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Stor-spec

Stor-spec-fix

Fixing function for stor-spec structures.

Signature
(stor-spec-fix x) → new-x
Arguments: x — Guard (stor-specp x).
Returns: new-x — Type (stor-specp new-x).

Definitions and Theorems

Function: stor-spec-fix$inline

(defun stor-spec-fix$inline (x)
  (declare (xargs :guard (stor-specp x)))
  (mbe :logic
       (case (stor-spec-kind x)
         (:typedef (cons :typedef nil))
         (:extern (cons :extern nil))
         (:static (cons :static nil))
         (:thread (b* ((local (bool-fix (cdr x))))
                    (cons :thread local)))
         (:auto (cons :auto nil))
         (:register (cons :register nil)))
       :exec x))

Theorem: stor-specp-of-stor-spec-fix

(defthm stor-specp-of-stor-spec-fix
  (b* ((new-x (stor-spec-fix$inline x)))
    (stor-specp new-x))
  :rule-classes :rewrite)

Theorem: stor-spec-fix-when-stor-specp

(defthm stor-spec-fix-when-stor-specp
  (implies (stor-specp x)
           (equal (stor-spec-fix x) x)))

Function: stor-spec-equiv$inline

(defun stor-spec-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (stor-specp acl2::x)
                              (stor-specp acl2::y))))
  (equal (stor-spec-fix acl2::x)
         (stor-spec-fix acl2::y)))

Theorem: stor-spec-equiv-is-an-equivalence

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

Theorem: stor-spec-equiv-implies-equal-stor-spec-fix-1

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

Theorem: stor-spec-fix-under-stor-spec-equiv

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

Theorem: equal-of-stor-spec-fix-1-forward-to-stor-spec-equiv

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

Theorem: equal-of-stor-spec-fix-2-forward-to-stor-spec-equiv

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

Theorem: stor-spec-equiv-of-stor-spec-fix-1-forward

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

Theorem: stor-spec-equiv-of-stor-spec-fix-2-forward

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

Theorem: stor-spec-kind$inline-of-stor-spec-fix-x

(defthm stor-spec-kind$inline-of-stor-spec-fix-x
  (equal (stor-spec-kind$inline (stor-spec-fix x))
         (stor-spec-kind$inline x)))

Theorem: stor-spec-kind$inline-stor-spec-equiv-congruence-on-x

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

Theorem: consp-of-stor-spec-fix

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

Theorem: stor-spec-fix$inline-of-stor-spec-fix-x

(defthm stor-spec-fix$inline-of-stor-spec-fix-x
  (equal (stor-spec-fix$inline (stor-spec-fix x))
         (stor-spec-fix$inline x)))

Theorem: stor-spec-fix$inline-stor-spec-equiv-congruence-on-x

(defthm stor-spec-fix$inline-stor-spec-equiv-congruence-on-x
  (implies (stor-spec-equiv x x-equiv)
           (equal (stor-spec-fix$inline x)
                  (stor-spec-fix$inline x-equiv)))
  :rule-classes :congruence)