是否可以为每个 monad 转换器 `t` 编写类型为 `Monad m => t Identity a -> t m a` 的函数？

Question

假设我们有以下类型class。

class MonadTrans t => MonadLower t where
    lower :: Monad m => t Identity a -> t m a

作为一个简单的例子，我们可以为 MaybeT 实现一个 MonadLower 的实例，如下所示。

instance MonadLower MaybeT where
    lower (MaybeT (Identity maybe)) = MaybeT (return maybe)

但是，我不知道如何为 ContT r 实现 MonadLower 的实例。

instance MonadLower (ContT r) where
    lower (ContT f) = ContT $ \k -> ???

甚至可以为每个 MonadTrans t 创建一个 MonadLower t 的实例吗？

如果不是，哪些 monad 转换器（ContT r 旁边）不能有 MonadLower 个实例？

编辑： Edward Kmett has defined a similar type class called MonadHoist.

class MonadHoist t where
    hoist :: (Monad m, Monad n) => (forall a. m a -> n a) -> t m a -> t n a

原来是lower = hoist (return . runIdentity).

Answer 1

根据Mauro we can't define a MonadHoist instance for ContT^[1].

What Edward is proposing is to have a class of functorial monad transformers (transformers which are endofunctors in the category Mon(C) of monads over a category C and monad morphisms)

Note that some transformers, like the continuation monad transformer, are not functorial.

是否可以为每个 monad 转换器 `t` 编写类型为 `Monad m => t Identity a -> t m a` 的函数？

Is it possible to write a function of the type `Monad m => t Identity a -> t m a` for every monad transformer `t`?

haskell

monads

monad-transformers