Question

想象一下，我想定义一个向量空间类型类。我做了以下（灵感来自Yampa）：

{-# LANGUAGE TypeFamilies           #-}
{-# LANGUAGE FlexibleContexts       #-}
{-# LANGUAGE FlexibleInstances      #-}
{-# LANGUAGE UndecidableInstances   #-}

class Fractional (Groundfield v) => VectorSpace v where
    type Groundfield v
    (^+^)      :: v -> v -> v
    zeroVector :: v
    (^*)       :: v -> Groundfield v -> v

完美无缺。现在针对一些常见情况。当然，分数元组是一个向量空间：

instance Fractional a => VectorSpace (a,a) where
    type Groundfield (a,a) = a
    (a, b) ^+^ (c, d)      = (a + c, b + d)
    zeroVector             = (0,0)
    (a, b) ^* c            = (a * c, b * c)

甚至更简单，分数是自身的向量空间：

instance Fractional a => VectorSpace a where
    type Groundfield a = a
    (^+^)              = (+)
    zeroVector         = 0
    (^*)               = (*)

每个实例本身都是完全有效的。但如果我把它们放在同一模块中，我就会遇到这个问题：

VectorSpielwiese.hs:15:10:
  Conflicting family instance declarations:
    Groundfield (a, a) -- Defined at VectorSpielwiese.hs:15:10
    Groundfield a -- Defined at VectorSpielwiese.hs:21:10

我意识到第二个实例定义中的a匹配也会捕获元组模式。但是，如果我之前编写(a,a)的实例定义，我本可以预期我已经匹配了该模式。显然不是！我怎样才能做到这一点？

Answer 1

在GHC（相对）新型封闭式家庭的帮助下，我认为我们可以将其拉下来。以下所有类型检查：

type family Groundfield v where
    Groundfield (a,a) = a
    Groundfield a = a

class Fractional (Groundfield v) => VectorSpace v where
    (^+^)      :: v -> v -> v
    zeroVector :: v
    (^*)       :: v -> Groundfield v -> v

instance (Fractional (Groundfield a), Num a, a ~ Groundfield a) => VectorSpace a where
    (^+^)              = (+)
    zeroVector         = 0
    (^*)               = (*)

instance Fractional a => VectorSpace (a,a) where
    (a, b) ^+^ (c, d)      = (a + c, b + d)
    zeroVector             = (0,0)
    (a, b) ^* c            = (a * c, b * c)

如何使用类型系列定义这些重叠实例？

1 个答案: