src/HOL/Bali/WellForm.thy
author ballarin
Fri Aug 29 15:19:02 2003 +0200 (2003-08-29)
changeset 14174 f3cafd2929d5
parent 14030 cd928c0ac225
child 14981 e73f8140af78
permissions -rw-r--r--
Methods rule_tac etc support static (Isar) contexts.
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(*  Title:      HOL/Bali/WellForm.thy
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    ID:         $Id$
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    Author:     David von Oheimb and Norbert Schirmer
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    License:    GPL (GNU GENERAL PUBLIC LICENSE)
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*)
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header {* Well-formedness of Java programs *}
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theory WellForm = DefiniteAssignment:
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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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constdefs
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  wf_fdecl :: "prog \<Rightarrow> pname \<Rightarrow> fdecl \<Rightarrow> bool"
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 "wf_fdecl G P \<equiv> \<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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constdefs
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  wf_mhead :: "prog \<Rightarrow> pname \<Rightarrow> sig \<Rightarrow> mhead \<Rightarrow> bool"
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 "wf_mhead G P \<equiv> \<lambda> sig mh. length (parTs sig) = length (pars mh) \<and>
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			    \<spacespace> ( \<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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			    \<spacespace> 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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constdefs callee_lcl:: "qtname \<Rightarrow> sig \<Rightarrow> methd \<Rightarrow> lenv"
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"callee_lcl C sig m 
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 \<equiv> \<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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constdefs parameters :: "methd \<Rightarrow> lname set"
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"parameters m \<equiv>  set (map (EName \<circ> VNam) (pars m)) 
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                  \<union> (if (static m) then {} else {This})"
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constdefs
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  wf_mdecl :: "prog \<Rightarrow> qtname \<Rightarrow> mdecl \<Rightarrow> bool"
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 "wf_mdecl G C \<equiv> 
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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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constdefs
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  wf_idecl :: "prog  \<Rightarrow> idecl \<Rightarrow> bool"
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 "wf_idecl G \<equiv> 
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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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        (o2s \<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. o2s (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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   301
            access as the overwritten one.
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   302
      \item for all methods hiding a method (of a superclass) the hidden 
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   303
            method must be static and offer at least as much access rights.
schirmer@12854
   304
            Remark: In contrast to the Java Language Specification we don't
schirmer@12854
   305
            restrict the result types of the method
schirmer@12854
   306
            (as in case of overriding), because there seems to be no reason,
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   307
            since there is no dynamic binding of static methods.
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   308
            (cf. 8.4.6.3 vs. 15.12.1).
schirmer@12854
   309
            Stricly speaking the restrictions on the access rights aren't 
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   310
            necessary to, since the static type and the access rights 
schirmer@12854
   311
            together determine which method is to be called statically. 
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   312
            But if a class gains more then one static method with the 
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   313
            same signature due to inheritance, it is confusing when the 
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   314
            method selection depends on the access rights only: 
schirmer@12854
   315
            e.g.
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   316
              Class C declares static public method foo().
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   317
              Class D is subclass of C and declares static method foo()
schirmer@12854
   318
              with default package access.
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   319
              D.foo() ? if this call is in the same package as D then
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   320
                        foo of class D is called, otherwise foo of class C.
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   321
      \end{itemize}
schirmer@12854
   322
schirmer@12854
   323
\end{itemize}
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   324
*}
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   325
(* to Table *)
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   326
constdefs entails:: "('a,'b) table \<Rightarrow> ('b \<Rightarrow> bool) \<Rightarrow> bool"
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   327
                                 ("_ entails _" 20)
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   328
"t entails P \<equiv> \<forall>k. \<forall> x \<in> t k: P x"
schirmer@12854
   329
schirmer@12854
   330
lemma entailsD:
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   331
 "\<lbrakk>t entails P; t k = Some x\<rbrakk> \<Longrightarrow> P x"
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   332
by (simp add: entails_def)
schirmer@12854
   333
schirmer@12854
   334
lemma empty_entails[simp]: "empty entails P"
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   335
by (simp add: entails_def)
schirmer@12854
   336
schirmer@12854
   337
constdefs
schirmer@12854
   338
 wf_cdecl :: "prog \<Rightarrow> cdecl \<Rightarrow> bool"
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   339
"wf_cdecl G \<equiv> 
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   340
   \<lambda>(C,c).
schirmer@12854
   341
      \<not>is_iface G C \<and>
schirmer@12854
   342
      (\<forall>I\<in>set (superIfs c). is_acc_iface G (pid C) I \<and>
schirmer@12854
   343
        (\<forall>s. \<forall> im \<in> imethds G I s.
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   344
      	    (\<exists> cm \<in> methd  G C s: G\<turnstile>resTy cm\<preceq>resTy im \<and>
schirmer@12854
   345
      	                             \<not> is_static cm \<and>
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   346
                                     accmodi im \<le> accmodi cm))) \<and>
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   347
      (\<forall>f\<in>set (cfields c). wf_fdecl G (pid C) f) \<and> unique (cfields c) \<and> 
schirmer@13688
   348
      (\<forall>m\<in>set (methods c). wf_mdecl G C m) \<and> unique (methods c) \<and>
schirmer@13688
   349
      jumpNestingOkS {} (init c) \<and>
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   350
      (\<exists> A. \<lparr>prg=G,cls=C,lcl=empty\<rparr>\<turnstile> {} \<guillemotright>\<langle>init c\<rangle>\<guillemotright> A) \<and>
schirmer@12854
   351
      \<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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   352
      (C \<noteq> Object \<longrightarrow> 
schirmer@12854
   353
            (is_acc_class G (pid C) (super c) \<and>
schirmer@12854
   354
            (table_of (map (\<lambda> (s,m). (s,C,m)) (methods c)) 
schirmer@12854
   355
             entails (\<lambda> new. \<forall> old sig. 
schirmer@12854
   356
                       (G,sig\<turnstile>new overrides\<^sub>S old 
schirmer@12854
   357
                        \<longrightarrow> (G\<turnstile>resTy new\<preceq>resTy old \<and>
schirmer@12854
   358
                             accmodi old \<le> accmodi new \<and>
schirmer@12854
   359
      	                     \<not>is_static old)) \<and>
schirmer@12854
   360
                       (G,sig\<turnstile>new hides old 
schirmer@12854
   361
                         \<longrightarrow> (accmodi old \<le> accmodi new \<and>
schirmer@12854
   362
      	                      is_static old)))) 
schirmer@12854
   363
            ))"
schirmer@12854
   364
schirmer@12854
   365
(*
schirmer@12854
   366
constdefs
schirmer@12854
   367
 wf_cdecl :: "prog \<Rightarrow> cdecl \<Rightarrow> bool"
schirmer@12854
   368
"wf_cdecl G \<equiv> 
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   369
   \<lambda>(C,c).
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   370
      \<not>is_iface G C \<and>
schirmer@12854
   371
      (\<forall>I\<in>set (superIfs c). is_acc_iface G (pid C) I \<and>
schirmer@12854
   372
        (\<forall>s. \<forall> im \<in> imethds G I s.
schirmer@12854
   373
      	    (\<exists> cm \<in> methd  G C s: G\<turnstile>resTy (mthd cm)\<preceq>resTy (mthd im) \<and>
schirmer@12854
   374
      	                             \<not> is_static cm \<and>
schirmer@12854
   375
                                     accmodi im \<le> accmodi cm))) \<and>
schirmer@12854
   376
      (\<forall>f\<in>set (cfields c). wf_fdecl G (pid C) f) \<and> unique (cfields c) \<and> 
schirmer@12854
   377
      (\<forall>m\<in>set (methods c). wf_mdecl G C m) \<and> unique (methods c) \<and> 
schirmer@12854
   378
      \<lparr>prg=G,cls=C,lcl=empty\<rparr>\<turnstile>(init c)\<Colon>\<surd> \<and> ws_cdecl G C (super c) \<and>
schirmer@12854
   379
      (C \<noteq> Object \<longrightarrow> 
schirmer@12854
   380
            (is_acc_class G (pid C) (super c) \<and>
schirmer@12854
   381
            (table_of (map (\<lambda> (s,m). (s,C,m)) (methods c)) 
schirmer@12854
   382
              hiding methd G (super c)
schirmer@12854
   383
              under (\<lambda> new old. G\<turnstile>new overrides old)
schirmer@12854
   384
              entails (\<lambda> new old. 
schirmer@12854
   385
                           (G\<turnstile>resTy (mthd new)\<preceq>resTy (mthd old) \<and>
schirmer@12854
   386
                            accmodi old \<le> accmodi new \<and>
schirmer@12854
   387
      	                   \<not> is_static old)))  \<and>
schirmer@12854
   388
            (table_of (map (\<lambda> (s,m). (s,C,m)) (methods c)) 
schirmer@12854
   389
              hiding methd G (super c)
schirmer@12854
   390
              under (\<lambda> new old. G\<turnstile>new hides old)
schirmer@12854
   391
              entails (\<lambda> new old. is_static old \<and> 
schirmer@12854
   392
                                  accmodi old \<le> accmodi new))  \<and>
schirmer@12854
   393
            (table_of (cfields c) hiding accfield G C (super c)
schirmer@12854
   394
              entails (\<lambda> newF oldF. accmodi oldF \<le> access newF))))"
schirmer@12854
   395
*)
schirmer@12854
   396
schirmer@13688
   397
lemma wf_cdeclE [consumes 1]: 
schirmer@13688
   398
 "\<lbrakk>wf_cdecl G (C,c);
schirmer@13688
   399
   \<lbrakk>\<not>is_iface G C;
schirmer@13688
   400
    (\<forall>I\<in>set (superIfs c). is_acc_iface G (pid C) I \<and>
schirmer@13688
   401
        (\<forall>s. \<forall> im \<in> imethds G I s.
schirmer@13688
   402
      	    (\<exists> cm \<in> methd  G C s: G\<turnstile>resTy cm\<preceq>resTy im \<and>
schirmer@13688
   403
      	                             \<not> is_static cm \<and>
schirmer@13688
   404
                                     accmodi im \<le> accmodi cm))); 
schirmer@13688
   405
      \<forall>f\<in>set (cfields c). wf_fdecl G (pid C) f; unique (cfields c); 
schirmer@13688
   406
      \<forall>m\<in>set (methods c). wf_mdecl G C m; unique (methods c);
schirmer@13688
   407
      jumpNestingOkS {} (init c);
schirmer@13688
   408
      \<exists> A. \<lparr>prg=G,cls=C,lcl=empty\<rparr>\<turnstile> {} \<guillemotright>\<langle>init c\<rangle>\<guillemotright> A;
schirmer@13688
   409
      \<lparr>prg=G,cls=C,lcl=empty\<rparr>\<turnstile>(init c)\<Colon>\<surd>; 
schirmer@13688
   410
      ws_cdecl G C (super c); 
schirmer@13688
   411
      (C \<noteq> Object \<longrightarrow> 
schirmer@13688
   412
            (is_acc_class G (pid C) (super c) \<and>
schirmer@13688
   413
            (table_of (map (\<lambda> (s,m). (s,C,m)) (methods c)) 
schirmer@13688
   414
             entails (\<lambda> new. \<forall> old sig. 
schirmer@13688
   415
                       (G,sig\<turnstile>new overrides\<^sub>S old 
schirmer@13688
   416
                        \<longrightarrow> (G\<turnstile>resTy new\<preceq>resTy old \<and>
schirmer@13688
   417
                             accmodi old \<le> accmodi new \<and>
schirmer@13688
   418
      	                     \<not>is_static old)) \<and>
schirmer@13688
   419
                       (G,sig\<turnstile>new hides old 
schirmer@13688
   420
                         \<longrightarrow> (accmodi old \<le> accmodi new \<and>
schirmer@13688
   421
      	                      is_static old)))) 
schirmer@13688
   422
            ))\<rbrakk> \<Longrightarrow> P
schirmer@13688
   423
  \<rbrakk> \<Longrightarrow> P"
schirmer@13688
   424
by (unfold wf_cdecl_def) simp
schirmer@13688
   425
schirmer@12854
   426
lemma wf_cdecl_unique: 
schirmer@12854
   427
"wf_cdecl G (C,c) \<Longrightarrow> unique (cfields c) \<and> unique (methods c)"
schirmer@12854
   428
apply (unfold wf_cdecl_def)
schirmer@12854
   429
apply auto
schirmer@12854
   430
done
schirmer@12854
   431
schirmer@12854
   432
lemma wf_cdecl_fdecl: 
schirmer@12854
   433
"\<lbrakk>wf_cdecl G (C,c); f\<in>set (cfields c)\<rbrakk> \<Longrightarrow> wf_fdecl G (pid C) f"
schirmer@12854
   434
apply (unfold wf_cdecl_def)
schirmer@12854
   435
apply auto
schirmer@12854
   436
done
schirmer@12854
   437
schirmer@12854
   438
lemma wf_cdecl_mdecl: 
schirmer@12854
   439
"\<lbrakk>wf_cdecl G (C,c); m\<in>set (methods c)\<rbrakk> \<Longrightarrow> wf_mdecl G C m"
schirmer@12854
   440
apply (unfold wf_cdecl_def)
schirmer@12854
   441
apply auto
schirmer@12854
   442
done
schirmer@12854
   443
schirmer@12854
   444
lemma wf_cdecl_impD: 
schirmer@12854
   445
"\<lbrakk>wf_cdecl G (C,c); I\<in>set (superIfs c)\<rbrakk> 
schirmer@12854
   446
\<Longrightarrow> is_acc_iface G (pid C) I \<and>  
schirmer@12854
   447
    (\<forall>s. \<forall>im \<in> imethds G I s.  
schirmer@12854
   448
        (\<exists>cm \<in> methd G C s: G\<turnstile>resTy cm\<preceq>resTy im \<and> \<not>is_static cm \<and>
schirmer@12854
   449
                                   accmodi im \<le> accmodi cm))"
schirmer@12854
   450
apply (unfold wf_cdecl_def)
schirmer@12854
   451
apply auto
schirmer@12854
   452
done
schirmer@12854
   453
schirmer@12854
   454
lemma wf_cdecl_supD: 
schirmer@12854
   455
"\<lbrakk>wf_cdecl G (C,c); C \<noteq> Object\<rbrakk> \<Longrightarrow>  
schirmer@12854
   456
  is_acc_class G (pid C) (super c) \<and> (super c,C) \<notin> (subcls1 G)^+ \<and> 
schirmer@12854
   457
   (table_of (map (\<lambda> (s,m). (s,C,m)) (methods c)) 
schirmer@12854
   458
    entails (\<lambda> new. \<forall> old sig. 
schirmer@12854
   459
                 (G,sig\<turnstile>new overrides\<^sub>S old 
schirmer@12854
   460
                  \<longrightarrow> (G\<turnstile>resTy new\<preceq>resTy old \<and>
schirmer@12854
   461
                       accmodi old \<le> accmodi new \<and>
schirmer@12854
   462
                       \<not>is_static old)) \<and>
schirmer@12854
   463
                 (G,sig\<turnstile>new hides old 
schirmer@12854
   464
                   \<longrightarrow> (accmodi old \<le> accmodi new \<and>
schirmer@12854
   465
                        is_static old))))"
schirmer@12854
   466
apply (unfold wf_cdecl_def ws_cdecl_def)
schirmer@12854
   467
apply auto
schirmer@12854
   468
done
schirmer@12854
   469
schirmer@12854
   470
schirmer@12854
   471
lemma wf_cdecl_overrides_SomeD:
schirmer@12854
   472
"\<lbrakk>wf_cdecl G (C,c); C \<noteq> Object; table_of (methods c) sig = Some newM;
schirmer@12854
   473
  G,sig\<turnstile>(C,newM) overrides\<^sub>S old
schirmer@12854
   474
\<rbrakk> \<Longrightarrow>  G\<turnstile>resTy newM\<preceq>resTy old \<and>
schirmer@12854
   475
       accmodi old \<le> accmodi newM \<and>
schirmer@12854
   476
       \<not> is_static old" 
schirmer@12854
   477
apply (drule (1) wf_cdecl_supD)
schirmer@12854
   478
apply (clarify)
schirmer@12854
   479
apply (drule entailsD)
schirmer@12854
   480
apply   (blast intro: table_of_map_SomeI)
schirmer@12854
   481
apply (drule_tac x="old" in spec)
schirmer@12854
   482
apply (auto dest: overrides_eq_sigD simp add: msig_def)
schirmer@12854
   483
done
schirmer@12854
   484
schirmer@12854
   485
lemma wf_cdecl_hides_SomeD:
schirmer@12854
   486
"\<lbrakk>wf_cdecl G (C,c); C \<noteq> Object; table_of (methods c) sig = Some newM;
schirmer@12854
   487
  G,sig\<turnstile>(C,newM) hides old
schirmer@12854
   488
\<rbrakk> \<Longrightarrow>  accmodi old \<le> access newM \<and>
schirmer@12854
   489
       is_static old" 
schirmer@12854
   490
apply (drule (1) wf_cdecl_supD)
schirmer@12854
   491
apply (clarify)
schirmer@12854
   492
apply (drule entailsD)
schirmer@12854
   493
apply   (blast intro: table_of_map_SomeI)
schirmer@12854
   494
apply (drule_tac x="old" in spec)
schirmer@12854
   495
apply (auto dest: hides_eq_sigD simp add: msig_def)
schirmer@12854
   496
done
schirmer@12854
   497
schirmer@12854
   498
lemma wf_cdecl_wt_init: 
schirmer@12854
   499
 "wf_cdecl G (C, c) \<Longrightarrow> \<lparr>prg=G,cls=C,lcl=empty\<rparr>\<turnstile>init c\<Colon>\<surd>"
schirmer@12854
   500
apply (unfold wf_cdecl_def)
schirmer@12854
   501
apply auto
schirmer@12854
   502
done
schirmer@12854
   503
schirmer@12854
   504
schirmer@12854
   505
section "well-formed programs"
schirmer@12854
   506
  (* well-formed program, cf. 8.1, 9.1 *)
schirmer@12854
   507
schirmer@12854
   508
text {*
schirmer@12854
   509
A program declaration is wellformed if:
schirmer@12854
   510
\begin{itemize}
schirmer@12854
   511
\item the class ObjectC of Object is defined
schirmer@14030
   512
\item every method of Object has an access modifier distinct from Package. 
schirmer@14030
   513
      This is
schirmer@12854
   514
      necessary since every interface automatically inherits from Object.  
