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• Ubdds

Ubddp

Recognizer for well-formed ubdds.

Note: memoized for efficiency.

Definitions and Theorems

Function: ubddp

(defun ubddp (x)
  (declare (xargs :guard t))
  (mbe :logic
       (if (atom x)
           (booleanp x)
         (and (ubddp (car x))
              (ubddp (cdr x))
              (if (atom (car x))
                  (not (equal (car x) (cdr x)))
                t)))
       :exec (cond ((eq x t) t)
                   ((eq x nil) t)
                   ((atom x) nil)
                   (t (let ((a (car x)) (d (cdr x)))
                        (cond ((eq a t)
                               (cond ((eq d nil) t)
                                     ((eq d t) nil)
                                     (t (ubddp d))))
                              ((eq a nil)
                               (cond ((eq d nil) nil)
                                     ((eq d t) t)
                                     (t (ubddp d))))
                              (t (and (ubddp a) (ubddp d)))))))))

Function: ubddp-memoize-condition

(defun ubddp-memoize-condition (x)
  (declare (ignorable x)
           (xargs :guard 't))
  (consp x))

Theorem: ubddp-compound-recognizer

(defthm ubddp-compound-recognizer
  (implies (ubddp x)
           (or (consp x) (booleanp x)))
  :rule-classes :compound-recognizer)