Heterogeneous equality

[Wolfgang Jeltsch]

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 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? Apparently, the latter, more general, kind is
possible, since we can define (:~~:) :: k -> l -> * as follows:

> {-# LANGUAGE GADTs, PolyKinds, TypeOperators #-}
> 
> data (a :: k) :~~: (b :: l) where
> 
>     HRefl :: a :~~: a

All the best,
Wolfgang