Can I get KnownNat n to imply KnownNat (n * 3), etc?

Question

I\'m working with data types of this shape, using V from linear:

type Foo n = V (n * 3) Double -> Double

Havin

Answer 1

I post another answer as it is more direct, editing the previous won't make sense.

In fact using the trick (popularised if not invented by Edward Kmett), from reflections reifyNat:

{-# LANGUAGE GADTs #-}
{-# LANGUAGE DataKinds #-}
{-# LANGUAGE KindSignatures #-}
{-# LANGUAGE TypeOperators #-}
{-# LANGUAGE ScopedTypeVariables #-}
{-# LANGUAGE FlexibleContexts #-}
import GHC.TypeLits
import Data.Proxy
import Unsafe.Coerce

newtype MagicNat3 r = MagicNat3 (forall (n :: Nat). KnownNat (n * 3) => Proxy n -> r)

trickValue :: Integer -> Integer
trickValue = (*3)

-- No type-level garantee that the function will be called with (n * 3)
-- you have to believe us
trick :: forall a n. KnownNat n => Proxy n -> (forall m. KnownNat (m * 3) => Proxy m -> a) -> a
trick p f = unsafeCoerce (MagicNat3 f :: MagicNat3 a) (trickValue (natVal p)) Proxy

test :: forall m. KnownNat (m * 3) => Proxy m -> Integer
test _ = natVal (Proxy :: Proxy (m * 3))

So when you run it:

λ *Main > :t trick (Proxy :: Proxy 4) test :: Integer
trick (Proxy :: Proxy 4) test :: Integer :: Integer
λ *Main > trick (Proxy :: Proxy 4) test :: Integer
12

The trick is based on the fact that in GHC the one member class dictionaries (like KnownNat) are represented by the member itself. In KnownNat situation it turns out to be Integer. So we just unsafeCoerce it there. Universal quantification makes it sound from the outside.