src/HOL/Bali/DeclConcepts.thy
author schirmer
Fri Feb 22 11:26:44 2002 +0100 (2002-02-22)
changeset 12925 99131847fb93
parent 12859 f63315dfffd4
child 12937 0c4fd7529467
permissions -rw-r--r--
Added check for field/method access to operational semantics and proved the acesses valid.
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(*  Title:      HOL/Bali/DeclConcepts.thy
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    ID:         $Id$
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    Author:     Norbert Schirmer
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    License:    GPL (GNU GENERAL PUBLIC LICENSE)
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*)
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header {* Advanced concepts on Java declarations like overriding, inheritance,
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dynamic method lookup*}
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theory DeclConcepts = TypeRel:
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section "access control (cf. 6.6), overriding and hiding (cf. 8.4.6.1)"
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constdefs
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is_public :: "prog \<Rightarrow> qtname \<Rightarrow> bool"
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"is_public G qn \<equiv> (case class G qn of
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                     None       \<Rightarrow> (case iface G qn of
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                                      None       \<Rightarrow> False
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                                    | Some iface \<Rightarrow> access iface = Public)
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                   | Some class \<Rightarrow> access class = Public)"
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subsection "accessibility of types (cf. 6.6.1)"
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text {* 
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Primitive types are always accessible, interfaces and classes are accessible
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in their package or if they are defined public, an array type is accessible if
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its element type is accessible *}
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consts accessible_in   :: "prog \<Rightarrow> ty     \<Rightarrow> pname \<Rightarrow> bool"  
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                                      ("_ \<turnstile> _ accessible'_in _" [61,61,61] 60)
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       rt_accessible_in:: "prog \<Rightarrow> ref_ty \<Rightarrow> pname \<Rightarrow> bool" 
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                                      ("_ \<turnstile> _ accessible'_in' _" [61,61,61] 60) 
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primrec
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"G\<turnstile>(PrimT p)   accessible_in pack  = True"
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accessible_in_RefT_simp: 
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"G\<turnstile>(RefT  r)   accessible_in pack  = G\<turnstile>r accessible_in' pack"
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"G\<turnstile>(NullT)     accessible_in' pack = True"
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"G\<turnstile>(IfaceT I)  accessible_in' pack = ((pid I = pack) \<or> is_public G I)"
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"G\<turnstile>(ClassT C)  accessible_in' pack = ((pid C = pack) \<or> is_public G C)"
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"G\<turnstile>(ArrayT ty) accessible_in' pack = G\<turnstile>ty accessible_in pack"
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declare accessible_in_RefT_simp [simp del]
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constdefs
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  is_acc_class :: "prog \<Rightarrow> pname \<Rightarrow> qtname \<Rightarrow> bool"
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    "is_acc_class G P C \<equiv> is_class G C \<and> G\<turnstile>(Class C) accessible_in P"
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  is_acc_iface :: "prog \<Rightarrow> pname \<Rightarrow> qtname \<Rightarrow> bool"
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    "is_acc_iface G P I \<equiv> is_iface G I \<and> G\<turnstile>(Iface I) accessible_in P"
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  is_acc_type  :: "prog \<Rightarrow> pname \<Rightarrow> ty     \<Rightarrow> bool"
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    "is_acc_type  G P T \<equiv> is_type G T  \<and> G\<turnstile>T accessible_in P"
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  is_acc_reftype  :: "prog \<Rightarrow> pname \<Rightarrow> ref_ty \<Rightarrow> bool"
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  "is_acc_reftype  G P T \<equiv> isrtype G T  \<and> G\<turnstile>T accessible_in' P"
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lemma is_acc_classD:
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 "is_acc_class G P C \<Longrightarrow>  is_class G C \<and> G\<turnstile>(Class C) accessible_in P"
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by (simp add: is_acc_class_def)
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lemma is_acc_class_is_class: "is_acc_class G P C \<Longrightarrow> is_class G C"
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by (auto simp add: is_acc_class_def)
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lemma is_acc_ifaceD:
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  "is_acc_iface G P I \<Longrightarrow> is_iface G I \<and> G\<turnstile>(Iface I) accessible_in P"
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by (simp add: is_acc_iface_def)
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lemma is_acc_typeD:
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 "is_acc_type  G P T \<Longrightarrow> is_type G T  \<and> G\<turnstile>T accessible_in P"
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by (simp add: is_acc_type_def)
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lemma is_acc_reftypeD:
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"is_acc_reftype  G P T \<Longrightarrow> isrtype G T  \<and> G\<turnstile>T accessible_in' P"
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by (simp add: is_acc_reftype_def)
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subsection "accessibility of members"
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text {*
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The accessibility of members is more involved as the accessibility of types.
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We have to distinguish several cases to model the different effects of 
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accessibility during inheritance, overriding and ordinary member access 
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*}
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subsubsection {* Various technical conversion and selection functions *}
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text {* overloaded selector @{text accmodi} to select the access modifier 
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out of various HOL types *}
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axclass has_accmodi < "type"
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consts accmodi:: "'a::has_accmodi \<Rightarrow> acc_modi"
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instance acc_modi::has_accmodi ..
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defs (overloaded)
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acc_modi_accmodi_def: "accmodi (a::acc_modi) \<equiv> a"
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lemma acc_modi_accmodi_simp[simp]: "accmodi (a::acc_modi) = a"
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by (simp add: acc_modi_accmodi_def)
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instance access_field_type:: ("type","type") has_accmodi ..
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defs (overloaded)
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decl_acc_modi_def: "accmodi (d::('a:: type) decl_scheme) \<equiv> access d"
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lemma decl_acc_modi_simp[simp]: "accmodi (d::('a::type) decl_scheme) = access d"
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by (simp add: decl_acc_modi_def)
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instance * :: ("type",has_accmodi) has_accmodi ..
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defs (overloaded)
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pair_acc_modi_def: "accmodi p \<equiv> (accmodi (snd p))"
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lemma pair_acc_modi_simp[simp]: "accmodi (x,a) = (accmodi a)"
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by (simp add: pair_acc_modi_def)
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instance memberdecl :: has_accmodi ..
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defs (overloaded)
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memberdecl_acc_modi_def: "accmodi m \<equiv> (case m of
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                                          fdecl f \<Rightarrow> accmodi f
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                                        | mdecl m \<Rightarrow> accmodi m)"
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lemma memberdecl_fdecl_acc_modi_simp[simp]:
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 "accmodi (fdecl m) = accmodi m"
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by (simp add: memberdecl_acc_modi_def)
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lemma memberdecl_mdecl_acc_modi_simp[simp]:
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 "accmodi (mdecl m) = accmodi m"
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by (simp add: memberdecl_acc_modi_def)
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text {* overloaded selector @{text declclass} to select the declaring class 
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out of various HOL types *}
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axclass has_declclass < "type"
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consts declclass:: "'a::has_declclass \<Rightarrow> qtname"
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instance pid_field_type::("type","type") has_declclass ..
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defs (overloaded)
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qtname_declclass_def: "declclass (q::qtname) \<equiv> q"
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lemma qtname_declclass_simp[simp]: "declclass (q::qtname) = q"
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by (simp add: qtname_declclass_def)
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instance * :: ("has_declclass","type") has_declclass ..
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defs (overloaded)
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pair_declclass_def: "declclass p \<equiv> declclass (fst p)"
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lemma pair_declclass_simp[simp]: "declclass (c,x) = declclass c" 
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by (simp add: pair_declclass_def)
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text {* overloaded selector @{text is_static} to select the static modifier 
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out of various HOL types *}
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axclass has_static < "type"
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consts is_static :: "'a::has_static \<Rightarrow> bool"
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(*
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consts is_static :: "'a \<Rightarrow> bool"
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*)
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instance access_field_type :: ("type","has_static") has_static ..
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defs (overloaded)
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decl_is_static_def: 
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 "is_static (m::('a::has_static) decl_scheme) \<equiv> is_static (Decl.decl.more m)" 
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instance static_field_type :: ("type","type") has_static ..
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defs (overloaded)
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static_field_type_is_static_def: 
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 "is_static (m::(bool,'b::type) static_field_type) \<equiv> static_val m"
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lemma member_is_static_simp: "is_static (m::'a member_scheme) = static m"
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apply (cases m)
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apply (simp add: static_field_type_is_static_def 
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                 decl_is_static_def Decl.member.dest_convs)
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done
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instance * :: ("type","has_static") has_static ..
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defs (overloaded)
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pair_is_static_def: "is_static p \<equiv> is_static (snd p)"
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lemma pair_is_static_simp [simp]: "is_static (x,s) = is_static s"
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by (simp add: pair_is_static_def)
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lemma pair_is_static_simp1: "is_static p = is_static (snd p)"
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by (simp add: pair_is_static_def)
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instance memberdecl:: has_static ..
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defs (overloaded)
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memberdecl_is_static_def: 
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 "is_static m \<equiv> (case m of
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                    fdecl f \<Rightarrow> is_static f
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                  | mdecl m \<Rightarrow> is_static m)"
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lemma memberdecl_is_static_fdecl_simp[simp]:
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 "is_static (fdecl f) = is_static f"
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by (simp add: memberdecl_is_static_def)
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lemma memberdecl_is_static_mdecl_simp[simp]:
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 "is_static (mdecl m) = is_static m"
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by (simp add: memberdecl_is_static_def)
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lemma mhead_static_simp [simp]: "is_static (mhead m) = is_static m"
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by (cases m) (simp add: mhead_def member_is_static_simp)
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constdefs  (* some mnemotic selectors for (qtname \<times> ('a::more) decl_scheme) 
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            * the first component is a class or interface name
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            * the second component is a method, field or method head *)
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(* "declclass":: "(qtname \<times> ('a::more) decl_scheme) \<Rightarrow> qtname"*)
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(* "declclass \<equiv> fst" *)          (* get the class component *)
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 "decliface":: "(qtname \<times> ('a::type) decl_scheme) \<Rightarrow> qtname"
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 "decliface \<equiv> fst"          (* get the interface component *)
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(*
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 "member"::   "(qtname \<times> ('a::type) decl_scheme) \<Rightarrow> ('a::type) decl_scheme"
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*)
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 "mbr"::   "(qtname \<times> memberdecl) \<Rightarrow> memberdecl"
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 "mbr \<equiv> snd"            (* get the memberdecl component *)
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 "mthd"::   "('b \<times> 'a) \<Rightarrow> 'a"
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                           (* also used for mdecl,mhead *)
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 "mthd \<equiv> snd"              (* get the method component *)
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 "fld"::   "('b \<times> ('a::type) decl_scheme) \<Rightarrow> ('a::type) decl_scheme"
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              (* also used for ((vname \<times> qtname)\<times> field) *)
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 "fld \<equiv> snd"               (* get the field component *)
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(* "accmodi" :: "('b \<times> ('a::type) decl_scheme) \<Rightarrow> acc_modi"*)
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                           (* also used for mdecl *)
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(* "accmodi \<equiv> access \<circ> snd"*)  (* get the access modifier *) 
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(*
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 "is_static" ::"('b \<times> ('a::type) member_scheme) \<Rightarrow> bool" *)
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                            (* also defined for emhead cf. WellType *)
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 (*"is_static \<equiv> static \<circ> snd"*) (* get the static modifier *)
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constdefs (* some mnemotic selectors for (vname \<times> qtname) *)
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 fname:: "(vname \<times> 'a) \<Rightarrow> vname" (* also used for fdecl *)
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 "fname \<equiv> fst"
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  declclassf:: "(vname \<times> qtname) \<Rightarrow> qtname"
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 "declclassf \<equiv> snd"
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(*
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lemma declclass_simp[simp]: "declclass (C,m) = C"
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by (simp add: declclass_def)
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*)
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lemma decliface_simp[simp]: "decliface (I,m) = I"
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by (simp add: decliface_def) 
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lemma mbr_simp[simp]: "mbr (C,m) = m"
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by (simp add: mbr_def)
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lemma access_mbr_simp [simp]: "(accmodi (mbr m)) = accmodi m"
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by (cases m) (simp add:  mbr_def) 
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lemma mthd_simp[simp]: "mthd (C,m) = m"
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by (simp add: mthd_def)
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lemma fld_simp[simp]: "fld (C,f) = f"
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by (simp add: fld_def)
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lemma accmodi_simp[simp]: "accmodi (C,m) = access m"
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by (simp )
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lemma access_mthd_simp [simp]: "(access (mthd m)) = accmodi m"
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by (cases m) (simp add: mthd_def) 
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lemma access_fld_simp [simp]: "(access (fld f)) = accmodi f"
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by (cases f) (simp add:  fld_def) 
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(*
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lemma is_static_simp[simp]: "is_static (C,m) = static m"
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by (simp add: is_static_def)
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*)
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lemma static_mthd_simp[simp]: "static (mthd m) = is_static m"
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by (cases m) (simp add:  mthd_def member_is_static_simp)
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lemma mthd_is_static_simp [simp]: "is_static (mthd m) = is_static m"
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by (cases m) simp
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lemma static_fld_simp[simp]: "static (fld f) = is_static f"
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by (cases f) (simp add:  fld_def member_is_static_simp)
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lemma ext_field_simp [simp]: "(declclass f,fld f) = f"
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by (cases f) (simp add:  fld_def)
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lemma ext_method_simp [simp]: "(declclass m,mthd m) = m"
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by (cases m) (simp add:  mthd_def)
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lemma ext_mbr_simp [simp]: "(declclass m,mbr m) = m"
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by (cases m) (simp add: mbr_def)
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lemma fname_simp[simp]:"fname (n,c) = n"
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by (simp add: fname_def)
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lemma declclassf_simp[simp]:"declclassf (n,c) = c"
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by (simp add: declclassf_def)
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constdefs  (* some mnemotic selectors for (vname \<times> qtname) *)
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  "fldname"  :: "(vname \<times> qtname) \<Rightarrow> vname" 
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  "fldname \<equiv> fst"
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  "fldclass" :: "(vname \<times> qtname) \<Rightarrow> qtname"
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  "fldclass \<equiv> snd"
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lemma fldname_simp[simp]: "fldname (n,c) = n"
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by (simp add: fldname_def)
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lemma fldclass_simp[simp]: "fldclass (n,c) = c"
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by (simp add: fldclass_def)
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   316
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   317
lemma ext_fieldname_simp[simp]: "(fldname f,fldclass f) = f"
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   318
by (simp add: fldname_def fldclass_def)
schirmer@12854
   319
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   320
text {* Convert a qualified method declaration (qualified with its declaring 
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   321
class) to a qualified member declaration:  @{text methdMembr}  *}
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   322
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   323
constdefs
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   324
methdMembr :: "(qtname \<times> mdecl) \<Rightarrow> (qtname \<times> memberdecl)"
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   325
 "methdMembr m \<equiv> (fst m,mdecl (snd m))"
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   326
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   327
lemma methdMembr_simp[simp]: "methdMembr (c,m) = (c,mdecl m)"
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   328
by (simp add: methdMembr_def)
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   329
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   330
lemma accmodi_methdMembr_simp[simp]: "accmodi (methdMembr m) = accmodi m"
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   331
by (cases m) (simp add: methdMembr_def)
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   332
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   333
lemma is_static_methdMembr_simp[simp]: "is_static (methdMembr m) = is_static m"
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   334
by (cases m) (simp add: methdMembr_def)
schirmer@12854
   335
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   336
lemma declclass_methdMembr_simp[simp]: "declclass (methdMembr m) = declclass m"
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   337
by (cases m) (simp add: methdMembr_def)
schirmer@12854
   338
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   339
text {* Convert a qualified method (qualified with its declaring 
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   340
class) to a qualified member declaration:  @{text method}  *}
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   341
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   342
constdefs
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   343
method :: "sig \<Rightarrow> (qtname \<times> methd) \<Rightarrow> (qtname \<times> memberdecl)" 
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   344
"method sig m \<equiv> (declclass m, mdecl (sig, mthd m))"
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   345
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   346
lemma method_simp[simp]: "method sig (C,m) = (C,mdecl (sig,m))"
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   347
by (simp add: method_def)
schirmer@12854
   348
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   349
lemma accmodi_method_simp[simp]: "accmodi (method sig m) = accmodi m"
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   350
by (simp add: method_def)
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   351
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   352
lemma declclass_method_simp[simp]: "declclass (method sig m) = declclass m"
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   353
by (simp add: method_def)
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   354
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   355
lemma is_static_method_simp[simp]: "is_static (method sig m) = is_static m"
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   356
by (cases m) (simp add: method_def)
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   357
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   358
lemma mbr_method_simp[simp]: "mbr (method sig m) = mdecl (sig,mthd m)"
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   359
by (simp add: mbr_def method_def)
schirmer@12854
   360
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   361
lemma memberid_method_simp[simp]:  "memberid (method sig m) = mid sig"
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   362
  by (simp add: method_def) 
schirmer@12854
   363
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   364
constdefs
schirmer@12854
   365
fieldm :: "vname \<Rightarrow> (qtname \<times> field) \<Rightarrow> (qtname \<times> memberdecl)" 
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   366
"fieldm n f \<equiv> (declclass f, fdecl (n, fld f))"
schirmer@12854
   367
schirmer@12854
   368
lemma fieldm_simp[simp]: "fieldm n (C,f) = (C,fdecl (n,f))"
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   369
by (simp add: fieldm_def)
schirmer@12854
   370
schirmer@12854
   371
lemma accmodi_fieldm_simp[simp]: "accmodi (fieldm n f) = accmodi f"
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   372
by (simp add: fieldm_def)
schirmer@12854
   373
schirmer@12854
   374
lemma declclass_fieldm_simp[simp]: "declclass (fieldm n f) = declclass f"
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   375
by (simp add: fieldm_def)
schirmer@12854
   376
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   377
lemma is_static_fieldm_simp[simp]: "is_static (fieldm n f) = is_static f"
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   378
by (cases f) (simp add: fieldm_def)
schirmer@12854
   379
schirmer@12854
   380
lemma mbr_fieldm_simp[simp]: "mbr (fieldm n f) = fdecl (n,fld f)"
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   381
by (simp add: mbr_def fieldm_def)
schirmer@12854
   382
schirmer@12854
   383
lemma memberid_fieldm_simp[simp]:  "memberid (fieldm n f) = fid n"
schirmer@12854
   384
by (simp add: fieldm_def) 
schirmer@12854
   385
schirmer@12854
   386
text {* Select the signature out of a qualified method declaration:
schirmer@12854
   387
 @{text msig} *}
schirmer@12854
   388
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   389
constdefs msig:: "(qtname \<times> mdecl) \<Rightarrow> sig"
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   390
"msig m \<equiv> fst (snd m)"
schirmer@12854
   391
schirmer@12854
   392
lemma msig_simp[simp]: "msig (c,(s,m)) = s"
schirmer@12854
   393
by (simp add: msig_def)
schirmer@12854
   394
schirmer@12854
   395
text {* Convert a qualified method (qualified with its declaring 
schirmer@12854
   396
class) to a qualified method declaration:  @{text qmdecl}  *}
schirmer@12854
   397
schirmer@12854
   398
constdefs qmdecl :: "sig \<Rightarrow> (qtname \<times> methd) \<Rightarrow> (qtname \<times> mdecl)"
schirmer@12854
   399
"qmdecl sig m \<equiv> (declclass m, (sig,mthd m))"
schirmer@12854
   400
schirmer@12854
   401
lemma qmdecl_simp[simp]: "qmdecl sig (C,m) = (C,(sig,m))"
schirmer@12854
   402
by (simp add: qmdecl_def)
schirmer@12854
   403
schirmer@12854
   404
lemma declclass_qmdecl_simp[simp]: "declclass (qmdecl sig m) = declclass m"
schirmer@12854
   405
by (simp add: qmdecl_def)
schirmer@12854
   406
schirmer@12854
   407
lemma accmodi_qmdecl_simp[simp]: "accmodi (qmdecl sig m) = accmodi m"
schirmer@12854
   408
by (simp add: qmdecl_def)
schirmer@12854
   409
schirmer@12854
   410
lemma is_static_qmdecl_simp[simp]: "is_static (qmdecl sig m) = is_static m"
schirmer@12854
   411
by (cases m) (simp add: qmdecl_def)
schirmer@12854
   412
schirmer@12854
   413
lemma msig_qmdecl_simp[simp]: "msig (qmdecl sig m) = sig"
schirmer@12854
   414
by (simp add: qmdecl_def)
schirmer@12854
   415
schirmer@12854
   416
lemma mdecl_qmdecl_simp[simp]:  
schirmer@12854
   417
 "mdecl (mthd (qmdecl sig new)) = mdecl (sig, mthd new)" 
schirmer@12854
   418
by (simp add: qmdecl_def) 
schirmer@12854
   419
schirmer@12854
   420
lemma methdMembr_qmdecl_simp [simp]: 
schirmer@12854
   421
 "methdMembr (qmdecl sig old) = method sig old"
schirmer@12854
   422
by (simp add: methdMembr_def qmdecl_def method_def)
schirmer@12854
   423
schirmer@12854
   424
text {* overloaded selector @{text resTy} to select the result type 
schirmer@12854
   425
out of various HOL types *}
schirmer@12854
   426
schirmer@12854
   427
axclass has_resTy < "type"
schirmer@12854
   428
consts resTy:: "'a::has_resTy \<Rightarrow> ty"
schirmer@12854
   429
wenzelm@12859
   430
instance access_field_type :: ("type","has_resTy") has_resTy ..
schirmer@12854
   431
schirmer@12854
   432
defs (overloaded)
schirmer@12854
   433
decl_resTy_def: 
schirmer@12854
   434
 "resTy (m::('a::has_resTy) decl_scheme) \<equiv> resTy (Decl.decl.more m)" 
schirmer@12854
   435
wenzelm@12859
   436
instance static_field_type :: ("type","has_resTy") has_resTy ..
schirmer@12854
   437
schirmer@12854
   438
defs (overloaded)
schirmer@12854
   439
static_field_type_resTy_def: 
schirmer@12854
   440
 "resTy (m::(bool,'b::has_resTy) static_field_type) 
schirmer@12854
   441
  \<equiv> resTy (static_more m)" 
schirmer@12854
   442
wenzelm@12859
   443
instance pars_field_type :: ("type","has_resTy") has_resTy ..
