;;; ================================
;;;  CMPU-145, Spring 2013
;;;  Code from class
;;;  Feb. 11, 2013
;;; ================================

(load "asmt-helper.txt")

(header "Code from class" "Feb. 11, 2013")

;;;  REFLEXIVE?
;;;--------------------------
;;; INPUTS:  RELN, a list of lists representing a relation
;;;          LISTA, a list 
;;; OUTPUT:  #t (or something that counts as true) if RELN is reflexive over LISTA
;;;          #f otherwise.

(define reflexive?
  (lambda (reln lista)
    (cond
      ;; Base Case:
      ((null? lista)
       #t)
      ;; Recursive Case: 
      ((member (list (first lista) (first lista))
               reln)
       (reflexive? reln (rest lista)))
      ;; Base Case 2:  We found a counter-example
      (else
       (printf "Counter-example:  ~A~%" (list (first lista) (first lista)))
       #f))))

(tester '(reflexive? '((1 2) (1 1) (2 1) (2 2) (1 3) (3 1))
                     '(1 2 3)))

;;;  DOMAIN
;;; --------------------------
;;;  INPUT:  RELN
;;;  OUTPUT:  Domain of the RELN

(define domain
  (lambda (reln)
    (map first reln)))

;;; Still need to remove duplicates.

(tester '(domain '((1 2) (2 1) (2 3) (2 4) (1 3) (3 3)))