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• Lifting

Lift-var-name-list

Lift a list of PFCS variable names to a list of ACL2 symbols.

Signature

(lift-var-name-list x state) → symbols

Returns

symbols — Type (symbol-listp symbols).

This is an ordinary std::defprojection.

Definitions and Theorems

Function: lift-var-name-list-exec

(defun lift-var-name-list-exec (x state acc)
  (declare (xargs :stobjs (state)))
  (declare (xargs :guard (name-listp x)))
  (let ((__function__ 'lift-var-name-list-exec))
    (declare (ignorable __function__))
    (if (consp x)
        (lift-var-name-list-exec (cdr x)
                                 state
                                 (cons (lift-var-name (car x) state)
                                       acc))
      acc)))

Function: lift-var-name-list-nrev

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

Function: lift-var-name-list

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

Theorem: symbol-listp-of-lift-var-name-list

(defthm symbol-listp-of-lift-var-name-list
  (b* ((symbols (lift-var-name-list x state)))
    (symbol-listp symbols))
  :rule-classes :rewrite)

Theorem: lift-var-name-list-of-take

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

Theorem: set-equiv-congruence-over-lift-var-name-list

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

Theorem: subsetp-of-lift-var-name-list-when-subsetp

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

Theorem: member-of-lift-var-name-in-lift-var-name-list

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

Theorem: lift-var-name-list-nrev-removal

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

Theorem: lift-var-name-list-exec-removal

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

Theorem: lift-var-name-list-of-rev

(defthm lift-var-name-list-of-rev
  (equal (lift-var-name-list (rev acl2::x) state)
         (rev (lift-var-name-list acl2::x state)))
  :rule-classes ((:rewrite)))

Theorem: lift-var-name-list-of-list-fix

(defthm lift-var-name-list-of-list-fix
  (equal (lift-var-name-list (list-fix acl2::x)
                             state)
         (lift-var-name-list acl2::x state))
  :rule-classes ((:rewrite)))

Theorem: lift-var-name-list-of-append

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

Theorem: cdr-of-lift-var-name-list

(defthm cdr-of-lift-var-name-list
  (equal (cdr (lift-var-name-list acl2::x state))
         (lift-var-name-list (cdr acl2::x)
                             state))
  :rule-classes ((:rewrite)))

Theorem: car-of-lift-var-name-list

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

Theorem: lift-var-name-list-under-iff

(defthm lift-var-name-list-under-iff
  (iff (lift-var-name-list acl2::x state)
       (consp acl2::x))
  :rule-classes ((:rewrite)))

Theorem: consp-of-lift-var-name-list

(defthm consp-of-lift-var-name-list
  (equal (consp (lift-var-name-list acl2::x state))
         (consp acl2::x))
  :rule-classes ((:rewrite)))

Theorem: len-of-lift-var-name-list

(defthm len-of-lift-var-name-list
  (equal (len (lift-var-name-list acl2::x state))
         (len acl2::x))
  :rule-classes ((:rewrite)))

Theorem: true-listp-of-lift-var-name-list

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

Theorem: lift-var-name-list-when-not-consp

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

Theorem: lift-var-name-list-of-cons

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