		Search-engine friendly clone of the ACL2 documentation.

Pnumber

Pnumberp

Recognizer for pnumber structures.

Signature
(pnumberp x) → *

Definitions and Theorems

Function: pnumberp

(defun pnumberp (x)
  (declare (xargs :guard t))
  (and (consp x)
       (cond ((or (atom x) (eq (car x) :digit))
              (and (true-listp (cdr x))
                   (eql (len (cdr x)) 1)
                   (b* ((digit (std::da-nth 0 (cdr x))))
                     (and (characterp digit)
                          (dec-digit-char-p digit)))))
             ((eq (car x) :dot-digit)
              (and (true-listp (cdr x))
                   (eql (len (cdr x)) 1)
                   (b* ((digit (std::da-nth 0 (cdr x))))
                     (and (characterp digit)
                          (dec-digit-char-p digit)))))
             ((eq (car x) :number-digit)
              (and (true-listp (cdr x))
                   (eql (len (cdr x)) 2)
                   (b* ((number (std::da-nth 0 (cdr x)))
                        (digit (std::da-nth 1 (cdr x))))
                     (and (pnumberp number)
                          (characterp digit)
                          (dec-digit-char-p digit)))))
             ((eq (car x) :number-nondigit)
              (and (true-listp (cdr x))
                   (eql (len (cdr x)) 2)
                   (b* ((number (std::da-nth 0 (cdr x)))
                        (nondigit (std::da-nth 1 (cdr x))))
                     (and (pnumberp number)
                          (characterp nondigit)
                          (str::letter/uscore-char-p nondigit)))))
             ((eq (car x) :number-locase-e-sign)
              (and (true-listp (cdr x))
                   (eql (len (cdr x)) 2)
                   (b* ((number (std::da-nth 0 (cdr x)))
                        (sign (std::da-nth 1 (cdr x))))
                     (and (pnumberp number) (signp sign)))))
             ((eq (car x) :number-upcase-e-sign)
              (and (true-listp (cdr x))
                   (eql (len (cdr x)) 2)
                   (b* ((number (std::da-nth 0 (cdr x)))
                        (sign (std::da-nth 1 (cdr x))))
                     (and (pnumberp number) (signp sign)))))
             ((eq (car x) :number-locase-p-sign)
              (and (true-listp (cdr x))
                   (eql (len (cdr x)) 2)
                   (b* ((number (std::da-nth 0 (cdr x)))
                        (sign (std::da-nth 1 (cdr x))))
                     (and (pnumberp number) (signp sign)))))
             ((eq (car x) :number-upcase-p-sign)
              (and (true-listp (cdr x))
                   (eql (len (cdr x)) 2)
                   (b* ((number (std::da-nth 0 (cdr x)))
                        (sign (std::da-nth 1 (cdr x))))
                     (and (pnumberp number) (signp sign)))))
             (t (and (eq (car x) :number-dot)
                     (and (true-listp (cdr x))
                          (eql (len (cdr x)) 1))
                     (b* ((number (std::da-nth 0 (cdr x))))
                       (pnumberp number)))))))

Theorem: consp-when-pnumberp

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