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Representation-of-integers

Integer-from-sshort

Accessor for values of type signed short.

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

Definitions and Theorems

Function: integer-from-sshort

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

Theorem: sshort-integerp-of-integer-from-sshort

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

Theorem: sshort-from-integer-of-integer-from-sshort

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

Theorem: integer-from-sshort-of-sshort-from-integer

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

Theorem: integer-from-sshort-upper-bound

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

Theorem: integer-from-sshort-lower-bound

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

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

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

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

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