module PeanoSum where
-- Written by Marcelo Camargo <marcelocamargo@linuxmail.org> on
-- Sat Oct 22 2016

-- Represent natural numbers
data Nat = Zero
         | Succ Nat

-- Let neutral element of Monoid be id
-- Let (Functor a) b become Functor (a .+. b)
infixl .+.
(.+.) :: Nat -> Nat -> Nat
(.+.) Zero     b = b
(.+.) (Succ a) b = Succ ((.+.) a b)

-- Built only for visual representation with pipes
instance Show Nat where
    show Zero     = ""
    show (Succ n) = "|" ++ (show n)

-- Create aliases for 1 up to 9
zero, one, two, three, four, five, six, seven, eight, nine :: Nat
zero   = Zero
one    = Succ zero
two    = Succ one
three  = Succ two
four   = Succ three
five   = Succ four
six    = Succ five
seven  = Succ six
eight  = Succ seven
nine   = Succ eight

-- Test our function definitions with pipes
main = putStrLn . show $ eight .+. nine