src/HOL/Bali/DeclConcepts.thy
author haftmann
Tue Feb 23 10:11:12 2010 +0100 (2010-02-23)
changeset 35315 fbdc860d87a3
parent 35067 af4c18c30593
child 35416 d8d7d1b785af
permissions -rw-r--r--
dropped axclass
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(*  Title:      HOL/Bali/DeclConcepts.thy
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    Author:     Norbert Schirmer
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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 imports TypeRel begin
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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 i \<Rightarrow> access i = Public)
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                   | Some c \<Rightarrow> access c = 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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class has_accmodi =
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  fixes accmodi:: "'a \<Rightarrow> acc_modi"
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instantiation acc_modi :: has_accmodi
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begin
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definition
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  acc_modi_accmodi_def: "accmodi (a::acc_modi) \<equiv> a"
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instance ..
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end
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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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instantiation decl_ext_type:: (type) has_accmodi
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begin
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definition
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  decl_acc_modi_def: "accmodi (d::('a:: type) decl_scheme) \<equiv> access d"
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instance ..
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end
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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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instantiation * :: (type, has_accmodi) has_accmodi
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begin
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definition
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  pair_acc_modi_def: "accmodi p \<equiv> (accmodi (snd p))"
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instance ..
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end
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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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instantiation memberdecl :: has_accmodi
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begin
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definition
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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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instance ..
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end
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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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class has_declclass =
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  fixes declclass:: "'a \<Rightarrow> qtname"
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instantiation qtname_ext_type :: (type) has_declclass
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begin
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definition
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  "declclass q \<equiv> \<lparr> pid = pid q, tid = tid q \<rparr>"
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instance ..
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end
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lemma qtname_declclass_def:
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  "declclass q \<equiv> (q::qtname)"
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  by (induct q) (simp add: declclass_qtname_ext_type_def)
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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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instantiation * :: (has_declclass, type) has_declclass
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begin
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definition
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  pair_declclass_def: "declclass p \<equiv> declclass (fst p)"
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instance ..
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end
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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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class has_static =
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  fixes is_static :: "'a \<Rightarrow> bool"
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instantiation decl_ext_type :: (has_static) has_static
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begin
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instance ..
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end
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instantiation member_ext_type :: (type) has_static
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begin
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instance ..
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end
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axiomatization where
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  static_field_type_is_static_def: "is_static (m::('a member_scheme)) \<equiv> static m"
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lemma member_is_static_simp: "is_static (m::'a member_scheme) = static m"
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by (simp add: static_field_type_is_static_def)
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instantiation * :: (type, has_static) has_static
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begin
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definition
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  pair_is_static_def: "is_static p \<equiv> is_static (snd p)"
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instance ..
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end
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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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instantiation memberdecl :: has_static
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begin
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definition
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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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instance ..
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end
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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 various pairs *} 
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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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 "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 @{text "((vname \<times> qtname)\<times> field)"} *}
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 "fld \<equiv> snd"               --{* get the field component *}
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constdefs --{* some mnemotic selectors for @{text "(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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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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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 @{text "(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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lemma ext_fieldname_simp[simp]: "(fldname f,fldclass f) = f"
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by (simp add: fldname_def fldclass_def)
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text {* Convert a qualified method declaration (qualified with its declaring 
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class) to a qualified member declaration:  @{text methdMembr}  *}
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constdefs
schirmer@12854
   340
methdMembr :: "(qtname \<times> mdecl) \<Rightarrow> (qtname \<times> memberdecl)"
schirmer@12854
   341
 "methdMembr m \<equiv> (fst m,mdecl (snd m))"
schirmer@12854
   342
schirmer@12854
   343
lemma methdMembr_simp[simp]: "methdMembr (c,m) = (c,mdecl m)"
schirmer@12854
   344
by (simp add: methdMembr_def)
schirmer@12854
   345
schirmer@12854
   346
lemma accmodi_methdMembr_simp[simp]: "accmodi (methdMembr m) = accmodi m"
schirmer@12854
   347
by (cases m) (simp add: methdMembr_def)
schirmer@12854
   348
schirmer@12854
   349
lemma is_static_methdMembr_simp[simp]: "is_static (methdMembr m) = is_static m"
schirmer@12854
   350
by (cases m) (simp add: methdMembr_def)
schirmer@12854
   351
schirmer@12854
   352
lemma declclass_methdMembr_simp[simp]: "declclass (methdMembr m) = declclass m"
schirmer@12854
   353
by (cases m) (simp add: methdMembr_def)
schirmer@12854
   354
schirmer@12854
   355
text {* Convert a qualified method (qualified with its declaring 
schirmer@12854
   356
class) to a qualified member declaration:  @{text method}  *}
schirmer@12854
   357
schirmer@12854
   358
constdefs
schirmer@12854
   359
method :: "sig \<Rightarrow> (qtname \<times> methd) \<Rightarrow> (qtname \<times> memberdecl)" 
schirmer@12854
   360
"method sig m \<equiv> (declclass m, mdecl (sig, mthd m))"
schirmer@12854
   361
schirmer@12854
   362
lemma method_simp[simp]: "method sig (C,m) = (C,mdecl (sig,m))"
schirmer@12854
   363
by (simp add: method_def)
schirmer@12854
   364
schirmer@12854
   365
lemma accmodi_method_simp[simp]: "accmodi (method sig m) = accmodi m"
schirmer@12854
   366
by (simp add: method_def)
schirmer@12854
   367
schirmer@12854
   368
lemma declclass_method_simp[simp]: "declclass (method sig m) = declclass m"
schirmer@12854
   369
by (simp add: method_def)
schirmer@12854
   370
schirmer@12854
   371
lemma is_static_method_simp[simp]: "is_static (method sig m) = is_static m"
schirmer@12854
   372
by (cases m) (simp add: method_def)
schirmer@12854
   373
schirmer@12854
   374
lemma mbr_method_simp[simp]: "mbr (method sig m) = mdecl (sig,mthd m)"
schirmer@12854
   375
by (simp add: mbr_def method_def)
schirmer@12854
   376
schirmer@12854
   377
lemma memberid_method_simp[simp]:  "memberid (method sig m) = mid sig"
schirmer@12854
   378
  by (simp add: method_def) 
schirmer@12854
   379
schirmer@12854
   380
constdefs
schirmer@12854
   381
fieldm :: "vname \<Rightarrow> (qtname \<times> field) \<Rightarrow> (qtname \<times> memberdecl)" 
schirmer@12854
   382
"fieldm n f \<equiv> (declclass f, fdecl (n, fld f))"
schirmer@12854
   383
schirmer@12854
   384
lemma fieldm_simp[simp]: "fieldm n (C,f) = (C,fdecl (n,f))"
schirmer@12854
   385
by (simp add: fieldm_def)
schirmer@12854
   386
schirmer@12854
   387
lemma accmodi_fieldm_simp[simp]: "accmodi (fieldm n f) = accmodi f"
schirmer@12854
   388
by (simp add: fieldm_def)
schirmer@12854
   389
schirmer@12854
   390
lemma declclass_fieldm_simp[simp]: "declclass (fieldm n f) = declclass f"
schirmer@12854
   391
by (simp add: fieldm_def)
schirmer@12854
   392
schirmer@12854
   393
lemma is_static_fieldm_simp[simp]: "is_static (fieldm n f) = is_static f"
schirmer@12854
   394
by (cases f) (simp add: fieldm_def)
schirmer@12854
   395
schirmer@12854
   396
lemma mbr_fieldm_simp[simp]: "mbr (fieldm n f) = fdecl (n,fld f)"
schirmer@12854
   397
by (simp add: mbr_def fieldm_def)
schirmer@12854
   398
schirmer@12854
   399
lemma memberid_fieldm_simp[simp]:  "memberid (fieldm n f) = fid n"
schirmer@12854
   400
by (simp add: fieldm_def) 
schirmer@12854
   401
schirmer@12854
   402
text {* Select the signature out of a qualified method declaration:
schirmer@12854
   403
 @{text msig} *}
schirmer@12854
   404
schirmer@12854
   405
constdefs msig:: "(qtname \<times> mdecl) \<Rightarrow> sig"
schirmer@12854
   406
"msig m \<equiv> fst (snd m)"
schirmer@12854
   407
schirmer@12854
   408
lemma msig_simp[simp]: "msig (c,(s,m)) = s"
schirmer@12854
   409
by (simp add: msig_def)
schirmer@12854
   410
schirmer@12854
   411
text {* Convert a qualified method (qualified with its declaring 
schirmer@12854
   412
class) to a qualified method declaration:  @{text qmdecl}  *}
schirmer@12854
   413
schirmer@12854
   414
constdefs qmdecl :: "sig \<Rightarrow> (qtname \<times> methd) \<Rightarrow> (qtname \<times> mdecl)"
schirmer@12854
   415
"qmdecl sig m \<equiv> (declclass m, (sig,mthd m))"
schirmer@12854
   416
schirmer@12854
   417
lemma qmdecl_simp[simp]: "qmdecl sig (C,m) = (C,(sig,m))"
schirmer@12854
   418
by (simp add: qmdecl_def)
schirmer@12854
   419
schirmer@12854
   420
lemma declclass_qmdecl_simp[simp]: "declclass (qmdecl sig m) = declclass m"
schirmer@12854
   421
by (simp add: qmdecl_def)
schirmer@12854
   422
schirmer@12854
   423
lemma accmodi_qmdecl_simp[simp]: "accmodi (qmdecl sig m) = accmodi m"
schirmer@12854
   424
by (simp add: qmdecl_def)
schirmer@12854
   425
schirmer@12854
   426
lemma is_static_qmdecl_simp[simp]: "is_static (qmdecl sig m) = is_static m"
schirmer@12854
   427
by (cases m) (simp add: qmdecl_def)
schirmer@12854
   428
schirmer@12854
   429
lemma msig_qmdecl_simp[simp]: "msig (qmdecl sig m) = sig"
schirmer@12854
   430
by (simp add: qmdecl_def)
schirmer@12854
   431
schirmer@12854
   432
lemma mdecl_qmdecl_simp[simp]:  
schirmer@12854
   433
 "mdecl (mthd (qmdecl sig new)) = mdecl (sig, mthd new)" 
schirmer@12854
   434
by (simp add: qmdecl_def) 
schirmer@12854
   435
schirmer@12854
   436
lemma methdMembr_qmdecl_simp [simp]: 
schirmer@12854
   437
 "methdMembr (qmdecl sig old) = method sig old"
schirmer@12854
   438
by (simp add: methdMembr_def qmdecl_def method_def)
schirmer@12854
   439
schirmer@12854
   440
text {* overloaded selector @{text resTy} to select the result type 
schirmer@12854
   441
out of various HOL types *}
schirmer@12854
   442
haftmann@35315
   443
class has_resTy =
haftmann@35315
   444
  fixes resTy:: "'a \<Rightarrow> ty"
haftmann@35315
   445
haftmann@35315
   446
instantiation decl_ext_type :: (has_resTy) has_resTy
haftmann@35315
   447
begin
schirmer@12854
   448
haftmann@35315
   449
instance ..
haftmann@35315
   450
haftmann@35315
   451
end
haftmann@35315
   452
haftmann@35315
   453
instantiation member_ext_type :: (has_resTy) has_resTy
haftmann@35315
   454
begin
schirmer@12854
   455
haftmann@35315
   456
instance ..
schirmer@12854
   457
haftmann@35315
   458
end
haftmann@35315
   459
haftmann@35315
   460
instantiation mhead_ext_type :: (type) has_resTy
haftmann@35315
   461
begin
schirmer@12854
   462
haftmann@35315
   463
instance ..
haftmann@35315
   464
haftmann@35315
   465
end
haftmann@35315
   466
haftmann@35315
   467
axiomatization where
haftmann@35315
   468
  mhead_ext_type_resTy_def: "resTy (m::('b mhead_scheme)) \<equiv> resT m"
schirmer@12854
   469
schirmer@12854
   470
lemma mhead_resTy_simp: "resTy (m::'a mhead_scheme) = resT m"
tsewell@32754
   471
by (simp add: mhead_ext_type_resTy_def)
schirmer@12854
   472
schirmer@12854
   473
lemma resTy_mhead [simp]:"resTy (mhead m) = resTy m"
schirmer@12854
   474
by (simp add: mhead_def mhead_resTy_simp)
schirmer@12854
   475
haftmann@35315
   476
instantiation * :: ("type","has_resTy") has_resTy
haftmann@35315
   477
begin
schirmer@12854
   478
haftmann@35315
   479
definition
haftmann@35315
   480
  pair_resTy_def: "resTy p \<equiv> resTy (snd p)"
haftmann@35315
   481
haftmann@35315
   482
instance ..
haftmann@35315
   483
haftmann@35315
   484
end
schirmer@12854
   485
schirmer@12854
   486
lemma pair_resTy_simp[simp]: "resTy (x,m) = resTy m"
schirmer@12854
   487
by (simp add: pair_resTy_def)
schirmer@12854
   488
schirmer@12854
   489
lemma qmdecl_resTy_simp [simp]: "resTy (qmdecl sig m) = resTy m"
schirmer@12854
   490
by (cases m) (simp)
schirmer@12854
   491
schirmer@12854
   492
lemma resTy_mthd [simp]:"resTy (mthd m) = resTy m"
schirmer@12854
   493
by (cases m) (simp add: mthd_def )
schirmer@12854
   494
schirmer@12854
   495
subsubsection "inheritable-in"
schirmer@12854
   496
text {*
schirmer@12854
   497
@{text "G\<turnstile>m inheritable_in P"}: m can be inherited by
schirmer@12854
   498
classes in package P if:
schirmer@12854
   499
\begin{itemize} 
schirmer@12854
   500
\item the declaration class of m is accessible in P and
schirmer@12854
   501
\item the member m is declared with protected or public access or if it is
schirmer@12854
   502
      declared with default (package) access, the package of the declaration 
schirmer@12854
   503
      class of m is also P. If the member m is declared with private access
schirmer@12854
   504
      it is not accessible for inheritance at all.
