; true if predicates p1 and p2 agree on args; false otherwise
(defun predicates-agree (p1 p2 args)
  (let ((p1-result (apply p1 args))
        (p2-result (apply p2 args)))
    (not (or (and p1-result (not p2-result))
             (and p2-result (not p1-result))))))


;; 1.a
(princ "1.a") (terpri)

(defun model-member? (element set) (member element set :test #'equal))

(loop for args in '((a (a b c))
                    (b (a b c))
                    (c (a b c))
                    (d (a b c))
                    (a ())
                    ((a b) ((a b) (b c)))
                    ((a b) ((a d) (a d e) (a b d e) (a b)))
                    (a ((a d) (a d e) (a b d e) (a b))))
      do (when (not (predicates-agree #'member? #'model-member? args))
           (princ "member? incorrect when applied to ") (princ args) (terpri)))


;; 1.b
(princ "1.b") (terpri)

(when (not (= 0 (length (union-of () () ))))
  (princ "failed p1.b test 1") (terpri))
(when (not (= 3 (length (union-of '(a b c) ()))))
  (princ "failed p1.b test 2") (terpri))
(when (not (= 3 (length (union-of () '(a b c)))))
  (princ "failed p1.b test 3") (terpri))
(when (not (= 4 (length (union-of '(a b) '(c d)))))
  (princ "failed p1.b test 4") (terpri))
(when (not (= 3 (length (union-of '(a b c) '(a b c)))))
  (princ "failed p1.b test 5") (terpri))
(when (not (= 3 (length (union-of '(a b c) '(c b a)))))
  (princ "failed p1.b test 6") (terpri))
(when (not (= 3 (length (union-of '(a b) '(b c)))))
  (princ "failed p1.b test 7") (terpri))
(when (not (= 4 (length (union-of
                          '((a d) (a d e) (a b d e))
                          '((a d e) (a b d e) (a b))))))
  (princ "failed p1.b test 8") (terpri))


;; 2
(princ "2") (terpri)

(when (not (equal '() (add-mag-to-each '())))
  (princ "failed p2 test 1") (terpri))
(when (not (equal '(2) (add-mag-to-each '(1))))
  (princ "failed p2 test 2") (terpri))
(when (not (equal '(4 5) (add-mag-to-each '(1 2))))
  (princ "failed p2 test 3") (terpri))
(when (not (equal '(7 8 9) (add-mag-to-each '(1 2 3))))
  (princ "failed p2 test 4") (terpri))
(when (not (equal '(11 12 13 14) (add-mag-to-each '(1 2 3 4))))
  (princ "failed p2 test 5") (terpri))


;; 3.a
(princ "3.a") (terpri)

(defun model-f (n m)
  (cond
    ((< m 2) t)
    ((= 0 (mod n m)) nil)
    (t (model-f n (- m 1)))))

(loop for i from 2 to 10
      do (loop for j from 1 to 10
               do (when (not (predicates-agree #'f #'model-f (list i j)))
                    (princ "f incorrect when applied to ")
                    (princ (list i j)) (terpri))))


;; 3.b
(princ "3.b") (terpri)

(defun model-prime (n)
  (model-f n (- n 1)))

(loop for i from 2 to 100
      do (when (not (predicates-agree #'prime #'model-prime (list i)))
           (princ "prime incorrect when applied to ")
           (princ (list i)) (terpri)))