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Value-type

Value-type-fix

Fixing function for value-type structures.

Signature
(value-type-fix x) → new-x
Arguments: x — Guard (value-typep x).
Returns: new-x — Type (value-typep new-x).

Definitions and Theorems

Function: value-type-fix$inline

(defun value-type-fix$inline (x)
 (declare (xargs :guard (value-typep x)))
 (let ((__function__ 'value-type-fix))
  (declare (ignorable __function__))
  (mbe
    :logic
    (case (value-type-kind x)
      (:plaintext
           (b* ((type (plaintext-type-fix (std::da-nth 0 (cdr x))))
                (vis (visibility-fix (std::da-nth 1 (cdr x)))))
             (cons :plaintext (list type vis))))
      (:record (b* ((name (identifier-fix (std::da-nth 0 (cdr x)))))
                 (cons :record (list name))))
      (:extrecord (b* ((loc (locator-fix (std::da-nth 0 (cdr x)))))
                    (cons :extrecord (list loc)))))
    :exec x)))

Theorem: value-typep-of-value-type-fix

(defthm value-typep-of-value-type-fix
  (b* ((new-x (value-type-fix$inline x)))
    (value-typep new-x))
  :rule-classes :rewrite)

Theorem: value-type-fix-when-value-typep

(defthm value-type-fix-when-value-typep
  (implies (value-typep x)
           (equal (value-type-fix x) x)))

Function: value-type-equiv$inline

(defun value-type-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (value-typep acl2::x)
                              (value-typep acl2::y))))
  (equal (value-type-fix acl2::x)
         (value-type-fix acl2::y)))

Theorem: value-type-equiv-is-an-equivalence

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

Theorem: value-type-equiv-implies-equal-value-type-fix-1

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

Theorem: value-type-fix-under-value-type-equiv

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

Theorem: equal-of-value-type-fix-1-forward-to-value-type-equiv

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

Theorem: equal-of-value-type-fix-2-forward-to-value-type-equiv

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

Theorem: value-type-equiv-of-value-type-fix-1-forward

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

Theorem: value-type-equiv-of-value-type-fix-2-forward

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

Theorem: value-type-kind$inline-of-value-type-fix-x

(defthm value-type-kind$inline-of-value-type-fix-x
  (equal (value-type-kind$inline (value-type-fix x))
         (value-type-kind$inline x)))

Theorem: value-type-kind$inline-value-type-equiv-congruence-on-x

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

Theorem: consp-of-value-type-fix

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