Hi,


On Sun, Oct 6, 2013 at 4:36 PM, Carter Schonwald <carter.schonwald@gmail.com> 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.