我必须实施Applicative和Functor来实施Monad [英] Must I implement Applicative and Functor to implement a Monad

问题描述

我试图实现一个Monad实例。作为一个简单的例子，假设如下：

$ $ $ $ $ $ $ $ $数据Maybee a = Notheeng | Juust a

实例Monad Maybee其中
return x = Juust x
Notheeng>> = f = Notheeng
Juust x>> = f = fx
失败_ = Notheeng

这应该是Maybe的标准实现，据我所知。然而，这不会编译，因为编译器抱怨：

lockquote
没有实例适用于Maybee

类似地，他希望Functor实例一旦给定Applicative。

所以：简单的问题：我必须在我实现Monad之前，总是实现Functor和Applicative？

解决方案

使用GHC 7.10或更高版本，必须实现 Functor 和 Applicative 。类的定义为 Monad 命令超类实例：

  class Functor f =>应用f其中... 
类应用m => Monad m其中... 
  

请注意，一旦您拥有 Monad 实例， Functor 和 Applicative 实例可以一般定义，不需要额外的努力：

  import Control.Monad 
 
  - 假设我们定义了一个Monad实例：
 instance Monad m where ... 
 
实例Functor m其中
 fmap = liftM 
 
实例应用程序m其中
 pure = return 
（< *> ;）= ap 
  

I'm trying to implement a Monad instance. As a simpler example, assume the following:

data Maybee a = Notheeng | Juust a 

instance Monad Maybee where
   return x = Juust x
   Notheeng >>= f = Notheeng
   Juust x >>= f = f x
   fail _ = Notheeng 

This should be the standard implementation of Maybe as far as I know. However, this doesn't compile, because the compiler complains:

No instance for (Applicative Maybee)

and similarly he wants a Functor instance once the Applicative is given.

So: Simple question: Must I always implement Functor and Applicative before I can implement a Monad?

解决方案

With GHC 7.10 and above, you must implement Functor and Applicative. The class definitions for Monad mandate the superclass instances:

class Functor f => Applicative f where ...
class Applicative m => Monad m where ...

Note that once you have a Monad instance, the Functor and Applicative instances can be defined generically with no additional effort:

import Control.Monad

-- suppose we defined a Monad instance:
instance Monad m where ...

instance Functor m where
    fmap = liftM

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

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