Subtraction of church numerals in haskell

Question

I\'m attempting to implement church numerals in Haskell, but I\'ve hit a minor problem. Haskell complains of an infinite type with

Occurs check: cannot construct th

Answer 1

I have encountered the same problem. And I solved it without adding type signature.

Here's the solution, with cons car copied from SICP.

cons x y = \m -> m x y
car z = z (\p q -> p)
cdr z = z (\p q -> q)

next z = cons (cdr z) (succ (cdr z))
pred n = car $ n next (cons undefined zero)

sub m n = n pred m

You can find full source here.

I'm really amazed after writing sub m n = n pred m, and load it in ghci without type error!

Haskell code is so concise! :-)