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Outcome

Outcome-fix

Fixing function for outcome structures.

Signature
(outcome-fix x) → new-x
Arguments: x — Guard (outcomep x).
Returns: new-x — Type (outcomep new-x).

Definitions and Theorems

Function: outcome-fix$inline

(defun outcome-fix$inline (x)
 (declare (xargs :guard (outcomep x)))
 (let ((__function__ 'outcome-fix))
   (declare (ignorable __function__))
   (mbe :logic
        (case (outcome-kind x)
          (:terminated (b* ((env (env-fix (std::da-nth 0 (cdr x)))))
                         (cons :terminated (list env))))
          (:nonterminating (cons :nonterminating (list))))
        :exec x)))

Theorem: outcomep-of-outcome-fix

(defthm outcomep-of-outcome-fix
  (b* ((new-x (outcome-fix$inline x)))
    (outcomep new-x))
  :rule-classes :rewrite)

Theorem: outcome-fix-when-outcomep

(defthm outcome-fix-when-outcomep
  (implies (outcomep x)
           (equal (outcome-fix x) x)))

Function: outcome-equiv$inline

(defun outcome-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (outcomep acl2::x)
                              (outcomep acl2::y))))
  (equal (outcome-fix acl2::x)
         (outcome-fix acl2::y)))

Theorem: outcome-equiv-is-an-equivalence

(defthm outcome-equiv-is-an-equivalence
  (and (booleanp (outcome-equiv x y))
       (outcome-equiv x x)
       (implies (outcome-equiv x y)
                (outcome-equiv y x))
       (implies (and (outcome-equiv x y)
                     (outcome-equiv y z))
                (outcome-equiv x z)))
  :rule-classes (:equivalence))

Theorem: outcome-equiv-implies-equal-outcome-fix-1

(defthm outcome-equiv-implies-equal-outcome-fix-1
  (implies (outcome-equiv acl2::x x-equiv)
           (equal (outcome-fix acl2::x)
                  (outcome-fix x-equiv)))
  :rule-classes (:congruence))

Theorem: outcome-fix-under-outcome-equiv

(defthm outcome-fix-under-outcome-equiv
  (outcome-equiv (outcome-fix acl2::x)
                 acl2::x)
  :rule-classes (:rewrite :rewrite-quoted-constant))

Theorem: equal-of-outcome-fix-1-forward-to-outcome-equiv

(defthm equal-of-outcome-fix-1-forward-to-outcome-equiv
  (implies (equal (outcome-fix acl2::x) acl2::y)
           (outcome-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)

Theorem: equal-of-outcome-fix-2-forward-to-outcome-equiv

(defthm equal-of-outcome-fix-2-forward-to-outcome-equiv
  (implies (equal acl2::x (outcome-fix acl2::y))
           (outcome-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)

Theorem: outcome-equiv-of-outcome-fix-1-forward

(defthm outcome-equiv-of-outcome-fix-1-forward
  (implies (outcome-equiv (outcome-fix acl2::x)
                          acl2::y)
           (outcome-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)

Theorem: outcome-equiv-of-outcome-fix-2-forward

(defthm outcome-equiv-of-outcome-fix-2-forward
  (implies (outcome-equiv acl2::x (outcome-fix acl2::y))
           (outcome-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)

Theorem: outcome-kind$inline-of-outcome-fix-x

(defthm outcome-kind$inline-of-outcome-fix-x
  (equal (outcome-kind$inline (outcome-fix x))
         (outcome-kind$inline x)))

Theorem: outcome-kind$inline-outcome-equiv-congruence-on-x

(defthm outcome-kind$inline-outcome-equiv-congruence-on-x
  (implies (outcome-equiv x x-equiv)
           (equal (outcome-kind$inline x)
                  (outcome-kind$inline x-equiv)))
  :rule-classes :congruence)

Theorem: consp-of-outcome-fix

(defthm consp-of-outcome-fix
  (consp (outcome-fix x))
  :rule-classes :type-prescription)