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• Abstract-syntax-operations

Name-simple-list

Lift name-simple to lists.

Signature

(name-simple-list x) → names

Returns

names — Type (name-listp names).

This is an ordinary std::defprojection.

Definitions and Theorems

Function: name-simple-list-exec

(defun name-simple-list-exec (x acc)
  (declare (xargs :guard (string-listp x)))
  (let ((__function__ 'name-simple-list-exec))
    (declare (ignorable __function__))
    (if (consp x)
        (name-simple-list-exec (cdr x)
                               (cons (name-simple (car x)) acc))
      acc)))

Function: name-simple-list-nrev

(defun name-simple-list-nrev (x acl2::nrev)
  (declare (xargs :stobjs (acl2::nrev)))
  (declare (xargs :guard (string-listp x)))
  (let ((__function__ 'name-simple-list-nrev))
    (declare (ignorable __function__))
    (if (atom x)
        (acl2::nrev-fix acl2::nrev)
      (let ((acl2::nrev (acl2::nrev-push (name-simple (car x))
                                         acl2::nrev)))
        (name-simple-list-nrev (cdr x)
                               acl2::nrev)))))

Function: name-simple-list

(defun name-simple-list (x)
 (declare (xargs :guard (string-listp x)))
 (let ((__function__ 'name-simple-list))
  (declare (ignorable __function__))
  (mbe
   :logic
   (if (consp x)
       (cons (name-simple (car x))
             (name-simple-list (cdr x)))
     nil)
   :exec
   (if (atom x)
       nil
    (acl2::with-local-nrev (name-simple-list-nrev x acl2::nrev))))))

Theorem: name-listp-of-name-simple-list

(defthm name-listp-of-name-simple-list
  (b* ((names (name-simple-list x)))
    (name-listp names))
  :rule-classes :rewrite)

Theorem: name-simple-list-of-take

(defthm name-simple-list-of-take
  (implies (<= (nfix acl2::n) (len acl2::x))
           (equal (name-simple-list (take acl2::n acl2::x))
                  (take acl2::n (name-simple-list acl2::x))))
  :rule-classes ((:rewrite)))

Theorem: set-equiv-congruence-over-name-simple-list

(defthm set-equiv-congruence-over-name-simple-list
  (implies (set-equiv acl2::x acl2::y)
           (set-equiv (name-simple-list acl2::x)
                      (name-simple-list acl2::y)))
  :rule-classes ((:congruence)))

Theorem: subsetp-of-name-simple-list-when-subsetp

(defthm subsetp-of-name-simple-list-when-subsetp
  (implies (subsetp acl2::x acl2::y)
           (subsetp (name-simple-list acl2::x)
                    (name-simple-list acl2::y)))
  :rule-classes ((:rewrite)))

Theorem: member-of-name-simple-in-name-simple-list

(defthm member-of-name-simple-in-name-simple-list
  (implies (member acl2::k acl2::x)
           (member (name-simple acl2::k)
                   (name-simple-list acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: name-simple-list-nrev-removal

(defthm name-simple-list-nrev-removal
  (equal (name-simple-list-nrev acl2::x acl2::nrev)
         (append acl2::nrev (name-simple-list acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: name-simple-list-exec-removal

(defthm name-simple-list-exec-removal
  (equal (name-simple-list-exec acl2::x acl2::acc)
         (revappend (name-simple-list acl2::x)
                    acl2::acc))
  :rule-classes ((:rewrite)))

Theorem: name-simple-list-of-rev

(defthm name-simple-list-of-rev
  (equal (name-simple-list (rev acl2::x))
         (rev (name-simple-list acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: name-simple-list-of-list-fix

(defthm name-simple-list-of-list-fix
  (equal (name-simple-list (list-fix acl2::x))
         (name-simple-list acl2::x))
  :rule-classes ((:rewrite)))

Theorem: name-simple-list-of-append

(defthm name-simple-list-of-append
  (equal (name-simple-list (append acl2::a acl2::b))
         (append (name-simple-list acl2::a)
                 (name-simple-list acl2::b)))
  :rule-classes ((:rewrite)))

Theorem: cdr-of-name-simple-list

(defthm cdr-of-name-simple-list
  (equal (cdr (name-simple-list acl2::x))
         (name-simple-list (cdr acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: car-of-name-simple-list

(defthm car-of-name-simple-list
  (equal (car (name-simple-list acl2::x))
         (and (consp acl2::x)
              (name-simple (car acl2::x))))
  :rule-classes ((:rewrite)))

Theorem: name-simple-list-under-iff

(defthm name-simple-list-under-iff
  (iff (name-simple-list acl2::x)
       (consp acl2::x))
  :rule-classes ((:rewrite)))

Theorem: consp-of-name-simple-list

(defthm consp-of-name-simple-list
  (equal (consp (name-simple-list acl2::x))
         (consp acl2::x))
  :rule-classes ((:rewrite)))

Theorem: len-of-name-simple-list

(defthm len-of-name-simple-list
  (equal (len (name-simple-list acl2::x))
         (len acl2::x))
  :rule-classes ((:rewrite)))

Theorem: true-listp-of-name-simple-list

(defthm true-listp-of-name-simple-list
  (true-listp (name-simple-list acl2::x))
  :rule-classes :type-prescription)

Theorem: name-simple-list-when-not-consp

(defthm name-simple-list-when-not-consp
  (implies (not (consp acl2::x))
           (equal (name-simple-list acl2::x) nil))
  :rule-classes ((:rewrite)))

Theorem: name-simple-list-of-cons

(defthm name-simple-list-of-cons
  (equal (name-simple-list (cons acl2::a acl2::b))
         (cons (name-simple acl2::a)
               (name-simple-list acl2::b)))
  :rule-classes ((:rewrite)))