schirmer@12854
   444
schirmer@12854
   445
defs (overloaded)
schirmer@12854
   446
pars_field_type_resTy_def: 
schirmer@12854
   447
 "resTy (m::(vname list,'b::has_resTy) pars_field_type) 
schirmer@12854
   448
  \<equiv> resTy (pars_more m)" 
schirmer@12854
   449
wenzelm@12859
   450
instance resT_field_type :: ("type","type") has_resTy ..
schirmer@12854
   451
schirmer@12854
   452
defs (overloaded)
schirmer@12854
   453
resT_field_type_resTy_def: 
schirmer@12854
   454
 "resTy (m::(ty,'b::type) resT_field_type) 
schirmer@12854
   455
  \<equiv> resT_val m" 
schirmer@12854
   456
schirmer@12854
   457
lemma mhead_resTy_simp: "resTy (m::'a mhead_scheme) = resT m"
schirmer@12854
   458
apply (cases m)
schirmer@12854
   459
apply (simp add: decl_resTy_def static_field_type_resTy_def 
schirmer@12854
   460
                 pars_field_type_resTy_def resT_field_type_resTy_def
schirmer@12854
   461
                 member.dest_convs mhead.dest_convs)
schirmer@12854
   462
done
schirmer@12854
   463
schirmer@12854
   464
lemma resTy_mhead [simp]:"resTy (mhead m) = resTy m"
schirmer@12854
   465
by (simp add: mhead_def mhead_resTy_simp)
schirmer@12854
   466
wenzelm@12859
   467
instance * :: ("type","has_resTy") has_resTy ..
schirmer@12854
   468
schirmer@12854
   469
defs (overloaded)
schirmer@12854
   470
pair_resTy_def: "resTy p \<equiv> resTy (snd p)"
schirmer@12854
   471
schirmer@12854
   472
lemma pair_resTy_simp[simp]: "resTy (x,m) = resTy m"
schirmer@12854
   473
by (simp add: pair_resTy_def)
schirmer@12854
   474
schirmer@12854
   475
lemma qmdecl_resTy_simp [simp]: "resTy (qmdecl sig m) = resTy m"
schirmer@12854
   476
by (cases m) (simp)
schirmer@12854
   477
schirmer@12854
   478
lemma resTy_mthd [simp]:"resTy (mthd m) = resTy m"
schirmer@12854
   479
by (cases m) (simp add: mthd_def )
schirmer@12854
   480
schirmer@12854
   481
subsubsection "inheritable-in"
schirmer@12854
   482
text {*
schirmer@12854
   483
@{text "G\<turnstile>m inheritable_in P"}: m can be inherited by
schirmer@12854
   484
classes in package P if:
schirmer@12854
   485
\begin{itemize} 
schirmer@12854
   486
\item the declaration class of m is accessible in P and
schirmer@12854
   487
\item the member m is declared with protected or public access or if it is
schirmer@12854
   488
      declared with default (package) access, the package of the declaration 
schirmer@12854
   489
      class of m is also P. If the member m is declared with private access
schirmer@12854
   490
      it is not accessible for inheritance at all.
schirmer@12854
   491
\end{itemize}
schirmer@12854
   492
*}
schirmer@12854
   493
constdefs
schirmer@12854
   494
inheritable_in:: 
schirmer@12854
   495
 "prog \<Rightarrow> (qtname \<times> memberdecl) \<Rightarrow> pname \<Rightarrow> bool"
schirmer@12854
   496
                  ("_ \<turnstile> _ inheritable'_in _" [61,61,61] 60)
schirmer@12854
   497
"G\<turnstile>membr inheritable_in pack 
schirmer@12854
   498
  \<equiv> (case (accmodi membr) of
schirmer@12854
   499
       Private   \<Rightarrow> False
schirmer@12854
   500
     | Package   \<Rightarrow> (pid (declclass membr)) = pack
schirmer@12854
   501
     | Protected \<Rightarrow> True
schirmer@12854
   502
     | Public    \<Rightarrow> True)"
schirmer@12854
   503
schirmer@12854
   504
syntax
schirmer@12854
   505
Method_inheritable_in::
schirmer@12854
   506
 "prog \<Rightarrow> (qtname \<times> mdecl) \<Rightarrow> pname \<Rightarrow> bool"
schirmer@12854
   507
                ("_ \<turnstile>Method _ inheritable'_in _ " [61,61,61] 60)
schirmer@12854
   508
schirmer@12854
   509
translations
schirmer@12854
   510
"G\<turnstile>Method m inheritable_in p" == "G\<turnstile>methdMembr m inheritable_in p"
schirmer@12854
   511
schirmer@12854
   512
syntax
schirmer@12854
   513
Methd_inheritable_in::
schirmer@12854
   514
 "prog \<Rightarrow> sig \<Rightarrow> (qtname \<times> methd) \<Rightarrow> pname \<Rightarrow> bool"
schirmer@12854
   515
                ("_ \<turnstile>Methd _ _ inheritable'_in _ " [61,61,61,61] 60)
schirmer@12854
   516
schirmer@12854
   517
translations
schirmer@12854
   518
"G\<turnstile>Methd s m inheritable_in p" == "G\<turnstile>(method s m) inheritable_in p"
schirmer@12854
   519
schirmer@12854
   520
subsubsection "declared-in/undeclared-in"
schirmer@12854
   521
schirmer@12854
   522
constdefs cdeclaredmethd:: "prog \<Rightarrow> qtname \<Rightarrow> (sig,methd) table"
schirmer@12854
   523
"cdeclaredmethd G C 
schirmer@12854
   524
  \<equiv> (case class G C of
schirmer@12854
   525
       None \<Rightarrow> \<lambda> sig. None
schirmer@12854
   526
     | Some c \<Rightarrow> table_of (methods c)
schirmer@12854
   527
    )"
schirmer@12854
   528
schirmer@12854
   529
constdefs
schirmer@12854
   530
cdeclaredfield:: "prog \<Rightarrow> qtname \<Rightarrow> (vname,field) table"
schirmer@12854
   531
"cdeclaredfield G C 
schirmer@12854
   532
  \<equiv> (case class G C of
schirmer@12854
   533
       None \<Rightarrow> \<lambda> sig. None
schirmer@12854
   534
     | Some c \<Rightarrow> table_of (cfields c)
schirmer@12854
   535
    )"
schirmer@12854
   536
schirmer@12854
   537
schirmer@12854
   538
constdefs
schirmer@12854
   539
declared_in:: "prog  \<Rightarrow> memberdecl \<Rightarrow> qtname \<Rightarrow> bool"
schirmer@12854
   540
                                 ("_\<turnstile> _ declared'_in _" [61,61,61] 60)
schirmer@12854
   541
"G\<turnstile>m declared_in C \<equiv> (case m of
schirmer@12854
   542
                        fdecl (fn,f ) \<Rightarrow> cdeclaredfield G C fn  = Some f
schirmer@12854
   543
                      | mdecl (sig,m) \<Rightarrow> cdeclaredmethd G C sig = Some m)"
schirmer@12854
   544
schirmer@12854
   545
syntax
schirmer@12854
   546
method_declared_in:: "prog  \<Rightarrow> (qtname \<times> mdecl) \<Rightarrow> qtname \<Rightarrow> bool"
schirmer@12854
   547
                                 ("_\<turnstile>Method _ declared'_in _" [61,61,61] 60)
schirmer@12854
   548
translations
schirmer@12854
   549
"G\<turnstile>Method m declared_in C" == "G\<turnstile>mdecl (mthd m) declared_in C"
schirmer@12854
   550
schirmer@12854
   551
syntax
schirmer@12854
   552
methd_declared_in:: "prog  \<Rightarrow> sig  \<Rightarrow>(qtname \<times> methd) \<Rightarrow> qtname \<Rightarrow> bool"
schirmer@12854
   553
                               ("_\<turnstile>Methd _  _ declared'_in _" [61,61,61,61] 60)
schirmer@12854
   554
translations
schirmer@12854
   555
"G\<turnstile>Methd s m declared_in C" == "G\<turnstile>mdecl (s,mthd m) declared_in C"
schirmer@12854
   556
schirmer@12854
   557
lemma declared_in_classD:
schirmer@12854
   558
 "G\<turnstile>m declared_in C \<Longrightarrow> is_class G C"
schirmer@12854
   559
by (cases m) 
schirmer@12854
   560
   (auto simp add: declared_in_def cdeclaredmethd_def cdeclaredfield_def)
schirmer@12854
   561
schirmer@12854
   562
constdefs
schirmer@12854
   563
undeclared_in:: "prog  \<Rightarrow> memberid \<Rightarrow> qtname \<Rightarrow> bool"
schirmer@12854
   564
                                 ("_\<turnstile> _ undeclared'_in _" [61,61,61] 60)
schirmer@12854
   565
schirmer@12854
   566
"G\<turnstile>m undeclared_in C \<equiv> (case m of
schirmer@12854
   567
                            fid fn  \<Rightarrow> cdeclaredfield G C fn  = None
schirmer@12854
   568
                          | mid sig \<Rightarrow> cdeclaredmethd G C sig = None)"
schirmer@12854
   569
schirmer@12854
   570
lemma method_declared_inI:
schirmer@12854
   571
  "\<lbrakk>class G C = Some c; table_of (methods c) sig = Some m\<rbrakk> 
schirmer@12854
   572
   \<Longrightarrow> G\<turnstile>mdecl (sig,m) declared_in C"
schirmer@12854
   573
by (auto simp add: declared_in_def cdeclaredmethd_def)
schirmer@12854
   574
schirmer@12854
   575
schirmer@12854
   576
subsubsection "members"
schirmer@12854
   577
schirmer@12854
   578
consts
schirmer@12854
   579
members:: "prog \<Rightarrow> (qtname \<times> (qtname \<times> memberdecl)) set"
schirmer@12854
   580
(* Can't just take a function: prog \<Rightarrow> qtname \<Rightarrow> memberdecl set because
schirmer@12854
   581
   the class qtname changes to the superclass in the inductive definition
schirmer@12854
   582
   below
schirmer@12854
   583
*)
schirmer@12854
   584
schirmer@12854
   585
syntax
schirmer@12854
   586
member_of:: "prog \<Rightarrow> (qtname \<times> memberdecl) \<Rightarrow> qtname \<Rightarrow> bool"
schirmer@12854
   587
                           ("_ \<turnstile> _ member'_of _" [61,61,61] 60)
schirmer@12854
   588
schirmer@12854
   589
translations
schirmer@12854
   590
 "G\<turnstile>m member_of C" \<rightleftharpoons> "(C,m) \<in> members G"
schirmer@12854
   591
schirmer@12854
   592
inductive "members G"  intros
schirmer@12854
   593
schirmer@12854
   594
Immediate: "\<lbrakk>G\<turnstile>mbr m declared_in C;declclass m = C\<rbrakk> \<Longrightarrow> G\<turnstile>m member_of C"
schirmer@12854
   595
Inherited: "\<lbrakk>G\<turnstile>m inheritable_in (pid C); G\<turnstile>memberid m undeclared_in C; 
schirmer@12854
   596
             G\<turnstile>C \<prec>\<^sub>C\<^sub>1 S; G\<turnstile>(Class S) accessible_in (pid C);G\<turnstile>m member_of S 
schirmer@12854
   597
            \<rbrakk> \<Longrightarrow> G\<turnstile>m member_of C"
schirmer@12854
   598
text {* Note that in the case of an inherited member only the members of the
schirmer@12854
   599
direct superclass are concerned. If a member of a superclass of the direct
schirmer@12854
   600
superclass isn't inherited in the direct superclass (not member of the
schirmer@12854
   601
direct superclass) than it can't be a member of the class. E.g. If a
schirmer@12854
   602
member of a class A is defined with package access it isn't member of a 
schirmer@12854
   603
subclass S if S isn't in the same package as A. Any further subclasses 
schirmer@12854
   604
of S will not inherit the member, regardless if they are in the same
schirmer@12854
   605
package as A or not.*}
schirmer@12854
   606
schirmer@12854
   607
syntax
schirmer@12854
   608
method_member_of:: "prog \<Rightarrow> (qtname \<times> mdecl) \<Rightarrow> qtname \<Rightarrow> bool"
schirmer@12854
   609
                           ("_ \<turnstile>Method _ member'_of _" [61,61,61] 60)
schirmer@12854
   610
schirmer@12854
   611
translations
schirmer@12854
   612
 "G\<turnstile>Method m member_of C" \<rightleftharpoons> "G\<turnstile>(methdMembr m) member_of C" 
schirmer@12854
   613
schirmer@12854
   614
syntax
schirmer@12854
   615
methd_member_of:: "prog \<Rightarrow> sig \<Rightarrow> (qtname \<times> methd) \<Rightarrow> qtname \<Rightarrow> bool"
schirmer@12854
   616
                           ("_ \<turnstile>Methd _ _ member'_of _" [61,61,61,61] 60)
schirmer@12854
   617
schirmer@12854
   618
translations
schirmer@12854
   619
 "G\<turnstile>Methd s m member_of C" \<rightleftharpoons> "G\<turnstile>(method s m) member_of C" 
schirmer@12854
   620
schirmer@12854
   621
syntax
schirmer@12854
   622
fieldm_member_of:: "prog \<Rightarrow> vname \<Rightarrow> (qtname \<times> field) \<Rightarrow> qtname \<Rightarrow> bool"
schirmer@12854
   623
                           ("_ \<turnstile>Field _  _ member'_of _" [61,61,61] 60)
schirmer@12854
   624
schirmer@12854
   625
translations
schirmer@12854
   626
 "G\<turnstile>Field n f member_of C" \<rightleftharpoons> "G\<turnstile>fieldm n f member_of C" 
schirmer@12854
   627
schirmer@12854
   628
constdefs
schirmer@12854
   629
inherits:: "prog \<Rightarrow> qtname \<Rightarrow> (qtname \<times> memberdecl) \<Rightarrow> bool"
schirmer@12854
   630
                           ("_ \<turnstile> _ inherits _" [61,61,61] 60)
schirmer@12854
   631
"G\<turnstile>C inherits m 
schirmer@12854
   632
  \<equiv> G\<turnstile>m inheritable_in (pid C) \<and> G\<turnstile>memberid m undeclared_in C \<and> 
schirmer@12854
   633
    (\<exists> S. G\<turnstile>C \<prec>\<^sub>C\<^sub>1 S \<and> G\<turnstile>(Class S) accessible_in (pid C) \<and> G\<turnstile>m member_of S)"
schirmer@12854
   634
schirmer@12854
   635
lemma inherits_member: "G\<turnstile>C inherits m \<Longrightarrow> G\<turnstile>m member_of C"
schirmer@12854
   636
by (auto simp add: inherits_def intro: members.Inherited)
schirmer@12854
   637
schirmer@12854
   638
schirmer@12854
   639
constdefs member_in::"prog \<Rightarrow> (qtname \<times> memberdecl) \<Rightarrow> qtname \<Rightarrow> bool"
schirmer@12854
   640
                           ("_ \<turnstile> _ member'_in _" [61,61,61] 60)
schirmer@12854
   641
"G\<turnstile>m member_in C \<equiv> \<exists> provC. G\<turnstile> C \<preceq>\<^sub>C provC \<and> G \<turnstile> m member_of provC"
schirmer@12854
   642
text {* A member is in a class if it is member of the class or a superclass.
schirmer@12854
   643
If a member is in a class we can select this member. This additional notion
schirmer@12854
   644
is necessary since not all members are inherited to subclasses. So such
schirmer@12854
   645
members are not member-of the subclass but member-in the subclass.*}
schirmer@12854
   646
schirmer@12854
   647
syntax
schirmer@12854
   648
method_member_in:: "prog \<Rightarrow> (qtname \<times> mdecl) \<Rightarrow> qtname \<Rightarrow> bool"
schirmer@12854
   649
                           ("_ \<turnstile>Method _ member'_in _" [61,61,61] 60)
schirmer@12854
   650
schirmer@12854
   651
translations
schirmer@12854
   652
 "G\<turnstile>Method m member_in C" \<rightleftharpoons> "G\<turnstile>(methdMembr m) member_in C" 
schirmer@12854
   653
schirmer@12854
   654
syntax
schirmer@12854
   655
methd_member_in:: "prog \<Rightarrow> sig \<Rightarrow> (qtname \<times> methd) \<Rightarrow> qtname \<Rightarrow> bool"
schirmer@12854
   656
                           ("_ \<turnstile>Methd _ _ member'_in _" [61,61,61,61] 60)
schirmer@12854
   657
schirmer@12854
   658
translations
schirmer@12854
   659
 "G\<turnstile>Methd s m member_in C" \<rightleftharpoons> "G\<turnstile>(method s m) member_in C" 
schirmer@12854
   660
schirmer@12854
   661
consts stat_overridesR::
schirmer@12854
   662
  "prog  \<Rightarrow> ((qtname \<times> mdecl) \<times> (qtname \<times> mdecl)) set"
schirmer@12854
   663
schirmer@12854
   664
lemma member_inD: "G\<turnstile>m member_in C 
schirmer@12854
   665
 \<Longrightarrow> \<exists> provC. G\<turnstile> C \<preceq>\<^sub>C provC \<and> G \<turnstile> m member_of provC"
schirmer@12854
   666
by (auto simp add: member_in_def)
schirmer@12854
   667
schirmer@12854
   668
lemma member_inI: "\<lbrakk>G \<turnstile> m member_of provC;G\<turnstile> C \<preceq>\<^sub>C provC\<rbrakk> \<Longrightarrow>  G\<turnstile>m member_in C"
schirmer@12854
   669
by (auto simp add: member_in_def)
schirmer@12854
   670
schirmer@12854
   671
lemma member_of_to_member_in: "G \<turnstile> m member_of C \<Longrightarrow> G \<turnstile>m member_in C"
schirmer@12854
   672
by (auto intro: member_inI)
schirmer@12854
   673
schirmer@12854
   674
schirmer@12854
   675
subsubsection "overriding"
schirmer@12854
   676
schirmer@12854
   677
text {* Unfortunately the static notion of overriding (used during the
schirmer@12854
   678
typecheck of the compiler) and the dynamic notion of overriding (used during
schirmer@12854
   679
execution in the JVM) are not exactly the same. 
