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Basic implementation of Church Numerals and Compound date in Scheme utilizing lambda calculus
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#lang scheme | |
;;---Lambda Calculus--- | |
(define I | |
(λ (x) x)) | |
(define K | |
(λ (x) (λ (y) x))) | |
(define KI | |
(λ (x) ((K I) x))) | |
(define V | |
(λ (x) (λ (y) (λ (f) ((f x) y))))) | |
;;---Constructor and Selector Functions--- | |
(define cons | |
(λ (x y) ((V x) y))) | |
(define car | |
(λ (l) (l K))) | |
(define cdr | |
(λ (l) (l KI))) | |
;;---Church Numerals and Arithmetic--- | |
(define zero | |
(λ (f) (λ (x) x))) | |
(define succ | |
(λ (n) | |
(λ (f) (λ (x) | |
(f ((n f) x)))))) | |
(define add | |
(λ (m) (λ (n) | |
(λ (f) (λ (x) | |
((m f) ((n f) x))))))) | |
(define one (λ (f) (λ (x) (f x)))) | |
(define two (λ (f) (λ (x) (f (f x))))) | |
(define three (λ (f) (λ (x) (f (f (f x)))))) | |
;;---Printing and Output Functions--- | |
(define printPair | |
(λ (p) (begin | |
newline | |
(display "(") | |
(display (car p)) | |
(display ",") | |
(display (cdr p)) | |
(display ")")))) | |
(define printNumeral | |
(λ (n) (display | |
((n (λ (x) (+ x 1))) 0)))) |
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