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• Database

Databasep

Recognizer for database.

Signature

(databasep x) → *

Definitions and Theorems

Function: databasep

(defun databasep (x)
  (declare (xargs :guard t))
  (if (atom x)
      (null x)
    (and (consp (car x))
         (byte-list32p (caar x))
         (byte-listp (cdar x))
         (or (null (cdr x))
             (and (consp (cdr x))
                  (consp (cadr x))
                  (acl2::fast-<< (caar x) (caadr x))
                  (databasep (cdr x)))))))

Theorem: booleanp-of-databasep

(defthm booleanp-of-databasep
  (booleanp (databasep x)))

Theorem: mapp-when-databasep

(defthm mapp-when-databasep
  (implies (databasep x) (omap::mapp x))
  :rule-classes (:rewrite :forward-chaining))

Theorem: databasep-of-tail

(defthm databasep-of-tail
  (implies (databasep x)
           (databasep (omap::tail x))))

Theorem: byte-list32p-of-head-key-when-databasep

(defthm byte-list32p-of-head-key-when-databasep
  (implies (and (databasep x)
                (not (omap::emptyp x)))
           (byte-list32p (mv-nth 0 (omap::head x)))))

Theorem: byte-listp-of-head-val-when-databasep

(defthm byte-listp-of-head-val-when-databasep
  (implies (and (databasep x)
                (not (omap::emptyp x)))
           (byte-listp (mv-nth 1 (omap::head x)))))

Theorem: databasep-of-update

(defthm databasep-of-update
  (implies (and (databasep x)
                (byte-list32p k)
                (byte-listp v))
           (databasep (omap::update k v x))))

Theorem: databasep-of-update*

(defthm databasep-of-update*
  (implies (and (databasep x) (databasep y))
           (databasep (omap::update* x y))))

Theorem: databasep-of-delete

(defthm databasep-of-delete
  (implies (databasep x)
           (databasep (omap::delete k x))))

Theorem: databasep-of-delete*

(defthm databasep-of-delete*
  (implies (databasep x)
           (databasep (omap::delete* k x))))

Theorem: byte-list32p-when-assoc-databasep-binds-free-x

(defthm byte-list32p-when-assoc-databasep-binds-free-x
  (implies (and (omap::assoc k x) (databasep x))
           (byte-list32p k)))

Theorem: byte-list32p-of-car-of-assoc-databasep

(defthm byte-list32p-of-car-of-assoc-databasep
  (implies (and (databasep x) (omap::assoc k x))
           (byte-list32p (car (omap::assoc k x)))))

Theorem: byte-listp-of-cdr-of-assoc-databasep

(defthm byte-listp-of-cdr-of-assoc-databasep
  (implies (and (databasep x) (omap::assoc k x))
           (byte-listp (cdr (omap::assoc k x)))))

Theorem: byte-listp-of-lookup-when-databasep

(defthm byte-listp-of-lookup-when-databasep
  (implies (and (databasep x) (omap::assoc k x))
           (byte-listp (omap::lookup k x))))