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Call-dinfo

Call-dinfo-fix

Fixing function for call-dinfo structures.

Signature
(call-dinfo-fix x) → new-x
Arguments: x — Guard (call-dinfop x).
Returns: new-x — Type (call-dinfop new-x).

Definitions and Theorems

Function: call-dinfo-fix$inline

(defun call-dinfo-fix$inline (x)
 (declare (xargs :guard (call-dinfop x)))
 (let ((__function__ 'call-dinfo-fix))
  (declare (ignorable __function__))
  (mbe
     :logic
     (b* ((fun (identifier-fix (cdr (std::da-nth 0 x))))
          (scopes (vcscope-dinfo-list-fix (cdr (std::da-nth 1 x)))))
       (list (cons 'fun fun)
             (cons 'scopes scopes)))
     :exec x)))

Theorem: call-dinfop-of-call-dinfo-fix

(defthm call-dinfop-of-call-dinfo-fix
  (b* ((new-x (call-dinfo-fix$inline x)))
    (call-dinfop new-x))
  :rule-classes :rewrite)

Theorem: call-dinfo-fix-when-call-dinfop

(defthm call-dinfo-fix-when-call-dinfop
  (implies (call-dinfop x)
           (equal (call-dinfo-fix x) x)))

Function: call-dinfo-equiv$inline

(defun call-dinfo-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (call-dinfop acl2::x)
                              (call-dinfop acl2::y))))
  (equal (call-dinfo-fix acl2::x)
         (call-dinfo-fix acl2::y)))

Theorem: call-dinfo-equiv-is-an-equivalence

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

Theorem: call-dinfo-equiv-implies-equal-call-dinfo-fix-1

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

Theorem: call-dinfo-fix-under-call-dinfo-equiv

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

Theorem: equal-of-call-dinfo-fix-1-forward-to-call-dinfo-equiv

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

Theorem: equal-of-call-dinfo-fix-2-forward-to-call-dinfo-equiv

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

Theorem: call-dinfo-equiv-of-call-dinfo-fix-1-forward

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

Theorem: call-dinfo-equiv-of-call-dinfo-fix-2-forward

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