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Format-string

Format-string-fix

Fixing function for format-string structures.

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

Definitions and Theorems

Function: format-string-fix$inline

(defun format-string-fix$inline (x)
 (declare (xargs :guard (format-stringp x)))
 (let ((__function__ 'format-string-fix))
  (declare (ignorable __function__))
  (mbe
    :logic
    (b*
     ((elements
           (char/container-list-fix (cdr (std::da-nth 0 (cdr x))))))
     (let
      ((elements
            (if (char/container-list-no-open/close-brace-p elements)
                elements
              nil)))
      (cons :format-string (list (cons 'elements elements)))))
    :exec x)))

Theorem: format-stringp-of-format-string-fix

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

Theorem: format-string-fix-when-format-stringp

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

Function: format-string-equiv$inline

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

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

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

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

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

Theorem: format-string-fix-under-format-string-equiv

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

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

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

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

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

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

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

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

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