		Search-engine friendly clone of the ACL2 documentation.

Vl-defines

Vl-defines-fix

(vl-defines-fix x) is an fty alist fixing function that follows the drop-keys strategy.

Signature
(vl-defines-fix x) → fty::newx
Arguments: x — Guard (vl-defines-p x).
Returns: fty::newx — Type (vl-defines-p fty::newx).

Note that in the execution this is just an inline identity function.

Definitions and Theorems

Function: vl-defines-fix$inline

(defun vl-defines-fix$inline (x)
 (declare (xargs :guard (vl-defines-p x)))
 (let ((__function__ 'vl-defines-fix))
  (declare (ignorable __function__))
  (mbe
      :logic
      (if (atom x)
          nil
        (let ((rest (vl-defines-fix (cdr x))))
          (if (and (consp (car x)) (stringp (caar x)))
              (let ((fty::first-key (caar x))
                    (fty::first-val (vl-maybe-define-fix (cdar x))))
                (cons (cons fty::first-key fty::first-val)
                      rest))
            rest)))
      :exec x)))

Theorem: vl-defines-p-of-vl-defines-fix

(defthm vl-defines-p-of-vl-defines-fix
  (b* ((fty::newx (vl-defines-fix$inline x)))
    (vl-defines-p fty::newx))
  :rule-classes :rewrite)

Theorem: vl-defines-fix-when-vl-defines-p

(defthm vl-defines-fix-when-vl-defines-p
  (implies (vl-defines-p x)
           (equal (vl-defines-fix x) x)))

Function: vl-defines-equiv$inline

(defun vl-defines-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (vl-defines-p acl2::x)
                              (vl-defines-p acl2::y))))
  (equal (vl-defines-fix acl2::x)
         (vl-defines-fix acl2::y)))

Theorem: vl-defines-equiv-is-an-equivalence

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

Theorem: vl-defines-equiv-implies-equal-vl-defines-fix-1

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

Theorem: vl-defines-fix-under-vl-defines-equiv

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

Theorem: equal-of-vl-defines-fix-1-forward-to-vl-defines-equiv

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

Theorem: equal-of-vl-defines-fix-2-forward-to-vl-defines-equiv

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

Theorem: vl-defines-equiv-of-vl-defines-fix-1-forward

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

Theorem: vl-defines-equiv-of-vl-defines-fix-2-forward

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

Theorem: cons-of-vl-maybe-define-fix-v-under-vl-defines-equiv

(defthm cons-of-vl-maybe-define-fix-v-under-vl-defines-equiv
  (vl-defines-equiv
       (cons (cons acl2::k (vl-maybe-define-fix acl2::v))
             acl2::x)
       (cons (cons acl2::k acl2::v) acl2::x)))

Theorem: cons-vl-maybe-define-equiv-congruence-on-v-under-vl-defines-equiv

(defthm
  cons-vl-maybe-define-equiv-congruence-on-v-under-vl-defines-equiv
  (implies (vl-maybe-define-equiv acl2::v v-equiv)
           (vl-defines-equiv (cons (cons acl2::k acl2::v) acl2::x)
                             (cons (cons acl2::k v-equiv) acl2::x)))
  :rule-classes :congruence)

Theorem: cons-of-vl-defines-fix-y-under-vl-defines-equiv

(defthm cons-of-vl-defines-fix-y-under-vl-defines-equiv
  (vl-defines-equiv (cons acl2::x (vl-defines-fix acl2::y))
                    (cons acl2::x acl2::y)))

Theorem: cons-vl-defines-equiv-congruence-on-y-under-vl-defines-equiv

(defthm cons-vl-defines-equiv-congruence-on-y-under-vl-defines-equiv
  (implies (vl-defines-equiv acl2::y y-equiv)
           (vl-defines-equiv (cons acl2::x acl2::y)
                             (cons acl2::x y-equiv)))
  :rule-classes :congruence)

Theorem: vl-defines-fix-of-acons

(defthm vl-defines-fix-of-acons
  (equal (vl-defines-fix (cons (cons acl2::a acl2::b) x))
         (let ((rest (vl-defines-fix x)))
           (if (and (stringp acl2::a))
               (let ((fty::first-key acl2::a)
                     (fty::first-val (vl-maybe-define-fix acl2::b)))
                 (cons (cons fty::first-key fty::first-val)
                       rest))
             rest))))

Theorem: hons-assoc-equal-of-vl-defines-fix

(defthm hons-assoc-equal-of-vl-defines-fix
  (equal (hons-assoc-equal acl2::k (vl-defines-fix acl2::x))
         (let ((fty::pair (hons-assoc-equal acl2::k acl2::x)))
           (and (stringp acl2::k)
                fty::pair
                (cons acl2::k
                      (vl-maybe-define-fix (cdr fty::pair)))))))

Theorem: vl-defines-fix-of-append

(defthm vl-defines-fix-of-append
  (equal (vl-defines-fix (append std::a std::b))
         (append (vl-defines-fix std::a)
                 (vl-defines-fix std::b))))

Theorem: consp-car-of-vl-defines-fix

(defthm consp-car-of-vl-defines-fix
  (equal (consp (car (vl-defines-fix x)))
         (consp (vl-defines-fix x))))