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• Address

Address-fix

Fixing function for address structures.

Signature

(address-fix x) → new-x

Arguments

x — Guard (address-p x).

Returns

new-x — Type (address-p new-x).

Definitions and Theorems

Function: address-fix$inline

(defun address-fix$inline (x)
 (declare (xargs :guard (address-p x)))
 (let ((__function__ 'address-fix))
  (declare (ignorable __function__))
  (mbe
   :logic
   (b*
    ((path (path-fix (if (or (atom x)
                             (not (eq (car x) :address)))
                         x
                       (nth 1 x))))
     (index
          (acl2::maybe-natp-fix (if (or (atom x)
                                        (not (eq (car x) :address)))
                                    nil
                                  (nth 2 x))))
     (scope (addr-scope-fix (if (or (atom x)
                                    (not (eq (car x) :address)))
                                0
                              (nth 3 x)))))
    (if (and (eql scope 0) (eq index nil))
        path
      (list :address path index scope)))
   :exec x)))

Theorem: address-p-of-address-fix

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

Theorem: address-fix-when-address-p

(defthm address-fix-when-address-p
  (implies (address-p x)
           (equal (address-fix x) x)))

Function: address-equiv$inline

(defun address-equiv$inline (x y)
  (declare (xargs :guard (and (address-p x) (address-p y))))
  (equal (address-fix x) (address-fix y)))

Theorem: address-equiv-is-an-equivalence

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

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

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

Theorem: address-fix-under-address-equiv

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

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

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

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

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

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

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

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

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