138 lines
5.7 KiB
Plaintext
138 lines
5.7 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_Tools.thy ---
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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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(* < *)
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theory UML_Tools
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imports UML_Logic
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begin
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lemmas substs1 = StrongEq_L_subst2_rev
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foundation15[THEN iffD2, THEN StrongEq_L_subst2_rev]
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foundation7'[THEN iffD2, THEN foundation15[THEN iffD2,
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THEN StrongEq_L_subst2_rev]]
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foundation14[THEN iffD2, THEN StrongEq_L_subst2_rev]
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foundation13[THEN iffD2, THEN StrongEq_L_subst2_rev]
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lemmas substs2 = StrongEq_L_subst3_rev
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foundation15[THEN iffD2, THEN StrongEq_L_subst3_rev]
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foundation7'[THEN iffD2, THEN foundation15[THEN iffD2,
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THEN StrongEq_L_subst3_rev]]
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foundation14[THEN iffD2, THEN StrongEq_L_subst3_rev]
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foundation13[THEN iffD2, THEN StrongEq_L_subst3_rev]
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lemmas substs4 = StrongEq_L_subst4_rev
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foundation15[THEN iffD2, THEN StrongEq_L_subst4_rev]
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foundation7'[THEN iffD2, THEN foundation15[THEN iffD2,
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THEN StrongEq_L_subst4_rev]]
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foundation14[THEN iffD2, THEN StrongEq_L_subst4_rev]
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foundation13[THEN iffD2, THEN StrongEq_L_subst4_rev]
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lemmas substs = substs1 substs2 substs4 [THEN iffD2] substs4
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thm substs
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ML\<open>
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fun ocl_subst_asm_tac ctxt = FIRST'(map (fn C => (eresolve0_tac [C]) THEN' (simp_tac ctxt))
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@{thms "substs"})
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val ocl_subst_asm = fn ctxt => SIMPLE_METHOD (ocl_subst_asm_tac ctxt 1);
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val _ = Theory.setup
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(Method.setup (Binding.name "ocl_subst_asm")
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(Scan.succeed (ocl_subst_asm))
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"ocl substition step")
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\<close>
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lemma test1 : "\<tau> \<Turnstile> A \<Longrightarrow> \<tau> \<Turnstile> (A and B \<triangleq> B)"
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apply(tactic "ocl_subst_asm_tac @{context} 1")
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apply(simp)
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done
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lemma test2 : "\<tau> \<Turnstile> A \<Longrightarrow> \<tau> \<Turnstile> (A and B \<triangleq> B)"
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by(ocl_subst_asm, simp)
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lemma test3 : "\<tau> \<Turnstile> A \<Longrightarrow> \<tau> \<Turnstile> (A and A)"
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by(ocl_subst_asm, simp)
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lemma test4 : "\<tau> \<Turnstile> not A \<Longrightarrow> \<tau> \<Turnstile> (A and B \<triangleq> false)"
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by(ocl_subst_asm, simp)
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lemma test5 : "\<tau> \<Turnstile> (A \<triangleq> null) \<Longrightarrow> \<tau> \<Turnstile> (B \<triangleq> null) \<Longrightarrow> \<not> (\<tau> \<Turnstile> (A and B))"
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by(ocl_subst_asm,ocl_subst_asm,simp)
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lemma test6 : "\<tau> \<Turnstile> not A \<Longrightarrow> \<not> (\<tau> \<Turnstile> (A and B))"
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by(ocl_subst_asm, simp)
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lemma test7 : "\<not> (\<tau> \<Turnstile> (\<upsilon> A)) \<Longrightarrow> \<tau> \<Turnstile> (not B) \<Longrightarrow> \<not> (\<tau> \<Turnstile> (A and B))"
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by(ocl_subst_asm,ocl_subst_asm,simp)
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(* a proof that shows that not everything is humpty dumpty ... *)
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lemma X: "\<not> (\<tau> \<Turnstile> (invalid and B))"
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apply(insert foundation8[of "\<tau>" "B"], elim disjE,
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simp add:defined_bool_split, elim disjE)
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apply(ocl_subst_asm, simp)
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apply(ocl_subst_asm, simp)
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apply(ocl_subst_asm, simp)
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apply(ocl_subst_asm, simp)
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done
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(* easier is: *)
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(* just to show the power of this extremely useful foundational rule:*)
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lemma X': "\<not> (\<tau> \<Turnstile> (invalid and B))"
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by(simp add:foundation10')
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lemma Y: "\<not> (\<tau> \<Turnstile> (null and B))"
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by(simp add: foundation10')
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lemma Z: "\<not> (\<tau> \<Turnstile> (false and B))"
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by(simp add: foundation10')
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lemma Z': "(\<tau> \<Turnstile> (true and B)) = (\<tau> \<Turnstile> B)"
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by(simp)
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end
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(* > *)
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