Eliminate dead code in lists of function definitions.
(fundef-list-dead x) → new-fundefs
This is an ordinary std::defprojection.
Function:
(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:
(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:
(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:
(defthm fundef-listp-of-fundef-list-dead (b* ((new-fundefs (fundef-list-dead x))) (fundef-listp new-fundefs)) :rule-classes :rewrite)
Theorem:
(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:
(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:
(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:
(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:
(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:
(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:
(defthm fundef-list-dead-of-rev (equal (fundef-list-dead (rev acl2::x)) (rev (fundef-list-dead acl2::x))) :rule-classes ((:rewrite)))
Theorem:
(defthm fundef-list-dead-of-list-fix (equal (fundef-list-dead (list-fix acl2::x)) (fundef-list-dead acl2::x)) :rule-classes ((:rewrite)))
Theorem:
(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:
(defthm cdr-of-fundef-list-dead (equal (cdr (fundef-list-dead acl2::x)) (fundef-list-dead (cdr acl2::x))) :rule-classes ((:rewrite)))
Theorem:
(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:
(defthm fundef-list-dead-under-iff (iff (fundef-list-dead acl2::x) (consp acl2::x)) :rule-classes ((:rewrite)))
Theorem:
(defthm consp-of-fundef-list-dead (equal (consp (fundef-list-dead acl2::x)) (consp acl2::x)) :rule-classes ((:rewrite)))
Theorem:
(defthm len-of-fundef-list-dead (equal (len (fundef-list-dead acl2::x)) (len acl2::x)) :rule-classes ((:rewrite)))
Theorem:
(defthm true-listp-of-fundef-list-dead (true-listp (fundef-list-dead acl2::x)) :rule-classes :type-prescription)
Theorem:
(defthm fundef-list-dead-when-not-consp (implies (not (consp acl2::x)) (equal (fundef-list-dead acl2::x) nil)) :rule-classes ((:rewrite)))
Theorem:
(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:
(defthm fundef-list-dead-of-fundef-list-fix-x (equal (fundef-list-dead (fundef-list-fix x)) (fundef-list-dead x)))
Theorem:
(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)