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• Omaps

List-lookup

List of values associated to a list of keys in an omap.

Signature

(list-lookup keys map) → vals

Arguments

keys — Guard (true-listp keys).

map — Guard (mapp map).

Returns

vals — Type (true-listp vals).

Definitions and Theorems

Function: list-lookup

(defun list-lookup (keys map)
  (declare (xargs :guard (and (true-listp keys) (mapp map))))
  (declare (xargs :guard (list-in keys map)))
  (let ((__function__ 'list-lookup))
    (declare (ignorable __function__))
    (cond ((endp keys) nil)
          (t (cons (lookup (car keys) map)
                   (list-lookup (cdr keys) map))))))

Theorem: true-listp-of-list-lookup

(defthm true-listp-of-list-lookup
  (b* ((vals (list-lookup keys map)))
    (true-listp vals))
  :rule-classes :rewrite)

Theorem: list-lookup-of-cons

(defthm list-lookup-of-cons
  (equal (list-lookup (cons key keys) map)
         (cons (lookup key map)
               (list-lookup keys map))))

Theorem: list-lookup-of-append

(defthm list-lookup-of-append
  (equal (list-lookup (append keys1 keys2) map)
         (append (list-lookup keys1 map)
                 (list-lookup keys2 map))))

Theorem: list-lookup-of-rev

(defthm list-lookup-of-rev
  (equal (list-lookup (rev keys) map)
         (rev (list-lookup keys map))))

Theorem: list-lookup-of-update*-when-list-in

(defthm list-lookup-of-update*-when-list-in
  (implies (list-in keys map1)
           (equal (list-lookup keys (update* map1 map2))
                  (list-lookup keys map1))))

Theorem: list-lookup-of-update*-when-list-notin

(defthm list-lookup-of-update*-when-list-notin
  (implies (list-notin keys map1)
           (equal (list-lookup keys (update* map1 map2))
                  (list-lookup keys (mfix map2)))))

Theorem: list-lookup-of-update-of-non-member

(defthm list-lookup-of-update-of-non-member
  (implies (not (member-equal key keys))
           (equal (list-lookup keys (update key val map))
                  (list-lookup keys map))))

Theorem: list-lookup-of-list-fix-keys

(defthm list-lookup-of-list-fix-keys
  (equal (list-lookup (list-fix keys) map)
         (list-lookup keys map)))

Theorem: list-lookup-list-equiv-congruence-on-keys

(defthm list-lookup-list-equiv-congruence-on-keys
  (implies (list-equiv keys keys-equiv)
           (equal (list-lookup keys map)
                  (list-lookup keys-equiv map)))
  :rule-classes :congruence)

Theorem: list-lookup-of-mfix-map

(defthm list-lookup-of-mfix-map
  (equal (list-lookup keys (mfix map))
         (list-lookup keys map)))

Theorem: list-lookup-mequiv-congruence-on-map

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