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Base64

Base64-decode-list

Base64 decode a character list.

Signature
(base64-decode-list x) → (mv okp ans)
Arguments: x — Character list to decode.
Guard (character-listp x).
Returns: okp — Was decoding successful? It can fail if we encounter non Base-64 alphabetic characters in the input, or if the input is not of the proper length (a multiple of 4), or if there is incorrect padding.
Type (booleanp okp).; ans — On success, the decoded version of x. On failure, it is some nonsensical character list that should not be relied on.
Type (character-listp ans).

Definitions and Theorems

Function: base64-decode-list

(defun base64-decode-list (x)
  (declare (xargs :guard (character-listp x)))
  (let ((acl2::__function__ 'base64-decode-list))
    (declare (ignorable acl2::__function__))
    (mbe :logic
         (b* (((when (atom x)) (mv t nil))
              ((when (atom (cdddr x))) (mv nil nil))
              (c1 (first x))
              (c2 (second x))
              (c3 (third x))
              (c4 (fourth x))
              (rest (cddddr x))
              ((when (atom rest))
               (b64-decode-last-group c1 c2 c3 c4))
              ((mv okp x1 x2 x3)
               (b64-dec3 c1 c2 c3 c4))
              ((unless okp) (mv nil nil))
              ((mv rest-ok rest-ans)
               (base64-decode-list (cddddr x))))
           (mv (and okp rest-ok)
               (list* x1 x2 x3 rest-ans)))
         :exec
         (b* (((mv okp acc)
               (b64-decode-list-impl x nil)))
           (mv okp (reverse acc))))))

Theorem: booleanp-of-base64-decode-list.okp

(defthm booleanp-of-base64-decode-list.okp
  (b* (((mv ?okp ?ans) (base64-decode-list x)))
    (booleanp okp))
  :rule-classes :type-prescription)

Theorem: character-listp-of-base64-decode-list.ans

(defthm character-listp-of-base64-decode-list.ans
  (b* (((mv ?okp ?ans) (base64-decode-list x)))
    (character-listp ans))
  :rule-classes :rewrite)

Theorem: b64-decode-list-impl-removal

(defthm b64-decode-list-impl-removal
  (equal (b64-decode-list-impl x acc)
         (mv (mv-nth 0 (base64-decode-list x))
             (revappend (mv-nth 1 (base64-decode-list x))
                        acc))))

Theorem: base64-decode-list-of-base64-encode-list

(defthm base64-decode-list-of-base64-encode-list
  (implies (character-listp x)
           (b* ((encoded (base64-encode-list x))
                ((mv okp decoded)
                 (base64-decode-list encoded)))
             (and okp (equal decoded x)))))