schirmer@12854
   680
*}
schirmer@12854
   681
schirmer@12854
   682
text {* Static overriding (used during the typecheck of the compiler) *}
schirmer@12854
   683
syntax
schirmer@12854
   684
stat_overrides:: "prog  \<Rightarrow> (qtname \<times> mdecl) \<Rightarrow> (qtname \<times> mdecl) \<Rightarrow> bool" 
schirmer@12854
   685
                                  ("_ \<turnstile> _ overrides\<^sub>S _" [61,61,61] 60)
schirmer@12854
   686
translations
schirmer@12854
   687
 "G\<turnstile>new overrides\<^sub>S  old" == "(new,old) \<in> stat_overridesR G "
schirmer@12854
   688
schirmer@12854
   689
inductive "stat_overridesR G" intros
schirmer@12854
   690
schirmer@12854
   691
Direct: "\<lbrakk>\<not> is_static new; msig new = msig old; 
schirmer@12854
   692
         G\<turnstile>(declclass new) \<prec>\<^sub>C (declclass old);
schirmer@12854
   693
         G\<turnstile>Method new declared_in (declclass new);  
schirmer@12854
   694
         G\<turnstile>Method old declared_in (declclass old); 
schirmer@12854
   695
         G\<turnstile>Method old inheritable_in pid (declclass new);
schirmer@12854
   696
         G\<turnstile>(declclass new) \<prec>\<^sub>C\<^sub>1 superNew;
schirmer@12854
   697
         G \<turnstile>Method old member_of superNew
schirmer@12854
   698
         \<rbrakk> \<Longrightarrow> G\<turnstile>new overrides\<^sub>S old"
schirmer@12854
   699
schirmer@12854
   700
Indirect: "\<lbrakk>G\<turnstile>new overrides\<^sub>S inter; G\<turnstile>inter overrides\<^sub>S old\<rbrakk>
schirmer@12854
   701
           \<Longrightarrow> G\<turnstile>new overrides\<^sub>S old"
schirmer@12854
   702
schirmer@12854
   703
text {* Dynamic overriding (used during the typecheck of the compiler) *}
schirmer@12854
   704
consts overridesR::
schirmer@12854
   705
  "prog  \<Rightarrow> ((qtname \<times> mdecl) \<times> (qtname \<times> mdecl)) set"
schirmer@12854
   706
schirmer@12854
   707
schirmer@12854
   708
overrides:: "prog  \<Rightarrow> (qtname \<times> mdecl) \<Rightarrow> (qtname \<times> mdecl) \<Rightarrow> bool" 
schirmer@12854
   709
                                  ("_ \<turnstile> _ overrides _" [61,61,61] 60)
schirmer@12854
   710
translations
schirmer@12854
   711
 "G\<turnstile>new overrides old" == "(new,old) \<in> overridesR G "
schirmer@12854
   712
schirmer@12854
   713
inductive "overridesR G" intros
schirmer@12854
   714
schirmer@12854
   715
Direct: "\<lbrakk>\<not> is_static new; \<not> is_static old; accmodi new \<noteq> Private;
schirmer@12854
   716
         msig new = msig old; 
schirmer@12854
   717
         G\<turnstile>(declclass new) \<prec>\<^sub>C (declclass old);
schirmer@12854
   718
         G\<turnstile>Method new declared_in (declclass new);  
schirmer@12854
   719
         G\<turnstile>Method old declared_in (declclass old);    
schirmer@12854
   720
         G\<turnstile>Method old inheritable_in pid (declclass new);
schirmer@12854
   721
         G\<turnstile>resTy new \<preceq> resTy old
schirmer@12854
   722
         \<rbrakk> \<Longrightarrow> G\<turnstile>new overrides old"
schirmer@12854
   723
schirmer@12854
   724
Indirect: "\<lbrakk>G\<turnstile>new overrides inter; G\<turnstile>inter overrides old\<rbrakk>
schirmer@12854
   725
           \<Longrightarrow> G\<turnstile>new overrides old"
schirmer@12854
   726
schirmer@12854
   727
syntax
schirmer@12854
   728
sig_stat_overrides:: 
schirmer@12854
   729
 "prog  \<Rightarrow> sig \<Rightarrow> (qtname \<times> methd) \<Rightarrow> (qtname \<times> methd) \<Rightarrow> bool" 
schirmer@12854
   730
                                  ("_,_\<turnstile> _ overrides\<^sub>S _" [61,61,61,61] 60)
schirmer@12854
   731
translations
schirmer@12854
   732
 "G,s\<turnstile>new overrides\<^sub>S old" \<rightharpoonup> "G\<turnstile>(qmdecl s new) overrides\<^sub>S (qmdecl s old)" 
schirmer@12854
   733
schirmer@12854
   734
syntax
schirmer@12854
   735
sig_overrides:: "prog  \<Rightarrow> sig \<Rightarrow> (qtname \<times> methd) \<Rightarrow> (qtname \<times> methd) \<Rightarrow> bool" 
schirmer@12854
   736
                                  ("_,_\<turnstile> _ overrides _" [61,61,61,61] 60)
schirmer@12854
   737
translations
schirmer@12854
   738
 "G,s\<turnstile>new overrides old" \<rightharpoonup> "G\<turnstile>(qmdecl s new) overrides (qmdecl s old)" 
schirmer@12854
   739
schirmer@12854
   740
subsubsection "Hiding"
schirmer@12854
   741
schirmer@12854
   742
constdefs hides::
schirmer@12854
   743
"prog \<Rightarrow> (qtname \<times> mdecl) \<Rightarrow> (qtname \<times> mdecl) \<Rightarrow> bool" 
schirmer@12854
   744
                                ("_\<turnstile> _ hides _" [61,61,61] 60)
schirmer@12854
   745
"G\<turnstile>new hides old
schirmer@12854
   746
  \<equiv> is_static new \<and> msig new = msig old \<and>
schirmer@12854
   747
    G\<turnstile>(declclass new) \<prec>\<^sub>C (declclass old) \<and>
schirmer@12854
   748
    G\<turnstile>Method new declared_in (declclass new) \<and>
schirmer@12854
   749
    G\<turnstile>Method old declared_in (declclass old) \<and> 
schirmer@12854
   750
    G\<turnstile>Method old inheritable_in pid (declclass new)"
schirmer@12854
   751
schirmer@12854
   752
syntax
schirmer@12854
   753
sig_hides:: "prog  \<Rightarrow> sig \<Rightarrow> (qtname \<times> mdecl) \<Rightarrow> (qtname \<times> mdecl) \<Rightarrow> bool" 
schirmer@12854
   754
                                  ("_,_\<turnstile> _ hides _" [61,61,61,61] 60)
schirmer@12854
   755
translations
schirmer@12854
   756
 "G,s\<turnstile>new hides old" \<rightharpoonup> "G\<turnstile>(qmdecl s new) hides (qmdecl s old)" 
schirmer@12854
   757
schirmer@12854
   758
lemma hidesI:
schirmer@12854
   759
"\<lbrakk>is_static new; msig new = msig old;
schirmer@12854
   760
  G\<turnstile>(declclass new) \<prec>\<^sub>C (declclass old);
schirmer@12854
   761
  G\<turnstile>Method new declared_in (declclass new);
schirmer@12854
   762
  G\<turnstile>Method old declared_in (declclass old);
schirmer@12854
   763
  G\<turnstile>Method old inheritable_in pid (declclass new)
schirmer@12854
   764
 \<rbrakk> \<Longrightarrow> G\<turnstile>new hides old"
schirmer@12854
   765
by (auto simp add: hides_def)
schirmer@12854
   766
schirmer@12854
   767
lemma hidesD:
schirmer@12854
   768
"\<lbrakk>G\<turnstile>new hides old\<rbrakk> \<Longrightarrow>  
schirmer@12854
   769
  declclass new \<noteq> Object \<and> is_static new \<and> msig new = msig old \<and> 
schirmer@12854
   770
  G\<turnstile>(declclass new) \<prec>\<^sub>C (declclass old) \<and>
schirmer@12854
   771
  G\<turnstile>Method new declared_in (declclass new) \<and>   
schirmer@12854
   772
  G\<turnstile>Method old declared_in (declclass old)"
schirmer@12854
   773
by (auto simp add: hides_def)
schirmer@12854
   774
schirmer@12854
   775
lemma overrides_commonD:
schirmer@12854
   776
"\<lbrakk>G\<turnstile>new overrides old\<rbrakk> \<Longrightarrow>  
schirmer@12854
   777
  declclass new \<noteq> Object \<and> \<not> is_static new \<and> \<not> is_static old \<and>
schirmer@12854
   778
  accmodi new \<noteq> Private \<and> 
schirmer@12854
   779
  msig new = msig old  \<and>
schirmer@12854
   780
  G\<turnstile>(declclass new) \<prec>\<^sub>C (declclass old) \<and>
schirmer@12854
   781
  G\<turnstile>Method new declared_in (declclass new) \<and>   
schirmer@12854
   782
  G\<turnstile>Method old declared_in (declclass old)"
schirmer@12854
   783
by (induct set: overridesR) (auto intro: trancl_trans)
schirmer@12854
   784
schirmer@12854
   785
lemma ws_overrides_commonD:
schirmer@12854
   786
"\<lbrakk>G\<turnstile>new overrides old;ws_prog G\<rbrakk> \<Longrightarrow>  
schirmer@12854
   787
  declclass new \<noteq> Object \<and> \<not> is_static new \<and> \<not> is_static old \<and>
schirmer@12854
   788
  accmodi new \<noteq> Private \<and> G\<turnstile>resTy new \<preceq> resTy old \<and>
schirmer@12854
   789
  msig new = msig old  \<and>
schirmer@12854
   790
  G\<turnstile>(declclass new) \<prec>\<^sub>C (declclass old) \<and>
schirmer@12854
   791
  G\<turnstile>Method new declared_in (declclass new) \<and>   
schirmer@12854
   792
  G\<turnstile>Method old declared_in (declclass old)"
schirmer@12854
   793
by (induct set: overridesR) (auto intro: trancl_trans ws_widen_trans)
schirmer@12854
   794
schirmer@12854
   795
lemma stat_overrides_commonD:
schirmer@12854
   796
"\<lbrakk>G\<turnstile>new overrides\<^sub>S old\<rbrakk> \<Longrightarrow>  
schirmer@12854
   797
  declclass new \<noteq> Object \<and> \<not> is_static new \<and> msig new = msig old \<and> 
schirmer@12854
   798
  G\<turnstile>(declclass new) \<prec>\<^sub>C (declclass old) \<and>
schirmer@12854
   799
  G\<turnstile>Method new declared_in (declclass new) \<and>   
schirmer@12854
   800
  G\<turnstile>Method old declared_in (declclass old)"
schirmer@12854
   801
by (induct set: stat_overridesR) (auto intro: trancl_trans)
schirmer@12854
   802
schirmer@12854
   803
lemma overrides_eq_sigD: 
schirmer@12854
   804
 "\<lbrakk>G\<turnstile>new overrides old\<rbrakk> \<Longrightarrow> msig old=msig new"
schirmer@12854
   805
by (auto dest: overrides_commonD)
schirmer@12854
   806
schirmer@12854
   807
lemma hides_eq_sigD: 
schirmer@12854
   808
 "\<lbrakk>G\<turnstile>new hides old\<rbrakk> \<Longrightarrow> msig old=msig new"
schirmer@12854
   809
by (auto simp add: hides_def)
schirmer@12854
   810
schirmer@12854
   811
subsubsection "permits access" 
schirmer@12854
   812
constdefs 
schirmer@12854
   813
permits_acc:: 
schirmer@12854
   814
 "prog \<Rightarrow> (qtname \<times> memberdecl) \<Rightarrow> qtname \<Rightarrow> qtname \<Rightarrow> bool"
schirmer@12854
   815
                   ("_ \<turnstile> _ in _ permits'_acc'_to _" [61,61,61,61] 60)
schirmer@12854
   816
schirmer@12854
   817
"G\<turnstile>membr in class permits_acc_to accclass 
schirmer@12854
   818
  \<equiv> (case (accmodi membr) of
schirmer@12854
   819
       Private   \<Rightarrow> (declclass membr = accclass)
schirmer@12854
   820
     | Package   \<Rightarrow> (pid (declclass membr) = pid accclass)
schirmer@12854
   821
     | Protected \<Rightarrow> (pid (declclass membr) = pid accclass)
schirmer@12854
   822
                    \<or>
schirmer@12925
   823
                    (G\<turnstile>accclass \<prec>\<^sub>C declclass membr 
schirmer@12925
   824
                     \<and> (G\<turnstile>class \<preceq>\<^sub>C accclass \<or> is_static membr)) 
schirmer@12854
   825
     | Public    \<Rightarrow> True)"
schirmer@12854
   826
text {*
schirmer@12854
   827
The subcondition of the @{term "Protected"} case: 
schirmer@12854
   828
@{term "G\<turnstile>accclass \<prec>\<^sub>C declclass membr"} could also be relaxed to:
schirmer@12854
   829
@{term "G\<turnstile>accclass \<preceq>\<^sub>C declclass membr"} since in case both classes are the
schirmer@12854
   830
same the other condition @{term "(pid (declclass membr) = pid accclass)"}
schirmer@12854
   831
holds anyway.
schirmer@12854
   832
*} 
schirmer@12854
   833
schirmer@12854
   834
text {* Like in case of overriding, the static and dynamic accessibility 
schirmer@12854
   835
of members is not uniform.
schirmer@12854
   836
\begin{itemize}
schirmer@12854
   837
\item Statically the class/interface of the member must be accessible for the
schirmer@12854
   838
      member to be accessible. During runtime this is not necessary. For
schirmer@12854
   839
      Example, if a class is accessible and we are allowed to access a member
schirmer@12854
   840
      of this class (statically) we expect that we can access this member in 
schirmer@12854
   841
      an arbitrary subclass (during runtime). It's not intended to restrict
schirmer@12854
   842
      the access to accessible subclasses during runtime.
schirmer@12854
   843
\item Statically the member we want to access must be "member of" the class.
schirmer@12854
   844
      Dynamically it must only be "member in" the class.
schirmer@12854
   845
\end{itemize} 
schirmer@12854
   846
*} 
schirmer@12854
   847
schirmer@12854
   848
schirmer@12854
   849
consts
schirmer@12854
   850
accessible_fromR:: 
schirmer@12854
   851
 "prog \<Rightarrow> qtname \<Rightarrow> ((qtname \<times> memberdecl) \<times>  qtname) set"
schirmer@12854
   852
schirmer@12854
   853
syntax 
schirmer@12854
   854
accessible_from:: 
schirmer@12854
   855
 "prog \<Rightarrow> (qtname \<times> memberdecl) \<Rightarrow> qtname \<Rightarrow> qtname \<Rightarrow> bool"
schirmer@12854
   856
                   ("_ \<turnstile> _ of _ accessible'_from _" [61,61,61,61] 60)
schirmer@12854
   857
schirmer@12854
   858
translations
schirmer@12854
   859
"G\<turnstile>membr of cls accessible_from accclass"  
schirmer@12854
   860
 \<rightleftharpoons> "(membr,cls) \<in> accessible_fromR G accclass"
schirmer@12854
   861
schirmer@12854
   862
syntax 
schirmer@12854
   863
method_accessible_from:: 
schirmer@12854
   864
 "prog \<Rightarrow> (qtname \<times> mdecl) \<Rightarrow> qtname \<Rightarrow> qtname \<Rightarrow> bool"
schirmer@12854
   865
                   ("_ \<turnstile>Method _ of _ accessible'_from _" [61,61,61,61] 60)
schirmer@12854
   866
schirmer@12854
   867
translations
schirmer@12854
   868
"G\<turnstile>Method m of cls accessible_from accclass"  
schirmer@12854
   869
 \<rightleftharpoons> "G\<turnstile>methdMembr m of cls accessible_from accclass"  
schirmer@12854
   870
schirmer@12854
   871
syntax 
schirmer@12854
   872
methd_accessible_from:: 
schirmer@12854
   873
 "prog \<Rightarrow> sig \<Rightarrow> (qtname \<times> methd) \<Rightarrow> qtname \<Rightarrow> qtname \<Rightarrow> bool"
schirmer@12854
   874
                 ("_ \<turnstile>Methd _ _ of _ accessible'_from _" [61,61,61,61,61] 60)
schirmer@12854
   875
schirmer@12854
   876
translations
schirmer@12854
   877
"G\<turnstile>Methd s m of cls accessible_from accclass"  
schirmer@12854
   878
 \<rightleftharpoons> "G\<turnstile>(method s m) of cls accessible_from accclass"  
schirmer@12854
   879
schirmer@12854
   880
syntax 
schirmer@12854
   881
field_accessible_from:: 
schirmer@12854
   882
 "prog \<Rightarrow> vname \<Rightarrow> (qtname \<times> field) \<Rightarrow> qtname \<Rightarrow> qtname \<Rightarrow> bool"
schirmer@12854
   883
                 ("_ \<turnstile>Field _  _ of _ accessible'_from _" [61,61,61,61,61] 60)
schirmer@12854
   884
schirmer@12854
   885
translations
schirmer@12854
   886
"G\<turnstile>Field fn f of C accessible_from accclass"  
schirmer@12854
   887
 \<rightleftharpoons> "G\<turnstile>(fieldm fn f) of C accessible_from accclass" 
schirmer@12854
   888
schirmer@12854
   889
inductive "accessible_fromR G accclass" intros
schirmer@12925
   890
Immediate:  "\<lbrakk>G\<turnstile>membr member_of class;
schirmer@12854
   891
              G\<turnstile>(Class class) accessible_in (pid accclass);
schirmer@12854
   892
              G\<turnstile>membr in class permits_acc_to accclass 
schirmer@12854
   893
             \<rbrakk> \<Longrightarrow> G\<turnstile>membr of class accessible_from accclass"
schirmer@12854
   894
schirmer@12925
   895
Overriding: "\<lbrakk>G\<turnstile>membr member_of class;
schirmer@12854
   896
              G\<turnstile>(Class class) accessible_in (pid accclass);
schirmer@12854
   897
              membr=(C,mdecl new);
schirmer@12854
   898
              G\<turnstile>(C,new) overrides\<^sub>S old; 
schirmer@12854
   899
              G\<turnstile>class \<prec>\<^sub>C sup;
schirmer@12854
   900
              G\<turnstile>Method old of sup accessible_from accclass
schirmer@12854
   901
             \<rbrakk>\<Longrightarrow> G\<turnstile>membr of class accessible_from accclass"
schirmer@12854
   902
schirmer@12854
   903
consts
schirmer@12854
   904
dyn_accessible_fromR:: 
schirmer@12854
   905
 "prog \<Rightarrow> qtname \<Rightarrow> ((qtname \<times> memberdecl) \<times>  qtname) set"
schirmer@12854
   906
schirmer@12854
   907
syntax 
schirmer@12854
   908
dyn_accessible_from:: 
schirmer@12854
   909
 "prog \<Rightarrow> (qtname \<times> memberdecl) \<Rightarrow> qtname \<Rightarrow> qtname \<Rightarrow> bool"
schirmer@12854
   910
                   ("_ \<turnstile> _ in _ dyn'_accessible'_from _" [61,61,61,61] 60)
schirmer@12854
   911
schirmer@12854
   912
translations
schirmer@12854
   913
"G\<turnstile>membr in C dyn_accessible_from accC"  
schirmer@12854
   914
 \<rightleftharpoons> "(membr,C) \<in> dyn_accessible_fromR G accC"
schirmer@12854
   915
schirmer@12854
   916
syntax 
schirmer@12854
   917
method_dyn_accessible_from:: 
schirmer@12854
   918
 "prog \<Rightarrow> (qtname \<times> mdecl) \<Rightarrow> qtname \<Rightarrow> qtname \<Rightarrow> bool"
schirmer@12854
   919
                 ("_ \<turnstile>Method _ in _ dyn'_accessible'_from _" [61,61,61,61] 60)
schirmer@12854
   920
schirmer@12854
   921
translations
schirmer@12854
   922
"G\<turnstile>Method m in C dyn_accessible_from accC"  
schirmer@12854
   923
 \<rightleftharpoons> "G\<turnstile>methdMembr m in C dyn_accessible_from accC"  
schirmer@12854
   924
schirmer@12854
   925
syntax 
schirmer@12854
   926
methd_dyn_accessible_from:: 
schirmer@12854
   927
 "prog \<Rightarrow> sig \<Rightarrow> (qtname \<times> methd) \<Rightarrow> qtname \<Rightarrow> qtname \<Rightarrow> bool"
schirmer@12854
   928
             ("_ \<turnstile>Methd _ _ in _ dyn'_accessible'_from _" [61,61,61,61,61] 60)
schirmer@12854
   929
schirmer@12854
   930
translations
schirmer@12854
   931
"G\<turnstile>Methd s m in C dyn_accessible_from accC"  
schirmer@12854
   932
 \<rightleftharpoons> "G\<turnstile>(method s m) in C dyn_accessible_from accC"  
schirmer@12854
   933
schirmer@12854
   934
syntax 
schirmer@12854
   935
field_dyn_accessible_from:: 
schirmer@12854
   936
 "prog \<Rightarrow> vname \<Rightarrow> (qtname \<times> field) \<Rightarrow> qtname \<Rightarrow> qtname \<Rightarrow> bool"
schirmer@12854
   937
         ("_ \<turnstile>Field _ _ in _ dyn'_accessible'_from _" [61,61,61,61,61] 60)
schirmer@12854
   938
schirmer@12854
   939
translations
schirmer@12854
   940
"G\<turnstile>Field fn f in dynC dyn_accessible_from accC"  
schirmer@12854
   941
 \<rightleftharpoons> "G\<turnstile>(fieldm fn f) in dynC dyn_accessible_from accC"
schirmer@12854
   942
  
schirmer@12854
   943
inductive "dyn_accessible_fromR G accclass" intros
schirmer@12925
   944
Immediate:  "\<lbrakk>G\<turnstile>membr member_in class;
schirmer@12854
   945
              G\<turnstile>membr in class permits_acc_to accclass 
schirmer@12854
   946
             \<rbrakk> \<Longrightarrow> G\<turnstile>membr in class dyn_accessible_from accclass"
schirmer@12854
   947
schirmer@12925
   948
Overriding: "\<lbrakk>G\<turnstile>membr member_in class;
schirmer@12854
   949
              membr=(C,mdecl new);
schirmer@12854
   950
              G\<turnstile>(C,new) overrides old; 
schirmer@12854
   951
              G\<turnstile>class \<prec>\<^sub>C sup;
schirmer@12854
   952
              G\<turnstile>Method old in sup dyn_accessible_from accclass
schirmer@12854
   953
             \<rbrakk>\<Longrightarrow> G\<turnstile>membr in class dyn_accessible_from accclass"
schirmer@12854
   954
schirmer@12854
   955
schirmer@12854
   956
