Numbers in Lambda Calculus - Following Destroy All Software approach

numbers_in_lambda_calculus.lisp

;; Church Numbers
(setq zero (lambda (f) (lambda (x) x)))
(setq one (lambda (f) (lambda (x) (funcall f x))))
(setq two (lambda (f) (lambda (x) (funcall f (funcall f x)))))

;; Manual Calc
(funcall (funcall zero (lambda (x) (+ 1 x))) 0)
(funcall (funcall one (lambda (x) (+ 1 x))) 0)
(funcall (funcall two (lambda (x) (+ 1 x))) 0)

;; Calc Function
(setq calc (lambda (f) (funcall (funcall f (lambda (x) (+ 1 x))) 0)))

(funcall calc zero)
(funcall calc one)
(funcall calc two)


;; Successor - Add 1
(setq succ (lambda (n) (lambda (f) (lambda (x) (funcall f (funcall (funcall n f) x))))))

(funcall calc (funcall succ zero))
(funcall calc (funcall succ one))
(funcall calc (funcall succ two))

;; Defining Three using succ function
(setq three (funcall succ two))
(funcall calc three)

numbers_in_lambda_calculus.rb

require 'irb'

CONVERT  = -> (x) { x + 1 }

ZERO  = -> (f) { -> (x) { x } }
ONE   = -> (f) { -> (x) { f.(x) } }
TWO   = -> (f) { -> (x) { f.(f.(x)) } }
THREE = -> (f) { -> (x) { f.(f.(f.(x))) } }
FOUR  = -> (f) { -> (x) { f.(f.(f.(f.(x)))) } }
FIVE  = -> (f) { -> (x) { f.(f.(f.(f.(f.(x))))) } }
SIX   = -> (f) { -> (x) { f.(f.(f.(f.(f.(f.(x)))))) } }
SEVEN = -> (f) { -> (x) { f.(f.(f.(f.(f.(f.(f.(x))))))) } }
EIGHT = -> (f) { -> (x) { f.(f.(f.(f.(f.(f.(f.(f.(x)))))))) } }
NINE  = -> (f) { -> (x) { f.(f.(f.(f.(f.(f.(f.(f.(f.(x))))))))) } }

IDENTITY = -> (x) { x }
ADD1     = -> (n) { -> (f) { -> (x) { f.(n.(f).(x)) } } }

ADD  = -> (n) { -> (m) { n.(ADD1).(m) }}
MULT = -> (n) { -> (m) { n.(->(acc) { ADD.(m).(acc) }).(ZERO) }}

#puts ADD1.(TWO).(CONVERT).(0)
#puts ADD.(TWO).(FIVE).(CONVERT).(0)
#puts MULT.(SEVEN).(THREE).(CONVERT).(0)