haskell - ConstraintKinds 解释了一个 super 简单的例子

Question

什么是Constraint kind ?

为什么有人会使用它(在实践中)？

到底有什么好处呢？

能否举一个简单的代码示例来说明前两个问题的答案？

为什么用在this例如代码？

Answer 1

好吧，我会提到它允许你做的两件实际的事情:

通过类型类约束参数化类型

编写允许其实例指定所需约束的类型类。

也许最好用一个例子来说明这一点。经典的 Haskell 疣之一是您无法制作 Functor对类型参数施加类约束的类型的实例；例如， Set containers 中的类库，需要 Ord对其元素的约束。原因是在“ Vanilla ”Haskell 中，您必须对类本身进行约束:

class OrdFunctor f where
    fmap :: Ord b => (a -> b) -> f a -> f b

...但是这个类只适用于需要一个 Ord 的类型。约束。不是通用解决方案!

那么，如果我们可以采用该类定义并将 Ord 抽象出来呢？约束，允许个别实例说出他们需要什么约束？好吧， ConstraintKinds加 TypeFamilies允许:

{-# LANGUAGE ConstraintKinds, TypeFamilies, FlexibleInstances #-}

import Prelude hiding (Functor(..))
import GHC.Exts (Constraint)
import Data.Set (Set)
import qualified Data.Set as Set

-- | A 'Functor' over types that satisfy some constraint.
class Functor f where
   -- | The constraint on the allowed element types.  Each
   -- instance gets to choose for itself what this is.
   type Allowed f :: * -> Constraint

   fmap :: Allowed f b => (a -> b) -> f a -> f b

instance Functor Set where
    -- | 'Set' gets to pick 'Ord' as the constraint.
    type Allowed Set = Ord
    fmap = Set.map

instance Functor [] where
    -- | And `[]` can pick a different constraint than `Set` does.
    type Allowed [] = NoConstraint
    fmap = map

-- | A dummy class that means "no constraint."
class NoConstraint a where

-- | All types are trivially instances of 'NoConstraint'.
instance NoConstraint a where

(请注意，这不是将 Functor 实例设为 Set 的唯一障碍；参见 this discussion 。另外， credit to this answer for the NoConstraint trick 。)

不过，这种解决方案还没有被普遍采用，因为 ConstraintKinds或多或少仍然是一个新功能。
ConstraintKinds 的另一种用法是通过类约束或类对类型进行参数化。我会复制 this Haskell "Shape Example" code that I wrote :

{-# LANGUAGE GADTs, ConstraintKinds, KindSignatures, DeriveDataTypeable #-}
{-# LANGUAGE TypeOperators, ScopedTypeVariables, FlexibleInstances #-}

module Shape where

import Control.Applicative ((<$>), (<|>))
import Data.Maybe (mapMaybe)
import Data.Typeable
import GHC.Exts (Constraint)

-- | Generic, reflective, heterogeneous container for instances
-- of a type class.
data Object (constraint :: * -> Constraint) where
    Obj :: (Typeable a, constraint a) => a -> Object constraint
           deriving Typeable

-- | Downcast an 'Object' to any type that satisfies the relevant
-- constraints.
downcast :: forall a constraint. (Typeable a, constraint a) =>
            Object constraint -> Maybe a
downcast (Obj (value :: b)) = 
  case eqT :: Maybe (a :~: b) of
    Just Refl -> Just value
    Nothing -> Nothing

这里是 Object的参数type 是一个类型类(种类 * -> Constraint )，所以你可以有像 Object Shape 这样的类型在哪里 Shape是一个类:

class Shape shape where
  getArea :: shape -> Double

-- Note how the 'Object' type is parametrized by 'Shape', a class 
-- constraint.  That's the sort of thing ConstraintKinds enables.
instance Shape (Object Shape) where
    getArea (Obj o) = getArea o

什么 Object类型确实是两个特征的组合:

存在类型(此处由 GADTs 启用)，它允许我们将异构类型的值存储在同一个 Object 中类型。

ConstraintKinds ，这使我们能够，而不是硬编码 Object对于某些特定的类约束集，拥有 Object 的用户类型指定他们想要的约束作为参数到Object类型。

现在有了它，我们不仅可以制作 Shape 的异构列表。实例:

data Circle = Circle { radius :: Double }
            deriving Typeable

instance Shape Circle where
  getArea (Circle radius) = pi * radius^2


data Rectangle = Rectangle { height :: Double, width :: Double }
               deriving Typeable

instance Shape Rectangle where
  getArea (Rectangle height width) = height * width

exampleData :: [Object Shape]
exampleData = [Obj (Circle 1.5), Obj (Rectangle 2 3)]

...但感谢 Typeable Object 中的约束我们可以 垂头丧气 : 如果我们猜对了 Object 中包含的类型，我们可以恢复原来的类型:

-- | For each 'Shape' in the list, try to cast it to a Circle.  If we
-- succeed, then pass the result to a monomorphic function that 
-- demands a 'Circle'.  Evaluates to:
--
-- >>> example
-- ["A Circle of radius 1.5","A Shape with area 6.0"]
example :: [String]
example = mapMaybe step exampleData
  where step shape = describeCircle <$> (downcast shape)
                 <|> Just (describeShape shape)

describeCircle :: Circle -> String
describeCircle (Circle radius) = "A Circle of radius " ++ show radius

describeShape :: Shape a => a -> String
describeShape shape = "A Shape with area " ++ show (getArea shape)