schirmer@12854
   515
      We must know, that every time a Object method is "overriden" by an 
schirmer@12854
   516
      interface method this is also overriden by the class implementing the
schirmer@12854
   517
      the interface (see @{text "implement_dynmethd and class_mheadsD"})
schirmer@12854
   518
\item all standard Exceptions are defined
schirmer@12854
   519
\item all defined interfaces are wellformed
schirmer@12854
   520
\item all defined classes are wellformed
schirmer@12854
   521
\end{itemize}
schirmer@12854
   522
*}
schirmer@12854
   523
constdefs
schirmer@12854
   524
  wf_prog  :: "prog \<Rightarrow> bool"
schirmer@12854
   525
 "wf_prog G \<equiv> let is = ifaces G; cs = classes G in
schirmer@12854
   526
	         ObjectC \<in> set cs \<and> 
schirmer@12854
   527
                (\<forall> m\<in>set Object_mdecls. accmodi m \<noteq> Package) \<and>
schirmer@12854
   528
                (\<forall>xn. SXcptC xn \<in> set cs) \<and>
schirmer@12854
   529
		(\<forall>i\<in>set is. wf_idecl G i) \<and> unique is \<and>
schirmer@12854
   530
		(\<forall>c\<in>set cs. wf_cdecl G c) \<and> unique cs"
schirmer@12854
   531
schirmer@12854
   532
lemma wf_prog_idecl: "\<lbrakk>iface G I = Some i; wf_prog G\<rbrakk> \<Longrightarrow> wf_idecl G (I,i)"
schirmer@12854
   533
apply (unfold wf_prog_def Let_def)
schirmer@12854
   534
apply simp
schirmer@12854
   535
apply (fast dest: map_of_SomeD)
schirmer@12854
   536
done
schirmer@12854
   537
schirmer@12854
   538
lemma wf_prog_cdecl: "\<lbrakk>class G C = Some c; wf_prog G\<rbrakk> \<Longrightarrow> wf_cdecl G (C,c)"
schirmer@12854
   539
apply (unfold wf_prog_def Let_def)
schirmer@12854
   540
apply simp
schirmer@12854
   541
apply (fast dest: map_of_SomeD)
schirmer@12854
   542
done
schirmer@12854
   543
schirmer@12854
   544
lemma wf_prog_Object_mdecls:
schirmer@12854
   545
"wf_prog G \<Longrightarrow> (\<forall> m\<in>set Object_mdecls. accmodi m \<noteq> Package)"
schirmer@12854
   546
apply (unfold wf_prog_def Let_def)
schirmer@12854
   547
apply simp
schirmer@12854
   548
done
schirmer@12854
   549
schirmer@12854
   550
lemma wf_prog_acc_superD:
schirmer@12854
   551
 "\<lbrakk>wf_prog G; class G C = Some c; C \<noteq> Object \<rbrakk> 
schirmer@12854
   552
  \<Longrightarrow> is_acc_class G (pid C) (super c)"
schirmer@12854
   553
by (auto dest: wf_prog_cdecl wf_cdecl_supD)
schirmer@12854
   554
schirmer@12854
   555
lemma wf_ws_prog [elim!,simp]: "wf_prog G \<Longrightarrow> ws_prog G"
schirmer@12854
   556
apply (unfold wf_prog_def Let_def)
schirmer@12854
   557
apply (rule ws_progI)
schirmer@12854
   558
apply  (simp_all (no_asm))
schirmer@12854
   559
apply  (auto simp add: is_acc_class_def is_acc_iface_def 
schirmer@12854
   560
             dest!: wf_idecl_supD wf_cdecl_supD )+
schirmer@12854
   561
done
schirmer@12854
   562
schirmer@12854
   563
lemma class_Object [simp]: 
schirmer@12854
   564
"wf_prog G \<Longrightarrow> 
schirmer@12854
   565
  class G Object = Some \<lparr>access=Public,cfields=[],methods=Object_mdecls,
schirmer@12854
   566
                                  init=Skip,super=arbitrary,superIfs=[]\<rparr>"
schirmer@12854
   567
apply (unfold wf_prog_def Let_def ObjectC_def)
schirmer@12854
   568
apply (fast dest!: map_of_SomeI)
schirmer@12854
   569
done
schirmer@12854
   570
schirmer@12854
   571
lemma methd_Object[simp]: "wf_prog G \<Longrightarrow> methd G Object =  
schirmer@12854
   572
  table_of (map (\<lambda>(s,m). (s, Object, m)) Object_mdecls)"
schirmer@12854
   573
apply (subst methd_rec)
schirmer@12854
   574
apply (auto simp add: Let_def)
schirmer@12854
   575
done
schirmer@12854
   576
schirmer@12854
   577
lemma wf_prog_Object_methd:
schirmer@12854
   578
"\<lbrakk>wf_prog G; methd G Object sig = Some m\<rbrakk> \<Longrightarrow> accmodi m \<noteq> Package"
schirmer@12854
   579
by (auto dest!: wf_prog_Object_mdecls) (auto dest!: map_of_SomeD) 
schirmer@12854
   580
schirmer@12854
   581
lemma wf_prog_Object_is_public[intro]:
schirmer@12854
   582
 "wf_prog G \<Longrightarrow> is_public G Object"
schirmer@12854
   583
by (auto simp add: is_public_def dest: class_Object)
schirmer@12854
   584
schirmer@12854
   585
lemma class_SXcpt [simp]: 
schirmer@12854
   586
"wf_prog G \<Longrightarrow> 
schirmer@12854
   587
  class G (SXcpt xn) = Some \<lparr>access=Public,cfields=[],methods=SXcpt_mdecls,
schirmer@12854
   588
                                   init=Skip,
schirmer@12854
   589
                                   super=if xn = Throwable then Object 
schirmer@12854
   590
                                                           else SXcpt Throwable,
schirmer@12854
   591
                                   superIfs=[]\<rparr>"
schirmer@12854
   592
apply (unfold wf_prog_def Let_def SXcptC_def)
schirmer@12854
   593
apply (fast dest!: map_of_SomeI)
schirmer@12854
   594
done
schirmer@12854
   595
schirmer@12854
   596
lemma wf_ObjectC [simp]: 
schirmer@12854
   597
	"wf_cdecl G ObjectC = (\<not>is_iface G Object \<and> Ball (set Object_mdecls)
schirmer@12854
   598
  (wf_mdecl G Object) \<and> unique Object_mdecls)"
schirmer@12854
   599
apply (unfold wf_cdecl_def ws_cdecl_def ObjectC_def)
schirmer@13688
   600
apply (auto intro: da.Skip)
schirmer@12854
   601
done
schirmer@12854
   602
schirmer@12854
   603
lemma Object_is_class [simp,elim!]: "wf_prog G \<Longrightarrow> is_class G Object"
schirmer@12854
   604
apply (simp (no_asm_simp))
schirmer@12854
   605
done
schirmer@12854
   606
 
schirmer@12854
   607
lemma Object_is_acc_class [simp,elim!]: "wf_prog G \<Longrightarrow> is_acc_class G S Object"
schirmer@12854
   608
apply (simp (no_asm_simp) add: is_acc_class_def is_public_def
schirmer@12854
   609
                               accessible_in_RefT_simp)
schirmer@12854
   610
done
schirmer@12854
   611
schirmer@12854
   612
lemma SXcpt_is_class [simp,elim!]: "wf_prog G \<Longrightarrow> is_class G (SXcpt xn)"
schirmer@12854
   613
apply (simp (no_asm_simp))
schirmer@12854
   614
done
schirmer@12854
   615
schirmer@12854
   616
lemma SXcpt_is_acc_class [simp,elim!]: 
schirmer@12854
   617
"wf_prog G \<Longrightarrow> is_acc_class G S (SXcpt xn)"
schirmer@12854
   618
apply (simp (no_asm_simp) add: is_acc_class_def is_public_def
schirmer@12854
   619
                               accessible_in_RefT_simp)
schirmer@12854
   620
done
schirmer@12854
   621
schirmer@12854
   622
lemma fields_Object [simp]: "wf_prog G \<Longrightarrow> DeclConcepts.fields G Object = []"
schirmer@12854
   623
by (force intro: fields_emptyI)
schirmer@12854
   624
schirmer@12854
   625
lemma accfield_Object [simp]: 
schirmer@12854
   626
 "wf_prog G \<Longrightarrow> accfield G S Object = empty"
schirmer@12854
   627
apply (unfold accfield_def)
schirmer@12854
   628
apply (simp (no_asm_simp) add: Let_def)
schirmer@12854
   629
done
schirmer@12854
   630
schirmer@12854
   631
lemma fields_Throwable [simp]: 
schirmer@12854
   632
 "wf_prog G \<Longrightarrow> DeclConcepts.fields G (SXcpt Throwable) = []"
schirmer@12854
   633
by (force intro: fields_emptyI)
schirmer@12854
   634
schirmer@12854
   635
lemma fields_SXcpt [simp]: "wf_prog G \<Longrightarrow> DeclConcepts.fields G (SXcpt xn) = []"
schirmer@12854
   636
apply (case_tac "xn = Throwable")
schirmer@12854
   637
apply  (simp (no_asm_simp))
schirmer@12854
   638
by (force intro: fields_emptyI)
schirmer@12854
   639
schirmer@12854
   640
lemmas widen_trans = ws_widen_trans [OF _ _ wf_ws_prog, elim]
schirmer@12854
   641
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
   642
apply (erule (2) widen_trans)
schirmer@12854
   643
done
schirmer@12854
   644
schirmer@12854
   645
lemma Xcpt_subcls_Throwable [simp]: 
schirmer@12854
   646
"wf_prog G \<Longrightarrow> G\<turnstile>SXcpt xn\<preceq>\<^sub>C SXcpt Throwable"
schirmer@12854
   647
apply (rule SXcpt_subcls_Throwable_lemma)
schirmer@12854
   648
apply auto
schirmer@12854
   649
done
schirmer@12854
   650
schirmer@12854
   651
lemma unique_fields: 
schirmer@12854
   652
 "\<lbrakk>is_class G C; wf_prog G\<rbrakk> \<Longrightarrow> unique (DeclConcepts.fields G C)"
schirmer@12854
   653
apply (erule ws_unique_fields)
schirmer@12854
   654
apply  (erule wf_ws_prog)
schirmer@12854
   655
apply (erule (1) wf_prog_cdecl [THEN wf_cdecl_unique [THEN conjunct1]])
schirmer@12854
   656
done
schirmer@12854
   657
schirmer@12854
   658
lemma fields_mono: 
schirmer@12854
   659
"\<lbrakk>table_of (DeclConcepts.fields G C) fn = Some f; G\<turnstile>D\<preceq>\<^sub>C C; 
schirmer@12854
   660
  is_class G D; wf_prog G\<rbrakk> 
schirmer@12854
   661
   \<Longrightarrow> table_of (DeclConcepts.fields G D) fn = Some f"
schirmer@12854
   662
apply (rule map_of_SomeI)
schirmer@12854
   663
apply  (erule (1) unique_fields)
schirmer@12854
   664
apply (erule (1) map_of_SomeD [THEN fields_mono_lemma])
schirmer@12854
   665
apply (erule wf_ws_prog)
schirmer@12854
   666
done
schirmer@12854
   667
schirmer@12854
   668
schirmer@12854
   669
lemma fields_is_type [elim]: 
schirmer@12854
   670
"\<lbrakk>table_of (DeclConcepts.fields G C) m = Some f; wf_prog G; is_class G C\<rbrakk> \<Longrightarrow> 
schirmer@12854
   671
      is_type G (type f)"
schirmer@12854
   672
apply (frule wf_ws_prog)
schirmer@12854
   673
apply (force dest: fields_declC [THEN conjunct1] 
schirmer@12854
   674
                   wf_prog_cdecl [THEN wf_cdecl_fdecl]
schirmer@12854
   675
             simp add: wf_fdecl_def2 is_acc_type_def)
schirmer@12854
   676
done
schirmer@12854
   677
schirmer@12854
   678
lemma imethds_wf_mhead [rule_format (no_asm)]: 
schirmer@12854
   679
"\<lbrakk>m \<in> imethds G I sig; wf_prog G; is_iface G I\<rbrakk> \<Longrightarrow>  
schirmer@12854
   680
  wf_mhead G (pid (decliface m)) sig (mthd m) \<and> 
schirmer@12854
   681
  \<not> is_static m \<and> accmodi m = Public"
schirmer@12854
   682
apply (frule wf_ws_prog)
schirmer@12854
   683
apply (drule (2) imethds_declI [THEN conjunct1])
schirmer@12854
   684
apply clarify
schirmer@12854
   685
apply (frule_tac I="(decliface m)" in wf_prog_idecl,assumption)
schirmer@12854
   686
apply (drule wf_idecl_mhead)
schirmer@12854
   687
apply (erule map_of_SomeD)
schirmer@12854
   688
apply (cases m, simp)
schirmer@12854
   689
done
schirmer@12854
   690
schirmer@12854
   691
lemma methd_wf_mdecl: 
schirmer@12854
   692
 "\<lbrakk>methd G C sig = Some m; wf_prog G; class G C = Some y\<rbrakk> \<Longrightarrow>  
schirmer@12854
   693
  G\<turnstile>C\<preceq>\<^sub>C (declclass m) \<and> is_class G (declclass m) \<and> 
schirmer@12854
   694
  wf_mdecl G (declclass m) (sig,(mthd m))"
schirmer@12854
   695
apply (frule wf_ws_prog)
schirmer@12854
   696
apply (drule (1) methd_declC)
schirmer@12854
   697
apply  fast
schirmer@12854
   698
apply clarsimp
schirmer@12854
   699
apply (frule (1) wf_prog_cdecl, erule wf_cdecl_mdecl, erule map_of_SomeD)
schirmer@12854
   700
done
schirmer@12854
   701
schirmer@12854
   702
(*
schirmer@12854
   703
This lemma doesn't hold!
schirmer@12854
   704
lemma methd_rT_is_acc_type: 
schirmer@12854
   705
"\<lbrakk>wf_prog G;methd G C C sig = Some (D,m);
schirmer@12854
   706
    class G C = Some y\<rbrakk>
schirmer@12854
   707
\<Longrightarrow> is_acc_type G (pid C) (resTy m)"
schirmer@12854
   708
The result Type is only visible in the scope of defining class D 
schirmer@12854
   709
"is_vis_type G (pid D) (resTy m)" but not necessarily in scope of class C!
schirmer@12854
   710
(The same is true for the type of pramaters of a method)
schirmer@12854
   711
*)
schirmer@12854
   712
schirmer@12854
   713
schirmer@12854
   714
lemma methd_rT_is_type: 
schirmer@12854
   715
"\<lbrakk>wf_prog G;methd G C sig = Some m;
schirmer@12854
   716
    class G C = Some y\<rbrakk>
schirmer@12854
   717
\<Longrightarrow> is_type G (resTy m)"
schirmer@12854
   718
apply (drule (2) methd_wf_mdecl)
schirmer@12854
   719
apply clarify
schirmer@12854
   720
apply (drule wf_mdeclD1)
schirmer@12854
   721
apply clarify
schirmer@12854
   722
apply (drule rT_is_acc_type)
schirmer@12854
   723
apply (cases m, simp add: is_acc_type_def)
schirmer@12854
   724
done
schirmer@12854
   725
schirmer@12854
   726
lemma accmethd_rT_is_type:
schirmer@12854
   727
"\<lbrakk>wf_prog G;accmethd G S C sig = Some m;
schirmer@12854
   728
    class G C = Some y\<rbrakk>
schirmer@12854
   729
\<Longrightarrow> is_type G (resTy m)"
schirmer@12854
   730
by (auto simp add: accmethd_def  
schirmer@12854
   731
         intro: methd_rT_is_type)
schirmer@12854
   732
schirmer@12854
   733
lemma methd_Object_SomeD:
schirmer@12854
   734
"\<lbrakk>wf_prog G;methd G Object sig = Some m\<rbrakk> 
schirmer@12854
   735
 \<Longrightarrow> declclass m = Object"
schirmer@12854
   736
by (auto dest: class_Object simp add: methd_rec )
schirmer@12854
   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"
schirmer@12854
   743
  have "wf_prog G \<longrightarrow> 
schirmer@12854
   744
         (\<forall> i im. iface G I = Some i \<longrightarrow> im \<in> imethds G I sig
schirmer@12854
   745
                  \<longrightarrow> \<not>is_static im \<and> accmodi im = Public)" (is "?P G I")
schirmer@12854
   746
  proof (rule iface_rec.induct,intro allI impI)
schirmer@12854
   747
    fix G I i im
schirmer@12854
   748
    assume hyp: "\<forall> J i. J \<in> set (isuperIfs i) \<and> ws_prog G \<and> iface G I = Some i
schirmer@12854
   749
                 \<longrightarrow> ?P G J"
schirmer@12854
   750
    assume wf: "wf_prog G" and if_I: "iface G I = Some i" and 
schirmer@12854
   751
           im: "im \<in> imethds G I sig" 
schirmer@12854
   752
    show "\<not>is_static im \<and> accmodi im = Public" 
schirmer@12854
   753
    proof -
schirmer@12854
   754
      let ?inherited = "Un_tables (imethds G ` set (isuperIfs i))"
schirmer@12854
   755
      let ?new = "(o2s \<circ> table_of (map (\<lambda>(s, mh). (s, I, mh)) (imethods i)))"
schirmer@12854
   756
      from if_I wf im have imethds:"im \<in> (?inherited \<oplus>\<oplus> ?new) sig"
schirmer@12854
   757
	by (simp add: imethds_rec)
schirmer@12854
   758
      from wf if_I have 
schirmer@12854
   759
	wf_supI: "\<forall> J. J \<in> set (isuperIfs i) \<longrightarrow> (\<exists> j. iface G J = Some j)"
schirmer@12854
   760
	by (blast dest: wf_prog_idecl wf_idecl_supD is_acc_ifaceD)
schirmer@12854
   761
      from wf if_I have
schirmer@12854
   762
	"\<forall> im \<in> set (imethods i). \<not> is_static im \<and> accmodi im = Public"
schirmer@12854
   763
	by (auto dest!: wf_prog_idecl wf_idecl_mhead)
schirmer@12854
   764
      then have new_ok: "\<forall> im. table_of (imethods i) sig = Some im 
schirmer@12854
   765
                         \<longrightarrow>  \<not> is_static im \<and> accmodi im = Public"
schirmer@12854
   766
	by (auto dest!: table_of_Some_in_set)
schirmer@12854
   767
      show ?thesis
schirmer@12854
   768
	proof (cases "?new sig = {}")
schirmer@12854
   769
	  case True
schirmer@12854
   770
	  from True wf wf_supI if_I imethds hyp 
schirmer@12854
   771
	  show ?thesis by (auto simp del:  split_paired_All)  
schirmer@12854
   772
	next
schirmer@12854
   773
	  case False
schirmer@12854
   774
	  from False wf wf_supI if_I imethds new_ok hyp 
schirmer@12854
   775
	  show ?thesis by (auto dest: wf_idecl_hidings hidings_entailsD)
schirmer@12854
   776
	qed
schirmer@12854
   777
      qed
schirmer@12854
   778
    qed
schirmer@12854
   779
  with asm show ?thesis by (auto simp del: split_paired_All)
schirmer@12854
   780
qed
schirmer@12854
   781
schirmer@12854
   782
lemma wf_prog_hidesD:
wenzelm@12937
   783
  assumes hides: "G \<turnstile>new hides old" and wf: "wf_prog G"
wenzelm@12937
   784
  shows
schirmer@12854
   785
   "accmodi old \<le> accmodi new \<and>
schirmer@12854
   786
    is_static old"
schirmer@12854
   787
proof -
schirmer@12854
   788
  from hides 
schirmer@12854
   789
  obtain c where 
schirmer@12854
   790
    clsNew: "class G (declclass new) = Some c" and
schirmer@12854
   791
    neqObj: "declclass new \<noteq> Object"
schirmer@12854
   792
    by (auto dest: hidesD declared_in_classD)
schirmer@12854
   793
  with hides obtain newM oldM where
schirmer@12854
   794
    newM: "table_of (methods c) (msig new) = Some newM" and 
schirmer@12854
   795
     new: "new = (declclass new,(msig new),newM)" and
schirmer@12854
   796
     old: "old = (declclass old,(msig old),oldM)" and
schirmer@12854
   797
          "msig new = msig old"
schirmer@12854
   798
    by (cases new,cases old) 
schirmer@12854
   799
       (auto dest: hidesD 
schirmer@12854
   800
         simp add: cdeclaredmethd_def declared_in_def)
schirmer@12854
   801
  with hides 
schirmer@12854
   802
  have hides':
schirmer@12854
   803
        "G,(msig new)\<turnstile>(declclass new,newM) hides (declclass old,oldM)"
schirmer@12854
   804
    by auto
schirmer@12854
   805
  from clsNew wf 
schirmer@12854
   806
  have "wf_cdecl G (declclass new,c)" by (blast intro: wf_prog_cdecl)
schirmer@12854
   807
  note wf_cdecl_hides_SomeD [OF this neqObj newM hides']
schirmer@12854
   808
  with new old 
schirmer@12854
   809
  show ?thesis
schirmer@12854
   810
    by (cases new, cases old) auto
schirmer@12854
   811
qed
schirmer@12854
   812
schirmer@12854
   813
text {* Compare this lemma about static  
schirmer@12854
   814
overriding @{term "G \<turnstile>new overrides\<^sub>S old"} with the definition of 
schirmer@12854
   815
dynamic overriding @{term "G \<turnstile>new overrides old"}. 
schirmer@12854
   816
Conforming result types and restrictions on the access modifiers of the old 
schirmer@12854
   817
and the new method are not part of the predicate for static overriding. But
schirmer@12854
   818
they are enshured in a wellfromed program.  Dynamic overriding has 
schirmer@12854
   819
no restrictions on the access modifiers but enforces confrom result types 
schirmer@12854
   820
as precondition. But with some efford we can guarantee the access modifier
schirmer@12854
   821
restriction for dynamic overriding, too. See lemma 
schirmer@12854
   822
@{text wf_prog_dyn_override_prop}.
