my attempt to do the exercises in sicp.

Monday, July 7, 2008

sicp exercise 2.6

;    Exercise 2.6. In case representing pairs as procedures wasn't mind-boggling enough, consider
;    that, in a language that can manipulate procedures, we can get by without numbers (at least
;    insofar as nonnegative integers are concerned) by implementing 0 and the operation of adding 1 as
;    (define zero (lambda (f) (lambda (x) x)))
;    (define (add-1 n)
;       (lambda (f) (lambda (x) (f ((n f) x)))))
;    This representation is known as Church numerals, after its inventor, Alonzo Church, the logician who
;    invented the calculus.
;    Define one and two directly (not in terms of zero and add-1). (Hint: Use substitution to evaluate
;    (add-1 zero)). Give a direct definition of the addition procedure + (not in terms of repeated
;    application of add-1).

(define zero (lambda (f) (lambda (x) x)))
(define (add-1 n)
       (lambda (f) (lambda (x) (f ((n f) x)))))

(define zero (lambda (f) (lambda(x) x)))
(define one  (lambda (f) (lambda(x) (f x))))
(define two  (lambda (f) (lambda(x) (f (f x)))))


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