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Plain-string

Plain-string-fix

Fixing function for plain-string structures.

Signature
(plain-string-fix x) → new-x
Arguments: x — Guard (plain-stringp x).
Returns: new-x — Type (plain-stringp new-x).

Definitions and Theorems

Function: plain-string-fix$inline

(defun plain-string-fix$inline (x)
 (declare (xargs :guard (plain-stringp x)))
 (let ((__function__ 'plain-string-fix))
  (declare (ignorable __function__))
  (mbe
   :logic
   (b*
     ((content
           (string-element-list-fix (cdr (std::da-nth 0 (cdr x)))))
      (double-quote-p
           (acl2::bool-fix (cdr (std::da-nth 1 (cdr x))))))
    (cons
        :plain-string (list (cons 'content content)
                            (cons 'double-quote-p double-quote-p))))
   :exec x)))

Theorem: plain-stringp-of-plain-string-fix

(defthm plain-stringp-of-plain-string-fix
  (b* ((new-x (plain-string-fix$inline x)))
    (plain-stringp new-x))
  :rule-classes :rewrite)

Theorem: plain-string-fix-when-plain-stringp

(defthm plain-string-fix-when-plain-stringp
  (implies (plain-stringp x)
           (equal (plain-string-fix x) x)))

Function: plain-string-equiv$inline

(defun plain-string-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (plain-stringp acl2::x)
                              (plain-stringp acl2::y))))
  (equal (plain-string-fix acl2::x)
         (plain-string-fix acl2::y)))

Theorem: plain-string-equiv-is-an-equivalence

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

Theorem: plain-string-equiv-implies-equal-plain-string-fix-1

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

Theorem: plain-string-fix-under-plain-string-equiv

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

Theorem: equal-of-plain-string-fix-1-forward-to-plain-string-equiv

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

Theorem: equal-of-plain-string-fix-2-forward-to-plain-string-equiv

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

Theorem: plain-string-equiv-of-plain-string-fix-1-forward

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

Theorem: plain-string-equiv-of-plain-string-fix-2-forward

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