SICP学习笔记第二章（2.2）（下）

设计原则：约定的界面（conventional interfaces）。

范例：“流结构”化的 sum-odd-squares 和 even-fibs

 1 (define (filter predicate sequence)
 2     (cond ((null? sequence) '())
 3           ((predicate (car sequence))
 4           (cons (car sequence)
 5                 (filter predicate (cdr sequence))))
 6           (else (filter predicate (cdr sequence)))))
 7 
 8 (define (accumulate op initial sequence)
 9     (if (null? sequence)
10         initial
11         (op (car sequence)
12             (accumulate op initial (cdr sequence)))))
13 
14 (define (enumerate-interval low high)
15     (if (> low high)
16         '()
17         (cons low (enumerate-interval (+ low 1) high))))
18 
19 (define (enumerate-tree tree)
20     (cond ((null? tree) '())
21           ((not (pair? tree)) (list tree))
22           (else (append (enumerate-tree (car tree))
23                         (enumerate-tree (cdr tree))))))
24 
25 (define (sum-odd-squares tree)
26     (accumulate +
27                 0
28                 (map square
29                      (filter odd?
30                              (enumerate-tree tree)))))
31 (define (even-fibs n)
32     (accumulate cons 
33                 '()
34                 (filter even?
35                         (map fib
36                         (enumerate-interval 0 n)))))

在描述一种语言时，应该将注意力集中到语言的基本原语，它的组合手段以及它的抽象手段，这是最重要的。

（We emphasized the importance of describing a language by focusing on the language's primitives, its means of combination, and its means of abstraction.）

部分习题：

exercise 2.33

 1 (define (map p sequence)
 2     (accumulate (lambda (x y)
 3                   (cons (p x)
 4                         y))
 5                 '()
 6                 sequence))
 7 
 8 (define (append seq1 seq2)
 9     (accumulate cons seq2 seq1))
10 
11 (define (length sequence)
12     (accumulate (lambda (x y)
13                   (+ 1 y))
14                 0
15                 sequence))

exercise 2.34

1 (define (horner-eval x coefficient-sequence)
2     (accumulate (lambda (this-coeff higher-terms)
3                   (+ this-coeff
4                      (* x higher-terms)))
5                 0
6                 coefficient-sequence))

exercise 2.35

 1 (define (map-tree p sequence)
 2     (map (lambda (sub-seq)
 3            (if (pair? sub-seq)
 4                (map-tree p sub-seq)
 5                (p sub-seq)))
 6          sequence))
 7 
 8 (define (count-leaves tree)
 9     (accumulate (lambda (x y)
10                   (if (pair? x)
11                       (+ (count-leaves x) y)
12                       (+ x y)))
13                 0
14                 (map-tree (lambda (x) 1) tree)))

exercise 2.36

1 (define (accumulate-n op init seqs)
2     (if (null? (car seqs))
3         '()
4         (cons (accumulate op init (map car seqs))
5               (accumulate-n op init (map cdr seqs)))))

exercise 2.38

exercise 2.39

 1 (define (reverse-right sequence)
 2     (fold-right (lambda (x y)
 3                    (append y (list x)))
 4                 '()
 5                 sequence))
 6 
 7 (define (reverse-left sequence)
 8     (fold-left (lambda (x y)
 9                   (cons y x))
10                '()
11                sequence))

exercise 2.40

1 (define (unique-pairs n)
2     (flatmap (lambda (i)
3                (map (lambda (j) (list i j))
4                     (enumerate-interval 1 (- i 1))))
5              (enumerate-interval 1 n)))

exercise 2.41

 1 (define (tri-pairs n)
 2     (let ((range (enumerate-interval 1 n)))
 3       (flatmap (lambda (i)
 4                  (flatmap (lambda (j)
 5                             (map (lambda (k) (list i j k))
 6                                  range))
 7                           range))
 8                range)))
 9 (define (tri-sum-s s n)
10     (filter (lambda (x)
11               (= (accumulate + 0 x) s))
12             (tri-pairs n)))

SICP学习笔记 第二章 （2.2）（下）

SICP学习笔记第二章（2.2）（下）