在应用中，如何用fmap_i，i = 0,1,2，...来表示*? [英] In applicative, how can `<*>` be represented in terms of `fmap_i, i=0,1,2,...`?

问题描述

Class Applicative声明为:

Class Applicative is declared as:

class Functor f   =>  Applicative f   where
pure  ::  a   ->  f   a
(<*>) ::  f   (a  ->  b)  ->  f   a   ->  f   b

我们可以用pure和(<*>)表示fmapi, i=0,1,2,...:

fmap0 ::  a   ->  f   a
fmap0 =   pure
fmap1 ::  (a  ->  b)  ->  f   a   ->  f   b
fmap1 g   x   =   pure    g   <*> x
fmap2 ::  (a  ->  b   ->  c)  ->  f   a   ->  f   b   ->  f   c
fmap2 g   x   y   =   pure    g   <*> x   <*> y
fmap3 ::  (a  ->  b   ->  c   ->  d)  ->  f   a   ->  f   b   ->  f   c   ->  f   d
fmap3 g   x   y   z   =   pure    g   <*> x   <*> y   <*> z

在应用上，如何用fmap_i, i=0,1,2,...表示<*>?

In applicative, how can <*> be represented in terms of fmap_i, i=0,1,2,...?

谢谢.

另请参见是基于fmap的`&*;>的实现可能是可应用的，还是可以推广到其他应用?

推荐答案

您可以编写:

(<*>) = fmap2 ($)

或者，如果您发现它不太晦涩，则:

or, if you find it less obscure:

f <*> a = fmap2 apply f a
  where apply g x = g x

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