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Escape

Escape-fix

Fixing function for escape structures.

Signature
(escape-fix x) → new-x
Arguments: x — Guard (escapep x).
Returns: new-x — Type (escapep new-x).

Definitions and Theorems

Function: escape-fix$inline

(defun escape-fix$inline (x)
 (declare (xargs :guard (escapep x)))
 (let ((__function__ 'escape-fix))
  (declare (ignorable __function__))
  (mbe
   :logic
   (case (escape-kind x)
    (:simple
         (b* ((unwrap (simple-escape-fix (std::da-nth 0 (cdr x)))))
           (cons :simple (list unwrap))))
    (:oct (b* ((unwrap (oct-escape-fix (std::da-nth 0 (cdr x)))))
            (cons :oct (list unwrap))))
    (:hex
     (b*
      ((unwrap
            (str::hex-digit-char-list-fix (std::da-nth 0 (cdr x)))))
      (cons :hex (list unwrap))))
    (:univ
         (b* ((unwrap (univ-char-name-fix (std::da-nth 0 (cdr x)))))
           (cons :univ (list unwrap)))))
   :exec x)))

Theorem: escapep-of-escape-fix

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

Theorem: escape-fix-when-escapep

(defthm escape-fix-when-escapep
  (implies (escapep x)
           (equal (escape-fix x) x)))

Function: escape-equiv$inline

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

Theorem: escape-equiv-is-an-equivalence

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

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

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

Theorem: escape-fix-under-escape-equiv

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

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

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

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

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

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

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

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

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

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

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

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

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

Theorem: consp-of-escape-fix

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