在实例声明中键入约束但不在类中键入

Question

我想创建一个具有类型约束的函数定义的实例,但我不想将类型约束添加到类中.

class Foo a where
  f :: a b -> b

instance Foo Maybe where
  f = fMaybe

fMaybe :: (Num a) => Maybe a -> a
fMaybe (Just i) = i+i
fMaybe _ = 0

如何指定这是Maybe包含s 的实例Nums？

这有效:

{-# LANGUAGE MultiParamTypeClasses #-}
class Foo a b where
  f :: a b -> b

instance Foo Maybe Int where
  f = fMaybe

fMaybe :: (Num a) => Maybe a -> a
fMaybe (Just i) = i+i
fMaybe _ = 0

但我不想为每种类型声明实例 Num

我试过这个:

class Foo a where
  f :: a -> b

instance (Num b) => Foo (Maybe b) where
  f = fMaybe

fMaybe :: (Num a) => Maybe a -> a
fMaybe (Just i) = i+i
fMaybe _ = 0

但是我收到一个错误:

Couldn't match type ‘b’ with ‘b1’
  ‘b’ is a rigid type variable bound by
      the instance declaration at Test.hs:31:10
  ‘b1’ is a rigid type variable bound by
       the type signature for f :: Maybe b -> b1 at Test.hs:32:3
Expected type: Maybe b -> b1
  Actual type: Maybe b1 -> b1
Relevant bindings include
  f :: Maybe b -> b1 (bound at Test.hs:32:3)
In the expression: fMaybe
In an equation for ‘f’: f = fMaybe

Answer 1

不改变类或类型是不可能的.

• 该MultiParamTypeClasses方法实际上并不要求您为所有Num类型编写单独的实例- 以下工作:

  class Foo a b where
    f :: a b -> b
  
  instance (Num b) => Foo Maybe b where
    f = fMaybe
  

  不过,我认为这不是一个特别好的方法.

• 您可以使用ConstraintKinds允许每个实例有选择地约束包含的类型.

  {-# LANGAUGE TypeFamilies, ConstraintKinds #-}
  
  import GHC.Exts (Constraint)
  
  class Foo a where
    type FooCstrt a b :: Constraint
    type FooCstrt a b = () -- default to unconstrained
    f :: FooCstrt a b => a b -> b
  
  instance Foo Maybe where
    type FooCstrt Maybe b = Num b
    f = fMaybe
  

• 您可以切换到仅允许首先包含Num类型的类型.

  {-# LANGUAGE GADTs #-}
  
  data NMaybe where
    NJust :: Num b => b -> NMaybe b
    NNothing :: Num b => NMaybe b
  

  然后,

  class Foo a where
    f :: a b -> b
  
  instance Foo NMaybe where
    f (NJust i) = i+1
    f (NNothing) = 0