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Bexp

Bexpp

Recognizer for bexp structures.

Signature
(bexpp x) → *

Definitions and Theorems

Function: bexpp

(defun bexpp (x)
  (declare (xargs :guard t))
  (let ((__function__ 'bexpp))
    (declare (ignorable __function__))
    (and (consp x)
         (cond ((or (atom x) (eq (car x) :const))
                (and (true-listp (cdr x))
                     (eql (len (cdr x)) 1)
                     (b* ((value (std::da-nth 0 (cdr x))))
                       (booleanp value))))
               ((eq (car x) :equal)
                (and (true-listp (cdr x))
                     (eql (len (cdr x)) 2)
                     (b* ((left (std::da-nth 0 (cdr x)))
                          (right (std::da-nth 1 (cdr x))))
                       (and (aexpp left) (aexpp right)))))
               ((eq (car x) :less)
                (and (true-listp (cdr x))
                     (eql (len (cdr x)) 2)
                     (b* ((left (std::da-nth 0 (cdr x)))
                          (right (std::da-nth 1 (cdr x))))
                       (and (aexpp left) (aexpp right)))))
               ((eq (car x) :not)
                (and (true-listp (cdr x))
                     (eql (len (cdr x)) 1)
                     (b* ((arg (std::da-nth 0 (cdr x))))
                       (bexpp arg))))
               (t (and (eq (car x) :and)
                       (and (true-listp (cdr x))
                            (eql (len (cdr x)) 2))
                       (b* ((left (std::da-nth 0 (cdr x)))
                            (right (std::da-nth 1 (cdr x))))
                         (and (bexpp left) (bexpp right)))))))))

Theorem: consp-when-bexpp

(defthm consp-when-bexpp
  (implies (bexpp x) (consp x))
  :rule-classes :compound-recognizer)