PRED/SUB1 function implemented in pure Lambda Calculus using Haskell!

Pred.hs

zero   = \f -> \x -> x
mySucc = \n -> \f -> \x -> f $ n f x
add    = \n -> \m -> n mySucc m
mkPair = \a -> \b -> \s -> s a b
myFst  = \a -> \b -> a
mySnd  = \a -> \b -> b
step   = \p -> mkPair (p mySnd) (mySucc (p mySnd))
nSteps = \n -> \p -> n step p
zz     = mkPair zero zero
myPred = \n -> (nSteps n zz) myFst

one    = mySucc zero
two    = mySucc (mySucc zero)
three  = mySucc (mySucc (mySucc zero))
six    = add (add two three) one

main :: IO ()
main = do
  let p = mkPair two three
  let n = nSteps three p
  putStrLn $ show $ (myPred six) (\x -> x + 1) 0 -- => 5