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• Types

Type-name-list-to-type-list

Lift tyname-to-type to lists.

Signature

(type-name-list-to-type-list x) → *

Arguments

x — Guard (tyname-listp x).

This is an ordinary std::defprojection.

Definitions and Theorems

Function: type-name-list-to-type-list-exec

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

Function: type-name-list-to-type-list-nrev

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

Function: type-name-list-to-type-list

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

Theorem: type-name-list-to-type-list-nrev-removal

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

Theorem: type-name-list-to-type-list-exec-removal

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

Theorem: type-name-list-to-type-list-of-rev

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

Theorem: type-name-list-to-type-list-of-list-fix

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

Theorem: type-name-list-to-type-list-of-append

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

Theorem: cdr-of-type-name-list-to-type-list

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

Theorem: car-of-type-name-list-to-type-list

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

Theorem: type-name-list-to-type-list-under-iff

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

Theorem: consp-of-type-name-list-to-type-list

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

Theorem: len-of-type-name-list-to-type-list

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

Theorem: true-listp-of-type-name-list-to-type-list

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

Theorem: type-name-list-to-type-list-when-not-consp

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

Theorem: type-name-list-to-type-list-of-cons

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

Theorem: type-listp-of-type-name-list-to-type-list

(defthm type-listp-of-type-name-list-to-type-list
  (type-listp (type-name-list-to-type-list x)))

Theorem: type-name-list-to-type-list-of-tyname-list-fix-x

(defthm type-name-list-to-type-list-of-tyname-list-fix-x
  (equal (type-name-list-to-type-list (tyname-list-fix x))
         (type-name-list-to-type-list x)))

Theorem: type-name-list-to-type-list-tyname-list-equiv-congruence-on-x

(defthm
      type-name-list-to-type-list-tyname-list-equiv-congruence-on-x
  (implies (tyname-list-equiv x x-equiv)
           (equal (type-name-list-to-type-list x)
                  (type-name-list-to-type-list x-equiv)))
  :rule-classes :congruence)