import Prelude hiding (succ, pred, and, or, not)
import Control.Arrow
 
-- Arrow style natural numbers by itchyny
 
 
toint = ($ ((1+), 0))
tobool = ($ (True, False))
 
-- Do not use except for
--    fst
--    snd
--    (,)
--    app
--    id
--    (>>>)
--    (&&&)
--    (***)
--
-- and following is allowed
--    (<<<) == flip (>>>)
--    curry == ((<<<) >>> ((,) >>>))
--    flip = uncurry >>> ((snd &&& fst) >>>) >>> curry
--
-- don't use
--    uncurry == (*** id) >>> (>>> app)
--            == \f -> (f *** id) >>> app
--    (.) f g == g >>> f
--    first f == f *** id
--    second g == id *** g
--    ($) == curry app
--    const == ((,) >>> (>>> fst))
--    etc.
 
 
-- zero = \(f, x) -> x
zero = snd
 
-- succ = \n (f, x) -> f (n (f, x))
succ = curry ((snd >>> fst) &&& app >>> app)
 
-- plus = \m n (f, x) -> m (f, (n (f, x)))
plus = (((snd >>> fst) &&& app) >>>) >>> curry
 
-- mult = \m n -> m ((plus n), zero)
mult = ((plus >>> (flip (,) zero)) >>>)
 
-- pred = \n f x -> n (\g h -> h (g f)) (\u -> x) (\u -> u)
 
-- true = \(x, y) -> x
true = fst
 
-- false = \(x, y) -> y
false = snd
 
-- and = \p q -> p (q, false)
and = (flip (,) false >>>)
 
-- or = \p q -> p (true, q)
or = ((,) true >>>)
 
-- not = \p -> p (false, true)
not = flip (curry app) ((,) false true)
 
main = do
  let one = succ zero
      two = succ one
      three = succ two
      four = succ three
      five = succ four
      six = succ five
  print $ toint zero
  print $ toint one
  print $ toint two
  print $ toint three
  print $ toint $ plus five three
  print $ toint $ mult four six
  -- print $ toint $ pred six
  -- print $ toint $ pred (plus (two six))
  print $ "Bool"
  print $ tobool true
  print $ tobool false
  print $ "and"
  print $ tobool $ and true true
  print $ tobool $ and true false
  print $ tobool $ and false true
  print $ tobool $ and false false
  print $ "or"
  print $ tobool $ or true true
  print $ tobool $ or true false
  print $ tobool $ or false true
  print $ tobool $ or false false
  print $ "not"
  print $ tobool $ not true
  print $ tobool $ not false
  return ()
 

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