Practicing with sets in Advanced Student Language

This is the version I did some time ago using the Advanced Student Language of the sets exercise from the Coursera Scala course:

	;; The first three lines of this file were inserted by DrRacket. They record metadata
	;; about the language level of this file in a form that our tools can easily process.
	#reader(lib "htdp-advanced-reader.ss" "lang")((modname sets) (read-case-sensitive #t) (teachpacks ()) (htdp-settings #(#t constructor repeating-decimal #t #t none #f ())))
	;; Number -> (Number => Boolean)
	;; Contains set an elem
	(define (contains set elem)
	(set elem))
	(check-expect
	(contains (lambda (x) (= 2 x)) 2)
	true)
	(check-expect
	(contains (lambda (x) (= 2 x)) 3)
	false)
	;; Number -> (Number => Boolean)
	;; Singleton set
	(define (singletonSet elem)
	(lambda (x)
	(= elem x)))
	(check-expect
	(contains (singletonSet 4) 4)
	true)
	(check-expect
	(contains (singletonSet 3) 4)
	false)
	;; (Number => Boolean), (Number => Boolean) -> (Number => Boolean)
	;; Union of sets
	(define (union set1 set2)
	(lambda (x)
	(or (set1 x)
	(set2 x))))
	(define set-created-using-union
	(union
	(lambda (x)
	(= (remainder x 2) 0))
	(lambda (x) (> x 2))))
	(check-expect
	(contains set-created-using-union 6)
	true)
	(check-expect
	(contains set-created-using-union 1)
	false)
	(check-expect
	(contains set-created-using-union 7)
	true)
	;; (Number => Boolean), (Number => Boolean) -> (Number => Boolean)
	;; Intersection of sets
	(define (intersection set1 set2)
	(lambda (x)
	(and (set1 x)
	(set2 x))))
	(define set-created-using-intersection
	(intersection
	(lambda (x) (< x 4))
	(lambda (x) (> x 2))))
	(check-expect
	(contains
	set-created-using-intersection 3)
	true)
	(check-expect
	(contains
	set-created-using-intersection 2)
	false)
	;; (Number => Boolean), (Number => Boolean) -> (Number => Boolean)
	;; Difference of sets
	(define (diff set1 set2)
	(lambda (x)
	(and (set1 x)
	(not (set2 x)))))
	(define set-created-using-diff
	(diff (lambda (x) (< x 4))
	(lambda (x) (> x 2))))
	(check-expect
	(contains set-created-using-diff 2)
	true)
	(check-expect
	(contains set-created-using-diff 3)
	false)
	;; (Number => Boolean), (Number => Boolean) -> Boolean
	;; Check if a predicate is true for all members of an interval which is inside [-1000, 1000]
	(define (forall? set pred)
	(iter (- BOUND) set pred))
	(define BOUND 1000)
	(define (iter a set pred)
	(cond ((> a BOUND)
	true)
	(((diff set pred) a)
	false)
	(else
	(iter (+ a 1) set pred))))
	(check-expect
	(forall? (lambda (x) (< -2 x 2))
	(lambda (x) (< x 3)))
	true)
	(check-expect
	(forall? (lambda (x) (< -2 x 2))
	(lambda (x) (= (remainder x 2) 0)))
	false)
	;; (Number => Boolean), (Number => Boolean) -> Boolean
	;; Check if a predicate is true for any member of an interval which is inside [-1000, 1000]
	(define (exists? set pred)
	(not (forall? set (diff set pred))))
	(check-expect
	(exists? (lambda (x) (< -2 x 2))
	(lambda (x) (= (remainder x 2) 0)))
	true)
	(check-expect
	(exists? (lambda (x) (< -2 x 2))
	(lambda (x) (> x 4)))
	false)
	;; (Number => Boolean), (Number => Number) -> (Number => Boolean)
	;; Maps using a given function a set in an interval which is inside [-1000, 1000]
	(define (mapset set func)
	(lambda (y) (exists? set (lambda (x) (= (func x) y)))))
	(define set-defined-using-mapset
	(mapset (lambda (x) (< -3 x 3))
	(lambda (x) (* x x))))
	(check-expect
	(contains set-defined-using-mapset 4)
	true)
	(check-expect
	(contains set-defined-using-mapset 1)
	true)
	(check-expect
	(contains set-defined-using-mapset -2)
	false)
	(check-expect
	(contains set-defined-using-mapset -1)
	false)
	(define other-set-defined-using-mapset
	(mapset (lambda (x) (< -3 x 3))
	(lambda (x) (- x x))))
	(check-expect
	(contains other-set-defined-using-mapset -2)
	false)
	(check-expect
	(contains other-set-defined-using-mapset -1)
	false)
	(check-expect
	(contains other-set-defined-using-mapset 0)
	true)
	(check-expect
	(contains other-set-defined-using-mapset 1)
	false)
	(check-expect
	(contains other-set-defined-using-mapset 2)
	false)

view raw sets.rkt hosted with ❤ by GitHub

It helped me to practice with lambdas and to blur the border between data and functions.