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; CUTIL - Centaur Basic Utilities
; Copyright (C) 2008-2011 Centaur Technology
;
; Contact:
;   Centaur Technology Formal Verification Group
;   7600-C N. Capital of Texas Highway, Suite 300, Austin, TX 78731, USA.
;   http://www.centtech.com/
;
; This program is free software; you can redistribute it and/or modify it under
; the terms of the GNU General Public License as published by the Free Software
; Foundation; either version 2 of the License, or (at your option) any later
; version.  This program is distributed in the hope that it will be useful but
; WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
; FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License for
; more details.  You should have received a copy of the GNU General Public
; License along with this program; if not, write to the Free Software
; Foundation, Inc., 51 Franklin Street, Suite 500, Boston, MA 02110-1335, USA.
;
; Original author: Jared Davis <jared@centtech.com>

(in-package "CUTIL")
(include-book "defmapappend")


(local
 (encapsulate
   ()
   (deflist nat-listp (x)
     (natp x)
     :elementp-of-nil nil)

   (defund nats (n)
     (declare (xargs :guard (natp n)))
     (if (zp n)
         nil
       (cons n (nats (- n 1)))))

   (defthm nat-listp-of-nats
     (nat-listp (nats n))
     :hints(("Goal" :in-theory (enable nats))))

   (defprojection map-nats (x)
     (nats x)
     :guard (nat-listp x)
     :optimize nil)

   (defmapappend append-nats (x)
     (nats x)
     :guard (nat-listp x))

   (value-triple (map-nats (nats 5)))
   (value-triple (append-nats (nats 5)))))