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Bytelist-to-nibblelist-keys

Bytelist-to-nibblelist-keys-aux

Turn a sequence of bytes into a sequence of nibbles.

Signature
(bytelist-to-nibblelist-keys-aux bytes) → nibbles
Arguments: bytes — Guard (byte-listp bytes).
Returns: nibbles — Type (nibble-listp nibbles).

This corresponds to [YP:(191)], but here the conversion is expressed via recursion instead of indexing.

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)