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Compustate

Compustate-fix

Fixing function for compustate structures.

Signature
(compustate-fix x) → new-x
Arguments: x — Guard (compustatep x).
Returns: new-x — Type (compustatep new-x).

Definitions and Theorems

Function: compustate-fix$inline

(defun compustate-fix$inline (x)
  (declare (xargs :guard (compustatep x)))
  (let ((__function__ 'compustate-fix))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((static (scope-fix (cdr (std::da-nth 0 x))))
              (frames (frame-list-fix (cdr (std::da-nth 1 x))))
              (heap (heap-fix (cdr (std::da-nth 2 x)))))
           (list (cons 'static static)
                 (cons 'frames frames)
                 (cons 'heap heap)))
         :exec x)))

Theorem: compustatep-of-compustate-fix

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

Theorem: compustate-fix-when-compustatep

(defthm compustate-fix-when-compustatep
  (implies (compustatep x)
           (equal (compustate-fix x) x)))

Function: compustate-equiv$inline

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

Theorem: compustate-equiv-is-an-equivalence

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

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

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

Theorem: compustate-fix-under-compustate-equiv

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

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

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

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

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

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

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

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

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