haskell - 在应用中，如何用 `<*>` 表示 `fmap_i, i=0,1,2,...` ？

Question

类 Applicative 声明为:

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

我们可以代表 fmapi, i=0,1,2,...在 pure 方面和 (<*>) :

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，怎么能 <*>表示为 fmap_i, i=0,1,2,... ?

谢谢。

另见 Is the implementation of `<*>` based on `fmap` special to Maybe applicative or can it be generalized to other applicatives?

Answer 1

你可以写:

(<*>) = fmap2 ($)

或者，如果你觉得它不那么晦涩:

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