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Macro-table

Macro-table-fix

Fixing function for macro-table structures.

Signature
(macro-table-fix x) → new-x
Arguments: x — Guard (macro-tablep x).
Returns: new-x — Type (macro-tablep new-x).

Definitions and Theorems

Function: macro-table-fix$inline

(defun macro-table-fix$inline (x)
 (declare (xargs :guard (macro-tablep x)))
 (mbe
   :logic
   (b* ((alist (ident-macroinfo-alist-fix (cdr (std::da-nth 0 x)))))
     (let ((alist (if (no-duplicatesp-equal (strip-cars alist))
                      alist
                    nil)))
       (list (cons 'alist alist))))
   :exec x))

Theorem: macro-tablep-of-macro-table-fix

(defthm macro-tablep-of-macro-table-fix
  (b* ((new-x (macro-table-fix$inline x)))
    (macro-tablep new-x))
  :rule-classes :rewrite)

Theorem: macro-table-fix-when-macro-tablep

(defthm macro-table-fix-when-macro-tablep
  (implies (macro-tablep x)
           (equal (macro-table-fix x) x)))

Function: macro-table-equiv$inline

(defun macro-table-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (macro-tablep acl2::x)
                              (macro-tablep acl2::y))))
  (equal (macro-table-fix acl2::x)
         (macro-table-fix acl2::y)))

Theorem: macro-table-equiv-is-an-equivalence

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

Theorem: macro-table-equiv-implies-equal-macro-table-fix-1

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

Theorem: macro-table-fix-under-macro-table-equiv

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

Theorem: equal-of-macro-table-fix-1-forward-to-macro-table-equiv

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

Theorem: equal-of-macro-table-fix-2-forward-to-macro-table-equiv

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

Theorem: macro-table-equiv-of-macro-table-fix-1-forward

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

Theorem: macro-table-equiv-of-macro-table-fix-2-forward

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

Theorem: macro-table-fix$inline-of-macro-table-fix-x

(defthm macro-table-fix$inline-of-macro-table-fix-x
  (equal (macro-table-fix$inline (macro-table-fix x))
         (macro-table-fix$inline x)))

Theorem: macro-table-fix$inline-macro-table-equiv-congruence-on-x

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