Peano goes Maybe
Just for the fun of it, let's represent Nats as Maybies in Haskell. import Prelude hiding (succ) -- A strange representation of Nats newtype Nat = Nat { getNat :: Maybe Nat } -- Peano zero zero :: Nat zero = Nat Nothing -- Peano successor succ :: Nat -> Nat succ = Nat . Just -- Primitive recursion for addition add :: Nat -> Nat -> Nat add x = maybe x (succ . add x) . getNat -- Convert primitive Int into strange Nat fromInt :: Int -> Nat fromInt 0 = Nat Nothing fromInt x = succ (fromInt (x-1)) -- Convert strange Nat into primitive Int toInt :: Nat -> Int toInt = maybe 0 ((+1) . toInt) . getNat -- Let's test main = print $ toInt (add (fromInt 20) (fromInt 22)) I wrote this code in response to a student question, whether and, if so, how one could code recursive functions on maybies. This inspired me towards the exam question as to how the above code compares to more straightforward code which would uses an algebraic datatype with Zero and Succ constructors in...