		Search-engine friendly clone of the ACL2 documentation.

Omaps

Empty

Check if an omap is empty.

Signature
(empty map) → yes/no
Arguments: map — Guard (mapp map).
Returns: yes/no — Type (booleanp yes/no).

This is similar to set::empty for osets.

Definitions and Theorems

Function: empty

(defun empty (map)
  (declare (xargs :guard (mapp map)))
  (let ((__function__ 'empty))
    (declare (ignorable __function__))
    (null (mfix map))))

Theorem: booleanp-of-empty

(defthm booleanp-of-empty
  (b* ((yes/no (empty map)))
    (booleanp yes/no))
  :rule-classes :rewrite)

Theorem: mapp-when-not-empty

(defthm mapp-when-not-empty
  (implies (not (empty map)) (mapp map)))

Theorem: mfix-when-empty

(defthm mfix-when-empty
  (implies (empty x)
           (equal (mfix x) nil)))

Theorem: mapp-non-nil-implies-non-empty

(defthm mapp-non-nil-implies-non-empty
  (implies (and (mapp map) map)
           (not (empty map))))

Theorem: acl2-count-head-when-non-empty

(defthm acl2-count-head-when-non-empty
  (implies (not (empty map))
           (< (+ (acl2-count (car (car map)))
                 (acl2-count (cdr (car map))))
              (acl2-count map))))