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Sparseint-impl

Sparseint$-val

Signature
(sparseint$-val x) → val
Arguments: x — Guard (sparseint$-p x).
Returns: val — Type (integerp val).

Definitions and Theorems

Function: sparseint$-val

(defun sparseint$-val (x)
  (declare (xargs :guard (sparseint$-p x)))
  (let ((__function__ 'sparseint$-val))
    (declare (ignorable __function__))
    (sparseint$-case x
                     :leaf x.val
                     :concat (logapp x.width (sparseint$-val x.lsbs)
                                     (sparseint$-val x.msbs)))))

Theorem: integerp-of-sparseint$-val

(defthm integerp-of-sparseint$-val
  (b* ((val (sparseint$-val x)))
    (integerp val))
  :rule-classes :type-prescription)

Theorem: sparseint$-val-of-leaf

(defthm sparseint$-val-of-leaf
  (b* nil
    (implies (sparseint$-case x :leaf)
             (equal (sparseint$-val x)
                    (sparseint$-leaf->val x)))))

Theorem: sparseint$-val-of-concat

(defthm sparseint$-val-of-concat
  (b* nil
    (implies (sparseint$-case x :concat)
             (equal (sparseint$-val x)
                    (b* (((sparseint$-concat x)))
                      (logapp x.width (sparseint$-val x.lsbs)
                              (sparseint$-val x.msbs)))))))

Theorem: sparseint$-val-of-sparseint$-fix-x

(defthm sparseint$-val-of-sparseint$-fix-x
  (equal (sparseint$-val (sparseint$-fix x))
         (sparseint$-val x)))

Theorem: sparseint$-val-sparseint$-equiv-congruence-on-x

(defthm sparseint$-val-sparseint$-equiv-congruence-on-x
  (implies (sparseint$-equiv x x-equiv)
           (equal (sparseint$-val x)
                  (sparseint$-val x-equiv)))
  :rule-classes :congruence)