如何使用免费monad实现Reader？

Question

好的,所以我已经想出如何使用包来实现Reader(并且ReaderT未显示)operational:

{-# LANGUAGE GADTs, ScopedTypeVariables #-}

import Control.Monad.Operational

data ReaderI r a where
    Ask :: ReaderI r r

type Reader r a = Program (ReaderI r) a

ask :: Reader r r
ask = singleton Ask

runReader :: forall r a. Reader r a -> r -> a
runReader = interpretWithMonad evalI
    where evalI :: forall b. ReaderI r b -> (r -> b)
          evalI Ask = id

但我无法弄清楚如何使用免费monad(我使用Edward Kmett的free包)来解决这个问题.我得到的最接近的是这个,我明白是作弊(关于如何((->) r)已经是monad):

import Control.Monad.Free

type Reader r a = Free ((->) r) a

ask :: Reader r r
ask = Free Pure

runReader :: Reader r a -> r -> a
runReader (Pure a) _ = a
runReader (Free k) r = runReader (k r) r

-- Or, more simply and tellingly:
--
-- > runReader = retract

即使这不像我怀疑的那样愚蠢,但这不是我想要的,因为我想要的,基本上就是能够检查Reader数据......

Answer 1

我认为除了你的方式之外这是不可能的。但是，我不认为这对读者来说是独一无二的。考虑 writer 的免费 monad 版本

data WriterF m a = WriterF m a deriving (Functor)

type Writer m = Free (WriterF m)

显然，WriterF与 writer 同构，但这确实符合我们对简单代数的期望

algebraWriter :: Monoid m => WriterF m (m,a) -> (m,a)
algebraWriter (WriterF m1 (m2,a)) = (m1 <> m2,a)

因此

runWriter :: Monoid m => Writer m a -> (m,a)
runWriter (Pure a) = (mempty,a)
runWriter (Free x) = algebraWriter . fmap runWriter $ x

同样，我认为免费阅读器是

type ReaderF r = (->) r

type Reader r = Free (ReaderF r)

我喜欢这个，因为添加它们会给你状态单子

type State x = Free ((ReaderF x) :+: (WriterF x))

runState :: State x a -> x -> (a,x)
runState (Pure a) x                    = (a,x)
runState (Free (Inl f)) x              = runState (f x) x
runState (Free (Inr (WriterF x f))) _  = runState f x

Free请注意，您的操作解决方案可以通过使用“自由函子”来使用，任何与操作一起使用的解决方案都可以使用

data FreeFunctor f x = forall a. FreeFunctor (f a) (a -> x)

但是，这FreeFunctor ReaderI也同构于(->).