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Atj-atype

Atj-atypep

Recognizer for atj-atype structures.

Signature
(atj-atypep x) → *

Definitions and Theorems

Function: atj-atypep

(defun atj-atypep (x)
  (declare (xargs :guard t))
  (let ((__function__ 'atj-atypep))
    (declare (ignorable __function__))
    (and (consp x)
         (cond ((or (atom x) (eq (car x) :integer))
                (and (true-listp (cdr x))
                     (eql (len (cdr x)) 0)
                     (b* nil t)))
               ((eq (car x) :rational)
                (and (true-listp (cdr x))
                     (eql (len (cdr x)) 0)
                     (b* nil t)))
               ((eq (car x) :number)
                (and (true-listp (cdr x))
                     (eql (len (cdr x)) 0)
                     (b* nil t)))
               ((eq (car x) :character)
                (and (true-listp (cdr x))
                     (eql (len (cdr x)) 0)
                     (b* nil t)))
               ((eq (car x) :string)
                (and (true-listp (cdr x))
                     (eql (len (cdr x)) 0)
                     (b* nil t)))
               ((eq (car x) :symbol)
                (and (true-listp (cdr x))
                     (eql (len (cdr x)) 0)
                     (b* nil t)))
               ((eq (car x) :boolean)
                (and (true-listp (cdr x))
                     (eql (len (cdr x)) 0)
                     (b* nil t)))
               ((eq (car x) :cons)
                (and (true-listp (cdr x))
                     (eql (len (cdr x)) 0)
                     (b* nil t)))
               (t (and (eq (car x) :value)
                       (and (true-listp (cdr x))
                            (eql (len (cdr x)) 0))
                       (b* nil t)))))))

Theorem: consp-when-atj-atypep

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