		Search-engine friendly clone of the ACL2 documentation.

Representation-of-integers

Integer-from-schar

Accessor for values of type signed char.

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

Definitions and Theorems

Function: integer-from-schar

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

Theorem: schar-integerp-of-integer-from-schar

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

Theorem: schar-from-integer-of-integer-from-schar

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

Theorem: integer-from-schar-of-schar-from-integer

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

Theorem: integer-from-schar-upper-bound

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

Theorem: integer-from-schar-lower-bound

(defthm integer-from-schar-lower-bound
  (>= (integer-from-schar x) (schar-min))
  :rule-classes :linear)

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

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

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

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