		Search-engine friendly clone of the ACL2 documentation.

Type

Type-fix

Fixing function for type structures.

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

Definitions and Theorems

Function: type-fix$inline

(defun type-fix$inline (x)
 (declare (xargs :guard (typep x)))
 (let ((__function__ 'type-fix))
  (declare (ignorable __function__))
  (mbe
   :logic
   (case (type-kind x)
    (:void (cons :void (list)))
    (:char (cons :char (list)))
    (:schar (cons :schar (list)))
    (:uchar (cons :uchar (list)))
    (:sshort (cons :sshort (list)))
    (:ushort (cons :ushort (list)))
    (:sint (cons :sint (list)))
    (:uint (cons :uint (list)))
    (:slong (cons :slong (list)))
    (:ulong (cons :ulong (list)))
    (:sllong (cons :sllong (list)))
    (:ullong (cons :ullong (list)))
    (:struct (b* ((tag (ident-fix (std::da-nth 0 (cdr x)))))
               (cons :struct (list tag))))
    (:pointer (b* ((to (type-fix (std::da-nth 0 (cdr x)))))
                (cons :pointer (list to))))
    (:array
         (b* ((of (type-fix (std::da-nth 0 (cdr x))))
              (size (acl2::pos-option-fix (std::da-nth 1 (cdr x)))))
           (cons :array (list of size)))))
   :exec x)))

Theorem: typep-of-type-fix

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

Theorem: type-fix-when-typep

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

Function: type-equiv$inline

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

Theorem: type-equiv-is-an-equivalence

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

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

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

Theorem: type-fix-under-type-equiv

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

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

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

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

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

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

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

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

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

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

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

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

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

Theorem: consp-of-type-fix

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