src/HOL/Bali/WellForm.thy
author wenzelm
Sat Jan 14 16:14:22 2012 +0100 (2012-01-14)
changeset 46212 d86ef6b96097
parent 45608 13b101cee425
child 47176 568fdc70e565
permissions -rw-r--r--
tuned white space;
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(*  Title:      HOL/Bali/WellForm.thy
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    Author:     David von Oheimb and Norbert Schirmer
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*)
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header {* Well-formedness of Java programs *}
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theory WellForm imports DefiniteAssignment begin
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text {*
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For static checks on expressions and statements, see WellType.thy
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improvements over Java Specification 1.0 (cf. 8.4.6.3, 8.4.6.4, 9.4.1):
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\begin{itemize}
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\item a method implementing or overwriting another method may have a result 
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      type that widens to the result type of the other method 
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      (instead of identical type)
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\item if a method hides another method (both methods have to be static!)
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  there are no restrictions to the result type 
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  since the methods have to be static and there is no dynamic binding of 
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  static methods
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\item if an interface inherits more than one method with the same signature, the
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  methods need not have identical return types
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\end{itemize}
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simplifications:
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\begin{itemize}
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\item Object and standard exceptions are assumed to be declared like normal 
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      classes
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\end{itemize}
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*}
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section "well-formed field declarations"
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text  {* well-formed field declaration (common part for classes and interfaces),
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        cf. 8.3 and (9.3) *}
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definition
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  wf_fdecl :: "prog \<Rightarrow> pname \<Rightarrow> fdecl \<Rightarrow> bool"
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  where "wf_fdecl G P = (\<lambda>(fn,f). is_acc_type G P (type f))"
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lemma wf_fdecl_def2: "\<And>fd. wf_fdecl G P fd = is_acc_type G P (type (snd fd))"
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apply (unfold wf_fdecl_def)
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apply simp
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done
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section "well-formed method declarations"
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  (*well-formed method declaration,cf. 8.4, 8.4.1, 8.4.3, 8.4.5, 14.3.2, (9.4)*)
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  (* cf. 14.15, 15.7.2, for scope issues cf. 8.4.1 and 14.3.2 *)
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text {*
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A method head is wellformed if:
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\begin{itemize}
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\item the signature and the method head agree in the number of parameters
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\item all types of the parameters are visible
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\item the result type is visible
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\item the parameter names are unique
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\end{itemize} 
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*}
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definition
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  wf_mhead :: "prog \<Rightarrow> pname \<Rightarrow> sig \<Rightarrow> mhead \<Rightarrow> bool" where
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  "wf_mhead G P = (\<lambda> sig mh. length (parTs sig) = length (pars mh) \<and>
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                            ( \<forall>T\<in>set (parTs sig). is_acc_type G P T) \<and> 
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                            is_acc_type G P (resTy mh) \<and>
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                            distinct (pars mh))"
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text {*
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A method declaration is wellformed if:
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\begin{itemize}
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\item the method head is wellformed
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\item the names of the local variables are unique
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\item the types of the local variables must be accessible
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\item the local variables don't shadow the parameters
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\item the class of the method is defined
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\item the body statement is welltyped with respect to the
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      modified environment of local names, were the local variables, 
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      the parameters the special result variable (Res) and This are assoziated
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      with there types. 
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\end{itemize}
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*}
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definition
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  callee_lcl :: "qtname \<Rightarrow> sig \<Rightarrow> methd \<Rightarrow> lenv" where
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  "callee_lcl C sig m =
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    (\<lambda>k. (case k of
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            EName e 
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            \<Rightarrow> (case e of 
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                  VNam v 
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                  \<Rightarrow>(table_of (lcls (mbody m))((pars m)[\<mapsto>](parTs sig))) v
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                | Res \<Rightarrow> Some (resTy m))
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          | This \<Rightarrow> if is_static m then None else Some (Class C)))"
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definition
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  parameters :: "methd \<Rightarrow> lname set" where
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  "parameters m = set (map (EName \<circ> VNam) (pars m)) \<union> (if (static m) then {} else {This})"
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definition
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  wf_mdecl :: "prog \<Rightarrow> qtname \<Rightarrow> mdecl \<Rightarrow> bool" where
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  "wf_mdecl G C =
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      (\<lambda>(sig,m).
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          wf_mhead G (pid C) sig (mhead m) \<and> 
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          unique (lcls (mbody m)) \<and> 
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          (\<forall>(vn,T)\<in>set (lcls (mbody m)). is_acc_type G (pid C) T) \<and> 
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          (\<forall>pn\<in>set (pars m). table_of (lcls (mbody m)) pn = None) \<and>
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          jumpNestingOkS {Ret} (stmt (mbody m)) \<and> 
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          is_class G C \<and>
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          \<lparr>prg=G,cls=C,lcl=callee_lcl C sig m\<rparr>\<turnstile>(stmt (mbody m))\<Colon>\<surd> \<and>
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          (\<exists> A. \<lparr>prg=G,cls=C,lcl=callee_lcl C sig m\<rparr> 
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                \<turnstile> parameters m \<guillemotright>\<langle>stmt (mbody m)\<rangle>\<guillemotright> A 
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               \<and> Result \<in> nrm A))"
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lemma callee_lcl_VNam_simp [simp]:
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"callee_lcl C sig m (EName (VNam v)) 
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  = (table_of (lcls (mbody m))((pars m)[\<mapsto>](parTs sig))) v"
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by (simp add: callee_lcl_def)
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lemma callee_lcl_Res_simp [simp]:
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"callee_lcl C sig m (EName Res) = Some (resTy m)" 
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by (simp add: callee_lcl_def)
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lemma callee_lcl_This_simp [simp]:
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"callee_lcl C sig m (This) = (if is_static m then None else Some (Class C))" 
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by (simp add: callee_lcl_def)
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lemma callee_lcl_This_static_simp:
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"is_static m \<Longrightarrow> callee_lcl C sig m (This) = None"
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by simp
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lemma callee_lcl_This_not_static_simp:
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"\<not> is_static m \<Longrightarrow> callee_lcl C sig m (This) = Some (Class C)"
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by simp
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lemma wf_mheadI: 
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"\<lbrakk>length (parTs sig) = length (pars m); \<forall>T\<in>set (parTs sig). is_acc_type G P T;
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  is_acc_type G P (resTy m); distinct (pars m)\<rbrakk> \<Longrightarrow>  
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  wf_mhead G P sig m"
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apply (unfold wf_mhead_def)
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apply (simp (no_asm_simp))
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done
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lemma wf_mdeclI: "\<lbrakk>  
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  wf_mhead G (pid C) sig (mhead m); unique (lcls (mbody m));  
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  (\<forall>pn\<in>set (pars m). table_of (lcls (mbody m)) pn = None); 
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  \<forall>(vn,T)\<in>set (lcls (mbody m)). is_acc_type G (pid C) T;
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  jumpNestingOkS {Ret} (stmt (mbody m));
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  is_class G C;
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  \<lparr>prg=G,cls=C,lcl=callee_lcl C sig m\<rparr>\<turnstile>(stmt (mbody m))\<Colon>\<surd>;
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  (\<exists> A. \<lparr>prg=G,cls=C,lcl=callee_lcl C sig m\<rparr> \<turnstile> parameters m \<guillemotright>\<langle>stmt (mbody m)\<rangle>\<guillemotright> A
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        \<and> Result \<in> nrm A)
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  \<rbrakk> \<Longrightarrow>  
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  wf_mdecl G C (sig,m)"
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apply (unfold wf_mdecl_def)
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apply simp
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done
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lemma wf_mdeclE [consumes 1]:  
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  "\<lbrakk>wf_mdecl G C (sig,m); 
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    \<lbrakk>wf_mhead G (pid C) sig (mhead m); unique (lcls (mbody m));  
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     \<forall>pn\<in>set (pars m). table_of (lcls (mbody m)) pn = None; 
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     \<forall>(vn,T)\<in>set (lcls (mbody m)). is_acc_type G (pid C) T;
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     jumpNestingOkS {Ret} (stmt (mbody m));
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     is_class G C;
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     \<lparr>prg=G,cls=C,lcl=callee_lcl C sig m\<rparr>\<turnstile>(stmt (mbody m))\<Colon>\<surd>;
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   (\<exists> A. \<lparr>prg=G,cls=C,lcl=callee_lcl C sig m\<rparr>\<turnstile> parameters m \<guillemotright>\<langle>stmt (mbody m)\<rangle>\<guillemotright> A
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        \<and> Result \<in> nrm A)
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    \<rbrakk> \<Longrightarrow> P
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  \<rbrakk> \<Longrightarrow> P"
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by (unfold wf_mdecl_def) simp
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lemma wf_mdeclD1: 
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"wf_mdecl G C (sig,m) \<Longrightarrow>  
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   wf_mhead G (pid C) sig (mhead m) \<and> unique (lcls (mbody m)) \<and>  
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  (\<forall>pn\<in>set (pars m). table_of (lcls (mbody m)) pn = None) \<and> 
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  (\<forall>(vn,T)\<in>set (lcls (mbody m)). is_acc_type G (pid C) T)"
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apply (unfold wf_mdecl_def)
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apply simp
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done
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lemma wf_mdecl_bodyD: 
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"wf_mdecl G C (sig,m) \<Longrightarrow>  
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 (\<exists>T. \<lparr>prg=G,cls=C,lcl=callee_lcl C sig m\<rparr>\<turnstile>Body C (stmt (mbody m))\<Colon>-T \<and> 
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      G\<turnstile>T\<preceq>(resTy m))"
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apply (unfold wf_mdecl_def)
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apply clarify
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apply (rule_tac x="(resTy m)" in exI)
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apply (unfold wf_mhead_def)
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apply (auto simp add: wf_mhead_def is_acc_type_def intro: wt.Body )
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done
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(*
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lemma static_Object_methodsE [elim!]: 
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 "\<lbrakk>wf_mdecl G Object (sig, m);static m\<rbrakk> \<Longrightarrow> R"
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apply (unfold wf_mdecl_def)
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apply auto
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done
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*)
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lemma rT_is_acc_type: 
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  "wf_mhead G P sig m \<Longrightarrow> is_acc_type G P (resTy m)"
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apply (unfold wf_mhead_def)
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apply auto
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done
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section "well-formed interface declarations"
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  (* well-formed interface declaration, cf. 9.1, 9.1.2.1, 9.1.3, 9.4 *)
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text {*
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A interface declaration is wellformed if:
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\begin{itemize}
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\item the interface hierarchy is wellstructured
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\item there is no class with the same name
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\item the method heads are wellformed and not static and have Public access
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\item the methods are uniquely named
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\item all superinterfaces are accessible
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\item the result type of a method overriding a method of Object widens to the
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      result type of the overridden method.
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      Shadowing static methods is forbidden.
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\item the result type of a method overriding a set of methods defined in the
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      superinterfaces widens to each of the corresponding result types
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\end{itemize}
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*}
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definition
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  wf_idecl :: "prog  \<Rightarrow> idecl \<Rightarrow> bool" where
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 "wf_idecl G =
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    (\<lambda>(I,i). 
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        ws_idecl G I (isuperIfs i) \<and> 
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        \<not>is_class G I \<and>
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        (\<forall>(sig,mh)\<in>set (imethods i). wf_mhead G (pid I) sig mh \<and> 
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                                     \<not>is_static mh \<and>
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                                      accmodi mh = Public) \<and>
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        unique (imethods i) \<and>
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        (\<forall> J\<in>set (isuperIfs i). is_acc_iface G (pid I) J) \<and>
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        (table_of (imethods i)
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          hiding (methd G Object)
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          under  (\<lambda> new old. accmodi old \<noteq> Private)
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          entails (\<lambda>new old. G\<turnstile>resTy new\<preceq>resTy old \<and> 
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                             is_static new = is_static old)) \<and> 
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        (Option.set \<circ> table_of (imethods i) 
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               hidings Un_tables((\<lambda>J.(imethds G J))`set (isuperIfs i))
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               entails (\<lambda>new old. G\<turnstile>resTy new\<preceq>resTy old)))"
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lemma wf_idecl_mhead: "\<lbrakk>wf_idecl G (I,i); (sig,mh)\<in>set (imethods i)\<rbrakk> \<Longrightarrow>  
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  wf_mhead G (pid I) sig mh \<and> \<not>is_static mh \<and> accmodi mh = Public"
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apply (unfold wf_idecl_def)
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apply auto
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done
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lemma wf_idecl_hidings: 
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"wf_idecl G (I, i) \<Longrightarrow> 
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  (\<lambda>s. Option.set (table_of (imethods i) s)) 
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  hidings Un_tables ((\<lambda>J. imethds G J) ` set (isuperIfs i))  
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  entails \<lambda>new old. G\<turnstile>resTy new\<preceq>resTy old"
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apply (unfold wf_idecl_def o_def)
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apply simp
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done
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lemma wf_idecl_hiding:
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"wf_idecl G (I, i) \<Longrightarrow> 
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 (table_of (imethods i)
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           hiding (methd G Object)
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           under  (\<lambda> new old. accmodi old \<noteq> Private)
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           entails (\<lambda>new old. G\<turnstile>resTy new\<preceq>resTy old \<and> 
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                              is_static new = is_static old))"
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apply (unfold wf_idecl_def)
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apply simp
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done
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lemma wf_idecl_supD: 
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"\<lbrakk>wf_idecl G (I,i); J \<in> set (isuperIfs i)\<rbrakk> 
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 \<Longrightarrow> is_acc_iface G (pid I) J \<and> (J, I) \<notin> (subint1 G)^+"
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apply (unfold wf_idecl_def ws_idecl_def)
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apply auto
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done
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section "well-formed class declarations"
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  (* well-formed class declaration, cf. 8.1, 8.1.2.1, 8.1.2.2, 8.1.3, 8.1.4 and
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   class method declaration, cf. 8.4.3.3, 8.4.6.1, 8.4.6.2, 8.4.6.3, 8.4.6.4 *)
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text {*
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A class declaration is wellformed if:
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\begin{itemize}
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\item there is no interface with the same name
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\item all superinterfaces are accessible and for all methods implementing 
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      an interface method the result type widens to the result type of 
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      the interface method, the method is not static and offers at least 
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      as much access 
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      (this actually means that the method has Public access, since all 
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      interface methods have public access)
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\item all field declarations are wellformed and the field names are unique
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\item all method declarations are wellformed and the method names are unique
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\item the initialization statement is welltyped
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\item the classhierarchy is wellstructured
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\item Unless the class is Object:
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      \begin{itemize}
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      \item the superclass is accessible
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      \item for all methods overriding another method (of a superclass )the
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            result type widens to the result type of the overridden method,
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            the access modifier of the new method provides at least as much
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            access as the overwritten one.
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      \item for all methods hiding a method (of a superclass) the hidden 
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            method must be static and offer at least as much access rights.
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   303
            Remark: In contrast to the Java Language Specification we don't
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   304
            restrict the result types of the method
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   305
            (as in case of overriding), because there seems to be no reason,
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   306
            since there is no dynamic binding of static methods.
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   307
            (cf. 8.4.6.3 vs. 15.12.1).
schirmer@12854
   308
            Stricly speaking the restrictions on the access rights aren't 
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   309
            necessary to, since the static type and the access rights 
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   310
            together determine which method is to be called statically. 
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   311
            But if a class gains more then one static method with the 
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   312
            same signature due to inheritance, it is confusing when the 
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   313
            method selection depends on the access rights only: 
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   314
            e.g.
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   315
              Class C declares static public method foo().
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   316
              Class D is subclass of C and declares static method foo()
schirmer@12854
   317
              with default package access.
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   318
              D.foo() ? if this call is in the same package as D then
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   319
                        foo of class D is called, otherwise foo of class C.
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   320
      \end{itemize}
schirmer@12854
   321
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   322
\end{itemize}
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   323
*}
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   324
(* to Table *)
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   325
definition
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   326
  entails :: "('a,'b) table \<Rightarrow> ('b \<Rightarrow> bool) \<Rightarrow> bool" ("_ entails _" 20)
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   327
  where "(t entails P) = (\<forall>k. \<forall> x \<in> t k: P x)"
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   328
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   329
lemma entailsD:
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   330
 "\<lbrakk>t entails P; t k = Some x\<rbrakk> \<Longrightarrow> P x"
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   331
by (simp add: entails_def)
schirmer@12854
   332
schirmer@12854
   333
lemma empty_entails[simp]: "empty entails P"
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   334
by (simp add: entails_def)
schirmer@12854
   335
wenzelm@37956
   336
definition
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   337
  wf_cdecl :: "prog \<Rightarrow> cdecl \<Rightarrow> bool" where
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   338
  "wf_cdecl G =
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   339
     (\<lambda>(C,c).
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   340
      \<not>is_iface G C \<and>
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   341
      (\<forall>I\<in>set (superIfs c). is_acc_iface G (pid C) I \<and>
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   342
        (\<forall>s. \<forall> im \<in> imethds G I s.
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   343
            (\<exists> cm \<in> methd  G C s: G\<turnstile>resTy cm\<preceq>resTy im \<and>
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   344
                                     \<not> is_static cm \<and>
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   345
                                     accmodi im \<le> accmodi cm))) \<and>
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   346
      (\<forall>f\<in>set (cfields c). wf_fdecl G (pid C) f) \<and> unique (cfields c) \<and> 
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   347
      (\<forall>m\<in>set (methods c). wf_mdecl G C m) \<and> unique (methods c) \<and>
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   348
      jumpNestingOkS {} (init c) \<and>
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   349
      (\<exists> A. \<lparr>prg=G,cls=C,lcl=empty\<rparr>\<turnstile> {} \<guillemotright>\<langle>init c\<rangle>\<guillemotright> A) \<and>
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   350
      \<lparr>prg=G,cls=C,lcl=empty\<rparr>\<turnstile>(init c)\<Colon>\<surd> \<and> ws_cdecl G C (super c) \<and>
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   351
      (C \<noteq> Object \<longrightarrow> 
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   352
            (is_acc_class G (pid C) (super c) \<and>
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   353
            (table_of (map (\<lambda> (s,m). (s,C,m)) (methods c)) 
schirmer@12854
   354
             entails (\<lambda> new. \<forall> old sig. 
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   355
                       (G,sig\<turnstile>new overrides\<^sub>S old 
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   356
                        \<longrightarrow> (G\<turnstile>resTy new\<preceq>resTy old \<and>
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   357
                             accmodi old \<le> accmodi new \<and>
wenzelm@32960
   358
                             \<not>is_static old)) \<and>
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   359
                       (G,sig\<turnstile>new hides old 
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   360
                         \<longrightarrow> (accmodi old \<le> accmodi new \<and>
wenzelm@32960
   361
                              is_static old)))) 
wenzelm@37956
   362
            )))"
schirmer@12854
   363
schirmer@12854
   364
(*
haftmann@35416
   365
definition wf_cdecl :: "prog \<Rightarrow> cdecl \<Rightarrow> bool" where
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   366
"wf_cdecl G \<equiv> 
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   367
   \<lambda>(C,c).
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   368
      \<not>is_iface G C \<and>
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   369
      (\<forall>I\<in>set (superIfs c). is_acc_iface G (pid C) I \<and>
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   370
        (\<forall>s. \<forall> im \<in> imethds G I s.
