chapter20.rkt

;; Exercise 20.1.1
(define (f x) x)

(equal? (list f) (cons f empty))
(equal? f (f f))
(equal? (list f 10 10) (cons f (cons 10 (cons (f 10) empty))))

;; Exercise 20.1.2
(define (f x) (x 10))
(equal? (f add1) 11)

(define (f x) f)
(equal? f (f 100))

(define (f x y) (x 'a y 'b))
(equal? (f list 'c) '(a c b))

;; Exercise 20.1.3
;; Develop a-function=?. The function determines whether two functions from
;; numbers to numbers produce the same results for 1.2, 3, and -5.7.
(define (a-function=? f1 f2)
  (and (= (f1 1.2) (f2 1.2))
       (= (f1 3) (f2 3))
       (= (f1 -5.7) (f2 -5.7))))

(equal? (a-function=? identity identity) true)
(equal? (a-function=? sub1 identity) false)

;; Exercise 20.2.2
;; sort: (listof number) (number number -> boolean) -> (listof number)
;; map: (number -> number) (listof number) -> (listof number)
;; project: (listof (listof symbol)) (listof symbol -> symbol) -> (listof symbol)


;; Exercise 20.2.3
;; Use filter1 to develop a function that consumes a list of symbols and
;; extracts all those that are not equal to 'car.
(define (filter1 op lon t)
  (cond
    [(empty? lon) empty]
    [(op (first lon) t) (cons (first lon) (filter1 op (rest lon) t))]
    [else (filter1 op (rest lon) t)]))

(define (find-all-not-car symbols)
  (filter1 (lambda (sym1 sym2) (not (symbol=? sym1 sym2)))
           symbols
           'car))

(equal? (find-all-not-car '(hello world car you rock))
        '(hello world you rock))

;; Exercise 20.2.4
;; sort: (listof X) (X X -> boolean) -> (listof X)
;; map: (X -> X) (listof X) -> (listof X)
;; project: (listof (listof X)) (listof X -> X) -> (listof X)