lemma accessible_from_commonD: "G\<turnstile>m of C accessible_from S
schirmer@12854
   957
 \<Longrightarrow> G\<turnstile>m member_of C \<and> G\<turnstile>(Class C) accessible_in (pid S)"
schirmer@12854
   958
by (auto elim: accessible_fromR.induct)
schirmer@12854
   959
schirmer@12925
   960
lemma unique_declaration: 
schirmer@12925
   961
 "\<lbrakk>G\<turnstile>m declared_in C;  G\<turnstile>n declared_in C; memberid m = memberid n \<rbrakk> 
schirmer@12925
   962
  \<Longrightarrow> m = n"
schirmer@12925
   963
apply (cases m)
schirmer@12925
   964
apply (cases n,
schirmer@12925
   965
        auto simp add: declared_in_def cdeclaredmethd_def cdeclaredfield_def)+
schirmer@12925
   966
done
schirmer@12925
   967
schirmer@12854
   968
lemma declared_not_undeclared:
schirmer@12854
   969
  "G\<turnstile>m declared_in C \<Longrightarrow> \<not> G\<turnstile> memberid m undeclared_in C"
schirmer@12854
   970
by (cases m) (auto simp add: declared_in_def undeclared_in_def)
schirmer@12854
   971
schirmer@12925
   972
lemma undeclared_not_declared:
schirmer@12925
   973
 "G\<turnstile> memberid m undeclared_in C \<Longrightarrow> \<not> G\<turnstile> m declared_in C" 
schirmer@12925
   974
by (cases m) (auto simp add: declared_in_def undeclared_in_def)
schirmer@12925
   975
schirmer@12854
   976
lemma not_undeclared_declared:
schirmer@12854
   977
  "\<not> G\<turnstile> membr_id undeclared_in C \<Longrightarrow> (\<exists> m. G\<turnstile>m declared_in C \<and> 
schirmer@12854
   978
                                           membr_id = memberid m)"
schirmer@12854
   979
proof -
schirmer@12854
   980
  assume not_undecl:"\<not> G\<turnstile> membr_id undeclared_in C"
schirmer@12854
   981
  show ?thesis (is "?P membr_id")
schirmer@12854
   982
  proof (cases membr_id)
schirmer@12854
   983
    case (fid vname)
schirmer@12854
   984
    with not_undecl
schirmer@12854
   985
    obtain fld where
schirmer@12854
   986
      "G\<turnstile>fdecl (vname,fld) declared_in C" 
schirmer@12854
   987
      by (auto simp add: undeclared_in_def declared_in_def
schirmer@12854
   988
                         cdeclaredfield_def)
schirmer@12854
   989
    with fid show ?thesis 
schirmer@12854
   990
      by auto
schirmer@12854
   991
  next
schirmer@12854
   992
    case (mid sig)
schirmer@12854
   993
    with not_undecl
schirmer@12854
   994
    obtain mthd where
schirmer@12854
   995
      "G\<turnstile>mdecl (sig,mthd) declared_in C" 
schirmer@12854
   996
      by (auto simp add: undeclared_in_def declared_in_def
schirmer@12854
   997
                         cdeclaredmethd_def)
schirmer@12854
   998
    with mid show ?thesis 
schirmer@12854
   999
      by auto
schirmer@12854
  1000
  qed
schirmer@12854
  1001
qed
schirmer@12854
  1002
schirmer@12854
  1003
lemma unique_declared_in:
schirmer@12854
  1004
 "\<lbrakk>G\<turnstile>m declared_in C; G\<turnstile>n declared_in C; memberid m = memberid n\<rbrakk>
schirmer@12854
  1005
 \<Longrightarrow> m = n"
schirmer@12854
  1006
by (auto simp add: declared_in_def cdeclaredmethd_def cdeclaredfield_def
schirmer@12854
  1007
            split: memberdecl.splits)
schirmer@12854
  1008
schirmer@12854
  1009
lemma unique_member_of: 
schirmer@12854
  1010
 (assumes n: "G\<turnstile>n member_of C" and  
schirmer@12854
  1011
          m: "G\<turnstile>m member_of C" and
schirmer@12854
  1012
       eqid: "memberid n = memberid m"
schirmer@12854
  1013
 ) "n=m"
schirmer@12854
  1014
proof -
schirmer@12854
  1015
  from n m eqid  
schirmer@12854
  1016
  show "n=m"
schirmer@12854
  1017
  proof (induct)
schirmer@12854
  1018
    case (Immediate C n)
schirmer@12854
  1019
    assume member_n: "G\<turnstile> mbr n declared_in C" "declclass n = C"
schirmer@12854
  1020
    assume eqid: "memberid n = memberid m"
schirmer@12854
  1021
    assume "G \<turnstile> m member_of C"
schirmer@12854
  1022
    then show "n=m"
schirmer@12854
  1023
    proof (cases)
schirmer@12854
  1024
      case (Immediate _ m')
schirmer@12854
  1025
      with eqid 
schirmer@12854
  1026
      have "m=m'"
schirmer@12854
  1027
           "memberid n = memberid m" 
schirmer@12854
  1028
           "G\<turnstile> mbr m declared_in C" 
schirmer@12854
  1029
           "declclass m = C"
schirmer@12854
  1030
	by auto
schirmer@12854
  1031
      with member_n   
schirmer@12854
  1032
      show ?thesis
schirmer@12854
  1033
	by (cases n, cases m) 
schirmer@12854
  1034
           (auto simp add: declared_in_def 
schirmer@12854
  1035
                           cdeclaredmethd_def cdeclaredfield_def
schirmer@12854
  1036
                    split: memberdecl.splits)
schirmer@12854
  1037
    next
schirmer@12854
  1038
      case (Inherited _ _ m')
schirmer@12854
  1039
      then have "G\<turnstile> memberid m undeclared_in C"
schirmer@12854
  1040
	by simp
schirmer@12854
  1041
      with eqid member_n
schirmer@12854
  1042
      show ?thesis
schirmer@12854
  1043
	by (cases n) (auto dest: declared_not_undeclared)
schirmer@12854
  1044
    qed
schirmer@12854
  1045
  next
schirmer@12854
  1046
    case (Inherited C S n)
schirmer@12854
  1047
    assume undecl: "G\<turnstile> memberid n undeclared_in C"
schirmer@12854
  1048
    assume  super: "G\<turnstile>C\<prec>\<^sub>C\<^sub>1S"
schirmer@12854
  1049
    assume    hyp: "\<lbrakk>G \<turnstile> m member_of S; memberid n = memberid m\<rbrakk> \<Longrightarrow> n = m"
schirmer@12854
  1050
    assume   eqid: "memberid n = memberid m"
schirmer@12854
  1051
    assume "G \<turnstile> m member_of C"
schirmer@12854
  1052
    then show "n=m"
schirmer@12854
  1053
    proof (cases)
schirmer@12854
  1054
      case Immediate
schirmer@12854
  1055
      then have "G\<turnstile> mbr m declared_in C" by simp
schirmer@12854
  1056
      with eqid undecl
schirmer@12854
  1057
      show ?thesis
schirmer@12854
  1058
	by (cases m) (auto dest: declared_not_undeclared)
schirmer@12854
  1059
    next
schirmer@12854
  1060
      case Inherited 
schirmer@12854
  1061
      with super have "G \<turnstile> m member_of S"
schirmer@12854
  1062
	by (auto dest!: subcls1D)
schirmer@12854
  1063
      with eqid hyp
schirmer@12854
  1064
      show ?thesis 
schirmer@12854
  1065
	by blast
schirmer@12854
  1066
    qed
schirmer@12854
  1067
  qed
schirmer@12854
  1068
qed
schirmer@12854
  1069
schirmer@12854
  1070
lemma member_of_is_classD: "G\<turnstile>m member_of C \<Longrightarrow> is_class G C"
schirmer@12854
  1071
proof (induct set: members)
schirmer@12854
  1072
  case (Immediate C m)
schirmer@12854
  1073
  assume "G\<turnstile> mbr m declared_in C"
schirmer@12854
  1074
  then show "is_class G C"
schirmer@12854
  1075
    by (cases "mbr m")
schirmer@12854
  1076
       (auto simp add: declared_in_def cdeclaredmethd_def cdeclaredfield_def)
schirmer@12854
  1077
next
schirmer@12854
  1078
  case (Inherited C S m)  
schirmer@12854
  1079
  assume "G\<turnstile>C\<prec>\<^sub>C\<^sub>1S" and "is_class G S"
schirmer@12854
  1080
  then show "is_class G C"
schirmer@12854
  1081
    by - (rule subcls_is_class2,auto)
schirmer@12854
  1082
qed
schirmer@12854
  1083
schirmer@12854
  1084
lemma member_of_declC: 
schirmer@12854
  1085
 "G\<turnstile>m member_of C 
schirmer@12854
  1086
  \<Longrightarrow> G\<turnstile>mbr m declared_in (declclass m)"
schirmer@12854
  1087
by (induct set: members) auto
schirmer@12854
  1088
schirmer@12854
  1089
lemma member_of_member_of_declC:
schirmer@12854
  1090
 "G\<turnstile>m member_of C 
schirmer@12854
  1091
  \<Longrightarrow> G\<turnstile>m member_of (declclass m)"
schirmer@12854
  1092
by (auto dest: member_of_declC intro: members.Immediate)
schirmer@12854
  1093
schirmer@12854
  1094
lemma member_of_class_relation:
schirmer@12854
  1095
  "G\<turnstile>m member_of C \<Longrightarrow> G\<turnstile>C \<preceq>\<^sub>C declclass m"
schirmer@12854
  1096
proof (induct set: members)
schirmer@12854
  1097
  case (Immediate C m)
schirmer@12854
  1098
  then show "G\<turnstile>C \<preceq>\<^sub>C declclass m" by simp
schirmer@12854
  1099
next
schirmer@12854
  1100
  case (Inherited C S m)
schirmer@12854
  1101
  then show "G\<turnstile>C \<preceq>\<^sub>C declclass m" 
schirmer@12854
  1102
    by (auto dest: r_into_rtrancl intro: rtrancl_trans)
schirmer@12854
  1103
qed
schirmer@12854
  1104
schirmer@12854
  1105
lemma member_in_class_relation:
schirmer@12854
  1106
  "G\<turnstile>m member_in C \<Longrightarrow> G\<turnstile>C \<preceq>\<^sub>C declclass m"
schirmer@12854
  1107
by (auto dest: member_inD member_of_class_relation
schirmer@12854
  1108
        intro: rtrancl_trans)
schirmer@12854
  1109
schirmer@12854
  1110
lemma member_of_Package: 
schirmer@12854
  1111
 "\<lbrakk>G\<turnstile>m member_of C; accmodi m = Package\<rbrakk> 
schirmer@12854
  1112
  \<Longrightarrow> pid (declclass m) = pid C" 
schirmer@12854
  1113
proof -
schirmer@12854
  1114
  assume   member: "G\<turnstile>m member_of C"
schirmer@12854
  1115
  then show " accmodi m = Package \<Longrightarrow> ?thesis" (is "PROP ?P m C")
schirmer@12854
  1116
  proof (induct rule: members.induct)
schirmer@12854
  1117
    fix C m
schirmer@12854
  1118
    assume     C: "declclass m = C"
schirmer@12854
  1119
    then show "pid (declclass m) = pid C"
schirmer@12854
  1120
      by simp
schirmer@12854
  1121
  next
schirmer@12854
  1122
    fix C S m  
schirmer@12854
  1123
    assume inheritable: "G \<turnstile> m inheritable_in pid C"
schirmer@12854
  1124
    assume         hyp: "PROP ?P m S" and
schirmer@12854
  1125
           package_acc: "accmodi m = Package" 
schirmer@12854
  1126
    with inheritable package_acc hyp
schirmer@12854
  1127
    show "pid (declclass m) = pid C" 
schirmer@12854
  1128
      by (auto simp add: inheritable_in_def)
schirmer@12854
  1129
  qed
schirmer@12854
  1130
qed
schirmer@12854
  1131
schirmer@12925
  1132
lemma member_in_declC: "G\<turnstile>m member_in C\<Longrightarrow> G\<turnstile>m member_in (declclass m)"
schirmer@12925
  1133
proof -
schirmer@12925
  1134
  assume member_in_C:  "G\<turnstile>m member_in C"
schirmer@12925
  1135
  from member_in_C
schirmer@12925
  1136
  obtain provC where
schirmer@12925
  1137
    subclseq_C_provC: "G\<turnstile> C \<preceq>\<^sub>C provC" and
schirmer@12925
  1138
     member_of_provC: "G \<turnstile> m member_of provC"
schirmer@12925
  1139
    by (auto simp add: member_in_def)
schirmer@12925
  1140
  from member_of_provC
schirmer@12925
  1141
  have "G \<turnstile> m member_of declclass m"
schirmer@12925
  1142
    by (rule member_of_member_of_declC)
schirmer@12925
  1143
  moreover
schirmer@12925
  1144
  from member_in_C
schirmer@12925
  1145
  have "G\<turnstile>C \<preceq>\<^sub>C declclass m"
schirmer@12925
  1146
    by (rule member_in_class_relation)
schirmer@12925
  1147
  ultimately
schirmer@12925
  1148
  show ?thesis
schirmer@12925
  1149
    by (auto simp add: member_in_def)
schirmer@12925
  1150
qed
schirmer@12925
  1151
schirmer@12854
  1152
lemma dyn_accessible_from_commonD: "G\<turnstile>m in C dyn_accessible_from S
schirmer@12854
  1153
 \<Longrightarrow> G\<turnstile>m member_in C"
schirmer@12854
  1154
by (auto elim: dyn_accessible_fromR.induct)
schirmer@12854
  1155
schirmer@12854
  1156
lemma no_Private_stat_override: 
schirmer@12854
  1157
 "\<lbrakk>G\<turnstile>new overrides\<^sub>S old\<rbrakk> \<Longrightarrow> accmodi old \<noteq> Private"
schirmer@12854
  1158
by (induct set:  stat_overridesR) (auto simp add: inheritable_in_def)
schirmer@12854
  1159
schirmer@12854
  1160
lemma no_Private_override: "\<lbrakk>G\<turnstile>new overrides old\<rbrakk> \<Longrightarrow> accmodi old \<noteq> Private"
schirmer@12854
  1161
by (induct set: overridesR) (auto simp add: inheritable_in_def)
schirmer@12854
  1162
schirmer@12854
  1163
lemma permits_acc_inheritance:
schirmer@12854
  1164
 "\<lbrakk>G\<turnstile>m in statC permits_acc_to accC; G\<turnstile>dynC \<preceq>\<^sub>C statC
schirmer@12854
  1165
  \<rbrakk> \<Longrightarrow> G\<turnstile>m in dynC permits_acc_to accC"
schirmer@12854
  1166
by (cases "accmodi m")
schirmer@12854
  1167
   (auto simp add: permits_acc_def
schirmer@12854
  1168
            intro: subclseq_trans) 
schirmer@12854
  1169
schirmer@12925
  1170
lemma permits_acc_static_declC:
schirmer@12925
  1171
 "\<lbrakk>G\<turnstile>m in C permits_acc_to accC; G\<turnstile>m member_in C; is_static m
schirmer@12925
  1172
  \<rbrakk> \<Longrightarrow> G\<turnstile>m in (declclass m) permits_acc_to accC"
schirmer@12925
  1173
by (cases "accmodi m") (auto simp add: permits_acc_def)
schirmer@12925
  1174
schirmer@12925
  1175
lemma dyn_accessible_from_static_declC: 
schirmer@12925
  1176
  (assumes  acc_C: "G\<turnstile>m in C dyn_accessible_from accC" and
schirmer@12925
  1177
           static: "is_static m"
schirmer@12925
  1178
  ) "G\<turnstile>m in (declclass m) dyn_accessible_from accC"
schirmer@12925
  1179
proof -
schirmer@12925
  1180
  from acc_C static
schirmer@12925
  1181
  show "G\<turnstile>m in (declclass m) dyn_accessible_from accC"
schirmer@12925
  1182
  proof (induct)
schirmer@12925
  1183
    case (Immediate C m)
schirmer@12925
  1184
    then show ?case 
schirmer@12925
  1185
      by (auto intro!: dyn_accessible_fromR.Immediate
schirmer@12925
  1186
                 dest: member_in_declC permits_acc_static_declC) 
schirmer@12925
  1187
  next 
schirmer@12925
  1188
    case (Overriding declCNew C m new old sup)
schirmer@12925
  1189
    then have "\<not> is_static m"
schirmer@12925
  1190
      by (auto dest: overrides_commonD)
schirmer@12925
  1191
    moreover
schirmer@12925
  1192
    assume "is_static m"
schirmer@12925
  1193
    ultimately show ?case 
schirmer@12925
  1194
      by contradiction
schirmer@12925
  1195
  qed
schirmer@12925
  1196
qed
schirmer@12925
  1197
schirmer@12854
  1198
lemma field_accessible_fromD:
schirmer@12854
  1199
 "\<lbrakk>G\<turnstile>membr of C accessible_from accC;is_field membr\<rbrakk> 
schirmer@12854
  1200
  \<Longrightarrow> G\<turnstile>membr member_of C \<and>
schirmer@12854
  1201
      G\<turnstile>(Class C) accessible_in (pid accC) \<and>
schirmer@12854
  1202
      G\<turnstile>membr in C permits_acc_to accC"
schirmer@12854
  1203
by (cases set: accessible_fromR)
schirmer@12854
  1204
   (auto simp add: is_field_def split: memberdecl.splits) 
schirmer@12854
  1205
schirmer@12854
  1206
lemma field_accessible_from_permits_acc_inheritance:
schirmer@12854
  1207
"\<lbrakk>G\<turnstile>membr of statC accessible_from accC; is_field membr; G \<turnstile> dynC \<preceq>\<^sub>C statC\<rbrakk>
schirmer@12854
  1208
\<Longrightarrow> G\<turnstile>membr in dynC permits_acc_to accC"
schirmer@12854
  1209
by (auto dest: field_accessible_fromD intro: permits_acc_inheritance)
schirmer@12854
  1210
schirmer@12854
  1211
schirmer@12854
  1212
(*
schirmer@12854
  1213
lemma accessible_Package:
schirmer@12854
  1214
 "\<lbrakk>G \<turnstile> m of C accessible_from S;accmodi m = Package;
schirmer@12854
  1215
   \<And> new old. G\<turnstile>new overrides\<^sub>S old \<Longrightarrow> accmodi old \<le> accmodi new\<rbrakk>
schirmer@12854
  1216
  \<Longrightarrow> pid S = pid C \<and> pid C = pid (declclass m)"
schirmer@12854
  1217
proof -
schirmer@12854
  1218
  assume wf: "\<And> new old. G\<turnstile>new overrides\<^sub>S old \<Longrightarrow> accmodi old \<le> accmodi new"
schirmer@12854
  1219
  assume "G \<turnstile> m of C accessible_from S"
schirmer@12854
  1220
  then show "accmodi m = Package \<Longrightarrow> pid S = pid C \<and> pid C = pid (declclass m)"
schirmer@12854
  1221
    (is "?Pack m \<Longrightarrow> ?P C m")
schirmer@12854
  1222
  proof (induct rule: accessible_fromR.induct)
schirmer@12854
  1223
    fix C m
schirmer@12854
  1224
    assume "G\<turnstile>m member_of C"
schirmer@12854
  1225
           "G \<turnstile> m in C permits_acc_to S"
schirmer@12854
  1226
           "accmodi m = Package"      
schirmer@12854
  1227
    then show "?P C m"
schirmer@12854
  1228
      by (auto dest: member_of_Package simp add: permits_acc_def)
schirmer@12854
  1229
  next
schirmer@12854
  1230
    fix declC C new newm old Sup
schirmer@12854
  1231
    assume member_new: "G \<turnstile> new member_of C" and 
schirmer@12854
  1232
                acc_C: "G \<turnstile> Class C accessible_in pid S" and
schirmer@12854
  1233
                  new: "new = (declC, mdecl newm)" and
schirmer@12854
  1234
             override: "G \<turnstile> (declC, newm) overrides\<^sub>S old" and
schirmer@12854
  1235
         subcls_C_Sup: "G\<turnstile>C \<prec>\<^sub>C Sup" and
schirmer@12854
  1236
              acc_old: "G \<turnstile> methdMembr old of Sup accessible_from S" and
schirmer@12854
  1237
                  hyp: "?Pack (methdMembr old) \<Longrightarrow> ?P Sup (methdMembr old)" and
schirmer@12854
  1238
          accmodi_new: "accmodi new = Package"
schirmer@12854
  1239
    from override wf 
schirmer@12854
  1240
    have accmodi_weaken: "accmodi old \<le> accmodi newm"
schirmer@12854
  1241
      by (cases old,cases newm) auto
schirmer@12854
  1242
    from override new
schirmer@12854
  1243
    have "accmodi old \<noteq> Private"
schirmer@12854
  1244
      by (simp add: no_Private_stat_override)
schirmer@12854
  1245
    with accmodi_weaken accmodi_new new
schirmer@12854
  1246
    have accmodi_old: "accmodi old = Package"
schirmer@12854
  1247
      by (cases "accmodi old") (auto simp add: le_acc_def less_acc_def) 
schirmer@12854
  1248
    with hyp 
schirmer@12854
  1249
    have P_sup: "?P Sup (methdMembr old)"
schirmer@12854
  1250
      by (simp)
schirmer@12854
  1251
    from wf override new accmodi_old accmodi_new
schirmer@12854
  1252
    have eq_pid_new_old: "pid (declclass new) = pid (declclass old)"
schirmer@12854
  1253
      by (auto dest: stat_override_Package) 
schirmer@12854
  1254
    from member_new accmodi_new
schirmer@12854
  1255
    have "pid (declclass new) = pid C"
schirmer@12854
  1256
      by (auto dest: member_of_Package)
schirmer@12854
  1257
    with eq_pid_new_old P_sup show "?P C new"
schirmer@12854
  1258
      by auto
schirmer@12854
  1259
  qed
schirmer@12854
  1260
qed
schirmer@12854
  1261
*)
schirmer@12854
  1262
lemma accessible_fieldD: 
schirmer@12854
  1263
 "\<lbrakk>G\<turnstile>membr of C accessible_from accC; is_field membr\<rbrakk>
schirmer@12854
  1264
 \<Longrightarrow> G\<turnstile>membr member_of C \<and>
schirmer@12854
  1265
     G\<turnstile>(Class C) accessible_in (pid accC) \<and>
schirmer@12854
  1266
     G\<turnstile>membr in C permits_acc_to accC"
schirmer@12854
  1267
by (induct rule: accessible_fromR.induct) (auto dest: is_fieldD)
schirmer@12854
  1268
      
schirmer@12854
  1269
(* lemmata:
schirmer@12854
  1270
 Wegen  G\<turnstile>Super accessible_in (pid C) folgt:
schirmer@12854
  1271
  G\<turnstile>m declared_in C; G\<turnstile>m member_of D; accmodi m = Package (G\<turnstile>D \<preceq>\<^sub>C C)
schirmer@12854
  1272
  \<Longrightarrow> pid C = pid D 
schirmer@12854
  1273
schirmer@12854
  1274
  C package
schirmer@12854
  1275
  m public in C
schirmer@12854
  1276
  für alle anderen D: G\<turnstile>m undeclared_in C
schirmer@12854
  1277
  m wird in alle subklassen vererbt, auch aus dem Package heraus!
