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• Vl-datatype-map

Vl-datatype-map-fix

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

Signature

(vl-datatype-map-fix x) → fty::newx

Arguments

x — Guard (vl-datatype-map-p x).

Returns

fty::newx — Type (vl-datatype-map-p fty::newx).

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

Definitions and Theorems

Function: vl-datatype-map-fix$inline

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

Theorem: vl-datatype-map-p-of-vl-datatype-map-fix

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

Theorem: vl-datatype-map-fix-when-vl-datatype-map-p

(defthm vl-datatype-map-fix-when-vl-datatype-map-p
  (implies (vl-datatype-map-p x)
           (equal (vl-datatype-map-fix x) x)))

Function: vl-datatype-map-equiv$inline

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

Theorem: vl-datatype-map-equiv-is-an-equivalence

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

Theorem: vl-datatype-map-equiv-implies-equal-vl-datatype-map-fix-1

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

Theorem: vl-datatype-map-fix-under-vl-datatype-map-equiv

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

Theorem: equal-of-vl-datatype-map-fix-1-forward-to-vl-datatype-map-equiv

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

Theorem: equal-of-vl-datatype-map-fix-2-forward-to-vl-datatype-map-equiv

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

Theorem: vl-datatype-map-equiv-of-vl-datatype-map-fix-1-forward

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

Theorem: vl-datatype-map-equiv-of-vl-datatype-map-fix-2-forward

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

Theorem: cons-of-vl-datatype-fix-v-under-vl-datatype-map-equiv

(defthm cons-of-vl-datatype-fix-v-under-vl-datatype-map-equiv
  (vl-datatype-map-equiv
       (cons (cons acl2::k (vl-datatype-fix acl2::v))
             acl2::x)
       (cons (cons acl2::k acl2::v) acl2::x)))

Theorem: cons-vl-datatype-equiv-congruence-on-v-under-vl-datatype-map-equiv

(defthm
 cons-vl-datatype-equiv-congruence-on-v-under-vl-datatype-map-equiv
 (implies
      (vl-datatype-equiv acl2::v v-equiv)
      (vl-datatype-map-equiv (cons (cons acl2::k acl2::v) acl2::x)
                             (cons (cons acl2::k v-equiv) acl2::x)))
 :rule-classes :congruence)

Theorem: cons-of-vl-datatype-map-fix-y-under-vl-datatype-map-equiv

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

Theorem: cons-vl-datatype-map-equiv-congruence-on-y-under-vl-datatype-map-equiv

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

Theorem: vl-datatype-map-fix-of-acons

(defthm vl-datatype-map-fix-of-acons
  (equal (vl-datatype-map-fix (cons (cons acl2::a acl2::b) x))
         (let ((rest (vl-datatype-map-fix x)))
           (if (and (vl-datatype-p acl2::a))
               (let ((fty::first-key acl2::a)
                     (fty::first-val (vl-datatype-fix acl2::b)))
                 (cons (cons fty::first-key fty::first-val)
                       rest))
             rest))))

Theorem: hons-assoc-equal-of-vl-datatype-map-fix

(defthm hons-assoc-equal-of-vl-datatype-map-fix
  (equal (hons-assoc-equal acl2::k (vl-datatype-map-fix acl2::x))
         (let ((fty::pair (hons-assoc-equal acl2::k acl2::x)))
           (and (vl-datatype-p acl2::k)
                fty::pair
                (cons acl2::k
                      (vl-datatype-fix (cdr fty::pair)))))))

Theorem: vl-datatype-map-fix-of-append

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

Theorem: consp-car-of-vl-datatype-map-fix

(defthm consp-car-of-vl-datatype-map-fix
  (equal (consp (car (vl-datatype-map-fix x)))
         (consp (vl-datatype-map-fix x))))