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• E-conversion

Vl-ealist-p

Alist binding module names to E modules.

Our main E conversion transform proceeds in dependency order, so that the E modules for all submodules should already be available.

A vl-ealist-p is an alist that binds module names to the E modules we have generated for them. We use it to look up the definitions for submodules. To make lookups fast, we generally expect it to be a fast alist.

Definitions and Theorems

Function: vl-ealist-p

(defun vl-ealist-p (x)
       (declare (xargs :guard t))
       (if (consp x)
           (and (consp (car x))
                (stringp (caar x))
                (good-esim-modulep (cdar x))
                (vl-ealist-p (cdr x)))
           t))

Theorem: vl-ealist-p-of-revappend

(defthm vl-ealist-p-of-revappend
        (equal (vl-ealist-p (revappend acl2::x acl2::y))
               (and (vl-ealist-p (list-fix acl2::x))
                    (vl-ealist-p acl2::y)))
        :rule-classes ((:rewrite)))

Theorem: vl-ealist-p-of-remove

(defthm vl-ealist-p-of-remove
        (implies (vl-ealist-p acl2::x)
                 (vl-ealist-p (remove acl2::a acl2::x)))
        :rule-classes ((:rewrite)))

Theorem: vl-ealist-p-of-last

(defthm vl-ealist-p-of-last
        (implies (vl-ealist-p (double-rewrite acl2::x))
                 (vl-ealist-p (last acl2::x)))
        :rule-classes ((:rewrite)))

Theorem: vl-ealist-p-of-nthcdr

(defthm vl-ealist-p-of-nthcdr
        (implies (vl-ealist-p (double-rewrite acl2::x))
                 (vl-ealist-p (nthcdr acl2::n acl2::x)))
        :rule-classes ((:rewrite)))

Theorem: vl-ealist-p-of-butlast

(defthm vl-ealist-p-of-butlast
        (implies (vl-ealist-p (double-rewrite acl2::x))
                 (vl-ealist-p (butlast acl2::x acl2::n)))
        :rule-classes ((:rewrite)))

Theorem: vl-ealist-p-of-update-nth

(defthm
    vl-ealist-p-of-update-nth
    (implies (vl-ealist-p (double-rewrite acl2::x))
             (iff (vl-ealist-p (update-nth acl2::n acl2::y acl2::x))
                  (and (and (consp acl2::y)
                            (stringp (car acl2::y))
                            (good-esim-modulep (cdr acl2::y)))
                       (or (<= (nfix acl2::n) (len acl2::x))
                           (and (consp nil)
                                (stringp (car nil))
                                (good-esim-modulep (cdr nil)))))))
    :rule-classes ((:rewrite)))

Theorem: vl-ealist-p-of-repeat

(defthm vl-ealist-p-of-repeat
        (iff (vl-ealist-p (repeat acl2::n acl2::x))
             (or (and (consp acl2::x)
                      (stringp (car acl2::x))
                      (good-esim-modulep (cdr acl2::x)))
                 (zp acl2::n)))
        :rule-classes ((:rewrite)))

Theorem: vl-ealist-p-of-take

(defthm vl-ealist-p-of-take
        (implies (vl-ealist-p (double-rewrite acl2::x))
                 (iff (vl-ealist-p (take acl2::n acl2::x))
                      (or (and (consp nil)
                               (stringp (car nil))
                               (good-esim-modulep (cdr nil)))
                          (<= (nfix acl2::n) (len acl2::x)))))
        :rule-classes ((:rewrite)))

Theorem: vl-ealist-p-of-union-equal

(defthm vl-ealist-p-of-union-equal
        (equal (vl-ealist-p (union-equal acl2::x acl2::y))
               (and (vl-ealist-p (list-fix acl2::x))
                    (vl-ealist-p (double-rewrite acl2::y))))
        :rule-classes ((:rewrite)))

Theorem: vl-ealist-p-of-intersection-equal-2

(defthm vl-ealist-p-of-intersection-equal-2
        (implies (vl-ealist-p (double-rewrite acl2::y))
                 (vl-ealist-p (intersection-equal acl2::x acl2::y)))
        :rule-classes ((:rewrite)))

Theorem: vl-ealist-p-of-intersection-equal-1

(defthm vl-ealist-p-of-intersection-equal-1
        (implies (vl-ealist-p (double-rewrite acl2::x))
                 (vl-ealist-p (intersection-equal acl2::x acl2::y)))
        :rule-classes ((:rewrite)))

Theorem: vl-ealist-p-of-set-difference-equal

(defthm
     vl-ealist-p-of-set-difference-equal
     (implies (vl-ealist-p acl2::x)
              (vl-ealist-p (set-difference-equal acl2::x acl2::y)))
     :rule-classes ((:rewrite)))