schirmer@12854
  1278
schirmer@12854
  1279
  G\<turnstile>m member_of C \<Longrightarrow> \<exists> D. G\<turnstile>C \<preceq>\<^sub>C D \<and> G\<turnstile>m declared_in D
schirmer@12854
  1280
*)
schirmer@12854
  1281
schirmer@12854
  1282
(* Begriff (C,m) overrides (D,m)
schirmer@12854
  1283
    3 Fälle: Direkt,
schirmer@12854
  1284
             Indirekt über eine Zwischenklasse (ohne weiteres override)
schirmer@12854
  1285
             Indirekt über override
schirmer@12854
  1286
*)
schirmer@12854
  1287
   
schirmer@12854
  1288
(*
schirmer@12854
  1289
"G\<turnstile>m member_of C \<equiv> 
schirmer@12854
  1290
constdefs declares_method:: "prog \<Rightarrow> sig \<Rightarrow> qtname \<Rightarrow> methd \<Rightarrow> bool"
schirmer@12854
  1291
                                 ("_,_\<turnstile> _ declares'_method _" [61,61,61,61] 60)
schirmer@12854
  1292
"G,sig\<turnstile>C declares_method m \<equiv> cdeclaredmethd G C sig = Some m" 
schirmer@12854
  1293
schirmer@12854
  1294
constdefs is_declared:: "prog \<Rightarrow> sig \<Rightarrow> (qtname \<times> methd) \<Rightarrow> bool"
schirmer@12854
  1295
"is_declared G sig em \<equiv> G,sig\<turnstile>declclass em declares_method mthd em"
schirmer@12854
  1296
*)
schirmer@12854
  1297
schirmer@12854
  1298
lemma member_of_Private:
schirmer@12854
  1299
"\<lbrakk>G\<turnstile>m member_of C; accmodi m = Private\<rbrakk> \<Longrightarrow> declclass m = C"
schirmer@12854
  1300
by (induct set: members) (auto simp add: inheritable_in_def)
schirmer@12854
  1301
schirmer@12854
  1302
lemma member_of_subclseq_declC:
schirmer@12854
  1303
  "G\<turnstile>m member_of C \<Longrightarrow> G\<turnstile>C \<preceq>\<^sub>C declclass m"
schirmer@12854
  1304
by (induct set: members) (auto dest: r_into_rtrancl intro: rtrancl_trans)
schirmer@12854
  1305
schirmer@12854
  1306
lemma member_of_inheritance:
schirmer@12854
  1307
  (assumes    m: "G\<turnstile>m member_of D" and 
schirmer@12854
  1308
     subclseq_D_C: "G\<turnstile>D \<preceq>\<^sub>C C" and
schirmer@12854
  1309
     subclseq_C_m: "G\<turnstile>C \<preceq>\<^sub>C declclass m" and
schirmer@12854
  1310
               ws: "ws_prog G" 
schirmer@12854
  1311
  ) "G\<turnstile>m member_of C"
schirmer@12854
  1312
proof -
schirmer@12854
  1313
  from m subclseq_D_C subclseq_C_m
schirmer@12854
  1314
  show ?thesis
schirmer@12854
  1315
  proof (induct)
schirmer@12854
  1316
    case (Immediate D m)
schirmer@12854
  1317
    assume "declclass m = D" and
schirmer@12854
  1318
           "G\<turnstile>D\<preceq>\<^sub>C C" and "G\<turnstile>C\<preceq>\<^sub>C declclass m"
schirmer@12854
  1319
    with ws have "D=C" 
schirmer@12854
  1320
      by (auto intro: subclseq_acyclic)
schirmer@12854
  1321
    with Immediate 
schirmer@12854
  1322
    show "G\<turnstile>m member_of C"
schirmer@12854
  1323
      by (auto intro: members.Immediate)
schirmer@12854
  1324
  next
schirmer@12854
  1325
    case (Inherited D S m)
schirmer@12854
  1326
    assume member_of_D_props: 
schirmer@12854
  1327
            "G \<turnstile> m inheritable_in pid D" 
schirmer@12854
  1328
            "G\<turnstile> memberid m undeclared_in D"  
schirmer@12854
  1329
            "G \<turnstile> Class S accessible_in pid D" 
schirmer@12854
  1330
            "G \<turnstile> m member_of S"
schirmer@12854
  1331
    assume super: "G\<turnstile>D\<prec>\<^sub>C\<^sub>1S"
schirmer@12854
  1332
    assume hyp: "\<lbrakk>G\<turnstile>S\<preceq>\<^sub>C C; G\<turnstile>C\<preceq>\<^sub>C declclass m\<rbrakk> \<Longrightarrow> G \<turnstile> m member_of C"
schirmer@12854
  1333
    assume subclseq_C_m: "G\<turnstile>C\<preceq>\<^sub>C declclass m"
schirmer@12854
  1334
    assume "G\<turnstile>D\<preceq>\<^sub>C C"
schirmer@12854
  1335
    then show "G\<turnstile>m member_of C"
schirmer@12854
  1336
    proof (cases rule: subclseq_cases)
schirmer@12854
  1337
      case Eq
schirmer@12854
  1338
      assume "D=C" 
schirmer@12854
  1339
      with super member_of_D_props 
schirmer@12854
  1340
      show ?thesis
schirmer@12854
  1341
	by (auto intro: members.Inherited)
schirmer@12854
  1342
    next
schirmer@12854
  1343
      case Subcls
schirmer@12854
  1344
      assume "G\<turnstile>D\<prec>\<^sub>C C"
schirmer@12854
  1345
      with super 
schirmer@12854
  1346
      have "G\<turnstile>S\<preceq>\<^sub>C C"
schirmer@12854
  1347
	by (auto dest: subcls1D subcls_superD)
schirmer@12854
  1348
      with subclseq_C_m hyp show ?thesis
schirmer@12854
  1349
	by blast
schirmer@12854
  1350
    qed
schirmer@12854
  1351
  qed
schirmer@12854
  1352
qed
schirmer@12854
  1353
schirmer@12854
  1354
lemma member_of_subcls:
schirmer@12854
  1355
  (assumes    old: "G\<turnstile>old member_of C" and 
schirmer@12854
  1356
              new: "G\<turnstile>new member_of D" and
schirmer@12854
  1357
             eqid: "memberid new = memberid old" and
schirmer@12854
  1358
     subclseq_D_C: "G\<turnstile>D \<preceq>\<^sub>C C" and 
schirmer@12854
  1359
   subcls_new_old: "G\<turnstile>declclass new \<prec>\<^sub>C declclass old" and
schirmer@12854
  1360
               ws: "ws_prog G"
schirmer@12854
  1361
  ) "G\<turnstile>D \<prec>\<^sub>C C"
schirmer@12854
  1362
proof -
schirmer@12854
  1363
  from old 
schirmer@12854
  1364
  have subclseq_C_old: "G\<turnstile>C \<preceq>\<^sub>C declclass old"
schirmer@12854
  1365
    by (auto dest: member_of_subclseq_declC)
schirmer@12854
  1366
  from new 
schirmer@12854
  1367
  have subclseq_D_new: "G\<turnstile>D \<preceq>\<^sub>C declclass new"
schirmer@12854
  1368
    by (auto dest: member_of_subclseq_declC)
schirmer@12854
  1369
  from subcls_new_old ws
schirmer@12854
  1370
  have neq_new_old: "new\<noteq>old"
schirmer@12854
  1371
    by (cases new,cases old) (auto dest: subcls_irrefl)
schirmer@12854
  1372
  from subclseq_D_new subclseq_D_C
schirmer@12854
  1373
  have "G\<turnstile>(declclass new) \<preceq>\<^sub>C C \<or> G\<turnstile>C \<preceq>\<^sub>C (declclass new)" 
schirmer@12854
  1374
    by (rule subcls_compareable)
schirmer@12854
  1375
  then have "G\<turnstile>(declclass new) \<preceq>\<^sub>C C"
schirmer@12854
  1376
  proof
schirmer@12854
  1377
    assume "G\<turnstile>declclass new\<preceq>\<^sub>C C" then show ?thesis .
schirmer@12854
  1378
  next
schirmer@12854
  1379
    assume "G\<turnstile>C \<preceq>\<^sub>C (declclass new)"
schirmer@12854
  1380
    with new subclseq_D_C ws 
schirmer@12854
  1381
    have "G\<turnstile>new member_of C"
schirmer@12854
  1382
      by (blast intro: member_of_inheritance)
schirmer@12854
  1383
    with eqid old 
schirmer@12854
  1384
    have "new=old"
schirmer@12854
  1385
      by (blast intro: unique_member_of)
schirmer@12854
  1386
    with neq_new_old 
schirmer@12854
  1387
    show ?thesis
schirmer@12854
  1388
      by contradiction
schirmer@12854
  1389
  qed
schirmer@12854
  1390
  then show ?thesis
schirmer@12854
  1391
  proof (cases rule: subclseq_cases)
schirmer@12854
  1392
    case Eq
schirmer@12854
  1393
    assume "declclass new = C"
schirmer@12854
  1394
    with new have "G\<turnstile>new member_of C"
schirmer@12854
  1395
      by (auto dest: member_of_member_of_declC)
schirmer@12854
  1396
    with eqid old 
schirmer@12854
  1397
    have "new=old"
schirmer@12854
  1398
      by (blast intro: unique_member_of)
schirmer@12854
  1399
    with neq_new_old 
schirmer@12854
  1400
    show ?thesis
schirmer@12854
  1401
      by contradiction
schirmer@12854
  1402
  next
schirmer@12854
  1403
    case Subcls
schirmer@12854
  1404
    assume "G\<turnstile>declclass new\<prec>\<^sub>C C"
schirmer@12854
  1405
    with subclseq_D_new
schirmer@12854
  1406
    show "G\<turnstile>D\<prec>\<^sub>C C"
schirmer@12854
  1407
      by (rule rtrancl_trancl_trancl)
schirmer@12854
  1408
  qed
schirmer@12854
  1409
qed
schirmer@12854
  1410
schirmer@12854
  1411
corollary member_of_overrides_subcls:
schirmer@12854
  1412
 "\<lbrakk>G\<turnstile>Methd sig old member_of C; G\<turnstile>Methd sig new member_of D;G\<turnstile>D \<preceq>\<^sub>C C;
schirmer@12854
  1413
   G,sig\<turnstile>new overrides old; ws_prog G\<rbrakk>
schirmer@12854
  1414
 \<Longrightarrow> G\<turnstile>D \<prec>\<^sub>C C"
schirmer@12854
  1415
by (drule overrides_commonD) (auto intro: member_of_subcls)    
schirmer@12854
  1416
schirmer@12854
  1417
corollary member_of_stat_overrides_subcls:
schirmer@12854
  1418
 "\<lbrakk>G\<turnstile>Methd sig old member_of C; G\<turnstile>Methd sig new member_of D;G\<turnstile>D \<preceq>\<^sub>C C;
schirmer@12854
  1419
   G,sig\<turnstile>new overrides\<^sub>S old; ws_prog G\<rbrakk>
schirmer@12854
  1420
 \<Longrightarrow> G\<turnstile>D \<prec>\<^sub>C C"
schirmer@12854
  1421
by (drule stat_overrides_commonD) (auto intro: member_of_subcls)    
schirmer@12854
  1422
schirmer@12854
  1423
schirmer@12854
  1424
schirmer@12854
  1425
lemma inherited_field_access: 
schirmer@12854
  1426
 (assumes stat_acc: "G\<turnstile>membr of statC accessible_from accC" and
schirmer@12854
  1427
          is_field: "is_field membr" and 
schirmer@12854
  1428
          subclseq: "G \<turnstile> dynC \<preceq>\<^sub>C statC"
schirmer@12854
  1429
 ) "G\<turnstile>membr in dynC dyn_accessible_from accC"
schirmer@12854
  1430
proof -
schirmer@12854
  1431
  from stat_acc is_field subclseq 
schirmer@12854
  1432
  show ?thesis
schirmer@12854
  1433
    by (auto dest: accessible_fieldD 
schirmer@12925
  1434
            intro: dyn_accessible_fromR.Immediate 
schirmer@12854
  1435
                   member_inI 
schirmer@12854
  1436
                   permits_acc_inheritance)
schirmer@12854
  1437
qed
schirmer@12854
  1438
schirmer@12854
  1439
lemma accessible_inheritance:
schirmer@12854
  1440
 (assumes stat_acc: "G\<turnstile>m of statC accessible_from accC" and
schirmer@12854
  1441
          subclseq: "G\<turnstile>dynC \<preceq>\<^sub>C statC" and
schirmer@12854
  1442
       member_dynC: "G\<turnstile>m member_of dynC" and
schirmer@12854
  1443
          dynC_acc: "G\<turnstile>(Class dynC) accessible_in (pid accC)"
schirmer@12854
  1444
 ) "G\<turnstile>m of dynC accessible_from accC"
schirmer@12854
  1445
proof -
schirmer@12854
  1446
  from stat_acc
schirmer@12854
  1447
  have member_statC: "G\<turnstile>m member_of statC" 
schirmer@12854
  1448
    by (auto dest: accessible_from_commonD)
schirmer@12854
  1449
  from stat_acc
schirmer@12854
  1450
  show ?thesis
schirmer@12854
  1451
  proof (cases)
schirmer@12925
  1452
    case Immediate
schirmer@12854
  1453
    with member_dynC member_statC subclseq dynC_acc
schirmer@12854
  1454
    show ?thesis
schirmer@12925
  1455
      by (auto intro: accessible_fromR.Immediate permits_acc_inheritance)
schirmer@12854
  1456
  next
schirmer@12925
  1457
    case Overriding
schirmer@12854
  1458
    with member_dynC subclseq dynC_acc
schirmer@12854
  1459
    show ?thesis
schirmer@12925
  1460
      by (auto intro: accessible_fromR.Overriding rtrancl_trancl_trancl)
schirmer@12854
  1461
  qed
schirmer@12854
  1462
qed
schirmer@12854
  1463
schirmer@12854
  1464
section "fields and methods"
schirmer@12854
  1465
schirmer@12854
  1466
schirmer@12854
  1467
types
schirmer@12854
  1468
  fspec = "vname \<times> qtname"
schirmer@12854
  1469
schirmer@12854
  1470
translations 
schirmer@12854
  1471
  "fspec" <= (type) "vname \<times> qtname" 
schirmer@12854
  1472
schirmer@12854
  1473
constdefs
schirmer@12854
  1474
imethds:: "prog \<Rightarrow> qtname \<Rightarrow> (sig,qtname \<times> mhead) tables"
schirmer@12854
  1475
"imethds G I 
schirmer@12854
  1476
  \<equiv> iface_rec (G,I)  
schirmer@12854
  1477
              (\<lambda>I i ts. (Un_tables ts) \<oplus>\<oplus> 
schirmer@12854
  1478
                        (o2s \<circ> table_of (map (\<lambda>(s,m). (s,I,m)) (imethods i))))"
schirmer@12854
  1479
text {* methods of an interface, with overriding and inheritance, cf. 9.2 *}
schirmer@12854
  1480
schirmer@12854
  1481
constdefs
schirmer@12854
  1482
accimethds:: "prog \<Rightarrow> pname \<Rightarrow> qtname \<Rightarrow> (sig,qtname \<times> mhead) tables"
schirmer@12854
  1483
"accimethds G pack I
schirmer@12854
  1484
  \<equiv> if G\<turnstile>Iface I accessible_in pack 
schirmer@12854
  1485
       then imethds G I
schirmer@12854
  1486
       else \<lambda> k. {}"
schirmer@12854
  1487
text {* only returns imethds if the interface is accessible *}
schirmer@12854
  1488
schirmer@12854
  1489
constdefs
schirmer@12854
  1490
methd:: "prog \<Rightarrow> qtname  \<Rightarrow> (sig,qtname \<times> methd) table"
schirmer@12854
  1491
schirmer@12854
  1492
"methd G C 
schirmer@12854
  1493
 \<equiv> class_rec (G,C) empty
schirmer@12854
  1494
             (\<lambda>C c subcls_mthds. 
schirmer@12854
  1495
               filter_tab (\<lambda>sig m. G\<turnstile>C inherits method sig m)
schirmer@12854
  1496
                          subcls_mthds 
schirmer@12854
  1497
               ++ 
schirmer@12854
  1498
               table_of (map (\<lambda>(s,m). (s,C,m)) (methods c)))"
schirmer@12854
  1499
text {* @{term "methd G C"}: methods of a class C (statically visible from C), 
schirmer@12854
  1500
     with inheritance and hiding cf. 8.4.6;
schirmer@12854
  1501
     Overriding is captured by @{text dynmethd}.
schirmer@12854
  1502
     Every new method with the same signature coalesces the
schirmer@12854
  1503
     method of a superclass. *}
schirmer@12854
  1504
schirmer@12854
  1505
constdefs                      
schirmer@12854
  1506
accmethd:: "prog \<Rightarrow> qtname \<Rightarrow> qtname  \<Rightarrow> (sig,qtname \<times> methd) table"
schirmer@12854
  1507
"accmethd G S C 
schirmer@12854
  1508
 \<equiv> filter_tab (\<lambda>sig m. G\<turnstile>method sig m of C accessible_from S) 
schirmer@12854
  1509
              (methd G C)"
schirmer@12854
  1510
text {* @{term "accmethd G S C"}: only those methods of @{term "methd G C"}, 
schirmer@12854
  1511
        accessible from S *}
schirmer@12854
  1512
schirmer@12854
  1513
text {* Note the class component in the accessibility filter. The class where
schirmer@12854
  1514
    method @{term m} is declared (@{term declC}) isn't necessarily accessible 
schirmer@12854
  1515
    from the current scope @{term S}. The method can be made accessible 
schirmer@12854
  1516
    through inheritance, too.
schirmer@12854
  1517
    So we must test accessibility of method @{term m} of class @{term C} 
schirmer@12854
  1518
    (not @{term "declclass m"}) *}
schirmer@12854
  1519
schirmer@12854
  1520
constdefs 
schirmer@12854
  1521
dynmethd:: "prog  \<Rightarrow> qtname \<Rightarrow> qtname \<Rightarrow> (sig,qtname \<times> methd) table"
schirmer@12854
  1522
"dynmethd G statC dynC  
schirmer@12854
  1523
  \<equiv> \<lambda> sig. 
schirmer@12854
  1524
     (if G\<turnstile>dynC \<preceq>\<^sub>C statC
schirmer@12854
  1525
        then (case methd G statC sig of
schirmer@12854
  1526
                None \<Rightarrow> None
schirmer@12854
  1527
              | Some statM 
schirmer@12854
  1528
                  \<Rightarrow> (class_rec (G,dynC) empty
schirmer@12854
  1529
                       (\<lambda>C c subcls_mthds. 
schirmer@12854
  1530
                          subcls_mthds
schirmer@12854
  1531
                          ++
schirmer@12854
  1532
                          (filter_tab 
schirmer@12854
  1533
                            (\<lambda> _ dynM. G,sig\<turnstile>dynM overrides statM \<or> dynM=statM)
schirmer@12854
  1534
                            (methd G C) ))
schirmer@12854
  1535
                      ) sig
schirmer@12854
  1536
              )
schirmer@12854
  1537
        else None)"
schirmer@12854
  1538
(*
schirmer@12854
  1539
"dynmethd G statC dynC  
schirmer@12854
  1540
  \<equiv> \<lambda> sig. 
schirmer@12854
  1541
     (if G\<turnstile>dynC \<preceq>\<^sub>C statC
schirmer@12854
  1542
        then (case methd G statC sig of
schirmer@12854
  1543
                None \<Rightarrow> None
schirmer@12854
  1544
              | Some statM 
schirmer@12854
  1545
                    \<Rightarrow> (class_rec (G,statC) empty
schirmer@12854
  1546
                         (\<lambda>C c subcls_mthds. 
schirmer@12854
  1547
                            subcls_mthds
schirmer@12854
  1548
                            ++
schirmer@12854
  1549
                            (filter_tab 
schirmer@12854
  1550
                              (\<lambda> _ dynM. G,sig\<turnstile>dynM overrides statM)  
schirmer@12854
  1551
                              (table_of (map (\<lambda>(s,m). (s,C,m)) (methods c)))))
schirmer@12854
  1552
                        ) sig
schirmer@12854
  1553
              )
schirmer@12854
  1554
        else None)"*)
schirmer@12854
  1555
text {* @{term "dynmethd G statC dynC"}: dynamic method lookup of a reference 
schirmer@12854
  1556
        with dynamic class @{term dynC} and static class @{term statC} *}
schirmer@12854
  1557
text {* Note some kind of duality between @{term methd} and @{term dynmethd} 
schirmer@12854
  1558
        in the @{term class_rec} arguments. Whereas @{term methd} filters the 
schirmer@12854
  1559
        subclass methods (to get only the inherited ones), @{term dynmethd} 
schirmer@12854
  1560
        filters the new methods (to get only those methods which actually
schirmer@12854
  1561
        override the methods of the static class) *}
schirmer@12854
  1562
schirmer@12854
  1563
constdefs 
schirmer@12854
  1564
dynimethd:: "prog \<Rightarrow> qtname \<Rightarrow> qtname \<Rightarrow> (sig,qtname \<times> methd) table"
schirmer@12854
  1565
"dynimethd G I dynC 
schirmer@12854
  1566
  \<equiv> \<lambda> sig. if imethds G I sig \<noteq> {}
schirmer@12854
  1567
               then methd G dynC sig
schirmer@12854
  1568
               else dynmethd G Object dynC sig"
schirmer@12854
  1569
text {* @{term "dynimethd G I dynC"}: dynamic method lookup of a reference with 
schirmer@12854
  1570
        dynamic class dynC and static interface type I *}
schirmer@12854
  1571
text {* 
schirmer@12854
  1572
   When calling an interface method, we must distinguish if the method signature
schirmer@12854
  1573
   was defined in the interface or if it must be an Object method in the other
schirmer@12854
  1574
   case. If it was an interface method we search the class hierarchy
schirmer@12854
  1575
   starting at the dynamic class of the object up to Object to find the 
schirmer@12854
  1576
   first matching method (@{term methd}). Since all interface methods have 
schirmer@12854
  1577
   public access the method can't be coalesced due to some odd visibility 
schirmer@12854
  1578
   effects like in case of dynmethd. The method will be inherited or 
schirmer@12854
  1579
   overridden in all classes from the first class implementing the interface 
schirmer@12854
  1580
   down to the actual dynamic class.
schirmer@12854
  1581
 *}
schirmer@12854
  1582
schirmer@12854
  1583
constdefs
schirmer@12854
  1584
dynlookup::"prog  \<Rightarrow> ref_ty \<Rightarrow> qtname \<Rightarrow> (sig,qtname \<times> methd) table"
schirmer@12854
  1585
"dynlookup G statT dynC
schirmer@12854
  1586
  \<equiv> (case statT of
schirmer@12854
  1587
       NullT        \<Rightarrow> empty
schirmer@12854
  1588
     | IfaceT I     \<Rightarrow> dynimethd G I      dynC
schirmer@12854
  1589
     | ClassT statC \<Rightarrow> dynmethd  G statC  dynC
schirmer@12854
  1590
     | ArrayT ty    \<Rightarrow> dynmethd  G Object dynC)"
schirmer@12854
  1591
text {* @{term "dynlookup G statT dynC"}: dynamic lookup of a method within the 
schirmer@12854
  1592
    static reference type statT and the dynamic class dynC. 
schirmer@12854
  1593
    In a wellformd context statT will not be NullT and in case
schirmer@12854
  1594
    statT is an array type, dynC=Object *}
schirmer@12854
  1595
schirmer@12854
  1596
constdefs
schirmer@12854
  1597
fields:: "prog \<Rightarrow> qtname \<Rightarrow> ((vname \<times> qtname) \<times> field) list"
schirmer@12854
  1598
"fields G C 
schirmer@12854
  1599
  \<equiv> class_rec (G,C) [] (\<lambda>C c ts. map (\<lambda>(n,t). ((n,C),t)) (cfields c) @ ts)"
schirmer@12854
  1600
text {* @{term "fields G C"} 
schirmer@12854
  1601
     list of fields of a class, including all the fields of the superclasses
schirmer@12854
  1602
     (private, inherited and hidden ones) not only the accessible ones
schirmer@12854
  1603
     (an instance of a object allocates all these fields *}
schirmer@12854
  1604
schirmer@12854
  1605
constdefs
schirmer@12854
  1606
accfield:: "prog \<Rightarrow> qtname \<Rightarrow> qtname \<Rightarrow> (vname, qtname  \<times>  field) table"
schirmer@12854
  1607
"accfield G S C
schirmer@12854
  1608
  \<equiv> let field_tab = table_of((map (\<lambda>((n,d),f).(n,(d,f)))) (fields G C))
schirmer@12854
  1609
    in filter_tab (\<lambda>n (declC,f). G\<turnstile> (declC,fdecl (n,f)) of C accessible_from S)
schirmer@12854
  1610
                  field_tab"
schirmer@12854
  1611
text  {* @{term "accfield G C S"}: fields of a class @{term C} which are 
schirmer@12854
  1612
         accessible from scope of class
schirmer@12854
  1613
         @{term S} with inheritance and hiding, cf. 8.3 *}
schirmer@12854
  1614
text {* note the class component in the accessibility filter (see also 
schirmer@12854
  1615
        @{term methd}).
