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• Octal

Oct-digit-char-value

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

Signature

(oct-digit-char-value x) → val

Arguments

x — Guard (oct-digit-char-p x).

Returns

val — Type (natp val).

For instance, (oct-digit-char-value #\a) is 10. For any non-oct-digit-char-p, 0 is returned.

Definitions and Theorems

Function: oct-digit-char-value$inline

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

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

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

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

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

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

(defthm oct-digit-char-value-upper-bound
  (< (oct-digit-char-value x) 8)
  :rule-classes ((:rewrite) (:linear)))

Theorem: unsigned-byte-p-of-oct-digit-char-value

(defthm unsigned-byte-p-of-oct-digit-char-value
  (unsigned-byte-p 3 (oct-digit-char-value x)))

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

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

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

(defthm oct-digit-char-value-of-digit-to-char
  (implies (and (natp n) (< n 8))
           (equal (oct-digit-char-value (digit-to-char n))
                  n)))