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Representation-of-integers

Integer-from-uchar

Accessor for values of type unsigned char.

Signature
(integer-from-uchar x) → y
Arguments: x — Guard (ucharp x).
Returns: y — Type (uchar-integerp y).

Definitions and Theorems

Function: integer-from-uchar

(defun integer-from-uchar (x)
  (declare (xargs :guard (ucharp x)))
  (let ((__function__ 'integer-from-uchar))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((x (and t x)))
           (uchar-integer-fix (std::da-nth 0 (cdr x))))
         :exec (std::da-nth 0 (cdr x)))))

Theorem: uchar-integerp-of-integer-from-uchar

(defthm uchar-integerp-of-integer-from-uchar
  (b* ((y (integer-from-uchar x)))
    (uchar-integerp y))
  :rule-classes :rewrite)

Theorem: uchar-from-integer-of-integer-from-uchar

(defthm uchar-from-integer-of-integer-from-uchar
  (equal (uchar-from-integer (integer-from-uchar x))
         (uchar-fix x)))

Theorem: integer-from-uchar-of-uchar-from-integer

(defthm integer-from-uchar-of-uchar-from-integer
  (equal (integer-from-uchar (uchar-from-integer get))
         (uchar-integer-fix get)))

Theorem: integer-from-uchar-upper-bound

(defthm integer-from-uchar-upper-bound
  (<= (integer-from-uchar x) (uchar-max))
  :rule-classes :linear)

Theorem: integer-from-uchar-of-uchar-fix-x

(defthm integer-from-uchar-of-uchar-fix-x
  (equal (integer-from-uchar (uchar-fix x))
         (integer-from-uchar x)))

Theorem: integer-from-uchar-uchar-equiv-congruence-on-x

(defthm integer-from-uchar-uchar-equiv-congruence-on-x
  (implies (uchar-equiv x x-equiv)
           (equal (integer-from-uchar x)
                  (integer-from-uchar x-equiv)))
  :rule-classes :congruence)