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Name

Name-fix

Fixing function for name structures.

Signature
(name-fix x) → new-x
Arguments: x — Guard (namep x).
Returns: new-x — Type (namep new-x).

Definitions and Theorems

Function: name-fix$inline

(defun name-fix$inline (x)
  (declare (xargs :guard (namep x)))
  (let ((__function__ 'name-fix))
    (declare (ignorable __function__))
    (mbe :logic
         (case (name-kind x)
           (:simple (b* ((string (str-fix (std::da-nth 0 (cdr x)))))
                      (cons :simple (list string))))
           (:indexed (b* ((string (str-fix (std::da-nth 0 (cdr x))))
                          (index (nfix (std::da-nth 1 (cdr x)))))
                       (cons :indexed (list string index)))))
         :exec x)))

Theorem: namep-of-name-fix

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

Theorem: name-fix-when-namep

(defthm name-fix-when-namep
  (implies (namep x)
           (equal (name-fix x) x)))

Function: name-equiv$inline

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

Theorem: name-equiv-is-an-equivalence

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

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

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

Theorem: name-fix-under-name-equiv

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

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

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

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

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

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

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

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

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

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

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

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

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

Theorem: consp-of-name-fix

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