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• Frame

Frame-fix

Fixing function for frame structures.

Signature

(frame-fix x) → new-x

Arguments

x — Guard (framep x).

Returns

new-x — Type (framep new-x).

Definitions and Theorems

Function: frame-fix$inline

(defun frame-fix$inline (x)
  (declare (xargs :guard (framep x)))
  (let ((__function__ 'frame-fix))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((term (tterm-fix (std::da-nth 0 (cdr x))))
              (binding (binding-fix (std::da-nth 1 (cdr x)))))
           (cons :frame (list term binding)))
         :exec x)))

Theorem: framep-of-frame-fix

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

Theorem: frame-fix-when-framep

(defthm frame-fix-when-framep
  (implies (framep x)
           (equal (frame-fix x) x)))

Function: frame-equiv$inline

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

Theorem: frame-equiv-is-an-equivalence

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

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

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

Theorem: frame-fix-under-frame-equiv

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

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

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

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

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

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

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

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

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