{-# LANGUAGE TypeNaturals, GADTs #-}
import GHC.TypeNats
import Unsafe.Coerce
--------------------------------------------------------------------------------
-- Extending GHC.TypeNats with these two function allows us to
-- write inductive definitions.
data UNat :: Nat -> * where
Zero :: UNat 0
Succ :: UNat n -> UNat (n + 1)
toUNat :: Nat n -> UNat n
toUNat n = unsafe (natToInteger n)
where unsafe :: Integer -> UNat n
unsafe 0 = unsafeCoerce Zero
unsafe n = unsafeCoerce (Succ (unsafe $! (n-1)))
--------------------------------------------------------------------------------
data Vec :: Nat -> * -> * where
Nil :: Vec 0 a
Cons :: a -> Vec n a -> Vec (n + 1) a
instance Show a => Show (Vec n a) where
show Nil = "[]"
show (Cons x xs) = show x ++ " : " ++ show xs
instance Functor (Vec n) where
fmap f Nil = Nil
fmap f (Cons x xs) = Cons (f x) (fmap f xs)
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)
vecLen :: NatI n => Vec n a -> Nat n
vecLen _ = nat
splitU :: UNat m -> Vec (m + n) a -> (Vec m a, Vec n a)
splitU Zero xs = (Nil, xs)
splitU (Succ n) (Cons x xs) = let (as,bs) = splitU n xs
in (Cons x as, bs)
vecSplitAt :: Nat m -> Vec (m + n) a -> (Vec m a, Vec n a)
vecSplitAt n = splitU (toUNat n)
vecSplit :: NatI m => Vec (m + n) a -> (Vec m a, Vec n a)
vecSplit = vecSplitAt nat