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• Decimal

Dec-digit-char-value

Coerces a dec-digit-char-p character into a number.

Signature

(dec-digit-char-value x) → val

Arguments

x — Guard (dec-digit-char-p x).

Returns

val — Type (natp val).

For instance, (dec-digit-char-value #\3) is 3. For any non-dec-digit-char-p, 0 is returned.

Definitions and Theorems

Function: dec-digit-char-value$inline

(defun dec-digit-char-value$inline (x)
  (declare (type character x))
  (declare (xargs :guard (dec-digit-char-p x)))
  (declare (xargs :split-types t))
  (let ((acl2::__function__ 'dec-digit-char-value))
    (declare (ignorable acl2::__function__))
    (mbe :logic
         (if (dec-digit-char-p x)
             (- (char-code (char-fix x))
                (char-code #\0))
           0)
         :exec (the (unsigned-byte 8)
                    (- (the (unsigned-byte 8)
                            (char-code (the character x)))
                       (the (unsigned-byte 8) 48))))))

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

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

Theorem: ichareqv-implies-equal-dec-digit-char-value-1

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

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

(defthm dec-digit-char-value-upper-bound
  (< (dec-digit-char-value x) 10)
  :rule-classes ((:rewrite) (:linear)))

Theorem: equal-of-dec-digit-char-value-and-dec-digit-char-value

(defthm equal-of-dec-digit-char-value-and-dec-digit-char-value
  (implies (and (dec-digit-char-p x)
                (dec-digit-char-p y))
           (equal (equal (dec-digit-char-value x)
                         (dec-digit-char-value y))
                  (equal x y))))

Theorem: dec-digit-char-value-of-digit-to-char

(defthm dec-digit-char-value-of-digit-to-char
  (implies (and (natp n) (< n 10))
           (equal (dec-digit-char-value (digit-to-char n))
                  n)))