Scheme

Racket
http://racket-lang.org/

#lang racket
(provide (all-defined-out))

(define x 3)
(define y (+ x 2))

(define cube1
    (lambda (x)
      (* x ( * x x))))

(define cube2
    (lambda (x)
      (* x x )))

(define (cube3 x)
  (* x x x))

> (+ 2 3)
5
> (+ (* 3(+ (* 2 4)(+ 3 5)))(+(- 10 7) 6))
57
======================================================================================
> (define size 2)
> size
2
> (* size size)
4
======================================================================================
> (define (square x)(* x x))                                           #最直接的子函数
> (square 10)
100
> (define (sum-squares x y)(+ (square x) (square y)))                  #嵌套过一层
> (sum-squares 9 1)
82
> (define (f a) (sum-squares (+ a 1) (* a 2)))           #嵌套两层，f的参数a +1和*2之
> (f 5)                                                  后传给sum-squares函数再继续传
136
======================================================================================
> (define (abs x)
    (cond ((< x 0) (- x))
          (else x)))
> (abs -10)
10
> (define (abs2 x)
    (if(< x 0)(- x)
     x))
> (abs2 -10)
10

> (define (>= x y)                                        #定义了一个新的谓语‘>=’
    (or (> x y)(= x y)))                                   就是（x>y）or (x==y)
> (>= 10 10)
#t
> (>= 9 10)
#f
======================================================================================
> (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)))
    (define (average x y)(/ (+ x y) 2))
    (sqrt-iter 1.0 x))
> (sqrt 100)
10.000000000139897
======================================================================================
(define (gcd a b)
    (if (= b 0) a 
        (gcd b (remainder a b))))
======================================================================================
> (define (factorial n)
    (if (= n 1) 
        1
        (* n (factorial (- n 1)))))
> (factorial 6)
720
> (define (factorial2 n)
    (define (re pro acc n)
      (if (> acc n) 
          pro
          (re (* pro acc) (+ 1 acc) n)))
    (re 1 1 n)
    )
> (factorial2 6)
720
======================================================================================
>(define (fib n)
  (define (f a b acc n)
    (if (= acc n) 
        b
        (f (+ a b) a (+ acc 1) n)))
  (f 0 1 0 n))
>(fib 5)
3
======================================================================================
(define (T m n)
  (cond((= m 0) 1)
       ((or(< m 0)(= n 0)) 0)
       (else (+ (T m (- n 1)) (T (- m (first-coin n))n)))))
  (define (first-coin kindsofn)
  (cond ((= kindsofn 1) 1)
        ((= kindsofn 2) 5)
        ((= kindsofn 3) 10)
        ((= kindsofn 4) 25)
        ((= kindsofn 5) 50)))
########################## T(m,n)=T(m,n-1)+T(m-a,n) ##################################
########################## T(0,n)=1,T(m<0,n)=T(m,0)=0 ################################
======================================================================================
(define (prime? n)
  (define (smallest-divisor n) (find-divisor n 2))
  (define (find-divisor n test-divisor)
    (cond ((> (* test-divisor test-divisor) n)n)
          ((divides? test-divisor n) test-divisor)
          (else (find-divisor n (+ test-divisor 1)))))
  (define (divides? a b)
    (= (remainder b a)0))
  (if (= (smallest-divisor n) n)(display "yes")(display"no")))
###################################### 简单素性检测 ##################################
======================================================================================
(define (add-rat x y)
  (make-rat (+(*(numer x)(denom y))
              (*(denom x)(numer y)))
            (* (denom x)(denom y))))
(define (sub-rat x y)
  (make-rat (-(*(numer x)(denom y))
              (*(denom x)(numer y)))
            (* (denom x)(denom y))))
(define (mul-rat x y)
  (make-rat (*(numer x)(numer y))
            (*(denom y)(denom x))))
(define (div-rat x y)
  (make-rat (*(numer x)(denom y))
            (*(denom x)(numer y))))
(define (equal-rat? x y)
  (= (*(numer x)(denom y))(*(denom x)(numer y))))
(define (make-rat n d)(cons n d))
(define (numer x)(car x))
(define (denom x)(cdr x))
(define (print-rat x)
    (newline)
    (display (numer x))
    (display "/")
    (display (denom x)))
======================================================================================
(define a (list 1 2 3 4))    //定义a是一个列表
(car a)
》1
(cdr a)
》'(2 3 4)
(cons 6 a)                   //a并没有改变
（define b （cons 5 a））    //b=（5，1，2，3，4），a=（1，2，3，4）
======================================================================================
(define a (list 1 2 3 4 5 6 7))
(define (list-ref list n)                 //取元素函数，如果要取list中的第k位，n取
  (if (= n 0) (car list)                  //（k-1）
      (list-ref (cdr list) (- n 1))))
(define (length list)                     //求长度函数
  (if (null? list)
      0
      (+ 1 (length (cdr list)))))
(define (len list)                        //求长度函数（迭代版本）
  (define (f list n)
    (if (null? list)
        n
        (f (cdr list) (+ n 1))))
  (f list 0)
  )
(define (append a b)                      //把b贴到a后面，实际上，a和b都没变
  (if (null? a)
      b
      (cons (car a)(append (cdr a) b))))
(define (last-pair list)                  //返回最后一个元素
  (if (null? (cdr list))
      (car list)
      (last-pair (cdr list))))
(define (count-leaves x)
  (cond ((null? x)0)
        ((not (pair? x))1)
        (else (+ (count-leaves (car x))(count-leaves (cdr x))))))
(define (reverse list)
  (define (f nu li)
    (if (null? li)
        nu
        (f (cons (car li) nu) (cdr li))))
    (f null list))
======================================================================================
(define (map pro list)
  (if (null? list)
      null
      (cons (pro (car list))
            (map pro (cdr list)))))
======================================================================================
(lambda (x y) (+ x y))
//just think as an op or a function without name