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【名词解释】Currying:因为是美国数理逻辑学家哈斯凯尔·加里(Haskell Curry)发明了这种函数使用技巧,所以这样用法就以他的名字命名为Currying,中文翻译为“加里化”。

我感觉很多人都对函数加里化(Currying)和偏函数应用(Partial Application)之间的区别搞不清楚,尤其是在相似的上下文环境中它们同时出现的时候。

偏函数解决这样的问题:如果我们有函数是多个参数的,我们希望能固定其中某几个参数的值。

几乎所有编程语言中都有非常明显的偏函数应用。在C语言中:

int foo(int a, int b, int c) {

return a + b + c;

}

int foo23(int a, int c) {

return foo(a, 23, c);

}

foo23函数实际上就是一个foo函数的偏函数应用,参数b的值被固定为23。

当然,像这样明显的偏函数并没有太大的用处;我们通常会希望编程语言能提供我们某些偏函数特征。

例如,在Python语言中,我们可以这样做:

from functools import partial

def foo(a,b,c):

return a + b + c

foo23 = partial(foo, b=23)

foo23(a = 1, c = 3) # => 27

函数加里化(Currying)明显解决的是一个完全不同的问题:如果我们有几个单参数函数,并且这是一种支持一等函数(first-class)的语言,如何去实现一个多参数函数?函数加里化是一种实现多参数函数的方法。

下面是一个单参数的Javascript函数:

var foo = function(a) {

return a * a;

}

如果我们受限只能写单参数函数,可以像下面这样模拟出一个多参数函数:

var foo = function(a) {

return function(b) {

return a * a + b * b;

}

}

通过这样调用它:(foo(3))(4),或直接 foo(3)(4)。

注意,函数加里化提供了一种非常自然的方式来实现某些偏函数应用。如果你希望函数foo的第一个参数值被固定成5,你需要做的就是var foo5 = foo(5)。这就OK了。函数foo5就是foo函数的偏函数。注意,尽管如此,我们没有很简单的方法对foo函数的第二个参数偏函数化(除非先偏函数化第一个参数)。

当然,Javascript是支持多参数函数的:

var bar = function(a, b) {

return a * a + b * b;

}

我们定义的bar函数并不是一个加里化的函数。调用bar(5)并不会返回一个可以输入12的函数。我们只能像bar(5,12)这样调用这个函数。

在一些其它语言里,比如 Haskell 和 OCaml,所有的多参数函数都是通过加里化实现的。

下面是一个把上面的foo函数用OCaml语言写成的例子:

let foo = fun a ->

fun b ->

a * a + b * b

下面是把上面的bar函数用OCaml语言写成的例子:

let bar = fun a b ->

a * a + b * b

头一个函数我们叫做“显式加里化”,第二个叫做“隐式加里化”。

跟Javascript不一样,在OCaml语言里,foo函数和bar函数是完全一样的。我们用完全一样的方式调用它们。

# foo 3 4;;

- : int = 25

# bar 3 4;;

- : int = 25

两个函数都能够通过提供一个参数值来创造一个偏函数:

# let foo5 = foo 5;;

val foo5 : int -> int =

# let bar5 = bar 5;;

val bar5 : int -> int =

# foo5 12;;

- : int = 169

# bar5 12;;

- : int = 169

事实上,我们可以把下面这个匿名函数:

fun arg1 arg2 … argN -> exp

当作是下面这个函数的简写:

fun arg1 -> fun arg2 -> … -> fun argN -> exp

函数加里化和偏函数应用的总结

偏函数应用是找一个函数,固定其中的几个参数值,从而得到一个新的函数。

函数加里化是一种使用匿名单参数函数来实现多参数函数的方法。

函数加里化能够让你轻松的实现某些偏函数应用。

有些语言(例如 Haskell, OCaml)所有的多参函数都是在内部通过函数加里化实现的。

[英文原文:Currying vs. Partial Application ]

作者:Aqee
____________________________________________________________________________________


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