schirmer@12854
   823
*}
schirmer@12854
   824
lemma wf_prog_stat_overridesD:
wenzelm@12937
   825
  assumes stat_override: "G \<turnstile>new overrides\<^sub>S old" and wf: "wf_prog G"
wenzelm@12937
   826
  shows
schirmer@12854
   827
   "G\<turnstile>resTy new\<preceq>resTy old \<and>
schirmer@12854
   828
    accmodi old \<le> accmodi new \<and>
schirmer@12854
   829
    \<not> is_static old"
schirmer@12854
   830
proof -
schirmer@12854
   831
  from stat_override 
schirmer@12854
   832
  obtain c where 
schirmer@12854
   833
    clsNew: "class G (declclass new) = Some c" and
schirmer@12854
   834
    neqObj: "declclass new \<noteq> Object"
schirmer@12854
   835
    by (auto dest: stat_overrides_commonD declared_in_classD)
schirmer@12854
   836
  with stat_override obtain newM oldM where
schirmer@12854
   837
    newM: "table_of (methods c) (msig new) = Some newM" and 
schirmer@12854
   838
     new: "new = (declclass new,(msig new),newM)" and
schirmer@12854
   839
     old: "old = (declclass old,(msig old),oldM)" and
schirmer@12854
   840
          "msig new = msig old"
schirmer@12854
   841
    by (cases new,cases old) 
schirmer@12854
   842
       (auto dest: stat_overrides_commonD 
schirmer@12854
   843
         simp add: cdeclaredmethd_def declared_in_def)
schirmer@12854
   844
  with stat_override 
schirmer@12854
   845
  have stat_override':
schirmer@12854
   846
        "G,(msig new)\<turnstile>(declclass new,newM) overrides\<^sub>S (declclass old,oldM)"
schirmer@12854
   847
    by auto
schirmer@12854
   848
  from clsNew wf 
schirmer@12854
   849
  have "wf_cdecl G (declclass new,c)" by (blast intro: wf_prog_cdecl)
schirmer@12854
   850
  note wf_cdecl_overrides_SomeD [OF this neqObj newM stat_override']
schirmer@12854
   851
  with new old 
schirmer@12854
   852
  show ?thesis
schirmer@12854
   853
    by (cases new, cases old) auto
schirmer@12854
   854
qed
schirmer@12854
   855
    
schirmer@12854
   856
lemma static_to_dynamic_overriding: 
wenzelm@12937
   857
  assumes stat_override: "G\<turnstile>new overrides\<^sub>S old" and wf : "wf_prog G"
wenzelm@12937
   858
  shows "G\<turnstile>new overrides old"
schirmer@12854
   859
proof -
schirmer@12854
   860
  from stat_override 
schirmer@12854
   861
  show ?thesis (is "?Overrides new old")
schirmer@12854
   862
  proof (induct)
schirmer@12854
   863
    case (Direct new old superNew)
schirmer@12854
   864
    then have stat_override:"G\<turnstile>new overrides\<^sub>S old" 
schirmer@12854
   865
      by (rule stat_overridesR.Direct)
schirmer@12854
   866
    from stat_override wf
schirmer@12854
   867
    have resTy_widen: "G\<turnstile>resTy new\<preceq>resTy old" and
schirmer@12854
   868
      not_static_old: "\<not> is_static old" 
schirmer@12854
   869
      by (auto dest: wf_prog_stat_overridesD)  
schirmer@12854
   870
    have not_private_new: "accmodi new \<noteq> Private"
schirmer@12854
   871
    proof -
schirmer@12854
   872
      from stat_override 
schirmer@12854
   873
      have "accmodi old \<noteq> Private"
schirmer@12854
   874
	by (rule no_Private_stat_override)
schirmer@12854
   875
      moreover
schirmer@12854
   876
      from stat_override wf
schirmer@12854
   877
      have "accmodi old \<le> accmodi new"
schirmer@12854
   878
	by (auto dest: wf_prog_stat_overridesD)
schirmer@12854
   879
      ultimately
schirmer@12854
   880
      show ?thesis
schirmer@12854
   881
	by (auto dest: acc_modi_bottom)
schirmer@12854
   882
    qed
schirmer@12854
   883
    with Direct resTy_widen not_static_old 
schirmer@12854
   884
    show "?Overrides new old" 
schirmer@12962
   885
      by (auto intro: overridesR.Direct stat_override_declclasses_relation) 
schirmer@12854
   886
  next
schirmer@12854
   887
    case (Indirect inter new old)
schirmer@12854
   888
    then show "?Overrides new old" 
schirmer@12854
   889
      by (blast intro: overridesR.Indirect) 
schirmer@12854
   890
  qed
schirmer@12854
   891
qed
schirmer@12854
   892
schirmer@12854
   893
lemma non_Package_instance_method_inheritance:
wenzelm@12937
   894
  assumes old_inheritable: "G\<turnstile>Method old inheritable_in (pid C)" and
wenzelm@12937
   895
              accmodi_old: "accmodi old \<noteq> Package" and 
wenzelm@12937
   896
          instance_method: "\<not> is_static old" and
wenzelm@12937
   897
                   subcls: "G\<turnstile>C \<prec>\<^sub>C declclass old" and
wenzelm@12937
   898
             old_declared: "G\<turnstile>Method old declared_in (declclass old)" and
wenzelm@12937
   899
                       wf: "wf_prog G"
wenzelm@12937
   900
  shows "G\<turnstile>Method old member_of C \<or>
wenzelm@12937
   901
   (\<exists> new. G\<turnstile> new overrides\<^sub>S old \<and> G\<turnstile>Method new member_of C)"
schirmer@12854
   902
proof -
schirmer@12854
   903
  from wf have ws: "ws_prog G" by auto
schirmer@12854
   904
  from old_declared have iscls_declC_old: "is_class G (declclass old)"
schirmer@12854
   905
    by (auto simp add: declared_in_def cdeclaredmethd_def)
schirmer@12854
   906
  from subcls have  iscls_C: "is_class G C"
schirmer@12854
   907
    by (blast dest:  subcls_is_class)
schirmer@12854
   908
  from iscls_C ws old_inheritable subcls 
schirmer@12854
   909
  show ?thesis (is "?P C old")
schirmer@12854
   910
  proof (induct rule: ws_class_induct')
schirmer@12854
   911
    case Object
schirmer@12854
   912
    assume "G\<turnstile>Object\<prec>\<^sub>C declclass old"
schirmer@12854
   913
    then show "?P Object old"
schirmer@12854
   914
      by blast
schirmer@12854
   915
  next
schirmer@12854
   916
    case (Subcls C c)
schirmer@12854
   917
    assume cls_C: "class G C = Some c" and 
schirmer@12854
   918
       neq_C_Obj: "C \<noteq> Object" and
schirmer@12854
   919
             hyp: "\<lbrakk>G \<turnstile>Method old inheritable_in pid (super c); 
schirmer@12854
   920
                   G\<turnstile>super c\<prec>\<^sub>C declclass old\<rbrakk> \<Longrightarrow> ?P (super c) old" and
schirmer@12854
   921
     inheritable: "G \<turnstile>Method old inheritable_in pid C" and
schirmer@12854
   922
         subclsC: "G\<turnstile>C\<prec>\<^sub>C declclass old"
schirmer@12854
   923
    from cls_C neq_C_Obj  
schirmer@12854
   924
    have super: "G\<turnstile>C \<prec>\<^sub>C\<^sub>1 super c" 
schirmer@12854
   925
      by (rule subcls1I)
schirmer@12854
   926
    from wf cls_C neq_C_Obj
schirmer@12854
   927
    have accessible_super: "G\<turnstile>(Class (super c)) accessible_in (pid C)" 
schirmer@12854
   928
      by (auto dest: wf_prog_cdecl wf_cdecl_supD is_acc_classD)
schirmer@12854
   929
    {
schirmer@12854
   930
      fix old
schirmer@12854
   931
      assume    member_super: "G\<turnstile>Method old member_of (super c)"
schirmer@12854
   932
      assume     inheritable: "G \<turnstile>Method old inheritable_in pid C"
schirmer@12854
   933
      assume instance_method: "\<not> is_static old"
schirmer@12854
   934
      from member_super
schirmer@12854
   935
      have old_declared: "G\<turnstile>Method old declared_in (declclass old)"
schirmer@12854
   936
       by (cases old) (auto dest: member_of_declC)
schirmer@12854
   937
      have "?P C old"
schirmer@12854
   938
      proof (cases "G\<turnstile>mid (msig old) undeclared_in C")
schirmer@12854
   939
	case True
schirmer@12854
   940
	with inheritable super accessible_super member_super
schirmer@12854
   941
	have "G\<turnstile>Method old member_of C"
schirmer@12854
   942
	  by (cases old) (auto intro: members.Inherited)
schirmer@12854
   943
	then show ?thesis
schirmer@12854
   944
	  by auto
schirmer@12854
   945
      next
schirmer@12854
   946
	case False
schirmer@12854
   947
	then obtain new_member where
schirmer@12854
   948
	     "G\<turnstile>new_member declared_in C" and
schirmer@12854
   949
             "mid (msig old) = memberid new_member"
schirmer@12854
   950
          by (auto dest: not_undeclared_declared)
schirmer@12854
   951
	then obtain new where
schirmer@12854
   952
	          new: "G\<turnstile>Method new declared_in C" and
schirmer@12854
   953
               eq_sig: "msig old = msig new" and
schirmer@12854
   954
	    declC_new: "declclass new = C" 
schirmer@12854
   955
	  by (cases new_member) auto
schirmer@12854
   956
	then have member_new: "G\<turnstile>Method new member_of C"
schirmer@12854
   957
	  by (cases new) (auto intro: members.Immediate)
schirmer@12854
   958
	from declC_new super member_super
schirmer@12854
   959
	have subcls_new_old: "G\<turnstile>declclass new \<prec>\<^sub>C declclass old"
schirmer@12854
   960
	  by (auto dest!: member_of_subclseq_declC
schirmer@12854
   961
	            dest: r_into_trancl intro: trancl_rtrancl_trancl)
schirmer@12854
   962
	show ?thesis
schirmer@12854
   963
	proof (cases "is_static new")
schirmer@12854
   964
	  case False
schirmer@12854
   965
	  with eq_sig declC_new new old_declared inheritable
schirmer@12854
   966
	       super member_super subcls_new_old
schirmer@12854
   967
	  have "G\<turnstile>new overrides\<^sub>S old"
schirmer@12854
   968
	    by (auto intro!: stat_overridesR.Direct)
schirmer@12854
   969
	  with member_new show ?thesis
schirmer@12854
   970
	    by blast
schirmer@12854
   971
	next
schirmer@12854
   972
	  case True
schirmer@12854
   973
	  with eq_sig declC_new subcls_new_old new old_declared inheritable
schirmer@12854
   974
	  have "G\<turnstile>new hides old"
schirmer@12854
   975
	    by (auto intro: hidesI)    
schirmer@12854
   976
	  with wf 
schirmer@12854
   977
	  have "is_static old"
schirmer@12854
   978
	    by (blast dest: wf_prog_hidesD)
schirmer@12854
   979
	  with instance_method
schirmer@12854
   980
	  show ?thesis
schirmer@12854
   981
	    by (contradiction)
schirmer@12854
   982
	qed
schirmer@12854
   983
      qed
schirmer@12854
   984
    } note hyp_member_super = this
schirmer@12854
   985
    from subclsC cls_C 
schirmer@12854
   986
    have "G\<turnstile>(super c)\<preceq>\<^sub>C declclass old"
schirmer@12854
   987
      by (rule subcls_superD)
schirmer@12854
   988
    then
schirmer@12854
   989
    show "?P C old"
schirmer@12854
   990
    proof (cases rule: subclseq_cases) 
schirmer@12854
   991
      case Eq
schirmer@12854
   992
      assume "super c = declclass old"
schirmer@12854
   993
      with old_declared 
schirmer@12854
   994
      have "G\<turnstile>Method old member_of (super c)" 
schirmer@12854
   995
	by (cases old) (auto intro: members.Immediate)
schirmer@12854
   996
      with inheritable instance_method 
schirmer@12854
   997
      show ?thesis
schirmer@12854
   998
	by (blast dest: hyp_member_super)
schirmer@12854
   999
    next
schirmer@12854
  1000
      case Subcls
schirmer@12854
  1001
      assume "G\<turnstile>super c\<prec>\<^sub>C declclass old"
schirmer@12854
  1002
      moreover
schirmer@12854
  1003
      from inheritable accmodi_old
schirmer@12854
  1004
      have "G \<turnstile>Method old inheritable_in pid (super c)"
schirmer@12854
  1005
	by (cases "accmodi old") (auto simp add: inheritable_in_def)
schirmer@12854
  1006
      ultimately
schirmer@12854
  1007
      have "?P (super c) old"
schirmer@12854
  1008
	by (blast dest: hyp)
schirmer@12854
  1009
      then show ?thesis
schirmer@12854
  1010
      proof
schirmer@12854
  1011
	assume "G \<turnstile>Method old member_of super c"
schirmer@12854
  1012
	with inheritable instance_method
schirmer@12854
  1013
	show ?thesis
schirmer@12854
  1014
	  by (blast dest: hyp_member_super)
schirmer@12854
  1015
      next
schirmer@12854
  1016
	assume "\<exists>new. G \<turnstile> new overrides\<^sub>S old \<and> G \<turnstile>Method new member_of super c"
schirmer@12854
  1017
	then obtain super_new where
schirmer@12854
  1018
	  super_new_override:  "G \<turnstile> super_new overrides\<^sub>S old" and
schirmer@12854
  1019
            super_new_member:  "G \<turnstile>Method super_new member_of super c"
schirmer@12854
  1020
	  by blast
schirmer@12854
  1021
	from super_new_override wf
schirmer@12854
  1022
	have "accmodi old \<le> accmodi super_new"
schirmer@12854
  1023
	  by (auto dest: wf_prog_stat_overridesD)
schirmer@12854
  1024
	with inheritable accmodi_old
schirmer@12854
  1025
	have "G \<turnstile>Method super_new inheritable_in pid C"
schirmer@12854
  1026
	  by (auto simp add: inheritable_in_def 
schirmer@12854
  1027
	              split: acc_modi.splits
schirmer@12854
  1028
                       dest: acc_modi_le_Dests)
schirmer@12854
  1029
	moreover
schirmer@12854
  1030
	from super_new_override 
schirmer@12854
  1031
	have "\<not> is_static super_new"
schirmer@12854
  1032
	  by (auto dest: stat_overrides_commonD)
schirmer@12854
  1033
	moreover
schirmer@12854
  1034
	note super_new_member
schirmer@12854
  1035
	ultimately have "?P C super_new"
schirmer@12854
  1036
	  by (auto dest: hyp_member_super)
schirmer@12854
  1037
	then show ?thesis
schirmer@12854
  1038
	proof 
schirmer@12854
  1039
	  assume "G \<turnstile>Method super_new member_of C"
schirmer@12854
  1040
	  with super_new_override
schirmer@12854
  1041
	  show ?thesis
schirmer@12854
  1042
	    by blast
schirmer@12854
  1043
	next
schirmer@12854
  1044
	  assume "\<exists>new. G \<turnstile> new overrides\<^sub>S super_new \<and> 
schirmer@12854
  1045
                  G \<turnstile>Method new member_of C"
schirmer@12854
  1046
	  with super_new_override show ?thesis
schirmer@12854
  1047
	    by (blast intro: stat_overridesR.Indirect) 
schirmer@12854
  1048
	qed
schirmer@12854
  1049
      qed
schirmer@12854
  1050
    qed
schirmer@12854
  1051
  qed
schirmer@12854
  1052
qed
schirmer@12854
  1053
schirmer@12854
  1054
lemma non_Package_instance_method_inheritance_cases [consumes 6,
schirmer@12854
  1055
         case_names Inheritance Overriding]:
wenzelm@12937
  1056
  assumes old_inheritable: "G\<turnstile>Method old inheritable_in (pid C)" and
wenzelm@12937
  1057
              accmodi_old: "accmodi old \<noteq> Package" and 
wenzelm@12937
  1058
          instance_method: "\<not> is_static old" and
wenzelm@12937
  1059
                   subcls: "G\<turnstile>C \<prec>\<^sub>C declclass old" and
wenzelm@12937
  1060
             old_declared: "G\<turnstile>Method old declared_in (declclass old)" and
wenzelm@12937
  1061
                       wf: "wf_prog G" and
wenzelm@12937
  1062
              inheritance: "G\<turnstile>Method old member_of C \<Longrightarrow> P" and
wenzelm@12937
  1063
               overriding: "\<And> new.
schirmer@12854
  1064
                           \<lbrakk>G\<turnstile> new overrides\<^sub>S old;G\<turnstile>Method new member_of C\<rbrakk>
schirmer@12854
  1065
                           \<Longrightarrow> P"
wenzelm@12937
  1066
  shows P
schirmer@12854
  1067
proof -
schirmer@12854
  1068
  from old_inheritable accmodi_old instance_method subcls old_declared wf 
schirmer@12854
  1069
       inheritance overriding
schirmer@12854
  1070
  show ?thesis
schirmer@12854
  1071
    by (auto dest: non_Package_instance_method_inheritance)
schirmer@12854
  1072
qed
schirmer@12854
  1073
schirmer@12854
  1074
lemma dynamic_to_static_overriding:
wenzelm@12937
  1075
  assumes dyn_override: "G\<turnstile> new overrides old" and
wenzelm@12937
  1076
           accmodi_old: "accmodi old \<noteq> Package" and
wenzelm@12937
  1077
                    wf: "wf_prog G"
wenzelm@12937
  1078
  shows "G\<turnstile> new overrides\<^sub>S old"  
schirmer@12854
  1079
proof - 
schirmer@12854
  1080
  from dyn_override accmodi_old
schirmer@12854
  1081
  show ?thesis (is "?Overrides new old")
schirmer@12854
  1082
  proof (induct rule: overridesR.induct)
schirmer@12854
  1083
    case (Direct new old)
schirmer@12854
  1084
    assume   new_declared: "G\<turnstile>Method new declared_in declclass new"
schirmer@12854
  1085
    assume eq_sig_new_old: "msig new = msig old"
schirmer@12854
  1086
    assume subcls_new_old: "G\<turnstile>declclass new \<prec>\<^sub>C declclass old"
schirmer@12854
  1087
    assume "G \<turnstile>Method old inheritable_in pid (declclass new)" and
schirmer@12854
  1088
           "accmodi old \<noteq> Package" and
schirmer@12854
  1089
           "\<not> is_static old" and
schirmer@12854
  1090
           "G\<turnstile>declclass new\<prec>\<^sub>C declclass old" and
schirmer@12854
  1091
           "G\<turnstile>Method old declared_in declclass old" 
schirmer@12854
  1092
    from this wf
schirmer@12854
  1093
    show "?Overrides new old"
schirmer@12854
  1094
    proof (cases rule: non_Package_instance_method_inheritance_cases)
schirmer@12854
  1095
      case Inheritance
schirmer@12854
  1096
      assume "G \<turnstile>Method old member_of declclass new"
schirmer@12854
  1097
      then have "G\<turnstile>mid (msig old) undeclared_in declclass new"
schirmer@12854
  1098
      proof cases
schirmer@12854
  1099
	case Immediate 
schirmer@12854
  1100
	with subcls_new_old wf show ?thesis 	
schirmer@12854
  1101
	  by (auto dest: subcls_irrefl)
schirmer@12854
  1102
      next
schirmer@12854
  1103
	case Inherited
schirmer@12854
  1104
	then show ?thesis
schirmer@12854
  1105
	  by (cases old) auto
schirmer@12854
  1106
      qed
schirmer@12854
  1107
      with eq_sig_new_old new_declared
schirmer@12854
  1108
      show ?thesis
schirmer@12854
  1109
	by (cases old,cases new) (auto dest!: declared_not_undeclared)
schirmer@12854
  1110
    next
schirmer@12854
  1111
      case (Overriding new') 
schirmer@12854
  1112
      assume stat_override_new': "G \<turnstile> new' overrides\<^sub>S old"
schirmer@12854
  1113
      then have "msig new' = msig old"
schirmer@12854
  1114
	by (auto dest: stat_overrides_commonD)
schirmer@12854
  1115
      with eq_sig_new_old have eq_sig_new_new': "msig new=msig new'"
schirmer@12854
  1116
	by simp
schirmer@12854
  1117
      assume "G \<turnstile>Method new' member_of declclass new"
schirmer@12854
  1118
      then show ?thesis
schirmer@12854
  1119
      proof (cases)
schirmer@12854
  1120
	case Immediate
schirmer@12854
  1121
	then have declC_new: "declclass new' = declclass new" 
schirmer@12854
  1122
	  by auto
schirmer@12854
  1123
	from Immediate 
schirmer@12854
  1124
	have "G\<turnstile>Method new' declared_in declclass new"
schirmer@12854
  1125
	  by (cases new') auto
schirmer@12854
  1126
	with new_declared eq_sig_new_new' declC_new 
schirmer@12854
  1127
	have "new=new'"
schirmer@12854
  1128
	  by (cases new, cases new') (auto dest: unique_declared_in) 
schirmer@12854
  1129
	with stat_override_new'
schirmer@12854
  1130
	show ?thesis
schirmer@12854
  1131
	  by simp
schirmer@12854
  1132
      next
schirmer@12854
  1133
	case Inherited
schirmer@12854
  1134
	then have "G\<turnstile>mid (msig new') undeclared_in declclass new"
schirmer@12854
  1135
	  by (cases new') (auto)
schirmer@12854
  1136
	with eq_sig_new_new' new_declared
schirmer@12854
  1137
	show ?thesis
schirmer@12854
  1138
	  by (cases new,cases new') (auto dest!: declared_not_undeclared)
schirmer@12854
  1139
      qed
schirmer@12854
  1140
    qed
schirmer@12854
  1141
  next
schirmer@12854
  1142
    case (Indirect inter new old)
schirmer@12854
  1143
    assume accmodi_old: "accmodi old \<noteq> Package"
schirmer@12854
  1144
    assume "accmodi old \<noteq> Package \<Longrightarrow> G \<turnstile> inter overrides\<^sub>S old"
schirmer@12854
  1145
    with accmodi_old 
schirmer@12854
  1146
    have stat_override_inter_old: "G \<turnstile> inter overrides\<^sub>S old"
schirmer@12854
  1147
      by blast
schirmer@12854
  1148
    moreover 
schirmer@12854
  1149
    assume hyp_inter: "accmodi inter \<noteq> Package \<Longrightarrow> G \<turnstile> new overrides\<^sub>S inter"
schirmer@12854
  1150
    moreover
schirmer@12854
  1151
    have "accmodi inter \<noteq> Package"
schirmer@12854
  1152
    proof -
schirmer@12854
  1153
      from stat_override_inter_old wf 
schirmer@12854
  1154
      have "accmodi old \<le> accmodi inter"
schirmer@12854
  1155
	by (auto dest: wf_prog_stat_overridesD)
schirmer@12854
  1156
      with stat_override_inter_old accmodi_old
schirmer@12854
  1157
      show ?thesis
schirmer@12854
  1158
	by (auto dest!: no_Private_stat_override
schirmer@12854
  1159
                 split: acc_modi.splits 
schirmer@12854
  1160
	         dest: acc_modi_le_Dests)
schirmer@12854
  1161
    qed
schirmer@12854
  1162
    ultimately show "?Overrides new old"
schirmer@12854
  1163
      by (blast intro: stat_overridesR.Indirect)
schirmer@12854
  1164
  qed
schirmer@12854
  1165
qed
schirmer@12854
  1166
schirmer@12854
  1167
lemma wf_prog_dyn_override_prop:
wenzelm@12937
  1168
  assumes dyn_override: "G \<turnstile> new overrides old" and
schirmer@12854
  1169
                    wf: "wf_prog G"
wenzelm@12937
  1170
  shows "accmodi old \<le> accmodi new"
schirmer@12854
  1171
proof (cases "accmodi old = Package")
schirmer@12854
  1172
  case True
schirmer@12854
  1173
  note old_Package = this
schirmer@12854
  1174
  show ?thesis
schirmer@12854
  1175
  proof (cases "accmodi old \<le> accmodi new")
schirmer@12854
  1176
    case True then show ?thesis .
