I see this in GHC.TypeNats sameNat :: (KnownNat a, KnownNat b) => Proxy a -> Proxy b -> Maybe (a :~: b) sameNat x y | natVal x == natVal y = Just (unsafeCoerce Refl) | otherwise = Nothing The unsafeCoerce says that sameNat is part of the trusted code base. And indeed, it’s only because SNat is a private newtype (i.e its data constructor is private to GHC.TypeNats) that you can’t bogusly say (SNat 7 :: SNat 8) You want exactly the same thing, but for a comparison oriented data CompareEv, rather than its equality counterpart :~:. So the same approach seems legitimate. I always want code with unsafeCoerce to be clear about (a) why it’s necessary and (b) why it’s sound. Simon From: Glasgow-haskell-users <glasgow-haskell-users-bounces@haskell.org> On Behalf Of Conal Elliott Sent: 24 May 2018 00:39 To: glasgow-haskell-users@haskell.org Subject: Natural number comparisons with evidence 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