Question

请考虑以下愿望程序。

{-# LANGUAGE ExtensibleGADTs #-}

data Free a where
    Lift :: a -> Free a

data Free (f a) => FreeFunctor f a where
    Map :: (a -> b) -> FreeFunctor f a -> FreeFunctor f b

instance Functor (FreeFunctor f) where
    fmap = Map

data FreeFunctor f a => FreeApplicative f a where
    Apply :: FreeApplicative f (a -> b) -> FreeApplicative f a -> FreeApplicative f b
    Pure  :: a -> FreeApplicative f a

instance Applicative (FreeApplicative f) where
    (<*>) = Apply
    pure  = Pure

data FreeApplicative m a => FreeMonad m a where
    Bind :: FreeMonad m a -> (a -> FreeMonad m b) -> FreeMonad m b

instance Monad (FreeMonad m) where
    (>>=) = Bind

这将引入substitutability的概念。例如，FreeApplicative f a可以用FreeFunctor f a代替，而不能用FreeMonad f a代替。同样，FreeApplicative f a -> Int可用FreeMonad f a -> Int代替，FreeFunctor f a -> Int不能代替。

subtyping的概念可以通过注入来捕获。

import Unsafe.Coerce

fromFreeToFreeFunctor :: Free (f a) -> FreeFunctor f a
fromFreeToFreeFunctor = unsafeCoerce

fromFreeFunctorToFreeApplicative :: FreeFunctor f a -> FreeApplicative f a
fromFreeFunctorToFreeApplicative = unsafeCoerce

fromFreeApplicativeToFreeMonad :: FreeApplicative m a -> FreeMonad m a
fromFreeApplicativeToFreeMonad = unsafeCoerce

编译器将在需要的地方插入这些注入。

我认为这是expression problem的很好的解决方案。然而，general consensus认为亚型多态性在Haskell中是有问题的。所以，我的问题是两个方面。

如上所述，子类型化会出现问题还是会干扰Haskell中的类型推断？
可扩展的GADT是否可以解决Haskell中的表达问题？

我尚未为可扩展GADT定义精确的语义。如果这似乎值得追求，那么我想为此编写一个GHC扩展。只是想把这个想法大肆宣传，并引起一些批评。

可扩展的GADT是否可以解决表达问题？

0 个答案: