• Top
  • Documentation
  • Books
  • Boolean-reasoning
  • Projects
  • Debugging
  • Std
  • Proof-automation
  • Macro-libraries
  • ACL2
  • Interfacing-tools
  • Hardware-verification
    • Gl
    • Esim
    • Vl2014
    • Sv
    • Fgl
    • Vwsim
    • Vl
      • Syntax
      • Loader
        • Preprocessor
          • Vl-iframe
          • Preprocessor-ifdef-minutia
          • Vl-preprocess
          • Vl-preprocess-loop
          • Vl-includeskips
          • Vl-read-until-end-of-define
          • Vl-define-formallist->defaults
          • Vl-define
          • Vl-expand-define
          • Vl-read-include
          • Vl-substitute-into-macro-text
          • Vl-process-ifdef
          • Ppst
          • Vl-read-define-default-text
          • Vl-process-define
          • Preprocessor-include-minutia
          • Vl-trim-for-preproc
          • Vl-line-up-define-formals-and-actuals
          • Vl-process-undef
          • Vl-split-define-text
          • Vl-def-context
          • Vl-process-endif
          • Scan-backward-for-non-whitespace
          • Vl-ifdef-context
          • Scan-backward-for-whitespace
          • Vl-atvl-atts-text
          • Scan-for-non-whitespace
          • Vl-check-remaining-formals-all-have-defaults
          • Vl-process-else
          • Vl-is-compiler-directive-p
          • Vl-includeskips-controller-lookup
          • Vl-ifdef-use-map
          • Vl-defines
            • Vl-defines-p
            • Vl-defines-fix
            • Vl-defines-equiv
          • Vl-def-use-map
          • Vl-nice-bytes
          • Vl-safe-previous-n
          • Vl-safe-next-n
          • Vl-ppst-pad
          • Vl-filename-to-string-literal
          • Vl-maybe-update-filemap
          • *vl-preprocess-clock*
          • Vl-ppst->warnings
          • Vl-ppst->iskips
          • Vl-ppst->ifdefmap
          • Vl-ppst->idcache
          • Vl-istack
          • Vl-ppst->istack
          • Vl-ppst->includes
          • Vl-ppst->filemap
          • Vl-ppst->defmap
          • Vl-ppst->defines
          • Vl-ppst->config
          • Vl-ppst->bytes
          • Vl-ppst->activep
          • Vl-ppst->acc
          • Vl-ppst-record-ifdef-use
          • Vl-ppst-record-def-use
          • Vl-ifdef-context-list
          • Vl-def-context-list
          • Vl-ppst-update-warnings
          • Vl-ppst-update-istack
          • Vl-ppst-update-iskips
          • Vl-ppst-update-includes
          • Vl-ppst-update-ifdefmap
          • Vl-ppst-update-idcache
          • Vl-ppst-update-filemap
          • Vl-ppst-update-defmap
          • Vl-ppst-update-defines
          • Vl-ppst-update-config
          • Vl-ppst-update-activep
          • Vl-ppst-update-bytes
          • Vl-ppst-update-acc
          • Vl-ppst-unsound-nreverse-acc
        • Vl-loadconfig
        • Vl-loadstate
        • Lexer
        • Parser
        • Vl-load-merge-descriptions
        • Vl-find-basename/extension
        • Vl-load-file
        • Vl-loadresult
        • Scope-of-defines
        • Vl-find-file
        • Vl-flush-out-descriptions
        • Vl-description
        • Vl-read-file
        • Vl-includeskips-report-gather
        • Vl-load-main
        • Extended-characters
        • Vl-load
        • Vl-load-description
        • Vl-descriptions-left-to-load
        • Inject-warnings
        • Vl-preprocess-debug
        • Vl-write-preprocessor-debug-file
        • Vl-read-file-report-gather
        • Vl-load-descriptions
        • Vl-load-files
        • Translate-off
        • Vl-load-read-file-hook
        • Vl-read-file-report
        • Vl-loadstate-pad
        • Vl-load-summary
        • Vl-collect-modules-from-descriptions
        • Vl-loadstate->warnings
        • Vl-iskips-report
        • Vl-descriptionlist
      • Warnings
      • Getting-started
      • Utilities
      • Printer
      • Kit
      • Mlib
      • Transforms
    • X86isa
    • Svl
    • Rtl
  • Software-verification
  • Math
  • Testing-utilities

• Vl-defines

Vl-defines-p

Recognizer for vl-defines.

Signature

(vl-defines-p x) → *

Definitions and Theorems

Function: vl-defines-p

(defun vl-defines-p (x)
  (declare (xargs :guard t))
  (let ((__function__ 'vl-defines-p))
    (declare (ignorable __function__))
    (if (atom x)
        (eq x nil)
      (and (consp (car x))
           (stringp (caar x))
           (vl-maybe-define-p (cdar x))
           (vl-defines-p (cdr x))))))

Theorem: vl-defines-p-of-revappend

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

Theorem: vl-defines-p-of-remove

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

Theorem: vl-defines-p-of-last

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

Theorem: vl-defines-p-of-nthcdr

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

Theorem: vl-defines-p-of-butlast

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

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

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

Theorem: vl-defines-p-of-repeat

(defthm vl-defines-p-of-repeat
  (iff (vl-defines-p (repeat acl2::n acl2::x))
       (or (and (consp acl2::x)
                (stringp (car acl2::x))
                (vl-maybe-define-p (cdr acl2::x)))
           (zp acl2::n)))
  :rule-classes ((:rewrite)))