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   371
            (\<exists> cm \<in> methd  G C s: G\<turnstile>resTy (mthd cm)\<preceq>resTy (mthd im) \<and>
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   372
                                     \<not> is_static cm \<and>
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   373
                                     accmodi im \<le> accmodi cm))) \<and>
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   374
      (\<forall>f\<in>set (cfields c). wf_fdecl G (pid C) f) \<and> unique (cfields c) \<and> 
schirmer@12854
   375
      (\<forall>m\<in>set (methods c). wf_mdecl G C m) \<and> unique (methods c) \<and> 
schirmer@12854
   376
      \<lparr>prg=G,cls=C,lcl=empty\<rparr>\<turnstile>(init c)\<Colon>\<surd> \<and> ws_cdecl G C (super c) \<and>
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   377
      (C \<noteq> Object \<longrightarrow> 
schirmer@12854
   378
            (is_acc_class G (pid C) (super c) \<and>
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   379
            (table_of (map (\<lambda> (s,m). (s,C,m)) (methods c)) 
schirmer@12854
   380
              hiding methd G (super c)
schirmer@12854
   381
              under (\<lambda> new old. G\<turnstile>new overrides old)
schirmer@12854
   382
              entails (\<lambda> new old. 
schirmer@12854
   383
                           (G\<turnstile>resTy (mthd new)\<preceq>resTy (mthd old) \<and>
schirmer@12854
   384
                            accmodi old \<le> accmodi new \<and>
wenzelm@32960
   385
                           \<not> is_static old)))  \<and>
schirmer@12854
   386
            (table_of (map (\<lambda> (s,m). (s,C,m)) (methods c)) 
schirmer@12854
   387
              hiding methd G (super c)
schirmer@12854
   388
              under (\<lambda> new old. G\<turnstile>new hides old)
schirmer@12854
   389
              entails (\<lambda> new old. is_static old \<and> 
schirmer@12854
   390
                                  accmodi old \<le> accmodi new))  \<and>
schirmer@12854
   391
            (table_of (cfields c) hiding accfield G C (super c)
schirmer@12854
   392
              entails (\<lambda> newF oldF. accmodi oldF \<le> access newF))))"
schirmer@12854
   393
*)
schirmer@12854
   394
schirmer@13688
   395
lemma wf_cdeclE [consumes 1]: 
schirmer@13688
   396
 "\<lbrakk>wf_cdecl G (C,c);
schirmer@13688
   397
   \<lbrakk>\<not>is_iface G C;
schirmer@13688
   398
    (\<forall>I\<in>set (superIfs c). is_acc_iface G (pid C) I \<and>
schirmer@13688
   399
        (\<forall>s. \<forall> im \<in> imethds G I s.
wenzelm@32960
   400
            (\<exists> cm \<in> methd  G C s: G\<turnstile>resTy cm\<preceq>resTy im \<and>
wenzelm@32960
   401
                                     \<not> is_static cm \<and>
schirmer@13688
   402
                                     accmodi im \<le> accmodi cm))); 
schirmer@13688
   403
      \<forall>f\<in>set (cfields c). wf_fdecl G (pid C) f; unique (cfields c); 
schirmer@13688
   404
      \<forall>m\<in>set (methods c). wf_mdecl G C m; unique (methods c);
schirmer@13688
   405
      jumpNestingOkS {} (init c);
schirmer@13688
   406
      \<exists> A. \<lparr>prg=G,cls=C,lcl=empty\<rparr>\<turnstile> {} \<guillemotright>\<langle>init c\<rangle>\<guillemotright> A;
schirmer@13688
   407
      \<lparr>prg=G,cls=C,lcl=empty\<rparr>\<turnstile>(init c)\<Colon>\<surd>; 
schirmer@13688
   408
      ws_cdecl G C (super c); 
schirmer@13688
   409
      (C \<noteq> Object \<longrightarrow> 
schirmer@13688
   410
            (is_acc_class G (pid C) (super c) \<and>
schirmer@13688
   411
            (table_of (map (\<lambda> (s,m). (s,C,m)) (methods c)) 
schirmer@13688
   412
             entails (\<lambda> new. \<forall> old sig. 
schirmer@13688
   413
                       (G,sig\<turnstile>new overrides\<^sub>S old 
schirmer@13688
   414
                        \<longrightarrow> (G\<turnstile>resTy new\<preceq>resTy old \<and>
schirmer@13688
   415
                             accmodi old \<le> accmodi new \<and>
wenzelm@32960
   416
                             \<not>is_static old)) \<and>
schirmer@13688
   417
                       (G,sig\<turnstile>new hides old 
schirmer@13688
   418
                         \<longrightarrow> (accmodi old \<le> accmodi new \<and>
wenzelm@32960
   419
                              is_static old)))) 
schirmer@13688
   420
            ))\<rbrakk> \<Longrightarrow> P
schirmer@13688
   421
  \<rbrakk> \<Longrightarrow> P"
schirmer@13688
   422
by (unfold wf_cdecl_def) simp
schirmer@13688
   423
schirmer@12854
   424
lemma wf_cdecl_unique: 
schirmer@12854
   425
"wf_cdecl G (C,c) \<Longrightarrow> unique (cfields c) \<and> unique (methods c)"
schirmer@12854
   426
apply (unfold wf_cdecl_def)
schirmer@12854
   427
apply auto
schirmer@12854
   428
done
schirmer@12854
   429
schirmer@12854
   430
lemma wf_cdecl_fdecl: 
schirmer@12854
   431
"\<lbrakk>wf_cdecl G (C,c); f\<in>set (cfields c)\<rbrakk> \<Longrightarrow> wf_fdecl G (pid C) f"
schirmer@12854
   432
apply (unfold wf_cdecl_def)
schirmer@12854
   433
apply auto
schirmer@12854
   434
done
schirmer@12854
   435
schirmer@12854
   436
lemma wf_cdecl_mdecl: 
schirmer@12854
   437
"\<lbrakk>wf_cdecl G (C,c); m\<in>set (methods c)\<rbrakk> \<Longrightarrow> wf_mdecl G C m"
schirmer@12854
   438
apply (unfold wf_cdecl_def)
schirmer@12854
   439
apply auto
schirmer@12854
   440
done
schirmer@12854
   441
schirmer@12854
   442
lemma wf_cdecl_impD: 
schirmer@12854
   443
"\<lbrakk>wf_cdecl G (C,c); I\<in>set (superIfs c)\<rbrakk> 
schirmer@12854
   444
\<Longrightarrow> is_acc_iface G (pid C) I \<and>  
schirmer@12854
   445
    (\<forall>s. \<forall>im \<in> imethds G I s.  
schirmer@12854
   446
        (\<exists>cm \<in> methd G C s: G\<turnstile>resTy cm\<preceq>resTy im \<and> \<not>is_static cm \<and>
schirmer@12854
   447
                                   accmodi im \<le> accmodi cm))"
schirmer@12854
   448
apply (unfold wf_cdecl_def)
schirmer@12854
   449
apply auto
schirmer@12854
   450
done
schirmer@12854
   451
schirmer@12854
   452
lemma wf_cdecl_supD: 
schirmer@12854
   453
"\<lbrakk>wf_cdecl G (C,c); C \<noteq> Object\<rbrakk> \<Longrightarrow>  
schirmer@12854
   454
  is_acc_class G (pid C) (super c) \<and> (super c,C) \<notin> (subcls1 G)^+ \<and> 
schirmer@12854
   455
   (table_of (map (\<lambda> (s,m). (s,C,m)) (methods c)) 
schirmer@12854
   456
    entails (\<lambda> new. \<forall> old sig. 
schirmer@12854
   457
                 (G,sig\<turnstile>new overrides\<^sub>S old 
schirmer@12854
   458
                  \<longrightarrow> (G\<turnstile>resTy new\<preceq>resTy old \<and>
schirmer@12854
   459
                       accmodi old \<le> accmodi new \<and>
schirmer@12854
   460
                       \<not>is_static old)) \<and>
schirmer@12854
   461
                 (G,sig\<turnstile>new hides old 
schirmer@12854
   462
                   \<longrightarrow> (accmodi old \<le> accmodi new \<and>
schirmer@12854
   463
                        is_static old))))"
schirmer@12854
   464
apply (unfold wf_cdecl_def ws_cdecl_def)
schirmer@12854
   465
apply auto
schirmer@12854
   466
done
schirmer@12854
   467
schirmer@12854
   468
schirmer@12854
   469
lemma wf_cdecl_overrides_SomeD:
schirmer@12854
   470
"\<lbrakk>wf_cdecl G (C,c); C \<noteq> Object; table_of (methods c) sig = Some newM;
schirmer@12854
   471
  G,sig\<turnstile>(C,newM) overrides\<^sub>S old
schirmer@12854
   472
\<rbrakk> \<Longrightarrow>  G\<turnstile>resTy newM\<preceq>resTy old \<and>
schirmer@12854
   473
       accmodi old \<le> accmodi newM \<and>
schirmer@12854
   474
       \<not> is_static old" 
schirmer@12854
   475
apply (drule (1) wf_cdecl_supD)
schirmer@12854
   476
apply (clarify)
schirmer@12854
   477
apply (drule entailsD)
schirmer@12854
   478
apply   (blast intro: table_of_map_SomeI)
schirmer@12854
   479
apply (drule_tac x="old" in spec)
schirmer@12854
   480
apply (auto dest: overrides_eq_sigD simp add: msig_def)
schirmer@12854
   481
done
schirmer@12854
   482
schirmer@12854
   483
lemma wf_cdecl_hides_SomeD:
schirmer@12854
   484
"\<lbrakk>wf_cdecl G (C,c); C \<noteq> Object; table_of (methods c) sig = Some newM;
schirmer@12854
   485
  G,sig\<turnstile>(C,newM) hides old
schirmer@12854
   486
\<rbrakk> \<Longrightarrow>  accmodi old \<le> access newM \<and>
schirmer@12854
   487
       is_static old" 
schirmer@12854
   488
apply (drule (1) wf_cdecl_supD)
schirmer@12854
   489
apply (clarify)
schirmer@12854
   490
apply (drule entailsD)
schirmer@12854
   491
apply   (blast intro: table_of_map_SomeI)
schirmer@12854
   492
apply (drule_tac x="old" in spec)
schirmer@12854
   493
apply (auto dest: hides_eq_sigD simp add: msig_def)
schirmer@12854
   494
done
schirmer@12854
   495
schirmer@12854
   496
lemma wf_cdecl_wt_init: 
schirmer@12854
   497
 "wf_cdecl G (C, c) \<Longrightarrow> \<lparr>prg=G,cls=C,lcl=empty\<rparr>\<turnstile>init c\<Colon>\<surd>"
schirmer@12854
   498
apply (unfold wf_cdecl_def)
schirmer@12854
   499
apply auto
schirmer@12854
   500
done
schirmer@12854
   501
schirmer@12854
   502
schirmer@12854
   503
section "well-formed programs"
schirmer@12854
   504
  (* well-formed program, cf. 8.1, 9.1 *)
schirmer@12854
   505
schirmer@12854
   506
text {*
schirmer@12854
   507
A program declaration is wellformed if:
schirmer@12854
   508
\begin{itemize}
schirmer@12854
   509
\item the class ObjectC of Object is defined
schirmer@14030
   510
\item every method of Object has an access modifier distinct from Package. 
schirmer@14030
   511
      This is
schirmer@12854
   512
      necessary since every interface automatically inherits from Object.  
schirmer@12854
   513
      We must know, that every time a Object method is "overriden" by an 
schirmer@12854
   514
      interface method this is also overriden by the class implementing the
schirmer@12854
   515
      the interface (see @{text "implement_dynmethd and class_mheadsD"})
schirmer@12854
   516
\item all standard Exceptions are defined
schirmer@12854
   517
\item all defined interfaces are wellformed
schirmer@12854
   518
\item all defined classes are wellformed
schirmer@12854
   519
\end{itemize}
schirmer@12854
   520
*}
wenzelm@37956
   521
definition
wenzelm@37956
   522
  wf_prog :: "prog \<Rightarrow> bool" where
wenzelm@37956
   523
 "wf_prog G = (let is = ifaces G; cs = classes G in
wenzelm@32960
   524
                 ObjectC \<in> set cs \<and> 
schirmer@12854
   525
                (\<forall> m\<in>set Object_mdecls. accmodi m \<noteq> Package) \<and>
schirmer@12854
   526
                (\<forall>xn. SXcptC xn \<in> set cs) \<and>
wenzelm@32960
   527
                (\<forall>i\<in>set is. wf_idecl G i) \<and> unique is \<and>
wenzelm@37956
   528
                (\<forall>c\<in>set cs. wf_cdecl G c) \<and> unique cs)"
schirmer@12854
   529
schirmer@12854
   530
lemma wf_prog_idecl: "\<lbrakk>iface G I = Some i; wf_prog G\<rbrakk> \<Longrightarrow> wf_idecl G (I,i)"
schirmer@12854
   531
apply (unfold wf_prog_def Let_def)
schirmer@12854
   532
apply simp
schirmer@12854
   533
apply (fast dest: map_of_SomeD)
schirmer@12854
   534
done
schirmer@12854
   535
schirmer@12854
   536
lemma wf_prog_cdecl: "\<lbrakk>class G C = Some c; wf_prog G\<rbrakk> \<Longrightarrow> wf_cdecl G (C,c)"
schirmer@12854
   537
apply (unfold wf_prog_def Let_def)
schirmer@12854
   538
apply simp
schirmer@12854
   539
apply (fast dest: map_of_SomeD)
schirmer@12854
   540
done
schirmer@12854
   541
schirmer@12854
   542
lemma wf_prog_Object_mdecls:
schirmer@12854
   543
"wf_prog G \<Longrightarrow> (\<forall> m\<in>set Object_mdecls. accmodi m \<noteq> Package)"
schirmer@12854
   544
apply (unfold wf_prog_def Let_def)
schirmer@12854
   545
apply simp
schirmer@12854
   546
done
schirmer@12854
   547
schirmer@12854
   548
lemma wf_prog_acc_superD:
schirmer@12854
   549
 "\<lbrakk>wf_prog G; class G C = Some c; C \<noteq> Object \<rbrakk> 
schirmer@12854
   550
  \<Longrightarrow> is_acc_class G (pid C) (super c)"
schirmer@12854
   551
by (auto dest: wf_prog_cdecl wf_cdecl_supD)
schirmer@12854
   552
schirmer@12854
   553
lemma wf_ws_prog [elim!,simp]: "wf_prog G \<Longrightarrow> ws_prog G"
schirmer@12854
   554
apply (unfold wf_prog_def Let_def)
schirmer@12854
   555
apply (rule ws_progI)
schirmer@12854
   556
apply  (simp_all (no_asm))
schirmer@12854
   557
apply  (auto simp add: is_acc_class_def is_acc_iface_def 
schirmer@12854
   558
             dest!: wf_idecl_supD wf_cdecl_supD )+
schirmer@12854
   559
done
schirmer@12854
   560
schirmer@12854
   561
lemma class_Object [simp]: 
schirmer@12854
   562
"wf_prog G \<Longrightarrow> 
schirmer@12854
   563
  class G Object = Some \<lparr>access=Public,cfields=[],methods=Object_mdecls,
haftmann@28524
   564
                                  init=Skip,super=undefined,superIfs=[]\<rparr>"
schirmer@12854
   565
apply (unfold wf_prog_def Let_def ObjectC_def)
schirmer@12854
   566
apply (fast dest!: map_of_SomeI)
schirmer@12854
   567
done
schirmer@12854
   568
schirmer@12854
   569
lemma methd_Object[simp]: "wf_prog G \<Longrightarrow> methd G Object =  
schirmer@12854
   570
  table_of (map (\<lambda>(s,m). (s, Object, m)) Object_mdecls)"
schirmer@12854
   571
apply (subst methd_rec)
schirmer@12854
   572
apply (auto simp add: Let_def)
schirmer@12854
   573
done
schirmer@12854
   574
schirmer@12854
   575
lemma wf_prog_Object_methd:
schirmer@12854
   576
"\<lbrakk>wf_prog G; methd G Object sig = Some m\<rbrakk> \<Longrightarrow> accmodi m \<noteq> Package"
schirmer@12854
   577
by (auto dest!: wf_prog_Object_mdecls) (auto dest!: map_of_SomeD) 
schirmer@12854
   578
schirmer@12854
   579
lemma wf_prog_Object_is_public[intro]:
schirmer@12854
   580
 "wf_prog G \<Longrightarrow> is_public G Object"
schirmer@12854
   581
by (auto simp add: is_public_def dest: class_Object)
schirmer@12854
   582
schirmer@12854
   583
lemma class_SXcpt [simp]: 
schirmer@12854
   584
"wf_prog G \<Longrightarrow> 
schirmer@12854
   585
  class G (SXcpt xn) = Some \<lparr>access=Public,cfields=[],methods=SXcpt_mdecls,
schirmer@12854
   586
                                   init=Skip,
schirmer@12854
   587
                                   super=if xn = Throwable then Object 
schirmer@12854
   588
                                                           else SXcpt Throwable,
schirmer@12854
   589
                                   superIfs=[]\<rparr>"
schirmer@12854
   590
apply (unfold wf_prog_def Let_def SXcptC_def)
schirmer@12854
   591
apply (fast dest!: map_of_SomeI)
schirmer@12854
   592
done
schirmer@12854
   593
schirmer@12854
   594
lemma wf_ObjectC [simp]: 
wenzelm@32960
   595
        "wf_cdecl G ObjectC = (\<not>is_iface G Object \<and> Ball (set Object_mdecls)
schirmer@12854
   596
  (wf_mdecl G Object) \<and> unique Object_mdecls)"
schirmer@12854
   597
apply (unfold wf_cdecl_def ws_cdecl_def ObjectC_def)
schirmer@13688
   598
apply (auto intro: da.Skip)
schirmer@12854
   599
done
schirmer@12854
   600
schirmer@12854
   601
lemma Object_is_class [simp,elim!]: "wf_prog G \<Longrightarrow> is_class G Object"
schirmer@12854
   602
apply (simp (no_asm_simp))
schirmer@12854
   603
done
schirmer@12854
   604
 
schirmer@12854
   605
lemma Object_is_acc_class [simp,elim!]: "wf_prog G \<Longrightarrow> is_acc_class G S Object"
schirmer@12854
   606
apply (simp (no_asm_simp) add: is_acc_class_def is_public_def
schirmer@12854
   607
                               accessible_in_RefT_simp)
schirmer@12854
   608
done
schirmer@12854
   609
schirmer@12854
   610
lemma SXcpt_is_class [simp,elim!]: "wf_prog G \<Longrightarrow> is_class G (SXcpt xn)"
schirmer@12854
   611
apply (simp (no_asm_simp))
schirmer@12854
   612
done
schirmer@12854
   613
schirmer@12854
   614
lemma SXcpt_is_acc_class [simp,elim!]: 
schirmer@12854
   615
"wf_prog G \<Longrightarrow> is_acc_class G S (SXcpt xn)"
schirmer@12854
   616
apply (simp (no_asm_simp) add: is_acc_class_def is_public_def
schirmer@12854
   617
                               accessible_in_RefT_simp)
schirmer@12854
   618
done
schirmer@12854
   619
schirmer@12854
   620
lemma fields_Object [simp]: "wf_prog G \<Longrightarrow> DeclConcepts.fields G Object = []"
schirmer@12854
   621
by (force intro: fields_emptyI)
schirmer@12854
   622
schirmer@12854
   623
lemma accfield_Object [simp]: 
schirmer@12854
   624
 "wf_prog G \<Longrightarrow> accfield G S Object = empty"
schirmer@12854
   625
apply (unfold accfield_def)
schirmer@12854
   626
apply (simp (no_asm_simp) add: Let_def)
schirmer@12854
   627
done
schirmer@12854
   628
schirmer@12854
   629
lemma fields_Throwable [simp]: 
schirmer@12854
   630
 "wf_prog G \<Longrightarrow> DeclConcepts.fields G (SXcpt Throwable) = []"
schirmer@12854
   631
by (force intro: fields_emptyI)
schirmer@12854
   632
schirmer@12854
   633
lemma fields_SXcpt [simp]: "wf_prog G \<Longrightarrow> DeclConcepts.fields G (SXcpt xn) = []"
schirmer@12854
   634
apply (case_tac "xn = Throwable")
schirmer@12854
   635
apply  (simp (no_asm_simp))
schirmer@12854
   636
by (force intro: fields_emptyI)
schirmer@12854
   637
schirmer@12854
   638
lemmas widen_trans = ws_widen_trans [OF _ _ wf_ws_prog, elim]
schirmer@12854
   639
lemma widen_trans2 [elim]: "\<lbrakk>G\<turnstile>U\<preceq>T; G\<turnstile>S\<preceq>U; wf_prog G\<rbrakk> \<Longrightarrow> G\<turnstile>S\<preceq>T"
schirmer@12854
   640
apply (erule (2) widen_trans)
schirmer@12854
   641
done
schirmer@12854
   642
schirmer@12854
   643
lemma Xcpt_subcls_Throwable [simp]: 
schirmer@12854
   644
"wf_prog G \<Longrightarrow> G\<turnstile>SXcpt xn\<preceq>\<^sub>C SXcpt Throwable"
schirmer@12854
   645
apply (rule SXcpt_subcls_Throwable_lemma)
schirmer@12854
   646
apply auto
schirmer@12854
   647
done
schirmer@12854
   648
schirmer@12854
   649
lemma unique_fields: 
schirmer@12854
   650
 "\<lbrakk>is_class G C; wf_prog G\<rbrakk> \<Longrightarrow> unique (DeclConcepts.fields G C)"
schirmer@12854
   651
apply (erule ws_unique_fields)
schirmer@12854
   652
apply  (erule wf_ws_prog)
schirmer@12854
   653
apply (erule (1) wf_prog_cdecl [THEN wf_cdecl_unique [THEN conjunct1]])
schirmer@12854
   654
done
schirmer@12854
   655
schirmer@12854
   656
lemma fields_mono: 
schirmer@12854
   657
"\<lbrakk>table_of (DeclConcepts.fields G C) fn = Some f; G\<turnstile>D\<preceq>\<^sub>C C; 
schirmer@12854
   658
  is_class G D; wf_prog G\<rbrakk> 
schirmer@12854
   659
   \<Longrightarrow> table_of (DeclConcepts.fields G D) fn = Some f"
schirmer@12854
   660
apply (rule map_of_SomeI)
schirmer@12854
   661
apply  (erule (1) unique_fields)
schirmer@12854
   662
apply (erule (1) map_of_SomeD [THEN fields_mono_lemma])
schirmer@12854
   663
apply (erule wf_ws_prog)
schirmer@12854
   664
done
schirmer@12854
   665
schirmer@12854
   666
schirmer@12854
   667
lemma fields_is_type [elim]: 
schirmer@12854
   668
"\<lbrakk>table_of (DeclConcepts.fields G C) m = Some f; wf_prog G; is_class G C\<rbrakk> \<Longrightarrow> 
schirmer@12854
   669
      is_type G (type f)"
schirmer@12854
   670
apply (frule wf_ws_prog)
schirmer@12854
   671
apply (force dest: fields_declC [THEN conjunct1] 
schirmer@12854
   672
                   wf_prog_cdecl [THEN wf_cdecl_fdecl]
schirmer@12854
   673
             simp add: wf_fdecl_def2 is_acc_type_def)
schirmer@12854
   674
done
schirmer@12854
   675
schirmer@12854
   676
lemma imethds_wf_mhead [rule_format (no_asm)]: 
schirmer@12854
   677
"\<lbrakk>m \<in> imethds G I sig; wf_prog G; is_iface G I\<rbrakk> \<Longrightarrow>  
schirmer@12854
   678
  wf_mhead G (pid (decliface m)) sig (mthd m) \<and> 
schirmer@12854
   679
  \<not> is_static m \<and> accmodi m = Public"
schirmer@12854
   680
apply (frule wf_ws_prog)
schirmer@12854
   681
apply (drule (2) imethds_declI [THEN conjunct1])
schirmer@12854
   682
apply clarify
schirmer@12854
   683
apply (frule_tac I="(decliface m)" in wf_prog_idecl,assumption)
schirmer@12854
   684
apply (drule wf_idecl_mhead)
schirmer@12854
   685
apply (erule map_of_SomeD)
schirmer@12854
   686
apply (cases m, simp)
schirmer@12854
   687
done
schirmer@12854
   688
schirmer@12854
   689
lemma methd_wf_mdecl: 
schirmer@12854
   690
 "\<lbrakk>methd G C sig = Some m; wf_prog G; class G C = Some y\<rbrakk> \<Longrightarrow>  
schirmer@12854
   691
  G\<turnstile>C\<preceq>\<^sub>C (declclass m) \<and> is_class G (declclass m) \<and> 
schirmer@12854
   692
  wf_mdecl G (declclass m) (sig,(mthd m))"
schirmer@12854
   693
apply (frule wf_ws_prog)
schirmer@12854
   694
apply (drule (1) methd_declC)
schirmer@12854
   695
apply  fast
schirmer@12854
   696
apply clarsimp
schirmer@12854
   697
apply (frule (1) wf_prog_cdecl, erule wf_cdecl_mdecl, erule map_of_SomeD)
schirmer@12854
   698
done
schirmer@12854
   699
schirmer@12854
   700
(*
schirmer@12854
   701
This lemma doesn't hold!
