139 lines
6.4 KiB
Plaintext
139 lines
6.4 KiB
Plaintext
(*****************************************************************************
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* Featherweight-OCL --- A Formal Semantics for UML-OCL Version OCL 2.5
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* for the OMG Standard.
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* http://www.brucker.ch/projects/hol-testgen/
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*
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* UML_Void.thy --- Library definitions.
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* This file is part of HOL-TestGen.
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*
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* Copyright (c) 2012-2015 Université Paris-Saclay, Univ. Paris-Sud, France
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* 2013-2015 IRT SystemX, France
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*
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* All rights reserved.
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*
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* Redistribution and use in source and binary forms, with or without
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* modification, are permitted provided that the following conditions are
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* met:
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*
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* * Redistributions of source code must retain the above copyright
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* notice, this list of conditions and the following disclaimer.
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*
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* * Redistributions in binary form must reproduce the above
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* copyright notice, this list of conditions and the following
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* disclaimer in the documentation and/or other materials provided
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* with the distribution.
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*
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* * Neither the name of the copyright holders nor the names of its
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* contributors may be used to endorse or promote products derived
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* from this software without specific prior written permission.
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*
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* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
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* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
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* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
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* A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
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* OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
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* SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
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* LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
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* DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
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* THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
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* (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
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* OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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******************************************************************************)
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theory UML_Void
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imports "../UML_PropertyProfiles"
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begin
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section\<open>Basic Type Void: Operations\<close>
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(* For technical reasons, the type does not contain to the null-class yet. *)
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text \<open>This \emph{minimal} OCL type contains only two elements:
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@{term "invalid"} and @{term "null"}.
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@{term "Void"} could initially be defined as @{typ "unit option option"},
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however the cardinal of this type is more than two, so it would have the cost to consider
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\<open>Some None\<close> and \<open>Some (Some ())\<close> seemingly everywhere.\<close>
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subsection\<open>Fundamental Properties on Voids: Strict Equality\<close>
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subsubsection\<open>Definition\<close>
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instantiation Void\<^sub>b\<^sub>a\<^sub>s\<^sub>e :: bot
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begin
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definition bot_Void_def: "(bot_class.bot :: Void\<^sub>b\<^sub>a\<^sub>s\<^sub>e) \<equiv> Abs_Void\<^sub>b\<^sub>a\<^sub>s\<^sub>e None"
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instance proof show "\<exists>x:: Void\<^sub>b\<^sub>a\<^sub>s\<^sub>e. x \<noteq> bot"
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apply(rule_tac x="Abs_Void\<^sub>b\<^sub>a\<^sub>s\<^sub>e \<lfloor>None\<rfloor>" in exI)
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apply(simp add:bot_Void_def, subst Abs_Void\<^sub>b\<^sub>a\<^sub>s\<^sub>e_inject)
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apply(simp_all add: null_option_def bot_option_def)
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done
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qed
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end
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instantiation Void\<^sub>b\<^sub>a\<^sub>s\<^sub>e :: null
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begin
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definition null_Void_def: "(null::Void\<^sub>b\<^sub>a\<^sub>s\<^sub>e) \<equiv> Abs_Void\<^sub>b\<^sub>a\<^sub>s\<^sub>e \<lfloor> None \<rfloor>"
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instance proof show "(null:: Void\<^sub>b\<^sub>a\<^sub>s\<^sub>e) \<noteq> bot"
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apply(simp add:null_Void_def bot_Void_def, subst Abs_Void\<^sub>b\<^sub>a\<^sub>s\<^sub>e_inject)
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apply(simp_all add: null_option_def bot_option_def)
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done
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qed
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end
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text\<open>The last basic operation belonging to the fundamental infrastructure
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of a value-type in OCL is the weak equality, which is defined similar
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to the @{typ "('\<AA>)Void"}-case as strict extension of the strong equality:\<close>
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overloading StrictRefEq \<equiv> "StrictRefEq :: [('\<AA>)Void,('\<AA>)Void] \<Rightarrow> ('\<AA>)Boolean"
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begin
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definition StrictRefEq\<^sub>V\<^sub>o\<^sub>i\<^sub>d[code_unfold] :
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"(x::('\<AA>)Void) \<doteq> y \<equiv> \<lambda> \<tau>. if (\<upsilon> x) \<tau> = true \<tau> \<and> (\<upsilon> y) \<tau> = true \<tau>
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then (x \<triangleq> y) \<tau>
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else invalid \<tau>"
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end
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text\<open>Property proof in terms of @{term "profile_bin\<^sub>S\<^sub>t\<^sub>r\<^sub>o\<^sub>n\<^sub>g\<^sub>E\<^sub>q_\<^sub>v_\<^sub>v"}\<close>
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interpretation StrictRefEq\<^sub>V\<^sub>o\<^sub>i\<^sub>d : profile_bin\<^sub>S\<^sub>t\<^sub>r\<^sub>o\<^sub>n\<^sub>g\<^sub>E\<^sub>q_\<^sub>v_\<^sub>v "\<lambda> x y. (x::('\<AA>)Void) \<doteq> y"
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by unfold_locales (auto simp: StrictRefEq\<^sub>V\<^sub>o\<^sub>i\<^sub>d)
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subsection\<open>Basic Void Constants\<close>
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subsection\<open>Validity and Definedness Properties\<close>
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lemma "\<delta>(null::('\<AA>)Void) = false" by simp
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lemma "\<upsilon>(null::('\<AA>)Void) = true" by simp
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lemma [simp,code_unfold]: "\<delta> (\<lambda>_. Abs_Void\<^sub>b\<^sub>a\<^sub>s\<^sub>e None) = false"
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apply(simp add:defined_def true_def
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bot_fun_def bot_option_def)
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apply(rule ext, simp split:, intro conjI impI)
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by(simp add: bot_Void_def)
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lemma [simp,code_unfold]: "\<upsilon> (\<lambda>_. Abs_Void\<^sub>b\<^sub>a\<^sub>s\<^sub>e None) = false"
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apply(simp add:valid_def true_def
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bot_fun_def bot_option_def)
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apply(rule ext, simp split:, intro conjI impI)
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by(simp add: bot_Void_def)
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lemma [simp,code_unfold]: "\<delta> (\<lambda>_. Abs_Void\<^sub>b\<^sub>a\<^sub>s\<^sub>e \<lfloor>None\<rfloor>) = false"
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apply(simp add:defined_def true_def
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bot_fun_def bot_option_def null_fun_def null_option_def)
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apply(rule ext, simp split:, intro conjI impI)
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by(simp add: null_Void_def)
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lemma [simp,code_unfold]: "\<upsilon> (\<lambda>_. Abs_Void\<^sub>b\<^sub>a\<^sub>s\<^sub>e \<lfloor>None\<rfloor>) = true"
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apply(simp add:valid_def true_def
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bot_fun_def bot_option_def)
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apply(rule ext, simp split:, intro conjI impI)
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by(metis null_Void_def null_is_valid, simp add: true_def)
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subsection\<open>Test Statements\<close>
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Assert "\<tau> \<Turnstile> ((null::('\<AA>)Void) \<doteq> null)"
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end
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