schirmer@12854
  1616
   The class declaring field @{term f} (@{term declC}) isn't necessarily 
schirmer@12854
  1617
   accessible from scope @{term S}. The field can be made visible through 
schirmer@12854
  1618
   inheritance, too. So we must test accessibility of field @{term f} of class 
schirmer@12854
  1619
   @{term C} (not @{term "declclass f"}) *} 
schirmer@12854
  1620
schirmer@12854
  1621
constdefs
schirmer@12854
  1622
schirmer@12854
  1623
  is_methd :: "prog \<Rightarrow> qtname  \<Rightarrow> sig \<Rightarrow> bool"
schirmer@12854
  1624
 "is_methd G \<equiv> \<lambda>C sig. is_class G C \<and> methd G C sig \<noteq> None"
schirmer@12854
  1625
schirmer@12854
  1626
constdefs efname:: "((vname \<times> qtname) \<times> field) \<Rightarrow> (vname \<times> qtname)"
schirmer@12854
  1627
"efname \<equiv> fst"
schirmer@12854
  1628
schirmer@12854
  1629
lemma efname_simp[simp]:"efname (n,f) = n"
schirmer@12854
  1630
by (simp add: efname_def) 
schirmer@12854
  1631
schirmer@12854
  1632
schirmer@12854
  1633
subsection "imethds"
schirmer@12854
  1634
schirmer@12854
  1635
lemma imethds_rec: "\<lbrakk>iface G I = Some i; ws_prog G\<rbrakk> \<Longrightarrow>  
schirmer@12854
  1636
  imethds G I = Un_tables ((\<lambda>J. imethds  G J)`set (isuperIfs i)) \<oplus>\<oplus>  
schirmer@12854
  1637
                      (o2s \<circ> table_of (map (\<lambda>(s,mh). (s,I,mh)) (imethods i)))"
schirmer@12854
  1638
apply (unfold imethds_def)
schirmer@12854
  1639
apply (rule iface_rec [THEN trans])
schirmer@12854
  1640
apply auto
schirmer@12854
  1641
done
schirmer@12854
  1642
schirmer@12854
  1643
schirmer@12854
  1644
(* local lemma *)
schirmer@12854
  1645
lemma imethds_norec:
schirmer@12854
  1646
  "\<lbrakk>iface G md = Some i; ws_prog G; table_of (imethods i) sig = Some mh\<rbrakk> \<Longrightarrow>  
schirmer@12854
  1647
  (md, mh) \<in> imethds G md sig"
schirmer@12854
  1648
apply (subst imethds_rec)
schirmer@12854
  1649
apply assumption+
schirmer@12854
  1650
apply (rule iffD2)
schirmer@12854
  1651
apply (rule overrides_t_Some_iff)
schirmer@12854
  1652
apply (rule disjI1)
schirmer@12854
  1653
apply (auto elim: table_of_map_SomeI)
schirmer@12854
  1654
done
schirmer@12854
  1655
schirmer@12854
  1656
lemma imethds_declI: "\<lbrakk>m \<in> imethds G I sig; ws_prog G; is_iface G I\<rbrakk> \<Longrightarrow> 
schirmer@12854
  1657
  (\<exists>i. iface G (decliface m) = Some i \<and> 
schirmer@12854
  1658
  table_of (imethods i) sig = Some (mthd m)) \<and>  
schirmer@12854
  1659
  (I,decliface m) \<in> (subint1 G)^* \<and> m \<in> imethds G (decliface m) sig"
schirmer@12854
  1660
apply (erule make_imp)
schirmer@12854
  1661
apply (rule ws_subint1_induct, assumption, assumption)
schirmer@12854
  1662
apply (subst imethds_rec, erule conjunct1, assumption)
schirmer@12854
  1663
apply (force elim: imethds_norec intro: rtrancl_into_rtrancl2)
schirmer@12854
  1664
done
schirmer@12854
  1665
schirmer@12854
  1666
lemma imethds_cases [consumes 3, case_names NewMethod InheritedMethod]:
schirmer@12854
  1667
 (assumes im: "im \<in> imethds G I sig" and  
schirmer@12854
  1668
         ifI: "iface G I = Some i" and
schirmer@12854
  1669
          ws: "ws_prog G" and
schirmer@12854
  1670
     hyp_new:  "table_of (map (\<lambda>(s, mh). (s, I, mh)) (imethods i)) sig 
schirmer@12854
  1671
                = Some im \<Longrightarrow> P" and
schirmer@12854
  1672
     hyp_inh: "\<And> J. \<lbrakk>J \<in> set (isuperIfs i); im \<in> imethds G J sig\<rbrakk> \<Longrightarrow> P"
schirmer@12854
  1673
  ) "P"
schirmer@12854
  1674
proof -
schirmer@12854
  1675
  from ifI ws im hyp_new hyp_inh
schirmer@12854
  1676
  show "P"
schirmer@12854
  1677
    by (auto simp add: imethds_rec)
schirmer@12854
  1678
qed
schirmer@12854
  1679
schirmer@12854
  1680
subsection "accimethd"
schirmer@12854
  1681
schirmer@12854
  1682
lemma accimethds_simp [simp]: 
schirmer@12854
  1683
"G\<turnstile>Iface I accessible_in pack \<Longrightarrow> accimethds G pack I = imethds G I"
schirmer@12854
  1684
by (simp add: accimethds_def)
schirmer@12854
  1685
schirmer@12854
  1686
lemma accimethdsD:
schirmer@12854
  1687
 "im \<in> accimethds G pack I sig 
schirmer@12854
  1688
  \<Longrightarrow> im \<in> imethds G I sig \<and> G\<turnstile>Iface I accessible_in pack"
schirmer@12854
  1689
by (auto simp add: accimethds_def)
schirmer@12854
  1690
schirmer@12854
  1691
lemma accimethdsI: 
schirmer@12854
  1692
"\<lbrakk>im \<in> imethds G I sig;G\<turnstile>Iface I accessible_in pack\<rbrakk>
schirmer@12854
  1693
 \<Longrightarrow> im \<in> accimethds G pack I sig"
schirmer@12854
  1694
by simp
schirmer@12854
  1695
schirmer@12854
  1696
subsection "methd"
schirmer@12854
  1697
schirmer@12854
  1698
lemma methd_rec: "\<lbrakk>class G C = Some c; ws_prog G\<rbrakk> \<Longrightarrow>  
schirmer@12854
  1699
  methd G C 
schirmer@12854
  1700
    = (if C = Object 
schirmer@12854
  1701
          then empty 
schirmer@12854
  1702
          else filter_tab (\<lambda>sig m. G\<turnstile>C inherits method sig m)
schirmer@12854
  1703
                          (methd G (super c))) 
schirmer@12854
  1704
      ++ table_of (map (\<lambda>(s,m). (s,C,m)) (methods c))"
schirmer@12854
  1705
apply (unfold methd_def)
schirmer@12854
  1706
apply (erule class_rec [THEN trans], assumption)
schirmer@12854
  1707
apply (simp)
schirmer@12854
  1708
done
schirmer@12854
  1709
schirmer@12854
  1710
(* local lemma *)
schirmer@12854
  1711
lemma methd_norec: 
schirmer@12854
  1712
 "\<lbrakk>class G declC = Some c; ws_prog G;table_of (methods c) sig = Some m\<rbrakk> 
schirmer@12854
  1713
  \<Longrightarrow> methd G declC sig = Some (declC, m)"
schirmer@12854
  1714
apply (simp only: methd_rec)
schirmer@12854
  1715
apply (rule disjI1 [THEN override_Some_iff [THEN iffD2]])
schirmer@12854
  1716
apply (auto elim: table_of_map_SomeI)
schirmer@12854
  1717
done
schirmer@12854
  1718
schirmer@12854
  1719
schirmer@12854
  1720
lemma methd_declC: 
schirmer@12854
  1721
"\<lbrakk>methd G C sig = Some m; ws_prog G;is_class G C\<rbrakk> \<Longrightarrow>
schirmer@12854
  1722
 (\<exists>d. class G (declclass m)=Some d \<and> table_of (methods d) sig=Some (mthd m)) \<and> 
schirmer@12854
  1723
 G\<turnstile>C \<preceq>\<^sub>C (declclass m) \<and> methd G (declclass m) sig = Some m"   
schirmer@12854
  1724
apply (erule make_imp)
schirmer@12854
  1725
apply (rule ws_subcls1_induct, assumption, assumption)
schirmer@12854
  1726
apply (subst methd_rec, assumption)
schirmer@12854
  1727
apply (case_tac "Ca=Object")
schirmer@12854
  1728
apply   (force elim: methd_norec )
schirmer@12854
  1729
schirmer@12854
  1730
apply   simp
schirmer@12854
  1731
apply   (case_tac "table_of (map (\<lambda>(s, m). (s, Ca, m)) (methods c)) sig")
schirmer@12854
  1732
apply     (force intro: rtrancl_into_rtrancl2)
schirmer@12854
  1733
schirmer@12854
  1734
apply     (auto intro: methd_norec)
schirmer@12854
  1735
done
schirmer@12854
  1736
schirmer@12854
  1737
lemma methd_inheritedD:
schirmer@12854
  1738
  "\<lbrakk>class G C = Some c; ws_prog G;methd G C sig = Some m\<rbrakk>
schirmer@12854
  1739
  \<Longrightarrow>  (declclass m \<noteq> C \<longrightarrow> G \<turnstile>C inherits method sig m)"
schirmer@12854
  1740
by (auto simp add: methd_rec)
schirmer@12854
  1741
schirmer@12854
  1742
lemma methd_diff_cls:
schirmer@12854
  1743
"\<lbrakk>ws_prog G; is_class G C; is_class G D;
schirmer@12854
  1744
 methd G C sig = m; methd G D sig = n; m\<noteq>n
schirmer@12854
  1745
\<rbrakk> \<Longrightarrow> C\<noteq>D"
schirmer@12854
  1746
by (auto simp add: methd_rec)
schirmer@12854
  1747
schirmer@12854
  1748
lemma method_declared_inI: 
schirmer@12854
  1749
 "\<lbrakk>table_of (methods c) sig = Some m; class G C = Some c\<rbrakk>
schirmer@12854
  1750
  \<Longrightarrow> G\<turnstile>mdecl (sig,m) declared_in C"
schirmer@12854
  1751
by (auto simp add: cdeclaredmethd_def declared_in_def)
schirmer@12854
  1752
schirmer@12854
  1753
lemma methd_declared_in_declclass: 
schirmer@12854
  1754
 "\<lbrakk>methd G C sig = Some m; ws_prog G;is_class G C\<rbrakk> 
schirmer@12854
  1755
 \<Longrightarrow> G\<turnstile>Methd sig m declared_in (declclass m)"
schirmer@12854
  1756
by (auto dest: methd_declC method_declared_inI)
schirmer@12854
  1757
schirmer@12854
  1758
lemma member_methd:
schirmer@12854
  1759
 (assumes member_of: "G\<turnstile>Methd sig m member_of C" and
schirmer@12854
  1760
                 ws: "ws_prog G"
schirmer@12854
  1761
 ) "methd G C sig = Some m"
schirmer@12854
  1762
proof -
schirmer@12854
  1763
  from member_of 
schirmer@12854
  1764
  have iscls_C: "is_class G C" 
schirmer@12854
  1765
    by (rule member_of_is_classD)
schirmer@12854
  1766
  from iscls_C ws member_of
schirmer@12854
  1767
  show ?thesis (is "?Methd C")
schirmer@12854
  1768
  proof (induct rule: ws_class_induct')
schirmer@12854
  1769
    case (Object co)
schirmer@12854
  1770
    assume "G \<turnstile>Methd sig m member_of Object"
schirmer@12854
  1771
    then have "G\<turnstile>Methd sig m declared_in Object \<and> declclass m = Object"
schirmer@12854
  1772
      by (cases set: members) (cases m, auto dest: subcls1D)
schirmer@12854
  1773
    with ws Object 
schirmer@12854
  1774
    show "?Methd Object"
schirmer@12854
  1775
      by (cases m)
schirmer@12854
  1776
         (auto simp add: declared_in_def cdeclaredmethd_def methd_rec
schirmer@12854
  1777
                  intro:  table_of_mapconst_SomeI)
schirmer@12854
  1778
  next
schirmer@12854
  1779
    case (Subcls C c)
schirmer@12854
  1780
    assume clsC: "class G C = Some c" and
schirmer@12854
  1781
      neq_C_Obj: "C \<noteq> Object" and
schirmer@12854
  1782
            hyp: "G \<turnstile>Methd sig m member_of super c \<Longrightarrow> ?Methd (super c)" and
schirmer@12854
  1783
      member_of: "G \<turnstile>Methd sig m member_of C"
schirmer@12854
  1784
    from member_of
schirmer@12854
  1785
    show "?Methd C"
schirmer@12854
  1786
    proof (cases)
schirmer@12854
  1787
      case (Immediate Ca membr)
schirmer@12854
  1788
      then have "Ca=C" "membr = method sig m" and 
schirmer@12854
  1789
                "G\<turnstile>Methd sig m declared_in C" "declclass m = C"
schirmer@12854
  1790
	by (cases m,auto)
schirmer@12854
  1791
      with clsC 
schirmer@12854
  1792
      have "table_of (map (\<lambda>(s, m). (s, C, m)) (methods c)) sig = Some m"
schirmer@12854
  1793
	by (cases m)
schirmer@12854
  1794
	   (auto simp add: declared_in_def cdeclaredmethd_def
schirmer@12854
  1795
	            intro: table_of_mapconst_SomeI)
schirmer@12854
  1796
      with clsC neq_C_Obj ws 
schirmer@12854
  1797
      show ?thesis
schirmer@12854
  1798
	by (simp add: methd_rec)
schirmer@12854
  1799
    next
schirmer@12854
  1800
      case (Inherited Ca S membr)
schirmer@12854
  1801
      with clsC
schirmer@12854
  1802
      have eq_Ca_C: "Ca=C" and
schirmer@12854
  1803
            undecl: "G\<turnstile>mid sig undeclared_in C" and
schirmer@12854
  1804
             super: "G \<turnstile>Methd sig m member_of (super c)"
schirmer@12854
  1805
	by (auto dest: subcls1D)
schirmer@12854
  1806
      from eq_Ca_C clsC undecl 
schirmer@12854
  1807
      have "table_of (map (\<lambda>(s, m). (s, C, m)) (methods c)) sig = None"
schirmer@12854
  1808
	by (auto simp add: undeclared_in_def cdeclaredmethd_def
schirmer@12854
  1809
	            intro: table_of_mapconst_NoneI)
schirmer@12854
  1810
      moreover
schirmer@12854
  1811
      from Inherited have "G \<turnstile> C inherits (method sig m)"
schirmer@12854
  1812
	by (auto simp add: inherits_def)
schirmer@12854
  1813
      moreover
schirmer@12854
  1814
      note clsC neq_C_Obj ws super hyp 
schirmer@12854
  1815
      ultimately
schirmer@12854
  1816
      show ?thesis
schirmer@12854
  1817
	by (auto simp add: methd_rec intro: filter_tab_SomeI)
schirmer@12854
  1818
    qed
schirmer@12854
  1819
  qed
schirmer@12854
  1820
qed
schirmer@12854
  1821
schirmer@12854
  1822
(*unused*)
schirmer@12854
  1823
lemma finite_methd:"ws_prog G \<Longrightarrow> finite {methd G C sig |sig C. is_class G C}"
schirmer@12854
  1824
apply (rule finite_is_class [THEN finite_SetCompr2])
schirmer@12854
  1825
apply (intro strip)
schirmer@12854
  1826
apply (erule_tac ws_subcls1_induct, assumption)
schirmer@12854
  1827
apply (subst methd_rec)
schirmer@12854
  1828
apply (assumption)
schirmer@12854
  1829
apply (auto intro!: finite_range_map_of finite_range_filter_tab finite_range_map_of_override)
schirmer@12854
  1830
done
schirmer@12854
  1831
schirmer@12854
  1832
lemma finite_dom_methd:
schirmer@12854
  1833
 "\<lbrakk>ws_prog G; is_class G C\<rbrakk> \<Longrightarrow> finite (dom (methd G C))"
schirmer@12854
  1834
apply (erule_tac ws_subcls1_induct)
schirmer@12854
  1835
apply assumption
schirmer@12854
  1836
apply (subst methd_rec)
schirmer@12854
  1837
apply (assumption)
schirmer@12854
  1838
apply (auto intro!: finite_dom_map_of finite_dom_filter_tab)
schirmer@12854
  1839
done
schirmer@12854
  1840
schirmer@12854
  1841
schirmer@12854
  1842
subsection "accmethd"
schirmer@12854
  1843
schirmer@12854
  1844
lemma accmethd_SomeD:
schirmer@12854
  1845
"accmethd G S C sig = Some m
schirmer@12854
  1846
 \<Longrightarrow> methd G C sig = Some m \<and> G\<turnstile>method sig m of C accessible_from S"
schirmer@12854
  1847
by (auto simp add: accmethd_def dest: filter_tab_SomeD)
schirmer@12854
  1848
schirmer@12854
  1849
lemma accmethd_SomeI:
schirmer@12854
  1850
"\<lbrakk>methd G C sig = Some m; G\<turnstile>method sig m of C accessible_from S\<rbrakk> 
schirmer@12854
  1851
 \<Longrightarrow> accmethd G S C sig = Some m"
schirmer@12854
  1852
by (auto simp add: accmethd_def intro: filter_tab_SomeI)
schirmer@12854
  1853
schirmer@12854
  1854
lemma accmethd_declC: 
schirmer@12854
  1855
"\<lbrakk>accmethd G S C sig = Some m; ws_prog G; is_class G C\<rbrakk> \<Longrightarrow>
schirmer@12854
  1856
 (\<exists>d. class G (declclass m)=Some d \<and> 
schirmer@12854
  1857
  table_of (methods d) sig=Some (mthd m)) \<and> 
schirmer@12854
  1858
 G\<turnstile>C \<preceq>\<^sub>C (declclass m) \<and> methd G (declclass m) sig = Some m \<and> 
schirmer@12854
  1859
 G\<turnstile>method sig m of C accessible_from S"
schirmer@12854
  1860
by (auto dest: accmethd_SomeD methd_declC accmethd_SomeI)
schirmer@12854
  1861
schirmer@12854
  1862
schirmer@12854
  1863
lemma finite_dom_accmethd:
schirmer@12854
  1864
 "\<lbrakk>ws_prog G; is_class G C\<rbrakk> \<Longrightarrow> finite (dom (accmethd G S C))"
schirmer@12854
  1865
by (auto simp add: accmethd_def intro: finite_dom_filter_tab finite_dom_methd)
schirmer@12854
  1866
schirmer@12854
  1867
schirmer@12854
  1868
subsection "dynmethd"
schirmer@12854
  1869
schirmer@12854
  1870
lemma dynmethd_rec:
schirmer@12854
  1871
"\<lbrakk>class G dynC = Some c; ws_prog G\<rbrakk> \<Longrightarrow>  
schirmer@12854
  1872
 dynmethd G statC dynC sig
schirmer@12854
  1873
   = (if G\<turnstile>dynC \<preceq>\<^sub>C statC
schirmer@12854
  1874
        then (case methd G statC sig of
schirmer@12854
  1875
                None \<Rightarrow> None
schirmer@12854
  1876
              | Some statM 
schirmer@12854
  1877
                  \<Rightarrow> (case methd G dynC sig of
schirmer@12854
  1878
                        None \<Rightarrow> dynmethd G statC (super c) sig
schirmer@12854
  1879
                      | Some dynM \<Rightarrow> 
schirmer@12854
  1880
                          (if G,sig\<turnstile> dynM overrides statM \<or> dynM = statM 
schirmer@12854
  1881
                              then Some dynM
schirmer@12854
  1882
                              else (dynmethd G statC (super c) sig)
schirmer@12854
  1883
                      )))
schirmer@12854
  1884
         else None)" 
schirmer@12854
  1885
   (is "_ \<Longrightarrow> _ \<Longrightarrow> ?Dynmethd_def dynC sig  = ?Dynmethd_rec dynC c sig") 
schirmer@12854
  1886
proof -
schirmer@12854
  1887
  assume clsDynC: "class G dynC = Some c" and 
schirmer@12854
  1888
              ws: "ws_prog G"
schirmer@12854
  1889
  then show "?Dynmethd_def dynC sig  = ?Dynmethd_rec dynC c sig" 
schirmer@12854
  1890
  proof (induct rule: ws_class_induct'')
schirmer@12854
  1891
    case (Object co)
schirmer@12854
  1892
    show "?Dynmethd_def Object sig = ?Dynmethd_rec Object co sig"
schirmer@12854
  1893
    proof (cases "G\<turnstile>Object \<preceq>\<^sub>C statC") 
schirmer@12854
  1894
      case False
schirmer@12854
  1895
      then show ?thesis by (simp add: dynmethd_def)
schirmer@12854
  1896
    next
schirmer@12854
  1897
      case True
schirmer@12854
  1898
      then have eq_statC_Obj: "statC = Object" ..
