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Location

Location-fix

Fixing function for location structures.

Signature
(location-fix x) → new-x
Arguments: x — Guard (locationp x).
Returns: new-x — Type (locationp new-x).

Definitions and Theorems

Function: location-fix$inline

(defun location-fix$inline (x)
 (declare (xargs :guard (locationp x)))
 (let ((__function__ 'location-fix))
  (declare (ignorable __function__))
  (mbe
   :logic
   (case (location-kind x)
    (:var (b* ((name (identifier-fix (std::da-nth 0 (cdr x)))))
            (cons :var (list name))))
    (:tuple-comp (b* ((tuple (location-fix (std::da-nth 0 (cdr x))))
                      (index (nfix (std::da-nth 1 (cdr x)))))
                   (cons :tuple-comp (list tuple index))))
    (:struct-comp
         (b* ((struct (location-fix (std::da-nth 0 (cdr x))))
              (name (identifier-fix (std::da-nth 1 (cdr x)))))
           (cons :struct-comp (list struct name)))))
   :exec x)))

Theorem: locationp-of-location-fix

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

Theorem: location-fix-when-locationp

(defthm location-fix-when-locationp
  (implies (locationp x)
           (equal (location-fix x) x)))

Function: location-equiv$inline

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

Theorem: location-equiv-is-an-equivalence

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

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

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

Theorem: location-fix-under-location-equiv

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

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

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

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

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

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

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

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

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

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

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

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

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

Theorem: consp-of-location-fix

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