Lambda Calculus in Coffeescript

lambda-calculus.coffee

# Combinators
I     = (x) -> x

# Church Numerals
int   = (n) -> n((x) -> ++x)(0) # Converts Chruch Numeral to literal integer
$0 = ZERO  = (f) -> (x) -> x
$1 = ONE   = (f) -> (x) -> f x
$2 = TWO   = (f) -> (x) -> f f x
$3 = THREE = (f) -> (x) -> f f f x
$4 = FOUR  = (f) -> (x) -> f f f f x
$5 = FIVE  = (f) -> (x) -> f f f f f x
w = window ? root ? exports
for n in [6..1000]
  w["$#{n}"] = (f) -> n=n; (x) -> mem = f(x); mem = f(mem) for i in [0..n]; mem

SUCC  = (n) -> (f) -> (x) -> f (n(f)(x))
PLUS  = (m) -> (n) -> (f) -> (x) -> m(f)(n(f)(x))

PLUS(ONE)(TWO)

# Church Booleans
b = (f) -> f(true)(false) # Converts Church Boolean to literal 'true' or 'false'
TRUE = (x) -> (y) -> x
FALSE = (x) -> (y) -> y

# Lambda Logic
AND = (p) -> (q) -> p(q)(p)
OR  = (p) -> (q) -> p(p)(q)
NOT = (p) -> (a) -> (b) -> p(b)(a)

AND(TRUE)(TRUE) #===> TRUE
b AND(TRUE)(TRUE)   #===> true
b AND(TRUE)(FALSE)  #===> false
b AND(FALSE)(TRUE)  #===> false
b AND(FALSE)(FALSE) #===> false