Constrained.hs

module Constrained where

-- | A constained function from @a@ to @b@, utilizing constraint @i@ and providing constraint @j@
--   C subsumes 'a -> b == C () () a b', 'Dict c = C () c a a', and 'c :- k == C c k a a'
newtype C i j a b = C {runC :: i => (j => a) -> b}

-- | Composition. Acts like function composition on the arrows, and 
(><) :: C j k a b -> C i j b c -> C i k a c
C f >< C g = C (\x -> g (f x))

-- | 'provide @j' is analogous to 'Dict @j'
provide :: j => C i j a a
provide = C (\a -> a)

-- | lift an unconstrained function 
arr :: (a -> b) -> C i i a b
arr f = C f

-- | (convenience function) Lift a constrained function. Requires an extra type parameter 
--   so must be called like 'constrained @(i :: * -> Constraint)'
constrained :: (i a => a -> b) -> C (i a) (i a) a b
constrained f = C f