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• Dead-code-eliminator

Fundef-list-dead

Eliminate dead code in lists of function definitions.

Signature

(fundef-list-dead x) → new-fundefs

Arguments

x — Guard (fundef-listp x).

Returns

new-fundefs — Type (fundef-listp new-fundefs).

This is an ordinary std::defprojection.

Definitions and Theorems

Function: fundef-list-dead-exec

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

Function: fundef-list-dead-nrev

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

Function: fundef-list-dead

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

Theorem: fundef-listp-of-fundef-list-dead

(defthm fundef-listp-of-fundef-list-dead
  (b* ((new-fundefs (fundef-list-dead x)))
    (fundef-listp new-fundefs))
  :rule-classes :rewrite)

Theorem: fundef-list-dead-nrev-removal

(defthm fundef-list-dead-nrev-removal
  (equal (fundef-list-dead-nrev acl2::x acl2::nrev)
         (append acl2::nrev (fundef-list-dead acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: fundef-list-dead-exec-removal

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

Theorem: fundef-list-dead-of-take

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

Theorem: set-equiv-congruence-over-fundef-list-dead

(defthm set-equiv-congruence-over-fundef-list-dead
  (implies (set-equiv acl2::x acl2::y)
           (set-equiv (fundef-list-dead acl2::x)
                      (fundef-list-dead acl2::y)))
  :rule-classes ((:congruence)))

Theorem: subsetp-of-fundef-list-dead-when-subsetp

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

Theorem: member-of-fundef-dead-in-fundef-list-dead

(defthm member-of-fundef-dead-in-fundef-list-dead
  (implies (member acl2::k acl2::x)
           (member (fundef-dead acl2::k)
                   (fundef-list-dead acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: fundef-list-dead-of-rev

(defthm fundef-list-dead-of-rev
  (equal (fundef-list-dead (rev acl2::x))
         (rev (fundef-list-dead acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: fundef-list-dead-of-list-fix

(defthm fundef-list-dead-of-list-fix
  (equal (fundef-list-dead (list-fix acl2::x))
         (fundef-list-dead acl2::x))
  :rule-classes ((:rewrite)))

Theorem: fundef-list-dead-of-append

(defthm fundef-list-dead-of-append
  (equal (fundef-list-dead (append acl2::a acl2::b))
         (append (fundef-list-dead acl2::a)
                 (fundef-list-dead acl2::b)))
  :rule-classes ((:rewrite)))

Theorem: cdr-of-fundef-list-dead

(defthm cdr-of-fundef-list-dead
  (equal (cdr (fundef-list-dead acl2::x))
         (fundef-list-dead (cdr acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: car-of-fundef-list-dead

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

Theorem: fundef-list-dead-under-iff

(defthm fundef-list-dead-under-iff
  (iff (fundef-list-dead acl2::x)
       (consp acl2::x))
  :rule-classes ((:rewrite)))

Theorem: consp-of-fundef-list-dead

(defthm consp-of-fundef-list-dead
  (equal (consp (fundef-list-dead acl2::x))
         (consp acl2::x))
  :rule-classes ((:rewrite)))

Theorem: len-of-fundef-list-dead

(defthm len-of-fundef-list-dead
  (equal (len (fundef-list-dead acl2::x))
         (len acl2::x))
  :rule-classes ((:rewrite)))

Theorem: true-listp-of-fundef-list-dead

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

Theorem: fundef-list-dead-when-not-consp

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

Theorem: fundef-list-dead-of-cons

(defthm fundef-list-dead-of-cons
  (equal (fundef-list-dead (cons acl2::a acl2::b))
         (cons (fundef-dead acl2::a)
               (fundef-list-dead acl2::b)))
  :rule-classes ((:rewrite)))

Theorem: fundef-list-dead-of-fundef-list-fix-x

(defthm fundef-list-dead-of-fundef-list-fix-x
  (equal (fundef-list-dead (fundef-list-fix x))
         (fundef-list-dead x)))

Theorem: fundef-list-dead-fundef-list-equiv-congruence-on-x

(defthm fundef-list-dead-fundef-list-equiv-congruence-on-x
  (implies (fundef-list-equiv x x-equiv)
           (equal (fundef-list-dead x)
                  (fundef-list-dead x-equiv)))
  :rule-classes :congruence)