schirmer@12854
  1177
  next
schirmer@12854
  1178
    case False
schirmer@12854
  1179
    with old_Package 
schirmer@12854
  1180
    have "accmodi new = Private"
schirmer@12854
  1181
      by (cases "accmodi new") (auto simp add: le_acc_def less_acc_def)
schirmer@12854
  1182
    with dyn_override 
schirmer@12854
  1183
    show ?thesis
schirmer@12854
  1184
      by (auto dest: overrides_commonD)
schirmer@12854
  1185
  qed    
schirmer@12854
  1186
next
schirmer@12854
  1187
  case False
schirmer@12854
  1188
  with dyn_override wf
schirmer@12854
  1189
  have "G \<turnstile> new overrides\<^sub>S old"
schirmer@12854
  1190
    by (blast intro: dynamic_to_static_overriding)
schirmer@12854
  1191
  with wf 
schirmer@12854
  1192
  show ?thesis
schirmer@12854
  1193
   by (blast dest: wf_prog_stat_overridesD)
schirmer@12854
  1194
qed 
schirmer@12854
  1195
schirmer@12854
  1196
lemma overrides_Package_old: 
wenzelm@12937
  1197
  assumes dyn_override: "G \<turnstile> new overrides old" and 
wenzelm@12937
  1198
           accmodi_new: "accmodi new = Package" and
wenzelm@12937
  1199
                    wf: "wf_prog G "
wenzelm@12937
  1200
  shows "accmodi old = Package"
schirmer@12854
  1201
proof (cases "accmodi old")
schirmer@12854
  1202
  case Private
schirmer@12854
  1203
  with dyn_override show ?thesis
schirmer@12854
  1204
    by (simp add: no_Private_override)
schirmer@12854
  1205
next
schirmer@12854
  1206
  case Package
schirmer@12854
  1207
  then show ?thesis .
schirmer@12854
  1208
next
schirmer@12854
  1209
  case Protected
schirmer@12854
  1210
  with dyn_override wf
schirmer@12854
  1211
  have "G \<turnstile> new overrides\<^sub>S old"
schirmer@12854
  1212
    by (auto intro: dynamic_to_static_overriding)
schirmer@12854
  1213
  with wf 
schirmer@12854
  1214
  have "accmodi old \<le> accmodi new"
schirmer@12854
  1215
    by (auto dest: wf_prog_stat_overridesD)
schirmer@12854
  1216
  with Protected accmodi_new
schirmer@12854
  1217
  show ?thesis
schirmer@12854
  1218
    by (simp add: less_acc_def le_acc_def)
schirmer@12854
  1219
next
schirmer@12854
  1220
  case Public
schirmer@12854
  1221
  with dyn_override wf
schirmer@12854
  1222
  have "G \<turnstile> new overrides\<^sub>S old"
schirmer@12854
  1223
    by (auto intro: dynamic_to_static_overriding)
schirmer@12854
  1224
  with wf 
schirmer@12854
  1225
  have "accmodi old \<le> accmodi new"
schirmer@12854
  1226
    by (auto dest: wf_prog_stat_overridesD)
schirmer@12854
  1227
  with Public accmodi_new
schirmer@12854
  1228
  show ?thesis
schirmer@12854
  1229
    by (simp add: less_acc_def le_acc_def)
schirmer@12854
  1230
qed
schirmer@12854
  1231
schirmer@12854
  1232
lemma dyn_override_Package:
wenzelm@12937
  1233
  assumes dyn_override: "G \<turnstile> new overrides old" and
wenzelm@12937
  1234
           accmodi_old: "accmodi old = Package" and 
wenzelm@12937
  1235
           accmodi_new: "accmodi new = Package" and
schirmer@12854
  1236
                    wf: "wf_prog G"
wenzelm@12937
  1237
  shows "pid (declclass old) = pid (declclass new)"
schirmer@12854
  1238
proof - 
schirmer@12854
  1239
  from dyn_override accmodi_old accmodi_new
schirmer@12854
  1240
  show ?thesis (is "?EqPid old new")
schirmer@12854
  1241
  proof (induct rule: overridesR.induct)
schirmer@12854
  1242
    case (Direct new old)
schirmer@12854
  1243
    assume "accmodi old = Package"
schirmer@12854
  1244
           "G \<turnstile>Method old inheritable_in pid (declclass new)"
schirmer@12854
  1245
    then show "pid (declclass old) =  pid (declclass new)"
schirmer@12854
  1246
      by (auto simp add: inheritable_in_def)
schirmer@12854
  1247
  next
schirmer@12854
  1248
    case (Indirect inter new old)
schirmer@12854
  1249
    assume accmodi_old: "accmodi old = Package" and
schirmer@12854
  1250
           accmodi_new: "accmodi new = Package" 
schirmer@12854
  1251
    assume "G \<turnstile> new overrides inter"
schirmer@12854
  1252
    with accmodi_new wf
schirmer@12854
  1253
    have "accmodi inter = Package"
schirmer@12854
  1254
      by  (auto intro: overrides_Package_old)
schirmer@12854
  1255
    with Indirect
schirmer@12854
  1256
    show "pid (declclass old) =  pid (declclass new)"
schirmer@12854
  1257
      by auto
schirmer@12854
  1258
  qed
schirmer@12854
  1259
qed
schirmer@12854
  1260
schirmer@12854
  1261
lemma dyn_override_Package_escape:
wenzelm@12937
  1262
  assumes dyn_override: "G \<turnstile> new overrides old" and
wenzelm@12937
  1263
           accmodi_old: "accmodi old = Package" and 
wenzelm@12937
  1264
          outside_pack: "pid (declclass old) \<noteq> pid (declclass new)" and
schirmer@12854
  1265
                    wf: "wf_prog G"
wenzelm@12937
  1266
  shows "\<exists> inter. G \<turnstile> new overrides inter \<and> G \<turnstile> inter overrides old \<and>
schirmer@12854
  1267
             pid (declclass old) = pid (declclass inter) \<and>
schirmer@12854
  1268
             Protected \<le> accmodi inter"
schirmer@12854
  1269
proof -
schirmer@12854
  1270
  from dyn_override accmodi_old outside_pack
schirmer@12854
  1271
  show ?thesis (is "?P new old")
schirmer@12854
  1272
  proof (induct rule: overridesR.induct)
schirmer@12854
  1273
    case (Direct new old)
schirmer@12854
  1274
    assume accmodi_old: "accmodi old = Package"
schirmer@12854
  1275
    assume outside_pack: "pid (declclass old) \<noteq> pid (declclass new)"
schirmer@12854
  1276
    assume "G \<turnstile>Method old inheritable_in pid (declclass new)"
schirmer@12854
  1277
    with accmodi_old 
schirmer@12854
  1278
    have "pid (declclass old) = pid (declclass new)"
schirmer@12854
  1279
      by (simp add: inheritable_in_def)
schirmer@12854
  1280
    with outside_pack 
schirmer@12854
  1281
    show "?P new old"
schirmer@12854
  1282
      by (contradiction)
schirmer@12854
  1283
  next
schirmer@12854
  1284
    case (Indirect inter new old)
schirmer@12854
  1285
    assume accmodi_old: "accmodi old = Package"
schirmer@12854
  1286
    assume outside_pack: "pid (declclass old) \<noteq> pid (declclass new)"
schirmer@12854
  1287
    assume override_new_inter: "G \<turnstile> new overrides inter"
schirmer@12854
  1288
    assume override_inter_old: "G \<turnstile> inter overrides old"
schirmer@12854
  1289
    assume hyp_new_inter: "\<lbrakk>accmodi inter = Package; 
schirmer@12854
  1290
                           pid (declclass inter) \<noteq> pid (declclass new)\<rbrakk>
schirmer@12854
  1291
                           \<Longrightarrow> ?P new inter"
schirmer@12854
  1292
    assume hyp_inter_old: "\<lbrakk>accmodi old = Package; 
schirmer@12854
  1293
                           pid (declclass old) \<noteq> pid (declclass inter)\<rbrakk>
schirmer@12854
  1294
                           \<Longrightarrow> ?P inter old"
schirmer@12854
  1295
    show "?P new old"
schirmer@12854
  1296
    proof (cases "pid (declclass old) = pid (declclass inter)")
schirmer@12854
  1297
      case True
schirmer@12854
  1298
      note same_pack_old_inter = this
schirmer@12854
  1299
      show ?thesis
schirmer@12854
  1300
      proof (cases "pid (declclass inter) = pid (declclass new)")
schirmer@12854
  1301
	case True
schirmer@12854
  1302
	with same_pack_old_inter outside_pack
schirmer@12854
  1303
	show ?thesis
schirmer@12854
  1304
	  by auto
schirmer@12854
  1305
      next
schirmer@12854
  1306
	case False
schirmer@12854
  1307
	note diff_pack_inter_new = this
schirmer@12854
  1308
	show ?thesis
schirmer@12854
  1309
	proof (cases "accmodi inter = Package")
schirmer@12854
  1310
	  case True
schirmer@12854
  1311
	  with diff_pack_inter_new hyp_new_inter  
schirmer@12854
  1312
	  obtain newinter where
schirmer@12854
  1313
	    over_new_newinter: "G \<turnstile> new overrides newinter" and
schirmer@12854
  1314
            over_newinter_inter: "G \<turnstile> newinter overrides inter" and 
schirmer@12854
  1315
            eq_pid: "pid (declclass inter) = pid (declclass newinter)" and
schirmer@12854
  1316
            accmodi_newinter: "Protected \<le> accmodi newinter"
schirmer@12854
  1317
	    by auto
schirmer@12854
  1318
	  from over_newinter_inter override_inter_old
schirmer@12854
  1319
	  have "G\<turnstile>newinter overrides old"
schirmer@12854
  1320
	    by (rule overridesR.Indirect)
schirmer@12854
  1321
	  moreover
schirmer@12854
  1322
	  from eq_pid same_pack_old_inter 
schirmer@12854
  1323
	  have "pid (declclass old) = pid (declclass newinter)"
schirmer@12854
  1324
	    by simp
schirmer@12854
  1325
	  moreover
schirmer@12854
  1326
	  note over_new_newinter accmodi_newinter
schirmer@12854
  1327
	  ultimately show ?thesis
schirmer@12854
  1328
	    by blast
schirmer@12854
  1329
	next
schirmer@12854
  1330
	  case False
schirmer@12854
  1331
	  with override_new_inter
schirmer@12854
  1332
	  have "Protected \<le> accmodi inter"
schirmer@12854
  1333
	    by (cases "accmodi inter") (auto dest: no_Private_override)
schirmer@12854
  1334
	  with override_new_inter override_inter_old same_pack_old_inter
schirmer@12854
  1335
	  show ?thesis
schirmer@12854
  1336
	    by blast
schirmer@12854
  1337
	qed
schirmer@12854
  1338
      qed
schirmer@12854
  1339
    next
schirmer@12854
  1340
      case False
schirmer@12854
  1341
      with accmodi_old hyp_inter_old
schirmer@12854
  1342
      obtain newinter where
schirmer@12854
  1343
	over_inter_newinter: "G \<turnstile> inter overrides newinter" and
schirmer@12854
  1344
          over_newinter_old: "G \<turnstile> newinter overrides old" and 
schirmer@12854
  1345
                eq_pid: "pid (declclass old) = pid (declclass newinter)" and
schirmer@12854
  1346
	accmodi_newinter: "Protected \<le> accmodi newinter"
schirmer@12854
  1347
	by auto
schirmer@12854
  1348
      from override_new_inter over_inter_newinter 
schirmer@12854
  1349
      have "G \<turnstile> new overrides newinter"
schirmer@12854
  1350
	by (rule overridesR.Indirect)
schirmer@12854
  1351
      with eq_pid over_newinter_old accmodi_newinter
schirmer@12854
  1352
      show ?thesis
schirmer@12854
  1353
	by blast
schirmer@12854
  1354
    qed
schirmer@12854
  1355
  qed
schirmer@12854
  1356
qed
schirmer@12854
  1357
schirmer@12854
  1358
lemma declclass_widen[rule_format]: 
schirmer@12854
  1359
 "wf_prog G 
schirmer@12854
  1360
 \<longrightarrow> (\<forall>c m. class G C = Some c \<longrightarrow> methd G C sig = Some m 
schirmer@12854
  1361
 \<longrightarrow> G\<turnstile>C \<preceq>\<^sub>C declclass m)" (is "?P G C")
schirmer@12854
  1362
proof (rule class_rec.induct,intro allI impI)
schirmer@12854
  1363
  fix G C c m
schirmer@12854
  1364
  assume Hyp: "\<forall>c. C \<noteq> Object \<and> ws_prog G \<and> class G C = Some c 
schirmer@12854
  1365
               \<longrightarrow> ?P G (super c)"
schirmer@12854
  1366
  assume wf: "wf_prog G" and cls_C: "class G C = Some c" and
schirmer@12854
  1367
         m:  "methd G C sig = Some m"
schirmer@12854
  1368
  show "G\<turnstile>C\<preceq>\<^sub>C declclass m" 
schirmer@12854
  1369
  proof (cases "C=Object")
schirmer@12854
  1370
    case True 
schirmer@12854
  1371
    with wf m show ?thesis by (simp add: methd_Object_SomeD)
schirmer@12854
  1372
  next
schirmer@12854
  1373
    let ?filter="filter_tab (\<lambda>sig m. G\<turnstile>C inherits method sig m)"
schirmer@12854
  1374
    let ?table = "table_of (map (\<lambda>(s, m). (s, C, m)) (methods c))"
schirmer@12854
  1375
    case False 
schirmer@12854
  1376
    with cls_C wf m
schirmer@12854
  1377
    have methd_C: "(?filter (methd G (super c)) ++ ?table) sig = Some m "
schirmer@12854
  1378
      by (simp add: methd_rec)
schirmer@12854
  1379
    show ?thesis
schirmer@12854
  1380
    proof (cases "?table sig")
schirmer@12854
  1381
      case None
schirmer@12854
  1382
      from this methd_C have "?filter (methd G (super c)) sig = Some m"
schirmer@12854
  1383
	by simp
schirmer@12854
  1384
      moreover
schirmer@12854
  1385
      from wf cls_C False obtain sup where "class G (super c) = Some sup"
schirmer@12854
  1386
	by (blast dest: wf_prog_cdecl wf_cdecl_supD is_acc_class_is_class)
schirmer@12925
  1387
      moreover note wf False cls_C  
schirmer@12925
  1388
      ultimately have "G\<turnstile>super c \<preceq>\<^sub>C declclass m"  
schirmer@12925
  1389
	by (auto intro: Hyp [rule_format])
schirmer@12854
  1390
      moreover from cls_C False have  "G\<turnstile>C \<prec>\<^sub>C\<^sub>1 super c" by (rule subcls1I)
schirmer@12854
  1391
      ultimately show ?thesis by - (rule rtrancl_into_rtrancl2)
schirmer@12854
  1392
    next
schirmer@12854
  1393
      case Some
schirmer@12854
  1394
      from this wf False cls_C methd_C show ?thesis by auto
schirmer@12854
  1395
    qed
schirmer@12854
  1396
  qed
schirmer@12854
  1397
qed
schirmer@12854
  1398
schirmer@12854
  1399
lemma declclass_methd_Object: 
schirmer@12854
  1400
 "\<lbrakk>wf_prog G; methd G Object sig = Some m\<rbrakk> \<Longrightarrow> declclass m = Object"
schirmer@12854
  1401
by auto
schirmer@12854
  1402
schirmer@12854
  1403
lemma methd_declaredD: 
schirmer@12854
  1404
 "\<lbrakk>wf_prog G; is_class G C;methd G C sig = Some m\<rbrakk> 
schirmer@12854
  1405
  \<Longrightarrow> G\<turnstile>(mdecl (sig,mthd m)) declared_in (declclass m)"
schirmer@12854
  1406
proof -
schirmer@12854
  1407
  assume    wf: "wf_prog G"
schirmer@12854
  1408
  then have ws: "ws_prog G" ..
