Church Numerals are a representation of the natural numbers using lambda notation.

A kind of base1 arithmetic, in which numbers are represented by function nesting over an empty list, can be constructed in Pure Lisp using only very few primtives. This document will present Church Numerals through the lens of Lisp, alternatively one might prefer to read it coming from the Avian Numerals tutorial.

The following file contains the basic building blocks as an example:

(LETREC church
	(church LAMBDA (INPUT)
		(greater?
			(incr (incr (incr (incr nil))))
			(incr (incr (incr nil))))
	)
	(nil QUOTE NULL)
	(#f QUOTE F)
	(#t QUOTE T)
	(incr LAMBDA (x)
		(CONS nil x))
	(decr LAMBDA (x)
		(CDR x))
	(zero? LAMBDA (x)
		(EQ x nil))
	(not LAMBDA (x)
		(IF x #f #t))
	(plus LAMBDA (x y)
		(IF (zero? x) y
			(plus (decr x) (incr y))))
	(minus LAMBDA (x y)
		(IF (zero? y) x
			(minus (decr x) (decr y))))
	(multiply LAMBDA (x y)
		(IF (zero? x) nil
			(plus y (multiply (decr x) y))))
	(equal? LAMBDA (x y)
		(IF (zero? x) (zero? y)
			(IF (zero? y) #f
				(equal? (decr x) (decr y)))))
	(greater? LAMBDA (x y)
		(IF (zero? x) #f
			(IF (zero? y) (not (zero? x))
				(greater? (decr x) (decr y)))))
	(lesser? LAMBDA (x y)
		(greater? y x))
)

incoming ornithomicon