Meta.show_sexpr(:(3 + 4))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2-element Array{Symbol,1}:\n",
       " :x\n",
       " :y"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "traverse(:(x^2 + y^2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3-element Array{Symbol,1}:\n",
       " :x\n",
       " :y\n",
       " :x"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "traverse(:(x^2 + y^2 + x))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercise"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Remove the duplication in the list."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Building a function"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's build a function using the list of symbols:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "build_function (generic function with 1 method)"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function build_function(ex::Expr)\n",
    "    symbols = unique(traverse(ex))\n",
    "    \n",
    "    symbol_tuple = Expr(:tuple, symbols...)\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       ":((x, y))"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "build_function(:(x^2 + y^2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "build_function (generic function with 1 method)"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function build_function(ex::Expr)\n",
    "    symbols = unique(traverse(ex))\n",
    "    \n",
    "    symbol_tuple = Expr(:tuple, symbols...)\n",
    "    \n",
    "    :($symbol_tuple -> $ex)\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       ":((x, y)->begin  # In[17], line 6:\n",
       "            x ^ 2 + y ^ 2 + x\n",
       "        end)"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "build_function(:(x^2 + y^2 + x))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Macros"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To make this user-friendly, we need to write a **macro**. \n",
    "This is a kind of \"super-function\": it takes as argument an expression, from which it calculates a new expression.\n",
    "When the macro returns, the new expression is **automatically evaluated**.    \n",
    "\n",
    "Furthermore, the argument of the macro is **automatically converted** into an `Expr` object:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "@make_function (macro with 1 method)"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "macro make_function(ex)\n",
    "    return build_function(ex)\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(::#3) (generic function with 1 method)"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f = @make_function x^2 + y^2 + x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "28"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f(3, 4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can use `@macroexpand` to see what effect a macro has:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The macro **replaces** the original piece of code before the new piece, before any evaluation takes place."
   ]
  }
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