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Escape-sequence

Escape-sequence-fix

Fixing function for escape-sequence structures.

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

Definitions and Theorems

Function: escape-sequence-fix$inline

(defun escape-sequence-fix$inline (x)
 (declare (xargs :guard (escape-sequence-p x)))
 (let ((__function__ 'escape-sequence-fix))
  (declare (ignorable __function__))
  (mbe
   :logic
   (case (escape-sequence-kind x)
    (:b (cons :b (list)))
    (:t (cons :t (list)))
    (:n (cons :n (list)))
    (:f (cons :f (list)))
    (:r (cons :r (list)))
    (:double-quote (cons :double-quote (list)))
    (:single-quote (cons :single-quote (list)))
    (:backslash (cons :backslash (list)))
    (:octal (b* ((value (acl2::ubyte8-fix (std::da-nth 0 (cdr x)))))
              (cons :octal (list value)))))
   :exec x)))

Theorem: escape-sequence-p-of-escape-sequence-fix

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

Theorem: escape-sequence-fix-when-escape-sequence-p

(defthm escape-sequence-fix-when-escape-sequence-p
  (implies (escape-sequence-p x)
           (equal (escape-sequence-fix x) x)))

Function: escape-sequence-equiv$inline

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

Theorem: escape-sequence-equiv-is-an-equivalence

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

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

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

Theorem: escape-sequence-fix-under-escape-sequence-equiv

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

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

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

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

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

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

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

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

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

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

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

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

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

Theorem: consp-of-escape-sequence-fix

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