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• String-literal-char

String-literal-char-fix

Fixing function for string-literal-char structures.

Signature

(string-literal-char-fix x) → new-x

Arguments

x — Guard (string-literal-char-p x).

Returns

new-x — Type (string-literal-char-p new-x).

Definitions and Theorems

Function: string-literal-char-fix$inline

(defun string-literal-char-fix$inline (x)
 (declare (xargs :guard (string-literal-char-p x)))
 (let ((__function__ 'string-literal-char-fix))
  (declare (ignorable __function__))
  (mbe
   :logic
   (case (string-literal-char-kind x)
    (:char
      (b*
        ((get (unicode-stringlit-char-fix (std::da-nth 0 (cdr x)))))
        (cons :char (list get))))
    (:escape
         (b* ((get (escape-sequence-fix (std::da-nth 0 (cdr x)))))
           (cons :escape (list get)))))
   :exec x)))

Theorem: string-literal-char-p-of-string-literal-char-fix

(defthm string-literal-char-p-of-string-literal-char-fix
  (b* ((new-x (string-literal-char-fix$inline x)))
    (string-literal-char-p new-x))
  :rule-classes :rewrite)

Theorem: string-literal-char-fix-when-string-literal-char-p

(defthm string-literal-char-fix-when-string-literal-char-p
  (implies (string-literal-char-p x)
           (equal (string-literal-char-fix x) x)))

Function: string-literal-char-equiv$inline

(defun string-literal-char-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (string-literal-char-p acl2::x)
                              (string-literal-char-p acl2::y))))
  (equal (string-literal-char-fix acl2::x)
         (string-literal-char-fix acl2::y)))

Theorem: string-literal-char-equiv-is-an-equivalence

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

Theorem: string-literal-char-equiv-implies-equal-string-literal-char-fix-1

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

Theorem: string-literal-char-fix-under-string-literal-char-equiv

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

Theorem: equal-of-string-literal-char-fix-1-forward-to-string-literal-char-equiv

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

Theorem: equal-of-string-literal-char-fix-2-forward-to-string-literal-char-equiv

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

Theorem: string-literal-char-equiv-of-string-literal-char-fix-1-forward

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

Theorem: string-literal-char-equiv-of-string-literal-char-fix-2-forward

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

Theorem: string-literal-char-kind$inline-of-string-literal-char-fix-x

(defthm string-literal-char-kind$inline-of-string-literal-char-fix-x
  (equal
       (string-literal-char-kind$inline (string-literal-char-fix x))
       (string-literal-char-kind$inline x)))

Theorem: string-literal-char-kind$inline-string-literal-char-equiv-congruence-on-x

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

Theorem: consp-of-string-literal-char-fix

(defthm consp-of-string-literal-char-fix
  (consp (string-literal-char-fix x))
  :rule-classes :type-prescription)