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• Omaps

Lookup

Value associated to a key in an omap.

Signature

(lookup key map) → val

Arguments

map — Guard (mapp map).

Definitions and Theorems

Function: lookup

(defun lookup (key map)
  (declare (xargs :guard (mapp map)))
  (declare (xargs :guard (assoc key map)))
  (let ((__function__ 'lookup))
    (declare (ignorable __function__))
    (cdr (assoc key map))))

Theorem: lookup-when-emptyp

(defthm lookup-when-emptyp
  (implies (emptyp map)
           (not (lookup key map)))
  :rule-classes (:rewrite :type-prescription))

Theorem: acl2-count-lookup-<-map

(defthm acl2-count-lookup-<-map
  (implies (not (emptyp map))
           (< (acl2-count (lookup key map))
              (acl2-count map))))

Theorem: lookup-of-tail-when-assoc-tail

(defthm lookup-of-tail-when-assoc-tail
  (implies (assoc key (tail map))
           (equal (lookup key (tail map))
                  (lookup key map))))

Theorem: lookup-of-update

(defthm lookup-of-update
  (equal (lookup key1 (update key val map))
         (if (equal key1 key)
             val
           (lookup key1 map))))

Theorem: lookup-of-update*

(defthm lookup-of-update*
  (equal (lookup key (update* map1 map2))
         (if (assoc key map1)
             (lookup key map1)
           (lookup key (mfix map2)))))

Theorem: lookup-of-mfix-map

(defthm lookup-of-mfix-map
  (equal (lookup key (mfix map))
         (lookup key map)))

Theorem: lookup-mequiv-congruence-on-map

(defthm lookup-mequiv-congruence-on-map
  (implies (mequiv map map-equiv)
           (equal (lookup key map)
                  (lookup key map-equiv)))
  :rule-classes :congruence)