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问题描述

我一直在教自己关于类型级编程,并想写一个简单的自然数加法类型函数。我的第一个版本工作如下:

pre code $ Z
data S

类型One = SZ
类型Two = S(SZ)

类型系列Plus mn :: *
类型实例Plus Z n = n
类型实例Plus(S m)n = S(Plus mn)

所以在GHCi中我可以这样做:

  ghci> :t undefined :: Plus One Two 
undefined :: Plus One Two :: S *(S *(S * Z))

其中按预期工作。然后我决定通过修改 Z S 类型来试用DataKinds扩展:

 数据Nat = Z | S Nat 

Plus系列现在返回一个 Nat kind:

  type family Plus mn :: Nat 

修改后的代码会编译,但问题是我现在在测试时遇到错误:

 种类不匹配
预期种类`OpenKind',但是`Plus One Two'种类'Nat'
在表达式类型签名中:Plus One Two
在表达式中:undefined :: Plus One Two

我已经在寻找解决方案,但Google让我失望了。解决方案是否存在或者我是否遇到了一些语言限制?

解决方案

我认为你测试的方式是不正确的。 undefined 可以是任何类型的类型 * (我可能在这里错了)。



在ghci中试试这个

  ghci>:t(undefined: :'Z)

<互动>:1:15:
种类不匹配
预期种类'OpenKind',但'Z'种类'Nat'
在表达式类型签名中:Z
在表达式中:(undefined :: Z)

通过在ghci中使用:kind!,你仍然可以获得 Plus One Two 类型

  ghci>:kind! Plus One Two 
Plus One Two :: Nat
= S(S(S'Z))


I've been teaching myself about type-level programming and wanted to write a simple natural number addition type function. My first version which works is as follows:

data Z
data S n

type One = S Z
type Two = S (S Z)

type family Plus m n :: *
type instance Plus Z n = n
type instance Plus (S m) n = S (Plus m n)

So in GHCi I can do:

ghci> :t undefined :: Plus One Two
undefined :: Plus One Two :: S * (S * (S * Z))

Which works as expected. I then decided to try out the DataKinds extension by modifying the Z and S types to:

data Nat = Z | S Nat

And the Plus family now returns a Nat kind:

type family Plus m n :: Nat

The modified code compiles but the problem is I now get an error when testing it:

Kind mis-match
Expected kind `OpenKind', but `Plus One Two' has kind `Nat'
In an expression type signature: Plus One Two
In the expression: undefined :: Plus One Two

I've searched for a solution but Google has failed me. Does a solution exist or have I hit some limit of the language?

解决方案

I think way you are testing is not correct. undefined can be of any type of kind * (I maybe wrong here).

Try this in ghci

ghci>:t (undefined :: 'Z)

<interactive>:1:15:
    Kind mis-match
    Expected kind `OpenKind', but `Z' has kind `Nat'
    In an expression type signature: Z
    In the expression: (undefined :: Z)

You can still get the type of Plus One Two by using :kind! in ghci

ghci>:kind! Plus One Two
Plus One Two :: Nat
= S (S (S 'Z))

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10-14 07:59