schirmer@12854
   702
lemma methd_rT_is_acc_type: 
schirmer@12854
   703
"\<lbrakk>wf_prog G;methd G C C sig = Some (D,m);
schirmer@12854
   704
    class G C = Some y\<rbrakk>
schirmer@12854
   705
\<Longrightarrow> is_acc_type G (pid C) (resTy m)"
schirmer@12854
   706
The result Type is only visible in the scope of defining class D 
schirmer@12854
   707
"is_vis_type G (pid D) (resTy m)" but not necessarily in scope of class C!
schirmer@12854
   708
(The same is true for the type of pramaters of a method)
schirmer@12854
   709
*)
schirmer@12854
   710
schirmer@12854
   711
schirmer@12854
   712
lemma methd_rT_is_type: 
schirmer@12854
   713
"\<lbrakk>wf_prog G;methd G C sig = Some m;
schirmer@12854
   714
    class G C = Some y\<rbrakk>
schirmer@12854
   715
\<Longrightarrow> is_type G (resTy m)"
schirmer@12854
   716
apply (drule (2) methd_wf_mdecl)
schirmer@12854
   717
apply clarify
schirmer@12854
   718
apply (drule wf_mdeclD1)
schirmer@12854
   719
apply clarify
schirmer@12854
   720
apply (drule rT_is_acc_type)
schirmer@12854
   721
apply (cases m, simp add: is_acc_type_def)
schirmer@12854
   722
done
schirmer@12854
   723
schirmer@12854
   724
lemma accmethd_rT_is_type:
schirmer@12854
   725
"\<lbrakk>wf_prog G;accmethd G S C sig = Some m;
schirmer@12854
   726
    class G C = Some y\<rbrakk>
schirmer@12854
   727
\<Longrightarrow> is_type G (resTy m)"
schirmer@12854
   728
by (auto simp add: accmethd_def  
schirmer@12854
   729
         intro: methd_rT_is_type)
schirmer@12854
   730
schirmer@12854
   731
lemma methd_Object_SomeD:
schirmer@12854
   732
"\<lbrakk>wf_prog G;methd G Object sig = Some m\<rbrakk> 
schirmer@12854
   733
 \<Longrightarrow> declclass m = Object"
schirmer@12854
   734
by (auto dest: class_Object simp add: methd_rec )
schirmer@12854
   735
wenzelm@45608
   736
lemmas iface_rec_induct' = iface_rec.induct [of "%x y z. P x y"] for P
wenzelm@45608
   737
schirmer@12854
   738
lemma wf_imethdsD: 
schirmer@12854
   739
 "\<lbrakk>im \<in> imethds G I sig;wf_prog G; is_iface G I\<rbrakk> 
schirmer@12854
   740
 \<Longrightarrow> \<not>is_static im \<and> accmodi im = Public"
schirmer@12854
   741
proof -
schirmer@12854
   742
  assume asm: "wf_prog G" "is_iface G I" "im \<in> imethds G I sig"
krauss@35440
   743
schirmer@12854
   744
  have "wf_prog G \<longrightarrow> 
schirmer@12854
   745
         (\<forall> i im. iface G I = Some i \<longrightarrow> im \<in> imethds G I sig
schirmer@12854
   746
                  \<longrightarrow> \<not>is_static im \<and> accmodi im = Public)" (is "?P G I")
krauss@35440
   747
  proof (induct G I rule: iface_rec_induct', intro allI impI)
schirmer@12854
   748
    fix G I i im
krauss@35440
   749
    assume hyp: "\<And> i J. iface G I = Some i \<Longrightarrow> ws_prog G \<Longrightarrow> J \<in> set (isuperIfs i)
krauss@35440
   750
                 \<Longrightarrow> ?P G J"
schirmer@12854
   751
    assume wf: "wf_prog G" and if_I: "iface G I = Some i" and 
schirmer@12854
   752
           im: "im \<in> imethds G I sig" 
schirmer@12854
   753
    show "\<not>is_static im \<and> accmodi im = Public" 
schirmer@12854
   754
    proof -
schirmer@12854
   755
      let ?inherited = "Un_tables (imethds G ` set (isuperIfs i))"
nipkow@30235
   756
      let ?new = "(Option.set \<circ> table_of (map (\<lambda>(s, mh). (s, I, mh)) (imethods i)))"
schirmer@12854
   757
      from if_I wf im have imethds:"im \<in> (?inherited \<oplus>\<oplus> ?new) sig"
wenzelm@32960
   758
        by (simp add: imethds_rec)
schirmer@12854
   759
      from wf if_I have 
wenzelm@32960
   760
        wf_supI: "\<forall> J. J \<in> set (isuperIfs i) \<longrightarrow> (\<exists> j. iface G J = Some j)"
wenzelm@32960
   761
        by (blast dest: wf_prog_idecl wf_idecl_supD is_acc_ifaceD)
schirmer@12854
   762
      from wf if_I have
wenzelm@32960
   763
        "\<forall> im \<in> set (imethods i). \<not> is_static im \<and> accmodi im = Public"
wenzelm@32960
   764
        by (auto dest!: wf_prog_idecl wf_idecl_mhead)
schirmer@12854
   765
      then have new_ok: "\<forall> im. table_of (imethods i) sig = Some im 
schirmer@12854
   766
                         \<longrightarrow>  \<not> is_static im \<and> accmodi im = Public"
wenzelm@32960
   767
        by (auto dest!: table_of_Some_in_set)
schirmer@12854
   768
      show ?thesis
wenzelm@32960
   769
        proof (cases "?new sig = {}")
wenzelm@32960
   770
          case True
wenzelm@32960
   771
          from True wf wf_supI if_I imethds hyp 
wenzelm@32960
   772
          show ?thesis by (auto simp del:  split_paired_All)  
wenzelm@32960
   773
        next
wenzelm@32960
   774
          case False
wenzelm@32960
   775
          from False wf wf_supI if_I imethds new_ok hyp 
wenzelm@32960
   776
          show ?thesis by (auto dest: wf_idecl_hidings hidings_entailsD)
wenzelm@32960
   777
        qed
schirmer@12854
   778
      qed
schirmer@12854
   779
    qed
schirmer@12854
   780
  with asm show ?thesis by (auto simp del: split_paired_All)
schirmer@12854
   781
qed
schirmer@12854
   782
schirmer@12854
   783
lemma wf_prog_hidesD:
wenzelm@12937
   784
  assumes hides: "G \<turnstile>new hides old" and wf: "wf_prog G"
wenzelm@12937
   785
  shows
schirmer@12854
   786
   "accmodi old \<le> accmodi new \<and>
schirmer@12854
   787
    is_static old"
schirmer@12854
   788
proof -
schirmer@12854
   789
  from hides 
schirmer@12854
   790
  obtain c where 
schirmer@12854
   791
    clsNew: "class G (declclass new) = Some c" and
schirmer@12854
   792
    neqObj: "declclass new \<noteq> Object"
schirmer@12854
   793
    by (auto dest: hidesD declared_in_classD)
schirmer@12854
   794
  with hides obtain newM oldM where
schirmer@12854
   795
    newM: "table_of (methods c) (msig new) = Some newM" and 
schirmer@12854
   796
     new: "new = (declclass new,(msig new),newM)" and
schirmer@12854
   797
     old: "old = (declclass old,(msig old),oldM)" and
schirmer@12854
   798
          "msig new = msig old"
schirmer@12854
   799
    by (cases new,cases old) 
schirmer@12854
   800
       (auto dest: hidesD 
schirmer@12854
   801
         simp add: cdeclaredmethd_def declared_in_def)
schirmer@12854
   802
  with hides 
schirmer@12854
   803
  have hides':
schirmer@12854
   804
        "G,(msig new)\<turnstile>(declclass new,newM) hides (declclass old,oldM)"
schirmer@12854
   805
    by auto
schirmer@12854
   806
  from clsNew wf 
schirmer@12854
   807
  have "wf_cdecl G (declclass new,c)" by (blast intro: wf_prog_cdecl)
schirmer@12854
   808
  note wf_cdecl_hides_SomeD [OF this neqObj newM hides']
schirmer@12854
   809
  with new old 
schirmer@12854
   810
  show ?thesis
schirmer@12854
   811
    by (cases new, cases old) auto
schirmer@12854
   812
qed
schirmer@12854
   813
schirmer@12854
   814
text {* Compare this lemma about static  
schirmer@12854
   815
overriding @{term "G \<turnstile>new overrides\<^sub>S old"} with the definition of 
schirmer@12854
   816
dynamic overriding @{term "G \<turnstile>new overrides old"}. 
schirmer@12854
   817
Conforming result types and restrictions on the access modifiers of the old 
schirmer@12854
   818
and the new method are not part of the predicate for static overriding. But
schirmer@12854
   819
they are enshured in a wellfromed program.  Dynamic overriding has 
schirmer@12854
   820
no restrictions on the access modifiers but enforces confrom result types 
schirmer@12854
   821
as precondition. But with some efford we can guarantee the access modifier
schirmer@12854
   822
restriction for dynamic overriding, too. See lemma 
schirmer@12854
   823
@{text wf_prog_dyn_override_prop}.
schirmer@12854
   824
*}
schirmer@12854
   825
lemma wf_prog_stat_overridesD:
wenzelm@12937
   826
  assumes stat_override: "G \<turnstile>new overrides\<^sub>S old" and wf: "wf_prog G"
wenzelm@12937
   827
  shows
schirmer@12854
   828
   "G\<turnstile>resTy new\<preceq>resTy old \<and>
schirmer@12854
   829
    accmodi old \<le> accmodi new \<and>
schirmer@12854
   830
    \<not> is_static old"
schirmer@12854
   831
proof -
schirmer@12854
   832
  from stat_override 
schirmer@12854
   833
  obtain c where 
schirmer@12854
   834
    clsNew: "class G (declclass new) = Some c" and
schirmer@12854
   835
    neqObj: "declclass new \<noteq> Object"
schirmer@12854
   836
    by (auto dest: stat_overrides_commonD declared_in_classD)
schirmer@12854
   837
  with stat_override obtain newM oldM where
schirmer@12854
   838
    newM: "table_of (methods c) (msig new) = Some newM" and 
schirmer@12854
   839
     new: "new = (declclass new,(msig new),newM)" and
schirmer@12854
   840
     old: "old = (declclass old,(msig old),oldM)" and
schirmer@12854
   841
          "msig new = msig old"
schirmer@12854
   842
    by (cases new,cases old) 
schirmer@12854
   843
       (auto dest: stat_overrides_commonD 
schirmer@12854
   844
         simp add: cdeclaredmethd_def declared_in_def)
schirmer@12854
   845
  with stat_override 
schirmer@12854
   846
  have stat_override':
schirmer@12854
   847
        "G,(msig new)\<turnstile>(declclass new,newM) overrides\<^sub>S (declclass old,oldM)"
schirmer@12854
   848
    by auto
schirmer@12854
   849
  from clsNew wf 
schirmer@12854
   850
  have "wf_cdecl G (declclass new,c)" by (blast intro: wf_prog_cdecl)
schirmer@12854
   851
  note wf_cdecl_overrides_SomeD [OF this neqObj newM stat_override']
schirmer@12854
   852
  with new old 
schirmer@12854
   853
  show ?thesis
schirmer@12854
   854
    by (cases new, cases old) auto
schirmer@12854
   855
qed
schirmer@12854
   856
    
schirmer@12854
   857
lemma static_to_dynamic_overriding: 
wenzelm@12937
   858
  assumes stat_override: "G\<turnstile>new overrides\<^sub>S old" and wf : "wf_prog G"
wenzelm@12937
   859
  shows "G\<turnstile>new overrides old"
schirmer@12854
   860
proof -
schirmer@12854
   861
  from stat_override 
schirmer@12854
   862
  show ?thesis (is "?Overrides new old")
schirmer@12854
   863
  proof (induct)
schirmer@12854
   864
    case (Direct new old superNew)
schirmer@12854
   865
    then have stat_override:"G\<turnstile>new overrides\<^sub>S old" 
schirmer@12854
   866
      by (rule stat_overridesR.Direct)
schirmer@12854
   867
    from stat_override wf
schirmer@12854
   868
    have resTy_widen: "G\<turnstile>resTy new\<preceq>resTy old" and
schirmer@12854
   869
      not_static_old: "\<not> is_static old" 
schirmer@12854
   870
      by (auto dest: wf_prog_stat_overridesD)  
schirmer@12854
   871
    have not_private_new: "accmodi new \<noteq> Private"
schirmer@12854
   872
    proof -
schirmer@12854
   873
      from stat_override 
schirmer@12854
   874
      have "accmodi old \<noteq> Private"
wenzelm@32960
   875
        by (rule no_Private_stat_override)
schirmer@12854
   876
      moreover
schirmer@12854
   877
      from stat_override wf
schirmer@12854
   878
      have "accmodi old \<le> accmodi new"
wenzelm@32960
   879
        by (auto dest: wf_prog_stat_overridesD)
schirmer@12854
   880
      ultimately
schirmer@12854
   881
      show ?thesis
wenzelm@32960
   882
        by (auto dest: acc_modi_bottom)
schirmer@12854
   883
    qed
schirmer@12854
   884
    with Direct resTy_widen not_static_old 
schirmer@12854
   885
    show "?Overrides new old" 
schirmer@12962
   886
      by (auto intro: overridesR.Direct stat_override_declclasses_relation) 
schirmer@12854
   887
  next
berghofe@21765
   888
    case (Indirect new inter old)
schirmer@12854
   889
    then show "?Overrides new old" 
schirmer@12854
   890
      by (blast intro: overridesR.Indirect) 
schirmer@12854
   891
  qed
schirmer@12854
   892
qed
schirmer@12854
   893
schirmer@12854
   894
lemma non_Package_instance_method_inheritance:
wenzelm@12937
   895
  assumes old_inheritable: "G\<turnstile>Method old inheritable_in (pid C)" and
wenzelm@12937
   896
              accmodi_old: "accmodi old \<noteq> Package" and 
wenzelm@12937
   897
          instance_method: "\<not> is_static old" and
wenzelm@12937
   898
                   subcls: "G\<turnstile>C \<prec>\<^sub>C declclass old" and
wenzelm@12937
   899
             old_declared: "G\<turnstile>Method old declared_in (declclass old)" and
wenzelm@12937
   900
                       wf: "wf_prog G"
wenzelm@12937
   901
  shows "G\<turnstile>Method old member_of C \<or>
wenzelm@12937
   902
   (\<exists> new. G\<turnstile> new overrides\<^sub>S old \<and> G\<turnstile>Method new member_of C)"
schirmer@12854
   903
proof -
schirmer@12854
   904
  from wf have ws: "ws_prog G" by auto
schirmer@12854
   905
  from old_declared have iscls_declC_old: "is_class G (declclass old)"
schirmer@12854
   906
    by (auto simp add: declared_in_def cdeclaredmethd_def)
schirmer@12854
   907
  from subcls have  iscls_C: "is_class G C"
schirmer@12854
   908
    by (blast dest:  subcls_is_class)
schirmer@12854
   909
  from iscls_C ws old_inheritable subcls 
schirmer@12854
   910
  show ?thesis (is "?P C old")
schirmer@12854
   911
  proof (induct rule: ws_class_induct')
schirmer@12854
   912
    case Object
schirmer@12854
   913
    assume "G\<turnstile>Object\<prec>\<^sub>C declclass old"
schirmer@12854
   914
    then show "?P Object old"
schirmer@12854
   915
      by blast
schirmer@12854
   916
  next
schirmer@12854
   917
    case (Subcls C c)
schirmer@12854
   918
    assume cls_C: "class G C = Some c" and 
schirmer@12854
   919
       neq_C_Obj: "C \<noteq> Object" and
schirmer@12854
   920
             hyp: "\<lbrakk>G \<turnstile>Method old inheritable_in pid (super c); 
schirmer@12854
   921
                   G\<turnstile>super c\<prec>\<^sub>C declclass old\<rbrakk> \<Longrightarrow> ?P (super c) old" and
schirmer@12854
   922
     inheritable: "G \<turnstile>Method old inheritable_in pid C" and
schirmer@12854
   923
         subclsC: "G\<turnstile>C\<prec>\<^sub>C declclass old"
schirmer@12854
   924
    from cls_C neq_C_Obj  
haftmann@35416
   925
    have super: "G\<turnstile>C \<prec>\<^sub>C1 super c" 
schirmer@12854
   926
      by (rule subcls1I)
schirmer@12854
   927
    from wf cls_C neq_C_Obj
schirmer@12854
   928
    have accessible_super: "G\<turnstile>(Class (super c)) accessible_in (pid C)" 
schirmer@12854
   929
      by (auto dest: wf_prog_cdecl wf_cdecl_supD is_acc_classD)
schirmer@12854
   930
    {
schirmer@12854
   931
      fix old
schirmer@12854
   932
      assume    member_super: "G\<turnstile>Method old member_of (super c)"
schirmer@12854
   933
      assume     inheritable: "G \<turnstile>Method old inheritable_in pid C"
schirmer@12854
   934
      assume instance_method: "\<not> is_static old"
schirmer@12854
   935
      from member_super
schirmer@12854
   936
      have old_declared: "G\<turnstile>Method old declared_in (declclass old)"
schirmer@12854
   937
       by (cases old) (auto dest: member_of_declC)
schirmer@12854
   938
      have "?P C old"
schirmer@12854
   939
      proof (cases "G\<turnstile>mid (msig old) undeclared_in C")
wenzelm@32960
   940
        case True
wenzelm@32960
   941
        with inheritable super accessible_super member_super
wenzelm@32960
   942
        have "G\<turnstile>Method old member_of C"
wenzelm@32960
   943
          by (cases old) (auto intro: members.Inherited)
wenzelm@32960
   944
        then show ?thesis
wenzelm@32960
   945
          by auto
schirmer@12854
   946
      next
wenzelm@32960
   947
        case False
wenzelm@32960
   948
        then obtain new_member where
wenzelm@32960
   949
             "G\<turnstile>new_member declared_in C" and
schirmer@12854
   950
             "mid (msig old) = memberid new_member"
schirmer@12854
   951
          by (auto dest: not_undeclared_declared)
wenzelm@32960
   952
        then obtain new where
wenzelm@32960
   953
                  new: "G\<turnstile>Method new declared_in C" and
schirmer@12854
   954
               eq_sig: "msig old = msig new" and
wenzelm@32960
   955
            declC_new: "declclass new = C" 
wenzelm@32960
   956
          by (cases new_member) auto
wenzelm@32960
   957
        then have member_new: "G\<turnstile>Method new member_of C"
wenzelm@32960
   958
          by (cases new) (auto intro: members.Immediate)
wenzelm@32960
   959
        from declC_new super member_super
wenzelm@32960
   960
        have subcls_new_old: "G\<turnstile>declclass new \<prec>\<^sub>C declclass old"
wenzelm@32960
   961
          by (auto dest!: member_of_subclseq_declC
wenzelm@32960
   962
                    dest: r_into_trancl intro: trancl_rtrancl_trancl)
wenzelm@32960
   963
        show ?thesis
wenzelm@32960
   964
        proof (cases "is_static new")
wenzelm@32960
   965
          case False
wenzelm@32960
   966
          with eq_sig declC_new new old_declared inheritable
wenzelm@32960
   967
               super member_super subcls_new_old
wenzelm@32960
   968
          have "G\<turnstile>new overrides\<^sub>S old"
wenzelm@32960
   969
            by (auto intro!: stat_overridesR.Direct)
wenzelm@32960
   970
          with member_new show ?thesis
wenzelm@32960
   971
            by blast
wenzelm@32960
   972
        next
wenzelm@32960
   973
          case True
wenzelm@32960
   974
          with eq_sig declC_new subcls_new_old new old_declared inheritable
wenzelm@32960
   975
          have "G\<turnstile>new hides old"
wenzelm@32960
   976
            by (auto intro: hidesI)    
wenzelm@32960
   977
          with wf 
wenzelm@32960
   978
          have "is_static old"
wenzelm@32960
   979
            by (blast dest: wf_prog_hidesD)
wenzelm@32960
   980
          with instance_method
wenzelm@32960
   981
          show ?thesis
wenzelm@32960
   982
            by (contradiction)
wenzelm@32960
   983
        qed
schirmer@12854
   984
      qed
schirmer@12854
   985
    } note hyp_member_super = this
schirmer@12854
   986
    from subclsC cls_C 
schirmer@12854
   987
    have "G\<turnstile>(super c)\<preceq>\<^sub>C declclass old"
schirmer@12854
   988
      by (rule subcls_superD)
schirmer@12854
   989
    then
schirmer@12854
   990
    show "?P C old"
schirmer@12854
   991
    proof (cases rule: subclseq_cases) 
schirmer@12854
   992
      case Eq
schirmer@12854
   993
      assume "super c = declclass old"
schirmer@12854
   994
      with old_declared 
schirmer@12854
   995
      have "G\<turnstile>Method old member_of (super c)" 
wenzelm@32960
   996
        by (cases old) (auto intro: members.Immediate)
schirmer@12854
   997
      with inheritable instance_method 
schirmer@12854
   998
      show ?thesis
wenzelm@32960
   999
        by (blast dest: hyp_member_super)
schirmer@12854
  1000
    next
schirmer@12854
  1001
      case Subcls
schirmer@12854
  1002
      assume "G\<turnstile>super c\<prec>\<^sub>C declclass old"
schirmer@12854
  1003
      moreover
schirmer@12854
  1004
      from inheritable accmodi_old
schirmer@12854
  1005
      have "G \<turnstile>Method old inheritable_in pid (super c)"
wenzelm@32960
  1006
        by (cases "accmodi old") (auto simp add: inheritable_in_def)
schirmer@12854
  1007
      ultimately
schirmer@12854
  1008
      have "?P (super c) old"
wenzelm@32960
  1009
        by (blast dest: hyp)
schirmer@12854
  1010
      then show ?thesis
schirmer@12854
  1011
      proof
wenzelm@32960
  1012
        assume "G \<turnstile>Method old member_of super c"
wenzelm@32960
  1013
        with inheritable instance_method
wenzelm@32960
  1014
        show ?thesis
wenzelm@32960
  1015
          by (blast dest: hyp_member_super)
schirmer@12854
  1016
      next
wenzelm@32960
  1017
        assume "\<exists>new. G \<turnstile> new overrides\<^sub>S old \<and> G \<turnstile>Method new member_of super c"
wenzelm@32960
  1018
        then obtain super_new where
wenzelm@32960
  1019
          super_new_override:  "G \<turnstile> super_new overrides\<^sub>S old" and
schirmer@12854
  1020
            super_new_member:  "G \<turnstile>Method super_new member_of super c"
wenzelm@32960
  1021
          by blast
wenzelm@32960
  1022
        from super_new_override wf
wenzelm@32960
  1023
        have "accmodi old \<le> accmodi super_new"
wenzelm@32960
  1024
          by (auto dest: wf_prog_stat_overridesD)
wenzelm@32960
  1025
        with inheritable accmodi_old
wenzelm@32960
  1026
        have "G \<turnstile>Method super_new inheritable_in pid C"
wenzelm@32960
  1027
          by (auto simp add: inheritable_in_def 
wenzelm@32960
  1028
                      split: acc_modi.splits
schirmer@12854
  1029
                       dest: acc_modi_le_Dests)
wenzelm@32960
  1030
        moreover
wenzelm@32960
  1031
        from super_new_override 
wenzelm@32960
  1032
        have "\<not> is_static super_new"
wenzelm@32960
  1033
          by (auto dest: stat_overrides_commonD)
wenzelm@32960
  1034
        moreover
wenzelm@32960
  1035
        note super_new_member
wenzelm@32960
  1036
        ultimately have "?P C super_new"
wenzelm@32960
  1037
          by (auto dest: hyp_member_super)
wenzelm@32960
  1038
        then show ?thesis
wenzelm@32960
  1039
        proof 
wenzelm@32960
  1040
          assume "G \<turnstile>Method super_new member_of C"
wenzelm@32960
  1041
          with super_new_override
wenzelm@32960
  1042
          show ?thesis
wenzelm@32960
  1043
            by blast
wenzelm@32960
  1044
        next
wenzelm@32960
  1045
          assume "\<exists>new. G \<turnstile> new overrides\<^sub>S super_new \<and> 
schirmer@12854
  1046
                  G \<turnstile>Method new member_of C"
wenzelm@32960
  1047
          with super_new_override show ?thesis
wenzelm@32960
  1048
            by (blast intro: stat_overridesR.Indirect) 
wenzelm@32960
  1049
        qed
schirmer@12854
  1050
      qed
schirmer@12854
  1051
    qed
schirmer@12854
  1052
  qed
schirmer@12854
  1053
qed
schirmer@12854
  1054
schirmer@12854
  1055
lemma non_Package_instance_method_inheritance_cases [consumes 6,
schirmer@12854
  1056
         case_names Inheritance Overriding]:
wenzelm@12937
  1057
  assumes old_inheritable: "G\<turnstile>Method old inheritable_in (pid C)" and
wenzelm@12937
  1058
              accmodi_old: "accmodi old \<noteq> Package" and 
wenzelm@12937
  1059
          instance_method: "\<not> is_static old" and
wenzelm@12937
  1060
                   subcls: "G\<turnstile>C \<prec>\<^sub>C declclass old" and
wenzelm@12937
  1061
             old_declared: "G\<turnstile>Method old declared_in (declclass old)" and
wenzelm@12937
  1062
                       wf: "wf_prog G" and
wenzelm@12937
  1063
              inheritance: "G\<turnstile>Method old member_of C \<Longrightarrow> P" and
wenzelm@12937
  1064
               overriding: "\<And> new.
