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• Obags

Bagp

Recognize obags.

Signature

(bagp x) → yes/no

Returns

yes/no — Type (booleanp yes/no).

This is similar to the definition of setp, but each element of the list is checked to be either equal or smaller than the next.

Since a strictly ordered list is also non-strictly ordered, an oset is an obag.

Definitions and Theorems

Function: bagp

(defun bagp (x)
       (declare (xargs :guard t))
       (let ((__function__ 'bagp))
            (declare (ignorable __function__))
            (if (atom x)
                (null x)
                (or (null (cdr x))
                    (and (consp (cdr x))
                         (or (equal (car x) (cadr x))
                             (fast-<< (car x) (cadr x)))
                         (bagp (cdr x)))))))

Theorem: booleanp-of-bagp

(defthm booleanp-of-bagp
        (b* ((yes/no (bagp x)))
            (booleanp yes/no))
        :rule-classes :rewrite)

Theorem: bagp-when-setp

(defthm bagp-when-setp
        (implies (setp x) (bagp x))
        :rule-classes (:rewrite :forward-chaining))