为异类操作创建类型类时出现问题

假设我想创建一个可以接受不同类型操作数的泛型差分操作。

class Diff a b c where
    diff :: a -> b -> c

当然,我们可以将这个运算应用于数字。

instance Num a ⇒ Diff a a a where
    diff = (-)

但不仅仅是数字。如果我们说两个时间点,那么它们之间的差别就是一个时间间隔。

newtype TimePoint = TP Integer deriving Show -- seconds since epoch
newtype TimeInterval = TI Integer deriving Show -- in seconds

instance Diff TimePoint TimePoint TimeInterval where
    diff (Tp x) (Tp y) = TI (x-y)

一切都很好。除非我试着测试我的 diff 在GHCi中,我得到:

*Example λ diff 5 3

<interactive>:1:1: error:
    • Could not deduce (Diff a0 b0 c)
      from the context: (Diff a b c, Num a, Num b)
        bound by the inferred type for ‘it’:
                   forall a b c. (Diff a b c, Num a, Num b) => c
        at <interactive>:1:1-8
      The type variables ‘a0’, ‘b0’ are ambiguous
    • In the ambiguity check for the inferred type for ‘it’
      To defer the ambiguity check to use sites, enable AllowAmbiguousTypes
      When checking the inferred type
        it :: forall a b c. (Diff a b c, Num a, Num b) => c
*Example λ

因此,我必须在类型对编译器来说应该是“明显”的地方编写类型签名。

让我们试着帮点忙。

class Diff a b c | a b -> c where
  diff ∷ a -> b -> c

现在应该可以确定结果的类型了!不幸的是,这无法编译:

[1 of 1] Compiling Example          ( Example.hs, interpreted )

Example.hs:8:10: error:
    Functional dependencies conflict between instance declarations:
      instance Num a => Diff a a a -- Defined at Example.hs:8:10
      instance Num a => Diff (TimePoint a) (TimePoint a) (TimeInterval a)
        -- Defined at Example.hs:14:10
  |
8 | instance Num a => Diff a a a where
  |          ^^^^^^^^^^^^^^^^^^^
Failed, no modules loaded.
Prelude GOA λ 

顺便说一句,我也尝试过用关联型家族来代替fundeps,可以预见的是类似的结果。

现在我完全明白为什么会这样。有两个例子 Diff a a a 和 Diff (TimePoint a) (TimePoint a) (TimeInterval a) ,它们不能与现有的fundep共存。问题是,我如何解决这个问题?将数字包装成新类型不是一个可行的解决方案,我需要能够写 diff 5 3 和 diff time1 time2

我知道我可以为 Diff Int Int Int 和 Diff Double Double Double 和 Diff Rational Rational Rational ,但这不是一个理想的解决方案,因为 Num 可以定义,并且代码必须处理它们,而不必定义 Diff

下面是一个最小的完整示例:

{-# LANGUAGE MultiParamTypeClasses, FunctionalDependencies, FlexibleInstances #-}

module Example where

class Diff a b c | a b -> c where
  diff :: a -> b -> c

instance Num a => Diff a a a where
  diff = (-)

data TimePoint a = TP a deriving Show
data TimeInterval a = TI a deriving Show

instance Num a => Diff (TimePoint a) (TimePoint a) (TimeInterval a) where
  diff (TP x) (TP y) = TI (x - y)