== Type-Naturals and GADTs ==
{{{
{-# LANGUAGE TypeNaturals, GADTs #-}
import GHC.TypeNats
data Vec :: Nat -> * -> * where
Nil :: Vec 0 a
Cons :: a -> Vec n a -> Vec (n + 1) a
cat :: Vec m a -> Vec n a -> Vec (m + n) a
cat Nil ys = ys
cat (Cons x xs) ys = Cons x (cat xs ys)
data UNat :: Nat -> * where
Zero :: UNat 0
Succ :: UNat n -> UNat (n + 1)
split :: UNat m -> Vec (m + n) a -> (Vec m a, Vec n a)
split Zero xs = (Nil, xs)
split (Succ n) (Cons x xs) = case split n xs of
(as,bs) -> (Cons x as, bs)
instance Show a => Show (Vec n a) where
show Nil = "[]"
show (Cons x xs) = show x ++ " : " ++ show xs
}}}