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• Mmp-trees

Mmp-encoding-p

Check if a root and database are an MMP encoding of a finite map from byte arrays to byte arrays.

This is a declarative, non-executable definition, which essentially characterizes the image of mmp-encode (over finite maps that can be encoded, i.e. such that mmp-encode returns a nil error flag, except that we allow the database to be larger.

The reason is the following. mmp-encode produces the minimum database that suffices to encode the map. However, it seems reasonable that there is one global database [YP:D.1] [YP:4.1], used to encode a variety of finite maps in the Ethereum state. Thus, given a root and the global database, we can say that they together encode a finite map, even though the database may be larger then needed to encode the map.

Definitions and Theorems

Theorem: mmp-encoding-p-suff

(defthm mmp-encoding-p-suff
 (implies
  (and (bytelist-bytelist-mapp map)
       (b* (((mv map-error? map-root map-database)
             (mmp-encode map)))
         (and (not map-error?)
              (equal map-root (byte-list-fix root))
              (omap::submap map-database (database-fix database)))))
  (mmp-encoding-p root database)))

Theorem: booleanp-of-mmp-encoding-p

(defthm booleanp-of-mmp-encoding-p
  (b* ((yes/no (mmp-encoding-p root database)))
    (booleanp yes/no))
  :rule-classes :rewrite)

Theorem: mmp-encoding-p-of-byte-list-fix-root

(defthm mmp-encoding-p-of-byte-list-fix-root
  (equal (mmp-encoding-p (byte-list-fix root)
                         database)
         (mmp-encoding-p root database)))

Theorem: mmp-encoding-p-byte-list-equiv-congruence-on-root

(defthm mmp-encoding-p-byte-list-equiv-congruence-on-root
  (implies (byte-list-equiv root root-equiv)
           (equal (mmp-encoding-p root database)
                  (mmp-encoding-p root-equiv database)))
  :rule-classes :congruence)

Theorem: mmp-encoding-p-of-database-fix-database

(defthm mmp-encoding-p-of-database-fix-database
  (equal (mmp-encoding-p root (database-fix database))
         (mmp-encoding-p root database)))

Theorem: mmp-encoding-p-database-equiv-congruence-on-database

(defthm mmp-encoding-p-database-equiv-congruence-on-database
  (implies (database-equiv database database-equiv)
           (equal (mmp-encoding-p root database)
                  (mmp-encoding-p root database-equiv)))
  :rule-classes :congruence)