schirmer@12854
  1899
      show ?thesis 
schirmer@12854
  1900
      proof (cases "methd G statC sig")
schirmer@12854
  1901
	case None then show ?thesis by (simp add: dynmethd_def)
schirmer@12854
  1902
      next
schirmer@12854
  1903
	case Some
schirmer@12854
  1904
	with True Object ws eq_statC_Obj 
schirmer@12854
  1905
	show ?thesis
schirmer@12854
  1906
	  by (auto simp add: dynmethd_def class_rec
schirmer@12854
  1907
                      intro: filter_tab_SomeI)
schirmer@12854
  1908
      qed
schirmer@12854
  1909
    qed
schirmer@12854
  1910
  next  
schirmer@12854
  1911
    case (Subcls dynC c sc)
schirmer@12854
  1912
    show "?Dynmethd_def dynC sig = ?Dynmethd_rec dynC c sig"
schirmer@12854
  1913
    proof (cases "G\<turnstile>dynC \<preceq>\<^sub>C statC") 
schirmer@12854
  1914
      case False
schirmer@12854
  1915
      then show ?thesis by (simp add: dynmethd_def)
schirmer@12854
  1916
    next
schirmer@12854
  1917
      case True
schirmer@12854
  1918
      note subclseq_dynC_statC = True
schirmer@12854
  1919
      show ?thesis
schirmer@12854
  1920
      proof (cases "methd G statC sig")
schirmer@12854
  1921
	case None then show ?thesis by (simp add: dynmethd_def)
schirmer@12854
  1922
      next
schirmer@12854
  1923
	case (Some statM)
schirmer@12854
  1924
	note statM = Some
schirmer@12854
  1925
	let "?filter C" = 
schirmer@12854
  1926
              "filter_tab
schirmer@12854
  1927
                (\<lambda>_ dynM. G,sig \<turnstile> dynM overrides statM \<or> dynM = statM)
schirmer@12854
  1928
                (methd G C)"
schirmer@12854
  1929
        let "?class_rec C" =
schirmer@12854
  1930
              "(class_rec (G, C) empty
schirmer@12854
  1931
                           (\<lambda>C c subcls_mthds. subcls_mthds ++ (?filter C)))"
schirmer@12854
  1932
	from statM Subcls ws subclseq_dynC_statC
schirmer@12854
  1933
	have dynmethd_dynC_def:
schirmer@12854
  1934
             "?Dynmethd_def dynC sig =
schirmer@12854
  1935
                ((?class_rec (super c)) 
schirmer@12854
  1936
                 ++
schirmer@12854
  1937
                (?filter dynC)) sig"
schirmer@12854
  1938
         by (simp (no_asm_simp) only: dynmethd_def class_rec)
schirmer@12854
  1939
	    auto
schirmer@12854
  1940
       show ?thesis
schirmer@12854
  1941
       proof (cases "dynC = statC")
schirmer@12854
  1942
	 case True
schirmer@12854
  1943
	 with subclseq_dynC_statC statM dynmethd_dynC_def
schirmer@12854
  1944
	 have "?Dynmethd_def dynC sig = Some statM"
schirmer@12854
  1945
	   by (auto intro: override_find_right filter_tab_SomeI)
schirmer@12854
  1946
	 with subclseq_dynC_statC True Some 
schirmer@12854
  1947
	 show ?thesis
schirmer@12854
  1948
	   by auto
schirmer@12854
  1949
       next
schirmer@12854
  1950
	 case False
schirmer@12854
  1951
	 with subclseq_dynC_statC Subcls 
schirmer@12854
  1952
	 have subclseq_super_statC: "G\<turnstile>(super c) \<preceq>\<^sub>C statC"
schirmer@12854
  1953
	   by (blast dest: subclseq_superD)
schirmer@12854
  1954
	 show ?thesis
schirmer@12854
  1955
	 proof (cases "methd G dynC sig") 
schirmer@12854
  1956
	   case None
schirmer@12854
  1957
	   then have "?filter dynC sig = None"
schirmer@12854
  1958
	     by (rule filter_tab_None)
schirmer@12854
  1959
           then have "?Dynmethd_def dynC sig=?class_rec (super c) sig"
schirmer@12854
  1960
	     by (simp add: dynmethd_dynC_def)
schirmer@12854
  1961
	   with  subclseq_super_statC statM None
schirmer@12854
  1962
	   have "?Dynmethd_def dynC sig = ?Dynmethd_def (super c) sig"
schirmer@12854
  1963
	     by (auto simp add: empty_def dynmethd_def)
schirmer@12854
  1964
           with None subclseq_dynC_statC statM
schirmer@12854
  1965
	   show ?thesis 
schirmer@12854
  1966
	     by simp
schirmer@12854
  1967
	 next
schirmer@12854
  1968
	   case (Some dynM)
schirmer@12854
  1969
	   note dynM = Some
schirmer@12854
  1970
	   let ?Termination = "G \<turnstile> qmdecl sig dynM overrides qmdecl sig statM \<or>
schirmer@12854
  1971
                               dynM = statM"
schirmer@12854
  1972
	   show ?thesis
schirmer@12854
  1973
	   proof (cases "?filter dynC sig")
schirmer@12854
  1974
	     case None
schirmer@12854
  1975
	     with dynM 
schirmer@12854
  1976
	     have no_termination: "\<not> ?Termination"
schirmer@12854
  1977
	       by (simp add: filter_tab_def)
schirmer@12854
  1978
	     from None 
schirmer@12854
  1979
	     have "?Dynmethd_def dynC sig=?class_rec (super c) sig"
schirmer@12854
  1980
	       by (simp add: dynmethd_dynC_def)
schirmer@12854
  1981
	     with subclseq_super_statC statM dynM no_termination
schirmer@12854
  1982
	     show ?thesis
schirmer@12854
  1983
	       by (auto simp add: empty_def dynmethd_def)
schirmer@12854
  1984
	   next
schirmer@12854
  1985
	     case Some
schirmer@12854
  1986
	     with dynM
schirmer@12854
  1987
	     have termination: "?Termination"
schirmer@12854
  1988
	       by (auto)
schirmer@12854
  1989
	     with Some dynM
schirmer@12854
  1990
	     have "?Dynmethd_def dynC sig=Some dynM"
schirmer@12854
  1991
	      by (auto simp add: dynmethd_dynC_def)
schirmer@12854
  1992
	     with subclseq_super_statC statM dynM termination
schirmer@12854
  1993
	     show ?thesis
schirmer@12854
  1994
	       by (auto simp add: dynmethd_def)
schirmer@12854
  1995
	   qed
schirmer@12854
  1996
	 qed
schirmer@12854
  1997
       qed
schirmer@12854
  1998
     qed
schirmer@12854
  1999
   qed
schirmer@12854
  2000
 qed
schirmer@12854
  2001
qed
schirmer@12854
  2002
	       
schirmer@12854
  2003
lemma dynmethd_C_C:"\<lbrakk>is_class G C; ws_prog G\<rbrakk> 
schirmer@12854
  2004
\<Longrightarrow> dynmethd G C C sig = methd G C sig"          
schirmer@12854
  2005
apply (auto simp add: dynmethd_rec)
schirmer@12854
  2006
done
schirmer@12854
  2007
 
schirmer@12854
  2008
lemma dynmethdSomeD: 
schirmer@12854
  2009
 "\<lbrakk>dynmethd G statC dynC sig = Some dynM; is_class G dynC; ws_prog G\<rbrakk> 
schirmer@12854
  2010
  \<Longrightarrow> G\<turnstile>dynC \<preceq>\<^sub>C statC \<and> (\<exists> statM. methd G statC sig = Some statM)"
schirmer@12854
  2011
apply clarify
schirmer@12854
  2012
apply rotate_tac
schirmer@12854
  2013
by (auto simp add: dynmethd_rec)
schirmer@12854
  2014
 
schirmer@12854
  2015
lemma dynmethd_Some_cases [consumes 3, case_names Static Overrides]:
schirmer@12854
  2016
  (assumes dynM: "dynmethd G statC dynC sig = Some dynM" and
schirmer@12854
  2017
        is_cls_dynC: "is_class G dynC" and
schirmer@12854
  2018
                 ws: "ws_prog G" and
schirmer@12854
  2019
         hyp_static: "methd G statC sig = Some dynM \<Longrightarrow> P" and
schirmer@12854
  2020
       hyp_override: "\<And> statM. \<lbrakk>methd G statC sig = Some statM;dynM\<noteq>statM;
schirmer@12854
  2021
                       G,sig\<turnstile>dynM overrides statM\<rbrakk> \<Longrightarrow> P"
schirmer@12854
  2022
   ) "P"
schirmer@12854
  2023
proof -
schirmer@12854
  2024
  from is_cls_dynC obtain dc where clsDynC: "class G dynC = Some dc" by blast
schirmer@12854
  2025
  from clsDynC ws dynM hyp_static hyp_override
schirmer@12854
  2026
  show "P"
schirmer@12854
  2027
  proof (induct rule: ws_class_induct)
schirmer@12854
  2028
    case (Object co)
schirmer@12854
  2029
    with ws  have "statC = Object" 
schirmer@12854
  2030
      by (auto simp add: dynmethd_rec)
schirmer@12854
  2031
    with ws Object show ?thesis by (auto simp add: dynmethd_C_C)
schirmer@12854
  2032
  next
schirmer@12854
  2033
    case (Subcls C c)
schirmer@12854
  2034
    with ws show ?thesis
schirmer@12854
  2035
      by (auto simp add: dynmethd_rec)
schirmer@12854
  2036
  qed
schirmer@12854
  2037
qed
schirmer@12854
  2038
schirmer@12854
  2039
lemma no_override_in_Object:
schirmer@12854
  2040
  (assumes     dynM: "dynmethd G statC dynC sig = Some dynM" and
schirmer@12854
  2041
            is_cls_dynC: "is_class G dynC" and
schirmer@12854
  2042
                     ws: "ws_prog G" and
schirmer@12854
  2043
                  statM: "methd G statC sig = Some statM" and
schirmer@12854
  2044
         neq_dynM_statM: "dynM\<noteq>statM"
schirmer@12854
  2045
   )
schirmer@12854
  2046
   "dynC \<noteq> Object"
schirmer@12854
  2047
proof -
schirmer@12854
  2048
  from is_cls_dynC obtain dc where clsDynC: "class G dynC = Some dc" by blast
schirmer@12854
  2049
  from clsDynC ws dynM statM neq_dynM_statM 
schirmer@12854
  2050
  show ?thesis (is "?P dynC")
schirmer@12854
  2051
  proof (induct rule: ws_class_induct)
schirmer@12854
  2052
    case (Object co)
schirmer@12854
  2053
    with ws  have "statC = Object" 
schirmer@12854
  2054
      by (auto simp add: dynmethd_rec)
schirmer@12854
  2055
    with ws Object show "?P Object" by (auto simp add: dynmethd_C_C)
schirmer@12854
  2056
  next
schirmer@12854
  2057
    case (Subcls dynC c)
schirmer@12854
  2058
    with ws show "?P dynC"
schirmer@12854
  2059
      by (auto simp add: dynmethd_rec)
schirmer@12854
  2060
  qed
schirmer@12854
  2061
qed
schirmer@12854
  2062
schirmer@12854
  2063
schirmer@12854
  2064
lemma dynmethd_Some_rec_cases [consumes 3, 
schirmer@12854
  2065
                               case_names Static Override  Recursion]:
schirmer@12854
  2066
(assumes     dynM: "dynmethd G statC dynC sig = Some dynM" and
schirmer@12854
  2067
                clsDynC: "class G dynC = Some c" and
schirmer@12854
  2068
                     ws: "ws_prog G" and
schirmer@12854
  2069
             hyp_static: "methd G statC sig = Some dynM \<Longrightarrow> P" and
schirmer@12854
  2070
           hyp_override: "\<And> statM. \<lbrakk>methd G statC sig = Some statM;
schirmer@12854
  2071
                                     methd G dynC sig = Some dynM; statM\<noteq>dynM;
schirmer@12854
  2072
                                     G,sig\<turnstile> dynM overrides statM\<rbrakk> \<Longrightarrow> P" and
schirmer@12854
  2073
schirmer@12854
  2074
          hyp_recursion: "\<lbrakk>dynC\<noteq>Object;
schirmer@12854
  2075
                           dynmethd G statC (super c) sig = Some dynM\<rbrakk> \<Longrightarrow> P" 
schirmer@12854
  2076
  ) "P"
schirmer@12854
  2077
proof -
schirmer@12854
  2078
  from clsDynC have "is_class G dynC" by simp
schirmer@12854
  2079
  note no_override_in_Object' = no_override_in_Object [OF dynM this ws]
schirmer@12854
  2080
  from ws clsDynC dynM hyp_static hyp_override hyp_recursion
schirmer@12854
  2081
  show ?thesis
schirmer@12854
  2082
    by (auto simp add: dynmethd_rec dest: no_override_in_Object')
schirmer@12854
  2083
qed
schirmer@12854
  2084
schirmer@12854
  2085
lemma dynmethd_declC: 
schirmer@12854
  2086
"\<lbrakk>dynmethd G statC dynC sig = Some m;
schirmer@12854
  2087
  is_class G statC;ws_prog G
schirmer@12854
  2088
 \<rbrakk> \<Longrightarrow>
schirmer@12854
  2089
  (\<exists>d. class G (declclass m)=Some d \<and> table_of (methods d) sig=Some (mthd m)) \<and>
schirmer@12854
  2090
  G\<turnstile>dynC \<preceq>\<^sub>C (declclass m) \<and> methd G (declclass m) sig = Some m"
schirmer@12854
  2091
proof - 
schirmer@12854
  2092
  assume  is_cls_statC: "is_class G statC" 
schirmer@12854
  2093
  assume            ws: "ws_prog G"  
schirmer@12854
  2094
  assume             m: "dynmethd G statC dynC sig = Some m"
schirmer@12854
  2095
  from m 
schirmer@12854
  2096
  have "G\<turnstile>dynC \<preceq>\<^sub>C statC" by (auto simp add: dynmethd_def)
schirmer@12854
  2097
  from this is_cls_statC 
schirmer@12854
  2098
  have is_cls_dynC: "is_class G dynC" by (rule subcls_is_class2)
schirmer@12854
  2099
  from is_cls_dynC ws m  
schirmer@12854
  2100
  show ?thesis (is "?P dynC") 
schirmer@12854
  2101
  proof (induct rule: ws_class_induct')
schirmer@12854
  2102
    case (Object co)
schirmer@12854
  2103
    with ws have "statC=Object" by (auto simp add: dynmethd_rec)
schirmer@12854
  2104
    with ws Object  
schirmer@12854
  2105
    show "?P Object" 
schirmer@12854
  2106
      by (auto simp add: dynmethd_C_C dest: methd_declC)
schirmer@12854
  2107
  next
schirmer@12854
  2108
    case (Subcls dynC c)
schirmer@12854
  2109
    assume   hyp: "dynmethd G statC (super c) sig = Some m \<Longrightarrow> ?P (super c)" and
schirmer@12854
  2110
         clsDynC: "class G dynC = Some c"  and
schirmer@12854
  2111
              m': "dynmethd G statC dynC sig = Some m" and
schirmer@12854
  2112
    neq_dynC_Obj: "dynC \<noteq> Object"
schirmer@12854
  2113
    from ws this obtain statM where
schirmer@12854
  2114
      subclseq_dynC_statC: "G\<turnstile>dynC \<preceq>\<^sub>C statC" and 
schirmer@12854
  2115
                     statM: "methd G statC sig = Some statM"
schirmer@12854
  2116
      by (blast dest: dynmethdSomeD)
schirmer@12854
  2117
    from clsDynC neq_dynC_Obj 
schirmer@12854
  2118
    have subclseq_dynC_super: "G\<turnstile>dynC \<preceq>\<^sub>C (super c)" 
schirmer@12854
  2119
      by (auto intro: subcls1I) 
schirmer@12854
  2120
    from m' clsDynC ws 
schirmer@12854
  2121
    show "?P dynC"
schirmer@12854
  2122
    proof (cases rule: dynmethd_Some_rec_cases) 
schirmer@12854
  2123
      case Static
schirmer@12854
  2124
      with is_cls_statC ws subclseq_dynC_statC 
schirmer@12854
  2125
      show ?thesis 
schirmer@12854
  2126
	by (auto intro: rtrancl_trans dest: methd_declC)
schirmer@12854
  2127
    next
schirmer@12854
  2128
      case Override
schirmer@12854
  2129
      with clsDynC ws 
schirmer@12854
  2130
      show ?thesis 
schirmer@12854
  2131
	by (auto dest: methd_declC)
schirmer@12854
  2132
    next
schirmer@12854
  2133
      case Recursion
schirmer@12854
  2134
      with hyp subclseq_dynC_super 
schirmer@12854
  2135
      show ?thesis 
schirmer@12854
  2136
	by (auto intro: rtrancl_trans) 
schirmer@12854
  2137
    qed
schirmer@12854
  2138
  qed
schirmer@12854
  2139
qed
schirmer@12854
  2140
schirmer@12854
  2141
lemma methd_Some_dynmethd_Some:
schirmer@12854
  2142
  (assumes    statM: "methd G statC sig = Some statM" and 
schirmer@12854
  2143
           subclseq: "G\<turnstile>dynC \<preceq>\<^sub>C statC" and
schirmer@12854
  2144
       is_cls_statC: "is_class G statC" and
schirmer@12854
  2145
                 ws: "ws_prog G"
schirmer@12854
  2146
   ) "\<exists> dynM. dynmethd G statC dynC sig = Some dynM"
schirmer@12854
  2147
   (is "?P dynC")
schirmer@12854
  2148
proof -
schirmer@12854
  2149
  from subclseq is_cls_statC 
schirmer@12854
  2150
  have is_cls_dynC: "is_class G dynC" by (rule subcls_is_class2)
schirmer@12854
  2151
  then obtain dc where
schirmer@12854
  2152
    clsDynC: "class G dynC = Some dc" by blast
schirmer@12854
  2153
  from clsDynC ws subclseq 
schirmer@12854
  2154
  show "?thesis"
schirmer@12854
  2155
  proof (induct rule: ws_class_induct)
schirmer@12854
  2156
    case (Object co)
schirmer@12854
  2157
    with ws  have "statC = Object" 
schirmer@12854
  2158
      by (auto)
schirmer@12854
  2159
    with ws Object statM
schirmer@12854
  2160
    show "?P Object"  
schirmer@12854
  2161
      by (auto simp add: dynmethd_C_C)
schirmer@12854
  2162
  next
schirmer@12854
  2163
    case (Subcls dynC dc)
schirmer@12854
  2164
    assume clsDynC': "class G dynC = Some dc"
schirmer@12854
  2165
    assume neq_dynC_Obj: "dynC \<noteq> Object"
schirmer@12854
  2166
    assume hyp: "G\<turnstile>super dc\<preceq>\<^sub>C statC \<Longrightarrow> ?P (super dc)"
schirmer@12854
  2167
    assume subclseq': "G\<turnstile>dynC\<preceq>\<^sub>C statC"
schirmer@12854
  2168
    then
schirmer@12854
  2169
    show "?P dynC"
schirmer@12854
  2170
    proof (cases rule: subclseq_cases)
schirmer@12854
  2171
      case Eq
schirmer@12854
  2172
      with ws statM clsDynC' 
schirmer@12854
  2173
      show ?thesis
schirmer@12854
  2174
	by (auto simp add: dynmethd_rec)
schirmer@12854
  2175
    next
schirmer@12854
  2176
      case Subcls
schirmer@12854
  2177
      assume "G\<turnstile>dynC\<prec>\<^sub>C statC"
schirmer@12854
  2178
      from this clsDynC' 
schirmer@12854
  2179
      have "G\<turnstile>super dc\<preceq>\<^sub>C statC" by (rule subcls_superD)
schirmer@12854
  2180
      with hyp ws clsDynC' subclseq' statM
schirmer@12854
  2181
      show ?thesis
schirmer@12854
  2182
	by (auto simp add: dynmethd_rec)
schirmer@12854
  2183
    qed
schirmer@12854
  2184
  qed
schirmer@12854
  2185
qed
schirmer@12854
  2186
schirmer@12854
  2187
lemma dynmethd_cases [consumes 4, case_names Static Overrides]:
schirmer@12854
  2188
  (assumes    statM: "methd G statC sig = Some statM" and 
schirmer@12854
  2189
           subclseq: "G\<turnstile>dynC \<preceq>\<^sub>C statC" and
schirmer@12854
  2190
       is_cls_statC: "is_class G statC" and
schirmer@12854
  2191
                 ws: "ws_prog G" and
schirmer@12854
  2192
         hyp_static: "dynmethd G statC dynC sig = Some statM \<Longrightarrow> P" and
schirmer@12854
  2193
       hyp_override: "\<And> dynM. \<lbrakk>dynmethd G statC dynC sig = Some dynM;
schirmer@12854
  2194
                                 dynM\<noteq>statM;
schirmer@12854
  2195
                           G,sig\<turnstile>dynM overrides statM\<rbrakk> \<Longrightarrow> P"
schirmer@12854
  2196
   ) "P"
schirmer@12854
  2197
proof -
schirmer@12854
  2198
  from subclseq is_cls_statC 
schirmer@12854
  2199
  have is_cls_dynC: "is_class G dynC" by (rule subcls_is_class2)
schirmer@12854
  2200
  then obtain dc where
schirmer@12854
  2201
    clsDynC: "class G dynC = Some dc" by blast
schirmer@12854
  2202
  from statM subclseq is_cls_statC ws 
schirmer@12854
  2203
  obtain dynM
schirmer@12854
  2204
    where dynM: "dynmethd G statC dynC sig = Some dynM"
schirmer@12854
  2205
    by (blast dest: methd_Some_dynmethd_Some)
schirmer@12854
  2206
  from dynM is_cls_dynC ws 
schirmer@12854
  2207
  show ?thesis
schirmer@12854
  2208
  proof (cases rule: dynmethd_Some_cases)
schirmer@12854
  2209
    case Static
schirmer@12854
  2210
    with hyp_static dynM statM show ?thesis by simp
