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Jtype

Jtype-fix

Fixing function for jtype structures.

Signature
(jtype-fix x) → new-x
Arguments: x — Guard (jtypep x).
Returns: new-x — Type (jtypep new-x).

Definitions and Theorems

Function: jtype-fix$inline

(defun jtype-fix$inline (x)
 (declare (xargs :guard (jtypep x)))
 (let ((__function__ 'jtype-fix))
  (declare (ignorable __function__))
  (mbe
   :logic
   (case (jtype-kind x)
    (:prim (b* ((type (primitive-type-fix (std::da-nth 0 (cdr x)))))
             (cons :prim (list type))))
    (:class (b* ((name (str-fix (std::da-nth 0 (cdr x)))))
              (cons :class (list name))))
    (:array (b* ((comp (jtype-fix (std::da-nth 0 (cdr x)))))
              (cons :array (list comp)))))
   :exec x)))

Theorem: jtypep-of-jtype-fix

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

Theorem: jtype-fix-when-jtypep

(defthm jtype-fix-when-jtypep
  (implies (jtypep x)
           (equal (jtype-fix x) x)))

Function: jtype-equiv$inline

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

Theorem: jtype-equiv-is-an-equivalence

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

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

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

Theorem: jtype-fix-under-jtype-equiv

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

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

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

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

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

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

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

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

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

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

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

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

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

Theorem: consp-of-jtype-fix

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