schirmer@12854
  1065
                           \<lbrakk>G\<turnstile> new overrides\<^sub>S old;G\<turnstile>Method new member_of C\<rbrakk>
schirmer@12854
  1066
                           \<Longrightarrow> P"
wenzelm@12937
  1067
  shows P
schirmer@12854
  1068
proof -
schirmer@12854
  1069
  from old_inheritable accmodi_old instance_method subcls old_declared wf 
schirmer@12854
  1070
       inheritance overriding
schirmer@12854
  1071
  show ?thesis
schirmer@12854
  1072
    by (auto dest: non_Package_instance_method_inheritance)
schirmer@12854
  1073
qed
schirmer@12854
  1074
schirmer@12854
  1075
lemma dynamic_to_static_overriding:
wenzelm@12937
  1076
  assumes dyn_override: "G\<turnstile> new overrides old" and
wenzelm@12937
  1077
           accmodi_old: "accmodi old \<noteq> Package" and
wenzelm@12937
  1078
                    wf: "wf_prog G"
wenzelm@12937
  1079
  shows "G\<turnstile> new overrides\<^sub>S old"  
schirmer@12854
  1080
proof - 
schirmer@12854
  1081
  from dyn_override accmodi_old
schirmer@12854
  1082
  show ?thesis (is "?Overrides new old")
schirmer@12854
  1083
  proof (induct rule: overridesR.induct)
schirmer@12854
  1084
    case (Direct new old)
schirmer@12854
  1085
    assume   new_declared: "G\<turnstile>Method new declared_in declclass new"
schirmer@12854
  1086
    assume eq_sig_new_old: "msig new = msig old"
schirmer@12854
  1087
    assume subcls_new_old: "G\<turnstile>declclass new \<prec>\<^sub>C declclass old"
schirmer@12854
  1088
    assume "G \<turnstile>Method old inheritable_in pid (declclass new)" and
schirmer@12854
  1089
           "accmodi old \<noteq> Package" and
schirmer@12854
  1090
           "\<not> is_static old" and
schirmer@12854
  1091
           "G\<turnstile>declclass new\<prec>\<^sub>C declclass old" and
schirmer@12854
  1092
           "G\<turnstile>Method old declared_in declclass old" 
schirmer@12854
  1093
    from this wf
schirmer@12854
  1094
    show "?Overrides new old"
schirmer@12854
  1095
    proof (cases rule: non_Package_instance_method_inheritance_cases)
schirmer@12854
  1096
      case Inheritance
schirmer@12854
  1097
      assume "G \<turnstile>Method old member_of declclass new"
schirmer@12854
  1098
      then have "G\<turnstile>mid (msig old) undeclared_in declclass new"
schirmer@12854
  1099
      proof cases
wenzelm@32960
  1100
        case Immediate 
wenzelm@32960
  1101
        with subcls_new_old wf show ?thesis     
wenzelm@32960
  1102
          by (auto dest: subcls_irrefl)
schirmer@12854
  1103
      next
wenzelm@32960
  1104
        case Inherited
wenzelm@32960
  1105
        then show ?thesis
wenzelm@32960
  1106
          by (cases old) auto
schirmer@12854
  1107
      qed
schirmer@12854
  1108
      with eq_sig_new_old new_declared
schirmer@12854
  1109
      show ?thesis
wenzelm@32960
  1110
        by (cases old,cases new) (auto dest!: declared_not_undeclared)
schirmer@12854
  1111
    next
schirmer@12854
  1112
      case (Overriding new') 
schirmer@12854
  1113
      assume stat_override_new': "G \<turnstile> new' overrides\<^sub>S old"
schirmer@12854
  1114
      then have "msig new' = msig old"
wenzelm@32960
  1115
        by (auto dest: stat_overrides_commonD)
schirmer@12854
  1116
      with eq_sig_new_old have eq_sig_new_new': "msig new=msig new'"
wenzelm@32960
  1117
        by simp
schirmer@12854
  1118
      assume "G \<turnstile>Method new' member_of declclass new"
schirmer@12854
  1119
      then show ?thesis
schirmer@12854
  1120
      proof (cases)
wenzelm@32960
  1121
        case Immediate
wenzelm@32960
  1122
        then have declC_new: "declclass new' = declclass new" 
wenzelm@32960
  1123
          by auto
wenzelm@32960
  1124
        from Immediate 
wenzelm@32960
  1125
        have "G\<turnstile>Method new' declared_in declclass new"
wenzelm@32960
  1126
          by (cases new') auto
wenzelm@32960
  1127
        with new_declared eq_sig_new_new' declC_new 
wenzelm@32960
  1128
        have "new=new'"
wenzelm@32960
  1129
          by (cases new, cases new') (auto dest: unique_declared_in) 
wenzelm@32960
  1130
        with stat_override_new'
wenzelm@32960
  1131
        show ?thesis
wenzelm@32960
  1132
          by simp
schirmer@12854
  1133
      next
wenzelm@32960
  1134
        case Inherited
wenzelm@32960
  1135
        then have "G\<turnstile>mid (msig new') undeclared_in declclass new"
wenzelm@32960
  1136
          by (cases new') (auto)
wenzelm@32960
  1137
        with eq_sig_new_new' new_declared
wenzelm@32960
  1138
        show ?thesis
wenzelm@32960
  1139
          by (cases new,cases new') (auto dest!: declared_not_undeclared)
schirmer@12854
  1140
      qed
schirmer@12854
  1141
    qed
schirmer@12854
  1142
  next
berghofe@21765
  1143
    case (Indirect new inter old)
schirmer@12854
  1144
    assume accmodi_old: "accmodi old \<noteq> Package"
schirmer@12854
  1145
    assume "accmodi old \<noteq> Package \<Longrightarrow> G \<turnstile> inter overrides\<^sub>S old"
schirmer@12854
  1146
    with accmodi_old 
schirmer@12854
  1147
    have stat_override_inter_old: "G \<turnstile> inter overrides\<^sub>S old"
schirmer@12854
  1148
      by blast
schirmer@12854
  1149
    moreover 
schirmer@12854
  1150
    assume hyp_inter: "accmodi inter \<noteq> Package \<Longrightarrow> G \<turnstile> new overrides\<^sub>S inter"
schirmer@12854
  1151
    moreover
schirmer@12854
  1152
    have "accmodi inter \<noteq> Package"
schirmer@12854
  1153
    proof -
schirmer@12854
  1154
      from stat_override_inter_old wf 
schirmer@12854
  1155
      have "accmodi old \<le> accmodi inter"
wenzelm@32960
  1156
        by (auto dest: wf_prog_stat_overridesD)
schirmer@12854
  1157
      with stat_override_inter_old accmodi_old
schirmer@12854
  1158
      show ?thesis
wenzelm@32960
  1159
        by (auto dest!: no_Private_stat_override
schirmer@12854
  1160
                 split: acc_modi.splits 
wenzelm@32960
  1161
                 dest: acc_modi_le_Dests)
schirmer@12854
  1162
    qed
schirmer@12854
  1163
    ultimately show "?Overrides new old"
schirmer@12854
  1164
      by (blast intro: stat_overridesR.Indirect)
schirmer@12854
  1165
  qed
schirmer@12854
  1166
qed
schirmer@12854
  1167
schirmer@12854
  1168
lemma wf_prog_dyn_override_prop:
wenzelm@12937
  1169
  assumes dyn_override: "G \<turnstile> new overrides old" and
schirmer@12854
  1170
                    wf: "wf_prog G"
wenzelm@12937
  1171
  shows "accmodi old \<le> accmodi new"
schirmer@12854
  1172
proof (cases "accmodi old = Package")
schirmer@12854
  1173
  case True
schirmer@12854
  1174
  note old_Package = this
schirmer@12854
  1175
  show ?thesis
schirmer@12854
  1176
  proof (cases "accmodi old \<le> accmodi new")
schirmer@12854
  1177
    case True then show ?thesis .
schirmer@12854
  1178
  next
schirmer@12854
  1179
    case False
schirmer@12854
  1180
    with old_Package 
schirmer@12854
  1181
    have "accmodi new = Private"
schirmer@12854
  1182
      by (cases "accmodi new") (auto simp add: le_acc_def less_acc_def)
schirmer@12854
  1183
    with dyn_override 
schirmer@12854
  1184
    show ?thesis
schirmer@12854
  1185
      by (auto dest: overrides_commonD)
schirmer@12854
  1186
  qed    
schirmer@12854
  1187
next
schirmer@12854
  1188
  case False
schirmer@12854
  1189
  with dyn_override wf
schirmer@12854
  1190
  have "G \<turnstile> new overrides\<^sub>S old"
schirmer@12854
  1191
    by (blast intro: dynamic_to_static_overriding)
schirmer@12854
  1192
  with wf 
schirmer@12854
  1193
  show ?thesis
schirmer@12854
  1194
   by (blast dest: wf_prog_stat_overridesD)
schirmer@12854
  1195
qed 
schirmer@12854
  1196
schirmer@12854
  1197
lemma overrides_Package_old: 
wenzelm@12937
  1198
  assumes dyn_override: "G \<turnstile> new overrides old" and 
wenzelm@12937
  1199
           accmodi_new: "accmodi new = Package" and
wenzelm@12937
  1200
                    wf: "wf_prog G "
wenzelm@12937
  1201
  shows "accmodi old = Package"
schirmer@12854
  1202
proof (cases "accmodi old")
schirmer@12854
  1203
  case Private
schirmer@12854
  1204
  with dyn_override show ?thesis
schirmer@12854
  1205
    by (simp add: no_Private_override)
schirmer@12854
  1206
next
schirmer@12854
  1207
  case Package
schirmer@12854
  1208
  then show ?thesis .
schirmer@12854
  1209
next
schirmer@12854
  1210
  case Protected
schirmer@12854
  1211
  with dyn_override wf
schirmer@12854
  1212
  have "G \<turnstile> new overrides\<^sub>S old"
schirmer@12854
  1213
    by (auto intro: dynamic_to_static_overriding)
schirmer@12854
  1214
  with wf 
schirmer@12854
  1215
  have "accmodi old \<le> accmodi new"
schirmer@12854
  1216
    by (auto dest: wf_prog_stat_overridesD)
schirmer@12854
  1217
  with Protected accmodi_new
schirmer@12854
  1218
  show ?thesis
schirmer@12854
  1219
    by (simp add: less_acc_def le_acc_def)
schirmer@12854
  1220
next
schirmer@12854
  1221
  case Public
schirmer@12854
  1222
  with dyn_override wf
schirmer@12854
  1223
  have "G \<turnstile> new overrides\<^sub>S old"
schirmer@12854
  1224
    by (auto intro: dynamic_to_static_overriding)
schirmer@12854
  1225
  with wf 
schirmer@12854
  1226
  have "accmodi old \<le> accmodi new"
schirmer@12854
  1227
    by (auto dest: wf_prog_stat_overridesD)
schirmer@12854
  1228
  with Public accmodi_new
schirmer@12854
  1229
  show ?thesis
schirmer@12854
  1230
    by (simp add: less_acc_def le_acc_def)
schirmer@12854
  1231
qed
schirmer@12854
  1232
schirmer@12854
  1233
lemma dyn_override_Package:
wenzelm@12937
  1234
  assumes dyn_override: "G \<turnstile> new overrides old" and
wenzelm@12937
  1235
           accmodi_old: "accmodi old = Package" and 
wenzelm@12937
  1236
           accmodi_new: "accmodi new = Package" and
schirmer@12854
  1237
                    wf: "wf_prog G"
wenzelm@12937
  1238
  shows "pid (declclass old) = pid (declclass new)"
schirmer@12854
  1239
proof - 
schirmer@12854
  1240
  from dyn_override accmodi_old accmodi_new
schirmer@12854
  1241
  show ?thesis (is "?EqPid old new")
schirmer@12854
  1242
  proof (induct rule: overridesR.induct)
schirmer@12854
  1243
    case (Direct new old)
schirmer@12854
  1244
    assume "accmodi old = Package"
schirmer@12854
  1245
           "G \<turnstile>Method old inheritable_in pid (declclass new)"
schirmer@12854
  1246
    then show "pid (declclass old) =  pid (declclass new)"
schirmer@12854
  1247
      by (auto simp add: inheritable_in_def)
schirmer@12854
  1248
  next
berghofe@21765
  1249
    case (Indirect new inter old)
schirmer@12854
  1250
    assume accmodi_old: "accmodi old = Package" and
schirmer@12854
  1251
           accmodi_new: "accmodi new = Package" 
schirmer@12854
  1252
    assume "G \<turnstile> new overrides inter"
schirmer@12854
  1253
    with accmodi_new wf
schirmer@12854
  1254
    have "accmodi inter = Package"
schirmer@12854
  1255
      by  (auto intro: overrides_Package_old)
schirmer@12854
  1256
    with Indirect
schirmer@12854
  1257
    show "pid (declclass old) =  pid (declclass new)"
schirmer@12854
  1258
      by auto
schirmer@12854
  1259
  qed
schirmer@12854
  1260
qed
schirmer@12854
  1261
schirmer@12854
  1262
lemma dyn_override_Package_escape:
wenzelm@12937
  1263
  assumes dyn_override: "G \<turnstile> new overrides old" and
wenzelm@12937
  1264
           accmodi_old: "accmodi old = Package" and 
wenzelm@12937
  1265
          outside_pack: "pid (declclass old) \<noteq> pid (declclass new)" and
schirmer@12854
  1266
                    wf: "wf_prog G"
wenzelm@12937
  1267
  shows "\<exists> inter. G \<turnstile> new overrides inter \<and> G \<turnstile> inter overrides old \<and>
schirmer@12854
  1268
             pid (declclass old) = pid (declclass inter) \<and>
schirmer@12854
  1269
             Protected \<le> accmodi inter"
schirmer@12854
  1270
proof -
schirmer@12854
  1271
  from dyn_override accmodi_old outside_pack
schirmer@12854
  1272
  show ?thesis (is "?P new old")
schirmer@12854
  1273
  proof (induct rule: overridesR.induct)
schirmer@12854
  1274
    case (Direct new old)
schirmer@12854
  1275
    assume accmodi_old: "accmodi old = Package"
schirmer@12854
  1276
    assume outside_pack: "pid (declclass old) \<noteq> pid (declclass new)"
schirmer@12854
  1277
    assume "G \<turnstile>Method old inheritable_in pid (declclass new)"
schirmer@12854
  1278
    with accmodi_old 
schirmer@12854
  1279
    have "pid (declclass old) = pid (declclass new)"
schirmer@12854
  1280
      by (simp add: inheritable_in_def)
schirmer@12854
  1281
    with outside_pack 
schirmer@12854
  1282
    show "?P new old"
schirmer@12854
  1283
      by (contradiction)
schirmer@12854
  1284
  next
berghofe@21765
  1285
    case (Indirect new inter old)
schirmer@12854
  1286
    assume accmodi_old: "accmodi old = Package"
schirmer@12854
  1287
    assume outside_pack: "pid (declclass old) \<noteq> pid (declclass new)"
schirmer@12854
  1288
    assume override_new_inter: "G \<turnstile> new overrides inter"
schirmer@12854
  1289
    assume override_inter_old: "G \<turnstile> inter overrides old"
schirmer@12854
  1290
    assume hyp_new_inter: "\<lbrakk>accmodi inter = Package; 
schirmer@12854
  1291
                           pid (declclass inter) \<noteq> pid (declclass new)\<rbrakk>
schirmer@12854
  1292
                           \<Longrightarrow> ?P new inter"
schirmer@12854
  1293
    assume hyp_inter_old: "\<lbrakk>accmodi old = Package; 
schirmer@12854
  1294
                           pid (declclass old) \<noteq> pid (declclass inter)\<rbrakk>
schirmer@12854
  1295
                           \<Longrightarrow> ?P inter old"
schirmer@12854
  1296
    show "?P new old"
schirmer@12854
  1297
    proof (cases "pid (declclass old) = pid (declclass inter)")
schirmer@12854
  1298
      case True
schirmer@12854
  1299
      note same_pack_old_inter = this
schirmer@12854
  1300
      show ?thesis
schirmer@12854
  1301
      proof (cases "pid (declclass inter) = pid (declclass new)")
wenzelm@32960
  1302
        case True
wenzelm@32960
  1303
        with same_pack_old_inter outside_pack
wenzelm@32960
  1304
        show ?thesis
wenzelm@32960
  1305
          by auto
schirmer@12854
  1306
      next
wenzelm@32960
  1307
        case False
wenzelm@32960
  1308
        note diff_pack_inter_new = this
wenzelm@32960
  1309
        show ?thesis
wenzelm@32960
  1310
        proof (cases "accmodi inter = Package")
wenzelm@32960
  1311
          case True
wenzelm@32960
  1312
          with diff_pack_inter_new hyp_new_inter  
wenzelm@32960
  1313
          obtain newinter where
wenzelm@32960
  1314
            over_new_newinter: "G \<turnstile> new overrides newinter" and
schirmer@12854
  1315
            over_newinter_inter: "G \<turnstile> newinter overrides inter" and 
schirmer@12854
  1316
            eq_pid: "pid (declclass inter) = pid (declclass newinter)" and
schirmer@12854
  1317
            accmodi_newinter: "Protected \<le> accmodi newinter"
wenzelm@32960
  1318
            by auto
wenzelm@32960
  1319
          from over_newinter_inter override_inter_old
wenzelm@32960
  1320
          have "G\<turnstile>newinter overrides old"
wenzelm@32960
  1321
            by (rule overridesR.Indirect)
wenzelm@32960
  1322
          moreover
wenzelm@32960
  1323
          from eq_pid same_pack_old_inter 
wenzelm@32960
  1324
          have "pid (declclass old) = pid (declclass newinter)"
wenzelm@32960
  1325
            by simp
wenzelm@32960
  1326
          moreover
wenzelm@32960
  1327
          note over_new_newinter accmodi_newinter
wenzelm@32960
  1328
          ultimately show ?thesis
wenzelm@32960
  1329
            by blast
wenzelm@32960
  1330
        next
wenzelm@32960
  1331
          case False
wenzelm@32960
  1332
          with override_new_inter
wenzelm@32960
  1333
          have "Protected \<le> accmodi inter"
wenzelm@32960
  1334
            by (cases "accmodi inter") (auto dest: no_Private_override)
wenzelm@32960
  1335
          with override_new_inter override_inter_old same_pack_old_inter
wenzelm@32960
  1336
          show ?thesis
wenzelm@32960
  1337
            by blast
wenzelm@32960
  1338
        qed
schirmer@12854
  1339
      qed
schirmer@12854
  1340
    next
schirmer@12854
  1341
      case False
schirmer@12854
  1342
      with accmodi_old hyp_inter_old
schirmer@12854
  1343
      obtain newinter where
wenzelm@32960
  1344
        over_inter_newinter: "G \<turnstile> inter overrides newinter" and
schirmer@12854
  1345
          over_newinter_old: "G \<turnstile> newinter overrides old" and 
schirmer@12854
  1346
                eq_pid: "pid (declclass old) = pid (declclass newinter)" and
wenzelm@32960
  1347
        accmodi_newinter: "Protected \<le> accmodi newinter"
wenzelm@32960
  1348
        by auto
schirmer@12854
  1349
      from override_new_inter over_inter_newinter 
schirmer@12854
  1350
      have "G \<turnstile> new overrides newinter"
wenzelm@32960
  1351
        by (rule overridesR.Indirect)
schirmer@12854
  1352
      with eq_pid over_newinter_old accmodi_newinter
schirmer@12854
  1353
      show ?thesis
wenzelm@32960
  1354
        by blast
schirmer@12854
  1355
    qed
schirmer@12854
  1356
  qed
schirmer@12854
  1357
qed
schirmer@12854
  1358
wenzelm@45605
  1359
lemmas class_rec_induct' = class_rec.induct [of "%x y z w. P x y"] for P
krauss@35440
  1360
schirmer@12854
  1361
lemma declclass_widen[rule_format]: 
schirmer@12854
  1362
 "wf_prog G 
schirmer@12854
  1363
 \<longrightarrow> (\<forall>c m. class G C = Some c \<longrightarrow> methd G C sig = Some m 
schirmer@12854
  1364
 \<longrightarrow> G\<turnstile>C \<preceq>\<^sub>C declclass m)" (is "?P G C")
krauss@35440
  1365
proof (induct G C rule: class_rec_induct', intro allI impI)
schirmer@12854
  1366
  fix G C c m
krauss@35440
  1367
  assume Hyp: "\<And>c. class G C = Some c \<Longrightarrow> ws_prog G \<Longrightarrow> C \<noteq> Object
krauss@35440
  1368
               \<Longrightarrow> ?P G (super c)"
schirmer@12854
  1369
  assume wf: "wf_prog G" and cls_C: "class G C = Some c" and
schirmer@12854
  1370
         m:  "methd G C sig = Some m"
schirmer@12854
  1371
  show "G\<turnstile>C\<preceq>\<^sub>C declclass m" 
schirmer@12854
  1372
  proof (cases "C=Object")
schirmer@12854
  1373
    case True 
schirmer@12854
  1374
    with wf m show ?thesis by (simp add: methd_Object_SomeD)
schirmer@12854
  1375
  next
schirmer@12854
  1376
    let ?filter="filter_tab (\<lambda>sig m. G\<turnstile>C inherits method sig m)"
schirmer@12854
  1377
    let ?table = "table_of (map (\<lambda>(s, m). (s, C, m)) (methods c))"
schirmer@12854
  1378
    case False 
schirmer@12854
  1379
    with cls_C wf m
schirmer@12854
  1380
    have methd_C: "(?filter (methd G (super c)) ++ ?table) sig = Some m "
schirmer@12854
  1381
      by (simp add: methd_rec)
schirmer@12854
  1382
    show ?thesis
schirmer@12854
  1383
    proof (cases "?table sig")
schirmer@12854
  1384
      case None
schirmer@12854
  1385
      from this methd_C have "?filter (methd G (super c)) sig = Some m"
wenzelm@32960
  1386
        by simp
schirmer@12854
  1387
      moreover
schirmer@12854
  1388
      from wf cls_C False obtain sup where "class G (super c) = Some sup"
wenzelm@32960
  1389
        by (blast dest: wf_prog_cdecl wf_cdecl_supD is_acc_class_is_class)
schirmer@12925
  1390
      moreover note wf False cls_C  
schirmer@12925
  1391
      ultimately have "G\<turnstile>super c \<preceq>\<^sub>C declclass m"  
wenzelm@32960
  1392
        by (auto intro: Hyp [rule_format])
haftmann@35416
  1393
      moreover from cls_C False have  "G\<turnstile>C \<prec>\<^sub>C1 super c" by (rule subcls1I)
schirmer@12854
  1394
      ultimately show ?thesis by - (rule rtrancl_into_rtrancl2)
schirmer@12854
  1395
    next
schirmer@12854
  1396
      case Some
schirmer@12854
  1397
      from this wf False cls_C methd_C show ?thesis by auto
schirmer@12854
  1398
    qed
schirmer@12854
  1399
  qed
schirmer@12854
  1400
qed
schirmer@12854
  1401
schirmer@12854
  1402
lemma declclass_methd_Object: 
schirmer@12854
  1403
 "\<lbrakk>wf_prog G; methd G Object sig = Some m\<rbrakk> \<Longrightarrow> declclass m = Object"
schirmer@12854
  1404
by auto
schirmer@12854
  1405
schirmer@12854
  1406
lemma methd_declaredD: 
schirmer@12854
  1407
 "\<lbrakk>wf_prog G; is_class G C;methd G C sig = Some m\<rbrakk> 
schirmer@12854
  1408
  \<Longrightarrow> G\<turnstile>(mdecl (sig,mthd m)) declared_in (declclass m)"
schirmer@12854
  1409
proof -
schirmer@12854
  1410
  assume    wf: "wf_prog G"
schirmer@12854
  1411
  then have ws: "ws_prog G" ..
