Theory UML_Tools

(*****************************************************************************
 * Featherweight-OCL --- A Formal Semantics for UML-OCL Version OCL 2.5 
 *                       for the OMG Standard.
 *                       http://www.brucker.ch/projects/hol-testgen/
 *
 * UML_Tools.thy ---
 * This file is part of HOL-TestGen.
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 * Copyright (c) 2012-2015 Université Paris-Saclay, Univ. Paris-Sud, France
 *               2013-2015 IRT SystemX, France
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(* < *)
theory UML_Tools
imports UML_Logic
begin


lemmas substs1 = StrongEq_L_subst2_rev
                 foundation15[THEN iffD2, THEN StrongEq_L_subst2_rev]
                 foundation7'[THEN iffD2, THEN foundation15[THEN iffD2, 
                                       THEN StrongEq_L_subst2_rev]]                
                 foundation14[THEN iffD2, THEN StrongEq_L_subst2_rev]
                 foundation13[THEN iffD2, THEN StrongEq_L_subst2_rev]
                
lemmas substs2 = StrongEq_L_subst3_rev
                 foundation15[THEN iffD2, THEN StrongEq_L_subst3_rev]
                 foundation7'[THEN iffD2, THEN foundation15[THEN iffD2, 
                                       THEN StrongEq_L_subst3_rev]]                
                 foundation14[THEN iffD2, THEN StrongEq_L_subst3_rev]
                 foundation13[THEN iffD2, THEN StrongEq_L_subst3_rev]
                 
lemmas substs4 = StrongEq_L_subst4_rev
                 foundation15[THEN iffD2, THEN StrongEq_L_subst4_rev]
                 foundation7'[THEN iffD2, THEN foundation15[THEN iffD2, 
                                       THEN StrongEq_L_subst4_rev]]                
                 foundation14[THEN iffD2, THEN StrongEq_L_subst4_rev]
                 foundation13[THEN iffD2, THEN StrongEq_L_subst4_rev]

                 
lemmas substs = substs1 substs2 substs4 [THEN iffD2] substs4
thm substs
ML‹
fun ocl_subst_asm_tac ctxt  = FIRST'(map (fn C => (eresolve0_tac [C]) THEN' (simp_tac ctxt)) 
                                         @{thms "substs"})

val ocl_subst_asm = fn ctxt => SIMPLE_METHOD (ocl_subst_asm_tac ctxt 1); 

val _ = Theory.setup 
             (Method.setup (Binding.name "ocl_subst_asm") 
             (Scan.succeed (ocl_subst_asm)) 
             "ocl substition step") 
 
›

lemma test1 : "τ ⊨ A ⟹ τ ⊨ (A and B ≜ B)"
apply(tactic "ocl_subst_asm_tac @{context} 1")
apply(simp)
done

lemma test2 : "τ ⊨ A ⟹ τ ⊨ (A and B ≜ B)"
by(ocl_subst_asm, simp)

lemma test3 : "τ ⊨ A ⟹ τ ⊨ (A and A)"
by(ocl_subst_asm, simp)

lemma test4 : "τ ⊨ not A ⟹ τ ⊨ (A and B ≜ false)"
by(ocl_subst_asm, simp)

lemma test5 : "τ ⊨ (A ≜ null) ⟹ τ ⊨ (B ≜ null) ⟹ ¬ (τ ⊨ (A and B))"
by(ocl_subst_asm,ocl_subst_asm,simp)

lemma test6 : "τ ⊨ not A ⟹ ¬ (τ ⊨ (A and B))"
by(ocl_subst_asm, simp)

lemma test7 : "¬ (τ ⊨ (υ A)) ⟹ τ ⊨ (not B) ⟹ ¬ (τ ⊨ (A and B))"
by(ocl_subst_asm,ocl_subst_asm,simp)

                  
    


(* a proof that shows that not everything is humpty dumpty ... *)
lemma X: "¬ (τ ⊨ (invalid and B))"
apply(insert foundation8[of "τ" "B"], elim disjE, 
      simp add:defined_bool_split, elim disjE)
apply(ocl_subst_asm, simp)
apply(ocl_subst_asm, simp)
apply(ocl_subst_asm, simp)
apply(ocl_subst_asm, simp)
done

(* easier is: *)
(* just to show the power of this extremely useful foundational rule:*)
lemma X': "¬ (τ ⊨ (invalid and B))"
by(simp add:foundation10')
lemma Y: "¬ (τ ⊨ (null and B))"
by(simp add: foundation10')
lemma Z: "¬ (τ ⊨ (false and B))"
by(simp add: foundation10')
lemma Z': "(τ ⊨ (true and B)) = (τ ⊨ B)"
by(simp)

 
end

(* > *)