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Abstract-syntax

Alternative-list->name-list

Lift alternative->name to lists.

Signature
(alternative-list->name-list x) → *
Arguments: x — Guard (alternative-listp x).

Definitions and Theorems

Function: alternative-list->name-list-exec

(defun alternative-list->name-list-exec (x acc)
  (declare (xargs :guard (alternative-listp x)))
  (declare (xargs :guard t))
  (let ((__function__ 'alternative-list->name-list-exec))
    (declare (ignorable __function__))
    (if (consp x)
        (alternative-list->name-list-exec
             (cdr x)
             (cons (alternative->name (car x)) acc))
      acc)))

Function: alternative-list->name-list-nrev

(defun alternative-list->name-list-nrev (x acl2::nrev)
  (declare (xargs :stobjs (acl2::nrev)))
  (declare (xargs :guard (alternative-listp x)))
  (declare (xargs :guard t))
  (let ((__function__ 'alternative-list->name-list-nrev))
    (declare (ignorable __function__))
    (if (atom x)
        (acl2::nrev-fix acl2::nrev)
      (let ((acl2::nrev (acl2::nrev-push (alternative->name (car x))
                                         acl2::nrev)))
        (alternative-list->name-list-nrev (cdr x)
                                          acl2::nrev)))))

Function: alternative-list->name-list

(defun alternative-list->name-list (x)
  (declare (xargs :guard (alternative-listp x)))
  (declare (xargs :guard t))
  (let ((__function__ 'alternative-list->name-list))
    (declare (ignorable __function__))
    (mbe :logic
         (if (consp x)
             (cons (alternative->name (car x))
                   (alternative-list->name-list (cdr x)))
           nil)
         :exec
         (if (atom x)
             nil
           (acl2::with-local-nrev
                (alternative-list->name-list-nrev x acl2::nrev))))))

Theorem: nth-of-alternative-list->name-list

(defthm nth-of-alternative-list->name-list
  (equal (nth acl2::n
              (alternative-list->name-list acl2::x))
         (and (< (nfix acl2::n) (len acl2::x))
              (alternative->name (nth acl2::n acl2::x))))
  :rule-classes ((:rewrite)))

Theorem: alternative-list->name-list-nrev-removal

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

Theorem: alternative-list->name-list-exec-removal

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

Theorem: alternative-list->name-list-of-rev

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

Theorem: alternative-list->name-list-of-list-fix

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

Theorem: alternative-list->name-list-of-append

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

Theorem: cdr-of-alternative-list->name-list

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

Theorem: car-of-alternative-list->name-list

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

Theorem: alternative-list->name-list-under-iff

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

Theorem: consp-of-alternative-list->name-list

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

Theorem: len-of-alternative-list->name-list

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

Theorem: true-listp-of-alternative-list->name-list

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

Theorem: alternative-list->name-list-when-not-consp

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

Theorem: alternative-list->name-list-of-cons

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

Theorem: identifier-listp-of-alternative-list->name-list

(defthm identifier-listp-of-alternative-list->name-list
  (identifier-listp (alternative-list->name-list x)))

Theorem: alternative-list->name-list-of-alternative-list-fix-x

(defthm alternative-list->name-list-of-alternative-list-fix-x
  (equal (alternative-list->name-list (alternative-list-fix x))
         (alternative-list->name-list x)))

Theorem: alternative-list->name-list-alternative-list-equiv-congruence-on-x

(defthm
 alternative-list->name-list-alternative-list-equiv-congruence-on-x
 (implies (alternative-list-equiv x x-equiv)
          (equal (alternative-list->name-list x)
                 (alternative-list->name-list x-equiv)))
 :rule-classes :congruence)