Some "magic" classes and instances to get the GHC.TypeLits.KnownNat.Solver type checker plugin working.

Usage

Let's say you defined a closed type family Max:

import Data.Type.Bool (If)
import GHC.TypeLits

type family Max (a :: Nat) (b :: Nat) :: Nat where
  Max 0 b = b
  Max a b = If (a <=? b) b a

if you then want the GHC.TypeLits.KnownNat.Solver to solve KnownNat constraints over Max, given just KnownNat constraints for the arguments of Max, then you must define:

{-# LANGUAGE DataKinds, FlexibleInstances, GADTs, KindSignatures,
             MultiParamTypeClasses, ScopedTypeVariables, TemplateHaskell,
             TypeApplications, TypeFamilies, TypeOperators,
             UndecidableInstances #-}

import Data.Proxy            (Proxy (..))
import GHC.TypeLits.KnownNat

instance (KnownNat a, KnownNat b) => KnownNat2 $(nameToSymbol ''Max) a b where
  natSing2 = let x = natVal (Proxy a)
                 y = natVal (Proxy b)
                 z = max x y
             in  SNatKn z
  {-# INLINE natSing2 #-}

FAQ

1. GHC.TypeLits.KnownNat.Solver does not seem to find the corresponding KnownNat2 instance for my type-level operation

At the Core-level, GHCs internal mini-Haskell, type families that only have a single equation are treated like type synonyms.

For example, let's say we defined a closed type family Max:

import Data.Type.Bool (If)
import GHC.TypeLits

type family Max (a :: Nat) (b :: Nat) :: Nat where
  Max a b = If (a <=? b) b a

Now, a Haskell-level program might contain a constraint

KnownNat (Max a b)

, however, at the Core-level, this constraint is expanded to:

KnownNat (If (a <=? b) b a)

GHC.TypeLits.KnownNat.Solver never sees any reference to the Max type family, so it will not look for the corresponding KnownNat2 instance either. To fix this, ensure that your type-level operations always have at least two equations. For Max this means we have to redefine it as:

type family Max (a :: Nat) (b :: Nat) :: Nat where
  Max 0 b = b
  Max a b = If (a <=? b) b a