> On Jul 5, 2017, at 5:23 PM, Wolfgang Jeltsch <wolfgang...@jeltsch.info> wrote:
>
> Hi!
>
> The base package contains the module Data.Type.Equality, which contains
> the type (:~:) for homogeneous equality. I was a bit surprised that
> there is no type for heterogeneous equality there. Is there such a type
> somewhere else in the standard library?
I don't believe it is, but (in my opinion) it should be.
>
> I tried to define a type for heterogeneous equality myself as follows:
>
>> {-# LANGUAGE GADTs, PolyKinds, TypeOperators #-}
>>
>> data a :~~: b where
>>
>> HRefl :: a :~~: a
>
> To my surprise, the kind of (:~~:) defined this way is k -> k -> *, not
> k -> l -> *. Why is this?
Because the definition of heterogeneous equality requires polymorphic
recursion, in that the usage of (:~~:) in the type of HRefl has different kind
indices than the declaration head. Polymorphic recursion is allowed only when
you have a *complete user-supplied kind signature*, as documented here
(https://downloads.haskell.org/~ghc/latest/docs/html/users_guide/glasgow_exts.html#complete-user-supplied-kind-signatures-and-polymorphic-recursion).
This surprised me, too, when I first encountered it, but I believe it's the
correct behavior.
Richard
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