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Message

Message-fix

Fixing function for message structures.

Signature
(message-fix x) → new-x
Arguments: x — Guard (messagep x).
Returns: new-x — Type (messagep new-x).

Definitions and Theorems

Function: message-fix$inline

(defun message-fix$inline (x)
 (declare (xargs :guard (messagep x)))
 (let ((__function__ 'message-fix))
  (declare (ignorable __function__))
  (mbe
   :logic
   (case (message-kind x)
    (:proposal
         (b* ((proposal (proposal-fix (std::da-nth 0 (cdr x))))
              (destination (address-fix (std::da-nth 1 (cdr x)))))
           (cons :proposal (list proposal destination))))
    (:endorsement
         (b* ((proposal (proposal-fix (std::da-nth 0 (cdr x))))
              (endorser (address-fix (std::da-nth 1 (cdr x)))))
           (cons :endorsement (list proposal endorser))))
    (:certificate
        (b* ((certificate (certificate-fix (std::da-nth 0 (cdr x))))
             (destination (address-fix (std::da-nth 1 (cdr x)))))
          (cons :certificate (list certificate destination)))))
   :exec x)))

Theorem: messagep-of-message-fix

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

Theorem: message-fix-when-messagep

(defthm message-fix-when-messagep
  (implies (messagep x)
           (equal (message-fix x) x)))

Function: message-equiv$inline

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

Theorem: message-equiv-is-an-equivalence

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

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

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

Theorem: message-fix-under-message-equiv

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

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

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

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

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

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

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

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

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

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

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

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

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

Theorem: consp-of-message-fix

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