schirmer@12854
  1412
  assume  clsC: "is_class G C"
schirmer@12854
  1413
  from clsC ws 
schirmer@12854
  1414
  show "methd G C sig = Some m 
schirmer@12854
  1415
        \<Longrightarrow> G\<turnstile>(mdecl (sig,mthd m)) declared_in (declclass m)"
berghofe@34915
  1416
  proof (induct C rule: ws_class_induct')
schirmer@12854
  1417
    case Object
schirmer@12854
  1418
    assume "methd G Object sig = Some m" 
schirmer@12854
  1419
    with wf show ?thesis
schirmer@12854
  1420
      by - (rule method_declared_inI, auto) 
schirmer@12854
  1421
  next
schirmer@12854
  1422
    case Subcls
schirmer@12854
  1423
    fix C c
schirmer@12854
  1424
    assume clsC: "class G C = Some c"
schirmer@12854
  1425
    and       m: "methd G C sig = Some m"
schirmer@12854
  1426
    and     hyp: "methd G (super c) sig = Some m \<Longrightarrow> ?thesis" 
schirmer@12854
  1427
    let ?newMethods = "table_of (map (\<lambda>(s, m). (s, C, m)) (methods c))"
schirmer@12854
  1428
    show ?thesis
schirmer@12854
  1429
    proof (cases "?newMethods sig")
schirmer@12854
  1430
      case None
schirmer@12854
  1431
      from None ws clsC m hyp 
schirmer@12854
  1432
      show ?thesis by (auto intro: method_declared_inI simp add: methd_rec)
schirmer@12854
  1433
    next
schirmer@12854
  1434
      case Some
schirmer@12854
  1435
      from Some ws clsC m 
schirmer@12854
  1436
      show ?thesis by (auto intro: method_declared_inI simp add: methd_rec) 
schirmer@12854
  1437
    qed
schirmer@12854
  1438
  qed
schirmer@12854
  1439
qed
schirmer@12854
  1440
schirmer@12854
  1441
lemma methd_rec_Some_cases [consumes 4, case_names NewMethod InheritedMethod]:
wenzelm@12937
  1442
  assumes methd_C: "methd G C sig = Some m" and
wenzelm@12937
  1443
               ws: "ws_prog G" and
wenzelm@12937
  1444
             clsC: "class G C = Some c" and
wenzelm@12937
  1445
        neq_C_Obj: "C\<noteq>Object"
wenzelm@12937
  1446
  shows
schirmer@12854
  1447
"\<lbrakk>table_of (map (\<lambda>(s, m). (s, C, m)) (methods c)) sig = Some m \<Longrightarrow> P;
schirmer@12854
  1448
  \<lbrakk>G\<turnstile>C inherits (method sig m); methd G (super c) sig = Some m\<rbrakk> \<Longrightarrow> P 
schirmer@12854
  1449
 \<rbrakk> \<Longrightarrow> P"
schirmer@12854
  1450
proof -
schirmer@12854
  1451
  let ?inherited   = "filter_tab (\<lambda>sig m. G\<turnstile>C inherits method sig m) 
schirmer@12854
  1452
                              (methd G (super c))"
schirmer@12854
  1453
  let ?new = "table_of (map (\<lambda>(s, m). (s, C, m)) (methods c))"
schirmer@12854
  1454
  from ws clsC neq_C_Obj methd_C 
schirmer@12854
  1455
  have methd_unfold: "(?inherited ++ ?new) sig = Some m"
schirmer@12854
  1456
    by (simp add: methd_rec)
schirmer@12854
  1457
  assume NewMethod: "?new sig = Some m \<Longrightarrow> P"
schirmer@12854
  1458
  assume InheritedMethod: "\<lbrakk>G\<turnstile>C inherits (method sig m); 
schirmer@12854
  1459
                            methd G (super c) sig = Some m\<rbrakk> \<Longrightarrow> P"
schirmer@12854
  1460
  show P
schirmer@12854
  1461
  proof (cases "?new sig")
schirmer@12854
  1462
    case None
schirmer@12854
  1463
    with methd_unfold have "?inherited sig = Some m"
schirmer@12854
  1464
      by (auto)
schirmer@12854
  1465
    with InheritedMethod show P by blast
schirmer@12854
  1466
  next
schirmer@12854
  1467
    case Some
schirmer@12854
  1468
    with methd_unfold have "?new sig = Some m"
schirmer@12854
  1469
      by auto
schirmer@12854
  1470
    with NewMethod show P by blast
schirmer@12854
  1471
  qed
schirmer@12854
  1472
qed
schirmer@12854
  1473
schirmer@12854
  1474
  
schirmer@12854
  1475
lemma methd_member_of:
wenzelm@12937
  1476
  assumes wf: "wf_prog G"
wenzelm@12937
  1477
  shows
wenzelm@12937
  1478
    "\<lbrakk>is_class G C; methd G C sig = Some m\<rbrakk> \<Longrightarrow> G\<turnstile>Methd sig m member_of C" 
schirmer@12854
  1479
  (is "?Class C \<Longrightarrow> ?Method C \<Longrightarrow> ?MemberOf C") 
schirmer@12854
  1480
proof -
schirmer@12854
  1481
  from wf   have   ws: "ws_prog G" ..
schirmer@12854
  1482
  assume defC: "is_class G C"
schirmer@12854
  1483
  from defC ws 
schirmer@12854
  1484
  show "?Class C \<Longrightarrow> ?Method C \<Longrightarrow> ?MemberOf C"
schirmer@12854
  1485
  proof (induct rule: ws_class_induct')  
schirmer@12854
  1486
    case Object
berghofe@13601
  1487
    with wf have declC: "Object = declclass m"
berghofe@13601
  1488
      by (simp add: declclass_methd_Object)
berghofe@13601
  1489
    from Object wf have "G\<turnstile>Methd sig m declared_in Object"
berghofe@13601
  1490
      by (auto intro: methd_declaredD simp add: declC)
schirmer@12854
  1491
    with declC 
schirmer@12854
  1492
    show "?MemberOf Object"
schirmer@12854
  1493
      by (auto intro!: members.Immediate
schirmer@12854
  1494
                  simp del: methd_Object)
schirmer@12854
  1495
  next
schirmer@12854
  1496
    case (Subcls C c)
schirmer@12854
  1497
    assume  clsC: "class G C = Some c" and
schirmer@12854
  1498
       neq_C_Obj: "C \<noteq> Object"  
schirmer@12854
  1499
    assume methd: "?Method C"
schirmer@12854
  1500
    from methd ws clsC neq_C_Obj
schirmer@12854
  1501
    show "?MemberOf C"
schirmer@12854
  1502
    proof (cases rule: methd_rec_Some_cases)
schirmer@12854
  1503
      case NewMethod
schirmer@12854
  1504
      with clsC show ?thesis
wenzelm@32960
  1505
        by (auto dest: method_declared_inI intro!: members.Immediate)
schirmer@12854
  1506
    next
schirmer@12854
  1507
      case InheritedMethod
schirmer@12854
  1508
      then show "?thesis"
wenzelm@32960
  1509
        by (blast dest: inherits_member)
schirmer@12854
  1510
    qed
schirmer@12854
  1511
  qed
schirmer@12854
  1512
qed
schirmer@12854
  1513
schirmer@12854
  1514
lemma current_methd: 
schirmer@12854
  1515
      "\<lbrakk>table_of (methods c) sig = Some new;
schirmer@12854
  1516
        ws_prog G; class G C = Some c; C \<noteq> Object; 
schirmer@12854
  1517
        methd G (super c) sig = Some old\<rbrakk> 
schirmer@12854
  1518
    \<Longrightarrow> methd G C sig = Some (C,new)"
schirmer@12854
  1519
by (auto simp add: methd_rec
nipkow@14025
  1520
            intro: filter_tab_SomeI map_add_find_right table_of_map_SomeI)
schirmer@12854
  1521
schirmer@12854
  1522
lemma wf_prog_staticD:
wenzelm@12937
  1523
  assumes     wf: "wf_prog G" and
schirmer@12854
  1524
            clsC: "class G C = Some c" and
schirmer@12854
  1525
       neq_C_Obj: "C \<noteq> Object" and 
schirmer@12854
  1526
             old: "methd G (super c) sig = Some old" and 
schirmer@12854
  1527
     accmodi_old: "Protected \<le> accmodi old" and
schirmer@12854
  1528
             new: "table_of (methods c) sig = Some new"
wenzelm@12937
  1529
  shows "is_static new = is_static old"
schirmer@12854
  1530
proof -
schirmer@12854
  1531
  from clsC wf 
schirmer@12854
  1532
  have wf_cdecl: "wf_cdecl G (C,c)" by (rule wf_prog_cdecl)
schirmer@12854
  1533
  from wf clsC neq_C_Obj
schirmer@12854
  1534
  have is_cls_super: "is_class G (super c)" 
schirmer@12854
  1535
    by (blast dest: wf_prog_acc_superD is_acc_classD)
schirmer@12854
  1536
  from wf is_cls_super old 
schirmer@12854
  1537
  have old_member_of: "G\<turnstile>Methd sig old member_of (super c)"  
schirmer@12854
  1538
    by (rule methd_member_of)
schirmer@12854
  1539
  from old wf is_cls_super 
schirmer@12854
  1540
  have old_declared: "G\<turnstile>Methd sig old declared_in (declclass old)"
schirmer@12854
  1541
    by (auto dest: methd_declared_in_declclass)
schirmer@12854
  1542
  from new clsC 
schirmer@12854
  1543
  have new_declared: "G\<turnstile>Methd sig (C,new) declared_in C"
schirmer@12854
  1544
    by (auto intro: method_declared_inI)
schirmer@12854
  1545
  note trancl_rtrancl_tranc = trancl_rtrancl_trancl [trans] (* ### in Basis *)
schirmer@12854
  1546
  from clsC neq_C_Obj
haftmann@35416
  1547
  have subcls1_C_super: "G\<turnstile>C \<prec>\<^sub>C1 super c"
schirmer@12854
  1548
    by (rule subcls1I)
schirmer@12854
  1549
  then have "G\<turnstile>C \<prec>\<^sub>C super c" ..
schirmer@12854
  1550
  also from old wf is_cls_super
schirmer@12854
  1551
  have "G\<turnstile>super c \<preceq>\<^sub>C (declclass old)" by (auto dest: methd_declC)
schirmer@12854
  1552
  finally have subcls_C_old:  "G\<turnstile>C \<prec>\<^sub>C (declclass old)" .
schirmer@12854
  1553
  from accmodi_old 
schirmer@12854
  1554
  have inheritable: "G\<turnstile>Methd sig old inheritable_in pid C"
schirmer@12854
  1555
    by (auto simp add: inheritable_in_def
schirmer@12854
  1556
                 dest: acc_modi_le_Dests)
schirmer@12854
  1557
  show ?thesis
schirmer@12854
  1558
  proof (cases "is_static new")
schirmer@12854
  1559
    case True
schirmer@12854
  1560
    with subcls_C_old new_declared old_declared inheritable
schirmer@12854
  1561
    have "G,sig\<turnstile>(C,new) hides old"
schirmer@12854
  1562
      by (auto intro: hidesI)
schirmer@12854
  1563
    with True wf_cdecl neq_C_Obj new 
schirmer@12854
  1564
    show ?thesis
schirmer@12854
  1565
      by (auto dest: wf_cdecl_hides_SomeD)
schirmer@12854
  1566
  next
schirmer@12854
  1567
    case False
schirmer@12854
  1568
    with subcls_C_old new_declared old_declared inheritable subcls1_C_super
schirmer@12854
  1569
         old_member_of
schirmer@12854
  1570
    have "G,sig\<turnstile>(C,new) overrides\<^sub>S old"
schirmer@12854
  1571
      by (auto intro: stat_overridesR.Direct)
schirmer@12854
  1572
    with False wf_cdecl neq_C_Obj new 
schirmer@12854
  1573
    show ?thesis
schirmer@12854
  1574
      by (auto dest: wf_cdecl_overrides_SomeD)
schirmer@12854
  1575
  qed
schirmer@12854
  1576
qed
schirmer@12854
  1577
schirmer@12854
  1578
lemma inheritable_instance_methd: 
wenzelm@12937
  1579
  assumes subclseq_C_D: "G\<turnstile>C \<preceq>\<^sub>C D" and
schirmer@12854
  1580
              is_cls_D: "is_class G D" and
schirmer@12854
  1581
                    wf: "wf_prog G" and 
schirmer@12854
  1582
                   old: "methd G D sig = Some old" and
schirmer@12854
  1583
           accmodi_old: "Protected \<le> accmodi old" and  
schirmer@12854
  1584
        not_static_old: "\<not> is_static old"
wenzelm@12937
  1585
  shows
schirmer@12854
  1586
  "\<exists>new. methd G C sig = Some new \<and>
schirmer@12854
  1587
         (new = old \<or> G,sig\<turnstile>new overrides\<^sub>S old)"
schirmer@12854
  1588
 (is "(\<exists>new. (?Constraint C new old))")
schirmer@12854
  1589
proof -
schirmer@12854
  1590
  from subclseq_C_D is_cls_D 
schirmer@12854
  1591
  have is_cls_C: "is_class G C" by (rule subcls_is_class2) 
schirmer@12854
  1592
  from wf 
schirmer@12854
  1593
  have ws: "ws_prog G" ..