schirmer@12854
  1409
  assume  clsC: "is_class G C"
schirmer@12854
  1410
  from clsC ws 
schirmer@12854
  1411
  show "methd G C sig = Some m 
schirmer@12854
  1412
        \<Longrightarrow> G\<turnstile>(mdecl (sig,mthd m)) declared_in (declclass m)"
schirmer@12854
  1413
    (is "PROP ?P C") 
schirmer@12854
  1414
  proof (induct ?P C rule: ws_class_induct')
schirmer@12854
  1415
    case Object
schirmer@12854
  1416
    assume "methd G Object sig = Some m" 
schirmer@12854
  1417
    with wf show ?thesis
schirmer@12854
  1418
      by - (rule method_declared_inI, auto) 
schirmer@12854
  1419
  next
schirmer@12854
  1420
    case Subcls
schirmer@12854
  1421
    fix C c
schirmer@12854
  1422
    assume clsC: "class G C = Some c"
schirmer@12854
  1423
    and       m: "methd G C sig = Some m"
schirmer@12854
  1424
    and     hyp: "methd G (super c) sig = Some m \<Longrightarrow> ?thesis" 
schirmer@12854
  1425
    let ?newMethods = "table_of (map (\<lambda>(s, m). (s, C, m)) (methods c))"
schirmer@12854
  1426
    show ?thesis
schirmer@12854
  1427
    proof (cases "?newMethods sig")
schirmer@12854
  1428
      case None
schirmer@12854
  1429
      from None ws clsC m hyp 
schirmer@12854
  1430
      show ?thesis by (auto intro: method_declared_inI simp add: methd_rec)
schirmer@12854
  1431
    next
schirmer@12854
  1432
      case Some
schirmer@12854
  1433
      from Some ws clsC m 
schirmer@12854
  1434
      show ?thesis by (auto intro: method_declared_inI simp add: methd_rec) 
schirmer@12854
  1435
    qed
schirmer@12854
  1436
  qed
schirmer@12854
  1437
qed
schirmer@12854
  1438
schirmer@12854
  1439
lemma methd_rec_Some_cases [consumes 4, case_names NewMethod InheritedMethod]:
wenzelm@12937
  1440
  assumes methd_C: "methd G C sig = Some m" and
wenzelm@12937
  1441
               ws: "ws_prog G" and
wenzelm@12937
  1442
             clsC: "class G C = Some c" and
wenzelm@12937
  1443
        neq_C_Obj: "C\<noteq>Object"
wenzelm@12937
  1444
  shows
schirmer@12854
  1445
"\<lbrakk>table_of (map (\<lambda>(s, m). (s, C, m)) (methods c)) sig = Some m \<Longrightarrow> P;
schirmer@12854
  1446
  \<lbrakk>G\<turnstile>C inherits (method sig m); methd G (super c) sig = Some m\<rbrakk> \<Longrightarrow> P 
schirmer@12854
  1447
 \<rbrakk> \<Longrightarrow> P"
schirmer@12854
  1448
proof -
schirmer@12854
  1449
  let ?inherited   = "filter_tab (\<lambda>sig m. G\<turnstile>C inherits method sig m) 
schirmer@12854
  1450
                              (methd G (super c))"
schirmer@12854
  1451
  let ?new = "table_of (map (\<lambda>(s, m). (s, C, m)) (methods c))"
schirmer@12854
  1452
  from ws clsC neq_C_Obj methd_C 
schirmer@12854
  1453
  have methd_unfold: "(?inherited ++ ?new) sig = Some m"
schirmer@12854
  1454
    by (simp add: methd_rec)
schirmer@12854
  1455
  assume NewMethod: "?new sig = Some m \<Longrightarrow> P"
schirmer@12854
  1456
  assume InheritedMethod: "\<lbrakk>G\<turnstile>C inherits (method sig m); 
schirmer@12854
  1457
                            methd G (super c) sig = Some m\<rbrakk> \<Longrightarrow> P"
schirmer@12854
  1458
  show P
schirmer@12854
  1459
  proof (cases "?new sig")
schirmer@12854
  1460
    case None
schirmer@12854
  1461
    with methd_unfold have "?inherited sig = Some m"
schirmer@12854
  1462
      by (auto)
schirmer@12854
  1463
    with InheritedMethod show P by blast
schirmer@12854
  1464
  next
schirmer@12854
  1465
    case Some
schirmer@12854
  1466
    with methd_unfold have "?new sig = Some m"
schirmer@12854
  1467
      by auto
schirmer@12854
  1468
    with NewMethod show P by blast
schirmer@12854
  1469
  qed
schirmer@12854
  1470
qed
schirmer@12854
  1471
schirmer@12854
  1472
  
schirmer@12854
  1473
lemma methd_member_of:
wenzelm@12937
  1474
  assumes wf: "wf_prog G"
wenzelm@12937
  1475
  shows
wenzelm@12937
  1476
    "\<lbrakk>is_class G C; methd G C sig = Some m\<rbrakk> \<Longrightarrow> G\<turnstile>Methd sig m member_of C" 
schirmer@12854
  1477
  (is "?Class C \<Longrightarrow> ?Method C \<Longrightarrow> ?MemberOf C") 
schirmer@12854
  1478
proof -
schirmer@12854
  1479
  from wf   have   ws: "ws_prog G" ..
schirmer@12854
  1480
  assume defC: "is_class G C"
schirmer@12854
  1481
  from defC ws 
schirmer@12854
  1482
  show "?Class C \<Longrightarrow> ?Method C \<Longrightarrow> ?MemberOf C"
schirmer@12854
  1483
  proof (induct rule: ws_class_induct')  
schirmer@12854
  1484
    case Object
berghofe@13601
  1485
    with wf have declC: "Object = declclass m"
berghofe@13601
  1486
      by (simp add: declclass_methd_Object)
berghofe@13601
  1487
    from Object wf have "G\<turnstile>Methd sig m declared_in Object"
berghofe@13601
  1488
      by (auto intro: methd_declaredD simp add: declC)
schirmer@12854
  1489
    with declC 
schirmer@12854
  1490
    show "?MemberOf Object"
schirmer@12854
  1491
      by (auto intro!: members.Immediate
schirmer@12854
  1492
                  simp del: methd_Object)
schirmer@12854
  1493
  next
schirmer@12854
  1494
    case (Subcls C c)
schirmer@12854
  1495
    assume  clsC: "class G C = Some c" and
schirmer@12854
  1496
       neq_C_Obj: "C \<noteq> Object"  
schirmer@12854
  1497
    assume methd: "?Method C"
schirmer@12854
  1498
    from methd ws clsC neq_C_Obj
schirmer@12854
  1499
    show "?MemberOf C"
schirmer@12854
  1500
    proof (cases rule: methd_rec_Some_cases)
schirmer@12854
  1501
      case NewMethod
schirmer@12854
  1502
      with clsC show ?thesis
schirmer@12854
  1503
	by (auto dest: method_declared_inI intro!: members.Immediate)
schirmer@12854
  1504
    next
schirmer@12854
  1505
      case InheritedMethod
schirmer@12854
  1506
      then show "?thesis"
schirmer@12854
  1507
	by (blast dest: inherits_member)
schirmer@12854
  1508
    qed
schirmer@12854
  1509
  qed
schirmer@12854
  1510
qed
schirmer@12854
  1511
schirmer@12854
  1512
lemma current_methd: 
schirmer@12854
  1513
      "\<lbrakk>table_of (methods c) sig = Some new;
schirmer@12854
  1514
        ws_prog G; class G C = Some c; C \<noteq> Object; 
schirmer@12854
  1515
        methd G (super c) sig = Some old\<rbrakk> 
schirmer@12854
  1516
    \<Longrightarrow> methd G C sig = Some (C,new)"
schirmer@12854
  1517
by (auto simp add: methd_rec
nipkow@14025
  1518
            intro: filter_tab_SomeI map_add_find_right table_of_map_SomeI)
schirmer@12854
  1519
schirmer@12854
  1520
lemma wf_prog_staticD:
wenzelm@12937
  1521
  assumes     wf: "wf_prog G" and
schirmer@12854
  1522
            clsC: "class G C = Some c" and
schirmer@12854
  1523
       neq_C_Obj: "C \<noteq> Object" and 
schirmer@12854
  1524
             old: "methd G (super c) sig = Some old" and 
schirmer@12854
  1525
     accmodi_old: "Protected \<le> accmodi old" and
schirmer@12854
  1526
             new: "table_of (methods c) sig = Some new"
wenzelm@12937
  1527
  shows "is_static new = is_static old"
schirmer@12854
  1528
proof -
schirmer@12854
  1529
  from clsC wf 
schirmer@12854
  1530
  have wf_cdecl: "wf_cdecl G (C,c)" by (rule wf_prog_cdecl)
schirmer@12854
  1531
  from wf clsC neq_C_Obj
schirmer@12854
  1532
  have is_cls_super: "is_class G (super c)" 
schirmer@12854
  1533
    by (blast dest: wf_prog_acc_superD is_acc_classD)
schirmer@12854
  1534
  from wf is_cls_super old 
schirmer@12854
  1535
  have old_member_of: "G\<turnstile>Methd sig old member_of (super c)"  
schirmer@12854
  1536
    by (rule methd_member_of)
schirmer@12854
  1537
  from old wf is_cls_super 
schirmer@12854
  1538
  have old_declared: "G\<turnstile>Methd sig old declared_in (declclass old)"
schirmer@12854
  1539
    by (auto dest: methd_declared_in_declclass)
schirmer@12854
  1540
  from new clsC 
schirmer@12854
  1541
  have new_declared: "G\<turnstile>Methd sig (C,new) declared_in C"
schirmer@12854
  1542
    by (auto intro: method_declared_inI)
schirmer@12854
  1543
  note trancl_rtrancl_tranc = trancl_rtrancl_trancl [trans] (* ### in Basis *)
schirmer@12854
  1544
  from clsC neq_C_Obj
schirmer@12854
  1545
  have subcls1_C_super: "G\<turnstile>C \<prec>\<^sub>C\<^sub>1 super c"
schirmer@12854
  1546
    by (rule subcls1I)
schirmer@12854
  1547
  then have "G\<turnstile>C \<prec>\<^sub>C super c" ..
schirmer@12854
  1548
  also from old wf is_cls_super
schirmer@12854
  1549
  have "G\<turnstile>super c \<preceq>\<^sub>C (declclass old)" by (auto dest: methd_declC)
schirmer@12854
  1550
  finally have subcls_C_old:  "G\<turnstile>C \<prec>\<^sub>C (declclass old)" .
schirmer@12854
  1551
  from accmodi_old 
schirmer@12854
  1552
  have inheritable: "G\<turnstile>Methd sig old inheritable_in pid C"
schirmer@12854
  1553
    by (auto simp add: inheritable_in_def
schirmer@12854
  1554
                 dest: acc_modi_le_Dests)
schirmer@12854
  1555
  show ?thesis
schirmer@12854
  1556
  proof (cases "is_static new")
schirmer@12854
  1557
    case True
schirmer@12854
  1558
    with subcls_C_old new_declared old_declared inheritable
schirmer@12854
  1559
    have "G,sig\<turnstile>(C,new) hides old"
schirmer@12854
  1560
      by (auto intro: hidesI)
schirmer@12854
  1561
    with True wf_cdecl neq_C_Obj new 
schirmer@12854
  1562
    show ?thesis
schirmer@12854
  1563
      by (auto dest: wf_cdecl_hides_SomeD)
schirmer@12854
  1564
  next
schirmer@12854
  1565
    case False
schirmer@12854
  1566
    with subcls_C_old new_declared old_declared inheritable subcls1_C_super
schirmer@12854
  1567
         old_member_of
schirmer@12854
  1568
    have "G,sig\<turnstile>(C,new) overrides\<^sub>S old"
schirmer@12854
  1569
      by (auto intro: stat_overridesR.Direct)
schirmer@12854
  1570
    with False wf_cdecl neq_C_Obj new 
schirmer@12854
  1571
    show ?thesis
schirmer@12854
  1572
      by (auto dest: wf_cdecl_overrides_SomeD)
schirmer@12854
  1573
  qed
schirmer@12854
  1574
qed
schirmer@12854
  1575
schirmer@12854
  1576
lemma inheritable_instance_methd: 
wenzelm@12937
  1577
  assumes subclseq_C_D: "G\<turnstile>C \<preceq>\<^sub>C D" and
schirmer@12854
  1578
              is_cls_D: "is_class G D" and
schirmer@12854
  1579
                    wf: "wf_prog G" and 
schirmer@12854
  1580
                   old: "methd G D sig = Some old" and
schirmer@12854
  1581
           accmodi_old: "Protected \<le> accmodi old" and  
schirmer@12854
  1582
        not_static_old: "\<not> is_static old"
wenzelm@12937
  1583
  shows
schirmer@12854
  1584
  "\<exists>new. methd G C sig = Some new \<and>
schirmer@12854
  1585
         (new = old \<or> G,sig\<turnstile>new overrides\<^sub>S old)"
schirmer@12854
  1586
 (is "(\<exists>new. (?Constraint C new old))")
schirmer@12854
  1587
proof -
schirmer@12854
  1588
  from subclseq_C_D is_cls_D 
schirmer@12854
  1589
  have is_cls_C: "is_class G C" by (rule subcls_is_class2) 
schirmer@12854
  1590
  from wf 
schirmer@12854
  1591
  have ws: "ws_prog G" ..
schirmer@12854
  1592
  from is_cls_C ws subclseq_C_D 
schirmer@12854
  1593
  show "\<exists>new. ?Constraint C new old"
schirmer@12854
  1594
  proof (induct rule: ws_class_induct')
schirmer@12854
  1595
    case (Object co)
schirmer@12854
  1596
    then have eq_D_Obj: "D=Object" by auto
schirmer@12854
  1597
    with old 
schirmer@12854
  1598
    have "?Constraint Object old old"
schirmer@12854
  1599
      by auto
schirmer@12854
  1600
    with eq_D_Obj 
schirmer@12854
  1601
    show "\<exists> new. ?Constraint Object new old" by auto
schirmer@12854
  1602
  next
schirmer@12854
  1603
    case (Subcls C c)
schirmer@12854
  1604
    assume hyp: "G\<turnstile>super c\<preceq>\<^sub>C D \<Longrightarrow> \<exists>new. ?Constraint (super c) new old"
schirmer@12854
  1605
    assume clsC: "class G C = Some c"
schirmer@12854
  1606
    assume neq_C_Obj: "C\<noteq>Object"
schirmer@12854
  1607
    from clsC wf 
schirmer@12854
  1608
    have wf_cdecl: "wf_cdecl G (C,c)" 
schirmer@12854
  1609
      by (rule wf_prog_cdecl)
schirmer@12854
  1610
    from ws clsC neq_C_Obj
schirmer@12854
  1611
    have is_cls_super: "is_class G (super c)"
schirmer@12854
  1612
      by (auto dest: ws_prog_cdeclD)
schirmer@12854
  1613
    from clsC wf neq_C_Obj 
schirmer@12854
  1614
    have superAccessible: "G\<turnstile>(Class (super c)) accessible_in (pid C)" and
schirmer@12854
  1615
	 subcls1_C_super: "G\<turnstile>C \<prec>\<^sub>C\<^sub>1 super c"
schirmer@12854
  1616
      by (auto dest: wf_prog_cdecl wf_cdecl_supD is_acc_classD
schirmer@12854
  1617
              intro: subcls1I)
schirmer@12854
  1618
    show "\<exists>new. ?Constraint C new old"
schirmer@12854
  1619
    proof (cases "G\<turnstile>super c\<preceq>\<^sub>C D")
schirmer@12854
  1620
      case False
schirmer@12854
  1621
      from False Subcls 
schirmer@12854
  1622
      have eq_C_D: "C=D"
schirmer@12854
  1623
	by (auto dest: subclseq_superD)
schirmer@12854
  1624
      with old 
schirmer@12854
  1625
      have "?Constraint C old old"
schirmer@12854
  1626
	by auto
schirmer@12854
  1627
      with eq_C_D 
schirmer@12854
  1628
      show "\<exists> new. ?Constraint C new old" by auto
schirmer@12854
  1629
    next
schirmer@12854
  1630
      case True
schirmer@12854
  1631
      with hyp obtain super_method
schirmer@12854
  1632
	where super: "?Constraint (super c) super_method old" by blast
schirmer@12854
  1633
      from super not_static_old
schirmer@12854
  1634
      have not_static_super: "\<not> is_static super_method"
schirmer@12854
  1635
	by (auto dest!: stat_overrides_commonD)
schirmer@12854
  1636
      from super old wf accmodi_old
schirmer@12854
  1637
      have accmodi_super_method: "Protected \<le> accmodi super_method"
schirmer@12854
  1638
	by (auto dest!: wf_prog_stat_overridesD
schirmer@12854
  1639
                 intro: order_trans)
schirmer@12854
  1640
      from super accmodi_old wf
schirmer@12854
  1641
      have inheritable: "G\<turnstile>Methd sig super_method inheritable_in (pid C)"
schirmer@12854
  1642
	by (auto dest!: wf_prog_stat_overridesD
schirmer@12854
  1643
                        acc_modi_le_Dests
schirmer@12854
  1644
              simp add: inheritable_in_def)	           
schirmer@12854
  1645
      from super wf is_cls_super
schirmer@12854
  1646
      have member: "G\<turnstile>Methd sig super_method member_of (super c)"
schirmer@12854
  1647
	by (auto intro: methd_member_of) 
schirmer@12854
  1648
      from member
schirmer@12854
  1649
      have decl_super_method:
schirmer@12854
  1650
        "G\<turnstile>Methd sig super_method declared_in (declclass super_method)"
schirmer@12854
  1651
	by (auto dest: member_of_declC)
schirmer@12854
  1652
      from super subcls1_C_super ws is_cls_super 
schirmer@12854
  1653
      have subcls_C_super: "G\<turnstile>C \<prec>\<^sub>C (declclass super_method)"
schirmer@12854
  1654
	by (auto intro: rtrancl_into_trancl2 dest: methd_declC) 
schirmer@12854
  1655
      show "\<exists> new. ?Constraint C new old"
schirmer@12854
  1656
      proof (cases "methd G C sig")
schirmer@12854
  1657
	case None
schirmer@12854
  1658
	have "methd G (super c) sig = None"
schirmer@12854
  1659
	proof -
schirmer@12854
  1660
	  from clsC ws None 
schirmer@12854
  1661
	  have no_new: "table_of (methods c) sig = None" 
schirmer@12854
  1662
	    by (auto simp add: methd_rec)
schirmer@12854
  1663
	  with clsC 
schirmer@12854
  1664
	  have undeclared: "G\<turnstile>mid sig undeclared_in C"
schirmer@12854
  1665
	    by (auto simp add: undeclared_in_def cdeclaredmethd_def)
schirmer@12854
  1666
	  with inheritable member superAccessible subcls1_C_super
schirmer@12854
  1667
	  have inherits: "G\<turnstile>C inherits (method sig super_method)"
schirmer@12854
  1668
	    by (auto simp add: inherits_def)
schirmer@12854
  1669
	  with clsC ws no_new super neq_C_Obj
schirmer@12854
  1670
	  have "methd G C sig = Some super_method"
nipkow@14025
  1671
	    by (auto simp add: methd_rec map_add_def intro: filter_tab_SomeI)
schirmer@12854
  1672
          with None show ?thesis
schirmer@12854
  1673
	    by simp
schirmer@12854
  1674
	qed
schirmer@12854
  1675
	with super show ?thesis by auto
schirmer@12854
  1676
      next
schirmer@12854
  1677
	case (Some new)
schirmer@12854
  1678
	from this ws clsC neq_C_Obj
schirmer@12854
  1679
	show ?thesis
schirmer@12854
  1680
	proof (cases rule: methd_rec_Some_cases)
schirmer@12854
  1681
	  case InheritedMethod
schirmer@12854
  1682
	  with super Some show ?thesis 
schirmer@12854
  1683
	    by auto
schirmer@12854
  1684
	next
schirmer@12854
  1685
	  case NewMethod
schirmer@12854
  1686
	  assume new: "table_of (map (\<lambda>(s, m). (s, C, m)) (methods c)) sig 
schirmer@12854
  1687
                       = Some new"
schirmer@12854
  1688
	  from new 
schirmer@12854
  1689
	  have declcls_new: "declclass new = C" 
schirmer@12854
  1690
	    by auto
schirmer@12854
  1691
	  from wf clsC neq_C_Obj super new not_static_super accmodi_super_method
schirmer@12854
  1692
	  have not_static_new: "\<not> is_static new" 
schirmer@12854
  1693
	    by (auto dest: wf_prog_staticD) 
schirmer@12854
  1694
	  from clsC new
schirmer@12854
  1695
