-- Sparcl: A Language for Partially-Invertible Computation
-- Simple bijective functions example
-- Based on: Matsuda, K. and Wang, M. (ICFP 2018)

data Nat = Z | S Nat

-- Successor bijection: forward adds S, backward removes S
succN :: Nat <-> Nat
succN n = S n

-- Swap pair elements (self-inverse bijection)
swap :: (a, b) <-> (b, a)
swap (x, y) = (y, x)

-- Negate integer (self-inverse bijection)
negateZ :: Int <-> Int
negateZ n = -n

-- Add a constant to the first component of a pair
-- forward: (x, y) -> (x+y, y)
-- backward: (x, y) -> (x-y, y)
addFst :: (Int, Int) <-> (Int, Int)
addFst (x, y) = (x + y, y)