adicity.hs

runAdicity_0_1 :: (() -> (a, ()))
               -> a
runAdicity_0_1 f = fst (f ())

adicity_0_1 :: a
            -> t -> (a, t)
adicity_0_1 x t = (x, t)

adicity_1_1 :: (a -> b)
            -> (a, t) -> (b, t)
adicity_1_1 f (a, t) = (f a, t)

adicity_2_1 :: (a -> b -> c)
            -> (a, (b, t)) -> (c, t)
adicity_2_1 f (x, (y, t)) = (f x y, t)


-- | 
-- >>> (+1) . (*2) $ 3
-- 7
-- >>> (+1) $ (*2) 3
-- 7
-- >>> example1
-- 7
example1 :: Int
example1 = runAdicity_0_1
         $ adicity_1_1 (+1) . adicity_1_1 (*2) . adicity_0_1 3

-- |
-- >>> (+) (2 * 3) 4
-- 10
-- >>> ((+) . (* 2)) 3 4
-- 10
-- >>> example2
-- 10
example2 :: Int
example2 = runAdicity_0_1
         $ adicity_2_1 (+) . adicity_2_1 (*)
         . adicity_0_1 2 . adicity_0_1 3 . adicity_0_1 4


main :: IO ()
main = do print example1
          print example2