schirmer@12854
  1594
  from is_cls_C ws subclseq_C_D 
schirmer@12854
  1595
  show "\<exists>new. ?Constraint C new old"
schirmer@12854
  1596
  proof (induct rule: ws_class_induct')
schirmer@12854
  1597
    case (Object co)
schirmer@12854
  1598
    then have eq_D_Obj: "D=Object" by auto
schirmer@12854
  1599
    with old 
schirmer@12854
  1600
    have "?Constraint Object old old"
schirmer@12854
  1601
      by auto
schirmer@12854
  1602
    with eq_D_Obj 
schirmer@12854
  1603
    show "\<exists> new. ?Constraint Object new old" by auto
schirmer@12854
  1604
  next
schirmer@12854
  1605
    case (Subcls C c)
schirmer@12854
  1606
    assume hyp: "G\<turnstile>super c\<preceq>\<^sub>C D \<Longrightarrow> \<exists>new. ?Constraint (super c) new old"
schirmer@12854
  1607
    assume clsC: "class G C = Some c"
schirmer@12854
  1608
    assume neq_C_Obj: "C\<noteq>Object"
schirmer@12854
  1609
    from clsC wf 
schirmer@12854
  1610
    have wf_cdecl: "wf_cdecl G (C,c)" 
schirmer@12854
  1611
      by (rule wf_prog_cdecl)
schirmer@12854
  1612
    from ws clsC neq_C_Obj
schirmer@12854
  1613
    have is_cls_super: "is_class G (super c)"
schirmer@12854
  1614
      by (auto dest: ws_prog_cdeclD)
schirmer@12854
  1615
    from clsC wf neq_C_Obj 
schirmer@12854
  1616
    have superAccessible: "G\<turnstile>(Class (super c)) accessible_in (pid C)" and
haftmann@35416
  1617
         subcls1_C_super: "G\<turnstile>C \<prec>\<^sub>C1 super c"
schirmer@12854
  1618
      by (auto dest: wf_prog_cdecl wf_cdecl_supD is_acc_classD
schirmer@12854
  1619
              intro: subcls1I)
schirmer@12854
  1620
    show "\<exists>new. ?Constraint C new old"
schirmer@12854
  1621
    proof (cases "G\<turnstile>super c\<preceq>\<^sub>C D")
schirmer@12854
  1622
      case False
schirmer@12854
  1623
      from False Subcls 
schirmer@12854
  1624
      have eq_C_D: "C=D"
wenzelm@32960
  1625
        by (auto dest: subclseq_superD)
schirmer@12854
  1626
      with old 
schirmer@12854
  1627
      have "?Constraint C old old"
wenzelm@32960
  1628
        by auto
schirmer@12854
  1629
      with eq_C_D 
schirmer@12854
  1630
      show "\<exists> new. ?Constraint C new old" by auto
schirmer@12854
  1631
    next
schirmer@12854
  1632
      case True
schirmer@12854
  1633
      with hyp obtain super_method
wenzelm@32960
  1634
        where super: "?Constraint (super c) super_method old" by blast
schirmer@12854
  1635
      from super not_static_old
schirmer@12854
  1636
      have not_static_super: "\<not> is_static super_method"
wenzelm@32960
  1637
        by (auto dest!: stat_overrides_commonD)
schirmer@12854
  1638
      from super old wf accmodi_old
schirmer@12854
  1639
      have accmodi_super_method: "Protected \<le> accmodi super_method"
wenzelm@32960
  1640
        by (auto dest!: wf_prog_stat_overridesD)
schirmer@12854
  1641
      from super accmodi_old wf
schirmer@12854
  1642
      have inheritable: "G\<turnstile>Methd sig super_method inheritable_in (pid C)"
wenzelm@32960
  1643
        by (auto dest!: wf_prog_stat_overridesD
schirmer@12854
  1644
                        acc_modi_le_Dests
wenzelm@32960
  1645
              simp add: inheritable_in_def)                
schirmer@12854
  1646
      from super wf is_cls_super
schirmer@12854
  1647
      have member: "G\<turnstile>Methd sig super_method member_of (super c)"
wenzelm@32960
  1648
        by (auto intro: methd_member_of) 
schirmer@12854
  1649
      from member
schirmer@12854
  1650
      have decl_super_method:
schirmer@12854
  1651
        "G\<turnstile>Methd sig super_method declared_in (declclass super_method)"
wenzelm@32960
  1652
        by (auto dest: member_of_declC)
schirmer@12854
  1653
      from super subcls1_C_super ws is_cls_super 
schirmer@12854
  1654
      have subcls_C_super: "G\<turnstile>C \<prec>\<^sub>C (declclass super_method)"
wenzelm@32960
  1655
        by (auto intro: rtrancl_into_trancl2 dest: methd_declC) 
schirmer@12854
  1656
      show "\<exists> new. ?Constraint C new old"
schirmer@12854
  1657
      proof (cases "methd G C sig")
wenzelm@32960
  1658
        case None
wenzelm@32960
  1659
        have "methd G (super c) sig = None"
wenzelm@32960
  1660
        proof -
wenzelm@32960
  1661
          from clsC ws None 
wenzelm@32960
  1662
          have no_new: "table_of (methods c) sig = None" 
wenzelm@32960
  1663
            by (auto simp add: methd_rec)
wenzelm@32960
  1664
          with clsC 
wenzelm@32960
  1665
          have undeclared: "G\<turnstile>mid sig undeclared_in C"
wenzelm@32960
  1666
            by (auto simp add: undeclared_in_def cdeclaredmethd_def)
wenzelm@32960
  1667
          with inheritable member superAccessible subcls1_C_super
wenzelm@32960
  1668
          have inherits: "G\<turnstile>C inherits (method sig super_method)"
wenzelm@32960
  1669
            by (auto simp add: inherits_def)
wenzelm@32960
  1670
          with clsC ws no_new super neq_C_Obj
wenzelm@32960
  1671
          have "methd G C sig = Some super_method"
wenzelm@32960
  1672
            by (auto simp add: methd_rec map_add_def intro: filter_tab_SomeI)
schirmer@12854
  1673
          with None show ?thesis
wenzelm@32960
  1674
            by simp
wenzelm@32960
  1675
        qed
wenzelm@32960
  1676
        with super show ?thesis by auto
schirmer@12854
  1677
      next
wenzelm@32960
  1678
        case (Some new)
wenzelm@32960
  1679
        from this ws clsC neq_C_Obj
wenzelm@32960
  1680
        show ?thesis
wenzelm@32960
  1681
        proof (cases rule: methd_rec_Some_cases)
wenzelm@32960
  1682
          case InheritedMethod
wenzelm@32960
  1683
          with super Some show ?thesis 
wenzelm@32960
  1684
            by auto
wenzelm@32960
  1685
        next
wenzelm@32960
  1686
          case NewMethod
wenzelm@32960
  1687
          assume new: "table_of (map (\<lambda>(s, m). (s, C, m)) (methods c)) sig 
schirmer@12854
  1688
                       = Some new"
wenzelm@32960
  1689
          from new 
wenzelm@32960
  1690
          have declcls_new: "declclass new = C" 
wenzelm@32960
  1691
            by auto
wenzelm@32960
  1692
          from wf clsC neq_C_Obj super new not_static_super accmodi_super_method
wenzelm@32960
  1693
          have not_static_new: "\<not> is_static new" 
wenzelm@32960
  1694
            by (auto dest: wf_prog_staticD) 
wenzelm@32960
  1695
          from clsC new
wenzelm@32960
  1696
          have decl_new: "G\<turnstile>Methd sig new declared_in C"
wenzelm@32960
  1697
            by (auto simp add: declared_in_def cdeclaredmethd_def)
wenzelm@32960
  1698
          from not_static_new decl_new decl_super_method
wenzelm@32960
  1699
               member subcls1_C_super inheritable declcls_new subcls_C_super 
wenzelm@32960
  1700
          have "G,sig\<turnstile> new overrides\<^sub>S super_method"
wenzelm@32960
  1701
            by (auto intro: stat_overridesR.Direct) 
wenzelm@32960
  1702
          with super Some
wenzelm@32960
  1703
          show ?thesis
wenzelm@32960
  1704
            by (auto intro: stat_overridesR.Indirect)
wenzelm@32960
  1705
        qed
schirmer@12854
  1706
      qed
schirmer@12854
  1707
    qed
schirmer@12854
  1708
  qed
schirmer@12854
  1709
qed
schirmer@12854
  1710
schirmer@12854
  1711
lemma inheritable_instance_methd_cases [consumes 6
schirmer@12854
  1712
                                       , case_names Inheritance Overriding]: 
wenzelm@12937
  1713
  assumes subclseq_C_D: "G\<turnstile>C \<preceq>\<^sub>C D" and
schirmer@12854
  1714
              is_cls_D: "is_class G D" and
schirmer@12854
  1715
                    wf: "wf_prog G" and 
schirmer@12854
  1716
                   old: "methd G D sig = Some old" and
schirmer@12854
  1717
           accmodi_old: "Protected \<le> accmodi old" and  
schirmer@12854
  1718
        not_static_old: "\<not> is_static old" and
schirmer@12854
  1719
           inheritance:  "methd G C sig = Some old \<Longrightarrow> P" and
schirmer@12854
  1720
            overriding:  "\<And> new. \<lbrakk>methd G C sig = Some new;
schirmer@12854
  1721
                                   G,sig\<turnstile>new overrides\<^sub>S old\<rbrakk> \<Longrightarrow> P"
schirmer@12854
  1722
        
wenzelm@12937
  1723
  shows P
schirmer@12854
  1724
proof -
schirmer@12854
  1725
from subclseq_C_D is_cls_D wf old accmodi_old not_static_old 
schirmer@12854
  1726
show ?thesis
schirmer@12925
  1727
  by (auto dest: inheritable_instance_methd intro: inheritance overriding)
schirmer@12854
  1728
qed
schirmer@12854
  1729
schirmer@12854
  1730
lemma inheritable_instance_methd_props: 
wenzelm@12937
  1731
  assumes subclseq_C_D: "G\<turnstile>C \<preceq>\<^sub>C D" and
schirmer@12854
  1732
              is_cls_D: "is_class G D" and
schirmer@12854
  1733
                    wf: "wf_prog G" and 
schirmer@12854
  1734
                   old: "methd G D sig = Some old" and
schirmer@12854
  1735
           accmodi_old: "Protected \<le> accmodi old" and  
schirmer@12854
  1736
        not_static_old: "\<not> is_static old"
wenzelm@12937
  1737
  shows
schirmer@12854
  1738
  "\<exists>new. methd G C sig = Some new \<and>
schirmer@12854
  1739
          \<not> is_static new \<and> G\<turnstile>resTy new\<preceq>resTy old \<and> accmodi old \<le>accmodi new"
schirmer@12854
  1740
 (is "(\<exists>new. (?Constraint C new old))")
schirmer@12854
  1741
proof -
schirmer@12854
  1742
  from subclseq_C_D is_cls_D wf old accmodi_old not_static_old 
schirmer@12854
  1743
  show ?thesis
schirmer@12854
  1744
  proof (cases rule: inheritable_instance_methd_cases)
schirmer@12854
  1745
    case Inheritance
schirmer@12854
  1746
    with not_static_old accmodi_old show ?thesis by auto
schirmer@12854
  1747
  next
schirmer@12854
  1748
    case (Overriding new)
schirmer@12854
  1749
    then have "\<not> is_static new" by (auto dest: stat_overrides_commonD)
schirmer@12854
  1750
    with Overriding not_static_old accmodi_old wf 
schirmer@12854
  1751
    show ?thesis 
haftmann@22424
  1752
      by (auto dest!: wf_prog_stat_overridesD)
schirmer@12854
  1753
  qed
schirmer@12854
  1754
qed
wenzelm@32960
  1755
              
schirmer@12854
  1756
(* local lemma *)
wenzelm@24019
  1757
lemma bexI': "x \<in> A \<Longrightarrow> P x \<Longrightarrow> \<exists>x\<in>A. P x" by blast
wenzelm@24019
  1758
lemma ballE': "\<forall>x\<in>A. P x \<Longrightarrow> (x \<notin> A \<Longrightarrow> Q) \<Longrightarrow> (P x \<Longrightarrow> Q) \<Longrightarrow> Q" by blast
wenzelm@24019
  1759
schirmer@12854
  1760
lemma subint_widen_imethds: 
berghofe@34915
  1761
  assumes irel: "G\<turnstile>I\<preceq>I J"
berghofe@34915
  1762
  and wf: "wf_prog G"
berghofe@34915
  1763
  and is_iface: "is_iface G J"
berghofe@34915
  1764
  and jm: "jm \<in> imethds G J sig"
berghofe@34915
  1765
  shows "\<exists>im \<in> imethds G I sig. is_static im = is_static jm \<and> 
schirmer@12854
  1766
                          accmodi im = accmodi jm \<and>
schirmer@12854
  1767
                          G\<turnstile>resTy im\<preceq>resTy jm"
berghofe@34915
  1768
  using irel jm
berghofe@34915
  1769
proof (induct rule: converse_rtrancl_induct)
berghofe@34915
  1770
    case base
berghofe@34915
  1771
    then show ?case by  (blast elim: bexI')
schirmer@12854
  1772
  next
berghofe@34915
  1773
    case (step I SI)
berghofe@34915
  1774
    from `G\<turnstile>I \<prec>I1 SI`
schirmer@12854
  1775
    obtain i where
schirmer@12854
  1776
      ifI: "iface G I = Some i" and
schirmer@12854
  1777
       SI: "SI \<in> set (isuperIfs i)"
schirmer@12854
  1778
      by (blast dest: subint1D)
schirmer@12854
  1779
schirmer@12854
  1780
    let ?newMethods 
nipkow@30235
  1781
          = "(Option.set \<circ> table_of (map (\<lambda>(sig, mh). (sig, I, mh)) (imethods i)))"
berghofe@34915
  1782
    show ?case
schirmer@12854
  1783
    proof (cases "?newMethods sig = {}")
schirmer@12854
  1784
      case True
berghofe@34915
  1785
      with ifI SI step wf
schirmer@12854
  1786
      show "?thesis" 
wenzelm@32960
  1787
        by (auto simp add: imethds_rec) 
schirmer@12854
  1788
    next
schirmer@12854
  1789
      case False
schirmer@12854
  1790
      from ifI wf False
schirmer@12854
  1791
      have imethds: "imethds G I sig = ?newMethods sig"
wenzelm@32960
  1792
        by (simp add: imethds_rec)
schirmer@12854
  1793
      from False
schirmer@12854
  1794
      obtain im where
schirmer@12854
  1795
        imdef: "im \<in> ?newMethods sig" 
wenzelm@32960
  1796
        by (blast)
schirmer@12854
  1797
      with imethds 
schirmer@12854
  1798
      have im: "im \<in> imethds G I sig"
wenzelm@32960
  1799
        by (blast)
schirmer@12854
  1800
      with im wf ifI 
schirmer@12854
  1801
      obtain
wenzelm@32960
  1802
         imStatic: "\<not> is_static im" and
schirmer@12854
  1803
         imPublic: "accmodi im = Public"
wenzelm@32960
  1804
        by (auto dest!: imethds_wf_mhead)       
schirmer@12854
  1805
      from ifI wf 
schirmer@12854
  1806
      have wf_I: "wf_idecl G (I,i)" 
wenzelm@32960
  1807
        by (rule wf_prog_idecl)
schirmer@12854
  1808
      with SI wf  
schirmer@12854
  1809
      obtain si where
wenzelm@32960
  1810
         ifSI: "iface G SI = Some si" and
wenzelm@32960
  1811
        wf_SI: "wf_idecl G (SI,si)" 
wenzelm@32960
  1812
        by (auto dest!: wf_idecl_supD is_acc_ifaceD
schirmer@12854
  1813
                  dest: wf_prog_idecl)
berghofe@34915
  1814
      from step
schirmer@12854
  1815
      obtain sim::"qtname \<times> mhead"  where
schirmer@12854
  1816
                      sim: "sim \<in> imethds G SI sig" and
schirmer@12854
  1817
         eq_static_sim_jm: "is_static sim = is_static jm" and 
schirmer@12854
  1818
         eq_access_sim_jm: "accmodi sim = accmodi jm" and 
schirmer@12854
  1819
        resTy_widen_sim_jm: "G\<turnstile>resTy sim\<preceq>resTy jm"
wenzelm@32960
  1820
        by blast
schirmer@12854
  1821
      with wf_I SI imdef sim 
schirmer@12854
  1822
      have "G\<turnstile>resTy im\<preceq>resTy sim"   
wenzelm@32960
  1823
        by (auto dest!: wf_idecl_hidings hidings_entailsD)
schirmer@12854
  1824
      with wf resTy_widen_sim_jm 
schirmer@12854
  1825
      have resTy_widen_im_jm: "G\<turnstile>resTy im\<preceq>resTy jm"
wenzelm@32960
  1826
        by (blast intro: widen_trans)
schirmer@12854
  1827
      from sim wf ifSI  
schirmer@12854
  1828
      obtain
wenzelm@32960
  1829
        simStatic: "\<not> is_static sim" and
schirmer@12854
  1830
        simPublic: "accmodi sim = Public"
wenzelm@32960
  1831
        by (auto dest!: imethds_wf_mhead)
schirmer@12854
  1832
      from im 
schirmer@12854
  1833
           imStatic simStatic eq_static_sim_jm
schirmer@12854
  1834
           imPublic simPublic eq_access_sim_jm
schirmer@12854
  1835
           resTy_widen_im_jm
schirmer@12854
  1836
      show ?thesis 
wenzelm@32960
  1837
        by auto 
schirmer@12854
  1838
    qed
schirmer@12854
  1839
qed
schirmer@12854
  1840
     
schirmer@12854
  1841
(* Tactical version *)
schirmer@12854
  1842
(* 
schirmer@12854
  1843
lemma subint_widen_imethds: "\<lbrakk>G\<turnstile>I\<preceq>I J; wf_prog G; is_iface G J\<rbrakk> \<Longrightarrow>  
schirmer@12854
  1844
  \<forall> jm \<in> imethds G J sig.  
schirmer@12854
  1845
  \<exists> im \<in> imethds G I sig. static (mthd im)=static (mthd jm) \<and> 
schirmer@12854
  1846
                          access (mthd im)= access (mthd jm) \<and>
schirmer@12854
  1847
                          G\<turnstile>resTy (mthd im)\<preceq>resTy (mthd jm)"
schirmer@12854
  1848
apply (erule converse_rtrancl_induct)
schirmer@12854
  1849
apply  (clarsimp elim!: bexI')
schirmer@12854
  1850
apply (frule subint1D)
schirmer@12854
  1851
apply clarify
schirmer@12854
  1852
apply (erule ballE')
schirmer@12854
  1853
apply  fast
schirmer@12854
  1854
apply (erule_tac V = "?x \<in> imethds G J sig" in thin_rl)
schirmer@12854
  1855
apply clarsimp
schirmer@12854
  1856
apply (subst imethds_rec, assumption, erule wf_ws_prog)
schirmer@12854
  1857
apply (unfold overrides_t_def)
schirmer@12854
  1858
apply (drule (1) wf_prog_idecl)
schirmer@12854
  1859
apply (frule (3) imethds_wf_mhead [OF _ _ wf_idecl_supD [THEN conjunct1 
schirmer@12854
  1860
                                       [THEN is_acc_ifaceD [THEN conjunct1]]]])
nipkow@30235
  1861
apply (case_tac "(Option.set \<circ> table_of (map (\<lambda>(s, mh). (s, y, mh)) (imethods i)))
schirmer@12854
  1862
                  sig ={}")
schirmer@12854
  1863
apply   force
schirmer@12854
  1864
schirmer@12854
  1865
apply   (simp only:)
schirmer@12854
  1866
apply   (simp)
schirmer@12854
  1867
apply   clarify
schirmer@12854
  1868
apply   (frule wf_idecl_hidings [THEN hidings_entailsD])
schirmer@12854
  1869
apply     blast
schirmer@12854
  1870
apply     blast
schirmer@12854
  1871
apply   (rule bexI')
schirmer@12854
  1872
apply     simp
schirmer@12854
  1873
apply     (drule table_of_map_SomeI [of _ "sig"])
schirmer@12854
  1874
apply     simp
schirmer@12854
  1875
schirmer@12854
  1876
apply     (frule wf_idecl_mhead [of _ _ _ "sig"])
schirmer@12854
  1877
apply       (rule table_of_Some_in_set)
schirmer@12854
  1878
apply       assumption
schirmer@12854
  1879
apply     auto
schirmer@12854
  1880
done
schirmer@12854
  1881
*)
schirmer@12854
  1882
    
schirmer@12854
  1883
schirmer@12854
  1884
(* local lemma *)
schirmer@12854
  1885
lemma implmt1_methd: 
schirmer@12854
  1886
 "\<And>sig. \<lbrakk>G\<turnstile>C\<leadsto>1I; wf_prog G; im \<in> imethds G I sig\<rbrakk> \<Longrightarrow>  
schirmer@12854
  1887
  \<exists>cm \<in>methd G C sig: \<not> is_static cm \<and> \<not> is_static im \<and> 
schirmer@12854
  1888
                       G\<turnstile>resTy cm\<preceq>resTy im \<and>
schirmer@12854
  1889
                       accmodi im = Public \<and> accmodi cm = Public"
schirmer@12854
  1890
apply (drule implmt1D)
schirmer@12854
  1891
apply clarify
schirmer@12854
  1892
apply (drule (2) wf_prog_cdecl [THEN wf_cdecl_impD])
schirmer@12854
  1893
apply (frule (1) imethds_wf_mhead)
schirmer@12854
  1894
apply  (simp add: is_acc_iface_def)
schirmer@12854
  1895
apply (force)
schirmer@12854
  1896
done
schirmer@12854
  1897
schirmer@12854
  1898
schirmer@12854
  1899
(* local lemma *)
schirmer@12854
  1900
lemma implmt_methd [rule_format (no_asm)]: 
schirmer@12854
  1901
"\<lbrakk>wf_prog G; G\<turnstile>C\<leadsto>I\<rbrakk> \<Longrightarrow> is_iface G I \<longrightarrow>  
schirmer@12854
  1902
 (\<forall> im    \<in>imethds G I   sig.  
schirmer@12854
  1903
  \<exists> cm\<in>methd G C sig: \<not>is_static cm \<and> \<not> is_static im \<and> 
schirmer@12854
  1904
                      G\<turnstile>resTy cm\<preceq>resTy im \<and>
schirmer@12854
  1905
                      accmodi im = Public \<and> accmodi cm = Public)"
schirmer@12854
  1906
apply (frule implmt_is_class)
schirmer@12854
  1907
apply (erule implmt.induct)
schirmer@12854
  1908
apply   safe
schirmer@12854
  1909
apply   (drule (2) implmt1_methd)
schirmer@12854
  1910
apply   fast
schirmer@12854
  1911
apply  (drule (1) subint_widen_imethds)
schirmer@12854
  1912
apply   simp
schirmer@12854
  1913
apply   assumption
schirmer@12854
  1914
apply  clarify
schirmer@12854
  1915
apply  (drule (2) implmt1_methd)
schirmer@12854
  1916
apply  (force)
schirmer@12854
  1917
apply (frule subcls1D)
schirmer@12854
  1918
apply (drule (1) bspec)
schirmer@12854
  1919
apply clarify
schirmer@12854
  1920
apply (drule (3) r_into_rtrancl [THEN inheritable_instance_methd_props, 
schirmer@12854
  1921
                                 OF _ implmt_is_class])
schirmer@12854
  1922
apply auto 
schirmer@12854
  1923
done
schirmer@12854
  1924
schirmer@12854
  1925
lemma mheadsD [rule_format (no_asm)]: 
schirmer@12854
  1926
"emh \<in> mheads G S t sig \<longrightarrow> wf_prog G \<longrightarrow>
schirmer@12854
  1927
 (\<exists>C D m. t = ClassT C \<and> declrefT emh = ClassT D \<and> 
schirmer@12854
  1928
          accmethd G S C sig = Some m \<and>
schirmer@12854
  1929
          (declclass m = D) \<and> mhead (mthd m) = (mhd emh)) \<or>
schirmer@12854
  1930
 (\<exists>I. t = IfaceT I \<and> ((\<exists>im. im  \<in> accimethds G (pid S) I sig \<and> 
schirmer@12854
  1931
          mthd im = mhd emh) \<or> 
schirmer@12854
  1932
  (\<exists>m. G\<turnstile>Iface I accessible_in (pid S) \<and> accmethd G S Object sig = Some m \<and> 
schirmer@12854
  1933
       accmodi m \<noteq> Private \<and> 
schirmer@12854
  1934
       declrefT emh = ClassT Object \<and> mhead (mthd m) = mhd emh))) \<or>
schirmer@12854
  1935
 (\<exists>T m. t = ArrayT T \<and> G\<turnstile>Array T accessible_in (pid S) \<and>
schirmer@12854
  1936
        accmethd G S Object sig = Some m \<and> accmodi m \<noteq> Private \<and> 
schirmer@12854
  1937
        declrefT emh = ClassT Object \<and> mhead (mthd m) = mhd emh)"
ballarin@14174
  1938
apply (rule_tac ref_ty1="t" in ref_ty_ty.induct [THEN conjunct1])
schirmer@12854
  1939
apply auto
schirmer@12854
  1940
apply (auto simp add: cmheads_def accObjectmheads_def Objectmheads_def)
schirmer@12854
  1941
apply (auto  dest!: accmethd_SomeD)
schirmer@12854
  1942
done
schirmer@12854
  1943
schirmer@12854
  1944
lemma mheads_cases [consumes 2, case_names Class_methd 
schirmer@12854
  1945
                    Iface_methd Iface_Object_methd Array_Object_methd]: 
schirmer@12854
  1946
"\<lbrakk>emh \<in> mheads G S t sig; wf_prog G;
schirmer@12854
  1947
 \<And> C D m. \<lbrakk>t = ClassT C;declrefT emh = ClassT D; accmethd G S C sig = Some m;
schirmer@12854
  1948
           (declclass m = D); mhead (mthd m) = (mhd emh)\<rbrakk> \<Longrightarrow> P emh; 
schirmer@12854
  1949
 \<And> I im. \<lbrakk>t = IfaceT I; im  \<in> accimethds G (pid S) I sig; mthd im = mhd emh\<rbrakk>
schirmer@12854
  1950
          \<Longrightarrow> P emh;
schirmer@12854
  1951
 \<And> I m. \<lbrakk>t = IfaceT I; G\<turnstile>Iface I accessible_in (pid S);
schirmer@12854
  1952
          accmethd G S Object sig = Some m; accmodi m \<noteq> Private;
schirmer@12854
  1953
         declrefT emh = ClassT Object; mhead (mthd m) = mhd emh\<rbrakk> \<Longrightarrow> P emh;
schirmer@12854
  1954
 \<And> T m. \<lbrakk>t = ArrayT T;G\<turnstile>Array T accessible_in (pid S);
schirmer@12854
  1955
          accmethd G S Object sig = Some m; accmodi m \<noteq> Private; 
schirmer@12854
  1956
          declrefT emh = ClassT Object; mhead (mthd m) = mhd emh\<rbrakk> \<Longrightarrow>  P emh 
schirmer@12854
  1957
\<rbrakk> \<Longrightarrow> P emh"
schirmer@12854
  1958
by (blast dest!: mheadsD)
schirmer@12854
  1959
schirmer@12854
  1960
lemma declclassD[rule_format]:
schirmer@12854
  1961
 "\<lbrakk>wf_prog G;class G C = Some c; methd G C sig = Some m; 
schirmer@12854
  1962
   class G (declclass m) = Some d\<rbrakk>
schirmer@12854
  1963
  \<Longrightarrow> table_of (methods d) sig  = Some (mthd m)"
schirmer@12854
  1964
proof -
schirmer@12854
  1965
  assume    wf: "wf_prog G"
schirmer@12854
  1966
  then have ws: "ws_prog G" ..