schirmer@12854
   505
\end{itemize}
schirmer@12854
   506
*}
schirmer@12854
   507
constdefs
schirmer@12854
   508
inheritable_in:: 
schirmer@12854
   509
 "prog \<Rightarrow> (qtname \<times> memberdecl) \<Rightarrow> pname \<Rightarrow> bool"
schirmer@12854
   510
                  ("_ \<turnstile> _ inheritable'_in _" [61,61,61] 60)
schirmer@12854
   511
"G\<turnstile>membr inheritable_in pack 
schirmer@12854
   512
  \<equiv> (case (accmodi membr) of
schirmer@12854
   513
       Private   \<Rightarrow> False
schirmer@12854
   514
     | Package   \<Rightarrow> (pid (declclass membr)) = pack
schirmer@12854
   515
     | Protected \<Rightarrow> True
schirmer@12854
   516
     | Public    \<Rightarrow> True)"
schirmer@12854
   517
wenzelm@35067
   518
abbreviation
wenzelm@35067
   519
Method_inheritable_in_syntax::
schirmer@12854
   520
 "prog \<Rightarrow> (qtname \<times> mdecl) \<Rightarrow> pname \<Rightarrow> bool"
schirmer@12854
   521
                ("_ \<turnstile>Method _ inheritable'_in _ " [61,61,61] 60)
wenzelm@35067
   522
 where "G\<turnstile>Method m inheritable_in p == G\<turnstile>methdMembr m inheritable_in p"
schirmer@12854
   523
wenzelm@35067
   524
abbreviation
schirmer@12854
   525
Methd_inheritable_in::
schirmer@12854
   526
 "prog \<Rightarrow> sig \<Rightarrow> (qtname \<times> methd) \<Rightarrow> pname \<Rightarrow> bool"
schirmer@12854
   527
                ("_ \<turnstile>Methd _ _ inheritable'_in _ " [61,61,61,61] 60)
wenzelm@35067
   528
 where "G\<turnstile>Methd s m inheritable_in p == G\<turnstile>(method s m) inheritable_in p"
schirmer@12854
   529
schirmer@12854
   530
subsubsection "declared-in/undeclared-in"
schirmer@12854
   531
schirmer@12854
   532
constdefs cdeclaredmethd:: "prog \<Rightarrow> qtname \<Rightarrow> (sig,methd) table"
schirmer@12854
   533
"cdeclaredmethd G C 
schirmer@12854
   534
  \<equiv> (case class G C of
schirmer@12854
   535
       None \<Rightarrow> \<lambda> sig. None
schirmer@12854
   536
     | Some c \<Rightarrow> table_of (methods c)
schirmer@12854
   537
    )"
schirmer@12854
   538
schirmer@12854
   539
constdefs
schirmer@12854
   540
cdeclaredfield:: "prog \<Rightarrow> qtname \<Rightarrow> (vname,field) table"
schirmer@12854
   541
"cdeclaredfield G C 
schirmer@12854
   542
  \<equiv> (case class G C of
schirmer@12854
   543
       None \<Rightarrow> \<lambda> sig. None
schirmer@12854
   544
     | Some c \<Rightarrow> table_of (cfields c)
schirmer@12854
   545
    )"
schirmer@12854
   546
schirmer@12854
   547
schirmer@12854
   548
constdefs
schirmer@12854
   549
declared_in:: "prog  \<Rightarrow> memberdecl \<Rightarrow> qtname \<Rightarrow> bool"
schirmer@12854
   550
                                 ("_\<turnstile> _ declared'_in _" [61,61,61] 60)
schirmer@12854
   551
"G\<turnstile>m declared_in C \<equiv> (case m of
schirmer@12854
   552
                        fdecl (fn,f ) \<Rightarrow> cdeclaredfield G C fn  = Some f
schirmer@12854
   553
                      | mdecl (sig,m) \<Rightarrow> cdeclaredmethd G C sig = Some m)"
schirmer@12854
   554
wenzelm@35067
   555
abbreviation
schirmer@12854
   556
method_declared_in:: "prog  \<Rightarrow> (qtname \<times> mdecl) \<Rightarrow> qtname \<Rightarrow> bool"
schirmer@12854
   557
                                 ("_\<turnstile>Method _ declared'_in _" [61,61,61] 60)
wenzelm@35067
   558
 where "G\<turnstile>Method m declared_in C == G\<turnstile>mdecl (mthd m) declared_in C"
schirmer@12854
   559
wenzelm@35067
   560
abbreviation
schirmer@12854
   561
methd_declared_in:: "prog  \<Rightarrow> sig  \<Rightarrow>(qtname \<times> methd) \<Rightarrow> qtname \<Rightarrow> bool"
schirmer@12854
   562
                               ("_\<turnstile>Methd _  _ declared'_in _" [61,61,61,61] 60)
wenzelm@35067
   563
 where "G\<turnstile>Methd s m declared_in C == G\<turnstile>mdecl (s,mthd m) declared_in C"
schirmer@12854
   564
schirmer@12854
   565
lemma declared_in_classD:
schirmer@12854
   566
 "G\<turnstile>m declared_in C \<Longrightarrow> is_class G C"
schirmer@12854
   567
by (cases m) 
schirmer@12854
   568
   (auto simp add: declared_in_def cdeclaredmethd_def cdeclaredfield_def)
schirmer@12854
   569
schirmer@12854
   570
constdefs
schirmer@12854
   571
undeclared_in:: "prog  \<Rightarrow> memberid \<Rightarrow> qtname \<Rightarrow> bool"
schirmer@12854
   572
                                 ("_\<turnstile> _ undeclared'_in _" [61,61,61] 60)
schirmer@12854
   573
schirmer@12854
   574
"G\<turnstile>m undeclared_in C \<equiv> (case m of
schirmer@12854
   575
                            fid fn  \<Rightarrow> cdeclaredfield G C fn  = None
schirmer@12854
   576
                          | mid sig \<Rightarrow> cdeclaredmethd G C sig = None)"
schirmer@12854
   577
schirmer@12854
   578
schirmer@12854
   579
subsubsection "members"
schirmer@12854
   580
schirmer@12854
   581
(* Can't just take a function: prog \<Rightarrow> qtname \<Rightarrow> memberdecl set because
schirmer@12854
   582
   the class qtname changes to the superclass in the inductive definition
schirmer@12854
   583
   below
schirmer@12854
   584
*)
schirmer@12854
   585
berghofe@23747
   586
inductive
berghofe@21765
   587
  members :: "prog \<Rightarrow> (qtname \<times> memberdecl) \<Rightarrow> qtname \<Rightarrow> bool"
berghofe@21765
   588
    ("_ \<turnstile> _ member'_of _" [61,61,61] 60)
berghofe@21765
   589
  for G :: prog
berghofe@21765
   590
where
schirmer@12854
   591
berghofe@21765
   592
  Immediate: "\<lbrakk>G\<turnstile>mbr m declared_in C;declclass m = C\<rbrakk> \<Longrightarrow> G\<turnstile>m member_of C"
berghofe@21765
   593
| Inherited: "\<lbrakk>G\<turnstile>m inheritable_in (pid C); G\<turnstile>memberid m undeclared_in C; 
berghofe@21765
   594
               G\<turnstile>C \<prec>\<^sub>C\<^sub>1 S; G\<turnstile>(Class S) accessible_in (pid C);G\<turnstile>m member_of S 
berghofe@21765
   595
              \<rbrakk> \<Longrightarrow> G\<turnstile>m member_of C"
schirmer@12854
   596
text {* Note that in the case of an inherited member only the members of the
schirmer@12854
   597
direct superclass are concerned. If a member of a superclass of the direct
schirmer@12854
   598
superclass isn't inherited in the direct superclass (not member of the
schirmer@12854
   599
direct superclass) than it can't be a member of the class. E.g. If a
schirmer@12854
   600
member of a class A is defined with package access it isn't member of a 
schirmer@12854
   601
subclass S if S isn't in the same package as A. Any further subclasses 
schirmer@12854
   602
of S will not inherit the member, regardless if they are in the same
schirmer@12854
   603
package as A or not.*}
schirmer@12854
   604
wenzelm@35067
   605
abbreviation
schirmer@12854
   606
method_member_of:: "prog \<Rightarrow> (qtname \<times> mdecl) \<Rightarrow> qtname \<Rightarrow> bool"
schirmer@12854
   607
                           ("_ \<turnstile>Method _ member'_of _" [61,61,61] 60)
wenzelm@35067
   608
 where "G\<turnstile>Method m member_of C == G\<turnstile>(methdMembr m) member_of C"
schirmer@12854
   609
wenzelm@35067
   610
abbreviation
schirmer@12854
   611
methd_member_of:: "prog \<Rightarrow> sig \<Rightarrow> (qtname \<times> methd) \<Rightarrow> qtname \<Rightarrow> bool"
schirmer@12854
   612
                           ("_ \<turnstile>Methd _ _ member'_of _" [61,61,61,61] 60)
wenzelm@35067
   613
 where "G\<turnstile>Methd s m member_of C == G\<turnstile>(method s m) member_of C" 
schirmer@12854
   614
wenzelm@35067
   615
abbreviation
schirmer@12854
   616
fieldm_member_of:: "prog \<Rightarrow> vname \<Rightarrow> (qtname \<times> field) \<Rightarrow> qtname \<Rightarrow> bool"
schirmer@12854
   617
                           ("_ \<turnstile>Field _  _ member'_of _" [61,61,61] 60)
wenzelm@35067
   618
 where "G\<turnstile>Field n f member_of C == G\<turnstile>fieldm n f member_of C"
schirmer@12854
   619
schirmer@12854
   620
constdefs
schirmer@12854
   621
inherits:: "prog \<Rightarrow> qtname \<Rightarrow> (qtname \<times> memberdecl) \<Rightarrow> bool"
schirmer@12854
   622
                           ("_ \<turnstile> _ inherits _" [61,61,61] 60)
schirmer@12854
   623
"G\<turnstile>C inherits m 
schirmer@12854
   624
  \<equiv> G\<turnstile>m inheritable_in (pid C) \<and> G\<turnstile>memberid m undeclared_in C \<and> 
schirmer@12854
   625
    (\<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
   626
schirmer@12854
   627
lemma inherits_member: "G\<turnstile>C inherits m \<Longrightarrow> G\<turnstile>m member_of C"
schirmer@12854
   628
by (auto simp add: inherits_def intro: members.Inherited)
schirmer@12854
   629
schirmer@12854
   630
schirmer@12854
   631
constdefs member_in::"prog \<Rightarrow> (qtname \<times> memberdecl) \<Rightarrow> qtname \<Rightarrow> bool"
schirmer@12854
   632
                           ("_ \<turnstile> _ member'_in _" [61,61,61] 60)
schirmer@12854
   633
"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
   634
text {* A member is in a class if it is member of the class or a superclass.
schirmer@12854
   635
If a member is in a class we can select this member. This additional notion
schirmer@12854
   636
is necessary since not all members are inherited to subclasses. So such
schirmer@12854
   637
members are not member-of the subclass but member-in the subclass.*}
schirmer@12854
   638
wenzelm@35067
   639
abbreviation
schirmer@12854
   640
method_member_in:: "prog \<Rightarrow> (qtname \<times> mdecl) \<Rightarrow> qtname \<Rightarrow> bool"
schirmer@12854
   641
                           ("_ \<turnstile>Method _ member'_in _" [61,61,61] 60)
wenzelm@35067
   642
 where "G\<turnstile>Method m member_in C == G\<turnstile>(methdMembr m) member_in C"
schirmer@12854
   643
wenzelm@35067
   644
abbreviation
schirmer@12854
   645
methd_member_in:: "prog \<Rightarrow> sig \<Rightarrow> (qtname \<times> methd) \<Rightarrow> qtname \<Rightarrow> bool"
schirmer@12854
   646
                           ("_ \<turnstile>Methd _ _ member'_in _" [61,61,61,61] 60)
wenzelm@35067
   647
 where "G\<turnstile>Methd s m member_in C == G\<turnstile>(method s m) member_in C"
schirmer@12854
   648
schirmer@12854
   649
lemma member_inD: "G\<turnstile>m member_in C 
schirmer@12854
   650
 \<Longrightarrow> \<exists> provC. G\<turnstile> C \<preceq>\<^sub>C provC \<and> G \<turnstile> m member_of provC"
schirmer@12854
   651
by (auto simp add: member_in_def)
schirmer@12854
   652
schirmer@12854
   653
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
   654
by (auto simp add: member_in_def)
schirmer@12854
   655
schirmer@12854
   656
lemma member_of_to_member_in: "G \<turnstile> m member_of C \<Longrightarrow> G \<turnstile>m member_in C"
schirmer@12854
   657
by (auto intro: member_inI)
schirmer@12854
   658
schirmer@12854
   659
schirmer@12854
   660
subsubsection "overriding"
schirmer@12854
   661
schirmer@12854
   662
text {* Unfortunately the static notion of overriding (used during the
schirmer@12854
   663
typecheck of the compiler) and the dynamic notion of overriding (used during
schirmer@12854
   664
execution in the JVM) are not exactly the same. 
schirmer@12854
   665
*}
schirmer@12854
   666
schirmer@12854
   667
text {* Static overriding (used during the typecheck of the compiler) *}
schirmer@12854
   668
berghofe@23747
   669
inductive
berghofe@21765
   670
  stat_overridesR :: "prog \<Rightarrow> (qtname \<times> mdecl) \<Rightarrow> (qtname \<times> mdecl) \<Rightarrow> bool"
berghofe@21765
   671
    ("_ \<turnstile> _ overrides\<^sub>S _" [61,61,61] 60)
berghofe@21765
   672
  for G :: prog
berghofe@21765
   673
where
schirmer@12854
   674
berghofe@21765
   675
  Direct: "\<lbrakk>\<not> is_static new; msig new = msig old; 
berghofe@21765
   676
           G\<turnstile>Method new declared_in (declclass new);  
berghofe@21765
   677
           G\<turnstile>Method old declared_in (declclass old); 
berghofe@21765
   678
           G\<turnstile>Method old inheritable_in pid (declclass new);
berghofe@21765
   679
           G\<turnstile>(declclass new) \<prec>\<^sub>C\<^sub>1 superNew;
berghofe@21765
   680
           G \<turnstile>Method old member_of superNew
berghofe@21765
   681
           \<rbrakk> \<Longrightarrow> G\<turnstile>new overrides\<^sub>S old"
schirmer@12854
   682
haftmann@32134
   683
| Indirect: "\<lbrakk>G\<turnstile>new overrides\<^sub>S intr; G\<turnstile>intr overrides\<^sub>S old\<rbrakk>
berghofe@21765
   684
             \<Longrightarrow> G\<turnstile>new overrides\<^sub>S old"
schirmer@12854
   685
schirmer@12854
   686
text {* Dynamic overriding (used during the typecheck of the compiler) *}
schirmer@12854
   687
berghofe@23747
   688
inductive
berghofe@21765
   689
  overridesR :: "prog \<Rightarrow> (qtname \<times> mdecl) \<Rightarrow> (qtname \<times> mdecl) \<Rightarrow> bool"
berghofe@21765
   690
    ("_ \<turnstile> _ overrides _" [61,61,61] 60)
berghofe@21765
   691
  for G :: prog
berghofe@21765
   692
where
schirmer@12854
   693
berghofe@21765
   694
  Direct: "\<lbrakk>\<not> is_static new; \<not> is_static old; accmodi new \<noteq> Private;
berghofe@21765
   695
           msig new = msig old; 
berghofe@21765
   696
           G\<turnstile>(declclass new) \<prec>\<^sub>C (declclass old);
berghofe@21765
   697
           G\<turnstile>Method new declared_in (declclass new);  
berghofe@21765
   698
           G\<turnstile>Method old declared_in (declclass old);    
berghofe@21765
   699
           G\<turnstile>Method old inheritable_in pid (declclass new);
berghofe@21765
   700
           G\<turnstile>resTy new \<preceq> resTy old
berghofe@21765
   701
           \<rbrakk> \<Longrightarrow> G\<turnstile>new overrides old"
schirmer@12854
   702
haftmann@32134
   703
| Indirect: "\<lbrakk>G\<turnstile>new overrides intr; G\<turnstile>intr overrides old\<rbrakk>
berghofe@21765
   704
            \<Longrightarrow> G\<turnstile>new overrides old"
schirmer@12854
   705
wenzelm@35067
   706
abbreviation (input)
schirmer@12854
   707
sig_stat_overrides:: 
schirmer@12854
   708
 "prog  \<Rightarrow> sig \<Rightarrow> (qtname \<times> methd) \<Rightarrow> (qtname \<times> methd) \<Rightarrow> bool" 
schirmer@12854
   709
                                  ("_,_\<turnstile> _ overrides\<^sub>S _" [61,61,61,61] 60)
wenzelm@35067
   710
 where "G,s\<turnstile>new overrides\<^sub>S old == G\<turnstile>(qmdecl s new) overrides\<^sub>S (qmdecl s old)" 
schirmer@12854
   711
wenzelm@35067
   712
abbreviation (input)
schirmer@12854
   713
sig_overrides:: "prog  \<Rightarrow> sig \<Rightarrow> (qtname \<times> methd) \<Rightarrow> (qtname \<times> methd) \<Rightarrow> bool" 
schirmer@12854
   714
                                  ("_,_\<turnstile> _ overrides _" [61,61,61,61] 60)
wenzelm@35067
   715
 where "G,s\<turnstile>new overrides old == G\<turnstile>(qmdecl s new) overrides (qmdecl s old)"
schirmer@12854
   716
schirmer@12854
   717
subsubsection "Hiding"
schirmer@12854
   718
schirmer@12854
   719
constdefs hides::
schirmer@12854
   720
"prog \<Rightarrow> (qtname \<times> mdecl) \<Rightarrow> (qtname \<times> mdecl) \<Rightarrow> bool" 
schirmer@12854
   721
                                ("_\<turnstile> _ hides _" [61,61,61] 60)
schirmer@12854
   722
"G\<turnstile>new hides old
schirmer@12854
   723
  \<equiv> is_static new \<and> msig new = msig old \<and>
schirmer@12854
   724
    G\<turnstile>(declclass new) \<prec>\<^sub>C (declclass old) \<and>
schirmer@12854
   725
    G\<turnstile>Method new declared_in (declclass new) \<and>
schirmer@12854
   726
    G\<turnstile>Method old declared_in (declclass old) \<and> 
schirmer@12854
   727
    G\<turnstile>Method old inheritable_in pid (declclass new)"
schirmer@12854
   728
wenzelm@35067
   729
abbreviation
wenzelm@35067
   730
sig_hides:: "prog  \<Rightarrow> sig \<Rightarrow> (qtname \<times> methd) \<Rightarrow> (qtname \<times> methd) \<Rightarrow> bool" 
schirmer@12854
   731
                                  ("_,_\<turnstile> _ hides _" [61,61,61,61] 60)
wenzelm@35067
   732
 where "G,s\<turnstile>new hides old == G\<turnstile>(qmdecl s new) hides (qmdecl s old)"
schirmer@12854
   733
schirmer@12854
   734
lemma hidesI:
schirmer@12854
   735
"\<lbrakk>is_static new; msig new = msig old;
schirmer@12854
   736
  G\<turnstile>(declclass new) \<prec>\<^sub>C (declclass old);
schirmer@12854
   737
  G\<turnstile>Method new declared_in (declclass new);
schirmer@12854
   738
  G\<turnstile>Method old declared_in (declclass old);
schirmer@12854
   739
  G\<turnstile>Method old inheritable_in pid (declclass new)
schirmer@12854
   740
 \<rbrakk> \<Longrightarrow> G\<turnstile>new hides old"
schirmer@12854
   741
by (auto simp add: hides_def)
schirmer@12854
   742
schirmer@12854
   743
lemma hidesD:
schirmer@12854
   744
"\<lbrakk>G\<turnstile>new hides old\<rbrakk> \<Longrightarrow>  
schirmer@12854
   745
  declclass new \<noteq> Object \<and> is_static new \<and> msig new = msig old \<and> 
schirmer@12854
   746
  G\<turnstile>(declclass new) \<prec>\<^sub>C (declclass old) \<and>
schirmer@12854
   747
  G\<turnstile>Method new declared_in (declclass new) \<and>   
schirmer@12854
   748
  G\<turnstile>Method old declared_in (declclass old)"
schirmer@12854
   749
by (auto simp add: hides_def)
schirmer@12854
   750
schirmer@12854
   751
lemma overrides_commonD:
schirmer@12854
   752
"\<lbrakk>G\<turnstile>new overrides old\<rbrakk> \<Longrightarrow>  
schirmer@12854
   753
  declclass new \<noteq> Object \<and> \<not> is_static new \<and> \<not> is_static old \<and>
schirmer@12854
   754
  accmodi new \<noteq> Private \<and> 
schirmer@12854
   755
  msig new = msig old  \<and>
schirmer@12854
   756
  G\<turnstile>(declclass new) \<prec>\<^sub>C (declclass old) \<and>
schirmer@12854
   757
  G\<turnstile>Method new declared_in (declclass new) \<and>   
schirmer@12854
   758
  G\<turnstile>Method old declared_in (declclass old)"
schirmer@12854
   759
by (induct set: overridesR) (auto intro: trancl_trans)
schirmer@12854
   760
schirmer@12854
   761
lemma ws_overrides_commonD:
schirmer@12854
   762
"\<lbrakk>G\<turnstile>new overrides old;ws_prog G\<rbrakk> \<Longrightarrow>  
schirmer@12854
   763
  declclass new \<noteq> Object \<and> \<not> is_static new \<and> \<not> is_static old \<and>
schirmer@12854
   764
  accmodi new \<noteq> Private \<and> G\<turnstile>resTy new \<preceq> resTy old \<and>
schirmer@12854
   765
  msig new = msig old  \<and>
schirmer@12854
   766
  G\<turnstile>(declclass new) \<prec>\<^sub>C (declclass old) \<and>
schirmer@12854
   767
  G\<turnstile>Method new declared_in (declclass new) \<and>   
schirmer@12854
   768
  G\<turnstile>Method old declared_in (declclass old)"
schirmer@12854
   769
by (induct set: overridesR) (auto intro: trancl_trans ws_widen_trans)
schirmer@12854
   770
schirmer@12854
   771
lemma overrides_eq_sigD: 
schirmer@12854
   772
 "\<lbrakk>G\<turnstile>new overrides old\<rbrakk> \<Longrightarrow> msig old=msig new"
schirmer@12854
   773
by (auto dest: overrides_commonD)
schirmer@12854
   774
schirmer@12854
   775
lemma hides_eq_sigD: 
schirmer@12854
   776
 "\<lbrakk>G\<turnstile>new hides old\<rbrakk> \<Longrightarrow> msig old=msig new"
schirmer@12854
   777
by (auto simp add: hides_def)
schirmer@12854
   778
schirmer@12854
   779
subsubsection "permits access" 
schirmer@12854
   780
constdefs 
schirmer@12854
   781
permits_acc:: 
schirmer@12854
   782
 "prog \<Rightarrow> (qtname \<times> memberdecl) \<Rightarrow> qtname \<Rightarrow> qtname \<Rightarrow> bool"
schirmer@14030
   783
                   ("_ \<turnstile> _ in _ permits'_acc'_from _" [61,61,61,61] 60)
schirmer@12854
   784
wenzelm@35067
   785
"G\<turnstile>membr in cls permits_acc_from accclass 
schirmer@12854
   786
  \<equiv> (case (accmodi membr) of
schirmer@12854
   787
       Private   \<Rightarrow> (declclass membr = accclass)
schirmer@12854
   788
     | Package   \<Rightarrow> (pid (declclass membr) = pid accclass)
schirmer@12854
   789
     | Protected \<Rightarrow> (pid (declclass membr) = pid accclass)
schirmer@12854
   790
                    \<or>
schirmer@12925
   791
                    (G\<turnstile>accclass \<prec>\<^sub>C declclass membr 
wenzelm@35067
   792
                     \<and> (G\<turnstile>cls \<preceq>\<^sub>C accclass \<or> is_static membr)) 
schirmer@12854
   793
     | Public    \<Rightarrow> True)"
schirmer@12854
   794
text {*
schirmer@12854
   795
The subcondition of the @{term "Protected"} case: 
schirmer@12854
   796
@{term "G\<turnstile>accclass \<prec>\<^sub>C declclass membr"} could also be relaxed to:
schirmer@12854
   797
@{term "G\<turnstile>accclass \<preceq>\<^sub>C declclass membr"} since in case both classes are the
schirmer@12854
   798
same the other condition @{term "(pid (declclass membr) = pid accclass)"}
schirmer@12854
   799
holds anyway.
