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• Ubdd-constructors

Q-not

Negate a UBDD.

(q-not x) builds a new UBDD representing (not x). That is, the the following is a theorem:

(equal (eval-bdd (q-not x) values)
       (not (eval-bdd x values)))

Note: memoized for efficiency.

Definitions and Theorems

Function: q-not

(defun q-not (x)
       (declare (xargs :guard t))
       (if (atom x)
           (if x nil t)
           (hons (q-not (car x)) (q-not (cdr x)))))

Function: q-not-memoize-condition

(defun q-not-memoize-condition (x)
       (declare (ignorable x)
                (xargs :guard 't))
       (and (consp x)
            (or (consp (car x)) (consp (cdr x)))))

Theorem: consp-of-q-not

(defthm consp-of-q-not
        (equal (consp (q-not x)) (consp x)))

Theorem: equal-t-and-q-not

(defthm equal-t-and-q-not
        (equal (equal t (q-not x)) (not x)))

Theorem: equal-nil-and-q-not

(defthm equal-nil-and-q-not
        (equal (equal nil (q-not x))
               (and (atom x) (if x t nil))))

Theorem: q-not-under-iff

(defthm q-not-under-iff
        (iff (q-not x)
             (if (consp x) t (if x nil t))))

Theorem: ubddp-of-q-not

(defthm ubddp-of-q-not
        (implies (force (ubddp x))
                 (equal (ubddp (q-not x)) t)))

Theorem: eval-bdd-of-q-not

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

Theorem: canonicalize-q-not

(defthm canonicalize-q-not
        (implies (force (ubddp x))
                 (equal (q-not x) (q-ite x nil t)))
        :rule-classes :definition)