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• Binary

Parse-bits-from-charlist

Parse a binary number from the beginning of a character list.

Signature

(parse-bits-from-charlist x val len) → (mv val len rest)

Arguments

x — Characters to read from.
    Guard (character-listp x).

val — Accumulator for the value of the bits we have read so far; typically 0 to start with.
    Guard (natp val).

len — Accumulator for the number of bits we have read; typically 0 to start with.
    Guard (natp len).

Returns

val — Value of the initial bits as a natural number.

len — Number of initial bits we read.

rest — The rest of x, past the leading bits.

This function is somewhat complicated. See also (bin-digit-chars-value x), which is a simpler way to interpret strings where all of the characters are 0 or 1.

Definitions and Theorems

Function: parse-bits-from-charlist

(defun parse-bits-from-charlist (x val len)
 (declare (xargs :guard (and (character-listp x)
                             (natp val)
                             (natp len))))
 (declare (type unsigned-byte val len))
 (declare (xargs :split-types t))
 (let ((acl2::__function__ 'parse-bits-from-charlist))
  (declare (ignorable acl2::__function__))
  (mbe
   :logic
   (cond
       ((atom x)
        (mv (nfix val) (nfix len) nil))
       ((bin-digit-char-p (car x))
        (let ((digit-val (bin-digit-char-value (car x))))
          (parse-bits-from-charlist (cdr x)
                                    (+ digit-val (ash (nfix val) 1))
                                    (+ 1 (nfix len)))))
       (t (mv (nfix val) (nfix len) x)))
   :exec
   (b* (((when (atom x)) (mv val len nil))
        (car (car x))
        ((when (equal car #\0))
         (parse-bits-from-charlist (cdr x)
                                   (the unsigned-byte (ash val 1))
                                   (the unsigned-byte (+ 1 len))))
        ((when (equal car #\1))
         (parse-bits-from-charlist
              (cdr x)
              (the unsigned-byte
                   (+ 1 (the unsigned-byte (ash val 1))))
              (the unsigned-byte (+ 1 len)))))
     (mv val len x)))))

Theorem: val-of-parse-bits-from-charlist

(defthm val-of-parse-bits-from-charlist
  (equal (mv-nth 0 (parse-bits-from-charlist x val len))
         (+ (bin-digit-chars-value (take-leading-bin-digit-chars x))
            (ash (nfix val)
                 (len (take-leading-bin-digit-chars x))))))

Theorem: len-of-parse-bits-from-charlist

(defthm len-of-parse-bits-from-charlist
  (equal (mv-nth 1 (parse-bits-from-charlist x val len))
         (+ (nfix len)
            (len (take-leading-bin-digit-chars x)))))

Theorem: rest-of-parse-bits-from-charlist

(defthm rest-of-parse-bits-from-charlist
  (equal (mv-nth 2 (parse-bits-from-charlist x val len))
         (skip-leading-bit-digits x)))