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| 1 | - | #lang racket |
| 1 | + | #lang racket |
| 2 | - | |
| 2 | + | |
| 3 | - | (require rackunit) |
| 3 | + | (require rackunit) |
| 4 | - | |
| 4 | + | |
| 5 | - | ; A fixed point of f is x such that f(x) = x. |
| 5 | + | ; A fixed point of f is x such that f(x) = x. |
| 6 | - | ; We need to develop means to get a fixed point of f. |
| 6 | + | ; We need to develop means to get a fixed point of f. |
| 7 | - | |
| 7 | + | |
| 8 | - | ;; Curry's Paradoxical Combinator of Y |
| 8 | + | ;; Curry's Paradoxical Combinator of Y |
| 9 | - | (define (Y f) |
| 9 | + | (define (Y f) |
| 10 | - | ((λ (r) (f (delay r r))) |
| 10 | + | ((λ (r) (f (delay r r))) |
| 11 | - | (λ (r) (f (delay r r))))) |
| 11 | + | (λ (r) (f (delay r r))))) |
| 12 | - | |
| 12 | + | |
| 13 | - | ; (Y F) = (F (F (... (Y F)))) |
| 13 | + | ; (Y F) = (F (F (... (Y F)))) |
| 14 | - | ; Y produces the fixed point of F |
| 14 | + | ; Y produces the fixed point of F |
| 15 | - | |
| 15 | + | |
| 16 | - | ;; Recursive exponentiation via Y-combinator |
| 16 | + | ;; Recursive exponentiation via Y-combinator |
| 17 | - | (define (pow r) |
| 17 | + | (define (pow r) |
| 18 | - | (λ (x n) |
| 18 | + | (λ (x n) |
| 19 | - | (define next-call ((force r) (force r))) |
| 19 | + | (define next-call ((force r) (force r))) |
| 20 | - | (cond ((= n 0) 1) |
| 20 | + | (cond ((= n 0) 1) |
| 21 | - | (else (* x (next-call x (sub1 n))))))) |
| 21 | + | (else (* x (next-call x (sub1 n))))))) |
| 22 | - | |
| 22 | + | |
| 23 | - | ;; Base to the power of exponent |
| 23 | + | ;; Base to the power of exponent |
| 24 | - | (define (power base exponent) |
| 24 | + | (define (power base exponent) |
| 25 | - | ((Y pow) base exponent)) |
| 25 | + | ((Y pow) base exponent)) |
| 26 | - | |
| 26 | + | |
| 27 | - | ;; Tests |
| 27 | + | ;; Tests |
| 28 | - | (check-equal? (power 0 99) 0) |
| 28 | + | (check-equal? (power 0 99) 0) |
| 29 | - | (check-equal? (power 1 99) 1) |
| 29 | + | (check-equal? (power 1 99) 1) |
| 30 | - | (check-equal? (power 2 4) 16) |
| 30 | + | (check-equal? (power 2 4) 16) |
| 31 | - | (check-equal? (power 3 3) 27) |
| 31 | + | (check-equal? (power 3 3) 27) |
| 32 | (check-equal? (power 10 5) 100000) |