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• Call-graph

Call-graph-fix

(call-graph-fix x) is a usual ACL2::fty omap fixing function.

Signature

(call-graph-fix x) → *

Arguments

x — Guard (call-graphp x).

Definitions and Theorems

Function: call-graph-fix

(defun call-graph-fix (x)
  (declare (xargs :guard (call-graphp x)))
  (mbe :logic (if (call-graphp x) x nil)
       :exec x))

Theorem: call-graphp-of-call-graph-fix

(defthm call-graphp-of-call-graph-fix
  (call-graphp (call-graph-fix x)))

Theorem: call-graph-fix-when-call-graphp

(defthm call-graph-fix-when-call-graphp
  (implies (call-graphp x)
           (equal (call-graph-fix x) x)))

Theorem: emptyp-call-graph-fix

(defthm emptyp-call-graph-fix
  (implies (or (omap::emptyp x)
               (not (call-graphp x)))
           (omap::emptyp (call-graph-fix x))))

Theorem: emptyp-of-call-graph-fix-to-not-call-graph-or-emptyp

(defthm emptyp-of-call-graph-fix-to-not-call-graph-or-emptyp
  (equal (omap::emptyp (call-graph-fix x))
         (or (not (call-graphp x))
             (omap::emptyp x))))

Function: call-graph-equiv$inline

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

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

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

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

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

Theorem: call-graph-fix-under-call-graph-equiv

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

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

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

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

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

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

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

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

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