schirmer@12854
  1967
  assume  clsC: "class G C = Some c"
schirmer@12854
  1968
  from clsC ws 
schirmer@12854
  1969
  show "\<And> m d. \<lbrakk>methd G C sig = Some m; class G (declclass m) = Some d\<rbrakk>
schirmer@12854
  1970
        \<Longrightarrow> table_of (methods d) sig  = Some (mthd m)" 
berghofe@34915
  1971
  proof (induct rule: ws_class_induct)
schirmer@12854
  1972
    case Object
schirmer@12854
  1973
    with wf show "?thesis m d" by auto
schirmer@12854
  1974
  next
berghofe@34915
  1975
    case (Subcls C c)
schirmer@12854
  1976
    let ?newMethods = "table_of (map (\<lambda>(s, m). (s, C, m)) (methods c)) sig"
schirmer@12854
  1977
    show "?thesis m d" 
schirmer@12854
  1978
    proof (cases "?newMethods")
schirmer@12854
  1979
      case None
berghofe@34915
  1980
      from None ws Subcls
berghofe@34915
  1981
      show "?thesis" by (auto simp add: methd_rec) (rule Subcls)
schirmer@12854
  1982
    next
schirmer@12854
  1983
      case Some
berghofe@34915
  1984
      from Some ws Subcls
schirmer@12854
  1985
      show "?thesis" 
wenzelm@32960
  1986
        by (auto simp add: methd_rec
schirmer@12854
  1987
                     dest: wf_prog_cdecl wf_cdecl_supD is_acc_class_is_class)
schirmer@12854
  1988
    qed
schirmer@12854
  1989
  qed
schirmer@12854
  1990
qed
schirmer@12854
  1991
schirmer@12854
  1992
lemma dynmethd_Object:
wenzelm@12937
  1993
  assumes statM: "methd G Object sig = Some statM" and
schirmer@12854
  1994
        private: "accmodi statM = Private" and 
schirmer@12854
  1995
       is_cls_C: "is_class G C" and
schirmer@12854
  1996
             wf: "wf_prog G"
wenzelm@12937
  1997
  shows "dynmethd G Object C sig = Some statM"
schirmer@12854
  1998
proof -
schirmer@12854
  1999
  from is_cls_C wf 
schirmer@12854
  2000
  have subclseq: "G\<turnstile>C \<preceq>\<^sub>C Object" 
schirmer@12854
  2001
    by (auto intro: subcls_ObjectI)
schirmer@12854
  2002
  from wf have ws: "ws_prog G" 
schirmer@12854
  2003
    by simp
schirmer@12854
  2004
  from wf 
schirmer@12854
  2005
  have is_cls_Obj: "is_class G Object" 
schirmer@12854
  2006
    by simp
schirmer@12854
  2007
  from statM subclseq is_cls_Obj ws private
schirmer@12854
  2008
  show ?thesis
schirmer@12854
  2009
  proof (cases rule: dynmethd_cases)
schirmer@12854
  2010
    case Static then show ?thesis .
schirmer@12854
  2011
  next
schirmer@12854
  2012
    case Overrides 
schirmer@12854
  2013
    with private show ?thesis 
schirmer@12854
  2014
      by (auto dest: no_Private_override)
schirmer@12854
  2015
  qed
schirmer@12854
  2016
qed
schirmer@12854
  2017
schirmer@12854
  2018
lemma wf_imethds_hiding_objmethdsD: 
wenzelm@12937
  2019
  assumes     old: "methd G Object sig = Some old" and
wenzelm@12937
  2020
          is_if_I: "is_iface G I" and
wenzelm@12937
  2021
               wf: "wf_prog G" and    
wenzelm@12937
  2022
      not_private: "accmodi old \<noteq> Private" and
wenzelm@12937
  2023
              new: "new \<in> imethds G I sig" 
wenzelm@12937
  2024
  shows "G\<turnstile>resTy new\<preceq>resTy old \<and> is_static new = is_static old" (is "?P new")
schirmer@12854
  2025
proof -
schirmer@12854
  2026
  from wf have ws: "ws_prog G" by simp
schirmer@12854
  2027
  {
schirmer@12854
  2028
    fix I i new
schirmer@12854
  2029
    assume ifI: "iface G I = Some i"
schirmer@12854
  2030
    assume new: "table_of (imethods i) sig = Some new" 
schirmer@12854
  2031
    from ifI new not_private wf old  
schirmer@12854
  2032
    have "?P (I,new)"
schirmer@12854
  2033
      by (auto dest!: wf_prog_idecl wf_idecl_hiding cond_hiding_entailsD
schirmer@12854
  2034
            simp del: methd_Object)
schirmer@12854
  2035
  } note hyp_newmethod = this  
schirmer@12854
  2036
  from is_if_I ws new 
schirmer@12854
  2037
  show ?thesis
schirmer@12854
  2038
  proof (induct rule: ws_interface_induct)
schirmer@12854
  2039
    case (Step I i)
schirmer@12854
  2040
    assume ifI: "iface G I = Some i" 
schirmer@12854
  2041
    assume new: "new \<in> imethds G I sig" 
schirmer@12854
  2042
    from Step
schirmer@12854
  2043
    have hyp: "\<forall> J \<in> set (isuperIfs i). (new \<in> imethds G J sig \<longrightarrow> ?P new)"
schirmer@12854
  2044
      by auto 
schirmer@12854
  2045
    from new ifI ws
schirmer@12854
  2046
    show "?P new"
schirmer@12854
  2047
    proof (cases rule: imethds_cases)
schirmer@12854
  2048
      case NewMethod
schirmer@12854
  2049
      with ifI hyp_newmethod
schirmer@12854
  2050
      show ?thesis
wenzelm@32960
  2051
        by auto
schirmer@12854
  2052
    next
schirmer@12854
  2053
      case (InheritedMethod J)
schirmer@12854
  2054
      assume "J \<in> set (isuperIfs i)" 
schirmer@12854
  2055
             "new \<in> imethds G J sig"
schirmer@12854
  2056
      with hyp 
schirmer@12854
  2057
      show "?thesis"
wenzelm@32960
  2058
        by auto
schirmer@12854
  2059
    qed
schirmer@12854
  2060
  qed
schirmer@12854
  2061
qed
schirmer@12854
  2062
schirmer@12854
  2063
text {*
schirmer@12854
  2064
Which dynamic classes are valid to look up a member of a distinct static type?
schirmer@12854
  2065
We have to distinct class members (named static members in Java) 
schirmer@12854
  2066
from instance members. Class members are global to all Objects of a class,
schirmer@12854
  2067
instance members are local to a single Object instance. If a member is
schirmer@12854
  2068
equipped with the static modifier it is a class member, else it is an 
schirmer@12854
  2069
instance member.
schirmer@12854
  2070
The following table gives an overview of the current framework. We assume
schirmer@12854
  2071
to have a reference with static type statT and a dynamic class dynC. Between
schirmer@12854
  2072
both of these types the widening relation holds 
schirmer@12854
  2073
@{term "G\<turnstile>Class dynC\<preceq> statT"}. Unfortunately this ordinary widening relation 
schirmer@12854
  2074
isn't enough to describe the valid lookup classes, since we must cope the
schirmer@12854
  2075
special cases of arrays and interfaces,too. If we statically expect an array or
schirmer@12854
  2076
inteface we may lookup a field or a method in Object which isn't covered in 
schirmer@12854
  2077
the widening relation.
schirmer@12925
  2078
schirmer@12854
  2079
statT      field         instance method       static (class) method
schirmer@12854
  2080
------------------------------------------------------------------------
schirmer@12854
  2081
 NullT      /                  /                   /
schirmer@12854
  2082
 Iface      /                dynC                Object
schirmer@12854
  2083
 Class    dynC               dynC                 dynC
schirmer@12854
  2084
 Array      /                Object              Object
schirmer@12925
  2085
schirmer@12854
  2086
In most cases we con lookup the member in the dynamic class. But as an
schirmer@12854
  2087
interface can't declare new static methods, nor an array can define new
schirmer@12854
  2088
methods at all, we have to lookup methods in the base class Object.
schirmer@12854
  2089
schirmer@12854
  2090
The limitation to classes in the field column is artificial  and comes out
schirmer@12854
  2091
of the typing rule for the field access (see rule @{text "FVar"} in the 
schirmer@12854
  2092
welltyping relation @{term "wt"} in theory WellType). 
schirmer@12854
  2093
I stems out of the fact, that Object
schirmer@12854
  2094
indeed has no non private fields. So interfaces and arrays can actually
schirmer@12854
  2095
have no fields at all and a field access would be senseless. (In Java
schirmer@12854
  2096
interfaces are allowed to declare new fields but in current Bali not!).
schirmer@12854
  2097
So there is no principal reason why we should not allow Objects to declare
schirmer@12854
  2098
non private fields. Then we would get the following column:
schirmer@12925
  2099
       
schirmer@12854
  2100
 statT    field
schirmer@12854
  2101
----------------- 
schirmer@12854
  2102
 NullT      /  
schirmer@12854
  2103
 Iface    Object 
schirmer@12854
  2104
 Class    dynC 
schirmer@12854
  2105
 Array    Object
schirmer@12854
  2106
*}
wenzelm@37956
  2107
primrec valid_lookup_cls:: "prog \<Rightarrow> ref_ty \<Rightarrow> qtname \<Rightarrow> bool \<Rightarrow> bool"
schirmer@12854
  2108
                        ("_,_ \<turnstile> _ valid'_lookup'_cls'_for _" [61,61,61,61] 60)
wenzelm@37956
  2109
where
wenzelm@37956
  2110
  "G,NullT    \<turnstile> dynC valid_lookup_cls_for static_membr = False"
wenzelm@37956
  2111
| "G,IfaceT I \<turnstile> dynC valid_lookup_cls_for static_membr 
wenzelm@37956
  2112
                = (if static_membr 
wenzelm@37956
  2113
                      then dynC=Object 
wenzelm@37956
  2114
                      else G\<turnstile>Class dynC\<preceq> Iface I)"
wenzelm@37956
  2115
| "G,ClassT C \<turnstile> dynC valid_lookup_cls_for static_membr = G\<turnstile>Class dynC\<preceq> Class C"
wenzelm@37956
  2116
| "G,ArrayT T \<turnstile> dynC valid_lookup_cls_for static_membr = (dynC=Object)"
schirmer@12854
  2117
schirmer@12854
  2118
lemma valid_lookup_cls_is_class:
wenzelm@12937
  2119
  assumes dynC: "G,statT \<turnstile> dynC valid_lookup_cls_for static_membr" and
schirmer@12854
  2120
      ty_statT: "isrtype G statT" and
schirmer@12854
  2121
            wf: "wf_prog G"
wenzelm@12937
  2122
  shows "is_class G dynC"
schirmer@12854
  2123
proof (cases statT)
schirmer@12854
  2124
  case NullT
schirmer@12854
  2125
  with dynC ty_statT show ?thesis
schirmer@12854
  2126
    by (auto dest: widen_NT2)
schirmer@12854
  2127
next
schirmer@12854
  2128
  case (IfaceT I)
schirmer@12854
  2129
  with dynC wf show ?thesis
schirmer@12854
  2130
    by (auto dest: implmt_is_class)
schirmer@12854
  2131
next
schirmer@12854
  2132
  case (ClassT C)
schirmer@12854
  2133
  with dynC ty_statT show ?thesis
schirmer@12854
  2134
    by (auto dest: subcls_is_class2)
schirmer@12854
  2135
next
schirmer@12854
  2136
  case (ArrayT T)
schirmer@12854
  2137
  with dynC wf show ?thesis
schirmer@12854
  2138
    by (auto)
schirmer@12854
  2139
qed
schirmer@12854
  2140
schirmer@12854
  2141
declare split_paired_All [simp del] split_paired_Ex [simp del]
wenzelm@24019
  2142
declaration {* K (Simplifier.map_ss (fn ss => ss delloop "split_all_tac")) *}
wenzelm@24019
  2143
declaration {* K (Classical.map_cs (fn cs => cs delSWrapper "split_all_tac")) *}
wenzelm@24019
  2144
schirmer@12854
  2145
lemma dynamic_mheadsD:   
schirmer@12854
  2146
"\<lbrakk>emh \<in> mheads G S statT sig;    
schirmer@12854
  2147
  G,statT \<turnstile> dynC valid_lookup_cls_for (is_static emh);
schirmer@12854
  2148
  isrtype G statT; wf_prog G
schirmer@12854
  2149
 \<rbrakk> \<Longrightarrow> \<exists>m \<in> dynlookup G statT dynC sig: 
schirmer@12854
  2150
          is_static m=is_static emh \<and> G\<turnstile>resTy m\<preceq>resTy emh"
schirmer@12854
  2151
proof - 
schirmer@12854
  2152
  assume      emh: "emh \<in> mheads G S statT sig"
schirmer@12854
  2153
  and          wf: "wf_prog G"
schirmer@12854
  2154
  and   dynC_Prop: "G,statT \<turnstile> dynC valid_lookup_cls_for (is_static emh)"
schirmer@12854
  2155
  and      istype: "isrtype G statT"
schirmer@12854
  2156
  from dynC_Prop istype wf 
schirmer@12854
  2157
  obtain y where
schirmer@12854
  2158
    dynC: "class G dynC = Some y" 
schirmer@12854
  2159
    by (auto dest: valid_lookup_cls_is_class)
schirmer@12854
  2160
  from emh wf show ?thesis
schirmer@12854
  2161
  proof (cases rule: mheads_cases)
schirmer@12854
  2162
    case Class_methd
schirmer@12854
  2163
    fix statC statDeclC sm
schirmer@12854
  2164
    assume     statC: "statT = ClassT statC"
schirmer@12854
  2165
    assume            "accmethd G S statC sig = Some sm"
schirmer@12854
  2166
    then have     sm: "methd G statC sig = Some sm" 
schirmer@12854
  2167
      by (blast dest: accmethd_SomeD)  
schirmer@12854
  2168
    assume eq_mheads: "mhead (mthd sm) = mhd emh"
schirmer@12854
  2169
    from statC 
schirmer@12854
  2170
    have dynlookup: "dynlookup G statT dynC sig = dynmethd G statC dynC sig"
schirmer@12854
  2171
      by (simp add: dynlookup_def)
schirmer@12854
  2172
    from wf statC istype dynC_Prop sm 
schirmer@12854
  2173
    obtain dm where
schirmer@12854
  2174
      "dynmethd G statC dynC sig = Some dm"
schirmer@12854
  2175
      "is_static dm = is_static sm" 
schirmer@12854
  2176
      "G\<turnstile>resTy dm\<preceq>resTy sm"  
schirmer@12925
  2177
      by (force dest!: ws_dynmethd accmethd_SomeD)
schirmer@12854
  2178
    with dynlookup eq_mheads 
schirmer@12854
  2179
    show ?thesis 
haftmann@37678
  2180
      by (cases emh type: prod) (auto)
schirmer@12854
  2181
  next
schirmer@12854
  2182
    case Iface_methd
schirmer@12854
  2183
    fix I im
schirmer@12854
  2184
    assume    statI: "statT = IfaceT I" and
schirmer@12854
  2185
          eq_mheads: "mthd im = mhd emh" and
schirmer@12854
  2186
                     "im \<in> accimethds G (pid S) I sig" 
schirmer@12854
  2187
    then have im: "im \<in> imethds G I sig" 
schirmer@12854
  2188
      by (blast dest: accimethdsD)
schirmer@12854
  2189
    with istype statI eq_mheads wf 
schirmer@12854
  2190
    have not_static_emh: "\<not> is_static emh"
schirmer@12854
  2191
      by (cases emh) (auto dest: wf_prog_idecl imethds_wf_mhead)
schirmer@12854
  2192
    from statI im
schirmer@12854
  2193
    have dynlookup: "dynlookup G statT dynC sig = methd G dynC sig"
schirmer@12854
  2194
      by (auto simp add: dynlookup_def dynimethd_def) 
schirmer@12854
  2195
    from wf dynC_Prop statI istype im not_static_emh 
schirmer@12854
  2196
    obtain dm where
schirmer@12854
  2197
      "methd G dynC sig = Some dm"
schirmer@12854
  2198
      "is_static dm = is_static im" 
schirmer@12854
  2199
      "G\<turnstile>resTy (mthd dm)\<preceq>resTy (mthd im)" 
schirmer@12925
  2200
      by (force dest: implmt_methd)
schirmer@12854
  2201
    with dynlookup eq_mheads
schirmer@12854
  2202
    show ?thesis 
haftmann@37678
  2203
      by (cases emh type: prod) (auto)
schirmer@12854
  2204
  next
schirmer@12854
  2205
    case Iface_Object_methd
schirmer@12854
  2206
    fix I sm
schirmer@12854
  2207
    assume   statI: "statT = IfaceT I" and
schirmer@12854
  2208
                sm: "accmethd G S Object sig = Some sm" and 
schirmer@12854
  2209
         eq_mheads: "mhead (mthd sm) = mhd emh" and
schirmer@12854
  2210
             nPriv: "accmodi sm \<noteq> Private"
schirmer@12854
  2211
     show ?thesis 
schirmer@12854
  2212
     proof (cases "imethds G I sig = {}")
schirmer@12854
  2213
       case True
schirmer@12854
  2214
       with statI 
schirmer@12854
  2215
       have dynlookup: "dynlookup G statT dynC sig = dynmethd G Object dynC sig"
wenzelm@32960
  2216
         by (simp add: dynlookup_def dynimethd_def)
schirmer@12854
  2217
       from wf dynC 
schirmer@12854
  2218
       have subclsObj: "G\<turnstile>dynC \<preceq>\<^sub>C Object"
wenzelm@32960
  2219
         by (auto intro: subcls_ObjectI)
schirmer@12854
  2220
       from wf dynC dynC_Prop istype sm subclsObj 
schirmer@12854
  2221
       obtain dm where
wenzelm@32960
  2222
         "dynmethd G Object dynC sig = Some dm"
wenzelm@32960
  2223
         "is_static dm = is_static sm" 
wenzelm@32960
  2224
         "G\<turnstile>resTy (mthd dm)\<preceq>resTy (mthd sm)"  
wenzelm@32960
  2225
         by (auto dest!: ws_dynmethd accmethd_SomeD 
schirmer@12925
  2226
                  intro: class_Object [OF wf] intro: that)
schirmer@12854
  2227
       with dynlookup eq_mheads
schirmer@12854
  2228
       show ?thesis 
haftmann@37678
  2229
         by (cases emh type: prod) (auto)
schirmer@12854
  2230
     next
schirmer@12854
  2231
       case False
schirmer@12854
  2232
       with statI
schirmer@12854
  2233
       have dynlookup: "dynlookup G statT dynC sig = methd G dynC sig"
wenzelm@32960
  2234
         by (simp add: dynlookup_def dynimethd_def)
schirmer@12854
  2235
       from istype statI
schirmer@12854
  2236
       have "is_iface G I"
wenzelm@32960
  2237
         by auto
schirmer@12854
  2238
       with wf sm nPriv False 
schirmer@12854
  2239
       obtain im where
wenzelm@32960
  2240
              im: "im \<in> imethds G I sig" and
wenzelm@32960
  2241
         eq_stat: "is_static im = is_static sm" and
schirmer@12854
  2242
         resProp: "G\<turnstile>resTy (mthd im)\<preceq>resTy (mthd sm)"
wenzelm@32960
  2243
         by (auto dest: wf_imethds_hiding_objmethdsD accmethd_SomeD)
schirmer@12854
  2244
       from im wf statI istype eq_stat eq_mheads
schirmer@12854
  2245
       have not_static_sm: "\<not> is_static emh"
wenzelm@32960
  2246
         by (cases emh) (auto dest: wf_prog_idecl imethds_wf_mhead)
schirmer@12854
  2247
       from im wf dynC_Prop dynC istype statI not_static_sm
schirmer@12854
  2248
       obtain dm where
wenzelm@32960
  2249
         "methd G dynC sig = Some dm"
wenzelm@32960
  2250
         "is_static dm = is_static im" 
