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Backtrace-frame

Backtrace-frame-fix

Fixing function for backtrace-frame structures.

Signature
(backtrace-frame-fix x) → new-x
Arguments: x — Guard (backtrace-frame-p x).
Returns: new-x — Type (backtrace-frame-p new-x).

Definitions and Theorems

Function: backtrace-frame-fix$inline

(defun backtrace-frame-fix$inline (x)
  (declare (xargs :guard (backtrace-frame-p x)))
  (let ((__function__ 'backtrace-frame-fix))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((index (nfix (std::da-nth 0 x)))
              (rune (maybe-fgl-generic-rune-fix (std::da-nth 1 x)))
              (objs (fgl-object-bindings-fix (std::da-nth 2 x))))
           (list index rune objs))
         :exec x)))

Theorem: backtrace-frame-p-of-backtrace-frame-fix

(defthm backtrace-frame-p-of-backtrace-frame-fix
  (b* ((new-x (backtrace-frame-fix$inline x)))
    (backtrace-frame-p new-x))
  :rule-classes :rewrite)

Theorem: backtrace-frame-fix-when-backtrace-frame-p

(defthm backtrace-frame-fix-when-backtrace-frame-p
  (implies (backtrace-frame-p x)
           (equal (backtrace-frame-fix x) x)))

Function: backtrace-frame-equiv$inline

(defun backtrace-frame-equiv$inline (x y)
  (declare (xargs :guard (and (backtrace-frame-p x)
                              (backtrace-frame-p y))))
  (equal (backtrace-frame-fix x)
         (backtrace-frame-fix y)))

Theorem: backtrace-frame-equiv-is-an-equivalence

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

Theorem: backtrace-frame-equiv-implies-equal-backtrace-frame-fix-1

(defthm backtrace-frame-equiv-implies-equal-backtrace-frame-fix-1
  (implies (backtrace-frame-equiv x x-equiv)
           (equal (backtrace-frame-fix x)
                  (backtrace-frame-fix x-equiv)))
  :rule-classes (:congruence))

Theorem: backtrace-frame-fix-under-backtrace-frame-equiv

(defthm backtrace-frame-fix-under-backtrace-frame-equiv
  (backtrace-frame-equiv (backtrace-frame-fix x)
                         x)
  :rule-classes (:rewrite :rewrite-quoted-constant))

Theorem: equal-of-backtrace-frame-fix-1-forward-to-backtrace-frame-equiv

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

Theorem: equal-of-backtrace-frame-fix-2-forward-to-backtrace-frame-equiv

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

Theorem: backtrace-frame-equiv-of-backtrace-frame-fix-1-forward

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

Theorem: backtrace-frame-equiv-of-backtrace-frame-fix-2-forward

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