非单射闭式族

Question

我有这段公认的人为设计的代码块

{-# LANGUAGE DataKinds, TypeFamilies #-}

data Foo = Foo

type family Id (n :: Foo) a where
    Id 'Foo a = a

data Bar (n :: Foo) = Bar

class Dispatch (n :: Foo) where
    consume :: Id n a -> Bar n -> a

consume' :: Dispatch n => Id n [Bool] -> Bar n -> [Bool]
consume' = consume

consume'' :: Dispatch n => Id n [Bool] -> Bar n -> Bool
consume'' g x = and (consume' g x)

这可以编译并且工作正常。但是，如果我将最终的 consume'' 定义替换为

consume'' :: Dispatch n => Id n [Bool] -> Bar n -> Bool
consume'' g x = and (consume g x)

（注意 consume 而不是 consume'），然后我得到一个错误

noinject.hs:17:30: error:
    • Couldn't match expected type ‘Id n (t0 Bool)’
                  with actual type ‘Id n [Bool]’
      NB: ‘Id’ is a non-injective type family
      The type variable ‘t0’ is ambiguous
    • In the first argument of ‘consume’, namely ‘g’
      In the first argument of ‘and’, namely ‘(consume g x)’
      In the expression: and (consume g x)
    • Relevant bindings include
        x :: Bar n (bound at noinject.hs:17:13)
        g :: Id n [Bool] (bound at noinject.hs:17:11)
        consume'' :: Id n [Bool] -> Bar n -> Bool
          (bound at noinject.hs:17:1)
   |
17 | consume'' g x = and (consume g x)
   |                              ^
Failed, no modules loaded.

如果我们假设 Id 是非单射的，那么会发生错误，因为 consume 可以专门化为 consume :: Id n (t0 Bool) -> Bar n -> t0 Bool，对于一些不是单射的可折叠 t0 []。我明白这么多。我的问题是：为什么 Id 而不是 实际上是单射的。它有两个参数：第一个参数只有一个有效值，而 Id 在第二个参数中显然是单射的，那么为什么 GHC 认为这是一个非单射族？

Answer 1

Injective type families 是类型族之上的单独扩展，您需要特殊的语法来将类型族声明为一个。无法推断单射性。

非单射闭式族

Non-Injective Closed Type Family

haskell

type-families

injective-function