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  {
   "cells": [
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# Partial Evalutation and Currying\n",
      "\n",
      "Often when programming we want to evaluate a function only halfway.  Consider the following definition of cumulative sum\n",
      "\n",
      "```\n",
      "def cumsum(data):\n",
      "    return accumulate(add, data)\n",
      "```\n",
      "\n",
      "or of `fib_many` which applies the Fibonacci function, `fib`, onto a list\n",
      "\n",
      "```\n",
      "def fib_many(data):\n",
      "    return map(fib, data)\n",
      "```\n",
      "\n",
      "In each case we specialize a higher order function (`accumulate` or `map`) with a single specific argument, leaving the second argument open for future use.  "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Obligatory set of small functions\n",
      "\n",
      "from toolz import accumulate\n",
      "\n",
      "def add(x, y):\n",
      "    return x + y\n",
      "\n",
      "def mul(x, y):\n",
      "    return x * y\n",
      "\n",
      "def fib(n):\n",
      "    a, b = 0, 1\n",
      "    for i in range(n):\n",
      "        a, b = b, a + b\n",
      "    return b"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# We commonly use a lambda expression and the equals sign\n",
      "cumsum = lambda data: accumulate(add, data)\n",
      "\n",
      "# This is perfectly equivalent to the function definition\n",
      "def cumsum(data):\n",
      "    return accumulate(add, data)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Or we can use the `partial` function from functools\n",
      "# Partial inserts an argument into the first place\n",
      "from functools import partial\n",
      "cumsum = partial(accumulate, add)\n",
      "\n",
      "# Semantically like the following:\n",
      "# cumsum(whatever) = accumulate(add, whatever)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 3
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Exercise\n",
      "\n",
      "Partially evaluate the `mul` function to create a new function `double`"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "double = ...\n",
      "assert double(5) = 10"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "ename": "SyntaxError",
       "evalue": "invalid syntax (<ipython-input-4-854a2ed35155>, line 1)",
       "output_type": "pyerr",
       "traceback": [
        "\u001b[1;36m  File \u001b[1;32m\"<ipython-input-4-854a2ed35155>\"\u001b[1;36m, line \u001b[1;32m1\u001b[0m\n\u001b[1;33m    double = ...\u001b[0m\n\u001b[1;37m             ^\u001b[0m\n\u001b[1;31mSyntaxError\u001b[0m\u001b[1;31m:\u001b[0m invalid syntax\n"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Curry\n",
      "\n",
      "Currying provides syntacic sugar for partial evaluation.  \n",
      "\n",
      "Curry is a higher order function that changes the behavior of what a function does when it is called with an incomplete set of arguments\n",
      "\n",
      "Normally Python would raise a TypeError.\n",
      "\n",
      "Now it returns a partial"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "mul(2)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "ename": "TypeError",
       "evalue": "mul() takes exactly 2 arguments (1 given)",
       "output_type": "pyerr",
       "traceback": [
        "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m\n\u001b[1;31mTypeError\u001b[0m                                 Traceback (most recent call last)",
        "\u001b[1;32m<ipython-input-5-74f550b0a831>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[1;32m----> 1\u001b[1;33m \u001b[0mmul\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m2\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m",
        "\u001b[1;31mTypeError\u001b[0m: mul() takes exactly 2 arguments (1 given)"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from toolz import curry\n",
      "mul = curry(mul)\n",
      "mul(2)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 6,
       "text": [
        "<functools.partial at 0x17c1578>"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "This allows for the idiomatic expression of functional statements"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "accumulate = curry(accumulate)\n",
      "map = curry(map)\n",
      "\n",
      "cumsum = accumulate(add)\n",
      "cumprod = accumulate(mul)\n",
      "\n",
      "fibMany = map(fib)\n",
      "\n",
      "fibMany(range(10))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 7,
       "text": [
        "[1, 1, 2, 3, 5, 8, 13, 21, 34, 55]"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Curried namespace\n",
      "\n",
      "Toolz contains a separate namespace for curried functions"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from toolz.curried import map"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 8
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "This is the same as the following:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from toolz import map, curry\n",
      "map = curry(map)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 9
    }
   ],
   "metadata": {}
  }
 ]
}