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• Char-literal

Char-literal-fix

Fixing function for char-literal structures.

Signature

(char-literal-fix x) → new-x

Arguments

x — Guard (char-literalp x).

Returns

new-x — Type (char-literalp new-x).

Definitions and Theorems

Function: char-literal-fix$inline

(defun char-literal-fix$inline (x)
 (declare (xargs :guard (char-literalp x)))
 (let ((__function__ 'char-literal-fix))
  (declare (ignorable __function__))
  (mbe
   :logic
   (case (char-literal-kind x)
    (:char
      (b* ((get (unicode-charlit-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: char-literalp-of-char-literal-fix

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

Theorem: char-literal-fix-when-char-literalp

(defthm char-literal-fix-when-char-literalp
  (implies (char-literalp x)
           (equal (char-literal-fix x) x)))

Function: char-literal-equiv$inline

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Theorem: consp-of-char-literal-fix

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