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; Proof Script Using :Type-prescription 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 type-prescription rules with a
; conjunction of consequences be used effectively?" When used in a simple
; example like this, the answer appears to be "yes".
; Note that :type-prescription rules can only describe a single "typed term."
(in-theory
; Tau will prove whatever simple tests we concoct, so we disable it.
(disable (tau-system)))
(in-theory
; To reduce the amount of things we need to think about.
(disable natp))
(defund foo (x)
(* (nfix x) 2))
(defund bar (x)
(* (nfix x) 4))
(defthm my-foo-type
(and (natp (foo x))
(integerp (foo x)))
:rule-classes :type-prescription)
(defthm call-of-bar
(implies (natp x)
(natp (bar x))))
(in-theory
; Disable the automatically generated type-prescription rules. We do this
; now instead of earlier, because we needed the :type-prescription for bar to
; prove call-of-bar.
(disable (:type-prescription foo) (:type-prescription bar)))
(defthm use-foo-app
; Proving this theorem in the current theory requires using call-of-bar. When
; call-of-bar goes to relieve its hypothesis, it will use the
; :type-prescription rule my-foo-type. Thus, we know ACL2 is able to use
; conclusions that have more than one type description.
(natp (bar (foo x))))
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