Exercise 1.9
Evaluate (+ 4 5) using the following procedure definition:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 | (define (+ a b) (if (= a 0) b (inc (+ (dec a) b)))) (+ 4 5) (inc (+ (dec 4) 5)) (inc (+ 3 5)) (inc (inc (+ (dec 3) 5))) (inc (inc (+ 2 5))) (inc (inc (inc (+ (dec 2) 5)))) (inc (inc (inc (+ 1 5)))) (inc (inc (inc (inc (+ (dec 1) 5))))) (inc (inc (inc (inc (+ 0 5))))) (inc (inc (inc (inc 5)))) (inc (inc (inc 6))) (inc (inc 7)) (inc 8) 9 |
This is a linear recursive process.
Now, use the following definition instead to evaluate the same combination:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 | (define (+ a b) (if (= a 0) b (+ (dec a) (inc b)))) (+ 4 5) (+ (dec 4) (inc 5)) (+ 3 6) (+ (dec 3) (inc 6)) (+ 2 7) (+ (dec 2) (inc 7)) (+ 1 8) (+ (dec 1) (inc 8)) (+ 0 9) 9 |
This is an linear iterative process.
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