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Plexeme

Plexeme-fix

Fixing function for plexeme structures.

Signature
(plexeme-fix x) → new-x
Arguments: x — Guard (plexemep x).
Returns: new-x — Type (plexemep new-x).

Definitions and Theorems

Function: plexeme-fix$inline

(defun plexeme-fix$inline (x)
 (declare (xargs :guard (plexemep x)))
 (mbe
  :logic
  (case (plexeme-kind x)
    (:header (b* ((name (header-name-fix (std::da-nth 0 (cdr x)))))
               (cons :header (list name))))
    (:ident (b* ((ident (ident-fix (std::da-nth 0 (cdr x)))))
              (cons :ident (list ident))))
    (:number (b* ((number (pnumber-fix (std::da-nth 0 (cdr x)))))
               (cons :number (list number))))
    (:char (b* ((const (cconst-fix (std::da-nth 0 (cdr x)))))
             (cons :char (list const))))
    (:string (b* ((literal (stringlit-fix (std::da-nth 0 (cdr x)))))
               (cons :string (list literal))))
    (:punctuator
         (b* ((punctuator (acl2::str-fix (std::da-nth 0 (cdr x)))))
           (cons :punctuator (list punctuator))))
    (:other (b* ((char (nfix (std::da-nth 0 (cdr x)))))
              (cons :other (list char))))
    (:block-comment
         (b* ((content (nat-list-fix (std::da-nth 0 (cdr x)))))
           (cons :block-comment (list content))))
    (:line-comment
         (b* ((content (nat-list-fix (std::da-nth 0 (cdr x)))))
           (cons :line-comment (list content))))
    (:newline (b* ((chars (newline-fix (std::da-nth 0 (cdr x)))))
                (cons :newline (list chars))))
    (:spaces (b* ((count (pos-fix (std::da-nth 0 (cdr x)))))
               (cons :spaces (list count))))
    (:horizontal-tab (cons :horizontal-tab (list)))
    (:vertical-tab (cons :vertical-tab (list)))
    (:form-feed (cons :form-feed (list))))
  :exec x))

Theorem: plexemep-of-plexeme-fix

(defthm plexemep-of-plexeme-fix
  (b* ((new-x (plexeme-fix$inline x)))
    (plexemep new-x))
  :rule-classes :rewrite)

Theorem: plexeme-fix-when-plexemep

(defthm plexeme-fix-when-plexemep
  (implies (plexemep x)
           (equal (plexeme-fix x) x)))

Function: plexeme-equiv$inline

(defun plexeme-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (plexemep acl2::x)
                              (plexemep acl2::y))))
  (equal (plexeme-fix acl2::x)
         (plexeme-fix acl2::y)))

Theorem: plexeme-equiv-is-an-equivalence

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

Theorem: plexeme-equiv-implies-equal-plexeme-fix-1

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

Theorem: plexeme-fix-under-plexeme-equiv

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

Theorem: equal-of-plexeme-fix-1-forward-to-plexeme-equiv

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

Theorem: equal-of-plexeme-fix-2-forward-to-plexeme-equiv

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

Theorem: plexeme-equiv-of-plexeme-fix-1-forward

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

Theorem: plexeme-equiv-of-plexeme-fix-2-forward

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

Theorem: plexeme-kind$inline-of-plexeme-fix-x

(defthm plexeme-kind$inline-of-plexeme-fix-x
  (equal (plexeme-kind$inline (plexeme-fix x))
         (plexeme-kind$inline x)))

Theorem: plexeme-kind$inline-plexeme-equiv-congruence-on-x

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

Theorem: consp-of-plexeme-fix

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

Theorem: plexeme-fix$inline-of-plexeme-fix-x

(defthm plexeme-fix$inline-of-plexeme-fix-x
  (equal (plexeme-fix$inline (plexeme-fix x))
         (plexeme-fix$inline x)))

Theorem: plexeme-fix$inline-plexeme-equiv-congruence-on-x

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