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• Binary

Bin-digit-chars-value

Coerces a list of bit digits into a natural number.

Signature

(bin-digit-chars-value x) → value

Arguments

x — Guard (bin-digit-char-list*p x).

Returns

value — Type (natp value).

For instance, (bin-digit-chars-value '(#1 #0 #0 #0)) is 8. See also parse-bits-from-charlist for a more flexible function that can tolerate non-bit digits after the number.

Definitions and Theorems

Function: bin-digit-chars-value$inline

(defun bin-digit-chars-value$inline (x)
  (declare (xargs :guard (bin-digit-char-list*p x)))
  (let ((acl2::__function__ 'bin-digit-chars-value))
    (declare (ignorable acl2::__function__))
    (mbe :logic
         (if (consp x)
             (+ (ash (bin-digit-char-value (car x))
                     (1- (len x)))
                (bin-digit-chars-value (cdr x)))
           0)
         :exec (bin-digit-chars-value1 x 0))))

Theorem: natp-of-bin-digit-chars-value

(defthm natp-of-bin-digit-chars-value
  (b* ((value (bin-digit-chars-value$inline x)))
    (natp value))
  :rule-classes :type-prescription)

Theorem: icharlisteqv-implies-equal-bin-digit-chars-value-1

(defthm icharlisteqv-implies-equal-bin-digit-chars-value-1
  (implies (icharlisteqv x x-equiv)
           (equal (bin-digit-chars-value x)
                  (bin-digit-chars-value x-equiv)))
  :rule-classes (:congruence))

Theorem: unsigned-byte-p-of-bin-digit-chars-value

(defthm unsigned-byte-p-of-bin-digit-chars-value
  (unsigned-byte-p (len x)
                   (bin-digit-chars-value x)))

Theorem: bin-digit-chars-value-upper-bound

(defthm bin-digit-chars-value-upper-bound
  (< (bin-digit-chars-value x)
     (expt 2 (len x)))
  :rule-classes ((:rewrite) (:linear)))

Theorem: bin-digit-chars-value-upper-bound-free

(defthm bin-digit-chars-value-upper-bound-free
  (implies (equal n (len x))
           (< (bin-digit-chars-value x)
              (expt 2 n))))

Theorem: bin-digit-chars-value1-removal

(defthm bin-digit-chars-value1-removal
  (equal (bin-digit-chars-value1 x val)
         (+ (bin-digit-chars-value x)
            (ash (nfix val) (len x)))))

Theorem: bin-digit-chars-value-of-append

(defthm bin-digit-chars-value-of-append
  (equal (bin-digit-chars-value (append x (list a)))
         (+ (ash (bin-digit-chars-value x) 1)
            (bin-digit-char-value a))))

Subtopics

Bin-digit-chars-value1