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Event

Event-fix

Fixing function for event structures.

Signature
(event-fix x) → new-x
Arguments: x — Guard (eventp x).
Returns: new-x — Type (eventp new-x).

Definitions and Theorems

Function: event-fix$inline

(defun event-fix$inline (x)
 (declare (xargs :guard (eventp x)))
 (let ((__function__ 'event-fix))
  (declare (ignorable __function__))
  (mbe
   :logic
   (case (event-kind x)
    (:create-certificate
       (b* ((certificate (certificate-fix (std::da-nth 0 (cdr x)))))
         (cons :create-certificate (list certificate))))
    (:receive-certificate
         (b* ((message (message-fix (std::da-nth 0 (cdr x)))))
           (cons :receive-certificate (list message))))
    (:store-certificate
        (b* ((certificate (certificate-fix (std::da-nth 0 (cdr x))))
             (validator (address-fix (std::da-nth 1 (cdr x)))))
          (cons :store-certificate (list certificate validator))))
    (:advance-round
         (b* ((validator (address-fix (std::da-nth 0 (cdr x)))))
           (cons :advance-round (list validator))))
    (:commit-anchors
         (b* ((validator (address-fix (std::da-nth 0 (cdr x)))))
           (cons :commit-anchors (list validator))))
    (:timer-expires
         (b* ((validator (address-fix (std::da-nth 0 (cdr x)))))
           (cons :timer-expires (list validator)))))
   :exec x)))

Theorem: eventp-of-event-fix

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

Theorem: event-fix-when-eventp

(defthm event-fix-when-eventp
  (implies (eventp x)
           (equal (event-fix x) x)))

Function: event-equiv$inline

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

Theorem: event-equiv-is-an-equivalence

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

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

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

Theorem: event-fix-under-event-equiv

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

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

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

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

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

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

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

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

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

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

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

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

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

Theorem: consp-of-event-fix

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