[英]Generalized `fold` or how to perform `fold` and `map` at a time
(Apology by the title, I can't do better) (通过标题道歉,我不能做得更好)
My question is to find some generalized struct or "standard" function to perform the next thing: 我的问题是找到一些通用的结构或“标准”函数来执行下一件事:
xmap :: (a -> b) -> f a -> g b
then, we can map not only elements, by also the entire struct. 那么,我们不仅可以映射元素,还可以映射整个结构。
Some (not real) example 一些(不是真实的)例子
xmap id myBinaryTree :: [a]
at the moment, I must to do a explicit structure conversor (typical fromList
, toList
) then 目前,我必须做一个显式的结构转换(典型的fromList
, toList
)
toList . fmap id -- if source struct has map
fmap id . fromList -- if destination struct has map
(to perform toStruct
, fromStruct
I use fold
). (执行toStruct
, fromStruct
我使用fold
)。
Exists some way to generalize to
/ from
structs? 存在某种方式来推广to
/ from
结构? (should be) Exists that function ( xmap
)? (应该)存在该功能( xmap
)?
Thank you!! 谢谢!! :) :)
As f
and g
are functors, a natural transformation is what you're looking for (see also You Could Have Defined Natural Transformations ). 由于f
和g
是仿函数,因此您正在寻找自然变换 (另请参阅“ 您可以定义自然变换” )。 So a transformation like 所以转型就好
f :~> g = forall a. f a -> g a
is needed to create xmap which is then just 需要创建xmap然后才是
xmap :: (a -> b) -> (f :~> g) -> (f a -> g b)
xmap f n = map f . n
You still need to define types of (f :~> g)
, but there' not a general way of doing that. 你仍然需要定义(f :~> g)
,但是没有一般的方法。
I'd like to add to tel's answer (I got my idea only after reading it) that in many cases you can make general natural transformation that will work similarly to foldMap
. 我想补充一下tel的答案 (我只是在阅读之后得到了我的想法),在许多情况下,你可以进行一般自然变换,它将与foldMap
类似。 If we can use foldMap
, we know that f
is Foldable
. 如果我们可以使用foldMap
,我们知道f
是Foldable
。 Then we need some way how to constructs elements of ga
and combine them together. 然后我们需要一些方法来构建ga
元素并将它们组合在一起。 We can use Alternative
for that, it has all we need ( pure
, empty
and <|>
), although we could also construct some less general type class for this purpose (we don't need <*>
anywhere). 我们可以使用Alternative
,它有我们需要的所有( pure
, empty
和<|>
),虽然我们也可以为此目的构造一些不太通用的类型类(我们不需要<*>
任何地方)。
{-# LANGUAGE TypeOperators, RankNTypes #-}
import Prelude hiding (foldr)
import Control.Applicative
import Data.Foldable
type f :~> g = forall a. f a -> g a
nt :: (Functor f, Foldable f, Alternative g) => f :~> g
nt = foldr ((<|>) . pure) empty
Then using tel's xmap
然后使用tel的xmap
xmap :: (a -> b) -> (f :~> g) -> (f a -> g b)
xmap f n = map f . n
we can do things like 我们可以做的事情
> xmap (+1) nt (Just 1) :: [Int]
[2]
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