schirmer@12854
   800
*} 
schirmer@12854
   801
schirmer@12854
   802
text {* Like in case of overriding, the static and dynamic accessibility 
schirmer@12854
   803
of members is not uniform.
schirmer@12854
   804
\begin{itemize}
schirmer@12854
   805
\item Statically the class/interface of the member must be accessible for the
schirmer@12854
   806
      member to be accessible. During runtime this is not necessary. For
schirmer@12854
   807
      Example, if a class is accessible and we are allowed to access a member
schirmer@12854
   808
      of this class (statically) we expect that we can access this member in 
schirmer@12854
   809
      an arbitrary subclass (during runtime). It's not intended to restrict
schirmer@12854
   810
      the access to accessible subclasses during runtime.
schirmer@12854
   811
\item Statically the member we want to access must be "member of" the class.
schirmer@12854
   812
      Dynamically it must only be "member in" the class.
schirmer@12854
   813
\end{itemize} 
schirmer@12854
   814
*} 
schirmer@12854
   815
berghofe@23747
   816
inductive
berghofe@21765
   817
  accessible_fromR :: "prog \<Rightarrow> qtname \<Rightarrow> (qtname \<times> memberdecl) \<Rightarrow> qtname \<Rightarrow> bool"
berghofe@21765
   818
  and accessible_from :: "prog \<Rightarrow> (qtname \<times> memberdecl) \<Rightarrow> qtname \<Rightarrow> qtname \<Rightarrow> bool"
berghofe@21765
   819
    ("_ \<turnstile> _ of _ accessible'_from _" [61,61,61,61] 60)
berghofe@21765
   820
  and method_accessible_from :: "prog \<Rightarrow> (qtname \<times> mdecl) \<Rightarrow> qtname \<Rightarrow> qtname \<Rightarrow> bool"
berghofe@21765
   821
    ("_ \<turnstile>Method _ of _ accessible'_from _" [61,61,61,61] 60)
berghofe@21765
   822
  for G :: prog and accclass :: qtname
berghofe@21765
   823
where
berghofe@21765
   824
  "G\<turnstile>membr of cls accessible_from accclass \<equiv> accessible_fromR G accclass membr cls"
schirmer@12854
   825
wenzelm@25143
   826
| "G\<turnstile>Method m of cls accessible_from accclass \<equiv> accessible_fromR G accclass (methdMembr m) cls"
schirmer@12854
   827
wenzelm@35067
   828
| Immediate:  "!!membr class.
wenzelm@35067
   829
               \<lbrakk>G\<turnstile>membr member_of class;
berghofe@21765
   830
                G\<turnstile>(Class class) accessible_in (pid accclass);
berghofe@21765
   831
                G\<turnstile>membr in class permits_acc_from accclass 
berghofe@21765
   832
               \<rbrakk> \<Longrightarrow> G\<turnstile>membr of class accessible_from accclass"
schirmer@12854
   833
wenzelm@35067
   834
| Overriding: "!!membr class C new old supr.
wenzelm@35067
   835
               \<lbrakk>G\<turnstile>membr member_of class;
berghofe@21765
   836
                G\<turnstile>(Class class) accessible_in (pid accclass);
berghofe@21765
   837
                membr=(C,mdecl new);
berghofe@21765
   838
                G\<turnstile>(C,new) overrides\<^sub>S old; 
haftmann@22426
   839
                G\<turnstile>class \<prec>\<^sub>C supr;
haftmann@22426
   840
                G\<turnstile>Method old of supr accessible_from accclass
berghofe@21765
   841
               \<rbrakk>\<Longrightarrow> G\<turnstile>membr of class accessible_from accclass"
schirmer@12854
   842
wenzelm@35067
   843
abbreviation
schirmer@12854
   844
methd_accessible_from:: 
schirmer@12854
   845
 "prog \<Rightarrow> sig \<Rightarrow> (qtname \<times> methd) \<Rightarrow> qtname \<Rightarrow> qtname \<Rightarrow> bool"
schirmer@12854
   846
                 ("_ \<turnstile>Methd _ _ of _ accessible'_from _" [61,61,61,61,61] 60)
wenzelm@35067
   847
 where
wenzelm@35067
   848
 "G\<turnstile>Methd s m of cls accessible_from accclass ==
wenzelm@35067
   849
   G\<turnstile>(method s m) of cls accessible_from accclass"
schirmer@12854
   850
wenzelm@35067
   851
abbreviation
schirmer@12854
   852
field_accessible_from:: 
schirmer@12854
   853
 "prog \<Rightarrow> vname \<Rightarrow> (qtname \<times> field) \<Rightarrow> qtname \<Rightarrow> qtname \<Rightarrow> bool"
schirmer@12854
   854
                 ("_ \<turnstile>Field _  _ of _ accessible'_from _" [61,61,61,61,61] 60)
wenzelm@35067
   855
 where
wenzelm@35067
   856
 "G\<turnstile>Field fn f of C accessible_from accclass ==
wenzelm@35067
   857
  G\<turnstile>(fieldm fn f) of C accessible_from accclass"
schirmer@12854
   858
berghofe@23747
   859
inductive
berghofe@21765
   860
  dyn_accessible_fromR :: "prog \<Rightarrow> qtname \<Rightarrow> (qtname \<times> memberdecl) \<Rightarrow> qtname \<Rightarrow> bool"
berghofe@21765
   861
  and dyn_accessible_from' ::  "prog \<Rightarrow> (qtname \<times> memberdecl) \<Rightarrow> qtname \<Rightarrow> qtname \<Rightarrow> bool"
berghofe@21765
   862
    ("_ \<turnstile> _ in _ dyn'_accessible'_from _" [61,61,61,61] 60)
berghofe@21765
   863
  and method_dyn_accessible_from :: "prog \<Rightarrow> (qtname \<times> mdecl) \<Rightarrow> qtname \<Rightarrow> qtname \<Rightarrow> bool"
berghofe@21765
   864
    ("_ \<turnstile>Method _ in _ dyn'_accessible'_from _" [61,61,61,61] 60)
berghofe@21765
   865
  for G :: prog and accclass :: qtname
berghofe@21765
   866
where
berghofe@21765
   867
  "G\<turnstile>membr in C dyn_accessible_from accC \<equiv> dyn_accessible_fromR G accC membr C"
schirmer@12854
   868
wenzelm@25143
   869
| "G\<turnstile>Method m in C dyn_accessible_from accC \<equiv> dyn_accessible_fromR G accC (methdMembr m) C"
schirmer@12854
   870
wenzelm@35067
   871
| Immediate:  "!!class. \<lbrakk>G\<turnstile>membr member_in class;
berghofe@21765
   872
                G\<turnstile>membr in class permits_acc_from accclass 
berghofe@21765
   873
               \<rbrakk> \<Longrightarrow> G\<turnstile>membr in class dyn_accessible_from accclass"
schirmer@12854
   874
wenzelm@35067
   875
| Overriding: "!!class. \<lbrakk>G\<turnstile>membr member_in class;
berghofe@21765
   876
                membr=(C,mdecl new);
berghofe@21765
   877
                G\<turnstile>(C,new) overrides old; 
haftmann@22426
   878
                G\<turnstile>class \<prec>\<^sub>C supr;
haftmann@22426
   879
                G\<turnstile>Method old in supr dyn_accessible_from accclass
berghofe@21765
   880
               \<rbrakk>\<Longrightarrow> G\<turnstile>membr in class dyn_accessible_from accclass"
schirmer@12854
   881
wenzelm@35067
   882
abbreviation
schirmer@12854
   883
methd_dyn_accessible_from:: 
schirmer@12854
   884
 "prog \<Rightarrow> sig \<Rightarrow> (qtname \<times> methd) \<Rightarrow> qtname \<Rightarrow> qtname \<Rightarrow> bool"
schirmer@12854
   885
             ("_ \<turnstile>Methd _ _ in _ dyn'_accessible'_from _" [61,61,61,61,61] 60)
wenzelm@35067
   886
 where
wenzelm@35067
   887
 "G\<turnstile>Methd s m in C dyn_accessible_from accC ==
wenzelm@35067
   888
  G\<turnstile>(method s m) in C dyn_accessible_from accC"  
schirmer@12854
   889
wenzelm@35067
   890
abbreviation
schirmer@12854
   891
field_dyn_accessible_from:: 
schirmer@12854
   892
 "prog \<Rightarrow> vname \<Rightarrow> (qtname \<times> field) \<Rightarrow> qtname \<Rightarrow> qtname \<Rightarrow> bool"
schirmer@12854
   893
         ("_ \<turnstile>Field _ _ in _ dyn'_accessible'_from _" [61,61,61,61,61] 60)
wenzelm@35067
   894
 where
wenzelm@35067
   895
 "G\<turnstile>Field fn f in dynC dyn_accessible_from accC ==
wenzelm@35067
   896
  G\<turnstile>(fieldm fn f) in dynC dyn_accessible_from accC"
schirmer@12854
   897
schirmer@12854
   898
schirmer@12854
   899
lemma accessible_from_commonD: "G\<turnstile>m of C accessible_from S
schirmer@12854
   900
 \<Longrightarrow> G\<turnstile>m member_of C \<and> G\<turnstile>(Class C) accessible_in (pid S)"
schirmer@12854
   901
by (auto elim: accessible_fromR.induct)
schirmer@12854
   902
schirmer@12925
   903
lemma unique_declaration: 
schirmer@12925
   904
 "\<lbrakk>G\<turnstile>m declared_in C;  G\<turnstile>n declared_in C; memberid m = memberid n \<rbrakk> 
schirmer@12925
   905
  \<Longrightarrow> m = n"
schirmer@12925
   906
apply (cases m)
schirmer@12925
   907
apply (cases n,
schirmer@12925
   908
        auto simp add: declared_in_def cdeclaredmethd_def cdeclaredfield_def)+
schirmer@12925
   909
done
schirmer@12925
   910
schirmer@12854
   911
lemma declared_not_undeclared:
schirmer@12854
   912
  "G\<turnstile>m declared_in C \<Longrightarrow> \<not> G\<turnstile> memberid m undeclared_in C"
schirmer@12854
   913
by (cases m) (auto simp add: declared_in_def undeclared_in_def)
schirmer@12854
   914
schirmer@12925
   915
lemma undeclared_not_declared:
schirmer@12925
   916
 "G\<turnstile> memberid m undeclared_in C \<Longrightarrow> \<not> G\<turnstile> m declared_in C" 
schirmer@12925
   917
by (cases m) (auto simp add: declared_in_def undeclared_in_def)
schirmer@12925
   918
schirmer@12854
   919
lemma not_undeclared_declared:
schirmer@12854
   920
  "\<not> G\<turnstile> membr_id undeclared_in C \<Longrightarrow> (\<exists> m. G\<turnstile>m declared_in C \<and> 
schirmer@12854
   921
                                           membr_id = memberid m)"
schirmer@12854
   922
proof -
schirmer@12854
   923
  assume not_undecl:"\<not> G\<turnstile> membr_id undeclared_in C"
schirmer@12854
   924
  show ?thesis (is "?P membr_id")
schirmer@12854
   925
  proof (cases membr_id)
schirmer@12854
   926
    case (fid vname)
schirmer@12854
   927
    with not_undecl
schirmer@12854
   928
    obtain fld where
schirmer@12854
   929
      "G\<turnstile>fdecl (vname,fld) declared_in C" 
schirmer@12854
   930
      by (auto simp add: undeclared_in_def declared_in_def
schirmer@12854
   931
                         cdeclaredfield_def)
schirmer@12854
   932
    with fid show ?thesis 
schirmer@12854
   933
      by auto
schirmer@12854
   934
  next
schirmer@12854
   935
    case (mid sig)
schirmer@12854
   936
    with not_undecl
schirmer@12854
   937
    obtain mthd where
schirmer@12854
   938
      "G\<turnstile>mdecl (sig,mthd) declared_in C" 
schirmer@12854
   939
      by (auto simp add: undeclared_in_def declared_in_def
schirmer@12854
   940
                         cdeclaredmethd_def)
schirmer@12854
   941
    with mid show ?thesis 
schirmer@12854
   942
      by auto
schirmer@12854
   943
  qed
schirmer@12854
   944
qed
schirmer@12854
   945
schirmer@12854
   946
lemma unique_declared_in:
schirmer@12854
   947
 "\<lbrakk>G\<turnstile>m declared_in C; G\<turnstile>n declared_in C; memberid m = memberid n\<rbrakk>
schirmer@12854
   948
 \<Longrightarrow> m = n"
schirmer@12854
   949
by (auto simp add: declared_in_def cdeclaredmethd_def cdeclaredfield_def
schirmer@12854
   950
            split: memberdecl.splits)
schirmer@12854
   951
schirmer@12854
   952
lemma unique_member_of: 
wenzelm@12937
   953
  assumes n: "G\<turnstile>n member_of C" and  
schirmer@12854
   954
          m: "G\<turnstile>m member_of C" and
schirmer@12854
   955
       eqid: "memberid n = memberid m"
wenzelm@12937
   956
  shows "n=m"
schirmer@12854
   957
proof -
schirmer@12854
   958
  from n m eqid  
schirmer@12854
   959
  show "n=m"
schirmer@12854
   960
  proof (induct)
berghofe@21765
   961
    case (Immediate n C)
schirmer@12854
   962
    assume member_n: "G\<turnstile> mbr n declared_in C" "declclass n = C"
schirmer@12854
   963
    assume eqid: "memberid n = memberid m"
schirmer@12854
   964
    assume "G \<turnstile> m member_of C"
schirmer@12854
   965
    then show "n=m"
schirmer@12854
   966
    proof (cases)
berghofe@34990
   967
      case Immediate
berghofe@34990
   968
      with eqid member_n
schirmer@12854
   969
      show ?thesis
wenzelm@32960
   970
        by (cases n, cases m) 
schirmer@12854
   971
           (auto simp add: declared_in_def 
schirmer@12854
   972
                           cdeclaredmethd_def cdeclaredfield_def
schirmer@12854
   973
                    split: memberdecl.splits)
schirmer@12854
   974
    next
berghofe@34990
   975
      case Inherited
schirmer@12854
   976
      with eqid member_n
schirmer@12854
   977
      show ?thesis
wenzelm@32960
   978
        by (cases n) (auto dest: declared_not_undeclared)
schirmer@12854
   979
    qed
schirmer@12854
   980
  next
berghofe@21765
   981
    case (Inherited n C S)
schirmer@12854
   982
    assume undecl: "G\<turnstile> memberid n undeclared_in C"
schirmer@12854
   983
    assume  super: "G\<turnstile>C\<prec>\<^sub>C\<^sub>1S"
schirmer@12854
   984
    assume    hyp: "\<lbrakk>G \<turnstile> m member_of S; memberid n = memberid m\<rbrakk> \<Longrightarrow> n = m"
schirmer@12854
   985
    assume   eqid: "memberid n = memberid m"
schirmer@12854
   986
    assume "G \<turnstile> m member_of C"
schirmer@12854
   987
    then show "n=m"
schirmer@12854
   988
    proof (cases)
schirmer@12854
   989
      case Immediate
schirmer@12854
   990
      then have "G\<turnstile> mbr m declared_in C" by simp
schirmer@12854
   991
      with eqid undecl
schirmer@12854
   992
      show ?thesis
wenzelm@32960
   993
        by (cases m) (auto dest: declared_not_undeclared)
schirmer@12854
   994
    next
schirmer@12854
   995
      case Inherited 
schirmer@12854
   996
      with super have "G \<turnstile> m member_of S"
wenzelm@32960
   997
        by (auto dest!: subcls1D)
schirmer@12854
   998
      with eqid hyp
schirmer@12854
   999
      show ?thesis 
wenzelm@32960
  1000
        by blast
schirmer@12854
  1001
    qed
schirmer@12854
  1002
  qed
schirmer@12854
  1003
qed
schirmer@12854
  1004
schirmer@12854
  1005
