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Omaps

Lookup*

Set of values associated to a set of keys in an omap.

Signature
(lookup* keys map) → vals
Arguments: keys — Guard (setp keys).; map — Guard (mapp map).
Returns: vals — Type (setp vals).

This lifts lookup to sets of keys.

Definitions and Theorems

Function: lookup*

(defun lookup* (keys map)
  (declare (xargs :guard (and (setp keys) (mapp map))))
  (declare (xargs :guard (in* keys map)))
  (let ((__function__ 'lookup*))
    (declare (ignorable __function__))
    (cond ((set::emptyp keys) nil)
          ((mbt (if (assoc (set::head keys) map) t nil))
           (insert (lookup (set::head keys) map)
                   (lookup* (set::tail keys) map)))
          (t (lookup* (set::tail keys) map)))))

Theorem: setp-of-lookup*

(defthm setp-of-lookup*
  (b* ((vals (lookup* keys map)))
    (setp vals))
  :rule-classes :rewrite)

Theorem: lookup*-when-left-emptyp

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

Theorem: lookup*-when-right-emptyp

(defthm lookup*-when-right-emptyp
  (implies (emptyp map)
           (equal (lookup* keys map) nil)))