	  have decl_new: "G\<turnstile>Methd sig new declared_in C"
schirmer@12854
  1696
	    by (auto simp add: declared_in_def cdeclaredmethd_def)
schirmer@12854
  1697
	  from not_static_new decl_new decl_super_method
schirmer@12854
  1698
	       member subcls1_C_super inheritable declcls_new subcls_C_super 
schirmer@12854
  1699
	  have "G,sig\<turnstile> new overrides\<^sub>S super_method"
schirmer@12854
  1700
	    by (auto intro: stat_overridesR.Direct) 
schirmer@12854
  1701
	  with super Some
schirmer@12854
  1702
	  show ?thesis
schirmer@12854
  1703
	    by (auto intro: stat_overridesR.Indirect)
schirmer@12854
  1704
	qed
schirmer@12854
  1705
      qed
schirmer@12854
  1706
    qed
schirmer@12854
  1707
  qed
schirmer@12854
  1708
qed
schirmer@12854
  1709
schirmer@12854
  1710
lemma inheritable_instance_methd_cases [consumes 6
schirmer@12854
  1711
                                       , case_names Inheritance Overriding]: 
wenzelm@12937
  1712
  assumes subclseq_C_D: "G\<turnstile>C \<preceq>\<^sub>C D" and
schirmer@12854
  1713
              is_cls_D: "is_class G D" and
schirmer@12854
  1714
                    wf: "wf_prog G" and 
schirmer@12854
  1715
                   old: "methd G D sig = Some old" and
schirmer@12854
  1716
           accmodi_old: "Protected \<le> accmodi old" and  
schirmer@12854
  1717
        not_static_old: "\<not> is_static old" and
schirmer@12854
  1718
           inheritance:  "methd G C sig = Some old \<Longrightarrow> P" and
schirmer@12854
  1719
            overriding:  "\<And> new. \<lbrakk>methd G C sig = Some new;
schirmer@12854
  1720
                                   G,sig\<turnstile>new overrides\<^sub>S old\<rbrakk> \<Longrightarrow> P"
schirmer@12854
  1721
        
wenzelm@12937
  1722
  shows P
schirmer@12854
  1723
proof -
schirmer@12854
  1724
from subclseq_C_D is_cls_D wf old accmodi_old not_static_old 
schirmer@12854
  1725
show ?thesis
schirmer@12925
  1726
  by (auto dest: inheritable_instance_methd intro: inheritance overriding)
schirmer@12854
  1727
qed
schirmer@12854
  1728
schirmer@12854
  1729
lemma inheritable_instance_methd_props: 
wenzelm@12937
  1730
  assumes subclseq_C_D: "G\<turnstile>C \<preceq>\<^sub>C D" and
schirmer@12854
  1731
              is_cls_D: "is_class G D" and
schirmer@12854
  1732
                    wf: "wf_prog G" and 
schirmer@12854
  1733
                   old: "methd G D sig = Some old" and
schirmer@12854
  1734
           accmodi_old: "Protected \<le> accmodi old" and  
schirmer@12854
  1735
        not_static_old: "\<not> is_static old"
wenzelm@12937
  1736
  shows
schirmer@12854
  1737
  "\<exists>new. methd G C sig = Some new \<and>
schirmer@12854
  1738
          \<not> is_static new \<and> G\<turnstile>resTy new\<preceq>resTy old \<and> accmodi old \<le>accmodi new"
schirmer@12854
  1739
 (is "(\<exists>new. (?Constraint C new old))")
schirmer@12854
  1740
proof -
schirmer@12854
  1741
  from subclseq_C_D is_cls_D wf old accmodi_old not_static_old 
schirmer@12854
  1742
  show ?thesis
schirmer@12854
  1743
  proof (cases rule: inheritable_instance_methd_cases)
schirmer@12854
  1744
    case Inheritance
schirmer@12854
  1745
    with not_static_old accmodi_old show ?thesis by auto
schirmer@12854
  1746
  next
schirmer@12854
  1747
    case (Overriding new)
schirmer@12854
  1748
    then have "\<not> is_static new" by (auto dest: stat_overrides_commonD)
schirmer@12854
  1749
    with Overriding not_static_old accmodi_old wf 
schirmer@12854
  1750
    show ?thesis 
schirmer@12854
  1751
      by (auto dest!: wf_prog_stat_overridesD
schirmer@12854
  1752
               intro: order_trans)
schirmer@12854
  1753
  qed
schirmer@12854
  1754
qed
schirmer@13688
  1755
 	      
schirmer@12854
  1756
(* local lemma *)
schirmer@12854
  1757
ML {* bind_thm("bexI'",permute_prems 0 1 bexI) *}
schirmer@12854
  1758
ML {* bind_thm("ballE'",permute_prems 1 1 ballE) *}
schirmer@12854
  1759
lemma subint_widen_imethds: 
schirmer@12854
  1760
 "\<lbrakk>G\<turnstile>I\<preceq>I J; wf_prog G; is_iface G J; jm \<in> imethds G J sig\<rbrakk> \<Longrightarrow>   
schirmer@12854
  1761
  \<exists> im \<in> imethds G I sig. is_static im = is_static jm \<and> 
schirmer@12854
  1762
                          accmodi im = accmodi jm \<and>
schirmer@12854
  1763
                          G\<turnstile>resTy im\<preceq>resTy jm"
schirmer@12854
  1764
proof -
schirmer@12854
  1765
  assume irel: "G\<turnstile>I\<preceq>I J" and
schirmer@12854
  1766
           wf: "wf_prog G" and
schirmer@12854
  1767
     is_iface: "is_iface G J"
schirmer@12854
  1768
  from irel show "jm \<in> imethds G J sig \<Longrightarrow> ?thesis" 
schirmer@12854
  1769
               (is "PROP ?P I" is "PROP ?Prem J \<Longrightarrow> ?Concl I")
schirmer@12854
  1770
  proof (induct ?P I rule: converse_rtrancl_induct) 
schirmer@12854
  1771
    case Id
schirmer@12854
  1772
    assume "jm \<in> imethds G J sig"
schirmer@12854
  1773
    then show "?Concl J" by  (blast elim: bexI')
schirmer@12854
  1774
  next
schirmer@12854
  1775
    case Step
schirmer@12854
  1776
    fix I SI
schirmer@12854
  1777
    assume subint1_I_SI: "G\<turnstile>I \<prec>I1 SI" and 
schirmer@12854
  1778
            subint_SI_J: "G\<turnstile>SI \<preceq>I J" and
schirmer@12854
  1779
                    hyp: "PROP ?P SI" and
schirmer@12854
  1780
                     jm: "jm \<in> imethds G J sig"
schirmer@12854
  1781
    from subint1_I_SI 
schirmer@12854
  1782
    obtain i where
schirmer@12854
  1783
      ifI: "iface G I = Some i" and
schirmer@12854
  1784
       SI: "SI \<in> set (isuperIfs i)"
schirmer@12854
  1785
      by (blast dest: subint1D)
schirmer@12854
  1786
schirmer@12854
  1787
    let ?newMethods 
schirmer@12854
  1788
          = "(o2s \<circ> table_of (map (\<lambda>(sig, mh). (sig, I, mh)) (imethods i)))"
schirmer@12854
  1789
    show "?Concl I"
schirmer@12854
  1790
    proof (cases "?newMethods sig = {}")
schirmer@12854
  1791
      case True
schirmer@12854
  1792
      with ifI SI hyp wf jm 
schirmer@12854
  1793
      show "?thesis" 
schirmer@12854
  1794
	by (auto simp add: imethds_rec) 
schirmer@12854
  1795
    next
schirmer@12854
  1796
      case False
schirmer@12854
  1797
      from ifI wf False
schirmer@12854
  1798
      have imethds: "imethds G I sig = ?newMethods sig"
schirmer@12854
  1799
	by (simp add: imethds_rec)
schirmer@12854
  1800
      from False
schirmer@12854
  1801
      obtain im where
schirmer@12854
  1802
        imdef: "im \<in> ?newMethods sig" 
schirmer@12854
  1803
	by (blast)
schirmer@12854
  1804
      with imethds 
schirmer@12854
  1805
      have im: "im \<in> imethds G I sig"
schirmer@12854
  1806
	by (blast)
schirmer@12854
  1807
      with im wf ifI 
schirmer@12854
  1808
      obtain
schirmer@12854
  1809
	 imStatic: "\<not> is_static im" and
schirmer@12854
  1810
         imPublic: "accmodi im = Public"
schirmer@12854
  1811
	by (auto dest!: imethds_wf_mhead)	
schirmer@12854
  1812
      from ifI wf 
schirmer@12854
  1813
      have wf_I: "wf_idecl G (I,i)" 
schirmer@12854
  1814
	by (rule wf_prog_idecl)
schirmer@12854
  1815
      with SI wf  
schirmer@12854
  1816
      obtain si where
schirmer@12854
  1817
	 ifSI: "iface G SI = Some si" and
schirmer@12854
  1818
	wf_SI: "wf_idecl G (SI,si)" 
schirmer@12854
  1819
	by (auto dest!: wf_idecl_supD is_acc_ifaceD
schirmer@12854
  1820
                  dest: wf_prog_idecl)
schirmer@12854
  1821
      from jm hyp 
schirmer@12854
  1822
      obtain sim::"qtname \<times> mhead"  where
schirmer@12854
  1823
                      sim: "sim \<in> imethds G SI sig" and
schirmer@12854
  1824
         eq_static_sim_jm: "is_static sim = is_static jm" and 
schirmer@12854
  1825
         eq_access_sim_jm: "accmodi sim = accmodi jm" and 
schirmer@12854
  1826
        resTy_widen_sim_jm: "G\<turnstile>resTy sim\<preceq>resTy jm"
schirmer@12854
  1827
	by blast
schirmer@12854
  1828
      with wf_I SI imdef sim 
schirmer@12854
  1829
      have "G\<turnstile>resTy im\<preceq>resTy sim"   
schirmer@12854
  1830
	by (auto dest!: wf_idecl_hidings hidings_entailsD)
schirmer@12854
  1831
      with wf resTy_widen_sim_jm 
schirmer@12854
  1832
      have resTy_widen_im_jm: "G\<turnstile>resTy im\<preceq>resTy jm"
schirmer@12854
  1833
	by (blast intro: widen_trans)
schirmer@12854
  1834
      from sim wf ifSI  
schirmer@12854
  1835
      obtain
schirmer@12854
  1836
	simStatic: "\<not> is_static sim" and
schirmer@12854
  1837
        simPublic: "accmodi sim = Public"
schirmer@12854
  1838
	by (auto dest!: imethds_wf_mhead)
schirmer@12854
  1839
      from im 
schirmer@12854
  1840
           imStatic simStatic eq_static_sim_jm
schirmer@12854
  1841
           imPublic simPublic eq_access_sim_jm
schirmer@12854
  1842
           resTy_widen_im_jm
schirmer@12854
  1843
      show ?thesis 
schirmer@12854
  1844
	by auto 
schirmer@12854
  1845
    qed
schirmer@12854
  1846
  qed
schirmer@12854
  1847
qed
schirmer@12854
  1848
     
schirmer@12854
  1849
(* Tactical version *)
schirmer@12854
  1850
(* 
schirmer@12854
  1851
lemma subint_widen_imethds: "\<lbrakk>G\<turnstile>I\<preceq>I J; wf_prog G; is_iface G J\<rbrakk> \<Longrightarrow>  
schirmer@12854
  1852
  \<forall> jm \<in> imethds G J sig.  
schirmer@12854
  1853
  \<exists> im \<in> imethds G I sig. static (mthd im)=static (mthd jm) \<and> 
schirmer@12854
  1854
                          access (mthd im)= access (mthd jm) \<and>
schirmer@12854
  1855
                          G\<turnstile>resTy (mthd im)\<preceq>resTy (mthd jm)"
schirmer@12854
  1856
apply (erule converse_rtrancl_induct)
schirmer@12854
  1857
apply  (clarsimp elim!: bexI')
schirmer@12854
  1858
apply (frule subint1D)
schirmer@12854
  1859
apply clarify
schirmer@12854
  1860
apply (erule ballE')
schirmer@12854
  1861
apply  fast
schirmer@12854
  1862
apply (erule_tac V = "?x \<in> imethds G J sig" in thin_rl)
schirmer@12854
  1863
apply clarsimp
schirmer@12854
  1864
apply (subst imethds_rec, assumption, erule wf_ws_prog)
schirmer@12854
  1865
apply (unfold overrides_t_def)
schirmer@12854
  1866
apply (drule (1) wf_prog_idecl)
schirmer@12854
  1867
apply (frule (3) imethds_wf_mhead [OF _ _ wf_idecl_supD [THEN conjunct1 
schirmer@12854
  1868
                                       [THEN is_acc_ifaceD [THEN conjunct1]]]])
schirmer@12854
  1869
apply (case_tac "(o2s \<circ> table_of (map (\<lambda>(s, mh). (s, y, mh)) (imethods i)))
schirmer@12854
  1870
                  sig ={}")
schirmer@12854
  1871
apply   force
schirmer@12854
  1872
schirmer@12854
  1873
apply   (simp only:)
schirmer@12854
  1874
apply   (simp)
schirmer@12854
  1875
apply   clarify
schirmer@12854
  1876
apply   (frule wf_idecl_hidings [THEN hidings_entailsD])
schirmer@12854
  1877
apply     blast
schirmer@12854
  1878
apply     blast
schirmer@12854
  1879
apply   (rule bexI')
schirmer@12854
  1880
apply     simp
schirmer@12854
  1881
apply     (drule table_of_map_SomeI [of _ "sig"])
schirmer@12854
  1882
apply     simp
schirmer@12854
  1883
schirmer@12854
  1884
apply     (frule wf_idecl_mhead [of _ _ _ "sig"])
schirmer@12854
  1885
apply       (rule table_of_Some_in_set)
schirmer@12854
  1886
apply       assumption
schirmer@12854
  1887
apply     auto
schirmer@12854
  1888
done
schirmer@12854
  1889
*)
schirmer@12854
  1890
    
schirmer@12854
  1891
schirmer@12854
  1892
(* local lemma *)
schirmer@12854
  1893
lemma implmt1_methd: 
schirmer@12854
  1894
 "\<And>sig. \<lbrakk>G\<turnstile>C\<leadsto>1I; wf_prog G; im \<in> imethds G I sig\<rbrakk> \<Longrightarrow>  
schirmer@12854
  1895
  \<exists>cm \<in>methd G C sig: \<not> is_static cm \<and> \<not> is_static im \<and> 
schirmer@12854
  1896
                       G\<turnstile>resTy cm\<preceq>resTy im \<and>
schirmer@12854
  1897
                       accmodi im = Public \<and> accmodi cm = Public"
schirmer@12854
  1898
apply (drule implmt1D)
schirmer@12854
  1899
apply clarify
schirmer@12854
  1900
apply (drule (2) wf_prog_cdecl [THEN wf_cdecl_impD])
schirmer@12854
  1901
apply (frule (1) imethds_wf_mhead)
schirmer@12854
  1902
apply  (simp add: is_acc_iface_def)
schirmer@12854
  1903
apply (force)
schirmer@12854
  1904
done
schirmer@12854
  1905
schirmer@12854
  1906
schirmer@12854
  1907
(* local lemma *)
schirmer@12854
  1908
lemma implmt_methd [rule_format (no_asm)]: 
schirmer@12854
  1909
"\<lbrakk>wf_prog G; G\<turnstile>C\<leadsto>I\<rbrakk> \<Longrightarrow> is_iface G I \<longrightarrow>  
schirmer@12854
  1910
 (\<forall> im    \<in>imethds G I   sig.  
schirmer@12854
  1911
  \<exists> cm\<in>methd G C sig: \<not>is_static cm \<and> \<not> is_static im \<and> 
schirmer@12854
  1912
                      G\<turnstile>resTy cm\<preceq>resTy im \<and>
schirmer@12854
  1913
                      accmodi im = Public \<and> accmodi cm = Public)"
schirmer@12854
  1914
apply (frule implmt_is_class)
schirmer@12854
  1915
apply (erule implmt.induct)
schirmer@12854
  1916
apply   safe
schirmer@12854
  1917
apply   (drule (2) implmt1_methd)
schirmer@12854
  1918
apply   fast
schirmer@12854
  1919
apply  (drule (1) subint_widen_imethds)
schirmer@12854
  1920
apply   simp
schirmer@12854
  1921
apply   assumption
schirmer@12854
  1922
apply  clarify
schirmer@12854
  1923
apply  (drule (2) implmt1_methd)
schirmer@12854
  1924
apply  (force)
schirmer@12854
  1925
apply (frule subcls1D)
schirmer@12854
  1926
apply (drule (1) bspec)
schirmer@12854
  1927
apply clarify
schirmer@12854
  1928
apply (drule (3) r_into_rtrancl [THEN inheritable_instance_methd_props, 
schirmer@12854
  1929
                                 OF _ implmt_is_class])
schirmer@12854
  1930
apply auto 
schirmer@12854
  1931
done
schirmer@12854
  1932
schirmer@12854
  1933
lemma mheadsD [rule_format (no_asm)]: 
schirmer@12854
  1934
"emh \<in> mheads G S t sig \<longrightarrow> wf_prog G \<longrightarrow>
schirmer@12854
  1935
 (\<exists>C D m. t = ClassT C \<and> declrefT emh = ClassT D \<and> 
schirmer@12854
  1936
          accmethd G S C sig = Some m \<and>
schirmer@12854
  1937
          (declclass m = D) \<and> mhead (mthd m) = (mhd emh)) \<or>
schirmer@12854
  1938
 (\<exists>I. t = IfaceT I \<and> ((\<exists>im. im  \<in> accimethds G (pid S) I sig \<and> 
schirmer@12854
  1939
          mthd im = mhd emh) \<or> 
schirmer@12854
  1940
  (\<exists>m. G\<turnstile>Iface I accessible_in (pid S) \<and> accmethd G S Object sig = Some m \<and> 
schirmer@12854
  1941
       accmodi m \<noteq> Private \<and> 
schirmer@12854
  1942
       declrefT emh = ClassT Object \<and> mhead (mthd m) = mhd emh))) \<or>
schirmer@12854
  1943
 (\<exists>T m. t = ArrayT T \<and> G\<turnstile>Array T accessible_in (pid S) \<and>
schirmer@12854
  1944
        accmethd G S Object sig = Some m \<and> accmodi m \<noteq> Private \<and> 
schirmer@12854
  1945
        declrefT emh = ClassT Object \<and> mhead (mthd m) = mhd emh)"
ballarin@14174
  1946
apply (rule_tac ref_ty1="t" in ref_ty_ty.induct [THEN conjunct1])
schirmer@12854
  1947
apply auto
schirmer@12854
  1948
apply (auto simp add: cmheads_def accObjectmheads_def Objectmheads_def)
schirmer@12854
  1949
apply (auto  dest!: accmethd_SomeD)
schirmer@12854
  1950
done
schirmer@12854
  1951
schirmer@12854
  1952
lemma mheads_cases [consumes 2, case_names Class_methd 
schirmer@12854
  1953
                    Iface_methd Iface_Object_methd Array_Object_methd]: 
schirmer@12854
  1954
"\<lbrakk>emh \<in> mheads G S t sig; wf_prog G;
schirmer@12854
  1955
 \<And> C D m. \<lbrakk>t = ClassT C;declrefT emh = ClassT D; accmethd G S C sig = Some m;
schirmer@12854
  1956
           (declclass m = D); mhead (mthd m) = (mhd emh)\<rbrakk> \<Longrightarrow> P emh; 
schirmer@12854
  1957
 \<And> I im. \<lbrakk>t = IfaceT I; im  \<in> accimethds G (pid S) I sig; mthd im = mhd emh\<rbrakk>
schirmer@12854
  1958
          \<Longrightarrow> P emh;
schirmer@12854
  1959
 \<And> I m. \<lbrakk>t = IfaceT I; G\<turnstile>Iface I accessible_in (pid S);
schirmer@12854
  1960
          accmethd G S Object sig = Some m; accmodi m \<noteq> Private;
schirmer@12854
  1961
         declrefT emh = ClassT Object; mhead (mthd m) = mhd emh\<rbrakk> \<Longrightarrow> P emh;
schirmer@12854
  1962
 \<And> T m. \<lbrakk>t = ArrayT T;G\<turnstile>Array T accessible_in (pid S);
schirmer@12854
  1963
          accmethd G S Object sig = Some m; accmodi m \<noteq> Private; 
schirmer@12854
  1964
          declrefT emh = ClassT Object; mhead (mthd m) = mhd emh\<rbrakk> \<Longrightarrow>  P emh 
schirmer@12854
  1965
\<rbrakk> \<Longrightarrow> P emh"
schirmer@12854
  1966
by (blast dest!: mheadsD)
schirmer@12854
  1967
schirmer@12854
  1968
lemma declclassD[rule_format]:
schirmer@12854
  1969
 "\<lbrakk>wf_prog G;class G C = Some c; methd G C sig = Some m; 
schirmer@12854
  1970
   class G (declclass m) = Some d\<rbrakk>
schirmer@12854
  1971
  \<Longrightarrow> table_of (methods d) sig  = Some (mthd m)"
schirmer@12854
  1972
proof -
schirmer@12854
  1973
  assume    wf: "wf_prog G"
schirmer@12854
  1974
  then have ws: "ws_prog G" ..
