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• Octal-integer-literals

Octdig/uscore-list-wfp

Check if an octal numeral is well-formed.

Signature

(octdig/uscore-list-wfp dus) → yes/no

Arguments

dus — Guard (octdig/uscore-listp dus).

Returns

yes/no — Type (booleanp yes/no).

An octal-numeral in the grammar is a list of octal digits and underscores subject to the following constraints, derived from the grammar:

• It must start with the digit 0, not an underscore or other digit.
• It must end with a digit, not an underscore.
• It must contain at least two digits (which implies that it cannot be confused with the decimal numeral 0).

Definitions and Theorems

Function: octdig/uscore-list-wfp

(defun octdig/uscore-list-wfp (dus)
  (declare (xargs :guard (octdig/uscore-listp dus)))
  (let ((__function__ 'octdig/uscore-list-wfp))
    (declare (ignorable __function__))
    (and (consp dus)
         (equal (octdig/uscore-fix (car dus))
                (octdig/uscore-digit (char-code #\0)))
         (octdig/uscore-case (car (last dus))
                             :digit)
         (> (len (octdig/uscores-to-digits dus))
            1))))

Theorem: booleanp-of-octdig/uscore-list-wfp

(defthm booleanp-of-octdig/uscore-list-wfp
  (b* ((yes/no (octdig/uscore-list-wfp dus)))
    (booleanp yes/no))
  :rule-classes :rewrite)

Theorem: octdig/uscore-list-wfp-of-octdig/uscore-list-fix-dus

(defthm octdig/uscore-list-wfp-of-octdig/uscore-list-fix-dus
  (equal (octdig/uscore-list-wfp (octdig/uscore-list-fix dus))
         (octdig/uscore-list-wfp dus)))

Theorem: octdig/uscore-list-wfp-octdig/uscore-list-equiv-congruence-on-dus

(defthm
  octdig/uscore-list-wfp-octdig/uscore-list-equiv-congruence-on-dus
  (implies (octdig/uscore-list-equiv dus dus-equiv)
           (equal (octdig/uscore-list-wfp dus)
                  (octdig/uscore-list-wfp dus-equiv)))
  :rule-classes :congruence)