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The Elements of Programming
1. Expressions
486
1 486
(+ 137 349) 486 (- 1000 334) 666 (* 5 99) 495 (/ 10 5) 2 (+ 2.7 10) 12.7
(+ 21 35 12 7) 75 (* 25 4 12) 1200
或者
reduce(int.__add__, [21, 35, 12, 7]) reduce(int.__mul__, [25, 4, 12])
(+ (* 3 5) (- 10 6)) 19
1 (3 * 5) + (10 - 6)
(+ (* 3 (+ (* 2 4) (+ 3 5))) (+ (- 10 7) 6))
1 (3 * ((2*4)+(3+5)) ) + ((10-7)+6)
2. Naming and the Environment
(define size 2)
1 size = 2
size 2 (* 5 size) 10
(define pi 3.14159) (define radius 10) (* pi (* radius radius)) 314.159 (define circumference (* 2 pi radius)) circumference 62.8318
3. Evaluating Combinations
(* (+ 2 (* 4 6)) (+ 3 5 7))
1 (2+(4*6)) * (3+5+7)
4. Compound Procedures
(define (square x) (* x x))
1 square = lambda x: x*x
(square 21) 441 (square (+ 2 5)) 49 (square (square 3)) 81
(define (sum-of-squares x y) (+ (square x) (square y))) (sum-of-squares 3 4) 25
(define (f a) (sum-of-squares (+ a 1) (* a 2))) (f 5) 136
5. The Substitution Model for Procedure Application
6. Conditional Expressions and Predicates
(define (abs x) (cond ((> x 0) x) ((= x 0) 0) ((< x 0) (- x))))
1 abs = lambda x: x if x > 0 else ( 0 if x == 0 else (-x if x < 0 else 0))
或者
1 abs = lambda x: x if x > 0 else (0 if x == 0 else -x)
(define (abs x) (cond ((< x 0) (- x)) (else x)))
1 abs = lambda x: -x if x < 0 else x
(define (abs x) (if (< x 0) (- x) x))
abs = lambda x: -x if x < 0 else x
(and (> x 5) (< x 10))
1 x > 5 and x < 10
(define (>= x y) (or (> x y) (= x y)))
1 greater_or_equal = lambda x, y: x>y or x==y
(define (>= x y) (not (< x y)))
1 greater_or_equal = lambda x, y: not x < y
7. Example: Square Roots by Newton's Method
(define (sqrt-iter guess x) (if (good-enough? guess x) guess (sqrt-iter (improve guess x) x)))
1 sqrt_iter = lambda guess, x: guess if good_enough(guess, x) else sqrt_iter(improve(guess, x), x)
(define (improve guess x) (average guess (/ x guess)))
1 improve = lambda guess, x: average(guess, x/guess)
(define (average x y) (/ (+ x y) 2))
1 average = lambda x, y: (x+y)/2.0
(define (good-enough? guess x) (< (abs (- (square guess) x)) 0.001))
1 good_enough = lambda guess, x: abs(square(guess)-x)< 0.001
(define (sqrt x) (sqrt-iter 1.0 x))
1 sqrt = lambda x:sqrt_iter(1.0, x)
(sqrt 9) 3.00009155413138 (sqrt (+ 100 37)) 11.704699917758145 (sqrt (+ (sqrt 2) (sqrt 3))) 1.7739279023207892 (square (sqrt 1000)) 1000.000369924366
8. Procedures as Black-Box Abstractions
(define (square x) (* x x)) (define (square x) (exp (double (log x)))) (define (double x) (+ x x))
(define (square x) (* x x)) (define (square y) (* y y))
(define (sqrt x) (define (good-enough? guess x) (< (abs (- (square guess) x)) 0.001)) (define (improve guess x) (average guess (/ x guess))) (define (sqrt-iter guess x) (if (good-enough? guess x) guess (sqrt-iter (improve guess x) x))) (sqrt-iter 1.0 x))
(define (sqrt x) (define (good-enough? guess) (< (abs (- (square guess) x)) 0.001)) (define (improve guess) (average guess (/ x guess))) (define (sqrt-iter guess) (if (good-enough? guess) guess (sqrt-iter (improve guess)))) (sqrt-iter 1.0))