;; CS 3520
;; Fall 2000
;; HW 1 example solution

;; 1.1

(define (square x)
  (* x x))

(define (poly x)
  (+ (* 3 x x)
     (* 7 x)
     42))

(define (xor a b)
  (and (or a b)
       (not (and a b))))

(define (sign x)
 (cond
  [(> x 0) 1]
  [(< x 0) -1]
  [else 0]))

(define (sum-pair p)
  (+ (car p) (cdr p)))

(define (flip p)
  (cons (cdr p) (car p)))

(define (pair->list p)
  (list (car p) (cdr p)))

(define (sym-in-pair? s p)
  (or (eq? s (car p))
      (eq? s (cdr p))))

(define (two-elem-list? x)
  (and (pair? x)
       (pair? (cdr x))
       (null? (cddr x))))

(define (make-five-list)
  '(1 2 3 4 5))

(define (make-identity-list)
  (list 'lambda (list 'x) 'x))

;; 1.2

(define (answer-for-1.2)
  '(#t #f #t #t #t #t #f #f #t #t #f #t))

;; 1.3

(define (step n)
  (cond
   [(= n 0) '(((lambda (x) (lambda (y) (- x y))) 2) 1)]
   [(= n 1) '((lambda (y) (- 2 y)) 1)]
   [(= n 2) '(- 2 1)]
   [else 1]))