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Jparam

Jparam-fix

Fixing function for jparam structures.

Signature
(jparam-fix x) → new-x
Arguments: x — Guard (jparamp x).
Returns: new-x — Type (jparamp new-x).

Definitions and Theorems

Function: jparam-fix$inline

(defun jparam-fix$inline (x)
  (declare (xargs :guard (jparamp x)))
  (let ((__function__ 'jparam-fix))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((final? (acl2::bool-fix (cdr (std::da-nth 0 x))))
              (type (jtype-fix (cdr (std::da-nth 1 x))))
              (name (str-fix (cdr (std::da-nth 2 x)))))
           (list (cons 'final? final?)
                 (cons 'type type)
                 (cons 'name name)))
         :exec x)))

Theorem: jparamp-of-jparam-fix

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

Theorem: jparam-fix-when-jparamp

(defthm jparam-fix-when-jparamp
  (implies (jparamp x)
           (equal (jparam-fix x) x)))

Function: jparam-equiv$inline

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

Theorem: jparam-equiv-is-an-equivalence

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

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

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

Theorem: jparam-fix-under-jparam-equiv

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

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

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

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

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

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

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

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

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