lemma member_of_is_classD: "G\<turnstile>m member_of C \<Longrightarrow> is_class G C"
schirmer@12854
  1006
proof (induct set: members)
berghofe@21765
  1007
  case (Immediate m C)
schirmer@12854
  1008
  assume "G\<turnstile> mbr m declared_in C"
schirmer@12854
  1009
  then show "is_class G C"
schirmer@12854
  1010
    by (cases "mbr m")
schirmer@12854
  1011
       (auto simp add: declared_in_def cdeclaredmethd_def cdeclaredfield_def)
schirmer@12854
  1012
next
berghofe@21765
  1013
  case (Inherited m C S)  
schirmer@12854
  1014
  assume "G\<turnstile>C\<prec>\<^sub>C\<^sub>1S" and "is_class G S"
schirmer@12854
  1015
  then show "is_class G C"
schirmer@12854
  1016
    by - (rule subcls_is_class2,auto)
schirmer@12854
  1017
qed
schirmer@12854
  1018
schirmer@12854
  1019
lemma member_of_declC: 
schirmer@12854
  1020
 "G\<turnstile>m member_of C 
schirmer@12854
  1021
  \<Longrightarrow> G\<turnstile>mbr m declared_in (declclass m)"
schirmer@12854
  1022
by (induct set: members) auto
schirmer@12854
  1023
schirmer@12854
  1024
lemma member_of_member_of_declC:
schirmer@12854
  1025
 "G\<turnstile>m member_of C 
schirmer@12854
  1026
  \<Longrightarrow> G\<turnstile>m member_of (declclass m)"
schirmer@12854
  1027
by (auto dest: member_of_declC intro: members.Immediate)
schirmer@12854
  1028
schirmer@12854
  1029
lemma member_of_class_relation:
schirmer@12854
  1030
  "G\<turnstile>m member_of C \<Longrightarrow> G\<turnstile>C \<preceq>\<^sub>C declclass m"
schirmer@12854
  1031
proof (induct set: members)
berghofe@21765
  1032
  case (Immediate m C)
schirmer@12854
  1033
  then show "G\<turnstile>C \<preceq>\<^sub>C declclass m" by simp
schirmer@12854
  1034
next
berghofe@21765
  1035
  case (Inherited m C S)
schirmer@12854
  1036
  then show "G\<turnstile>C \<preceq>\<^sub>C declclass m" 
schirmer@12854
  1037
    by (auto dest: r_into_rtrancl intro: rtrancl_trans)
schirmer@12854
  1038
qed
schirmer@12854
  1039
schirmer@12854
  1040
lemma member_in_class_relation:
schirmer@12854
  1041
  "G\<turnstile>m member_in C \<Longrightarrow> G\<turnstile>C \<preceq>\<^sub>C declclass m"
schirmer@12854
  1042
by (auto dest: member_inD member_of_class_relation
schirmer@12854
  1043
        intro: rtrancl_trans)
schirmer@12854
  1044
schirmer@12962
  1045
lemma stat_override_declclasses_relation: 
schirmer@12962
  1046
"\<lbrakk>G\<turnstile>(declclass new) \<prec>\<^sub>C\<^sub>1 superNew; G \<turnstile>Method old member_of superNew \<rbrakk>
schirmer@12962
  1047
\<Longrightarrow> G\<turnstile>(declclass new) \<prec>\<^sub>C (declclass old)"
schirmer@12962
  1048
apply (rule trancl_rtrancl_trancl)
schirmer@12962
  1049
apply (erule r_into_trancl)
schirmer@12962
  1050
apply (cases old)
schirmer@12962
  1051
apply (auto dest: member_of_class_relation)
schirmer@12962
  1052
done
schirmer@12962
  1053
schirmer@12962
  1054
lemma stat_overrides_commonD:
schirmer@12962
  1055
"\<lbrakk>G\<turnstile>new overrides\<^sub>S old\<rbrakk> \<Longrightarrow>  
schirmer@12962
  1056
  declclass new \<noteq> Object \<and> \<not> is_static new \<and> msig new = msig old \<and> 
schirmer@12962
  1057
  G\<turnstile>(declclass new) \<prec>\<^sub>C (declclass old) \<and>
schirmer@12962
  1058
  G\<turnstile>Method new declared_in (declclass new) \<and>   
schirmer@12962
  1059
  G\<turnstile>Method old declared_in (declclass old)"
schirmer@12962
  1060
apply (induct set: stat_overridesR) 
schirmer@12962
  1061
apply (frule (1) stat_override_declclasses_relation) 
schirmer@12962
  1062
apply (auto intro: trancl_trans)
schirmer@12962
  1063
done
schirmer@12962
  1064
schirmer@12854
  1065
lemma member_of_Package: 
schirmer@12854
  1066
 "\<lbrakk>G\<turnstile>m member_of C; accmodi m = Package\<rbrakk> 
schirmer@12854
  1067
  \<Longrightarrow> pid (declclass m) = pid C" 
schirmer@12854
  1068
proof -
schirmer@12854
  1069
  assume   member: "G\<turnstile>m member_of C"
schirmer@12854
  1070
  then show " accmodi m = Package \<Longrightarrow> ?thesis" (is "PROP ?P m C")
schirmer@12854
  1071
  proof (induct rule: members.induct)
schirmer@12854
  1072
    fix C m
schirmer@12854
  1073
    assume     C: "declclass m = C"
schirmer@12854
  1074
    then show "pid (declclass m) = pid C"
schirmer@12854
  1075
      by simp
schirmer@12854
  1076
  next
schirmer@12854
  1077
    fix C S m  
schirmer@12854
  1078
    assume inheritable: "G \<turnstile> m inheritable_in pid C"
schirmer@12854
  1079
    assume         hyp: "PROP ?P m S" and
schirmer@12854
  1080
           package_acc: "accmodi m = Package" 
schirmer@12854
  1081
    with inheritable package_acc hyp
schirmer@12854
  1082
    show "pid (declclass m) = pid C" 
schirmer@12854
  1083
      by (auto simp add: inheritable_in_def)
schirmer@12854
  1084
  qed
schirmer@12854
  1085
qed
schirmer@12854
  1086
schirmer@12925
  1087
lemma member_in_declC: "G\<turnstile>m member_in C\<Longrightarrow> G\<turnstile>m member_in (declclass m)"
schirmer@12925
  1088
proof -
schirmer@12925
  1089
  assume member_in_C:  "G\<turnstile>m member_in C"
schirmer@12925
  1090
  from member_in_C
schirmer@12925
  1091
  obtain provC where
schirmer@12925
  1092
    subclseq_C_provC: "G\<turnstile> C \<preceq>\<^sub>C provC" and
schirmer@12925
  1093
     member_of_provC: "G \<turnstile> m member_of provC"
schirmer@12925
  1094
    by (auto simp add: member_in_def)
schirmer@12925
  1095
  from member_of_provC
schirmer@12925
  1096
  have "G \<turnstile> m member_of declclass m"
schirmer@12925
  1097
    by (rule member_of_member_of_declC)
schirmer@12925
  1098
  moreover
schirmer@12925
  1099
  from member_in_C
schirmer@12925
  1100
  have "G\<turnstile>C \<preceq>\<^sub>C declclass m"
schirmer@12925
  1101
    by (rule member_in_class_relation)
schirmer@12925
  1102
  ultimately
schirmer@12925
  1103
  show ?thesis
schirmer@12925
  1104
    by (auto simp add: member_in_def)
schirmer@12925
  1105
qed
schirmer@12925
  1106
schirmer@12854
  1107
lemma dyn_accessible_from_commonD: "G\<turnstile>m in C dyn_accessible_from S
schirmer@12854
  1108
 \<Longrightarrow> G\<turnstile>m member_in C"
schirmer@12854
  1109
by (auto elim: dyn_accessible_fromR.induct)
schirmer@12854
  1110
schirmer@12854
  1111
lemma no_Private_stat_override: 
schirmer@12854
  1112
 "\<lbrakk>G\<turnstile>new overrides\<^sub>S old\<rbrakk> \<Longrightarrow> accmodi old \<noteq> Private"
schirmer@12854
  1113
by (induct set:  stat_overridesR) (auto simp add: inheritable_in_def)
schirmer@12854
  1114
schirmer@12854
  1115
lemma no_Private_override: "\<lbrakk>G\<turnstile>new overrides old\<rbrakk> \<Longrightarrow> accmodi old \<noteq> Private"
schirmer@12854
  1116
by (induct set: overridesR) (auto simp add: inheritable_in_def)
schirmer@12854
  1117
schirmer@12854
  1118
lemma permits_acc_inheritance:
schirmer@14030
  1119
 "\<lbrakk>G\<turnstile>m in statC permits_acc_from accC; G\<turnstile>dynC \<preceq>\<^sub>C statC
schirmer@14030
  1120
  \<rbrakk> \<Longrightarrow> G\<turnstile>m in dynC permits_acc_from accC"
schirmer@12854
  1121
by (cases "accmodi m")
schirmer@12854
  1122
   (auto simp add: permits_acc_def
schirmer@12854
  1123
            intro: subclseq_trans) 
schirmer@12854
  1124
schirmer@12925
  1125
lemma permits_acc_static_declC:
schirmer@14030
  1126
 "\<lbrakk>G\<turnstile>m in C permits_acc_from accC; G\<turnstile>m member_in C; is_static m
schirmer@14030
  1127
  \<rbrakk> \<Longrightarrow> G\<turnstile>m in (declclass m) permits_acc_from accC"
schirmer@12925
  1128
by (cases "accmodi m") (auto simp add: permits_acc_def)
schirmer@12925
  1129
schirmer@12925
  1130
lemma dyn_accessible_from_static_declC: 
wenzelm@12937
  1131
  assumes  acc_C: "G\<turnstile>m in C dyn_accessible_from accC" and
schirmer@12925
  1132
           static: "is_static m"
wenzelm@12937
  1133
  shows "G\<turnstile>m in (declclass m) dyn_accessible_from accC"
schirmer@12925
  1134
proof -
schirmer@12925
  1135
  from acc_C static
schirmer@12925
  1136
  show "G\<turnstile>m in (declclass m) dyn_accessible_from accC"
schirmer@12925
  1137
  proof (induct)
berghofe@21765
  1138
    case (Immediate m C)
schirmer@12925
  1139
    then show ?case 
schirmer@12925
  1140
      by (auto intro!: dyn_accessible_fromR.Immediate
schirmer@12925
  1141
                 dest: member_in_declC permits_acc_static_declC) 
schirmer@12925
  1142
  next 
berghofe@21765
  1143
    case (Overriding m C declCNew new old sup)
schirmer@12925
  1144
    then have "\<not> is_static m"
schirmer@12925
  1145
      by (auto dest: overrides_commonD)
schirmer@12925
  1146
    moreover
schirmer@12925
  1147
    assume "is_static m"
schirmer@12925
  1148
    ultimately show ?case 
schirmer@12925
  1149
      by contradiction
schirmer@12925
  1150
  qed
schirmer@12925
  1151
qed
schirmer@12925
  1152
schirmer@12854
  1153
lemma field_accessible_fromD:
schirmer@12854
  1154
 "\<lbrakk>G\<turnstile>membr of C accessible_from accC;is_field membr\<rbrakk> 
schirmer@12854
  1155
  \<Longrightarrow> G\<turnstile>membr member_of C \<and>
schirmer@12854
  1156
      G\<turnstile>(Class C) accessible_in (pid accC) \<and>
schirmer@14030
  1157
      G\<turnstile>membr in C permits_acc_from accC"
schirmer@12854
  1158
by (cases set: accessible_fromR)
schirmer@12854
  1159
   (auto simp add: is_field_def split: memberdecl.splits) 
schirmer@12854
  1160
schirmer@12854
  1161
lemma field_accessible_from_permits_acc_inheritance:
schirmer@12854
  1162
"\<lbrakk>G\<turnstile>membr of statC accessible_from accC; is_field membr; G \<turnstile> dynC \<preceq>\<^sub>C statC\<rbrakk>
schirmer@14030
  1163
\<Longrightarrow> G\<turnstile>membr in dynC permits_acc_from accC"
schirmer@12854
  1164
by (auto dest: field_accessible_fromD intro: permits_acc_inheritance)
schirmer@12854
  1165
schirmer@12854
  1166
schirmer@12854
  1167
(*
schirmer@12854
  1168
lemma accessible_Package:
schirmer@12854
  1169
 "\<lbrakk>G \<turnstile> m of C accessible_from S;accmodi m = Package;
schirmer@12854
  1170
   \<And> new old. G\<turnstile>new overrides\<^sub>S old \<Longrightarrow> accmodi old \<le> accmodi new\<rbrakk>
schirmer@12854
  1171
  \<Longrightarrow> pid S = pid C \<and> pid C = pid (declclass m)"
schirmer@12854
  1172
proof -
schirmer@12854
  1173
  assume wf: "\<And> new old. G\<turnstile>new overrides\<^sub>S old \<Longrightarrow> accmodi old \<le> accmodi new"
schirmer@12854
  1174
  assume "G \<turnstile> m of C accessible_from S"
schirmer@12854
  1175
  then show "accmodi m = Package \<Longrightarrow> pid S = pid C \<and> pid C = pid (declclass m)"
schirmer@12854
  1176
    (is "?Pack m \<Longrightarrow> ?P C m")
schirmer@12854
  1177
  proof (induct rule: accessible_fromR.induct)
schirmer@12854
  1178
    fix C m
schirmer@12854
  1179
    assume "G\<turnstile>m member_of C"
schirmer@14030
  1180
           "G \<turnstile> m in C permits_acc_from S"
schirmer@12854
  1181
           "accmodi m = Package"      
schirmer@12854
  1182
    then show "?P C m"
schirmer@12854
  1183
      by (auto dest: member_of_Package simp add: permits_acc_def)
schirmer@12854
  1184
  next
schirmer@12854
  1185
    fix declC C new newm old Sup
schirmer@12854
  1186
    assume member_new: "G \<turnstile> new member_of C" and 
schirmer@12854
  1187
                acc_C: "G \<turnstile> Class C accessible_in pid S" and
schirmer@12854
  1188
                  new: "new = (declC, mdecl newm)" and
schirmer@12854
  1189
             override: "G \<turnstile> (declC, newm) overrides\<^sub>S old" and
schirmer@12854
  1190
         subcls_C_Sup: "G\<turnstile>C \<prec>\<^sub>C Sup" and
schirmer@12854
  1191
              acc_old: "G \<turnstile> methdMembr old of Sup accessible_from S" and
schirmer@12854
  1192
                  hyp: "?Pack (methdMembr old) \<Longrightarrow> ?P Sup (methdMembr old)" and
schirmer@12854
  1193
          accmodi_new: "accmodi new = Package"
schirmer@12854
  1194
    from override wf 
schirmer@12854
  1195
    have accmodi_weaken: "accmodi old \<le> accmodi newm"
schirmer@12854
  1196
      by (cases old,cases newm) auto
schirmer@12854
  1197
    from override new
schirmer@12854
  1198
    have "accmodi old \<noteq> Private"
schirmer@12854
  1199
      by (simp add: no_Private_stat_override)
schirmer@12854
  1200
    with accmodi_weaken accmodi_new new
schirmer@12854
  1201
    have accmodi_old: "accmodi old = Package"
schirmer@12854
  1202
      by (cases "accmodi old") (auto simp add: le_acc_def less_acc_def) 
schirmer@12854
  1203
    with hyp 
schirmer@12854
  1204
    have P_sup: "?P Sup (methdMembr old)"
schirmer@12854
  1205
      by (simp)
schirmer@12854
  1206
    from wf override new accmodi_old accmodi_new
schirmer@12854
  1207
    have eq_pid_new_old: "pid (declclass new) = pid (declclass old)"
schirmer@12854
  1208
      by (auto dest: stat_override_Package) 
schirmer@12854
  1209
    from member_new accmodi_new
schirmer@12854
  1210
    have "pid (declclass new) = pid C"
schirmer@12854
  1211
      by (auto dest: member_of_Package)
schirmer@12854
  1212
    with eq_pid_new_old P_sup show "?P C new"
schirmer@12854
  1213
      by auto
schirmer@12854
  1214
  qed
schirmer@12854
  1215
qed
schirmer@12854
  1216
*)
schirmer@13688
  1217
schirmer@12854
  1218
lemma accessible_fieldD: 
schirmer@12854
  1219
 "\<lbrakk>G\<turnstile>membr of C accessible_from accC; is_field membr\<rbrakk>
schirmer@12854
  1220
 \<Longrightarrow> G\<turnstile>membr member_of C \<and>
schirmer@12854
  1221
     G\<turnstile>(Class C) accessible_in (pid accC) \<and>
