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Objdesign

Objdesign-fix

Fixing function for objdesign structures.

Signature
(objdesign-fix x) → new-x
Arguments: x — Guard (objdesignp x).
Returns: new-x — Type (objdesignp new-x).

Definitions and Theorems

Function: objdesign-fix$inline

(defun objdesign-fix$inline (x)
 (declare (xargs :guard (objdesignp x)))
 (let ((__function__ 'objdesign-fix))
  (declare (ignorable __function__))
  (mbe
    :logic
    (case (objdesign-kind x)
      (:static (b* ((name (ident-fix (std::da-nth 0 (cdr x)))))
                 (cons :static (list name))))
      (:auto (b* ((name (ident-fix (std::da-nth 0 (cdr x))))
                  (frame (nfix (std::da-nth 1 (cdr x))))
                  (scope (nfix (std::da-nth 2 (cdr x)))))
               (cons :auto (list name frame scope))))
      (:alloc (b* ((get (address-fix (std::da-nth 0 (cdr x)))))
                (cons :alloc (list get))))
      (:element (b* ((super (objdesign-fix (std::da-nth 0 (cdr x))))
                     (index (nfix (std::da-nth 1 (cdr x)))))
                  (cons :element (list super index))))
      (:member (b* ((super (objdesign-fix (std::da-nth 0 (cdr x))))
                    (name (ident-fix (std::da-nth 1 (cdr x)))))
                 (cons :member (list super name)))))
    :exec x)))

Theorem: objdesignp-of-objdesign-fix

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

Theorem: objdesign-fix-when-objdesignp

(defthm objdesign-fix-when-objdesignp
  (implies (objdesignp x)
           (equal (objdesign-fix x) x)))

Function: objdesign-equiv$inline

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

Theorem: objdesign-equiv-is-an-equivalence

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

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

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

Theorem: objdesign-fix-under-objdesign-equiv

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

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

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

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

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

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

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

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

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

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

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

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

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

Theorem: consp-of-objdesign-fix

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