haskell - 约束含义作为约束

Question

如何将 Haskell 中的约束含义编码为新的约束？在我的示例中，我想要求每个 Functor c d f 都需要使得 Obj c x 隐含 Obj c (f x)。我正在编写约束 forall x 。 Obj c x => Obj d (f x).

{-# LANGUAGE AllowAmbiguousTypes       #-}
{-# LANGUAGE KindSignatures            #-}
{-# LANGUAGE MultiParamTypeClasses     #-}
{-# LANGUAGE RankNTypes                #-}
{-# LANGUAGE ScopedTypeVariables       #-}
{-# LANGUAGE TypeApplications          #-}
{-# LANGUAGE TypeFamilies              #-}
{-# LANGUAGE QuantifiedConstraints     #-}

import Prelude hiding (id, Functor, fmap)
import Data.Kind

class Category c where                            
  type Obj c a :: Constraint                    
  id :: (Obj c x) => c x x                        
  comp :: (Obj c x) => c y z -> c x y -> c x z    

class ( Category c, Category d, forall x . Obj c x => Obj d (f x))
      => Functor c d f where
  fmap :: (Obj c x, Obj c y) => c x y -> d (f x) (f y)

doublefmap :: forall c f x . (Category c , Functor c c f, Obj c x)
           => c x x -> c (f (f x)) (f (f x))
doublefmap = fmap @c @c @f . fmap @c @c @f

但这会产生以下错误:

Minimal.hs:27:14: error:
    • Could not deduce: Obj c (f x) arising from a use of ‘fmap’
      from the context: (Functor c c f, Obj c x)
        bound by the type signature for:
                   doublefmap :: forall (c :: * -> * -> *) (f :: * -> *) x.
                                 (Category c, Functor c c f, Obj c x) =>
                                 c x x -> c (f (f x)) (f (f x))
        at Minimal.hs:(25,1)-(26,44)
    • In the first argument of ‘(.)’, namely ‘fmap @c @c @f’
      In the expression: fmap @c @c @f . fmap @c @c @f
      In an equation for ‘doublefmap’:
          doublefmap = fmap @c @c @f . fmap @c @c @f
    • Relevant bindings include
        doublefmap :: c x x -> c (f (f x)) (f (f x))
          (bound at Minimal.hs:27:1)

我在这里做错了什么？我应该给编译器什么额外的提示？有没有更好的方法来实现这一目标？

我的猜测是我需要使用 Data.Constraint 和 :-，但是如何使用？

Answer 1

以下似乎可行，但我不知道这是否是一个更简单的方法。它使用 Data.Constraint 中的运算符 (\\)。

{-# LANGUAGE AllowAmbiguousTypes       #-}
{-# LANGUAGE KindSignatures            #-}
{-# LANGUAGE MultiParamTypeClasses     #-}
{-# LANGUAGE RankNTypes                #-}
{-# LANGUAGE ScopedTypeVariables       #-}
{-# LANGUAGE TypeApplications          #-}
{-# LANGUAGE TypeFamilies              #-}
{-# LANGUAGE TypeOperators             #-}
{-# LANGUAGE FlexibleContexts          #-}
{-# LANGUAGE QuantifiedConstraints     #-}

import Prelude hiding (id, Functor, fmap)
import Data.Constraint

class Category c where                            
  type Obj c a :: Constraint
  id :: (Obj c x) => c x x
  comp :: (Obj c x) => c y z -> c x y -> c x z    

class (Category c, Category d) => Functor c d f where
  fobj :: forall x. Obj c x :- Obj c (f x)
  fmap :: (Obj c x, Obj c y) => c x y -> d (f x) (f y)

doublefmap :: forall c f x . (Category c , Functor c c f, Obj c x)
           => c x x -> c (f (f x)) (f (f x))
doublefmap = (fmap @c @c @f . fmap @c @c @f) \\ fobj @c @c @f @x