《函数程序设计算法》读书笔记。

简单值

#t
#t
#f
#f
#\M
#\M
#\newline
#\newline
#\nul
#\nul
"sample"
"sample"
"\"Hi\""
"\"Hi\""
"\\A\\"
"\\A\\"
'midnight-blue
'midnight-blue
(quote midnight-blue)
'midnight-blue

算术函数

(+)
0
(+ 1 2 3 4 5)
15
(- 1)
-1
(- 2 1)
1
(- 1 2 3)
-4
(*)
1
(* 2 3 4)
24
3/1
3
(/ 3 1)
3
(/ 3 2)
3/2
(= 3/1 (/ 3 1))
#t
(/ 5)
1/5
(expt 3 4)
81
(expt 3 0)
1
(expt 0 0)
1

Lambda 表达式

(lambda (x y) 
  (/ (+ x y) 2))
<procedure>
((lambda (x y) 
  (/ (+ x y) 2)) 3/5 11/3)
32/15

变元过程

(lambda nums
  (/ (apply + nums) (apply * nums)))
<procedure>
((lambda nums
  (/ (apply + nums) (apply * nums))) 3 5 8 2 6)
1/60
(lambda nums
  (apply + 23 14 6 nums))
<procedure>
((lambda (x y z . others)
  (* (+ x y z) (apply + others))) 1 2 3 3 4 5)
72

构造列表

(list 3 8 7)
'(3 8 7)
(list)
'()

返回多个值

values
<procedure:values>
(lambda nums
  (values (apply + nums) (apply * nums)))
<procedure>
((lambda nums
  (values (apply + nums) (apply * nums))) 1 2 3 4 5)
15
120
(define delist (lambda (ls)
  (apply values ls)))
(delist (list 1 2 3 4 5))
1
2
3
4
5

谓词

(even? 2)
#t
(even? 3)
#f
(< 3 4)
#t
(< 4 3)
#f
(values <= = > >=)
<procedure:<=>
<procedure:=>
<procedure:>>
<procedure:>=>
(boolean? #f)
#t
(boolean? 0)
#f
(number? 0)
#t
(integer? 1)
#t
(integer? 1/2)
#f
(char? #\newline)
#t
(char? 'newline)
#f
(symbol? 'newline)
#t
(symbol? "newline")
#f
(string? "newline")
#t
(procedure? +)
#t
(procedure? (lambda (x) (+ x 1)))
#t
(equal? #t #t)
#t
(equal? + +)
#t
(equal? 3/1 3)
#t
(equal? (lambda (x) x) (lambda (x) x))
#f
(values zero? positive? negative? even? odd?)
<procedure:zero?>
<procedure:positive?>
<procedure:negative?>
<procedure:even?>
<procedure:odd?>

条件类型表达式

(if (= (+ 1 1) 2) 'eq 'neq)
'eq
(if (= (+ 1 1) 3) 'eq 'neq)
'neq
(and #t #t)
#t
(and #t #f)
#f
(and #f #f)
#f
(or #t #t)
#t
(or #t #f)
#t
(or #f #f)
#f
(and (= (+ 1 1) 2) 'eq)
'eq
(and (= (+ 1 1) 3) 'eq)
#f
(or (= (+ 1 1) 2) 'eq)
#t
(or (= (+ 1 1) 3) 'neq)
'neq

定义

(define meg 1048576)
(define inches-in-a-mile (* 12 5280))
meg
1048576
inches-in-a-mile
63360
(define (arithmetic-mean x y)
  (/ (+ x y) 2))
(arithmetic-mean 3 4)
7/2
(define lesser (lambda (l r)
                 (if (< l r) l r)))
(lesser 3 4)
3
(lesser 4 3)
3
(lesser 3 4)
3
(define (multi-arg . args) args)
(multi-arg 1 2 3)
'(1 2 3)
(define (multi-arg2 x y . args) (values (+ x y) args))
(multi-arg2 3 4 5 6)
7
'(5 6)
(define (factorial n)
  (if (= n 0)
      1
      (* n (factorial (- n 1)))))
(factorial 5)
120

局部绑定

(let ((hours-in-a-day 24)
      (seconds-in-an-hour (* 60 60)))
  (* hours-in-a-day seconds-in-an-hour))
86400
(let ((double (lambda (x) (* x 2))))
  (* (double 7) (double 12)))
336