#lang racket
(require "set-adt.rkt")

; The motivation for my new SECOND function comes from:
; https://blog.plover.com/math/wiener-pairs-3.html
;
; set, set-union-all, and set-intersect-all are variable arity functions.
; set-minus is binary.

(define MAKE-PAIR
  (lambda (a b)
    (set (set a) (set a b))))

(define FIRST
  (lambda (aSet)
    (set-one-elem (apply set-intersect-all aSet))))

(define SECOND
  (lambda (aSet)
    (let ((union-minus-intersection
            (set-minus (apply set-union-all aSet)
                       (apply set-intersect-all aSet))))
      (if (not (set-empty? union-minus-intersection))
          (set-one-elem union-minus-intersection)
          (set-one-elem (apply set-intersect-all aSet))))))  ; FIRST

; ----------------------------------------------------------------
; Using pairs, regardless of implementation.
; ----------------------------------------------------------------

(require rackunit)
(define pair1 (MAKE-PAIR 2 3))
(define pair2 (MAKE-PAIR 1 pair1))

(check-equal? (FIRST  pair2)          1)
(check-equal? (FIRST (SECOND pair2))  2)
(check-equal? (SECOND (SECOND pair2)) 3)

; ----------------------------------------------------------------
; The hard case for sets: when (eq? (FIRST p) (SECOND p)) 
; ----------------------------------------------------------------

(define pair3 (MAKE-PAIR 'a 'a))
(check-equal? (FIRST  pair3) 'a)
(check-equal? (SECOND pair3) 'a)

; ----------------------------------------------------------------