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Sparseint

Sparseint-compare

Compare the values of two sparseints and return -1, 0, or 1.

Signature
(sparseint-compare x y) → sign
Arguments: x — Guard (sparseint-p x).; y — Guard (sparseint-p y).
Returns: sign — Type (integerp sign).

Definitions and Theorems

Function: sparseint-compare$inline

(defun sparseint-compare$inline (x y)
  (declare (xargs :guard (and (sparseint-p x) (sparseint-p y))))
  (let ((__function__ 'sparseint-compare))
    (declare (ignorable __function__))
    (sparseint$-compare (sparseint-fix x)
                        (sparseint-fix y))))

Theorem: integerp-of-sparseint-compare

(defthm integerp-of-sparseint-compare
  (b* ((sign (sparseint-compare$inline x y)))
    (integerp sign))
  :rule-classes :type-prescription)

Theorem: sparseint-compare-correct

(defthm sparseint-compare-correct
  (b* ((?sign (sparseint-compare$inline x y)))
    (equal sign
           (compare (sparseint-val x)
                    (sparseint-val y)))))

Theorem: sparseint-compare$inline-of-sparseint-fix-x

(defthm sparseint-compare$inline-of-sparseint-fix-x
  (equal (sparseint-compare$inline (sparseint-fix x)
                                   y)
         (sparseint-compare$inline x y)))

Theorem: sparseint-compare$inline-sparseint-equiv-congruence-on-x

(defthm sparseint-compare$inline-sparseint-equiv-congruence-on-x
  (implies (sparseint-equiv x x-equiv)
           (equal (sparseint-compare$inline x y)
                  (sparseint-compare$inline x-equiv y)))
  :rule-classes :congruence)

Theorem: sparseint-compare$inline-of-sparseint-fix-y

(defthm sparseint-compare$inline-of-sparseint-fix-y
  (equal (sparseint-compare$inline x (sparseint-fix y))
         (sparseint-compare$inline x y)))

Theorem: sparseint-compare$inline-sparseint-equiv-congruence-on-y

(defthm sparseint-compare$inline-sparseint-equiv-congruence-on-y
  (implies (sparseint-equiv y y-equiv)
           (equal (sparseint-compare$inline x y)
                  (sparseint-compare$inline x y-equiv)))
  :rule-classes :congruence)