(*<*) ―‹ ******************************************************************** * Project : CSP-RefTK - A Refinement Toolkit for HOL-CSP * Version : 1.0 * * Author : Burkhart Wolff, Safouan Taha, Lina Ye. * * This file : The Copy-Buffer Example Revisited * * Copyright (c) 2020 Université Paris-Saclay, France * * All rights reserved. * * Redistribution and use in source and binary forms, with or without * modification, are permitted provided that the following conditions are * met: * * * Redistributions of source code must retain the above copyright * notice, this list of conditions and the following disclaimer. * * * Redistributions in binary form must reproduce the above * copyright notice, this list of conditions and the following * disclaimer in the documentation and/or other materials provided * with the distribution. * * * Neither the name of the copyright holders nor the names of its * contributors may be used to endorse or promote products derived * from this software without specific prior written permission. * * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR * A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT * OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT * LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE * OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ******************************************************************************› (*>*) chapter‹Examples› section‹CopyBuffer Refinement over an infinite alphabet› theory CopyBuffer_props imports "HOL-CSP.CopyBuffer" "HOL-CSP.Assertions" begin subsection‹ The Copy-Buffer vs. reference processes › lemma DF_COPY: "(DF (range left ∪ range right)) ⊑⇩F⇩D COPY" by (simp add: DF_COPY) subsection‹ ... and abstract consequences › corollary df_COPY: "deadlock_free COPY" and lf_COPY: "lifelock_free COPY" apply (meson DF_COPY DF_Univ_freeness UNIV_not_empty image_is_empty sup_eq_bot_iff) by (meson CHAOS_DF_refine_FD DF_COPY DF_Univ_freeness UNIV_not_empty deadlock_free_def image_is_empty lifelock_free_def sup_eq_bot_iff trans_FD) corollary df_v2_COPY: "deadlock_free_v2 COPY" and lf_v2_COPY: "lifelock_free_v2 COPY" and nt_COPY: "non_terminating COPY" apply (simp add: df_COPY deadlock_free_is_deadlock_free_v2) apply (simp add: lf_COPY lifelock_free_is_lifelock_free_v2) using lf_COPY lifelock_free_is_non_terminating by blast lemma DF_SYSTEM: "DF UNIV ⊑⇩F⇩D SYSTEM" using DF_subset[of "(range left ∪ range right)" UNIV, simplified] DF_COPY impl_refines_spec trans_FD by blast corollary df_SYSTEM: "deadlock_free SYSTEM" and lf_SYSTEM: "lifelock_free SYSTEM" apply (simp add: DF_SYSTEM deadlock_free_def) using CHAOS_DF_refine_FD DF_SYSTEM lifelock_free_def trans_FD by blast corollary df_v2_SYSTEM: "deadlock_free_v2 SYSTEM" and lf_v2_SYSTEM: "lifelock_free_v2 SYSTEM" and nt_SYSTEM: "non_terminating SYSTEM" apply (simp add: df_SYSTEM deadlock_free_is_deadlock_free_v2) apply (simp add: lf_SYSTEM lifelock_free_is_lifelock_free_v2) using lf_SYSTEM lifelock_free_is_non_terminating by blast end