schirmer@14030
  1222
     G\<turnstile>membr in C permits_acc_from accC"
schirmer@12854
  1223
by (induct rule: accessible_fromR.induct) (auto dest: is_fieldD)
schirmer@12854
  1224
      
schirmer@12854
  1225
schirmer@12854
  1226
schirmer@12854
  1227
lemma member_of_Private:
schirmer@12854
  1228
"\<lbrakk>G\<turnstile>m member_of C; accmodi m = Private\<rbrakk> \<Longrightarrow> declclass m = C"
schirmer@12854
  1229
by (induct set: members) (auto simp add: inheritable_in_def)
schirmer@12854
  1230
schirmer@12854
  1231
lemma member_of_subclseq_declC:
schirmer@12854
  1232
  "G\<turnstile>m member_of C \<Longrightarrow> G\<turnstile>C \<preceq>\<^sub>C declclass m"
schirmer@12854
  1233
by (induct set: members) (auto dest: r_into_rtrancl intro: rtrancl_trans)
schirmer@12854
  1234
schirmer@12854
  1235
lemma member_of_inheritance:
wenzelm@12937
  1236
  assumes       m: "G\<turnstile>m member_of D" and
schirmer@12854
  1237
     subclseq_D_C: "G\<turnstile>D \<preceq>\<^sub>C C" and
schirmer@12854
  1238
     subclseq_C_m: "G\<turnstile>C \<preceq>\<^sub>C declclass m" and
schirmer@12854
  1239
               ws: "ws_prog G" 
wenzelm@12937
  1240
  shows "G\<turnstile>m member_of C"
schirmer@12854
  1241
proof -
schirmer@12854
  1242
  from m subclseq_D_C subclseq_C_m
schirmer@12854
  1243
  show ?thesis
schirmer@12854
  1244
  proof (induct)
berghofe@21765
  1245
    case (Immediate m D)
schirmer@12854
  1246
    assume "declclass m = D" and
schirmer@12854
  1247
           "G\<turnstile>D\<preceq>\<^sub>C C" and "G\<turnstile>C\<preceq>\<^sub>C declclass m"
schirmer@12854
  1248
    with ws have "D=C" 
schirmer@12854
  1249
      by (auto intro: subclseq_acyclic)
schirmer@12854
  1250
    with Immediate 
schirmer@12854
  1251
    show "G\<turnstile>m member_of C"
schirmer@12854
  1252
      by (auto intro: members.Immediate)
schirmer@12854
  1253
  next
berghofe@21765
  1254
    case (Inherited m D S)
schirmer@12854
  1255
    assume member_of_D_props: 
schirmer@12854
  1256
            "G \<turnstile> m inheritable_in pid D" 
schirmer@12854
  1257
            "G\<turnstile> memberid m undeclared_in D"  
schirmer@12854
  1258
            "G \<turnstile> Class S accessible_in pid D" 
schirmer@12854
  1259
            "G \<turnstile> m member_of S"
schirmer@12854
  1260
    assume super: "G\<turnstile>D\<prec>\<^sub>C\<^sub>1S"
schirmer@12854
  1261
    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
  1262
    assume subclseq_C_m: "G\<turnstile>C\<preceq>\<^sub>C declclass m"
schirmer@12854
  1263
    assume "G\<turnstile>D\<preceq>\<^sub>C C"
schirmer@12854
  1264
    then show "G\<turnstile>m member_of C"
schirmer@12854
  1265
    proof (cases rule: subclseq_cases)
schirmer@12854
  1266
      case Eq
schirmer@12854
  1267
      assume "D=C" 
schirmer@12854
  1268
      with super member_of_D_props 
schirmer@12854
  1269
      show ?thesis
wenzelm@32960
  1270
        by (auto intro: members.Inherited)
schirmer@12854
  1271
    next
schirmer@12854
  1272
      case Subcls
schirmer@12854
  1273
      assume "G\<turnstile>D\<prec>\<^sub>C C"
schirmer@12854
  1274
      with super 
schirmer@12854
  1275
      have "G\<turnstile>S\<preceq>\<^sub>C C"
wenzelm@32960
  1276
        by (auto dest: subcls1D subcls_superD)
schirmer@12854
  1277
      with subclseq_C_m hyp show ?thesis
wenzelm@32960
  1278
        by blast
schirmer@12854
  1279
    qed
schirmer@12854
  1280
  qed
schirmer@12854
  1281
qed
schirmer@12854
  1282
schirmer@12854
  1283
lemma member_of_subcls:
wenzelm@12937
  1284
  assumes     old: "G\<turnstile>old member_of C" and 
schirmer@12854
  1285
              new: "G\<turnstile>new member_of D" and
schirmer@12854
  1286
             eqid: "memberid new = memberid old" and
schirmer@12854
  1287
     subclseq_D_C: "G\<turnstile>D \<preceq>\<^sub>C C" and 
schirmer@12854
  1288
   subcls_new_old: "G\<turnstile>declclass new \<prec>\<^sub>C declclass old" and
schirmer@12854
  1289
               ws: "ws_prog G"
wenzelm@12937
  1290
  shows "G\<turnstile>D \<prec>\<^sub>C C"
schirmer@12854
  1291
proof -
schirmer@12854
  1292
  from old 
schirmer@12854
  1293
  have subclseq_C_old: "G\<turnstile>C \<preceq>\<^sub>C declclass old"
schirmer@12854
  1294
    by (auto dest: member_of_subclseq_declC)
schirmer@12854
  1295
  from new 
schirmer@12854
  1296
  have subclseq_D_new: "G\<turnstile>D \<preceq>\<^sub>C declclass new"
schirmer@12854
  1297
    by (auto dest: member_of_subclseq_declC)
schirmer@12854
  1298
  from subcls_new_old ws
schirmer@12854
  1299
  have neq_new_old: "new\<noteq>old"
schirmer@12854
  1300
    by (cases new,cases old) (auto dest: subcls_irrefl)
schirmer@12854
  1301
  from subclseq_D_new subclseq_D_C
schirmer@12854
  1302
  have "G\<turnstile>(declclass new) \<preceq>\<^sub>C C \<or> G\<turnstile>C \<preceq>\<^sub>C (declclass new)" 
schirmer@12854
  1303
    by (rule subcls_compareable)
schirmer@12854
  1304
  then have "G\<turnstile>(declclass new) \<preceq>\<^sub>C C"
schirmer@12854
  1305
  proof
schirmer@12854
  1306
    assume "G\<turnstile>declclass new\<preceq>\<^sub>C C" then show ?thesis .
schirmer@12854
  1307
  next
schirmer@12854
  1308
    assume "G\<turnstile>C \<preceq>\<^sub>C (declclass new)"
schirmer@12854
  1309
    with new subclseq_D_C ws 
schirmer@12854
  1310
    have "G\<turnstile>new member_of C"
schirmer@12854
  1311
      by (blast intro: member_of_inheritance)
schirmer@12854
  1312
    with eqid old 
schirmer@12854
  1313
    have "new=old"
schirmer@12854
  1314
      by (blast intro: unique_member_of)
schirmer@12854
  1315
    with neq_new_old 
schirmer@12854
  1316
    show ?thesis
schirmer@12854
  1317
      by contradiction
schirmer@12854
  1318
  qed
schirmer@12854
  1319
  then show ?thesis
schirmer@12854
  1320
  proof (cases rule: subclseq_cases)
schirmer@12854
  1321
    case Eq
schirmer@12854
  1322
    assume "declclass new = C"
schirmer@12854
  1323
    with new have "G\<turnstile>new member_of C"
schirmer@12854
  1324
      by (auto dest: member_of_member_of_declC)
schirmer@12854
  1325
    with eqid old 
schirmer@12854
  1326
    have "new=old"
schirmer@12854
  1327
      by (blast intro: unique_member_of)
schirmer@12854
  1328
    with neq_new_old 
schirmer@12854
  1329
    show ?thesis
schirmer@12854
  1330
      by contradiction
schirmer@12854
  1331
  next
schirmer@12854
  1332
    case Subcls
schirmer@12854
  1333
    assume "G\<turnstile>declclass new\<prec>\<^sub>C C"
schirmer@12854
  1334
    with subclseq_D_new
schirmer@12854
  1335
    show "G\<turnstile>D\<prec>\<^sub>C C"
schirmer@12854
  1336
      by (rule rtrancl_trancl_trancl)
schirmer@12854
  1337
  qed
schirmer@12854
  1338
qed
schirmer@12854
  1339
schirmer@12854
  1340
corollary member_of_overrides_subcls:
schirmer@12854
  1341
 "\<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
  1342
   G,sig\<turnstile>new overrides old; ws_prog G\<rbrakk>
schirmer@12854
  1343
 \<Longrightarrow> G\<turnstile>D \<prec>\<^sub>C C"
schirmer@12854
  1344
by (drule overrides_commonD) (auto intro: member_of_subcls)    
schirmer@12854
  1345
schirmer@12854
  1346
corollary member_of_stat_overrides_subcls:
schirmer@12854
  1347
 "\<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
  1348
   G,sig\<turnstile>new overrides\<^sub>S old; ws_prog G\<rbrakk>
schirmer@12854
  1349
 \<Longrightarrow> G\<turnstile>D \<prec>\<^sub>C C"
schirmer@12854
  1350
by (drule stat_overrides_commonD) (auto intro: member_of_subcls)    
schirmer@12854
  1351
schirmer@12854
  1352
schirmer@12854
  1353
schirmer@12854
  1354
lemma inherited_field_access: 
wenzelm@12937
  1355
  assumes stat_acc: "G\<turnstile>membr of statC accessible_from accC" and
schirmer@12854
  1356
          is_field: "is_field membr" and 
schirmer@12854
  1357
          subclseq: "G \<turnstile> dynC \<preceq>\<^sub>C statC"
wenzelm@12937
  1358
  shows "G\<turnstile>membr in dynC dyn_accessible_from accC"
schirmer@12854
  1359
proof -
schirmer@12854
  1360
  from stat_acc is_field subclseq 
schirmer@12854
  1361
  show ?thesis
schirmer@12854
  1362
    by (auto dest: accessible_fieldD 
schirmer@12925
  1363
            intro: dyn_accessible_fromR.Immediate 
schirmer@12854
  1364
                   member_inI 
schirmer@12854
  1365
                   permits_acc_inheritance)
schirmer@12854
  1366
qed
schirmer@12854
  1367
schirmer@12854
  1368
lemma accessible_inheritance:
wenzelm@12937
  1369
  assumes stat_acc: "G\<turnstile>m of statC accessible_from accC" and
schirmer@12854
  1370
          subclseq: "G\<turnstile>dynC \<preceq>\<^sub>C statC" and
schirmer@12854
  1371
       member_dynC: "G\<turnstile>m member_of dynC" and
schirmer@12854
  1372
          dynC_acc: "G\<turnstile>(Class dynC) accessible_in (pid accC)"
wenzelm@12937
  1373
  shows "G\<turnstile>m of dynC accessible_from accC"
schirmer@12854
  1374
proof -
schirmer@12854
  1375
  from stat_acc
schirmer@12854
  1376
  have member_statC: "G\<turnstile>m member_of statC" 
schirmer@12854
  1377
    by (auto dest: accessible_from_commonD)
schirmer@12854
  1378
  from stat_acc
schirmer@12854
  1379
  show ?thesis
schirmer@12854
  1380
  proof (cases)
schirmer@12925
  1381
    case Immediate
schirmer@12854
  1382
    with member_dynC member_statC subclseq dynC_acc
schirmer@12854
  1383
    show ?thesis
schirmer@12925
  1384
      by (auto intro: accessible_fromR.Immediate permits_acc_inheritance)
schirmer@12854
  1385
  next
schirmer@12925
  1386
    case Overriding
schirmer@12854
  1387
    with member_dynC subclseq dynC_acc
schirmer@12854
  1388
    show ?thesis
schirmer@12925
  1389
      by (auto intro: accessible_fromR.Overriding rtrancl_trancl_trancl)
schirmer@12854
  1390
  qed
schirmer@12854
  1391
qed
schirmer@12854
  1392
schirmer@12854
  1393
section "fields and methods"
schirmer@12854
  1394
schirmer@12854
  1395
schirmer@12854
  1396
types
schirmer@12854
  1397
  fspec = "vname \<times> qtname"
schirmer@12854
  1398
schirmer@12854
  1399
translations 
schirmer@12854
  1400
  "fspec" <= (type) "vname \<times> qtname" 
schirmer@12854
  1401
schirmer@12854
  1402
constdefs
schirmer@12854
  1403
imethds:: "prog \<Rightarrow> qtname \<Rightarrow> (sig,qtname \<times> mhead) tables"
schirmer@12854
  1404
"imethds G I 
schirmer@12854
  1405
  \<equiv> iface_rec (G,I)  
schirmer@12854
  1406
              (\<lambda>I i ts. (Un_tables ts) \<oplus>\<oplus> 
nipkow@30235
  1407
                        (Option.set \<circ> table_of (map (\<lambda>(s,m). (s,I,m)) (imethods i))))"
schirmer@12854
  1408
text {* methods of an interface, with overriding and inheritance, cf. 9.2 *}
schirmer@12854
  1409
schirmer@12854
  1410
constdefs
schirmer@12854
  1411
accimethds:: "prog \<Rightarrow> pname \<Rightarrow> qtname \<Rightarrow> (sig,qtname \<times> mhead) tables"
schirmer@12854
  1412
"accimethds G pack I
schirmer@12854
  1413
  \<equiv> if G\<turnstile>Iface I accessible_in pack 
schirmer@12854
  1414
       then imethds G I
schirmer@12854
  1415
       else \<lambda> k. {}"
schirmer@12854
  1416
text {* only returns imethds if the interface is accessible *}
schirmer@12854
  1417
schirmer@12854
  1418
constdefs
schirmer@12854
  1419
methd:: "prog \<Rightarrow> qtname  \<Rightarrow> (sig,qtname \<times> methd) table"
schirmer@12854
  1420
schirmer@12854
  1421
"methd G C 
schirmer@12854
  1422
 \<equiv> class_rec (G,C) empty
schirmer@12854
  1423
             (\<lambda>C c subcls_mthds. 
schirmer@12854
  1424
               filter_tab (\<lambda>sig m. G\<turnstile>C inherits method sig m)
schirmer@12854
  1425
                          subcls_mthds 
schirmer@12854
  1426
               ++ 
schirmer@12854
  1427
               table_of (map (\<lambda>(s,m). (s,C,m)) (methods c)))"
schirmer@12854
  1428
text {* @{term "methd G C"}: methods of a class C (statically visible from C), 
schirmer@12854
  1429
     with inheritance and hiding cf. 8.4.6;
schirmer@12854
  1430
     Overriding is captured by @{text dynmethd}.
schirmer@12854
  1431
     Every new method with the same signature coalesces the
schirmer@12854
  1432
     method of a superclass. *}
schirmer@12854
  1433
schirmer@12854
  1434
constdefs                      
schirmer@12854
  1435
accmethd:: "prog \<Rightarrow> qtname \<Rightarrow> qtname  \<Rightarrow> (sig,qtname \<times> methd) table"
schirmer@12854
  1436
"accmethd G S C 
schirmer@12854
  1437
 \<equiv> filter_tab (\<lambda>sig m. G\<turnstile>method sig m of C accessible_from S) 
schirmer@12854
  1438
              (methd G C)"
schirmer@12854
  1439
text {* @{term "accmethd G S C"}: only those methods of @{term "methd G C"}, 
schirmer@12854
  1440
        accessible from S *}
schirmer@12854
  1441
schirmer@12854
  1442
text {* Note the class component in the accessibility filter. The class where
schirmer@12854
  1443
    method @{term m} is declared (@{term declC}) isn't necessarily accessible 
schirmer@12854
  1444
    from the current scope @{term S}. The method can be made accessible 
schirmer@12854
  1445
    through inheritance, too.
schirmer@12854
  1446
    So we must test accessibility of method @{term m} of class @{term C} 
schirmer@12854
  1447
    (not @{term "declclass m"}) *}
schirmer@12854
  1448
schirmer@12854
  1449
constdefs 
schirmer@12854
  1450
dynmethd:: "prog  \<Rightarrow> qtname \<Rightarrow> qtname \<Rightarrow> (sig,qtname \<times> methd) table"
schirmer@12854
  1451
"dynmethd G statC dynC  
schirmer@12854
  1452
  \<equiv> \<lambda> sig. 
