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Fundecl

Fundecl-fix

Fixing function for fundecl structures.

Signature
(fundecl-fix x) → new-x
Arguments: x — Guard (fundeclp x).
Returns: new-x — Type (fundeclp new-x).

Definitions and Theorems

Function: fundecl-fix$inline

(defun fundecl-fix$inline (x)
 (declare (xargs :guard (fundeclp x)))
 (let ((__function__ 'fundecl-fix))
  (declare (ignorable __function__))
  (mbe
    :logic
    (b* ((annotations
              (annotation-list-fix (cdr (std::da-nth 0 (cdr x)))))
         (sort (fun-sort-fix (cdr (std::da-nth 1 (cdr x)))))
         (name (identifier-fix (cdr (std::da-nth 2 (cdr x)))))
         (inputs (funparam-list-fix (cdr (std::da-nth 3 (cdr x)))))
         (output (type-fix (cdr (std::da-nth 4 (cdr x)))))
         (body (statement-list-fix (cdr (std::da-nth 5 (cdr x)))))
         (finalizer
              (finalizer-option-fix (cdr (std::da-nth 6 (cdr x))))))
      (cons :fundecl (list (cons 'annotations annotations)
                           (cons 'sort sort)
                           (cons 'name name)
                           (cons 'inputs inputs)
                           (cons 'output output)
                           (cons 'body body)
                           (cons 'finalizer finalizer))))
    :exec x)))

Theorem: fundeclp-of-fundecl-fix

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

Theorem: fundecl-fix-when-fundeclp

(defthm fundecl-fix-when-fundeclp
  (implies (fundeclp x)
           (equal (fundecl-fix x) x)))

Function: fundecl-equiv$inline

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

Theorem: fundecl-equiv-is-an-equivalence

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

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

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

Theorem: fundecl-fix-under-fundecl-equiv

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

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

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

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

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

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

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

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

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