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Bytelist-to-nibblelist-keys

Turn (i) a finite map from byte arrays to byte arrays into (ii) a finite map from nibble arrays to byte arrays.

Signature

(bytelist-to-nibblelist-keys map) → map1

Arguments

map — Guard (bytelist-bytelist-mapp map).

Returns

map1 — Type (nibblelist-bytelist-mapp map1).

This corresponds to y [YP:(190), YP:(191)].

Definitions and Theorems

Function: bytelist-to-nibblelist-keys-aux

(defun bytelist-to-nibblelist-keys-aux (bytes)
  (declare (xargs :guard (byte-listp bytes)))
  (b* (((when (endp bytes)) nil)
       (byte (byte-fix (car bytes)))
       (nibble-hi (floor byte 16))
       (nibble-lo (mod byte 16))
       (nibbles (bytelist-to-nibblelist-keys-aux (cdr bytes))))
    (list* nibble-hi nibble-lo nibbles)))

Theorem: nibble-listp-of-bytelist-to-nibblelist-keys-aux

(defthm nibble-listp-of-bytelist-to-nibblelist-keys-aux
  (b* ((nibbles (bytelist-to-nibblelist-keys-aux bytes)))
    (nibble-listp nibbles))
  :rule-classes :rewrite)

Theorem: bytelist-to-nibblelist-keys-aux-of-byte-list-fix-bytes

(defthm bytelist-to-nibblelist-keys-aux-of-byte-list-fix-bytes
  (equal (bytelist-to-nibblelist-keys-aux (byte-list-fix bytes))
         (bytelist-to-nibblelist-keys-aux bytes)))

Theorem: bytelist-to-nibblelist-keys-aux-byte-list-equiv-congruence-on-bytes

(defthm
 bytelist-to-nibblelist-keys-aux-byte-list-equiv-congruence-on-bytes
 (implies (byte-list-equiv bytes bytes-equiv)
          (equal (bytelist-to-nibblelist-keys-aux bytes)
                 (bytelist-to-nibblelist-keys-aux bytes-equiv)))
 :rule-classes :congruence)

Function: bytelist-to-nibblelist-keys

(defun bytelist-to-nibblelist-keys (map)
  (declare (xargs :guard (bytelist-bytelist-mapp map)))
  (b* (((unless (mbt (bytelist-bytelist-mapp map)))
        nil)
       ((when (omap::emptyp map)) nil)
       ((mv key val) (omap::head map))
       (key (byte-list-fix key))
       (val (byte-list-fix val))
       (key1 (bytelist-to-nibblelist-keys-aux key))
       (map1 (bytelist-to-nibblelist-keys (omap::tail map))))
    (omap::update key1 val map1)))

Theorem: nibblelist-bytelist-mapp-of-bytelist-to-nibblelist-keys

(defthm nibblelist-bytelist-mapp-of-bytelist-to-nibblelist-keys
  (b* ((map1 (bytelist-to-nibblelist-keys map)))
    (nibblelist-bytelist-mapp map1))
  :rule-classes :rewrite)

Theorem: bytelist-to-nibblelist-keys-of-bytelist-bytelist-mfix-map

(defthm bytelist-to-nibblelist-keys-of-bytelist-bytelist-mfix-map
  (equal (bytelist-to-nibblelist-keys (bytelist-bytelist-mfix map))
         (bytelist-to-nibblelist-keys map)))

Theorem: bytelist-to-nibblelist-keys-bytelist-bytelist-mequiv-congruence-on-map

(defthm
 bytelist-to-nibblelist-keys-bytelist-bytelist-mequiv-congruence-on-map
 (implies (bytelist-bytelist-mequiv map map-equiv)
          (equal (bytelist-to-nibblelist-keys map)
                 (bytelist-to-nibblelist-keys map-equiv)))
 :rule-classes :congruence)

Subtopics

Bytelist-to-nibblelist-keys-aux

Turn a sequence of bytes into a sequence of nibbles.