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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::empty 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::empty 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-in-databasep-binds-free-x

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

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

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

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

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

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

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