Church Numerals on CoffeeScript

gistfile1.coffee

# helpers

inc = (x) -> x + 1

church = (n) ->
  if n > 0
    succ church n-1
  else
    zero

unchurch = (n) ->
  n(inc) 0

# epic starts here
# numerals

succ = (n) -> (f) -> (x) -> f n(f) x

plus = (m) -> (n) -> (f) -> (x) -> m(f) n(f) x

mult = (m) -> (n) -> (f) -> n m f

exp = (m) -> (n) -> n m

is_zero = (n) -> (n (x) -> false) true

zero = (f) -> (x) -> x
one = (f) -> (x) -> f x # succ zero
two = (f) -> (x) -> f f x # succ succ zero

alert unchurch (f) -> (x) -> f f f x
alert unchurch church 9
alert unchurch succ church 9
alert unchurch plus(church 7) church(4)
alert is_zero zero
alert is_zero two
alert unchurch exp(two) succ(two)