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  • Haskell语言学习笔记(61)Distributive

    Distributive

    class Functor g => Distributive g where
      distribute  :: Functor f => f (g a) -> g (f a)
      distribute  = collect id
    
      collect     :: Functor f => (a -> g b) -> f a -> g (f b)
      collect f   = distribute . fmap f
    
      distributeM :: Monad m => m (g a) -> g (m a)
      distributeM = fmap unwrapMonad . distribute . WrapMonad
    
      collectM    :: Monad m => (a -> g b) -> m a -> g (m b)
      collectM f  = distributeM . liftM f
    
    cotraverse :: (Distributive g, Functor f) => (f a -> b) -> f (g a) -> g b
    cotraverse f = fmap f . distribute
    
    comapM :: (Distributive g, Monad m) => (m a -> b) -> m (g a) -> g b
    comapM f = fmap f . distributeM
    

    Distributive 是个类型类。功能上与 Traversable 类型类呈现对偶(dual)关系。
    Traversable 类型将一个函数应用到多个数值,而
    Distributive 类型将一个数值应用到多个函数。

    ((->)e) 是个 Distributive

    instance Distributive ((->)e) where
      distribute a e = fmap ($e) a
      collect f q e = fmap (flip f e) q
    

    Sum 是个 Distributive

    instance Distributive Monoid.Sum where
      collect = coerce (fmap :: (a -> b) -> f a -> f b)
        :: forall f a b . Functor f
        => (a -> Monoid.Sum b) -> f a -> Monoid.Sum (f b)
      distribute = Monoid.Sum . fmap Monoid.getSum
    

    应用 Distributive

    Prelude Data.Distributive> distribute [(+1),(+2)] 1
    [2,3]
    Prelude Data.Distributive> collect (^) [1,2] 3
    [1,8]
    Prelude Data.Distributive> cotraverse sum [(+1),(*2)] 3
    10
    Prelude Data.Distributive> comapM product [(+1),(*2)] 3
    24
    Prelude Data.Distributive Data.Monoid> distribute [Sum 1, Sum 2]
    Sum {getSum = [1,2]}
    Prelude Data.Distributive Data.Monoid> collect (x->Sum[x]) [3,4]
    Sum {getSum = [[3],[4]]}
    

    手动计算

    distribute [(+1),(+2)] 1
    = fmap ($1) [(+1),(+2)]
    = [1+1,1+2] = [2,3]
    collect (^) [1,2] 3
    = fmap (flip (^) 3) [1,2]
    = fmap (^3) [1,2]
    = [1^3,2^3] = [1,8]
    cotraverse sum [(+1),(*2)] 3
    = (fmap sum . distribute) [(+1),(*2)] 3
    = sum $ distribute [(+1),(*2)] 3
    = sum [4, 6] = 10
    
    这里
    (fmap f . g)  x y
    = (f . g x) y
    = f $ g x y
    
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  • 原文地址:https://www.cnblogs.com/zwvista/p/8016689.html
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