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Expr-grade

Expr-gradep

Recognizer for expr-grade structures.

Signature
(expr-gradep x) → *

Definitions and Theorems

Function: expr-gradep

(defun expr-gradep (x)
  (declare (xargs :guard t))
  (let ((__function__ 'expr-gradep))
    (declare (ignorable __function__))
    (and (consp x)
         (cond ((or (atom x) (eq (car x) :top))
                (and (true-listp (cdr x))
                     (eql (len (cdr x)) 0)
                     (b* nil t)))
               ((eq (car x) :conditional)
                (and (true-listp (cdr x))
                     (eql (len (cdr x)) 0)
                     (b* nil t)))
               ((eq (car x) :disjunctive)
                (and (true-listp (cdr x))
                     (eql (len (cdr x)) 0)
                     (b* nil t)))
               ((eq (car x) :conjunctive)
                (and (true-listp (cdr x))
                     (eql (len (cdr x)) 0)
                     (b* nil t)))
               ((eq (car x) :equality)
                (and (true-listp (cdr x))
                     (eql (len (cdr x)) 0)
                     (b* nil t)))
               ((eq (car x) :ordering)
                (and (true-listp (cdr x))
                     (eql (len (cdr x)) 0)
                     (b* nil t)))
               ((eq (car x) :bitwise-xor)
                (and (true-listp (cdr x))
                     (eql (len (cdr x)) 0)
                     (b* nil t)))
               ((eq (car x) :bitwise-ior)
                (and (true-listp (cdr x))
                     (eql (len (cdr x)) 0)
                     (b* nil t)))
               ((eq (car x) :bitwise-and)
                (and (true-listp (cdr x))
                     (eql (len (cdr x)) 0)
                     (b* nil t)))
               ((eq (car x) :shift)
                (and (true-listp (cdr x))
                     (eql (len (cdr x)) 0)
                     (b* nil t)))
               ((eq (car x) :additive)
                (and (true-listp (cdr x))
                     (eql (len (cdr x)) 0)
                     (b* nil t)))
               ((eq (car x) :multiplicative)
                (and (true-listp (cdr x))
                     (eql (len (cdr x)) 0)
                     (b* nil t)))
               ((eq (car x) :exponential)
                (and (true-listp (cdr x))
                     (eql (len (cdr x)) 0)
                     (b* nil t)))
               ((eq (car x) :unary)
                (and (true-listp (cdr x))
                     (eql (len (cdr x)) 0)
                     (b* nil t)))
               ((eq (car x) :postfix)
                (and (true-listp (cdr x))
                     (eql (len (cdr x)) 0)
                     (b* nil t)))
               (t (and (eq (car x) :primary)
                       (and (true-listp (cdr x))
                            (eql (len (cdr x)) 0))
                       (b* nil t)))))))

Theorem: consp-when-expr-gradep

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