Theorem: vl-ealist-p-set-equiv-congruence

(defthm vl-ealist-p-set-equiv-congruence
        (implies (set-equiv acl2::x acl2::y)
                 (equal (vl-ealist-p acl2::x)
                        (vl-ealist-p acl2::y)))
        :rule-classes :congruence)

Theorem: vl-ealist-p-when-subsetp-equal

(defthm vl-ealist-p-when-subsetp-equal
        (and (implies (and (subsetp-equal acl2::x acl2::y)
                           (vl-ealist-p acl2::y))
                      (vl-ealist-p acl2::x))
             (implies (and (vl-ealist-p acl2::y)
                           (subsetp-equal acl2::x acl2::y))
                      (vl-ealist-p acl2::x)))
        :rule-classes ((:rewrite)))

Theorem: vl-ealist-p-of-rcons

(defthm vl-ealist-p-of-rcons
        (iff (vl-ealist-p (acl2::rcons acl2::a acl2::x))
             (and (and (consp acl2::a)
                       (stringp (car acl2::a))
                       (good-esim-modulep (cdr acl2::a)))
                  (vl-ealist-p (list-fix acl2::x))))
        :rule-classes ((:rewrite)))

Theorem: vl-ealist-p-of-rev

(defthm vl-ealist-p-of-rev
        (equal (vl-ealist-p (rev acl2::x))
               (vl-ealist-p (list-fix acl2::x)))
        :rule-classes ((:rewrite)))

Theorem: vl-ealist-p-of-duplicated-members

(defthm vl-ealist-p-of-duplicated-members
        (implies (vl-ealist-p acl2::x)
                 (vl-ealist-p (duplicated-members acl2::x)))
        :rule-classes ((:rewrite)))

Theorem: vl-ealist-p-of-difference

(defthm vl-ealist-p-of-difference
        (implies (vl-ealist-p acl2::x)
                 (vl-ealist-p (difference acl2::x acl2::y)))
        :rule-classes ((:rewrite)))

Theorem: vl-ealist-p-of-intersect-2

(defthm vl-ealist-p-of-intersect-2
        (implies (vl-ealist-p acl2::y)
                 (vl-ealist-p (intersect acl2::x acl2::y)))
        :rule-classes ((:rewrite)))

Theorem: vl-ealist-p-of-intersect-1

(defthm vl-ealist-p-of-intersect-1
        (implies (vl-ealist-p acl2::x)
                 (vl-ealist-p (intersect acl2::x acl2::y)))
        :rule-classes ((:rewrite)))

Theorem: vl-ealist-p-of-union

(defthm vl-ealist-p-of-union
        (iff (vl-ealist-p (union acl2::x acl2::y))
             (and (vl-ealist-p (sfix acl2::x))
                  (vl-ealist-p (sfix acl2::y))))
        :rule-classes ((:rewrite)))

Theorem: vl-ealist-p-of-mergesort

(defthm vl-ealist-p-of-mergesort
        (iff (vl-ealist-p (mergesort acl2::x))
             (vl-ealist-p (list-fix acl2::x)))
        :rule-classes ((:rewrite)))

Theorem: vl-ealist-p-of-delete

(defthm vl-ealist-p-of-delete
        (implies (vl-ealist-p acl2::x)
                 (vl-ealist-p (delete acl2::k acl2::x)))
        :rule-classes ((:rewrite)))

Theorem: vl-ealist-p-of-insert

(defthm vl-ealist-p-of-insert
        (iff (vl-ealist-p (insert acl2::a acl2::x))
             (and (vl-ealist-p (sfix acl2::x))
                  (and (consp acl2::a)
                       (stringp (car acl2::a))
                       (good-esim-modulep (cdr acl2::a)))))
        :rule-classes ((:rewrite)))

Theorem: vl-ealist-p-of-sfix

(defthm vl-ealist-p-of-sfix
        (iff (vl-ealist-p (sfix acl2::x))
             (or (vl-ealist-p acl2::x)
                 (not (setp acl2::x))))
        :rule-classes ((:rewrite)))

Theorem: vl-ealist-p-of-list-fix

(defthm vl-ealist-p-of-list-fix
        (equal (vl-ealist-p (list-fix acl2::x))
               (vl-ealist-p acl2::x))
        :rule-classes ((:rewrite)))

Theorem: vl-ealist-p-of-append

(defthm vl-ealist-p-of-append
        (equal (vl-ealist-p (append acl2::a acl2::b))
               (and (vl-ealist-p acl2::a)
                    (vl-ealist-p acl2::b)))
        :rule-classes ((:rewrite)))

Theorem: vl-ealist-p-when-not-consp

(defthm vl-ealist-p-when-not-consp
        (implies (not (consp acl2::x))
                 (vl-ealist-p acl2::x))
        :rule-classes ((:rewrite)))

Theorem: vl-ealist-p-of-cdr-when-vl-ealist-p

(defthm vl-ealist-p-of-cdr-when-vl-ealist-p
        (implies (vl-ealist-p (double-rewrite acl2::x))
                 (vl-ealist-p (cdr acl2::x)))
        :rule-classes ((:rewrite)))

