Created
July 19, 2014 21:22
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{-# LANGUAGE InstanceSigs #-} | |
{-# LANGUAGE ScopedTypeVariables #-} | |
{-# LANGUAGE GADTs #-} | |
{-# LANGUAGE ScopedTypeVariables #-} | |
{-# LANGUAGE TypeFamilies #-} | |
{-# LANGUAGE TypeOperators #-} | |
module Sum where | |
import Data.Vector.Fixed (S,Z,Fun(..)) | |
import Data.Vector.Fixed.Cont (Fn,Arity(..)) | |
-- | Type family for sum of unary natural numbers. | |
type family n + m :: * | |
type instance Z + n = n | |
type instance S n + k = S (n + k) | |
-- | We need to extend Arity type class with ability generate proofs | |
-- that @Fn (n+k) a b ~ Fn n a (Fn k a b)@ which is needed for | |
-- 'uncurryMany'. | |
class Arity n => AritySum n where | |
witSum :: WitSum n k a b | |
instance AritySum Z where | |
witSum = WitSum | |
instance AritySum n => AritySum (S n) where | |
witSum :: forall k a b. WitSum (S n) k a b | |
witSum = case witSum :: WitSum n k a b of | |
WitSum -> WitSum | |
-- | Value that carry proof that `Fn (n+k) a b ~ Fn n a (Fn k a b)` | |
data WitSum n k a b where | |
WitSum :: (Fn (n+k) a b ~ Fn n a (Fn k a b)) => WitSum n k a b | |
uncurryMany :: forall n k a b. AritySum n | |
=> Fun n a (Fun k a b) -> Fun (n + k) a b | |
uncurryMany f = | |
case witSum :: WitSum n k a b of | |
WitSum -> | |
case fmap unFun f :: Fun n a (Fn k a b) of | |
Fun g -> Fun g | |
curryMany :: forall n k a b. Arity n | |
=> Fun (n + k) a b -> Fun n a (Fun k a b) | |
curryMany (Fun f0) = Fun $ accum | |
(\(T_curry f) a -> T_curry (f a)) | |
(\(T_curry f) -> Fun f :: Fun k a b) | |
( T_curry f0 :: T_curry a b k n) | |
newtype T_curry a b k n = T_curry (Fn (n + k) a b) |
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