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• Stat

Stat-fix

Fixing function for stat structures.

Signature

(stat-fix x) → new-x

Arguments

x — Guard (statp x).

Returns

new-x — Type (statp new-x).

Definitions and Theorems

Function: stat-fix$inline

(defun stat-fix$inline (x)
 (declare (xargs :guard (statp x)))
 (let ((__function__ 'stat-fix))
  (declare (ignorable __function__))
  (mbe :logic
       (b* ((xregs (cdr (std::da-nth 0 x)))
            (pc (cdr (std::da-nth 1 x)))
            (memory (acl2::ubyte8-list-fix (cdr (std::da-nth 2 x))))
            (error (acl2::bool-fix (cdr (std::da-nth 3 x)))))
         (list (cons 'xregs xregs)
               (cons 'pc pc)
               (cons 'memory memory)
               (cons 'error error)))
       :exec x)))

Theorem: statp-of-stat-fix

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

Theorem: stat-fix-when-statp

(defthm stat-fix-when-statp
  (implies (statp x)
           (equal (stat-fix x) x)))

Function: stat-equiv$inline

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

Theorem: stat-equiv-is-an-equivalence

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

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

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

Theorem: stat-fix-under-stat-equiv

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

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

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

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

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

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

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

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

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