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Binary-op

Binary-opp

Recognizer for binary-op structures.

Signature
(binary-opp x) → *

Definitions and Theorems

Function: binary-opp

(defun binary-opp (x)
  (declare (xargs :guard t))
  (let ((__function__ 'binary-opp))
    (declare (ignorable __function__))
    (and (consp x)
         (cond ((or (atom x) (eq (car x) :eq))
                (and (true-listp (cdr x))
                     (eql (len (cdr x)) 0)
                     (b* nil t)))
               ((eq (car x) :ne)
                (and (true-listp (cdr x))
                     (eql (len (cdr x)) 0)
                     (b* nil t)))
               ((eq (car x) :gt)
                (and (true-listp (cdr x))
                     (eql (len (cdr x)) 0)
                     (b* nil t)))
               ((eq (car x) :ge)
                (and (true-listp (cdr x))
                     (eql (len (cdr x)) 0)
                     (b* nil t)))
               ((eq (car x) :lt)
                (and (true-listp (cdr x))
                     (eql (len (cdr x)) 0)
                     (b* nil t)))
               ((eq (car x) :le)
                (and (true-listp (cdr x))
                     (eql (len (cdr x)) 0)
                     (b* nil t)))
               ((eq (car x) :and)
                (and (true-listp (cdr x))
                     (eql (len (cdr x)) 0)
                     (b* nil t)))
               ((eq (car x) :or)
                (and (true-listp (cdr x))
                     (eql (len (cdr x)) 0)
                     (b* nil t)))
               ((eq (car x) :implies)
                (and (true-listp (cdr x))
                     (eql (len (cdr x)) 0)
                     (b* nil t)))
               ((eq (car x) :implied)
                (and (true-listp (cdr x))
                     (eql (len (cdr x)) 0)
                     (b* nil t)))
               ((eq (car x) :iff)
                (and (true-listp (cdr x))
                     (eql (len (cdr x)) 0)
                     (b* nil t)))
               ((eq (car x) :add)
                (and (true-listp (cdr x))
                     (eql (len (cdr x)) 0)
                     (b* nil t)))
               ((eq (car x) :sub)
                (and (true-listp (cdr x))
                     (eql (len (cdr x)) 0)
                     (b* nil t)))
               ((eq (car x) :mul)
                (and (true-listp (cdr x))
                     (eql (len (cdr x)) 0)
                     (b* nil t)))
               ((eq (car x) :div)
                (and (true-listp (cdr x))
                     (eql (len (cdr x)) 0)
                     (b* nil t)))
               (t (and (eq (car x) :rem)
                       (and (true-listp (cdr x))
                            (eql (len (cdr x)) 0))
                       (b* nil t)))))))

Theorem: consp-when-binary-opp

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