		Search-engine friendly clone of the ACL2 documentation.

Field

Field-fix

Fixing function for field structures.

Signature
(field-fix x) → new-x
Arguments: x — Guard (fieldp x).
Returns: new-x — Type (fieldp new-x).

Definitions and Theorems

Function: field-fix$inline

(defun field-fix$inline (x)
  (declare (xargs :guard (fieldp x)))
  (let ((__function__ 'field-fix))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((name (identifier-fix (cdr (std::da-nth 0 x))))
              (type (type-fix (cdr (std::da-nth 1 x)))))
           (list (cons 'name name)
                 (cons 'type type)))
         :exec x)))

Theorem: fieldp-of-field-fix

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

Theorem: field-fix-when-fieldp

(defthm field-fix-when-fieldp
  (implies (fieldp x)
           (equal (field-fix x) x)))

Function: field-equiv$inline

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

Theorem: field-equiv-is-an-equivalence

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

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

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

Theorem: field-fix-under-field-equiv

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

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

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

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

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

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

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

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

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