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Omaps

Restrict

Restrict an omap to a set of keys.

Signature
(restrict keys map) → map1
Arguments: keys — Guard (setp keys).; map — Guard (mapp map).
Returns: map1 — Type (mapp map1).

This drops all the keys of the omap that are not in the given set of keys.

Definitions and Theorems

Function: restrict

(defun restrict (keys map)
  (declare (xargs :guard (and (setp keys) (mapp map))))
  (let ((__function__ 'restrict))
    (declare (ignorable __function__))
    (cond ((emptyp map) nil)
          (t (mv-let (key val)
                     (head map)
               (if (set::in key keys)
                   (update key val (restrict keys (tail map)))
                 (restrict keys (tail map))))))))

Theorem: mapp-of-restrict

(defthm mapp-of-restrict
  (b* ((map1 (restrict keys map)))
    (mapp map1))
  :rule-classes :rewrite)

Theorem: restrict-when-left-emptyp

(defthm restrict-when-left-emptyp
  (implies (set::emptyp keys)
           (equal (restrict keys map) nil))
  :rule-classes (:rewrite :type-prescription))

Theorem: restrict-when-right-emptyp

(defthm restrict-when-right-emptyp
  (implies (emptyp map)
           (equal (restrict keys map) nil))
  :rule-classes (:rewrite :type-prescription))

Theorem: assoc-of-restrict

(defthm assoc-of-restrict
  (equal (assoc key (restrict keys map))
         (and (set::in key keys)
              (assoc key map))))

Theorem: assoc-of-restrict-when-in-keys

(defthm assoc-of-restrict-when-in-keys
  (implies (set::in key keys)
           (equal (assoc key (restrict keys map))
                  (assoc key map))))