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Opcode

Opcode-fix

Fixing function for opcode structures.

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

Definitions and Theorems

Function: opcode-fix$inline

(defun opcode-fix$inline (x)
 (declare (xargs :guard (opcode-p x)))
 (let ((__function__ 'opcode-fix))
  (declare (ignorable __function__))
  (mbe
   :logic
   (b*
    ((op (24bits-fix
              (std::prod-car (std::prod-car (std::prod-car x)))))
     (mode
      (op-mode-fix
           (std::prod-car
                (std::prod-cdr (std::prod-car (std::prod-car x))))))
     (reg
      (maybe-3bits-fix
           (std::prod-cdr
                (std::prod-cdr (std::prod-car (std::prod-car x))))))
     (mod
        (mod-fix (std::prod-car (std::prod-cdr (std::prod-car x)))))
     (r/m
      (maybe-3bits-fix
           (std::prod-car
                (std::prod-cdr (std::prod-cdr (std::prod-car x))))))
     (pfx
      (op-pfx-fix
           (std::prod-cdr
                (std::prod-cdr (std::prod-cdr (std::prod-car x))))))
     (rex
        (rex-fix (std::prod-car (std::prod-car (std::prod-cdr x)))))
     (vex
      (maybe-vex-fix
           (std::prod-car
                (std::prod-cdr (std::prod-car (std::prod-cdr x))))))
     (evex
      (maybe-evex-fix
           (std::prod-cdr
                (std::prod-cdr (std::prod-car (std::prod-cdr x))))))
     (feat (acl2::symbol-list-fix
                (std::prod-car (std::prod-cdr (std::prod-cdr x)))))
     (superscripts
      (superscripts-fix
           (std::prod-car
                (std::prod-cdr (std::prod-cdr (std::prod-cdr x))))))
     (group
      (opcode-extension-group-fix
          (std::prod-cdr
               (std::prod-cdr (std::prod-cdr (std::prod-cdr x)))))))
    (std::prod-cons
      (std::prod-cons (std::prod-cons op (std::prod-cons mode reg))
                      (std::prod-cons mod (std::prod-cons r/m pfx)))
      (std::prod-cons
           (std::prod-cons rex (std::prod-cons vex evex))
           (std::prod-cons feat
                           (std::prod-cons superscripts group)))))
   :exec x)))

Theorem: opcode-p-of-opcode-fix

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

Theorem: opcode-fix-when-opcode-p

(defthm opcode-fix-when-opcode-p
  (implies (opcode-p x)
           (equal (opcode-fix x) x)))

Function: opcode-equiv$inline

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

Theorem: opcode-equiv-is-an-equivalence

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

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

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

Theorem: opcode-fix-under-opcode-equiv

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

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

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

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

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

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

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

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

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