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Representation-of-integers

Integer-from-sint

Accessor for values of type signed int.

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

Definitions and Theorems

Function: integer-from-sint

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

Theorem: sint-integerp-of-integer-from-sint

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

Theorem: sint-from-integer-of-integer-from-sint

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

Theorem: integer-from-sint-of-sint-from-integer

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

Theorem: integer-from-sint-upper-bound

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

Theorem: integer-from-sint-lower-bound

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

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

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

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

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