schirmer@12854
  1453
     (if G\<turnstile>dynC \<preceq>\<^sub>C statC
schirmer@12854
  1454
        then (case methd G statC sig of
schirmer@12854
  1455
                None \<Rightarrow> None
schirmer@12854
  1456
              | Some statM 
schirmer@12854
  1457
                  \<Rightarrow> (class_rec (G,dynC) empty
schirmer@12854
  1458
                       (\<lambda>C c subcls_mthds. 
schirmer@12854
  1459
                          subcls_mthds
schirmer@12854
  1460
                          ++
schirmer@12854
  1461
                          (filter_tab 
schirmer@12854
  1462
                            (\<lambda> _ dynM. G,sig\<turnstile>dynM overrides statM \<or> dynM=statM)
schirmer@12854
  1463
                            (methd G C) ))
schirmer@12854
  1464
                      ) sig
schirmer@12854
  1465
              )
schirmer@12854
  1466
        else None)"
schirmer@13688
  1467
schirmer@12854
  1468
text {* @{term "dynmethd G statC dynC"}: dynamic method lookup of a reference 
schirmer@12854
  1469
        with dynamic class @{term dynC} and static class @{term statC} *}
schirmer@12854
  1470
text {* Note some kind of duality between @{term methd} and @{term dynmethd} 
schirmer@12854
  1471
        in the @{term class_rec} arguments. Whereas @{term methd} filters the 
schirmer@12854
  1472
        subclass methods (to get only the inherited ones), @{term dynmethd} 
schirmer@12854
  1473
        filters the new methods (to get only those methods which actually
schirmer@12854
  1474
        override the methods of the static class) *}
schirmer@12854
  1475
schirmer@12854
  1476
constdefs 
schirmer@12854
  1477
dynimethd:: "prog \<Rightarrow> qtname \<Rightarrow> qtname \<Rightarrow> (sig,qtname \<times> methd) table"
schirmer@12854
  1478
"dynimethd G I dynC 
schirmer@12854
  1479
  \<equiv> \<lambda> sig. if imethds G I sig \<noteq> {}
schirmer@12854
  1480
               then methd G dynC sig
schirmer@12854
  1481
               else dynmethd G Object dynC sig"
schirmer@12854
  1482
text {* @{term "dynimethd G I dynC"}: dynamic method lookup of a reference with 
schirmer@12854
  1483
        dynamic class dynC and static interface type I *}
schirmer@12854
  1484
text {* 
schirmer@12854
  1485
   When calling an interface method, we must distinguish if the method signature
schirmer@12854
  1486
   was defined in the interface or if it must be an Object method in the other
schirmer@12854
  1487
   case. If it was an interface method we search the class hierarchy
schirmer@12854
  1488
   starting at the dynamic class of the object up to Object to find the 
schirmer@12854
  1489
   first matching method (@{term methd}). Since all interface methods have 
schirmer@12854
  1490
   public access the method can't be coalesced due to some odd visibility 
schirmer@12854
  1491
   effects like in case of dynmethd. The method will be inherited or 
schirmer@12854
  1492
   overridden in all classes from the first class implementing the interface 
schirmer@12854
  1493
   down to the actual dynamic class.
schirmer@12854
  1494
 *}
schirmer@12854
  1495
schirmer@12854
  1496
constdefs
schirmer@12854
  1497
dynlookup::"prog  \<Rightarrow> ref_ty \<Rightarrow> qtname \<Rightarrow> (sig,qtname \<times> methd) table"
schirmer@12854
  1498
"dynlookup G statT dynC
schirmer@12854
  1499
  \<equiv> (case statT of
schirmer@12854
  1500
       NullT        \<Rightarrow> empty
schirmer@12854
  1501
     | IfaceT I     \<Rightarrow> dynimethd G I      dynC
schirmer@12854
  1502
     | ClassT statC \<Rightarrow> dynmethd  G statC  dynC
schirmer@12854
  1503
     | ArrayT ty    \<Rightarrow> dynmethd  G Object dynC)"
schirmer@12854
  1504
text {* @{term "dynlookup G statT dynC"}: dynamic lookup of a method within the 
schirmer@12854
  1505
    static reference type statT and the dynamic class dynC. 
schirmer@12854
  1506
    In a wellformd context statT will not be NullT and in case
schirmer@12854
  1507
    statT is an array type, dynC=Object *}
schirmer@12854
  1508
schirmer@12854
  1509
constdefs
schirmer@12854
  1510
fields:: "prog \<Rightarrow> qtname \<Rightarrow> ((vname \<times> qtname) \<times> field) list"
schirmer@12854
  1511
"fields G C 
schirmer@12854
  1512
  \<equiv> class_rec (G,C) [] (\<lambda>C c ts. map (\<lambda>(n,t). ((n,C),t)) (cfields c) @ ts)"
schirmer@12854
  1513
text {* @{term "fields G C"} 
schirmer@12854
  1514
     list of fields of a class, including all the fields of the superclasses
schirmer@12854
  1515
     (private, inherited and hidden ones) not only the accessible ones
schirmer@12854
  1516
     (an instance of a object allocates all these fields *}
schirmer@12854
  1517
schirmer@12854
  1518
constdefs
schirmer@12854
  1519
accfield:: "prog \<Rightarrow> qtname \<Rightarrow> qtname \<Rightarrow> (vname, qtname  \<times>  field) table"
schirmer@12854
  1520
"accfield G S C
schirmer@12854
  1521
  \<equiv> let field_tab = table_of((map (\<lambda>((n,d),f).(n,(d,f)))) (fields G C))
schirmer@12854
  1522
    in filter_tab (\<lambda>n (declC,f). G\<turnstile> (declC,fdecl (n,f)) of C accessible_from S)
schirmer@12854
  1523
                  field_tab"
schirmer@12854
  1524
text  {* @{term "accfield G C S"}: fields of a class @{term C} which are 
schirmer@12854
  1525
         accessible from scope of class
schirmer@12854
  1526
         @{term S} with inheritance and hiding, cf. 8.3 *}
schirmer@12854
  1527
text {* note the class component in the accessibility filter (see also 
schirmer@12854
  1528
        @{term methd}).
schirmer@12854
  1529
   The class declaring field @{term f} (@{term declC}) isn't necessarily 
schirmer@12854
  1530
   accessible from scope @{term S}. The field can be made visible through 
schirmer@12854
  1531
   inheritance, too. So we must test accessibility of field @{term f} of class 
schirmer@12854
  1532
   @{term C} (not @{term "declclass f"}) *} 
schirmer@12854
  1533
schirmer@12854
  1534
constdefs
schirmer@12854
  1535
schirmer@12854
  1536
  is_methd :: "prog \<Rightarrow> qtname  \<Rightarrow> sig \<Rightarrow> bool"
schirmer@12854
  1537
 "is_methd G \<equiv> \<lambda>C sig. is_class G C \<and> methd G C sig \<noteq> None"
schirmer@12854
  1538
schirmer@12854
  1539
constdefs efname:: "((vname \<times> qtname) \<times> field) \<Rightarrow> (vname \<times> qtname)"
schirmer@12854
  1540
"efname \<equiv> fst"
schirmer@12854
  1541
schirmer@12854
  1542
lemma efname_simp[simp]:"efname (n,f) = n"
schirmer@12854
  1543
by (simp add: efname_def) 
schirmer@12854
  1544
schirmer@12854
  1545
schirmer@12854
  1546
subsection "imethds"
schirmer@12854
  1547
schirmer@12854
  1548
lemma imethds_rec: "\<lbrakk>iface G I = Some i; ws_prog G\<rbrakk> \<Longrightarrow>  
schirmer@12854
  1549
  imethds G I = Un_tables ((\<lambda>J. imethds  G J)`set (isuperIfs i)) \<oplus>\<oplus>  
nipkow@30235
  1550
                      (Option.set \<circ> table_of (map (\<lambda>(s,mh). (s,I,mh)) (imethods i)))"
schirmer@12854
  1551
apply (unfold imethds_def)
schirmer@12854
  1552
apply (rule iface_rec [THEN trans])
schirmer@12854
  1553
apply auto
schirmer@12854
  1554
done
schirmer@12854
  1555
schirmer@12854
  1556
schirmer@12854
  1557
(* local lemma *)
schirmer@12854
  1558
lemma imethds_norec:
schirmer@12854
  1559
  "\<lbrakk>iface G md = Some i; ws_prog G; table_of (imethods i) sig = Some mh\<rbrakk> \<Longrightarrow>  
schirmer@12854
  1560
  (md, mh) \<in> imethds G md sig"
schirmer@12854
  1561
apply (subst imethds_rec)
schirmer@12854
  1562
apply assumption+
schirmer@12854
  1563
apply (rule iffD2)
schirmer@12854
  1564
apply (rule overrides_t_Some_iff)
schirmer@12854
  1565
apply (rule disjI1)
schirmer@12854
  1566
apply (auto elim: table_of_map_SomeI)
schirmer@12854
  1567
done
schirmer@12854
  1568
schirmer@12854
  1569
lemma imethds_declI: "\<lbrakk>m \<in> imethds G I sig; ws_prog G; is_iface G I\<rbrakk> \<Longrightarrow> 
schirmer@12854
  1570
  (\<exists>i. iface G (decliface m) = Some i \<and> 
schirmer@12854
  1571
  table_of (imethods i) sig = Some (mthd m)) \<and>  
schirmer@12854
  1572
  (I,decliface m) \<in> (subint1 G)^* \<and> m \<in> imethds G (decliface m) sig"
wenzelm@24038
  1573
apply (erule rev_mp)
schirmer@12854
  1574
apply (rule ws_subint1_induct, assumption, assumption)
schirmer@12854
  1575
apply (subst imethds_rec, erule conjunct1, assumption)
schirmer@12854
  1576
apply (force elim: imethds_norec intro: rtrancl_into_rtrancl2)
schirmer@12854
  1577
done
schirmer@12854
  1578
schirmer@12854
  1579
lemma imethds_cases [consumes 3, case_names NewMethod InheritedMethod]:
wenzelm@12937
  1580
  assumes im: "im \<in> imethds G I sig" and  
schirmer@12854
  1581
         ifI: "iface G I = Some i" and
schirmer@12854
  1582
          ws: "ws_prog G" and
schirmer@12854
  1583
     hyp_new:  "table_of (map (\<lambda>(s, mh). (s, I, mh)) (imethods i)) sig 
schirmer@12854
  1584
                = Some im \<Longrightarrow> P" and
schirmer@12854
  1585
     hyp_inh: "\<And> J. \<lbrakk>J \<in> set (isuperIfs i); im \<in> imethds G J sig\<rbrakk> \<Longrightarrow> P"
wenzelm@12937
  1586
  shows P
schirmer@12854
  1587
proof -
schirmer@12854
  1588
  from ifI ws im hyp_new hyp_inh
schirmer@12854
  1589
  show "P"
schirmer@12854
  1590
    by (auto simp add: imethds_rec)
schirmer@12854
  1591
qed
schirmer@12854
  1592
schirmer@12854
  1593
subsection "accimethd"
schirmer@12854
  1594
schirmer@12854
  1595
lemma accimethds_simp [simp]: 
schirmer@12854
  1596
"G\<turnstile>Iface I accessible_in pack \<Longrightarrow> accimethds G pack I = imethds G I"
schirmer@12854
  1597
by (simp add: accimethds_def)
schirmer@12854
  1598
schirmer@12854
  1599
lemma accimethdsD:
schirmer@12854
  1600
 "im \<in> accimethds G pack I sig 
schirmer@12854
  1601
  \<Longrightarrow> im \<in> imethds G I sig \<and> G\<turnstile>Iface I accessible_in pack"
schirmer@12854
  1602
by (auto simp add: accimethds_def)
schirmer@12854
  1603
schirmer@12854
  1604
lemma accimethdsI: 
schirmer@12854
  1605
"\<lbrakk>im \<in> imethds G I sig;G\<turnstile>Iface I accessible_in pack\<rbrakk>
schirmer@12854
  1606
 \<Longrightarrow> im \<in> accimethds G pack I sig"
schirmer@12854
  1607
by simp
schirmer@12854
  1608
schirmer@12854
  1609
subsection "methd"
schirmer@12854
  1610
schirmer@12854
  1611
lemma methd_rec: "\<lbrakk>class G C = Some c; ws_prog G\<rbrakk> \<Longrightarrow>  
schirmer@12854
  1612
  methd G C 
schirmer@12854
  1613
    = (if C = Object 
schirmer@12854
  1614
          then empty 
schirmer@12854
  1615
          else filter_tab (\<lambda>sig m. G\<turnstile>C inherits method sig m)
schirmer@12854
  1616
                          (methd G (super c))) 
schirmer@12854
  1617
      ++ table_of (map (\<lambda>(s,m). (s,C,m)) (methods c))"
schirmer@12854
  1618
apply (unfold methd_def)
schirmer@12854
  1619
apply (erule class_rec [THEN trans], assumption)
schirmer@12854
  1620
apply (simp)
schirmer@12854
  1621
done
schirmer@12854
  1622
schirmer@12854
  1623
(* local lemma *)
schirmer@12854
  1624
lemma methd_norec: 
schirmer@12854
  1625
 "\<lbrakk>class G declC = Some c; ws_prog G;table_of (methods c) sig = Some m\<rbrakk> 
schirmer@12854
  1626
  \<Longrightarrow> methd G declC sig = Some (declC, m)"
schirmer@12854
  1627
apply (simp only: methd_rec)
nipkow@14025
  1628
apply (rule disjI1 [THEN map_add_Some_iff [THEN iffD2]])
schirmer@12854
  1629
apply (auto elim: table_of_map_SomeI)
schirmer@12854
  1630
done
schirmer@12854
  1631
schirmer@12854
  1632
schirmer@12854
  1633
lemma methd_declC: 
schirmer@12854
  1634
"\<lbrakk>methd G C sig = Some m; ws_prog G;is_class G C\<rbrakk> \<Longrightarrow>
schirmer@12854
  1635
 (\<exists>d. class G (declclass m)=Some d \<and> table_of (methods d) sig=Some (mthd m)) \<and> 
schirmer@12854
  1636
 G\<turnstile>C \<preceq>\<^sub>C (declclass m) \<and> methd G (declclass m) sig = Some m"   
wenzelm@24038
  1637
apply (erule rev_mp)
schirmer@12854
  1638
apply (rule ws_subcls1_induct, assumption, assumption)
schirmer@12854
  1639
apply (subst methd_rec, assumption)
schirmer@12854
  1640
apply (case_tac "Ca=Object")
schirmer@12854
  1641
apply   (force elim: methd_norec )
schirmer@12854
  1642
schirmer@12854
  1643
apply   simp
schirmer@12854
  1644
apply   (case_tac "table_of (map (\<lambda>(s, m). (s, Ca, m)) (methods c)) sig")
schirmer@12854
  1645
apply     (force intro: rtrancl_into_rtrancl2)
schirmer@12854
  1646
schirmer@12854
  1647
apply     (auto intro: methd_norec)
schirmer@12854
  1648
done
schirmer@12854
  1649
schirmer@12854
  1650
lemma methd_inheritedD:
schirmer@12854
  1651
  "\<lbrakk>class G C = Some c; ws_prog G;methd G C sig = Some m\<rbrakk>
schirmer@12854
  1652
  \<Longrightarrow>  (declclass m \<noteq> C \<longrightarrow> G \<turnstile>C inherits method sig m)"
schirmer@12854
  1653
by (auto simp add: methd_rec)
schirmer@12854
  1654
schirmer@12854
  1655
lemma methd_diff_cls:
schirmer@12854
  1656
"\<lbrakk>ws_prog G; is_class G C; is_class G D;
schirmer@12854
  1657
 methd G C sig = m; methd G D sig = n; m\<noteq>n
schirmer@12854
  1658
\<rbrakk> \<Longrightarrow> C\<noteq>D"
schirmer@12854
  1659
by (auto simp add: methd_rec)
schirmer@12854
  1660
schirmer@12854
  1661
lemma method_declared_inI: 
schirmer@12854
  1662
 "\<lbrakk>table_of (methods c) sig = Some m; class G C = Some c\<rbrakk>
schirmer@12854
  1663
  \<Longrightarrow> G\<turnstile>mdecl (sig,m) declared_in C"
schirmer@12854
  1664
by (auto simp add: cdeclaredmethd_def declared_in_def)
schirmer@12854
  1665
schirmer@12854
  1666
lemma methd_declared_in_declclass: 
schirmer@12854
  1667
 "\<lbrakk>methd G C sig = Some m; ws_prog G;is_class G C\<rbrakk> 
schirmer@12854
  1668
 \<Longrightarrow> G\<turnstile>Methd sig m declared_in (declclass m)"
schirmer@12854
  1669
by (auto dest: methd_declC method_declared_inI)
schirmer@12854
  1670
schirmer@12854
  1671
lemma member_methd:
wenzelm@12937
  1672
  assumes member_of: "G\<turnstile>Methd sig m member_of C" and
schirmer@12854
  1673
                 ws: "ws_prog G"
wenzelm@12937
  1674
  shows "methd G C sig = Some m"
schirmer@12854
  1675
proof -
schirmer@12854
  1676
  from member_of 
schirmer@12854
  1677
  have iscls_C: "is_class G C" 
schirmer@12854
  1678
    by (rule member_of_is_classD)
schirmer@12854
  1679
  from iscls_C ws member_of
schirmer@12854
