级联函数列表的类型是什么？ [英] What would the type of a list of cascading functions be?

问题描述

在Haskell语法中，我们可以有一个（抽象）类型，如 [a - > b] ，这是a到b的函数列表。具体的类型是 [Int - > Int] ，例如 map（*）[1..10] 。是否可以在类似 [a - > b，b - > c，c - > d，...] ？列表中的各个元素都是不同的（我认为），所以我不认为这是可能的。但是依赖类型可能吗？它的类型签名是什么（最好是使用伪Haskell语法）？

解决方案

，但你可以像下面这样构造自己的类列表类型：

  { - ＃LANGUAGE GADTs＃ - } 
 
 data CascadingList io其中
 Id :: CascadingList ii 
 Cascade ::（b  - > o） - > CascadingList i b  - > CascadingList io 
  

然后你可以使这些 CascadingList 如下所示：

p pre $ add pre $ add $ p $ add $ p $ add $ p $ add $ p $ add $ p $ add $ p $ add $ 1）$ Id

您可以'折叠'列表：

  collapse :: CascadingList ab  - > a  - > b 
 collapse id = id 
 collapse（Cascade f c）= f。折叠c 
  

然后您将拥有

  collapse addOnePositive 0 == True 
  

请注意，考虑到中间函数的类型，所以它可能不是你正在寻找的。

---

我刚才意识到这更接近于[c - > d，b - > c，a - > b]。让它更接近你的意图是一个容易的改变;我可以编辑它，但我认为你明白了。

In Haskell syntax, we can have a (abstract) type like [a -> b], which is a list of functions a to b. A concrete type of this would be [Int -> Int], such as map (*) [1..10]. Is it possible to have a list of cascading functions in a type like [a -> b, b -> c, c -> d, ...]? The individual elements of the list are all different (I think) so I don't think it's possible. But is it possible with dependent types? What would its type signature be (preferably in pseudo-Haskell syntax)?

解决方案

You can't do that with a plain list, but you could construct your own list-like type as follows:

{-# LANGUAGE GADTs #-}

data CascadingList i o where
    Id :: CascadingList i i
    Cascade :: (b -> o) -> CascadingList i b -> CascadingList i o

Then you could make these CascadingLists as follows:

addOnePositive :: CascadingList Int Bool
addOnePositive = Cascade (>0) $ Cascade (+1) $ Id

You could 'collapse' the lists:

collapse :: CascadingList a b -> a -> b
collapse Id = id
collapse (Cascade f c) = f . collapse c

Then you would have

collapse addOnePositive 0 == True

Note that this does not take into account the types of the intermediate functions, so it may not be what you are looking for.

---

I've just realised that this is closer to something like [c -> d, b -> c, a -> b]. It's an easy change to make it closer to your intentions; I could edit it but I think you get the idea.

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