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Abstract-syntax

Expression-variable-list

Lift expression-variable to lists.

Signature
(expression-variable-list x) → *
Arguments: x — Guard (identifier-listp x).

Definitions and Theorems

Function: expression-variable-list-exec

(defun expression-variable-list-exec (x acc)
  (declare (xargs :guard (identifier-listp x)))
  (declare (xargs :guard t))
  (let ((__function__ 'expression-variable-list-exec))
    (declare (ignorable __function__))
    (if (consp x)
        (expression-variable-list-exec
             (cdr x)
             (cons (expression-variable (car x))
                   acc))
      acc)))

Function: expression-variable-list-nrev

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

Function: expression-variable-list

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

Theorem: nth-of-expression-variable-list

(defthm nth-of-expression-variable-list
  (equal (nth acl2::n
              (expression-variable-list acl2::x))
         (and (< (nfix acl2::n) (len acl2::x))
              (expression-variable (nth acl2::n acl2::x))))
  :rule-classes ((:rewrite)))

Theorem: expression-variable-list-nrev-removal

(defthm expression-variable-list-nrev-removal
  (equal (expression-variable-list-nrev acl2::x acl2::nrev)
         (append acl2::nrev
                 (expression-variable-list acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: expression-variable-list-exec-removal

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

Theorem: expression-variable-list-of-rev

(defthm expression-variable-list-of-rev
  (equal (expression-variable-list (rev acl2::x))
         (rev (expression-variable-list acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: expression-variable-list-of-list-fix

(defthm expression-variable-list-of-list-fix
  (equal (expression-variable-list (list-fix acl2::x))
         (expression-variable-list acl2::x))
  :rule-classes ((:rewrite)))

Theorem: expression-variable-list-of-append

(defthm expression-variable-list-of-append
  (equal (expression-variable-list (append acl2::a acl2::b))
         (append (expression-variable-list acl2::a)
                 (expression-variable-list acl2::b)))
  :rule-classes ((:rewrite)))

Theorem: cdr-of-expression-variable-list

(defthm cdr-of-expression-variable-list
  (equal (cdr (expression-variable-list acl2::x))
         (expression-variable-list (cdr acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: car-of-expression-variable-list

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

Theorem: expression-variable-list-under-iff

(defthm expression-variable-list-under-iff
  (iff (expression-variable-list acl2::x)
       (consp acl2::x))
  :rule-classes ((:rewrite)))

Theorem: consp-of-expression-variable-list

(defthm consp-of-expression-variable-list
  (equal (consp (expression-variable-list acl2::x))
         (consp acl2::x))
  :rule-classes ((:rewrite)))

Theorem: len-of-expression-variable-list

(defthm len-of-expression-variable-list
  (equal (len (expression-variable-list acl2::x))
         (len acl2::x))
  :rule-classes ((:rewrite)))

Theorem: true-listp-of-expression-variable-list

(defthm true-listp-of-expression-variable-list
  (true-listp (expression-variable-list acl2::x))
  :rule-classes :type-prescription)

Theorem: expression-variable-list-when-not-consp

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

Theorem: expression-variable-list-of-cons

(defthm expression-variable-list-of-cons
  (equal (expression-variable-list (cons acl2::a acl2::b))
         (cons (expression-variable acl2::a)
               (expression-variable-list acl2::b)))
  :rule-classes ((:rewrite)))

Theorem: expression-listp-of-expression-variable-list

(defthm expression-listp-of-expression-variable-list
  (expression-listp (expression-variable-list x)))

Theorem: expression-variable-list-of-identifier-list-fix-x

(defthm expression-variable-list-of-identifier-list-fix-x
  (equal (expression-variable-list (identifier-list-fix x))
         (expression-variable-list x)))

Theorem: expression-variable-list-identifier-list-equiv-congruence-on-x

(defthm
     expression-variable-list-identifier-list-equiv-congruence-on-x
  (implies (identifier-list-equiv x x-equiv)
           (equal (expression-variable-list x)
                  (expression-variable-list x-equiv)))
  :rule-classes :congruence)