(*<*) ―‹ ******************************************************************** * Project : HOL-CSPM - Architectural operators for HOL-CSP * * Author : Benoît Ballenghien, Safouan Taha, Burkhart Wolff. * * This file : Extension of the step laws * * Copyright (c) 2025 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. ******************************************************************************› (*>*) (*<*) theory Step_CSPM_Laws_Extended imports Non_Deterministic_CSPM_Distributivity Step_CSPM_Laws begin (*>*) subsection ‹The Throw Operator› lemma Throw_Mndetprefix: ‹(⊓a ∈ A → P a) Θ b ∈ B. Q b = ⊓a ∈ A → (if a ∈ B then Q a else P a Θ b ∈ B. Q b)› by (auto simp add: Mndetprefix_GlobalNdet Throw_distrib_GlobalNdet_right write0_def Throw_Mprefix intro: mono_GlobalNdet_eq mono_Mprefix_eq) subsection ‹The Interrupt Operator› lemma Interrupt_Mndetprefix: ‹(⊓a ∈ A → P a) △ Q = Q □ (⊓a ∈ A → P a △ Q)› by (simp add: Mndetprefix_GlobalNdet Interrupt_distrib_GlobalNdet_right write0_def Interrupt_Mprefix Det_distrib_GlobalNdet_left) (*<*) end (*>*)