PLAI No. 1

1. Define the function "area-square'', which consumes an integer number denoting the length of two sides and produces the area of the square.

;;Q1             
;;area-square:  number -> number 【Contract】
;;to compute the area of a square 【Purpose】
(define (area-square a)
  (* a a))
;;【Test】
(test (area-square 2) 4)

2. Define the function ''volume-cuboid'', which consumes three integer numbers denoting lengths of three sides and produces the volume of the cuboid.

;;Q2
;;volumn-cuboid:  number number number -> number 【Contract】
;;given the length of the three sides to compute the volumn of a cuboid 【Purpose】
(define (volume-cuboid a b c)
  (* a b c))
;;【Test】
(test (volume-cuboid 1 2 3) 6)

3. Define the function ''is-multiple-of?'', which consumes two integer numbers and returns whether the first number is a multiple of the second one.

;;Q3
;;is-multiple-of?:  number number -> boolean 【Contract】
;;consumes two integer numbers and returns whether the first number is a multiple of the second one 【Purpose】
(define (is-multiple-of? x y)
  (= (/ x y) 2))
;;【Test】
(test (is-multiple-of? 8 4) true)
(test (is-multiple-of? 8 5) false)

4. Define the function ''factorial'', which consumes an integer number and returns the result of the factorial operation.

;;Q4
;;factorial:  number -> number 【Contract】
;;which consumes an integer number and returns the result of the factorial operation【Purpose】
(define (factorial n)
  (if (= n 1)
      1
      (* n (factorial (- n 1)))))
;;【Test】
(test (factorial 4) 24)
(test (factorial 5) 120)

5. Define the function ''fibonacci'', which consumes an integer number ''n'' and returns the ''n''-th fibonacci number. The 3rd fibonacci number is 2.

;;Q5 
;;fibonacci： number -> number 【Contract】
;; consumes an integer number ''n'' and returns the ''n''-th fibonacci number 【Purpose】
(define (fibonacci n)
  (cond
    [ (= n 1) 1]
    [ (= n 2) 1]
    [else (+
           (fibonacci (- n 1))
           (fibonacci (- n 2)))]))
;;【Test】
(test (fibonacci 2) 1)
(test (fibonacci 3) 2)
(test (fibonacci 4) 3)

6. Define the type ''COURSE'', which is either ''CS320'', ''CS311'', or ''CS330''. ''CS320'' has two attributes: ''quiz'' for the number of quizzes and''homework'' for the number of programming assignments. ''CS311'' has one attribute: ''homework'' which is the number too. ''CS330'' has two attributes: ''projects'' for the number of projects and ''homework''.

;;Q6       
;;define the type "COURSE" 【Purpose】
(define-type COURSE
  [CS320 (homework integer?)
         (quiz integer?)]
  [CS311 (homework integer?)]
  [CS330 (homework integer?)
         (project integer?)])
(define CS320_Course (CS320 5 6))
(define CS311_Course (CS311 6))
(define CS330_Course (CS330 6 7))
;;【test】
(test (CS320? CS320_Course) true)
(test (CS311? CS311_Course) true)
(test (CS330? CS330_Course) true)

7. Define the function ''total-assignments'', which consumes a single course and produces the total number of quizzes, homework, and projects for the given course.

;;Q7        
;;total-assignments：  COURSE -> number 【Contract】
;;consumes a single course and produces thetotal number of quizzes, homework, and projects for the given course【Purpose】

(define (total-assignments to-num)
  (type-case COURSE to-num
    [CS320 (l r) (+ l r)]
    [CS311 (l) l]
    [CS330 (l r) (+ l r)]))
;;【test】
(test (total-assignments CS320_Course) 11)
(test (total-assignments CS311_Course) 6)
(test (total-assignments CS330_Course) 13)

8. Define the function ''total-homework'', which consumes a list of courses and produces the total number of homework of the courses in the given list.

;;Q8         
;;total-homework：  a list of course -> number 【Contract】
;;consumes a list of courses and produces the total number of homework of the courses in the given list【Purpose】
(define (total-homework g)
  (type-case COURSE g
    [CS320 (l r) l]
    [CS311 (r) r]
    [CS330 (l r) l]))

(define HomeWorkTotal_1 (+ (total-homework CS320_Course) (total-homework CS311_Course) (total-homework CS330_Course)))

(define HomeWorkTotal_2 (+ (CS320-homework CS320_Course) (CS311-homework CS311_Course) (CS330-homework CS330_Course)))

(define (is? HomeWorkTotal_1 HomeWorkTotal_2)
  (= HomeWorkTotal_1 HomeWorkTotal_2))
;;【test】
(test (is? HomeWorkTotal_1 HomeWorkTotal_2) true)

(cons 'COURSE-1 (cons CS320_Course (cons CS311_Course(cons  CS330_Course (cons HomeWorkTotal_1 empty)))))

9. Define the function ''my-map'', which consumes a function ''f'' and a list of numbers ''l'', and produces a list of numbers generated by applying the input function ''f'' to each element of ''l''. Do not use the ''map'' function provided by DrRacket. For example,

(my-map (lambda (x) (+ 1 x))

(cons 1 (cons 2 (cons 3 empty)))))

produces '(2 3 4)

;;Q9       
;;my-map：  function list -> list【Contract】
;;consumes a function ''f'' and a list of numbers ''l'', and  produces a list of numbers generated by applying the input function ''f'' to each element of ''l''【Purpose】
(define (my-map f l)
  (if (null? l)
      '()
      (cons (f (car l)) (my-map f (cdr l)))))
;;【test】
(my-map (lambda (x) (+ 1 x))
        (cons 1 (cons 2(cons 3 empty))))