schirmer@12854
  2211
  next
schirmer@12854
  2212
    case Overrides
schirmer@12854
  2213
    with hyp_override dynM statM show ?thesis by simp
schirmer@12854
  2214
  qed
schirmer@12854
  2215
qed
schirmer@12854
  2216
schirmer@12854
  2217
lemma ws_dynmethd:
schirmer@12854
  2218
  (assumes statM: "methd G statC sig = Some statM" and
schirmer@12854
  2219
        subclseq: "G\<turnstile>dynC \<preceq>\<^sub>C statC" and
schirmer@12854
  2220
    is_cls_statC: "is_class G statC" and
schirmer@12854
  2221
              ws: "ws_prog G"
schirmer@12854
  2222
   )
schirmer@12854
  2223
   "\<exists> dynM. dynmethd G statC dynC sig = Some dynM \<and>
schirmer@12854
  2224
            is_static dynM = is_static statM \<and> G\<turnstile>resTy dynM\<preceq>resTy statM"
schirmer@12854
  2225
proof - 
schirmer@12854
  2226
  from statM subclseq is_cls_statC ws
schirmer@12854
  2227
  show ?thesis
schirmer@12854
  2228
  proof (cases rule: dynmethd_cases)
schirmer@12854
  2229
    case Static
schirmer@12854
  2230
    with statM 
schirmer@12854
  2231
    show ?thesis
schirmer@12854
  2232
      by simp
schirmer@12854
  2233
  next
schirmer@12854
  2234
    case Overrides
schirmer@12854
  2235
    with ws
schirmer@12854
  2236
    show ?thesis
schirmer@12854
  2237
      by (auto dest: ws_overrides_commonD)
schirmer@12854
  2238
  qed
schirmer@12854
  2239
qed
schirmer@12854
  2240
schirmer@12854
  2241
(*
schirmer@12854
  2242
lemma dom_dynmethd: 
schirmer@12854
  2243
  "dom (dynmethd G statC dynC) \<subseteq> dom (methd G statC) \<union> dom (methd G dynC)"
schirmer@12854
  2244
by (auto simp add: dynmethd_def dom_def)
schirmer@12854
  2245
schirmer@12854
  2246
lemma finite_dom_dynmethd:
schirmer@12854
  2247
 "\<lbrakk>ws_prog G; is_class G statC; is_class G dynC\<rbrakk> 
schirmer@12854
  2248
  \<Longrightarrow> finite (dom (dynmethd G statC dynC))"
schirmer@12854
  2249
apply (rule_tac B="dom (methd G statC) \<union> dom (methd G dynC)" in finite_subset)
schirmer@12854
  2250
apply (rule dom_dynmethd)
schirmer@12854
  2251
apply (rule finite_UnI)
schirmer@12854
  2252
apply (drule (2) finite_dom_methd)+
schirmer@12854
  2253
done
schirmer@12854
  2254
*)
schirmer@12854
  2255
(*
schirmer@12854
  2256
lemma dynmethd_SomeD: 
schirmer@12854
  2257
"\<lbrakk>ws_prog G; is_class G statC; is_class G dynC;
schirmer@12854
  2258
 methd G statC sig = Some sm; dynmethd G statC dynC sig = Some dm; sm \<noteq> dm
schirmer@12854
  2259
 \<rbrakk> \<Longrightarrow> G\<turnstile>dynC \<prec>\<^sub>C statC \<and> 
schirmer@12854
  2260
       (declclass dm \<noteq> dynC \<longrightarrow> G \<turnstile> dm accessible_through_inheritance_in dynC)"
schirmer@12854
  2261
by (auto simp add: dynmethd_def 
schirmer@12854
  2262
         dest: methd_inheritedD methd_diff_cls
schirmer@12854
  2263
         intro: rtrancl_into_trancl3)
schirmer@12854
  2264
*)
schirmer@12854
  2265
schirmer@12854
  2266
subsection "dynlookup"
schirmer@12854
  2267
schirmer@12854
  2268
lemma dynlookup_cases [consumes 1, case_names NullT IfaceT ClassT ArrayT]:
schirmer@12854
  2269
"\<lbrakk>dynlookup G statT dynC sig = x;
schirmer@12854
  2270
           \<lbrakk>statT = NullT       ; empty sig = x                  \<rbrakk> \<Longrightarrow> P;
schirmer@12854
  2271
  \<And> I.    \<lbrakk>statT = IfaceT I    ; dynimethd G I      dynC sig = x\<rbrakk> \<Longrightarrow> P;
schirmer@12854
  2272
  \<And> statC.\<lbrakk>statT = ClassT statC; dynmethd  G statC  dynC sig = x\<rbrakk> \<Longrightarrow> P;
schirmer@12854
  2273
  \<And> ty.   \<lbrakk>statT = ArrayT ty   ; dynmethd  G Object dynC sig = x\<rbrakk> \<Longrightarrow> P
schirmer@12854
  2274
 \<rbrakk> \<Longrightarrow> P"
schirmer@12854
  2275
by (cases statT) (auto simp add: dynlookup_def)
schirmer@12854
  2276
schirmer@12854
  2277
subsection "fields"
schirmer@12854
  2278
schirmer@12854
  2279
lemma fields_rec: "\<lbrakk>class G C = Some c; ws_prog G\<rbrakk> \<Longrightarrow>  
schirmer@12854
  2280
  fields G C = map (\<lambda>(fn,ft). ((fn,C),ft)) (cfields c) @  
schirmer@12854
  2281
  (if C = Object then [] else fields G (super c))"
schirmer@12854
  2282
apply (simp only: fields_def)
schirmer@12854
  2283
apply (erule class_rec [THEN trans])
schirmer@12854
  2284
apply assumption
schirmer@12854
  2285
apply clarsimp
schirmer@12854
  2286
done
schirmer@12854
  2287
schirmer@12854
  2288
(* local lemma *)
schirmer@12854
  2289
lemma fields_norec: 
schirmer@12854
  2290
"\<lbrakk>class G fd = Some c; ws_prog G;  table_of (cfields c) fn = Some f\<rbrakk> 
schirmer@12854
  2291
 \<Longrightarrow> table_of (fields G fd) (fn,fd) = Some f"
schirmer@12854
  2292
apply (subst fields_rec)
schirmer@12854
  2293
apply assumption+
schirmer@12854
  2294
apply (subst map_of_override [symmetric])
schirmer@12854
  2295
apply (rule disjI1 [THEN override_Some_iff [THEN iffD2]])
schirmer@12854
  2296
apply (auto elim: table_of_map2_SomeI)
schirmer@12854
  2297
done
schirmer@12854
  2298
schirmer@12854
  2299
(* local lemma *)
schirmer@12854
  2300
lemma table_of_fieldsD:
schirmer@12854
  2301
"table_of (map (\<lambda>(fn,ft). ((fn,C),ft)) (cfields c)) efn = Some f
schirmer@12854
  2302
\<Longrightarrow> (declclassf efn) = C \<and> table_of (cfields c) (fname efn) = Some f"
schirmer@12854
  2303
apply (case_tac "efn")
schirmer@12854
  2304
by auto
schirmer@12854
  2305
schirmer@12854
  2306
lemma fields_declC: 
schirmer@12854
  2307
 "\<lbrakk>table_of (fields G C) efn = Some f; ws_prog G; is_class G C\<rbrakk> \<Longrightarrow>  
schirmer@12854
  2308
  (\<exists>d. class G (declclassf efn) = Some d \<and> 
schirmer@12854
  2309
                    table_of (cfields d) (fname efn)=Some f) \<and> 
schirmer@12854
  2310
  G\<turnstile>C \<preceq>\<^sub>C (declclassf efn)  \<and> table_of (fields G (declclassf efn)) efn = Some f"
schirmer@12854
  2311
apply (erule make_imp)
schirmer@12854
  2312
apply (rule ws_subcls1_induct, assumption, assumption)
schirmer@12854
  2313
apply (subst fields_rec, assumption)
schirmer@12854
  2314
apply clarify
schirmer@12854
  2315
apply (simp only: map_of_override [symmetric] del: map_of_override)
schirmer@12854
  2316
apply (case_tac "table_of (map (split (\<lambda>fn. Pair (fn, Ca))) (cfields c)) efn") 
schirmer@12854
  2317
apply   (force intro:rtrancl_into_rtrancl2 simp add: override_def)
schirmer@12854
  2318
schirmer@12854
  2319
apply   (frule_tac fd="Ca" in fields_norec)
schirmer@12854
  2320
apply     assumption
schirmer@12854
  2321
apply     blast
schirmer@12854
  2322
apply   (frule table_of_fieldsD)  
schirmer@12854
  2323
apply   (frule_tac n="table_of (map (split (\<lambda>fn. Pair (fn, Ca))) (cfields c))"
schirmer@12854
  2324
              and  m="table_of (if Ca = Object then [] else fields G (super c))"
schirmer@12854
  2325
         in override_find_right)
schirmer@12854
  2326
apply   (case_tac "efn")
schirmer@12854
  2327
apply   (simp)
schirmer@12854
  2328
done
schirmer@12854
  2329
schirmer@12854
  2330
lemma fields_emptyI: "\<And>y. \<lbrakk>ws_prog G; class G C = Some c;cfields c = [];  
schirmer@12854
  2331
  C \<noteq> Object \<longrightarrow> class G (super c) = Some y \<and> fields G (super c) = []\<rbrakk> \<Longrightarrow>  
schirmer@12854
  2332
  fields G C = []"
schirmer@12854
  2333
apply (subst fields_rec)
schirmer@12854
  2334
apply assumption
schirmer@12854
  2335
apply auto
schirmer@12854
  2336
done
schirmer@12854
  2337
schirmer@12854
  2338
(* easier than with table_of *)
schirmer@12854
  2339
lemma fields_mono_lemma: 
schirmer@12854
  2340
"\<lbrakk>x \<in> set (fields G C); G\<turnstile>D \<preceq>\<^sub>C C; ws_prog G\<rbrakk> 
schirmer@12854
  2341
 \<Longrightarrow> x \<in> set (fields G D)"
schirmer@12854
  2342
apply (erule make_imp)
schirmer@12854
  2343
apply (erule converse_rtrancl_induct)
schirmer@12854
  2344
apply  fast
schirmer@12854
  2345
apply (drule subcls1D)
schirmer@12854
  2346
apply clarsimp
schirmer@12854
  2347
apply (subst fields_rec)
schirmer@12854
  2348
apply   auto
schirmer@12854
  2349
done
schirmer@12854
  2350
schirmer@12854
  2351
schirmer@12854
  2352
lemma ws_unique_fields_lemma: 
schirmer@12854
  2353
 "\<lbrakk>(efn,fd)  \<in> set (fields G (super c)); fc \<in> set (cfields c); ws_prog G;  
schirmer@12854
  2354
   fname efn = fname fc; declclassf efn = C;
schirmer@12854
  2355
   class G C = Some c; C \<noteq> Object; class G (super c) = Some d\<rbrakk> \<Longrightarrow> R"
schirmer@12854
  2356
apply (frule_tac ws_prog_cdeclD [THEN conjunct2], assumption, assumption)
schirmer@12854
  2357
apply (drule_tac weak_map_of_SomeI)
schirmer@12854
  2358
apply (frule_tac subcls1I [THEN subcls1_irrefl], assumption, assumption)
schirmer@12854
  2359
apply (auto dest: fields_declC [THEN conjunct2 [THEN conjunct1[THEN rtranclD]]])
schirmer@12854
  2360
done
schirmer@12854
  2361
schirmer@12854
  2362
lemma ws_unique_fields: "\<lbrakk>is_class G C; ws_prog G; 
schirmer@12854
  2363
       \<And>C c. \<lbrakk>class G C = Some c\<rbrakk> \<Longrightarrow> unique (cfields c) \<rbrakk> \<Longrightarrow>
schirmer@12854
  2364
      unique (fields G C)" 
schirmer@12854
  2365
apply (rule ws_subcls1_induct, assumption, assumption)
schirmer@12854
  2366
apply (subst fields_rec, assumption)            
schirmer@12854
  2367
apply (auto intro!: unique_map_inj injI 
schirmer@12854
  2368
            elim!: unique_append ws_unique_fields_lemma fields_norec
schirmer@12854
  2369
            )
schirmer@12854
  2370
done
schirmer@12854
  2371
schirmer@12854
  2372
schirmer@12854
  2373
subsection "accfield"
schirmer@12854
  2374
schirmer@12854
  2375
lemma accfield_fields: 
schirmer@12854
  2376
 "accfield G S C fn = Some f 
schirmer@12854
  2377
  \<Longrightarrow> table_of (fields G C) (fn, declclass f) = Some (fld f)"
schirmer@12854
  2378
apply (simp only: accfield_def Let_def)
schirmer@12854
  2379
apply (rule table_of_remap_SomeD)
schirmer@12854
  2380
apply (auto dest: filter_tab_SomeD)
schirmer@12854
  2381
done
schirmer@12854
  2382
schirmer@12854
  2383
schirmer@12854
  2384
lemma accfield_declC_is_class: 
schirmer@12854
  2385
 "\<lbrakk>is_class G C; accfield G S C en = Some (fd, f); ws_prog G\<rbrakk> \<Longrightarrow>  
schirmer@12854
  2386
   is_class G fd"
schirmer@12854
  2387
apply (drule accfield_fields)
schirmer@12854
  2388
apply (drule fields_declC [THEN conjunct1], assumption)
schirmer@12854
  2389
apply auto
schirmer@12854
  2390
done
schirmer@12854
  2391
schirmer@12854
  2392
lemma accfield_accessibleD: 
schirmer@12854
  2393
  "accfield G S C fn = Some f \<Longrightarrow> G\<turnstile>Field fn f of C accessible_from S"
schirmer@12854
  2394
by (auto simp add: accfield_def Let_def)
schirmer@12854
  2395
schirmer@12854
  2396
subsection "is methd"
schirmer@12854
  2397
schirmer@12854
  2398
lemma is_methdI: 
schirmer@12854
  2399
"\<lbrakk>class G C = Some y; methd G C sig = Some b\<rbrakk> \<Longrightarrow> is_methd G C sig"
schirmer@12854
  2400
apply (unfold is_methd_def)
schirmer@12854
  2401
apply auto
schirmer@12854
  2402
done
schirmer@12854
  2403
schirmer@12854
  2404
lemma is_methdD: 
schirmer@12854
  2405
"is_methd G C sig \<Longrightarrow> class G C \<noteq> None \<and> methd G C sig \<noteq> None"
schirmer@12854
  2406
apply (unfold is_methd_def)
schirmer@12854
  2407
apply auto
schirmer@12854
  2408
done
schirmer@12854
  2409
schirmer@12854
  2410
lemma finite_is_methd: 
schirmer@12854
  2411
 "ws_prog G \<Longrightarrow> finite (Collect (split (is_methd G)))"
schirmer@12854
  2412
apply (unfold is_methd_def)
schirmer@12854
  2413
apply (subst SetCompr_Sigma_eq)
schirmer@12854
  2414
apply (rule finite_is_class [THEN finite_SigmaI])
schirmer@12854
  2415
apply (simp only: mem_Collect_eq)
schirmer@12854
  2416
apply (fold dom_def)
schirmer@12854
  2417
apply (erule finite_dom_methd)
schirmer@12854
  2418
apply assumption
schirmer@12854
  2419
done
schirmer@12854
  2420
schirmer@12854
  2421
section "calculation of the superclasses of a class"
schirmer@12854
  2422
schirmer@12854
  2423
constdefs 
schirmer@12854
  2424
 superclasses:: "prog \<Rightarrow> qtname \<Rightarrow> qtname set"
schirmer@12854
  2425
 "superclasses G C \<equiv> class_rec (G,C) {} 
schirmer@12854
  2426
                       (\<lambda> C c superclss. (if C=Object 
schirmer@12854
  2427
                                            then {} 
schirmer@12854
  2428
                                            else insert (super c) superclss))"
schirmer@12854
  2429
   
schirmer@12854
  2430
lemma superclasses_rec: "\<lbrakk>class G C = Some c; ws_prog G\<rbrakk> \<Longrightarrow>  
schirmer@12854
  2431
 superclasses G C 
schirmer@12854
  2432
 = (if (C=Object) 
schirmer@12854
  2433
       then {}
schirmer@12854
  2434
       else insert (super c) (superclasses G (super c)))"
schirmer@12854
  2435
apply (unfold superclasses_def)
schirmer@12854
  2436
apply (erule class_rec [THEN trans], assumption)
schirmer@12854
  2437
apply (simp)
schirmer@12854
  2438
done
schirmer@12854
  2439
schirmer@12854
  2440
lemma superclasses_mono:
schirmer@12854
  2441
"\<lbrakk>G\<turnstile>C \<prec>\<^sub>C D;ws_prog G; class G C = Some c;
schirmer@12854
  2442
  \<And> C c. \<lbrakk>class G C = Some c;C\<noteq>Object\<rbrakk> \<Longrightarrow> \<exists> sc. class G (super c) = Some sc;
schirmer@12854
  2443
  x\<in>superclasses G D 
schirmer@12854
  2444
\<rbrakk> \<Longrightarrow> x\<in>superclasses G C" 
schirmer@12854
  2445
proof -
schirmer@12854
  2446
  
schirmer@12854
  2447
  assume     ws: "ws_prog G"          and 
schirmer@12854
  2448
          cls_C: "class G C = Some c" and
schirmer@12854
  2449
             wf: "\<And>C c. \<lbrakk>class G C = Some c; C \<noteq> Object\<rbrakk>
schirmer@12854
  2450
                  \<Longrightarrow> \<exists>sc. class G (super c) = Some sc"
schirmer@12854
  2451
  assume clsrel: "G\<turnstile>C\<prec>\<^sub>C D"           
schirmer@12854
  2452
  thus "\<And> c. \<lbrakk>class G C = Some c; x\<in>superclasses G D\<rbrakk>\<Longrightarrow>
schirmer@12854
  2453
        x\<in>superclasses G C" (is "PROP ?P C"  
schirmer@12854
  2454
                             is "\<And> c. ?CLS C c \<Longrightarrow> ?SUP D \<Longrightarrow> ?SUP C")
schirmer@12854
  2455
  proof (induct ?P C  rule: converse_trancl_induct)
schirmer@12854
  2456
    fix C c
schirmer@12854
  2457
    assume "G\<turnstile>C\<prec>\<^sub>C\<^sub>1D" "class G C = Some c" "x \<in> superclasses G D"
schirmer@12854
  2458
    with wf ws show "?SUP C"
schirmer@12854
  2459
      by (auto    intro: no_subcls1_Object 
schirmer@12854
  2460
               simp add: superclasses_rec subcls1_def)
schirmer@12854
  2461
  next
schirmer@12854
  2462
    fix C S c
schirmer@12854
  2463
    assume clsrel': "G\<turnstile>C \<prec>\<^sub>C\<^sub>1 S" "G\<turnstile>S \<prec>\<^sub>C D"
schirmer@12854
  2464
       and    hyp : "\<And> s. \<lbrakk>class G S = Some s; x \<in> superclasses G D\<rbrakk>
schirmer@12854
  2465
                           \<Longrightarrow> x \<in> superclasses G S"
schirmer@12854
  2466
       and  cls_C': "class G C = Some c"
schirmer@12854
  2467
       and       x: "x \<in> superclasses G D"
schirmer@12854
  2468
    moreover note wf ws
schirmer@12854
  2469
    moreover from calculation 
schirmer@12854
  2470
    have "?SUP S" 
schirmer@12854
  2471
      by (force intro: no_subcls1_Object simp add: subcls1_def)
schirmer@12854
  2472
    moreover from calculation 
schirmer@12854
  2473
    have "super c = S" 
schirmer@12854
  2474
      by (auto intro: no_subcls1_Object simp add: subcls1_def)
schirmer@12854
  2475
    ultimately show "?SUP C" 
schirmer@12854
  2476
      by (auto intro: no_subcls1_Object simp add: superclasses_rec)
schirmer@12854
  2477
  qed
schirmer@12854
  2478
qed
schirmer@12854
  2479
schirmer@12854
  2480
lemma subclsEval:
schirmer@12854
  2481
"\<lbrakk>G\<turnstile>C \<prec>\<^sub>C D;ws_prog G; class G C = Some c;
schirmer@12854
  2482
  \<And> C c. \<lbrakk>class G C = Some c;C\<noteq>Object\<rbrakk> \<Longrightarrow> \<exists> sc. class G (super c) = Some sc 
schirmer@12854
  2483
 \<rbrakk> \<Longrightarrow> D\<in>superclasses G C" 
schirmer@12854
  2484
proof -
schirmer@12854
  2485
  note converse_trancl_induct 
schirmer@12854
  2486
       = converse_trancl_induct [consumes 1,case_names Single Step]
schirmer@12854
  2487
  assume 
schirmer@12854
  2488
             ws: "ws_prog G"          and 
schirmer@12854
  2489
          cls_C: "class G C = Some c" and
schirmer@12854
  2490
             wf: "\<And>C c. \<lbrakk>class G C = Some c; C \<noteq> Object\<rbrakk>
schirmer@12854
  2491
                  \<Longrightarrow> \<exists>sc. class G (super c) = Some sc"
schirmer@12854
  2492
  assume clsrel: "G\<turnstile>C\<prec>\<^sub>C D"           
schirmer@12854
  2493
  thus "\<And> c. class G C = Some c\<Longrightarrow> D\<in>superclasses G C" 
schirmer@12854
  2494
    (is "PROP ?P C"  is "\<And> c. ?CLS C c  \<Longrightarrow> ?SUP C")
schirmer@12854
  2495
  proof (induct ?P C  rule: converse_trancl_induct)
schirmer@12854
  2496
    fix C c
schirmer@12854
  2497
    assume "G\<turnstile>C \<prec>\<^sub>C\<^sub>1 D" "class G C = Some c"
schirmer@12854
  2498
    with ws wf show "?SUP C"
schirmer@12854
  2499
      by (auto intro: no_subcls1_Object simp add: superclasses_rec subcls1_def)
schirmer@12854
  2500
  next
schirmer@12854
  2501
    fix C S c
schirmer@12854
  2502
    assume "G\<turnstile>C \<prec>\<^sub>C\<^sub>1 S" "G\<turnstile>S\<prec>\<^sub>C D" 
schirmer@12854
  2503
           "\<And>s. class G S = Some s \<Longrightarrow> D \<in> superclasses G S"
schirmer@12854
  2504
           "class G C = Some c" 
schirmer@12854
  2505
    with ws wf show "?SUP C"
schirmer@12854
  2506
      by - (rule superclasses_mono,
schirmer@12854
  2507
            auto dest: no_subcls1_Object simp add: subcls1_def )
schirmer@12854
  2508
  qed
schirmer@12854
  2509
qed
schirmer@12854
  2510
schirmer@12854
  2511
end