schirmer@12854
  1975
  assume  clsC: "class G C = Some c"
schirmer@12854
  1976
  from clsC ws 
schirmer@12854
  1977
  show "\<And> m d. \<lbrakk>methd G C sig = Some m; class G (declclass m) = Some d\<rbrakk>
schirmer@12854
  1978
        \<Longrightarrow> table_of (methods d) sig  = Some (mthd m)" 
schirmer@12854
  1979
         (is "PROP ?P C") 
schirmer@12854
  1980
  proof (induct ?P C rule: ws_class_induct)
schirmer@12854
  1981
    case Object
schirmer@12854
  1982
    fix m d
schirmer@12854
  1983
    assume "methd G Object sig = Some m" 
schirmer@12854
  1984
           "class G (declclass m) = Some d"
schirmer@12854
  1985
    with wf show "?thesis m d" by auto
schirmer@12854
  1986
  next
schirmer@12854
  1987
    case Subcls
schirmer@12854
  1988
    fix C c m d
schirmer@12854
  1989
    assume hyp: "PROP ?P (super c)"
schirmer@12854
  1990
    and      m: "methd G C sig = Some m"
schirmer@12854
  1991
    and  declC: "class G (declclass m) = Some d"
schirmer@12854
  1992
    and   clsC: "class G C = Some c"
schirmer@12854
  1993
    and   nObj: "C \<noteq> Object"
schirmer@12854
  1994
    let ?newMethods = "table_of (map (\<lambda>(s, m). (s, C, m)) (methods c)) sig"
schirmer@12854
  1995
    show "?thesis m d" 
schirmer@12854
  1996
    proof (cases "?newMethods")
schirmer@12854
  1997
      case None
schirmer@12854
  1998
      from None clsC nObj ws m declC hyp  
schirmer@12854
  1999
      show "?thesis" by (auto simp add: methd_rec)
schirmer@12854
  2000
    next
schirmer@12854
  2001
      case Some
schirmer@12854
  2002
      from Some clsC nObj ws m declC hyp  
schirmer@12854
  2003
      show "?thesis" 
schirmer@12854
  2004
	by (auto simp add: methd_rec
schirmer@12854
  2005
                     dest: wf_prog_cdecl wf_cdecl_supD is_acc_class_is_class)
schirmer@12854
  2006
    qed
schirmer@12854
  2007
  qed
schirmer@12854
  2008
qed
schirmer@12854
  2009
schirmer@12854
  2010
(* Tactical version *)
schirmer@12854
  2011
(*
schirmer@12854
  2012
lemma declclassD[rule_format]:
schirmer@12854
  2013
 "wf_prog G \<longrightarrow>  
schirmer@12854
  2014
 (\<forall> c d m. class G C = Some c \<longrightarrow> methd G C sig = Some m \<longrightarrow> 
schirmer@12854
  2015
  class G (declclass m) = Some d
schirmer@12854
  2016
 \<longrightarrow> table_of (methods d) sig  = Some (mthd m))"
schirmer@12854
  2017
apply (rule class_rec.induct)
schirmer@12854
  2018
apply (rule impI)
schirmer@12854
  2019
apply (rule allI)+
schirmer@12854
  2020
apply (rule impI)
schirmer@12854
  2021
apply (case_tac "C=Object")
schirmer@12854
  2022
apply   (force simp add: methd_rec)
schirmer@12854
  2023
schirmer@12854
  2024
apply   (subst methd_rec)
schirmer@12854
  2025
apply     (blast dest: wf_ws_prog)+
schirmer@12854
  2026
apply   (case_tac "table_of (map (\<lambda>(s, m). (s, C, m)) (methods c)) sig")
schirmer@12854
  2027
apply     (auto dest: wf_prog_cdecl wf_cdecl_supD is_acc_class_is_class)
schirmer@12854
  2028
done
schirmer@12854
  2029
*)
schirmer@12854
  2030
schirmer@12854
  2031
lemma dynmethd_Object:
wenzelm@12937
  2032
  assumes statM: "methd G Object sig = Some statM" and
schirmer@12854
  2033
        private: "accmodi statM = Private" and 
schirmer@12854
  2034
       is_cls_C: "is_class G C" and
schirmer@12854
  2035
             wf: "wf_prog G"
wenzelm@12937
  2036
  shows "dynmethd G Object C sig = Some statM"
schirmer@12854
  2037
proof -
schirmer@12854
  2038
  from is_cls_C wf 
schirmer@12854
  2039
  have subclseq: "G\<turnstile>C \<preceq>\<^sub>C Object" 
schirmer@12854
  2040
    by (auto intro: subcls_ObjectI)
schirmer@12854
  2041
  from wf have ws: "ws_prog G" 
schirmer@12854
  2042
    by simp
schirmer@12854
  2043
  from wf 
schirmer@12854
  2044
  have is_cls_Obj: "is_class G Object" 
schirmer@12854
  2045
    by simp
schirmer@12854
  2046
  from statM subclseq is_cls_Obj ws private
schirmer@12854
  2047
  show ?thesis
schirmer@12854
  2048
  proof (cases rule: dynmethd_cases)
schirmer@12854
  2049
    case Static then show ?thesis .
schirmer@12854
  2050
  next
schirmer@12854
  2051
    case Overrides 
schirmer@12854
  2052
    with private show ?thesis 
schirmer@12854
  2053
      by (auto dest: no_Private_override)
schirmer@12854
  2054
  qed
schirmer@12854
  2055
qed
schirmer@12854
  2056
schirmer@12854
  2057
lemma wf_imethds_hiding_objmethdsD: 
wenzelm@12937
  2058
  assumes     old: "methd G Object sig = Some old" and
wenzelm@12937
  2059
          is_if_I: "is_iface G I" and
wenzelm@12937
  2060
               wf: "wf_prog G" and    
wenzelm@12937
  2061
      not_private: "accmodi old \<noteq> Private" and
wenzelm@12937
  2062
              new: "new \<in> imethds G I sig" 
wenzelm@12937
  2063
  shows "G\<turnstile>resTy new\<preceq>resTy old \<and> is_static new = is_static old" (is "?P new")
schirmer@12854
  2064
proof -
schirmer@12854
  2065
  from wf have ws: "ws_prog G" by simp
schirmer@12854
  2066
  {
schirmer@12854
  2067
    fix I i new
schirmer@12854
  2068
    assume ifI: "iface G I = Some i"
schirmer@12854
  2069
    assume new: "table_of (imethods i) sig = Some new" 
schirmer@12854
  2070
    from ifI new not_private wf old  
schirmer@12854
  2071
    have "?P (I,new)"
schirmer@12854
  2072
      by (auto dest!: wf_prog_idecl wf_idecl_hiding cond_hiding_entailsD
schirmer@12854
  2073
            simp del: methd_Object)
schirmer@12854
  2074
  } note hyp_newmethod = this  
schirmer@12854
  2075
  from is_if_I ws new 
schirmer@12854
  2076
  show ?thesis
schirmer@12854
  2077
  proof (induct rule: ws_interface_induct)
schirmer@12854
  2078
    case (Step I i)
schirmer@12854
  2079
    assume ifI: "iface G I = Some i" 
schirmer@12854
  2080
    assume new: "new \<in> imethds G I sig" 
schirmer@12854
  2081
    from Step
schirmer@12854
  2082
    have hyp: "\<forall> J \<in> set (isuperIfs i). (new \<in> imethds G J sig \<longrightarrow> ?P new)"
schirmer@12854
  2083
      by auto 
schirmer@12854
  2084
    from new ifI ws
schirmer@12854
  2085
    show "?P new"
schirmer@12854
  2086
    proof (cases rule: imethds_cases)
schirmer@12854
  2087
      case NewMethod
schirmer@12854
  2088
      with ifI hyp_newmethod
schirmer@12854
  2089
      show ?thesis
schirmer@12854
  2090
	by auto
schirmer@12854
  2091
    next
schirmer@12854
  2092
      case (InheritedMethod J)
schirmer@12854
  2093
      assume "J \<in> set (isuperIfs i)" 
schirmer@12854
  2094
             "new \<in> imethds G J sig"
schirmer@12854
  2095
      with hyp 
schirmer@12854
  2096
      show "?thesis"
schirmer@12854
  2097
	by auto
schirmer@12854
  2098
    qed
schirmer@12854
  2099
  qed
schirmer@12854
  2100
qed
schirmer@12854
  2101
schirmer@12854
  2102
text {*
schirmer@12854
  2103
Which dynamic classes are valid to look up a member of a distinct static type?
schirmer@12854
  2104
We have to distinct class members (named static members in Java) 
schirmer@12854
  2105
from instance members. Class members are global to all Objects of a class,
schirmer@12854
  2106
instance members are local to a single Object instance. If a member is
schirmer@12854
  2107
equipped with the static modifier it is a class member, else it is an 
schirmer@12854
  2108
instance member.
schirmer@12854
  2109
The following table gives an overview of the current framework. We assume
schirmer@12854
  2110
to have a reference with static type statT and a dynamic class dynC. Between
schirmer@12854
  2111
both of these types the widening relation holds 
schirmer@12854
  2112
@{term "G\<turnstile>Class dynC\<preceq> statT"}. Unfortunately this ordinary widening relation 
schirmer@12854
  2113
isn't enough to describe the valid lookup classes, since we must cope the
schirmer@12854
  2114
special cases of arrays and interfaces,too. If we statically expect an array or
schirmer@12854
  2115
inteface we may lookup a field or a method in Object which isn't covered in 
schirmer@12854
  2116
the widening relation.
schirmer@12925
  2117
schirmer@12854
  2118
statT      field         instance method       static (class) method
schirmer@12854
  2119
------------------------------------------------------------------------
schirmer@12854
  2120
 NullT      /                  /                   /
schirmer@12854
  2121
 Iface      /                dynC                Object
schirmer@12854
  2122
 Class    dynC               dynC                 dynC
schirmer@12854
  2123
 Array      /                Object              Object
schirmer@12925
  2124
schirmer@12854
  2125
In most cases we con lookup the member in the dynamic class. But as an
schirmer@12854
  2126
interface can't declare new static methods, nor an array can define new
schirmer@12854
  2127
methods at all, we have to lookup methods in the base class Object.
schirmer@12854
  2128
schirmer@12854
  2129
The limitation to classes in the field column is artificial  and comes out
schirmer@12854
  2130
of the typing rule for the field access (see rule @{text "FVar"} in the 
schirmer@12854
  2131
welltyping relation @{term "wt"} in theory WellType). 
schirmer@12854
  2132
I stems out of the fact, that Object
schirmer@12854
  2133
indeed has no non private fields. So interfaces and arrays can actually
schirmer@12854
  2134
have no fields at all and a field access would be senseless. (In Java
schirmer@12854
  2135
interfaces are allowed to declare new fields but in current Bali not!).
schirmer@12854
  2136
So there is no principal reason why we should not allow Objects to declare
schirmer@12854
  2137
non private fields. Then we would get the following column:
schirmer@12925
  2138
       
schirmer@12854
  2139
 statT    field
schirmer@12854
  2140
----------------- 
schirmer@12854
  2141
 NullT      /  
schirmer@12854
  2142
 Iface    Object 
schirmer@12854
  2143
 Class    dynC 
schirmer@12854
  2144
 Array    Object
schirmer@12854
  2145
*}
schirmer@12854
  2146
consts valid_lookup_cls:: "prog \<Rightarrow> ref_ty \<Rightarrow> qtname \<Rightarrow> bool \<Rightarrow> bool"
schirmer@12854
  2147
                        ("_,_ \<turnstile> _ valid'_lookup'_cls'_for _" [61,61,61,61] 60)
schirmer@12854
  2148
primrec
schirmer@12854
  2149
"G,NullT    \<turnstile> dynC valid_lookup_cls_for static_membr = False"
schirmer@12854
  2150
"G,IfaceT I \<turnstile> dynC valid_lookup_cls_for static_membr 
schirmer@12854
  2151
              = (if static_membr 
schirmer@12854
  2152
                    then dynC=Object 
schirmer@12854
  2153
                    else G\<turnstile>Class dynC\<preceq> Iface I)"
schirmer@12854
  2154
"G,ClassT C \<turnstile> dynC valid_lookup_cls_for static_membr = G\<turnstile>Class dynC\<preceq> Class C"
schirmer@12854
  2155
"G,ArrayT T \<turnstile> dynC valid_lookup_cls_for static_membr = (dynC=Object)"
schirmer@12854
  2156
schirmer@12854
  2157
lemma valid_lookup_cls_is_class:
wenzelm@12937
  2158
  assumes dynC: "G,statT \<turnstile> dynC valid_lookup_cls_for static_membr" and
schirmer@12854
  2159
      ty_statT: "isrtype G statT" and
schirmer@12854
  2160
            wf: "wf_prog G"
wenzelm@12937
  2161
  shows "is_class G dynC"
schirmer@12854
  2162
proof (cases statT)
schirmer@12854
  2163
  case NullT
schirmer@12854
  2164
  with dynC ty_statT show ?thesis
schirmer@12854
  2165
    by (auto dest: widen_NT2)
schirmer@12854
  2166
next
schirmer@12854
  2167
  case (IfaceT I)
schirmer@12854
  2168
  with dynC wf show ?thesis
schirmer@12854
  2169
    by (auto dest: implmt_is_class)
schirmer@12854
  2170
next
schirmer@12854
  2171
  case (ClassT C)
schirmer@12854
  2172
  with dynC ty_statT show ?thesis
schirmer@12854
  2173
    by (auto dest: subcls_is_class2)
schirmer@12854
  2174
next
schirmer@12854
  2175
  case (ArrayT T)
schirmer@12854
  2176
  with dynC wf show ?thesis
schirmer@12854
  2177
    by (auto)
schirmer@12854
  2178
qed
schirmer@12854
  2179
schirmer@12854
  2180
declare split_paired_All [simp del] split_paired_Ex [simp del]
schirmer@12854
  2181
ML_setup {*
schirmer@12854
  2182
simpset_ref() := simpset() delloop "split_all_tac";
schirmer@12854
  2183
claset_ref () := claset () delSWrapper "split_all_tac"
schirmer@12854
  2184
*}
schirmer@12854
  2185
lemma dynamic_mheadsD:   
schirmer@12854
  2186
"\<lbrakk>emh \<in> mheads G S statT sig;    
schirmer@12854
  2187
  G,statT \<turnstile> dynC valid_lookup_cls_for (is_static emh);
schirmer@12854
  2188
  isrtype G statT; wf_prog G
schirmer@12854
  2189
 \<rbrakk> \<Longrightarrow> \<exists>m \<in> dynlookup G statT dynC sig: 
schirmer@12854
  2190
          is_static m=is_static emh \<and> G\<turnstile>resTy m\<preceq>resTy emh"
schirmer@12854
  2191
proof - 
schirmer@12854
  2192
  assume      emh: "emh \<in> mheads G S statT sig"
schirmer@12854
  2193
  and          wf: "wf_prog G"
schirmer@12854
  2194
  and   dynC_Prop: "G,statT \<turnstile> dynC valid_lookup_cls_for (is_static emh)"
schirmer@12854
  2195
  and      istype: "isrtype G statT"
schirmer@12854
  2196
  from dynC_Prop istype wf 
schirmer@12854
  2197
  obtain y where
schirmer@12854
  2198
    dynC: "class G dynC = Some y" 
schirmer@12854
  2199
    by (auto dest: valid_lookup_cls_is_class)
schirmer@12854
  2200
  from emh wf show ?thesis
schirmer@12854
  2201
  proof (cases rule: mheads_cases)
schirmer@12854
  2202
    case Class_methd
schirmer@12854
  2203
    fix statC statDeclC sm
schirmer@12854
  2204
    assume     statC: "statT = ClassT statC"
schirmer@12854
  2205
    assume            "accmethd G S statC sig = Some sm"
schirmer@12854
  2206
    then have     sm: "methd G statC sig = Some sm" 
schirmer@12854
  2207
      by (blast dest: accmethd_SomeD)  
schirmer@12854
  2208
    assume eq_mheads: "mhead (mthd sm) = mhd emh"
schirmer@12854
  2209
    from statC 
schirmer@12854
  2210
    have dynlookup: "dynlookup G statT dynC sig = dynmethd G statC dynC sig"
schirmer@12854
  2211
      by (simp add: dynlookup_def)
schirmer@12854
  2212
    from wf statC istype dynC_Prop sm 
schirmer@12854
  2213
    obtain dm where
schirmer@12854
  2214
      "dynmethd G statC dynC sig = Some dm"
schirmer@12854
  2215
      "is_static dm = is_static sm" 
schirmer@12854
  2216
      "G\<turnstile>resTy dm\<preceq>resTy sm"  
schirmer@12925
  2217
      by (force dest!: ws_dynmethd accmethd_SomeD)
schirmer@12854
  2218
    with dynlookup eq_mheads 
schirmer@12854
  2219
    show ?thesis 
schirmer@12854
  2220
      by (cases emh type: *) (auto)
schirmer@12854
  2221
  next
schirmer@12854
  2222
    case Iface_methd
schirmer@12854
  2223
    fix I im
schirmer@12854
  2224
    assume    statI: "statT = IfaceT I" and
schirmer@12854
  2225
          eq_mheads: "mthd im = mhd emh" and
schirmer@12854
  2226
                     "im \<in> accimethds G (pid S) I sig" 
schirmer@12854
  2227
    then have im: "im \<in> imethds G I sig" 
schirmer@12854
  2228
      by (blast dest: accimethdsD)
schirmer@12854
  2229
    with istype statI eq_mheads wf 
schirmer@12854
  2230
    have not_static_emh: "\<not> is_static emh"
schirmer@12854
  2231
      by (cases emh) (auto dest: wf_prog_idecl imethds_wf_mhead)
schirmer@12854
  2232
    from statI im
schirmer@12854
  2233
    have dynlookup: "dynlookup G statT dynC sig = methd G dynC sig"
schirmer@12854
  2234
      by (auto simp add: dynlookup_def dynimethd_def) 
schirmer@12854
  2235
    from wf dynC_Prop statI istype im not_static_emh 
schirmer@12854
  2236
    obtain dm where
schirmer@12854
  2237
      "methd G dynC sig = Some dm"
schirmer@12854
  2238
      "is_static dm = is_static im" 
schirmer@12854
  2239
      "G\<turnstile>resTy (mthd dm)\<preceq>resTy (mthd im)" 
schirmer@12925
  2240
      by (force dest: implmt_methd)
schirmer@12854
  2241
    with dynlookup eq_mheads
schirmer@12854
  2242
    show ?thesis 
schirmer@12854
  2243
      by (cases emh type: *) (auto)
schirmer@12854
  2244
  next
schirmer@12854
  2245
    case Iface_Object_methd
schirmer@12854
  2246
    fix I sm
schirmer@12854
  2247
    assume   statI: "statT = IfaceT I" and
schirmer@12854
  2248
                sm: "accmethd G S Object sig = Some sm" and 
schirmer@12854
  2249
         eq_mheads: "mhead (mthd sm) = mhd emh" and
schirmer@12854
  2250
             nPriv: "accmodi sm \<noteq> Private"
schirmer@12854
  2251
     show ?thesis 
schirmer@12854
  2252
     proof (cases "imethds G I sig = {}")
schirmer@12854
  2253
       case True
schirmer@12854
  2254
       with statI 
schirmer@12854
  2255
       have dynlookup: "dynlookup G statT dynC sig = dynmethd G Object dynC sig"
schirmer@12854
  2256
	 by (simp add: dynlookup_def dynimethd_def)
schirmer@12854
  2257
       from wf dynC 
schirmer@12854
  2258
       have subclsObj: "G\<turnstile>dynC \<preceq>\<^sub>C Object"
schirmer@12854
  2259
	 by (auto intro: subcls_ObjectI)
schirmer@12854
  2260
       from wf dynC dynC_Prop istype sm subclsObj 
schirmer@12854
  2261
       obtain dm where
schirmer@12854
  2262
	 "dynmethd G Object dynC sig = Some dm"
schirmer@12854
  2263
	 "is_static dm = is_static sm" 
schirmer@12854
  2264
	 "G\<turnstile>resTy (mthd dm)\<preceq>resTy (mthd sm)"  
schirmer@12854
  2265
	 by (auto dest!: ws_dynmethd accmethd_SomeD 
schirmer@12925
  2266
                  intro: class_Object [OF wf] intro: that)
schirmer@12854
  2267
       with dynlookup eq_mheads
schirmer@12854
  2268
       show ?thesis 
schirmer@12854
  2269
	 by (cases emh type: *) (auto)
schirmer@12854
  2270
     next
schirmer@12854
  2271
       case False
schirmer@12854
  2272
       with statI
schirmer@12854
  2273
       have dynlookup: "dynlookup G statT dynC sig = methd G dynC sig"
schirmer@12854
  2274
	 by (simp add: dynlookup_def dynimethd_def)
schirmer@12854
  2275
       from istype statI
schirmer@12854
  2276
       have "is_iface G I"
schirmer@12854
  2277
	 by auto
schirmer@12854
  2278
       with wf sm nPriv False 
schirmer@12854
  2279
       obtain im where
schirmer@12854
  2280
