Equality in singletons for star kind

Question

I did in ghci:

> :set -XTypeOperators

> import Data.Proxy
> import Data.Type.Equality
> import Data.Singletons.Prelude

> :let p1 = Proxy :: Proxy (Int == Int)
> :let p2 = Proxy :: Proxy (Int :== Int)

> :t p1
p1 :: Proxy 'True
> :t p2
p2 :: Proxy (Int :== Int)

Why in the second case type is not calculated? Can I workaround it somehow? Can I make an instance for class PEq (where :== is defined)?

(ghc 7.10.3)

Update: I found how to make an instance. Are there some reasons why it is not included?

> instance PEq ('KProxy :: KProxy *) where { type (:==) x y = x == y }

or simple (as pointed by dfeuer in comments)

> instance PEq ('KProxy :: KProxy *)

or import this instance from TypeRepStar:

> import Data.Singletons.TypeRepStar()

Answer 1

It seems that a reason for not including instance for PEq for kind * in singletons are similar to not including poly-kinded instances for Eq in base . It is described here . Such instance too common and if it exists we can't describe eg equalities of type arguments by result of type functions. For example:

Succ n == Succ m = n == m

For workaround in case of singletons one can define it:

instance PEq ('KProxy :: KProxy *)

Or just use it:

import Data.Singletons.TypeRepStar()