3-curry.ipynb

{
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   "source": [
    "# Partial Evalutation and Currying\n",
    "\n",
    "通常编程时，我们会想半途中评估函数(debug)。 考虑下cumulative sum的以下定义\n",
    "\n",
    "```\n",
    "def cumsum(data):\n",
    "    return accumulate(add, data)\n",
    "```\n",
    "\n",
    "还有函数 `fib_many` 执行了 Fibonacci 函数, `fib`, 对一个数字列表操作\n",
    "\n",
    "```\n",
    "def fib_many(data):\n",
    "    return map(fib, data)\n",
    "```\n",
    "\n",
    "在每种情况下，我们专门研究一个具有单一特定参数的高阶函数（`accumulate`或`map`），将第二个参数打开供将来使用。\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 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"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 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)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1, 3, 6, 7, 9, 12]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
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    }
   ],
   "source": [
    "# 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",
    "list(cumsum([1,2,3,1,2,3]))\n",
    "# Semantically like the following:\n",
    "# cumsum(whatever) = accumulate(add, whatever)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercise\n",
    "\n",
    "局部执行 `mul` 函数去创建新的double函数"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "ename": "SyntaxError",
     "evalue": "invalid syntax (<ipython-input-4-854a2ed35155>, line 1)",
     "output_type": "error",
     "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"
     ]
    }
   ],
   "source": [
    "double = ...\n",
    "assert double(5) = 10"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Curry\n",
    "\n",
    "\n",
    "柯里化提供合成糖进行部分评估。\n",
    "\n",
    "curry 是一个更高阶的函数，它改变了函数用一组不完整的参数调用时的行为\n",
    "\n",
    "通常Python会引发TypeError。\n",
    "\n",
    "现在它返回一个局部函数。\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "ename": "TypeError",
     "evalue": "mul() missing 1 required positional argument: 'y'",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mTypeError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-8-113614f7494a>\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() missing 1 required positional argument: 'y'"
     ]
    }
   ],
   "source": [
    "mul(2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "16"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from toolz import curry\n",
    "mul = curry(mul)\n",
    "mul2 = mul(2)\n",
    "mul2(8)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "functools.partial 允许函数性陈述的惯用表达式执行。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "ename": "TypeError",
     "evalue": "accumulate() missing 1 required positional argument: 'seq'",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mTypeError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-11-a4451ae4b8fc>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[1;32m----> 1\u001b[1;33m \u001b[0maccumulate\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0madd\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[1;31mTypeError\u001b[0m: accumulate() missing 1 required positional argument: 'seq'"
     ]
    }
   ],
   "source": [
    "accumulate(add)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1, 1, 2, 3, 5, 8, 13, 21, 34, 55]"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "accumulate = curry(accumulate)\n",
    "\n",
    "cumsum = accumulate(add)\n",
    "cumprod = accumulate(mul)\n",
    "\n",
    "fibMany = curry(map(fib))\n",
    "\n",
    "list(fibMany(range(10)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Curried namespace\n",
    "\n",
    "Toolz包含一个用于curried函数的独立命名空间\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "from toolz.curried import map\n",
    "fibMany = map(fib)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is the same as the following:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from toolz import map, curry\n",
    "map = curry(map)"
   ]
  }
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