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Expression

Expressionp

Recognizer for expression structures.

Signature
(expressionp x) → *

Definitions and Theorems

Function: expressionp

(defun expressionp (x)
  (declare (xargs :guard t))
  (let ((__function__ 'expressionp))
    (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))))
                       (integerp value))))
               ((eq (car x) :var)
                (and (true-listp (cdr x))
                     (eql (len (cdr x)) 1)
                     (b* ((name (std::da-nth 0 (cdr x))))
                       (stringp name))))
               ((eq (car x) :add)
                (and (true-listp (cdr x))
                     (eql (len (cdr x)) 2)
                     (b* ((arg1 (std::da-nth 0 (cdr x)))
                          (arg2 (std::da-nth 1 (cdr x))))
                       (and (expressionp arg1)
                            (expressionp arg2)))))
               (t (and (eq (car x) :mul)
                       (and (true-listp (cdr x))
                            (eql (len (cdr x)) 2))
                       (b* ((arg1 (std::da-nth 0 (cdr x)))
                            (arg2 (std::da-nth 1 (cdr x))))
                         (and (expressionp arg1)
                              (expressionp arg2)))))))))

Theorem: consp-when-expressionp

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