haskell - 单子(monad)法则在 Haskell 中执行吗？

Question

来自 Haskell 维基:

Monads can be viewed as a standard programming interface to various data or control structures, which is captured by the Monad class. All common monads are members of it:

class Monad m where
  (>>=) :: m a -> (a -> m b) -> m b
  (>>) :: m a -> m b -> m b
  return :: a -> m a
  fail :: String -> m a

In addition to implementing the class functions, all instances of Monad should obey the following equations, or Monad Laws:

return a >>= k  =  k a
m >>= return  =  m
m >>= (\x -> k x >>= h)  =  (m >>= k) >>= h

问题:底层的三个单子(monad)定律实际上是否由语言以任何方式执行？或者它们是 的额外公理吗？你 必须强制执行才能使您的“Monad”语言结构与“Monad”的数学概念相匹配？

Answer 1

你 负责执行 Monad实例遵守单子(monad)定律。这是一个简单的例子，不 .

即使它的类型与 Monad 兼容方法，计算使用绑定(bind)运算符的次数不是 Monad，因为它违反了法律 m >>= return = m

{-# Language DeriveFunctor #-}

import Control.Monad

data Count a = Count Int a
    deriving (Functor, Show)

instance Applicative Count where
    pure = return
    (<*>) = ap

instance Monad Count where
    return = Count 0
    (Count c0 a) >>= k = 
        case k a of
            Count c1 b -> Count (c0 + c1 + 1) b