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; Proof Script Using :Linear Rules
; Copyright (C) 2014, Oracle and/or its affiliates. All rights reserved.
;
; License: (An MIT/X11-style license)
;
; Permission is hereby granted, free of charge, to any person obtaining a
; copy of this software and associated documentation files (the "Software"),
; to deal in the Software without restriction, including without limitation
; the rights to use, copy, modify, merge, publish, distribute, sublicense,
; and/or sell copies of the Software, and to permit persons to whom the
; Software is furnished to do so, subject to the following conditions:
;
; The above copyright notice and this permission notice shall be included in
; all copies or substantial portions of the Software.
;
; THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
; IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
; FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
; AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
; LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
; FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
; DEALINGS IN THE SOFTWARE.
;
; Original author: David L. Rager <david.rager@oracle.com>
(in-package "ACL2")
; The below example answers the question, "Can :linear rules with a
; conjunction of consequences be used effectively?" When used in a simple
; example like this, the answer appears to be yes.
(in-theory
; Tau has some ability to reason about intervals, so we disable it.
(disable (tau-system)))
(in-theory
; To reduce the amount of things we need to think about.
(disable natp))
(defun foo (x)
(min (expt 2 32) (+ (nfix x) (nfix x))))
(defun bar (x)
(min (expt 2 64) (* (nfix x) 4)))
(defthm my-foo-bar-linear
(and (<= (foo x) (expt 2 32))
(<= (bar x) (expt 2 64)))
:rule-classes :linear)
(in-theory (disable foo bar))
(defthm call-of-foo
; Uses my-foo-bar-linear
(<= (foo x) (expt 2 40)))
; We've demonstrated the point, but our proof for baz-linear is slightly more
; fun, so we include it anyway.
(defun baz (x)
(* (bar x) 2))
(defthm baz-linear
; Uses my-foo-bar-linear
(<= (baz x) (expt 2 130)))
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