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• Binary

Bin-digit-char-value

Coerces a bin-digit-char-p character into a number, 0 or 1.

Signature

(bin-digit-char-value x) → bit

Arguments

x — Guard (bin-digit-char-p x).

Returns

bit — Type (bitp bit).

Definitions and Theorems

Function: bin-digit-char-value$inline

(defun bin-digit-char-value$inline (x)
  (declare (type character x))
  (declare (xargs :guard (bin-digit-char-p x)))
  (declare (xargs :split-types t))
  (let ((acl2::__function__ 'bin-digit-char-value))
    (declare (ignorable acl2::__function__))
    (if (eql x #\1) 1 0)))

Theorem: bitp-of-bin-digit-char-value

(defthm bitp-of-bin-digit-char-value
  (b* ((bit (bin-digit-char-value$inline x)))
    (bitp bit))
  :rule-classes :type-prescription)

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

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

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

(defthm unsigned-byte-p-of-bin-digit-char-value
  (unsigned-byte-p 1 (bin-digit-char-value x)))

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

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

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

(defthm bin-digit-char-value-of-digit-to-char
  (implies (bitp n)
           (equal (bin-digit-char-value (digit-to-char n))
                  n)))