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C-char

C-char-fix

Fixing function for c-char structures.

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

Definitions and Theorems

Function: c-char-fix$inline

(defun c-char-fix$inline (x)
  (declare (xargs :guard (c-char-p x)))
  (mbe :logic
       (case (c-char-kind x)
         (:char (b* ((code (nfix (cdr x))))
                  (cons :char code)))
         (:escape (b* ((escape (escape-fix (cdr x))))
                    (cons :escape escape))))
       :exec x))

Theorem: c-char-p-of-c-char-fix

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

Theorem: c-char-fix-when-c-char-p

(defthm c-char-fix-when-c-char-p
  (implies (c-char-p x)
           (equal (c-char-fix x) x)))

Function: c-char-equiv$inline

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

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

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

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

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

Theorem: c-char-fix-under-c-char-equiv

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

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

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

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

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

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

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

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

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

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

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

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

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

Theorem: consp-of-c-char-fix

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

Theorem: c-char-fix$inline-of-c-char-fix-x

(defthm c-char-fix$inline-of-c-char-fix-x
  (equal (c-char-fix$inline (c-char-fix x))
         (c-char-fix$inline x)))

Theorem: c-char-fix$inline-c-char-equiv-congruence-on-x

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