新类型的Haskell Monoid实例问题 [英] Haskell Monoid Instance Question for a newtype

问题描述

我正在尝试定义一个实例:

I am trying to define an instance:

newtype Join a = Join { getJoin :: a -> Bool }
   deriving Generic

instance Monoid (Join a) where
   f <> g = ???
   mempty = ???

目标是，如果列表中的所有函数均为true，则foldMap Join函数应返回True，否则，则返回false.

The goal is that the function foldMap Join should return True if all functions in the list are true, and false if all are not true.

我了解foldMap以及Monoid的Sum和Product实例，但在编写Monoid的新类型实例方面还很陌生.任何在正确方向上的帮助将不胜感激.谢谢.

I understand foldMap, and the instances of Sum and Product for Monoid but am otherwise quite new to writting newtype instances of Monoid. Any help in the right direction would be appreciated. Thank you.

推荐答案

如果第一个和第二个函数都返回True，则可以使用(&&)来创建一个返回True的新函数.那么mempty是Join函数，对于所有输入，该函数都是True:

You can make an new function that returns True if both the first and second function return True, by using (&&). Then the mempty is a Join function that is True for all input:

instance Monoid (Join a) where
    Join f <> Join g = Join (\x -> f x && g x)
    mempty = Join (const True)

由于引入了Semigroup，因此(<>)函数是Semigroup的一个实例.

Since the introduction of the Semigroup, the (<>) function is an instance of the Semigroup however:

import Control.Applicative(liftA2)

instance Semigroup (Join a) where
    Join f <> Join g = Join (liftA2 (&&) f g)

instance Monoid (Join a) where
    mappend = (<>)
    mconcat js = Join (\x -> all (($ x) . getJoin) js)
    mempty = Join (const True)

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