Theorem: vl-ealist-p-of-cons

(defthm vl-ealist-p-of-cons
        (equal (vl-ealist-p (cons acl2::a acl2::x))
               (and (and (consp acl2::a)
                         (stringp (car acl2::a))
                         (good-esim-modulep (cdr acl2::a)))
                    (vl-ealist-p acl2::x)))
        :rule-classes ((:rewrite)))

Theorem: vl-ealist-p-of-make-fal

(defthm vl-ealist-p-of-make-fal
        (implies (and (vl-ealist-p acl2::x)
                      (vl-ealist-p acl2::y))
                 (vl-ealist-p (make-fal acl2::x acl2::y)))
        :rule-classes ((:rewrite)))

Theorem: good-esim-modulep-of-cdr-when-member-equal-of-vl-ealist-p

(defthm good-esim-modulep-of-cdr-when-member-equal-of-vl-ealist-p
        (and (implies (and (vl-ealist-p acl2::x)
                           (member-equal acl2::a acl2::x))
                      (good-esim-modulep (cdr acl2::a)))
             (implies (and (member-equal acl2::a acl2::x)
                           (vl-ealist-p acl2::x))
                      (good-esim-modulep (cdr acl2::a))))
        :rule-classes ((:rewrite)))

Theorem: stringp-of-car-when-member-equal-of-vl-ealist-p

(defthm stringp-of-car-when-member-equal-of-vl-ealist-p
        (and (implies (and (vl-ealist-p acl2::x)
                           (member-equal acl2::a acl2::x))
                      (stringp (car acl2::a)))
             (implies (and (member-equal acl2::a acl2::x)
                           (vl-ealist-p acl2::x))
                      (stringp (car acl2::a))))
        :rule-classes ((:rewrite)))

Theorem: consp-when-member-equal-of-vl-ealist-p

(defthm
   consp-when-member-equal-of-vl-ealist-p
   (implies (and (vl-ealist-p acl2::x)
                 (member-equal acl2::a acl2::x))
            (consp acl2::a))
   :rule-classes
   ((:rewrite :backchain-limit-lst (0 0))
    (:rewrite :backchain-limit-lst (0 0)
              :corollary (implies (if (member-equal acl2::a acl2::x)
                                      (vl-ealist-p acl2::x)
                                      'nil)
                                  (consp acl2::a)))))

Theorem: good-esim-modulep-of-cdr-of-assoc-when-vl-ealist-p

(defthm
   good-esim-modulep-of-cdr-of-assoc-when-vl-ealist-p
   (implies (vl-ealist-p acl2::x)
            (good-esim-modulep (cdr (assoc-equal acl2::k acl2::x))))
   :rule-classes ((:rewrite)))

Theorem: vl-ealist-p-of-fast-alist-clean

(defthm vl-ealist-p-of-fast-alist-clean
        (implies (vl-ealist-p acl2::x)
                 (vl-ealist-p (fast-alist-clean acl2::x)))
        :rule-classes ((:rewrite)))

Theorem: vl-ealist-p-of-hons-shrink-alist

(defthm vl-ealist-p-of-hons-shrink-alist
        (implies (and (vl-ealist-p acl2::x)
                      (vl-ealist-p acl2::y))
                 (vl-ealist-p (hons-shrink-alist acl2::x acl2::y)))
        :rule-classes ((:rewrite)))

Theorem: vl-ealist-p-of-hons-acons

(defthm vl-ealist-p-of-hons-acons
        (equal (vl-ealist-p (hons-acons acl2::a acl2::n acl2::x))
               (and (stringp acl2::a)
                    (good-esim-modulep acl2::n)
                    (vl-ealist-p acl2::x)))
        :rule-classes ((:rewrite)))

Theorem: good-esim-modulep-of-cdr-of-hons-assoc-equal-when-vl-ealist-p

(defthm
  good-esim-modulep-of-cdr-of-hons-assoc-equal-when-vl-ealist-p
  (implies
       (vl-ealist-p acl2::x)
       (good-esim-modulep (cdr (hons-assoc-equal acl2::k acl2::x))))
  :rule-classes ((:rewrite)))

Theorem: stringp-of-caar-when-vl-ealist-p

(defthm stringp-of-caar-when-vl-ealist-p
        (implies (vl-ealist-p acl2::x)
                 (iff (stringp (caar acl2::x))
                      (consp acl2::x)))
        :rule-classes ((:rewrite)))

Theorem: good-esim-modulep-of-cdar-when-vl-ealist-p

(defthm good-esim-modulep-of-cdar-when-vl-ealist-p
        (implies (vl-ealist-p acl2::x)
                 (good-esim-modulep (cdar acl2::x)))
        :rule-classes ((:rewrite)))