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• Values

Type-list-of-value-list

Lift type-of-value to lists.

Signature

(type-list-of-value-list x) → types

Returns

types — Type (type-listp types).

This is an ordinary std::defprojection.

Definitions and Theorems

Function: type-list-of-value-list-exec

(defun type-list-of-value-list-exec (x acc)
 (declare (xargs :guard (value-listp x)))
 (let ((__function__ 'type-list-of-value-list-exec))
  (declare (ignorable __function__))
  (if
   (consp x)
   (type-list-of-value-list-exec (cdr x)
                                 (cons (type-of-value (car x)) acc))
   acc)))

Function: type-list-of-value-list-nrev

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

Function: type-list-of-value-list

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

Theorem: type-listp-of-type-list-of-value-list

(defthm type-listp-of-type-list-of-value-list
  (b* ((types (type-list-of-value-list x)))
    (type-listp types))
  :rule-classes :rewrite)

Theorem: type-list-of-value-list-of-take

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

Theorem: set-equiv-congruence-over-type-list-of-value-list

(defthm set-equiv-congruence-over-type-list-of-value-list
  (implies (set-equiv acl2::x acl2::y)
           (set-equiv (type-list-of-value-list acl2::x)
                      (type-list-of-value-list acl2::y)))
  :rule-classes ((:congruence)))

Theorem: subsetp-of-type-list-of-value-list-when-subsetp

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

Theorem: member-of-type-of-value-in-type-list-of-value-list

(defthm member-of-type-of-value-in-type-list-of-value-list
  (implies (common-lisp::member acl2::k acl2::x)
           (common-lisp::member (type-of-value acl2::k)
                                (type-list-of-value-list acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: type-list-of-value-list-nrev-removal

(defthm type-list-of-value-list-nrev-removal
  (equal (type-list-of-value-list-nrev acl2::x acl2::nrev)
         (append acl2::nrev
                 (type-list-of-value-list acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: type-list-of-value-list-exec-removal

(defthm type-list-of-value-list-exec-removal
  (equal (type-list-of-value-list-exec acl2::x acl2::acc)
         (revappend (type-list-of-value-list acl2::x)
                    acl2::acc))
  :rule-classes ((:rewrite)))

Theorem: type-list-of-value-list-of-rev

(defthm type-list-of-value-list-of-rev
  (equal (type-list-of-value-list (rev acl2::x))
         (rev (type-list-of-value-list acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: type-list-of-value-list-of-list-fix

(defthm type-list-of-value-list-of-list-fix
  (equal (type-list-of-value-list (list-fix acl2::x))
         (type-list-of-value-list acl2::x))
  :rule-classes ((:rewrite)))

Theorem: type-list-of-value-list-of-append

(defthm type-list-of-value-list-of-append
  (equal (type-list-of-value-list (append acl2::a acl2::b))
         (append (type-list-of-value-list acl2::a)
                 (type-list-of-value-list acl2::b)))
  :rule-classes ((:rewrite)))

Theorem: cdr-of-type-list-of-value-list

(defthm cdr-of-type-list-of-value-list
  (equal (cdr (type-list-of-value-list acl2::x))
         (type-list-of-value-list (cdr acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: car-of-type-list-of-value-list

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

Theorem: type-list-of-value-list-under-iff

(defthm type-list-of-value-list-under-iff
  (iff (type-list-of-value-list acl2::x)
       (consp acl2::x))
  :rule-classes ((:rewrite)))

Theorem: consp-of-type-list-of-value-list

(defthm consp-of-type-list-of-value-list
  (equal (consp (type-list-of-value-list acl2::x))
         (consp acl2::x))
  :rule-classes ((:rewrite)))

Theorem: len-of-type-list-of-value-list

(defthm len-of-type-list-of-value-list
  (equal (len (type-list-of-value-list acl2::x))
         (len acl2::x))
  :rule-classes ((:rewrite)))

Theorem: true-listp-of-type-list-of-value-list

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

Theorem: type-list-of-value-list-when-not-consp

(defthm type-list-of-value-list-when-not-consp
  (implies (not (consp acl2::x))
           (equal (type-list-of-value-list acl2::x)
                  nil))
  :rule-classes ((:rewrite)))

Theorem: type-list-of-value-list-of-cons

(defthm type-list-of-value-list-of-cons
  (equal (type-list-of-value-list (cons acl2::a acl2::b))
         (cons (type-of-value acl2::a)
               (type-list-of-value-list acl2::b)))
  :rule-classes ((:rewrite)))

Theorem: type-list-of-value-list-of-value-list-fix-x

(defthm type-list-of-value-list-of-value-list-fix-x
  (equal (type-list-of-value-list (value-list-fix x))
         (type-list-of-value-list x)))

Theorem: type-list-of-value-list-value-list-equiv-congruence-on-x

(defthm type-list-of-value-list-value-list-equiv-congruence-on-x
  (implies (value-list-equiv x x-equiv)
           (equal (type-list-of-value-list x)
                  (type-list-of-value-list x-equiv)))
  :rule-classes :congruence)