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• Ubdd-constructors

Q-xor

(q-xor a b &rest args) constructs a UBDD representing the exclusive OR of its arguments.

Definitions and Theorems

Function: q-binary-xor

(defun q-binary-xor (x y)
       (declare (xargs :guard t))
       (cond ((atom x) (if x (q-not y) y))
             ((atom y) (if y (q-not x) x))
             ((hons-equal x y) nil)
             (t (qcons (q-binary-xor (car x) (car y))
                       (q-binary-xor (cdr x) (cdr y))))))

Function: q-binary-xor-memoize-condition

(defun q-binary-xor-memoize-condition (x y)
       (declare (ignorable x y)
                (xargs :guard 't))
       (and (consp x) (consp y)))

Function: q-xor-macro-fn

(defun
 q-xor-macro-fn (args)
 (declare (xargs :guard (consp args)))
 (if (atom (cdr args))
     (car args)
     (cons 'prog2$
           (cons '(last-chance-wash-memory)
                 (cons (cons 'q-binary-xor
                             (cons (car args)
                                   (cons (q-xor-macro-fn (cdr args))
                                         'nil)))
                       'nil)))))

Theorem: ubddp-of-q-xor

(defthm ubddp-of-q-xor
        (implies (and (force (ubddp x))
                      (force (ubddp y)))
                 (equal (ubddp (q-xor x y)) t)))

Theorem: eval-bdd-of-q-xor

(defthm eval-bdd-of-q-xor
        (equal (eval-bdd (q-xor x y) values)
               (if (eval-bdd x values)
                   (not (eval-bdd y values))
                   (eval-bdd y values))))

Theorem: q-xor-of-self

(defthm q-xor-of-self (equal (q-xor x x) nil))

Theorem: canonicalize-q-xor

(defthm canonicalize-q-xor
        (implies (and (force (ubddp x))
                      (force (ubddp y)))
                 (equal (q-xor x y)
                        (q-ite x (q-not y) y))))