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Decimal

Dec-digit-chars-value

Coerces a dec-digit-char-list*p into a natural number.

Signature
(dec-digit-chars-value x) → value
Arguments: x — Guard (dec-digit-char-list*p x).
Returns: value — Type (natp value).

For instance, (dec-digit-chars-value '(#1 #0 #3)) is 103. See also parse-nat-from-charlist for a more flexible function that can tolerate non-numeric characters after the number.

Definitions and Theorems

Function: dec-digit-chars-value$inline

(defun dec-digit-chars-value$inline (x)
  (declare (xargs :guard (dec-digit-char-list*p x)))
  (let ((acl2::__function__ 'dec-digit-chars-value))
    (declare (ignorable acl2::__function__))
    (mbe :logic
         (if (consp x)
             (+ (* (expt 10 (1- (len x)))
                   (dec-digit-char-value (car x)))
                (dec-digit-chars-value (cdr x)))
           0)
         :exec (dec-digit-chars-value1 x 0))))

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

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

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

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

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

(defthm dec-digit-chars-value-upper-bound
  (< (dec-digit-chars-value x)
     (expt 10 (len x))))

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

(defthm dec-digit-chars-value-upper-bound-free
  (implies (equal n (len x))
           (< (dec-digit-chars-value x)
              (expt 10 n))))

Theorem: dec-digit-chars-value1-removal

(defthm dec-digit-chars-value1-removal
  (equal (dec-digit-chars-value1 x val)
         (+ (dec-digit-chars-value x)
            (* (nfix val) (expt 10 (len x))))))

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

(defthm dec-digit-chars-value-of-append
  (equal (dec-digit-chars-value (append x (list a)))
         (+ (* 10 (dec-digit-chars-value x))
            (dec-digit-char-value a))))

Subtopics

Dec-digit-chars-value1