Theorem: vl-defines-p-of-take

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

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

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

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

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

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

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

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

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

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

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

Theorem: vl-defines-p-of-rcons

(defthm vl-defines-p-of-rcons
  (iff (vl-defines-p (acl2::rcons acl2::a acl2::x))
       (and (and (consp acl2::a)
                 (stringp (car acl2::a))
                 (vl-maybe-define-p (cdr acl2::a)))
            (vl-defines-p (list-fix acl2::x))))
  :rule-classes ((:rewrite)))

Theorem: vl-defines-p-of-append

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

Theorem: vl-defines-p-of-rev

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

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

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

Theorem: vl-defines-p-of-difference

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

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

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

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

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

Theorem: vl-defines-p-of-union

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

Theorem: vl-defines-p-of-mergesort

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

Theorem: vl-defines-p-of-delete

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

Theorem: vl-defines-p-of-insert

(defthm vl-defines-p-of-insert
  (iff (vl-defines-p (insert acl2::a acl2::x))
       (and (vl-defines-p (sfix acl2::x))
            (and (consp acl2::a)
                 (stringp (car acl2::a))
                 (vl-maybe-define-p (cdr acl2::a)))))
  :rule-classes ((:rewrite)))

Theorem: vl-defines-p-of-sfix

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

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

(defthm vl-defines-p-of-list-fix
  (implies (vl-defines-p acl2::x)
           (vl-defines-p (list-fix acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: true-listp-when-vl-defines-p-compound-recognizer

(defthm true-listp-when-vl-defines-p-compound-recognizer
  (implies (vl-defines-p acl2::x)
           (true-listp acl2::x))
  :rule-classes :compound-recognizer)

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

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

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

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

Theorem: vl-defines-p-of-cons

(defthm vl-defines-p-of-cons
  (equal (vl-defines-p (cons acl2::a acl2::x))
         (and (and (consp acl2::a)
                   (stringp (car acl2::a))
                   (vl-maybe-define-p (cdr acl2::a)))
              (vl-defines-p acl2::x)))
  :rule-classes ((:rewrite)))

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

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

Theorem: vl-maybe-define-p-of-cdr-when-member-equal-of-vl-defines-p

(defthm vl-maybe-define-p-of-cdr-when-member-equal-of-vl-defines-p
  (and (implies (and (vl-defines-p acl2::x)
                     (member-equal acl2::a acl2::x))
                (vl-maybe-define-p (cdr acl2::a)))
       (implies (and (member-equal acl2::a acl2::x)
                     (vl-defines-p acl2::x))
                (vl-maybe-define-p (cdr acl2::a))))
  :rule-classes ((:rewrite)))

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

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

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

(defthm consp-when-member-equal-of-vl-defines-p
  (implies (and (vl-defines-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-defines-p acl2::x)
                                   'nil)
                                 (consp acl2::a)))))

Theorem: vl-defines-p-of-remove-assoc

(defthm vl-defines-p-of-remove-assoc
  (implies (vl-defines-p acl2::x)
           (vl-defines-p (remove-assoc-equal acl2::name acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: vl-defines-p-of-put-assoc

(defthm vl-defines-p-of-put-assoc
 (implies
  (and (vl-defines-p acl2::x))
  (iff (vl-defines-p (put-assoc-equal acl2::name acl2::val acl2::x))
       (and (stringp acl2::name)
            (vl-maybe-define-p acl2::val))))
 :rule-classes ((:rewrite)))

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

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

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

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

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

(defthm vl-defines-p-of-hons-acons
  (equal (vl-defines-p (hons-acons acl2::a acl2::n acl2::x))
         (and (stringp acl2::a)
              (vl-maybe-define-p acl2::n)
              (vl-defines-p acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: vl-maybe-define-p-of-cdr-of-hons-assoc-equal-when-vl-defines-p

(defthm
     vl-maybe-define-p-of-cdr-of-hons-assoc-equal-when-vl-defines-p
 (implies
   (vl-defines-p acl2::x)
   (iff (vl-maybe-define-p (cdr (hons-assoc-equal acl2::k acl2::x)))
        (or (hons-assoc-equal acl2::k acl2::x)
            (vl-maybe-define-p nil))))
 :rule-classes ((:rewrite)))

Theorem: alistp-when-vl-defines-p-rewrite

(defthm alistp-when-vl-defines-p-rewrite
  (implies (vl-defines-p acl2::x)
           (alistp acl2::x))
  :rule-classes ((:rewrite)))

Theorem: alistp-when-vl-defines-p

(defthm alistp-when-vl-defines-p
  (implies (vl-defines-p acl2::x)
           (alistp acl2::x))
  :rule-classes :tau-system)

Theorem: vl-maybe-define-p-of-cdar-when-vl-defines-p

(defthm vl-maybe-define-p-of-cdar-when-vl-defines-p
  (implies (vl-defines-p acl2::x)
           (iff (vl-maybe-define-p (cdar acl2::x))
                (or (consp acl2::x)
                    (vl-maybe-define-p nil))))
  :rule-classes ((:rewrite)))

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

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