  1680
  show ?thesis (is "?Methd C")
schirmer@12854
  1681
  proof (induct rule: ws_class_induct')
schirmer@12854
  1682
    case (Object co)
schirmer@12854
  1683
    assume "G \<turnstile>Methd sig m member_of Object"
schirmer@12854
  1684
    then have "G\<turnstile>Methd sig m declared_in Object \<and> declclass m = Object"
schirmer@12854
  1685
      by (cases set: members) (cases m, auto dest: subcls1D)
schirmer@12854
  1686
    with ws Object 
schirmer@12854
  1687
    show "?Methd Object"
schirmer@12854
  1688
      by (cases m)
schirmer@12854
  1689
         (auto simp add: declared_in_def cdeclaredmethd_def methd_rec
schirmer@12854
  1690
                  intro:  table_of_mapconst_SomeI)
schirmer@12854
  1691
  next
schirmer@12854
  1692
    case (Subcls C c)
schirmer@12854
  1693
    assume clsC: "class G C = Some c" and
schirmer@12854
  1694
      neq_C_Obj: "C \<noteq> Object" and
schirmer@12854
  1695
            hyp: "G \<turnstile>Methd sig m member_of super c \<Longrightarrow> ?Methd (super c)" and
schirmer@12854
  1696
      member_of: "G \<turnstile>Methd sig m member_of C"
schirmer@12854
  1697
    from member_of
schirmer@12854
  1698
    show "?Methd C"
schirmer@12854
  1699
    proof (cases)
berghofe@34990
  1700
      case Immediate
schirmer@12854
  1701
      with clsC 
schirmer@12854
  1702
      have "table_of (map (\<lambda>(s, m). (s, C, m)) (methods c)) sig = Some m"
wenzelm@32960
  1703
        by (cases m)
wenzelm@32960
  1704
           (auto simp add: declared_in_def cdeclaredmethd_def
wenzelm@32960
  1705
                    intro: table_of_mapconst_SomeI)
schirmer@12854
  1706
      with clsC neq_C_Obj ws 
schirmer@12854
  1707
      show ?thesis
wenzelm@32960
  1708
        by (simp add: methd_rec)
schirmer@12854
  1709
    next
berghofe@34990
  1710
      case (Inherited S)
schirmer@12854
  1711
      with clsC
berghofe@34990
  1712
      have  undecl: "G\<turnstile>mid sig undeclared_in C" and
schirmer@12854
  1713
             super: "G \<turnstile>Methd sig m member_of (super c)"
wenzelm@32960
  1714
        by (auto dest: subcls1D)
berghofe@34990
  1715
      from clsC undecl 
schirmer@12854
  1716
      have "table_of (map (\<lambda>(s, m). (s, C, m)) (methods c)) sig = None"
wenzelm@32960
  1717
        by (auto simp add: undeclared_in_def cdeclaredmethd_def
wenzelm@32960
  1718
                    intro: table_of_mapconst_NoneI)
schirmer@12854
  1719
      moreover
schirmer@12854
  1720
      from Inherited have "G \<turnstile> C inherits (method sig m)"
wenzelm@32960
  1721
        by (auto simp add: inherits_def)
schirmer@12854
  1722
      moreover
schirmer@12854
  1723
      note clsC neq_C_Obj ws super hyp 
schirmer@12854
  1724
      ultimately
schirmer@12854
  1725
      show ?thesis
wenzelm@32960
  1726
        by (auto simp add: methd_rec intro: filter_tab_SomeI)
schirmer@12854
  1727
    qed
schirmer@12854
  1728
  qed
schirmer@12854
  1729
qed
schirmer@12854
  1730
schirmer@12854
  1731
(*unused*)
schirmer@12854
  1732
lemma finite_methd:"ws_prog G \<Longrightarrow> finite {methd G C sig |sig C. is_class G C}"
schirmer@12854
  1733
apply (rule finite_is_class [THEN finite_SetCompr2])
schirmer@12854
  1734
apply (intro strip)
schirmer@12854
  1735
apply (erule_tac ws_subcls1_induct, assumption)
schirmer@12854
  1736
apply (subst methd_rec)
schirmer@12854
  1737
apply (assumption)
nipkow@14025
  1738
apply (auto intro!: finite_range_map_of finite_range_filter_tab finite_range_map_of_map_add)
schirmer@12854
  1739
done
schirmer@12854
  1740
schirmer@12854
  1741
lemma finite_dom_methd:
schirmer@12854
  1742
 "\<lbrakk>ws_prog G; is_class G C\<rbrakk> \<Longrightarrow> finite (dom (methd G C))"
schirmer@12854
  1743
apply (erule_tac ws_subcls1_induct)
schirmer@12854
  1744
apply assumption
schirmer@12854
  1745
apply (subst methd_rec)
schirmer@12854
  1746
apply (assumption)
schirmer@12854
  1747
apply (auto intro!: finite_dom_map_of finite_dom_filter_tab)
schirmer@12854
  1748
done
schirmer@12854
  1749
schirmer@12854
  1750
schirmer@12854
  1751
subsection "accmethd"
schirmer@12854
  1752
schirmer@12854
  1753
lemma accmethd_SomeD:
schirmer@12854
  1754
"accmethd G S C sig = Some m
schirmer@12854
  1755
 \<Longrightarrow> methd G C sig = Some m \<and> G\<turnstile>method sig m of C accessible_from S"
schirmer@12854
  1756
by (auto simp add: accmethd_def dest: filter_tab_SomeD)
schirmer@12854
  1757
schirmer@12854
  1758
lemma accmethd_SomeI:
schirmer@12854
  1759
"\<lbrakk>methd G C sig = Some m; G\<turnstile>method sig m of C accessible_from S\<rbrakk> 
schirmer@12854
  1760
 \<Longrightarrow> accmethd G S C sig = Some m"
schirmer@12854
  1761
by (auto simp add: accmethd_def intro: filter_tab_SomeI)
schirmer@12854
  1762
schirmer@12854
  1763
lemma accmethd_declC: 
schirmer@12854
  1764
"\<lbrakk>accmethd G S C sig = Some m; ws_prog G; is_class G C\<rbrakk> \<Longrightarrow>
schirmer@12854
  1765
 (\<exists>d. class G (declclass m)=Some d \<and> 
schirmer@12854
  1766
  table_of (methods d) sig=Some (mthd m)) \<and> 
schirmer@12854
  1767
 G\<turnstile>C \<preceq>\<^sub>C (declclass m) \<and> methd G (declclass m) sig = Some m \<and> 
schirmer@12854
  1768
 G\<turnstile>method sig m of C accessible_from S"
schirmer@12854
  1769
by (auto dest: accmethd_SomeD methd_declC accmethd_SomeI)
schirmer@12854
  1770
schirmer@12854
  1771
schirmer@12854
  1772
lemma finite_dom_accmethd:
schirmer@12854
  1773
 "\<lbrakk>ws_prog G; is_class G C\<rbrakk> \<Longrightarrow> finite (dom (accmethd G S C))"
schirmer@12854
  1774
by (auto simp add: accmethd_def intro: finite_dom_filter_tab finite_dom_methd)
schirmer@12854
  1775
schirmer@12854
  1776
schirmer@12854
  1777
subsection "dynmethd"
schirmer@12854
  1778
schirmer@12854
  1779
lemma dynmethd_rec:
schirmer@12854
  1780
"\<lbrakk>class G dynC = Some c; ws_prog G\<rbrakk> \<Longrightarrow>  
schirmer@12854
  1781
 dynmethd G statC dynC sig
schirmer@12854
  1782
   = (if G\<turnstile>dynC \<preceq>\<^sub>C statC
schirmer@12854
  1783
        then (case methd G statC sig of
schirmer@12854
  1784
                None \<Rightarrow> None
schirmer@12854
  1785
              | Some statM 
schirmer@12854
  1786
                  \<Rightarrow> (case methd G dynC sig of
schirmer@12854
  1787
                        None \<Rightarrow> dynmethd G statC (super c) sig
schirmer@12854
  1788
                      | Some dynM \<Rightarrow> 
schirmer@12854
  1789
                          (if G,sig\<turnstile> dynM overrides statM \<or> dynM = statM 
schirmer@12854
  1790
                              then Some dynM
schirmer@12854
  1791
                              else (dynmethd G statC (super c) sig)
schirmer@12854
  1792
                      )))
schirmer@12854
  1793
         else None)" 
schirmer@12854
  1794
   (is "_ \<Longrightarrow> _ \<Longrightarrow> ?Dynmethd_def dynC sig  = ?Dynmethd_rec dynC c sig") 
schirmer@12854
  1795
proof -
schirmer@12854
  1796
  assume clsDynC: "class G dynC = Some c" and 
schirmer@12854
  1797
              ws: "ws_prog G"
schirmer@12854
  1798
  then show "?Dynmethd_def dynC sig  = ?Dynmethd_rec dynC c sig" 
schirmer@12854
  1799
  proof (induct rule: ws_class_induct'')
schirmer@12854
  1800
    case (Object co)
schirmer@12854
  1801
    show "?Dynmethd_def Object sig = ?Dynmethd_rec Object co sig"
schirmer@12854
  1802
    proof (cases "G\<turnstile>Object \<preceq>\<^sub>C statC") 
schirmer@12854
  1803
      case False
schirmer@12854
  1804
      then show ?thesis by (simp add: dynmethd_def)
schirmer@12854
  1805
    next
schirmer@12854
  1806
      case True
schirmer@12854
  1807
      then have eq_statC_Obj: "statC = Object" ..
schirmer@12854
  1808
      show ?thesis 
schirmer@12854
  1809
      proof (cases "methd G statC sig")
wenzelm@32960
  1810
        case None then show ?thesis by (simp add: dynmethd_def)
schirmer@12854
  1811
      next
wenzelm@32960
  1812
        case Some
wenzelm@32960
  1813
        with True Object ws eq_statC_Obj 
wenzelm@32960
  1814
        show ?thesis
wenzelm@32960
  1815
          by (auto simp add: dynmethd_def class_rec
schirmer@12854
  1816
                      intro: filter_tab_SomeI)
schirmer@12854
  1817
      qed
schirmer@12854
  1818
    qed
schirmer@12854
  1819
  next  
schirmer@12854
  1820
    case (Subcls dynC c sc)
schirmer@12854
  1821
    show "?Dynmethd_def dynC sig = ?Dynmethd_rec dynC c sig"
schirmer@12854
  1822
    proof (cases "G\<turnstile>dynC \<preceq>\<^sub>C statC") 
schirmer@12854
  1823
      case False
schirmer@12854
  1824
      then show ?thesis by (simp add: dynmethd_def)
schirmer@12854
  1825
    next
schirmer@12854
  1826
      case True
schirmer@12854
  1827
      note subclseq_dynC_statC = True
schirmer@12854
  1828
      show ?thesis
schirmer@12854
  1829
      proof (cases "methd G statC sig")
wenzelm@32960
  1830
        case None then show ?thesis by (simp add: dynmethd_def)
schirmer@12854
  1831
      next
wenzelm@32960
  1832
        case (Some statM)
wenzelm@32960
  1833
        note statM = Some
wenzelm@32960
  1834
        let "?filter C" = 
schirmer@12854
  1835
              "filter_tab
schirmer@12854
  1836
                (\<lambda>_ dynM. G,sig \<turnstile> dynM overrides statM \<or> dynM = statM)
schirmer@12854
  1837
                (methd G C)"
schirmer@12854
  1838
        let "?class_rec C" =
schirmer@12854
  1839
              "(class_rec (G, C) empty
schirmer@12854
  1840
                           (\<lambda>C c subcls_mthds. subcls_mthds ++ (?filter C)))"
wenzelm@32960
  1841
        from statM Subcls ws subclseq_dynC_statC
wenzelm@32960
  1842
        have dynmethd_dynC_def:
schirmer@12854
  1843
             "?Dynmethd_def dynC sig =
schirmer@12854
  1844
                ((?class_rec (super c)) 
schirmer@12854
  1845
                 ++
schirmer@12854
  1846
                (?filter dynC)) sig"
schirmer@12854
  1847
         by (simp (no_asm_simp) only: dynmethd_def class_rec)
wenzelm@32960
  1848
            auto
schirmer@12854
  1849
       show ?thesis
schirmer@12854
  1850
       proof (cases "dynC = statC")
wenzelm@32960
  1851
         case True
wenzelm@32960
  1852
         with subclseq_dynC_statC statM dynmethd_dynC_def
wenzelm@32960
  1853
         have "?Dynmethd_def dynC sig = Some statM"
wenzelm@32960
  1854
           by (auto intro: map_add_find_right filter_tab_SomeI)
wenzelm@32960
  1855
         with subclseq_dynC_statC True Some 
wenzelm@32960
  1856
         show ?thesis
wenzelm@32960
  1857
           by auto
schirmer@12854
  1858
       next
wenzelm@32960
  1859
         case False
wenzelm@32960
  1860
         with subclseq_dynC_statC Subcls 
wenzelm@32960
  1861
         have subclseq_super_statC: "G\<turnstile>(super c) \<preceq>\<^sub>C statC"
wenzelm@32960
  1862
           by (blast dest: subclseq_superD)
wenzelm@32960
  1863
         show ?thesis
wenzelm@32960
  1864
         proof (cases "methd G dynC sig") 
wenzelm@32960
  1865
           case None
wenzelm@32960
  1866
           then have "?filter dynC sig = None"
wenzelm@32960
  1867
             by (rule filter_tab_None)
schirmer@12854
  1868
           then have "?Dynmethd_def dynC sig=?class_rec (super c) sig"
wenzelm@32960
  1869
             by (simp add: dynmethd_dynC_def)
wenzelm@32960
  1870
           with  subclseq_super_statC statM None
wenzelm@32960
  1871
           have "?Dynmethd_def dynC sig = ?Dynmethd_def (super c) sig"
wenzelm@32960
  1872
             by (auto simp add: empty_def dynmethd_def)
schirmer@12854
  1873
           with None subclseq_dynC_statC statM
wenzelm@32960
  1874
           show ?thesis 
wenzelm@32960
  1875
             by simp
wenzelm@32960
  1876
         next
wenzelm@32960
  1877
           case (Some dynM)
wenzelm@32960
  1878
           note dynM = Some
wenzelm@32960
  1879
           let ?Termination = "G \<turnstile> qmdecl sig dynM overrides qmdecl sig statM \<or>
schirmer@12854
  1880
                               dynM = statM"
wenzelm@32960
  1881
           show ?thesis
wenzelm@32960
  1882
           proof (cases "?filter dynC sig")
wenzelm@32960
  1883
             case None
wenzelm@32960
  1884
             with dynM 
wenzelm@32960
  1885
             have no_termination: "\<not> ?Termination"
wenzelm@32960
  1886
               by (simp add: filter_tab_def)
wenzelm@32960
  1887
             from None 
wenzelm@32960
  1888
             have "?Dynmethd_def dynC sig=?class_rec (super c) sig"
wenzelm@32960
  1889
               by (simp add: dynmethd_dynC_def)
wenzelm@32960
  1890
             with subclseq_super_statC statM dynM no_termination
wenzelm@32960
  1891
             show ?thesis
wenzelm@32960
  1892
               by (auto simp add: empty_def dynmethd_def)
wenzelm@32960
  1893
           next
wenzelm@32960
  1894
             case Some
wenzelm@32960
  1895
             with dynM
wenzelm@32960
  1896
             have "termination": "?Termination"
wenzelm@32960
  1897
               by (auto)
wenzelm@32960
  1898
             with Some dynM
wenzelm@32960
  1899
             have "?Dynmethd_def dynC sig=Some dynM"
wenzelm@32960
  1900
              by (auto simp add: dynmethd_dynC_def)
wenzelm@32960
  1901
             with subclseq_super_statC statM dynM "termination"
wenzelm@32960
  1902
             show ?thesis
wenzelm@32960
  1903
               by (auto simp add: dynmethd_def)
wenzelm@32960
  1904
           qed
wenzelm@32960
  1905
         qed
schirmer@12854
  1906
       qed
schirmer@12854
  1907
     qed
schirmer@12854
  1908
   qed
schirmer@12854
  1909
 qed
schirmer@12854
  1910
qed
wenzelm@32960
  1911
               
schirmer@12854
  1912
lemma dynmethd_C_C:"\<lbrakk>is_class G C; ws_prog G\<rbrakk> 
schirmer@12854
  1913
\<Longrightarrow> dynmethd G C C sig = methd G C sig"          
schirmer@12854
  1914
apply (auto simp add: dynmethd_rec)
schirmer@12854
  1915
done
schirmer@12854
  1916
 
schirmer@12854
  1917
lemma dynmethdSomeD: 
schirmer@12854
  1918
 "\<lbrakk>dynmethd G statC dynC sig = Some dynM; is_class G dynC; ws_prog G\<rbrakk> 
schirmer@12854
  1919
  \<Longrightarrow> G\<turnstile>dynC \<preceq>\<^sub>C statC \<and> (\<exists> statM. methd G statC sig = Some statM)"
schirmer@12854
  1920
by (auto simp add: dynmethd_rec)
schirmer@12854
  1921
 
schirmer@12854
  1922
