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; A simple example of how to model nondeterminism in ACL2 using the
; encapsulate feature.
; Copyright David Rager 2012.
; 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.
(in-package "ACL2")
(encapsulate
; Declare the signature of foo, so that foo can be exported. Think of this as
; a C header file.
(((foo) => *))
; Define a non-exported definition of foo, which will be thrown away after the
; scope of the encapsulate is exited. This definition serves as a "witness" to
; ACL2, which allows us to soundly proclaim that a function named foo with the
; properties we will later specify can actually exist.
(local (defun foo () t))
; Define the properties of foo that we want exported and to be available
; beyond the scope of the encapsulate.
(defthm foo-result
(booleanp (foo)))
) ; end encapsulate
(local
(defthm foo-returns-atom-lemma
(implies (booleanp x)
(atom x))))
; We now have a non-deterministic function named foo that is only known to
; return a t or nil. This function is admitted into the logic, and we can
; reason about it, but we can not execute it.
(defthm foo-returns-atom
(atom (foo))
:hints (("Goal" :in-theory (disable atom))))
(include-book "std/testing/must-fail" :dir :system)
(must-fail
(thm (equal (foo) t)))
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