	      im: "im \<in> imethds G I sig" and
schirmer@12854
  2281
	 eq_stat: "is_static im = is_static sm" and
schirmer@12854
  2282
         resProp: "G\<turnstile>resTy (mthd im)\<preceq>resTy (mthd sm)"
schirmer@12854
  2283
	 by (auto dest: wf_imethds_hiding_objmethdsD accmethd_SomeD)
schirmer@12854
  2284
       from im wf statI istype eq_stat eq_mheads
schirmer@12854
  2285
       have not_static_sm: "\<not> is_static emh"
schirmer@12854
  2286
	 by (cases emh) (auto dest: wf_prog_idecl imethds_wf_mhead)
schirmer@12854
  2287
       from im wf dynC_Prop dynC istype statI not_static_sm
schirmer@12854
  2288
       obtain dm where
schirmer@12854
  2289
	 "methd G dynC sig = Some dm"
schirmer@12854
  2290
	 "is_static dm = is_static im" 
schirmer@12854
  2291
	 "G\<turnstile>resTy (mthd dm)\<preceq>resTy (mthd im)" 
schirmer@12854
  2292
	 by (auto dest: implmt_methd)
schirmer@12854
  2293
       with wf eq_stat resProp dynlookup eq_mheads
schirmer@12854
  2294
       show ?thesis 
schirmer@12854
  2295
	 by (cases emh type: *) (auto intro: widen_trans)
schirmer@12854
  2296
     qed
schirmer@12854
  2297
  next
schirmer@12854
  2298
    case Array_Object_methd
schirmer@12854
  2299
    fix T sm
schirmer@12854
  2300
    assume statArr: "statT = ArrayT T" and
schirmer@12854
  2301
                sm: "accmethd G S Object sig = Some sm" and 
schirmer@12854
  2302
         eq_mheads: "mhead (mthd sm) = mhd emh" 
schirmer@12854
  2303
    from statArr dynC_Prop wf
schirmer@12854
  2304
    have dynlookup: "dynlookup G statT dynC sig = methd G Object sig"
schirmer@12854
  2305
      by (auto simp add: dynlookup_def dynmethd_C_C)
schirmer@12854
  2306
    with sm eq_mheads sm 
schirmer@12854
  2307
    show ?thesis 
schirmer@12854
  2308
      by (cases emh type: *) (auto dest: accmethd_SomeD)
schirmer@12854
  2309
  qed
schirmer@12854
  2310
qed
schirmer@12925
  2311
declare split_paired_All [simp] split_paired_Ex [simp]
schirmer@12925
  2312
ML_setup {*
schirmer@12925
  2313
claset_ref()  := claset() addSbefore ("split_all_tac", split_all_tac);
schirmer@12925
  2314
simpset_ref() := simpset() addloop ("split_all_tac", split_all_tac)
schirmer@12925
  2315
*}
schirmer@12854
  2316
schirmer@12854
  2317
(* Tactical version *)
schirmer@12854
  2318
(*
schirmer@12854
  2319
lemma dynamic_mheadsD: "  
schirmer@12854
  2320
 \<lbrakk>emh \<in> mheads G S statT sig; wf_prog G; class G dynC = Some y;  
schirmer@12854
  2321
   if (\<exists>T. statT=ArrayT T) then dynC=Object else G\<turnstile>Class dynC\<preceq>RefT statT; 
schirmer@12854
  2322
   isrtype G statT\<rbrakk> \<Longrightarrow>  
schirmer@12854
  2323
  \<exists>m \<in> dynlookup G statT dynC sig: 
schirmer@12854
  2324
     static (mthd m)=static (mhd emh) \<and> G\<turnstile>resTy (mthd m)\<preceq>resTy (mhd emh)"
schirmer@12854
  2325
apply (drule mheadsD)
schirmer@12854
  2326
apply safe
schirmer@12854
  2327
       -- reftype statT is a class  
schirmer@12854
  2328
apply  (case_tac "\<exists>T. ClassT C = ArrayT T")
schirmer@12854
  2329
apply    (simp)
schirmer@12854
  2330
schirmer@12854
  2331
apply    (clarsimp simp add: dynlookup_def )
schirmer@12854
  2332
apply    (frule_tac statC="C" and dynC="dynC"  and sig="sig"  
schirmer@12854
  2333
         in ws_dynmethd)
schirmer@12854
  2334
apply      assumption+
schirmer@12854
  2335
apply    (case_tac "emh")  
schirmer@12854
  2336
apply    (force dest: accmethd_SomeD)
schirmer@12854
  2337
schirmer@12854
  2338
       -- reftype statT is a interface, method defined in interface 
schirmer@12854
  2339
apply    (clarsimp simp add: dynlookup_def)
schirmer@12854
  2340
apply    (drule (1) implmt_methd)
schirmer@12854
  2341
apply      blast
schirmer@12854
  2342
apply      blast
schirmer@12854
  2343
apply    (clarify)  
schirmer@12854
  2344
apply    (unfold dynimethd_def)
schirmer@12854
  2345
apply    (rule_tac x="cm" in bexI)
schirmer@12854
  2346
apply      (case_tac "emh")
schirmer@12854
  2347
apply      force
schirmer@12854
  2348
schirmer@12854
  2349
apply      force
schirmer@12854
  2350
schirmer@12854
  2351
        -- reftype statT is a interface, method defined in Object 
schirmer@12854
  2352
apply    (simp add: dynlookup_def)
schirmer@12854
  2353
apply    (simp only: dynimethd_def)
schirmer@12854
  2354
apply    (case_tac "imethds G I sig = {}")
schirmer@12854
  2355
apply       simp
schirmer@12854
  2356
apply       (frule_tac statC="Object" and dynC="dynC"  and sig="sig"  
schirmer@12854
  2357
             in ws_dynmethd)
schirmer@12854
  2358
apply          (blast intro: subcls_ObjectI wf_ws_prog) 
schirmer@12854
  2359
apply          (blast dest: class_Object)
schirmer@12854
  2360
apply       (case_tac "emh") 
schirmer@12854
  2361
apply       (force dest: accmethd_SomeD)
schirmer@12854
  2362
schirmer@12854
  2363
apply       simp
schirmer@12854
  2364
apply       (subgoal_tac "\<exists> im. im \<in> imethds G I sig") 
schirmer@12854
  2365
prefer 2      apply blast
schirmer@12854
  2366
apply       clarify
schirmer@12854
  2367
apply       (frule (1) implmt_methd)
schirmer@12854
  2368
apply         simp
schirmer@12854
  2369
apply         blast  
schirmer@12854
  2370
apply       (clarify dest!: accmethd_SomeD)
schirmer@12854
  2371
apply       (frule (4) iface_overrides_Object)
schirmer@12854
  2372
apply       clarify
schirmer@12854
  2373
apply       (case_tac emh)
schirmer@12854
  2374
apply       force
schirmer@12854
  2375
schirmer@12854
  2376
        -- reftype statT is a array
schirmer@12854
  2377
apply    (simp add: dynlookup_def)
schirmer@12854
  2378
apply    (case_tac emh)
schirmer@12854
  2379
apply    (force dest: accmethd_SomeD simp add: dynmethd_def)
schirmer@12854
  2380
done
schirmer@12854
  2381
*)
schirmer@12854
  2382
schirmer@12925
  2383
(* FIXME occasionally convert to ws_class_induct*) 
schirmer@12854
  2384
lemma methd_declclass:
schirmer@12854
  2385
"\<lbrakk>class G C = Some c; wf_prog G; methd G C sig = Some m\<rbrakk> 
schirmer@12854
  2386
 \<Longrightarrow> methd G (declclass m) sig = Some m"
schirmer@12854
  2387
proof -
schirmer@12854
  2388
  assume asm: "class G C = Some c" "wf_prog G" "methd G C sig = Some m"
schirmer@12854
  2389
  have "wf_prog G  \<longrightarrow> 
schirmer@12854
  2390
	   (\<forall> c m. class G C = Some c \<longrightarrow>  methd G C sig = Some m 
schirmer@12854
  2391
                   \<longrightarrow>  methd G (declclass m) sig = Some m)"      (is "?P G C") 
schirmer@12854
  2392
  proof (rule class_rec.induct,intro allI impI)
schirmer@12854
  2393
    fix G C c m
schirmer@12854
  2394
    assume hyp: "\<forall>c. C \<noteq> Object \<and> ws_prog G \<and> class G C = Some c \<longrightarrow>
schirmer@12854
  2395
                     ?P G (super c)"
schirmer@12854
  2396
    assume wf: "wf_prog G" and cls_C: "class G C = Some c" and
schirmer@12854
  2397
            m: "methd G C sig = Some m"
schirmer@12854
  2398
    show "methd G (declclass m) sig = Some m"
schirmer@12854
  2399
    proof (cases "C=Object")
schirmer@12854
  2400
      case True
schirmer@12854
  2401
      with wf m show ?thesis by (auto intro: table_of_map_SomeI)
schirmer@12854
  2402
    next
schirmer@12854
  2403
      let ?filter="filter_tab (\<lambda>sig m. G\<turnstile>C inherits method sig m)"
schirmer@12854
  2404
      let ?table = "table_of (map (\<lambda>(s, m). (s, C, m)) (methods c))"
schirmer@12854
  2405
      case False
schirmer@12854
  2406
      with cls_C wf m
schirmer@12854
  2407
      have methd_C: "(?filter (methd G (super c)) ++ ?table) sig = Some m "
schirmer@12854
  2408
	by (simp add: methd_rec)
schirmer@12854
  2409
      show ?thesis
schirmer@12854
  2410
      proof (cases "?table sig")
schirmer@12854
  2411
	case None
schirmer@12854
  2412
	from this methd_C have "?filter (methd G (super c)) sig = Some m"
schirmer@12854
  2413
	  by simp
schirmer@12854
  2414
	moreover
schirmer@12854
  2415
	from wf cls_C False obtain sup where "class G (super c) = Some sup"
schirmer@12854
  2416
	  by (blast dest: wf_prog_cdecl wf_cdecl_supD is_acc_class_is_class)
schirmer@12925
  2417
	moreover note wf False cls_C 
schirmer@12925
  2418
	ultimately show ?thesis by (auto intro: hyp [rule_format])
schirmer@12854
  2419
      next
schirmer@12854
  2420
	case Some
schirmer@12854
  2421
	from this methd_C m show ?thesis by auto 
schirmer@12854
  2422
      qed
schirmer@12854
  2423
    qed
schirmer@12854
  2424
  qed	
schirmer@12854
  2425
  with asm show ?thesis by auto
schirmer@12854
  2426
qed
schirmer@12854
  2427
schirmer@12854
  2428
lemma dynmethd_declclass:
schirmer@12854
  2429
 "\<lbrakk>dynmethd G statC dynC sig = Some m;
schirmer@12854
  2430
   wf_prog G; is_class G statC
schirmer@12854
  2431
  \<rbrakk> \<Longrightarrow> methd G (declclass m) sig = Some m"
schirmer@12854
  2432
by (auto dest: dynmethd_declC)
schirmer@12854
  2433
schirmer@12854
  2434
lemma dynlookup_declC:
schirmer@12854
  2435
 "\<lbrakk>dynlookup G statT dynC sig = Some m; wf_prog G;
schirmer@12854
  2436
   is_class G dynC;isrtype G statT
schirmer@12854
  2437
  \<rbrakk> \<Longrightarrow> G\<turnstile>dynC \<preceq>\<^sub>C (declclass m) \<and> is_class G (declclass m)"
schirmer@12854
  2438
by (cases "statT")
schirmer@12854
  2439
   (auto simp add: dynlookup_def dynimethd_def 
schirmer@12854
  2440
             dest: methd_declC dynmethd_declC)
schirmer@12854
  2441
schirmer@12854
  2442
lemma dynlookup_Array_declclassD [simp]:
schirmer@12854
  2443
"\<lbrakk>dynlookup G (ArrayT T) Object sig = Some dm;wf_prog G\<rbrakk> 
schirmer@12854
  2444
 \<Longrightarrow> declclass dm = Object"
schirmer@12854
  2445
proof -
schirmer@12854
  2446
  assume dynL: "dynlookup G (ArrayT T) Object sig = Some dm"
schirmer@12854
  2447
  assume wf: "wf_prog G"
schirmer@12854
  2448
  from wf have ws: "ws_prog G" by auto
schirmer@12854
  2449
  from wf have is_cls_Obj: "is_class G Object" by auto
schirmer@12854
  2450
  from dynL wf
schirmer@12854
  2451
  show ?thesis
schirmer@12854
  2452
    by (auto simp add: dynlookup_def dynmethd_C_C [OF is_cls_Obj ws]
schirmer@12854
  2453
                 dest: methd_Object_SomeD)
schirmer@12854
  2454
qed   
schirmer@12854
  2455
  
schirmer@12925
  2456
schirmer@12854
  2457
declare split_paired_All [simp del] split_paired_Ex [simp del]
schirmer@12854
  2458
ML_setup {*
schirmer@12854
  2459
simpset_ref() := simpset() delloop "split_all_tac";
schirmer@12854
  2460
claset_ref () := claset () delSWrapper "split_all_tac"
schirmer@12854
  2461
*}
schirmer@12854
  2462
lemma wt_is_type: "E,dt\<Turnstile>v\<Colon>T \<Longrightarrow>  wf_prog (prg E) \<longrightarrow> 
schirmer@12854
  2463
  dt=empty_dt \<longrightarrow> (case T of 
schirmer@12854
  2464
                     Inl T \<Rightarrow> is_type (prg E) T 
schirmer@12854
  2465
                   | Inr Ts \<Rightarrow> Ball (set Ts) (is_type (prg E)))"
schirmer@12854
  2466
apply (unfold empty_dt_def)
schirmer@12854
  2467
apply (erule wt.induct)
schirmer@12854
  2468
apply (auto split del: split_if_asm simp del: snd_conv 
schirmer@12854
  2469
            simp add: is_acc_class_def is_acc_type_def)
schirmer@12854
  2470
apply    (erule typeof_empty_is_type)
schirmer@13688
  2471
apply   (frule (1) wf_prog_cdecl [THEN wf_cdecl_supD], 
schirmer@12854
  2472
        force simp del: snd_conv, clarsimp simp add: is_acc_class_def)
schirmer@12854
  2473
apply  (drule (1) max_spec2mheads [THEN conjunct1, THEN mheadsD])
schirmer@12854
  2474
apply  (drule_tac [2] accfield_fields) 
schirmer@12854
  2475
apply  (frule class_Object)
schirmer@12854
  2476
apply  (auto dest: accmethd_rT_is_type 
schirmer@12854
  2477
                   imethds_wf_mhead [THEN conjunct1, THEN rT_is_acc_type]
schirmer@12854
  2478
             dest!:accimethdsD
schirmer@12854
  2479
             simp del: class_Object
schirmer@12854
  2480
             simp add: is_acc_type_def
schirmer@12854
  2481
    )
schirmer@12854
  2482
done
schirmer@12854
  2483
declare split_paired_All [simp] split_paired_Ex [simp]
schirmer@12854
  2484
ML_setup {*
schirmer@12854
  2485
claset_ref()  := claset() addSbefore ("split_all_tac", split_all_tac);
schirmer@12854
  2486
simpset_ref() := simpset() addloop ("split_all_tac", split_all_tac)
schirmer@12854
  2487
*}
schirmer@12854
  2488
schirmer@12854
  2489
lemma ty_expr_is_type: 
schirmer@12854
  2490
"\<lbrakk>E\<turnstile>e\<Colon>-T; wf_prog (prg E)\<rbrakk> \<Longrightarrow> is_type (prg E) T"
schirmer@12854
  2491
by (auto dest!: wt_is_type)
schirmer@12854
  2492
lemma ty_var_is_type: 
schirmer@12854
  2493
"\<lbrakk>E\<turnstile>v\<Colon>=T; wf_prog (prg E)\<rbrakk> \<Longrightarrow> is_type (prg E) T"
schirmer@12854
  2494
by (auto dest!: wt_is_type)
schirmer@12854
  2495
lemma ty_exprs_is_type: 
schirmer@12854
  2496
"\<lbrakk>E\<turnstile>es\<Colon>\<doteq>Ts; wf_prog (prg E)\<rbrakk> \<Longrightarrow> Ball (set Ts) (is_type (prg E))"
schirmer@12854
  2497
by (auto dest!: wt_is_type)
schirmer@12854
  2498
schirmer@12854
  2499
schirmer@12854
  2500
lemma static_mheadsD: 
schirmer@12854
  2501
 "\<lbrakk> emh \<in> mheads G S t sig; wf_prog G; E\<turnstile>e\<Colon>-RefT t; prg E=G ; 
schirmer@12854
  2502
   invmode (mhd emh) e \<noteq> IntVir 
schirmer@12854
  2503
  \<rbrakk> \<Longrightarrow> \<exists>m. (   (\<exists> C. t = ClassT C \<and> accmethd G S C sig = Some m)
schirmer@12854
  2504
               \<or> (\<forall> C. t \<noteq> ClassT C \<and> accmethd G S Object sig = Some m )) \<and> 
schirmer@12854
  2505
          declrefT emh = ClassT (declclass m) \<and>  mhead (mthd m) = (mhd emh)"
schirmer@12854
  2506
apply (subgoal_tac "is_static emh \<or> e = Super")
schirmer@12854
  2507
defer apply (force simp add: invmode_def)
schirmer@12854
  2508
apply (frule  ty_expr_is_type)
schirmer@12854
  2509
apply   simp
schirmer@12854
  2510
apply (case_tac "is_static emh")
schirmer@12854
  2511
apply  (frule (1) mheadsD)
schirmer@12854
  2512
apply  clarsimp
schirmer@12854
  2513
apply  safe
schirmer@12854
  2514
apply    blast
schirmer@12854
  2515
apply   (auto dest!: imethds_wf_mhead
schirmer@12854
  2516
                     accmethd_SomeD 
schirmer@12854
  2517
                     accimethdsD
schirmer@12854
  2518
              simp add: accObjectmheads_def Objectmheads_def)
schirmer@12854
  2519
schirmer@12854
  2520
apply  (erule wt_elim_cases)
schirmer@12854
  2521
apply  (force simp add: cmheads_def)
schirmer@12854
  2522
done
schirmer@12854
  2523
schirmer@12854
  2524
lemma wt_MethdI:  
schirmer@12854
  2525
"\<lbrakk>methd G C sig = Some m; wf_prog G;  
schirmer@12854
  2526
  class G C = Some c\<rbrakk> \<Longrightarrow>  
schirmer@12854
  2527
 \<exists>T. \<lparr>prg=G,cls=(declclass m),
schirmer@13688
  2528
      lcl=callee_lcl (declclass m) sig (mthd m)\<rparr>\<turnstile> Methd C sig\<Colon>-T \<and> G\<turnstile>T\<preceq>resTy m"
schirmer@12854
  2529
apply (frule (2) methd_wf_mdecl, clarify)
schirmer@12854
  2530
apply (force dest!: wf_mdecl_bodyD intro!: wt.Methd)
schirmer@12854
  2531
done
schirmer@12854
  2532
schirmer@12854
  2533
subsection "accessibility concerns"
schirmer@12854
  2534
schirmer@12854
  2535
lemma mheads_type_accessible:
schirmer@12854
  2536
 "\<lbrakk>emh \<in> mheads G S T sig; wf_prog G\<rbrakk>
schirmer@12854
  2537
 \<Longrightarrow> G\<turnstile>RefT T accessible_in (pid S)"
schirmer@12854
  2538
by (erule mheads_cases)
schirmer@12854
  2539
   (auto dest: accmethd_SomeD accessible_from_commonD accimethdsD)
schirmer@12854
  2540
schirmer@12925
  2541
lemma static_to_dynamic_accessible_from_aux:
schirmer@12854
  2542
"\<lbrakk>G\<turnstile>m of C accessible_from accC;wf_prog G\<rbrakk> 
schirmer@12854
  2543
 \<Longrightarrow> G\<turnstile>m in C dyn_accessible_from accC"
schirmer@12854
  2544
proof (induct rule: accessible_fromR.induct)
schirmer@12854
  2545
qed (auto intro: dyn_accessible_fromR.intros 
schirmer@12854
  2546
                 member_of_to_member_in
schirmer@12854
  2547
                 static_to_dynamic_overriding)
schirmer@12854
  2548
schirmer@12854
  2549
lemma static_to_dynamic_accessible_from:
wenzelm@12937
  2550
  assumes stat_acc: "G\<turnstile>m of statC accessible_from accC" and
schirmer@12854
  2551
          subclseq: "G\<turnstile>dynC \<preceq>\<^sub>C statC" and
schirmer@12854
  2552
                wf: "wf_prog G"
wenzelm@12937
  2553
  shows "G\<turnstile>m in dynC dyn_accessible_from accC"
schirmer@12854
  2554
proof - 
schirmer@12854
  2555
  from stat_acc subclseq 
schirmer@12854
  2556
  show ?thesis (is "?Dyn_accessible m")
schirmer@12854
  2557
  proof (induct rule: accessible_fromR.induct)
schirmer@12925
  2558
    case (Immediate statC m)
schirmer@12854
  2559
    then show "?Dyn_accessible m"
schirmer@12925
  2560
      by (blast intro: dyn_accessible_fromR.Immediate
schirmer@12854
  2561
                       member_inI
schirmer@12854
  2562
                       permits_acc_inheritance)
schirmer@12854
  2563
  next
schirmer@12925
  2564
    case (Overriding _ _ m)
schirmer@12854
  2565
    with wf show "?Dyn_accessible m"
schirmer@12925
  2566
      by (blast intro: dyn_accessible_fromR.Overriding
schirmer@12854
  2567
                       member_inI
schirmer@12854
  2568
                       static_to_dynamic_overriding  
schirmer@12854
  2569
                       rtrancl_trancl_trancl 
schirmer@12925
  2570
                       static_to_dynamic_accessible_from_aux)
schirmer@12854
  2571
  qed
schirmer@12854
  2572
qed
schirmer@12854
  2573
schirmer@12925
  2574
lemma static_to_dynamic_accessible_from_static:
wenzelm@12937
  2575
  assumes stat_acc: "G\<turnstile>m of statC accessible_from accC" and
schirmer@12925
  2576
            static: "is_static m" and
schirmer@12925
  2577
                wf: "wf_prog G"
wenzelm@12937
  2578
  shows "G\<turnstile>m in (declclass m) dyn_accessible_from accC"
schirmer@12925
  2579
proof -