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Header-name

Header-name-fix

Fixing function for header-name structures.

Signature
(header-name-fix x) → new-x
Arguments: x — Guard (header-namep x).
Returns: new-x — Type (header-namep new-x).

Definitions and Theorems

Function: header-name-fix$inline

(defun header-name-fix$inline (x)
  (declare (xargs :guard (header-namep x)))
  (mbe :logic
       (case (header-name-kind x)
         (:angles (b* ((chars (h-char-list-fix (cdr x))))
                    (cons :angles chars)))
         (:quotes (b* ((chars (q-char-list-fix (cdr x))))
                    (cons :quotes chars))))
       :exec x))

Theorem: header-namep-of-header-name-fix

(defthm header-namep-of-header-name-fix
  (b* ((new-x (header-name-fix$inline x)))
    (header-namep new-x))
  :rule-classes :rewrite)

Theorem: header-name-fix-when-header-namep

(defthm header-name-fix-when-header-namep
  (implies (header-namep x)
           (equal (header-name-fix x) x)))

Function: header-name-equiv$inline

(defun header-name-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (header-namep acl2::x)
                              (header-namep acl2::y))))
  (equal (header-name-fix acl2::x)
         (header-name-fix acl2::y)))

Theorem: header-name-equiv-is-an-equivalence

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

Theorem: header-name-equiv-implies-equal-header-name-fix-1

(defthm header-name-equiv-implies-equal-header-name-fix-1
  (implies (header-name-equiv acl2::x x-equiv)
           (equal (header-name-fix acl2::x)
                  (header-name-fix x-equiv)))
  :rule-classes (:congruence))

Theorem: header-name-fix-under-header-name-equiv

(defthm header-name-fix-under-header-name-equiv
  (header-name-equiv (header-name-fix acl2::x)
                     acl2::x)
  :rule-classes (:rewrite :rewrite-quoted-constant))

Theorem: equal-of-header-name-fix-1-forward-to-header-name-equiv

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

Theorem: equal-of-header-name-fix-2-forward-to-header-name-equiv

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

Theorem: header-name-equiv-of-header-name-fix-1-forward

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

Theorem: header-name-equiv-of-header-name-fix-2-forward

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

Theorem: header-name-kind$inline-of-header-name-fix-x

(defthm header-name-kind$inline-of-header-name-fix-x
  (equal (header-name-kind$inline (header-name-fix x))
         (header-name-kind$inline x)))

Theorem: header-name-kind$inline-header-name-equiv-congruence-on-x

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

Theorem: consp-of-header-name-fix

(defthm consp-of-header-name-fix
  (consp (header-name-fix x))
  :rule-classes :type-prescription)

Theorem: header-name-fix$inline-of-header-name-fix-x

(defthm header-name-fix$inline-of-header-name-fix-x
  (equal (header-name-fix$inline (header-name-fix x))
         (header-name-fix$inline x)))

Theorem: header-name-fix$inline-header-name-equiv-congruence-on-x

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