wenzelm@32960
  2251
         "G\<turnstile>resTy (mthd dm)\<preceq>resTy (mthd im)" 
wenzelm@32960
  2252
         by (auto dest: implmt_methd)
schirmer@12854
  2253
       with wf eq_stat resProp dynlookup eq_mheads
schirmer@12854
  2254
       show ?thesis 
haftmann@37678
  2255
         by (cases emh type: prod) (auto intro: widen_trans)
schirmer@12854
  2256
     qed
schirmer@12854
  2257
  next
schirmer@12854
  2258
    case Array_Object_methd
schirmer@12854
  2259
    fix T sm
schirmer@12854
  2260
    assume statArr: "statT = ArrayT T" and
schirmer@12854
  2261
                sm: "accmethd G S Object sig = Some sm" and 
schirmer@12854
  2262
         eq_mheads: "mhead (mthd sm) = mhd emh" 
schirmer@12854
  2263
    from statArr dynC_Prop wf
schirmer@12854
  2264
    have dynlookup: "dynlookup G statT dynC sig = methd G Object sig"
schirmer@12854
  2265
      by (auto simp add: dynlookup_def dynmethd_C_C)
schirmer@12854
  2266
    with sm eq_mheads sm 
schirmer@12854
  2267
    show ?thesis 
haftmann@37678
  2268
      by (cases emh type: prod) (auto dest: accmethd_SomeD)
schirmer@12854
  2269
  qed
schirmer@12854
  2270
qed
schirmer@12925
  2271
declare split_paired_All [simp] split_paired_Ex [simp]
wenzelm@24019
  2272
declaration {* K (Classical.map_cs (fn cs => cs addSbefore ("split_all_tac", split_all_tac))) *}
wenzelm@24019
  2273
declaration {* K (Simplifier.map_ss (fn ss => ss addloop ("split_all_tac", split_all_tac))) *}
schirmer@12854
  2274
schirmer@12854
  2275
(* Tactical version *)
schirmer@12854
  2276
(*
schirmer@12854
  2277
lemma dynamic_mheadsD: "  
schirmer@12854
  2278
 \<lbrakk>emh \<in> mheads G S statT sig; wf_prog G; class G dynC = Some y;  
schirmer@12854
  2279
   if (\<exists>T. statT=ArrayT T) then dynC=Object else G\<turnstile>Class dynC\<preceq>RefT statT; 
schirmer@12854
  2280
   isrtype G statT\<rbrakk> \<Longrightarrow>  
schirmer@12854
  2281
  \<exists>m \<in> dynlookup G statT dynC sig: 
schirmer@12854
  2282
     static (mthd m)=static (mhd emh) \<and> G\<turnstile>resTy (mthd m)\<preceq>resTy (mhd emh)"
schirmer@12854
  2283
apply (drule mheadsD)
schirmer@12854
  2284
apply safe
schirmer@12854
  2285
       -- reftype statT is a class  
schirmer@12854
  2286
apply  (case_tac "\<exists>T. ClassT C = ArrayT T")
schirmer@12854
  2287
apply    (simp)
schirmer@12854
  2288
schirmer@12854
  2289
apply    (clarsimp simp add: dynlookup_def )
schirmer@12854
  2290
apply    (frule_tac statC="C" and dynC="dynC"  and sig="sig"  
schirmer@12854
  2291
         in ws_dynmethd)
schirmer@12854
  2292
apply      assumption+
schirmer@12854
  2293
apply    (case_tac "emh")  
schirmer@12854
  2294
apply    (force dest: accmethd_SomeD)
schirmer@12854
  2295
schirmer@12854
  2296
       -- reftype statT is a interface, method defined in interface 
schirmer@12854
  2297
apply    (clarsimp simp add: dynlookup_def)
schirmer@12854
  2298
apply    (drule (1) implmt_methd)
schirmer@12854
  2299
apply      blast
schirmer@12854
  2300
apply      blast
schirmer@12854
  2301
apply    (clarify)  
schirmer@12854
  2302
apply    (unfold dynimethd_def)
schirmer@12854
  2303
apply    (rule_tac x="cm" in bexI)
schirmer@12854
  2304
apply      (case_tac "emh")
schirmer@12854
  2305
apply      force
schirmer@12854
  2306
schirmer@12854
  2307
apply      force
schirmer@12854
  2308
schirmer@12854
  2309
        -- reftype statT is a interface, method defined in Object 
schirmer@12854
  2310
apply    (simp add: dynlookup_def)
schirmer@12854
  2311
apply    (simp only: dynimethd_def)
schirmer@12854
  2312
apply    (case_tac "imethds G I sig = {}")
schirmer@12854
  2313
apply       simp
schirmer@12854
  2314
apply       (frule_tac statC="Object" and dynC="dynC"  and sig="sig"  
schirmer@12854
  2315
             in ws_dynmethd)
schirmer@12854
  2316
apply          (blast intro: subcls_ObjectI wf_ws_prog) 
schirmer@12854
  2317
apply          (blast dest: class_Object)
schirmer@12854
  2318
apply       (case_tac "emh") 
schirmer@12854
  2319
apply       (force dest: accmethd_SomeD)
schirmer@12854
  2320
schirmer@12854
  2321
apply       simp
schirmer@12854
  2322
apply       (subgoal_tac "\<exists> im. im \<in> imethds G I sig") 
schirmer@12854
  2323
prefer 2      apply blast
schirmer@12854
  2324
apply       clarify
schirmer@12854
  2325
apply       (frule (1) implmt_methd)
schirmer@12854
  2326
apply         simp
schirmer@12854
  2327
apply         blast  
schirmer@12854
  2328
apply       (clarify dest!: accmethd_SomeD)
schirmer@12854
  2329
apply       (frule (4) iface_overrides_Object)
schirmer@12854
  2330
apply       clarify
schirmer@12854
  2331
apply       (case_tac emh)
schirmer@12854
  2332
apply       force
schirmer@12854
  2333
schirmer@12854
  2334
        -- reftype statT is a array
schirmer@12854
  2335
apply    (simp add: dynlookup_def)
schirmer@12854
  2336
apply    (case_tac emh)
schirmer@12854
  2337
apply    (force dest: accmethd_SomeD simp add: dynmethd_def)
schirmer@12854
  2338
done
schirmer@12854
  2339
*)
schirmer@12854
  2340
schirmer@12925
  2341
(* FIXME occasionally convert to ws_class_induct*) 
schirmer@12854
  2342
lemma methd_declclass:
schirmer@12854
  2343
"\<lbrakk>class G C = Some c; wf_prog G; methd G C sig = Some m\<rbrakk> 
schirmer@12854
  2344
 \<Longrightarrow> methd G (declclass m) sig = Some m"
schirmer@12854
  2345
proof -
schirmer@12854
  2346
  assume asm: "class G C = Some c" "wf_prog G" "methd G C sig = Some m"
schirmer@12854
  2347
  have "wf_prog G  \<longrightarrow> 
wenzelm@32960
  2348
           (\<forall> c m. class G C = Some c \<longrightarrow>  methd G C sig = Some m 
schirmer@12854
  2349
                   \<longrightarrow>  methd G (declclass m) sig = Some m)"      (is "?P G C") 
krauss@35440
  2350
  proof (induct G C rule: class_rec_induct', intro allI impI)
schirmer@12854
  2351
    fix G C c m
krauss@35440
  2352
    assume hyp: "\<And>c. class G C = Some c \<Longrightarrow> ws_prog G \<Longrightarrow> C \<noteq> Object \<Longrightarrow>
schirmer@12854
  2353
                     ?P G (super c)"
schirmer@12854
  2354
    assume wf: "wf_prog G" and cls_C: "class G C = Some c" and
schirmer@12854
  2355
            m: "methd G C sig = Some m"
schirmer@12854
  2356
    show "methd G (declclass m) sig = Some m"
schirmer@12854
  2357
    proof (cases "C=Object")
schirmer@12854
  2358
      case True
schirmer@12854
  2359
      with wf m show ?thesis by (auto intro: table_of_map_SomeI)
schirmer@12854
  2360
    next
schirmer@12854
  2361
      let ?filter="filter_tab (\<lambda>sig m. G\<turnstile>C inherits method sig m)"
schirmer@12854
  2362
      let ?table = "table_of (map (\<lambda>(s, m). (s, C, m)) (methods c))"
schirmer@12854
  2363
      case False
schirmer@12854
  2364
      with cls_C wf m
schirmer@12854
  2365
      have methd_C: "(?filter (methd G (super c)) ++ ?table) sig = Some m "
wenzelm@32960
  2366
        by (simp add: methd_rec)
schirmer@12854
  2367
      show ?thesis
schirmer@12854
  2368
      proof (cases "?table sig")
wenzelm@32960
  2369
        case None
wenzelm@32960
  2370
        from this methd_C have "?filter (methd G (super c)) sig = Some m"
wenzelm@32960
  2371
          by simp
wenzelm@32960
  2372
        moreover
wenzelm@32960
  2373
        from wf cls_C False obtain sup where "class G (super c) = Some sup"
wenzelm@32960
  2374
          by (blast dest: wf_prog_cdecl wf_cdecl_supD is_acc_class_is_class)
wenzelm@32960
  2375
        moreover note wf False cls_C 
wenzelm@32960
  2376
        ultimately show ?thesis by (auto intro: hyp [rule_format])
schirmer@12854
  2377
      next
wenzelm@32960
  2378
        case Some
wenzelm@32960
  2379
        from this methd_C m show ?thesis by auto 
schirmer@12854
  2380
      qed
schirmer@12854
  2381
    qed
wenzelm@32960
  2382
  qed   
schirmer@12854
  2383
  with asm show ?thesis by auto
schirmer@12854
  2384
qed
schirmer@12854
  2385
schirmer@12854
  2386
lemma dynmethd_declclass:
schirmer@12854
  2387
 "\<lbrakk>dynmethd G statC dynC sig = Some m;
schirmer@12854
  2388
   wf_prog G; is_class G statC
schirmer@12854
  2389
  \<rbrakk> \<Longrightarrow> methd G (declclass m) sig = Some m"
schirmer@12854
  2390
by (auto dest: dynmethd_declC)
schirmer@12854
  2391
schirmer@12854
  2392
lemma dynlookup_declC:
schirmer@12854
  2393
 "\<lbrakk>dynlookup G statT dynC sig = Some m; wf_prog G;
schirmer@12854
  2394
   is_class G dynC;isrtype G statT
schirmer@12854
  2395
  \<rbrakk> \<Longrightarrow> G\<turnstile>dynC \<preceq>\<^sub>C (declclass m) \<and> is_class G (declclass m)"
schirmer@12854
  2396
by (cases "statT")
schirmer@12854
  2397
   (auto simp add: dynlookup_def dynimethd_def 
schirmer@12854
  2398
             dest: methd_declC dynmethd_declC)
schirmer@12854
  2399
schirmer@12854
  2400
lemma dynlookup_Array_declclassD [simp]:
schirmer@12854
  2401
"\<lbrakk>dynlookup G (ArrayT T) Object sig = Some dm;wf_prog G\<rbrakk> 
schirmer@12854
  2402
 \<Longrightarrow> declclass dm = Object"
schirmer@12854
  2403
proof -
schirmer@12854
  2404
  assume dynL: "dynlookup G (ArrayT T) Object sig = Some dm"
schirmer@12854
  2405
  assume wf: "wf_prog G"
schirmer@12854
  2406
  from wf have ws: "ws_prog G" by auto
schirmer@12854
  2407
  from wf have is_cls_Obj: "is_class G Object" by auto
schirmer@12854
  2408
  from dynL wf
schirmer@12854
  2409
  show ?thesis
schirmer@12854
  2410
    by (auto simp add: dynlookup_def dynmethd_C_C [OF is_cls_Obj ws]
schirmer@12854
  2411
                 dest: methd_Object_SomeD)
schirmer@12854
  2412
qed   
schirmer@12854
  2413
  
schirmer@12925
  2414
schirmer@12854
  2415
declare split_paired_All [simp del] split_paired_Ex [simp del]
wenzelm@24019
  2416
declaration {* K (Simplifier.map_ss (fn ss => ss delloop "split_all_tac")) *}
wenzelm@24019
  2417
declaration {* K (Classical.map_cs (fn cs => cs delSWrapper "split_all_tac")) *}
wenzelm@24019
  2418
schirmer@12854
  2419
lemma wt_is_type: "E,dt\<Turnstile>v\<Colon>T \<Longrightarrow>  wf_prog (prg E) \<longrightarrow> 
schirmer@12854
  2420
  dt=empty_dt \<longrightarrow> (case T of 
schirmer@12854
  2421
                     Inl T \<Rightarrow> is_type (prg E) T 
schirmer@12854
  2422
                   | Inr Ts \<Rightarrow> Ball (set Ts) (is_type (prg E)))"
schirmer@12854
  2423
apply (unfold empty_dt_def)
schirmer@12854
  2424
apply (erule wt.induct)
schirmer@12854
  2425
apply (auto split del: split_if_asm simp del: snd_conv 
schirmer@12854
  2426
            simp add: is_acc_class_def is_acc_type_def)
schirmer@12854
  2427
apply    (erule typeof_empty_is_type)
schirmer@13688
  2428
apply   (frule (1) wf_prog_cdecl [THEN wf_cdecl_supD], 
schirmer@12854
  2429
        force simp del: snd_conv, clarsimp simp add: is_acc_class_def)
schirmer@12854
  2430
apply  (drule (1) max_spec2mheads [THEN conjunct1, THEN mheadsD])
schirmer@12854
  2431
apply  (drule_tac [2] accfield_fields) 
schirmer@12854
  2432
apply  (frule class_Object)
schirmer@12854
  2433
apply  (auto dest: accmethd_rT_is_type 
schirmer@12854
  2434
                   imethds_wf_mhead [THEN conjunct1, THEN rT_is_acc_type]
schirmer@12854
  2435
             dest!:accimethdsD
schirmer@12854
  2436
             simp del: class_Object
schirmer@12854
  2437
             simp add: is_acc_type_def
schirmer@12854
  2438
    )
schirmer@12854
  2439
done
schirmer@12854
  2440
declare split_paired_All [simp] split_paired_Ex [simp]
wenzelm@24019
  2441
declaration {* K (Classical.map_cs (fn cs => cs addSbefore ("split_all_tac", split_all_tac))) *}
wenzelm@24019
  2442
declaration {* K (Simplifier.map_ss (fn ss => ss addloop ("split_all_tac", split_all_tac))) *}
schirmer@12854
  2443
schirmer@12854
  2444
lemma ty_expr_is_type: 
schirmer@12854
  2445
"\<lbrakk>E\<turnstile>e\<Colon>-T; wf_prog (prg E)\<rbrakk> \<Longrightarrow> is_type (prg E) T"
schirmer@12854
  2446
by (auto dest!: wt_is_type)
schirmer@12854
  2447
lemma ty_var_is_type: 
schirmer@12854
  2448
"\<lbrakk>E\<turnstile>v\<Colon>=T; wf_prog (prg E)\<rbrakk> \<Longrightarrow> is_type (prg E) T"
schirmer@12854
  2449
by (auto dest!: wt_is_type)
schirmer@12854
  2450
lemma ty_exprs_is_type: 
schirmer@12854
  2451
"\<lbrakk>E\<turnstile>es\<Colon>\<doteq>Ts; wf_prog (prg E)\<rbrakk> \<Longrightarrow> Ball (set Ts) (is_type (prg E))"
schirmer@12854
  2452
by (auto dest!: wt_is_type)
schirmer@12854
  2453
schirmer@12854
  2454
schirmer@12854
  2455
lemma static_mheadsD: 
schirmer@12854
  2456
 "\<lbrakk> emh \<in> mheads G S t sig; wf_prog G; E\<turnstile>e\<Colon>-RefT t; prg E=G ; 
schirmer@12854
  2457
   invmode (mhd emh) e \<noteq> IntVir 
schirmer@12854
  2458
  \<rbrakk> \<Longrightarrow> \<exists>m. (   (\<exists> C. t = ClassT C \<and> accmethd G S C sig = Some m)
schirmer@12854
  2459
               \<or> (\<forall> C. t \<noteq> ClassT C \<and> accmethd G S Object sig = Some m )) \<and> 
schirmer@12854
  2460
          declrefT emh = ClassT (declclass m) \<and>  mhead (mthd m) = (mhd emh)"
schirmer@12854
  2461
apply (subgoal_tac "is_static emh \<or> e = Super")
schirmer@12854
  2462
defer apply (force simp add: invmode_def)
schirmer@12854
  2463
apply (frule  ty_expr_is_type)
schirmer@12854
  2464
apply   simp
schirmer@12854
  2465
apply (case_tac "is_static emh")
schirmer@12854
  2466
apply  (frule (1) mheadsD)
schirmer@12854
  2467
apply  clarsimp
schirmer@12854
  2468
apply  safe
schirmer@12854
  2469
apply    blast
schirmer@12854
  2470
apply   (auto dest!: imethds_wf_mhead
schirmer@12854
  2471
                     accmethd_SomeD 
schirmer@12854
  2472
                     accimethdsD
schirmer@12854
  2473
              simp add: accObjectmheads_def Objectmheads_def)
schirmer@12854
  2474
schirmer@12854
  2475
apply  (erule wt_elim_cases)
schirmer@12854
  2476
apply  (force simp add: cmheads_def)
schirmer@12854
  2477
done
schirmer@12854
  2478
schirmer@12854
  2479
lemma wt_MethdI:  
schirmer@12854
  2480
"\<lbrakk>methd G C sig = Some m; wf_prog G;  
schirmer@12854
  2481
  class G C = Some c\<rbrakk> \<Longrightarrow>  
schirmer@12854
  2482
 \<exists>T. \<lparr>prg=G,cls=(declclass m),
schirmer@13688
  2483
      lcl=callee_lcl (declclass m) sig (mthd m)\<rparr>\<turnstile> Methd C sig\<Colon>-T \<and> G\<turnstile>T\<preceq>resTy m"
schirmer@12854
  2484
apply (frule (2) methd_wf_mdecl, clarify)
schirmer@12854
  2485
apply (force dest!: wf_mdecl_bodyD intro!: wt.Methd)
schirmer@12854
  2486
done
schirmer@12854
  2487
schirmer@12854
  2488
subsection "accessibility concerns"
schirmer@12854
  2489
schirmer@12854
  2490
lemma mheads_type_accessible:
schirmer@12854
  2491
 "\<lbrakk>emh \<in> mheads G S T sig; wf_prog G\<rbrakk>
schirmer@12854
  2492
 \<Longrightarrow> G\<turnstile>RefT T accessible_in (pid S)"
schirmer@12854
  2493
by (erule mheads_cases)
schirmer@12854
  2494
   (auto dest: accmethd_SomeD accessible_from_commonD accimethdsD)
schirmer@12854
  2495
schirmer@12925
  2496
lemma static_to_dynamic_accessible_from_aux:
schirmer@12854
  2497
"\<lbrakk>G\<turnstile>m of C accessible_from accC;wf_prog G\<rbrakk> 
schirmer@12854
  2498
 \<Longrightarrow> G\<turnstile>m in C dyn_accessible_from accC"
schirmer@12854
  2499
proof (induct rule: accessible_fromR.induct)
schirmer@12854
  2500
qed (auto intro: dyn_accessible_fromR.intros 
schirmer@12854
  2501
                 member_of_to_member_in
schirmer@12854
  2502
                 static_to_dynamic_overriding)
schirmer@12854
  2503
schirmer@12854
  2504
lemma static_to_dynamic_accessible_from:
wenzelm@12937
  2505
  assumes stat_acc: "G\<turnstile>m of statC accessible_from accC" and
schirmer@12854
  2506
          subclseq: "G\<turnstile>dynC \<preceq>\<^sub>C statC" and
schirmer@12854
  2507
                wf: "wf_prog G"
wenzelm@12937
  2508
  shows "G\<turnstile>m in dynC dyn_accessible_from accC"
schirmer@12854
  2509
proof - 
schirmer@12854
  2510
  from stat_acc subclseq 
schirmer@12854
  2511
  show ?thesis (is "?Dyn_accessible m")
schirmer@12854
  2512
  proof (induct rule: accessible_fromR.induct)
berghofe@21765
  2513
    case (Immediate m statC)
schirmer@12854
  2514
    then show "?Dyn_accessible m"
schirmer@12925
  2515
      by (blast intro: dyn_accessible_fromR.Immediate
schirmer@12854
  2516
                       member_inI
schirmer@12854
  2517
                       permits_acc_inheritance)
schirmer@12854
  2518
  next
berghofe@21765
  2519
    case (Overriding m _ _)
schirmer@12854
  2520
    with wf show "?Dyn_accessible m"
schirmer@12925
  2521
      by (blast intro: dyn_accessible_fromR.Overriding
schirmer@12854
  2522
                       member_inI
schirmer@12854
  2523
                       static_to_dynamic_overriding  
schirmer@12854
  2524
                       rtrancl_trancl_trancl 
schirmer@12925
  2525
                       static_to_dynamic_accessible_from_aux)
schirmer@12854
  2526
  qed
schirmer@12854
  2527
qed
schirmer@12854
  2528
schirmer@12925
  2529
lemma static_to_dynamic_accessible_from_static:
wenzelm@12937
  2530
  assumes stat_acc: "G\<turnstile>m of statC accessible_from accC" and