		Search-engine friendly clone of the ACL2 documentation.

Operand

Operand-fix

Fixing function for operand structures.

Signature
(operand-fix x) → new-x
Arguments: x — Guard (operandp x).
Returns: new-x — Type (operandp new-x).

Definitions and Theorems

Function: operand-fix$inline

(defun operand-fix$inline (x)
 (declare (xargs :guard (operandp x)))
 (let ((__function__ 'operand-fix))
  (declare (ignorable __function__))
  (mbe
    :logic
    (case (operand-kind x)
      (:literal (b* ((get (literal-fix (std::da-nth 0 (cdr x)))))
                  (cons :literal (list get))))
      (:register (b* ((get (regaccess-fix (std::da-nth 0 (cdr x)))))
                   (cons :register (list get))))
      (:program (b* ((get (programid-fix (std::da-nth 0 (cdr x)))))
                  (cons :program (list get))))
      (:selfcaller (cons :selfcaller (list))))
    :exec x)))

Theorem: operandp-of-operand-fix

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

Theorem: operand-fix-when-operandp

(defthm operand-fix-when-operandp
  (implies (operandp x)
           (equal (operand-fix x) x)))

Function: operand-equiv$inline

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

Theorem: operand-equiv-is-an-equivalence

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

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

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

Theorem: operand-fix-under-operand-equiv

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

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

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

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

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

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

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

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

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

Theorem: operand-kind$inline-of-operand-fix-x

(defthm operand-kind$inline-of-operand-fix-x
  (equal (operand-kind$inline (operand-fix x))
         (operand-kind$inline x)))

Theorem: operand-kind$inline-operand-equiv-congruence-on-x

(defthm operand-kind$inline-operand-equiv-congruence-on-x
  (implies (operand-equiv x x-equiv)
           (equal (operand-kind$inline x)
                  (operand-kind$inline x-equiv)))
  :rule-classes :congruence)

Theorem: consp-of-operand-fix

(defthm consp-of-operand-fix
  (consp (operand-fix x))
  :rule-classes :type-prescription)