Hi,
On Sun, Oct 6, 2013 at 4:36 PM, Carter Schonwald wrote: hrmm, Why don't we have a proper bijection? lets assume we have ToPeano and a corresponding ToNat, as above, couldn't we have something like asPeano :: (b~ ToPeano a, a ~ ToNat b)=> Proxy a -> Proxy b or a suitable type level representaion thereof? I think it should be quite easy to define such a function, but I am
afraid I don't fully understand how to use it... or are you saying that in 7.8, i should be able to just efficiently work
directly on the nat rep and have class Cl (n::Nat) where instance CL 0 where instance Cl n => Cl (n+1) and essentially get peano for free? I am not sure if this would help with your specific task, but things like
this work: {-# LANGUAGE DataKinds, KindSignatures, TypeOperators #-}
{-# LANGUAGE FlexibleInstances, UndecidableInstances, OverlappingInstances
#-}
import GHC.TypeLits
import Data.Proxy
class C (n :: Nat) where
txt :: Proxy n -> String
instance C 0 where
txt _ = "0"
instance C (n - 1) => C n where
txt x = "1 + " ++ txt (prev x)
prev :: Proxy x -> Proxy (x - 1)
prev _ = Proxy
example = txt (Proxy :: Proxy 3)
*Main> example
"1 + 1 + 1 + 0"
-Iavor
PS: All of this is committed in HEAD, please try it out and let me know if
we need to do any last minute changes before the upcoming release.