When programming with GHC's type-level natural numbers and `KnownNat` constraints, how can one construct *evidence* of the result of comparisons to be used in further computations? For instance, we might define a type for augmenting the results of `compare` with evidence:

> data CompareEv u v

> = (u < v) => CompareLT

> | (u ~ v) => CompareEQ

> | (u > v) => CompareGT

Then I'd like to define a comparison operation (to be used with `AllowAmbiguousTypes` and `TypeApplications`, alternatively taking proxy arguments):

> compareEv :: (KnownNat m, KnownNat n) => CompareEv u v

With `compareEv`, we can bring evidence into scope in `case` expressions.

I don't know how to implement `compareEv`. The following attempt fails to type-check, since `compare` doesn't produce evidence (which is the motivation for `compareEv` over `compare`):

> compareEv = case natVal (Proxy @ u) `compare` natVal (Proxy @ v) of

> LT -> CompareLT

> EQ -> CompareEQ

> GT -> CompareGT

Can `compareEv` be implemented in GHC Haskell? Is there already an implementation of something similar? Any other advice?

Thanks, -- Conal