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• Dead-code-eliminator-execution

Eoutcome-result-okeq

Equality of expression outcome results modulo errors.

Signature

(eoutcome-result-okeq x y) → yes/no

Arguments

x — Guard (eoutcome-resultp x).

y — Guard (eoutcome-resultp y).

Returns

yes/no — Type (booleanp yes/no).

This is the equivalence relation on expression outcomes discussed in dead-code-eliminator-execution.

Definitions and Theorems

Function: eoutcome-result-okeq

(defun eoutcome-result-okeq (x y)
  (declare (xargs :guard (and (eoutcome-resultp x)
                              (eoutcome-resultp y))))
  (let ((__function__ 'eoutcome-result-okeq))
    (declare (ignorable __function__))
    (b* ((x (eoutcome-result-fix x))
         (y (eoutcome-result-fix y)))
      (cond ((reserrp x) (reserrp y))
            ((reserrp y) (reserrp x))
            (t (equal x y))))))

Theorem: booleanp-of-eoutcome-result-okeq

(defthm booleanp-of-eoutcome-result-okeq
  (b* ((yes/no (eoutcome-result-okeq x y)))
    (booleanp yes/no))
  :rule-classes :rewrite)

Theorem: eoutcome-result-okeq-is-an-equivalence

(defthm eoutcome-result-okeq-is-an-equivalence
  (and (booleanp (eoutcome-result-okeq x y))
       (eoutcome-result-okeq x x)
       (implies (eoutcome-result-okeq x y)
                (eoutcome-result-okeq y x))
       (implies (and (eoutcome-result-okeq x y)
                     (eoutcome-result-okeq y z))
                (eoutcome-result-okeq x z)))
  :rule-classes (:equivalence))

Theorem: eoutcome-result-okeq-of-eoutcome-result-fix-x

(defthm eoutcome-result-okeq-of-eoutcome-result-fix-x
  (equal (eoutcome-result-okeq (eoutcome-result-fix x)
                               y)
         (eoutcome-result-okeq x y)))

Theorem: eoutcome-result-okeq-eoutcome-result-equiv-congruence-on-x

(defthm eoutcome-result-okeq-eoutcome-result-equiv-congruence-on-x
  (implies (eoutcome-result-equiv x x-equiv)
           (equal (eoutcome-result-okeq x y)
                  (eoutcome-result-okeq x-equiv y)))
  :rule-classes :congruence)

Theorem: eoutcome-result-okeq-of-eoutcome-result-fix-y

(defthm eoutcome-result-okeq-of-eoutcome-result-fix-y
  (equal (eoutcome-result-okeq x (eoutcome-result-fix y))
         (eoutcome-result-okeq x y)))

Theorem: eoutcome-result-okeq-eoutcome-result-equiv-congruence-on-y

(defthm eoutcome-result-okeq-eoutcome-result-equiv-congruence-on-y
  (implies (eoutcome-result-equiv y y-equiv)
           (equal (eoutcome-result-okeq x y)
                  (eoutcome-result-okeq x y-equiv)))
  :rule-classes :congruence)