lemma dynmethd_Some_cases [consumes 3, case_names Static Overrides]:
wenzelm@12937
  1923
  assumes      dynM: "dynmethd G statC dynC sig = Some dynM" and
schirmer@12854
  1924
        is_cls_dynC: "is_class G dynC" and
schirmer@12854
  1925
                 ws: "ws_prog G" and
schirmer@12854
  1926
         hyp_static: "methd G statC sig = Some dynM \<Longrightarrow> P" and
schirmer@12854
  1927
       hyp_override: "\<And> statM. \<lbrakk>methd G statC sig = Some statM;dynM\<noteq>statM;
schirmer@12854
  1928
                       G,sig\<turnstile>dynM overrides statM\<rbrakk> \<Longrightarrow> P"
wenzelm@12937
  1929
  shows P
schirmer@12854
  1930
proof -
schirmer@12854
  1931
  from is_cls_dynC obtain dc where clsDynC: "class G dynC = Some dc" by blast
schirmer@12854
  1932
  from clsDynC ws dynM hyp_static hyp_override
schirmer@12854
  1933
  show "P"
schirmer@12854
  1934
  proof (induct rule: ws_class_induct)
schirmer@12854
  1935
    case (Object co)
schirmer@12854
  1936
    with ws  have "statC = Object" 
schirmer@12854
  1937
      by (auto simp add: dynmethd_rec)
schirmer@12854
  1938
    with ws Object show ?thesis by (auto simp add: dynmethd_C_C)
schirmer@12854
  1939
  next
schirmer@12854
  1940
    case (Subcls C c)
schirmer@12854
  1941
    with ws show ?thesis
schirmer@12854
  1942
      by (auto simp add: dynmethd_rec)
schirmer@12854
  1943
  qed
schirmer@12854
  1944
qed
schirmer@12854
  1945
schirmer@12854
  1946
lemma no_override_in_Object:
wenzelm@12937
  1947
  assumes          dynM: "dynmethd G statC dynC sig = Some dynM" and
schirmer@12854
  1948
            is_cls_dynC: "is_class G dynC" and
schirmer@12854
  1949
                     ws: "ws_prog G" and
schirmer@12854
  1950
                  statM: "methd G statC sig = Some statM" and
schirmer@12854
  1951
         neq_dynM_statM: "dynM\<noteq>statM"
wenzelm@12937
  1952
  shows "dynC \<noteq> Object"
schirmer@12854
  1953
proof -
schirmer@12854
  1954
  from is_cls_dynC obtain dc where clsDynC: "class G dynC = Some dc" by blast
schirmer@12854
  1955
  from clsDynC ws dynM statM neq_dynM_statM 
schirmer@12854
  1956
  show ?thesis (is "?P dynC")
schirmer@12854
  1957
  proof (induct rule: ws_class_induct)
schirmer@12854
  1958
    case (Object co)
schirmer@12854
  1959
    with ws  have "statC = Object" 
schirmer@12854
  1960
      by (auto simp add: dynmethd_rec)
schirmer@12854
  1961
    with ws Object show "?P Object" by (auto simp add: dynmethd_C_C)
schirmer@12854
  1962
  next
schirmer@12854
  1963
    case (Subcls dynC c)
schirmer@12854
  1964
    with ws show "?P dynC"
schirmer@12854
  1965
      by (auto simp add: dynmethd_rec)
schirmer@12854
  1966
  qed
schirmer@12854
  1967
qed
schirmer@12854
  1968
schirmer@12854
  1969
schirmer@12854
  1970
lemma dynmethd_Some_rec_cases [consumes 3, 
schirmer@12854
  1971
                               case_names Static Override  Recursion]:
wenzelm@12937
  1972
  assumes          dynM: "dynmethd G statC dynC sig = Some dynM" and
schirmer@12854
  1973
                clsDynC: "class G dynC = Some c" and
schirmer@12854
  1974
                     ws: "ws_prog G" and
schirmer@12854
  1975
             hyp_static: "methd G statC sig = Some dynM \<Longrightarrow> P" and
schirmer@12854
  1976
           hyp_override: "\<And> statM. \<lbrakk>methd G statC sig = Some statM;
schirmer@12854
  1977
                                     methd G dynC sig = Some dynM; statM\<noteq>dynM;
schirmer@12854
  1978
                                     G,sig\<turnstile> dynM overrides statM\<rbrakk> \<Longrightarrow> P" and
schirmer@12854
  1979
schirmer@12854
  1980
          hyp_recursion: "\<lbrakk>dynC\<noteq>Object;
wenzelm@12937
  1981
                           dynmethd G statC (super c) sig = Some dynM\<rbrakk> \<Longrightarrow> P"
wenzelm@12937
  1982
  shows P
schirmer@12854
  1983
proof -
schirmer@12854
  1984
  from clsDynC have "is_class G dynC" by simp
schirmer@12854
  1985
  note no_override_in_Object' = no_override_in_Object [OF dynM this ws]
schirmer@12854
  1986
  from ws clsDynC dynM hyp_static hyp_override hyp_recursion
schirmer@12854
  1987
  show ?thesis
schirmer@12854
  1988
    by (auto simp add: dynmethd_rec dest: no_override_in_Object')
schirmer@12854
  1989
qed
schirmer@12854
  1990
schirmer@12854
  1991
lemma dynmethd_declC: 
schirmer@12854
  1992
"\<lbrakk>dynmethd G statC dynC sig = Some m;
schirmer@12854
  1993
  is_class G statC;ws_prog G
schirmer@12854
  1994
 \<rbrakk> \<Longrightarrow>
schirmer@12854
  1995
  (\<exists>d. class G (declclass m)=Some d \<and> table_of (methods d) sig=Some (mthd m)) \<and>
schirmer@12854
  1996
  G\<turnstile>dynC \<preceq>\<^sub>C (declclass m) \<and> methd G (declclass m) sig = Some m"
schirmer@12854
  1997
proof - 
schirmer@12854
  1998
  assume  is_cls_statC: "is_class G statC" 
schirmer@12854
  1999
  assume            ws: "ws_prog G"  
schirmer@12854
  2000
  assume             m: "dynmethd G statC dynC sig = Some m"
schirmer@12854
  2001
  from m 
schirmer@12854
  2002
  have "G\<turnstile>dynC \<preceq>\<^sub>C statC" by (auto simp add: dynmethd_def)
schirmer@12854
  2003
  from this is_cls_statC 
schirmer@12854
  2004
  have is_cls_dynC: "is_class G dynC" by (rule subcls_is_class2)
schirmer@12854
  2005
  from is_cls_dynC ws m  
schirmer@12854
  2006
  show ?thesis (is "?P dynC") 
schirmer@12854
  2007
  proof (induct rule: ws_class_induct')
schirmer@12854
  2008
    case (Object co)
schirmer@12854
  2009
    with ws have "statC=Object" by (auto simp add: dynmethd_rec)
schirmer@12854
  2010
    with ws Object  
schirmer@12854
  2011
    show "?P Object" 
schirmer@12854
  2012
      by (auto simp add: dynmethd_C_C dest: methd_declC)
schirmer@12854
  2013
  next
schirmer@12854
  2014
    case (Subcls dynC c)
schirmer@12854
  2015
    assume   hyp: "dynmethd G statC (super c) sig = Some m \<Longrightarrow> ?P (super c)" and
schirmer@12854
  2016
         clsDynC: "class G dynC = Some c"  and
schirmer@12854
  2017
              m': "dynmethd G statC dynC sig = Some m" and
schirmer@12854
  2018
    neq_dynC_Obj: "dynC \<noteq> Object"
schirmer@12854
  2019
    from ws this obtain statM where
schirmer@12854
  2020
      subclseq_dynC_statC: "G\<turnstile>dynC \<preceq>\<^sub>C statC" and 
schirmer@12854
  2021
                     statM: "methd G statC sig = Some statM"
schirmer@12854
  2022
      by (blast dest: dynmethdSomeD)
schirmer@12854
  2023
    from clsDynC neq_dynC_Obj 
schirmer@12854
  2024
    have subclseq_dynC_super: "G\<turnstile>dynC \<preceq>\<^sub>C (super c)" 
schirmer@12854
  2025
      by (auto intro: subcls1I) 
schirmer@12854
  2026
    from m' clsDynC ws 
schirmer@12854
  2027
    show "?P dynC"
schirmer@12854
  2028
    proof (cases rule: dynmethd_Some_rec_cases) 
schirmer@12854
  2029
      case Static
schirmer@12854
  2030
      with is_cls_statC ws subclseq_dynC_statC 
schirmer@12854
  2031
      show ?thesis 
wenzelm@32960
  2032
        by (auto intro: rtrancl_trans dest: methd_declC)
schirmer@12854
  2033
    next
schirmer@12854
  2034
      case Override
schirmer@12854
  2035
      with clsDynC ws 
schirmer@12854
  2036
      show ?thesis 
wenzelm@32960
  2037
        by (auto dest: methd_declC)
schirmer@12854
  2038
    next
schirmer@12854
  2039
      case Recursion
schirmer@12854
  2040
      with hyp subclseq_dynC_super 
schirmer@12854
  2041
      show ?thesis 
wenzelm@32960
  2042
        by (auto intro: rtrancl_trans) 
schirmer@12854
  2043
    qed
schirmer@12854
  2044
  qed
schirmer@12854
  2045
qed
schirmer@12854
  2046
schirmer@12854
  2047
lemma methd_Some_dynmethd_Some:
wenzelm@12937
  2048
  assumes     statM: "methd G statC sig = Some statM" and
schirmer@12854
  2049
           subclseq: "G\<turnstile>dynC \<preceq>\<^sub>C statC" and
schirmer@12854
  2050
       is_cls_statC: "is_class G statC" and
schirmer@12854
  2051
                 ws: "ws_prog G"
wenzelm@12937
  2052
  shows "\<exists> dynM. dynmethd G statC dynC sig = Some dynM"
wenzelm@12937
  2053
    (is "?P dynC")
schirmer@12854
  2054
proof -
schirmer@12854
  2055
  from subclseq is_cls_statC 
schirmer@12854
  2056
  have is_cls_dynC: "is_class G dynC" by (rule subcls_is_class2)
schirmer@12854
  2057
  then obtain dc where
schirmer@12854
  2058
    clsDynC: "class G dynC = Some dc" by blast
schirmer@12854
  2059
  from clsDynC ws subclseq 
schirmer@12854
  2060
  show "?thesis"
schirmer@12854
  2061
  proof (induct rule: ws_class_induct)
schirmer@12854
  2062
    case (Object co)
schirmer@12854
  2063
    with ws  have "statC = Object" 
schirmer@12854
  2064
      by (auto)
schirmer@12854
  2065
    with ws Object statM
schirmer@12854
  2066
    show "?P Object"  
schirmer@12854
  2067
      by (auto simp add: dynmethd_C_C)
schirmer@12854
  2068
  next
schirmer@12854
  2069
    case (Subcls dynC dc)
schirmer@12854
  2070
    assume clsDynC': "class G dynC = Some dc"
schirmer@12854
  2071
    assume neq_dynC_Obj: "dynC \<noteq> Object"
schirmer@12854
  2072
    assume hyp: "G\<turnstile>super dc\<preceq>\<^sub>C statC \<Longrightarrow> ?P (super dc)"
schirmer@12854
  2073
    assume subclseq': "G\<turnstile>dynC\<preceq>\<^sub>C statC"
schirmer@12854
  2074
    then
schirmer@12854
  2075
    show "?P dynC"
schirmer@12854
  2076
    proof (cases rule: subclseq_cases)
schirmer@12854
  2077
      case Eq
schirmer@12854
  2078
      with ws statM clsDynC' 
schirmer@12854
  2079
      show ?thesis
wenzelm@32960
  2080
        by (auto simp add: dynmethd_rec)
schirmer@12854
  2081
    next
schirmer@12854
  2082
      case Subcls
schirmer@12854
  2083
      assume "G\<turnstile>dynC\<prec>\<^sub>C statC"
schirmer@12854
  2084
      from this clsDynC' 
schirmer@12854
  2085
      have "G\<turnstile>super dc\<preceq>\<^sub>C statC" by (rule subcls_superD)
schirmer@12854
  2086
      with hyp ws clsDynC' subclseq' statM
schirmer@12854
  2087
      show ?thesis
wenzelm@32960
  2088
        by (auto simp add: dynmethd_rec)
schirmer@12854
  2089
    qed
schirmer@12854
  2090
  qed
schirmer@12854
  2091
qed
schirmer@12854
  2092
schirmer@12854
  2093
lemma dynmethd_cases [consumes 4, case_names Static Overrides]:
wenzelm@12937
  2094
  assumes     statM: "methd G statC sig = Some statM" and 
schirmer@12854
  2095
           subclseq: "G\<turnstile>dynC \<preceq>\<^sub>C statC" and
schirmer@12854
  2096
       is_cls_statC: "is_class G statC" and
schirmer@12854
  2097
                 ws: "ws_prog G" and
schirmer@12854
  2098
         hyp_static: "dynmethd G statC dynC sig = Some statM \<Longrightarrow> P" and
schirmer@12854
  2099
       hyp_override: "\<And> dynM. \<lbrakk>dynmethd G statC dynC sig = Some dynM;
schirmer@12854
  2100
                                 dynM\<noteq>statM;
schirmer@12854
  2101
                           G,sig\<turnstile>dynM overrides statM\<rbrakk> \<Longrightarrow> P"
wenzelm@12937
  2102
  shows P
schirmer@12854
  2103
proof -
schirmer@12854
  2104
  from subclseq is_cls_statC 
schirmer@12854
  2105
  have is_cls_dynC: "is_class G dynC" by (rule subcls_is_class2)
schirmer@12854
  2106
  then obtain dc where
schirmer@12854
  2107
    clsDynC: "class G dynC = Some dc" by blast
schirmer@12854
  2108
  from statM subclseq is_cls_statC ws 
schirmer@12854
  2109
  obtain dynM
schirmer@12854
  2110
    where dynM: "dynmethd G statC dynC sig = Some dynM"
schirmer@12854
  2111
    by (blast dest: methd_Some_dynmethd_Some)
schirmer@12854
  2112
  from dynM is_cls_dynC ws 
schirmer@12854
  2113
  show ?thesis
schirmer@12854
  2114
  proof (cases rule: dynmethd_Some_cases)
schirmer@12854
  2115
    case Static
schirmer@12854
  2116
    with hyp_static dynM statM show ?thesis by simp
schirmer@12854
  2117
  next
schirmer@12854
  2118
    case Overrides
schirmer@12854
  2119
    with hyp_override dynM statM show ?thesis by simp
schirmer@12854
  2120
  qed
schirmer@12854
  2121
qed
schirmer@12854
  2122
schirmer@12854
  2123
lemma ws_dynmethd:
wenzelm@12937
  2124
  assumes  statM: "methd G statC sig = Some statM" and
schirmer@12854
  2125
        subclseq: "G\<turnstile>dynC \<preceq>\<^sub>C statC" and
schirmer@12854
  2126
    is_cls_statC: "is_class G statC" and
schirmer@12854
  2127
              ws: "ws_prog G"
wenzelm@12937
  2128
  shows
wenzelm@12937
  2129
    "\<exists> dynM. dynmethd G statC dynC sig = Some dynM \<and>
wenzelm@12937
  2130
             is_static dynM = is_static statM \<and> G\<turnstile>resTy dynM\<preceq>resTy statM"
schirmer@12854
  2131
proof - 
schirmer@12854
  2132
  from statM subclseq is_cls_statC ws
schirmer@12854
  2133
  show ?thesis
schirmer@12854
  2134
  proof (cases rule: dynmethd_cases)
schirmer@12854
  2135
    case Static
schirmer@12854
  2136
    with statM 
schirmer@12854
  2137
    show ?thesis
schirmer@12854
  2138
      by simp
schirmer@12854
  2139
  next
schirmer@12854
  2140
    case Overrides
schirmer@12854
  2141
    with ws
schirmer@12854
  2142
    show ?thesis
schirmer@12854
  2143
      by (auto dest: ws_overrides_commonD)
schirmer@12854
  2144
  qed
schirmer@12854
  2145
qed
schirmer@12854
  2146
schirmer@12854
  2147
subsection "dynlookup"
schirmer@12854
  2148
schirmer@12854
  2149
lemma dynlookup_cases [consumes 1, case_names NullT IfaceT ClassT ArrayT]:
schirmer@12854
  2150
"\<lbrakk>dynlookup G statT dynC sig = x;
schirmer@12854
  2151
           \<lbrakk>statT = NullT       ; empty sig = x                  \<rbrakk> \<Longrightarrow> P;
schirmer@12854
  2152
  \<And> I.    \<lbrakk>statT = IfaceT I    ; dynimethd G I      dynC sig = x\<rbrakk> \<Longrightarrow> P;
schirmer@12854
  2153
  \<And> statC.\<lbrakk>statT = ClassT statC; dynmethd  G statC  dynC sig = x\<rbrakk> \<Longrightarrow> P;
schirmer@12854
  2154
  \<And> ty.   \<lbrakk>statT = ArrayT ty   ; dynmethd  G Object dynC sig = x\<rbrakk> \<Longrightarrow> P
schirmer@12854
  2155
 \<rbrakk> \<Longrightarrow> P"
schirmer@12854
  2156
by (cases statT) (auto simp add: dynlookup_def)
schirmer@12854
  2157
schirmer@12854
  2158
subsection "fields"
schirmer@12854
  2159
schirmer@12854
  2160
lemma fields_rec: "\<lbrakk>class G C = Some c; ws_prog G\<rbrakk> \<Longrightarrow>  
schirmer@12854
  2161
  fields G C = map (\<lambda>(fn,ft). ((fn,C),ft)) (cfields c) @  
schirmer@12854
  2162
  (if C = Object then [] else fields G (super c))"
schirmer@12854
  2163
apply (simp only: fields_def)
schirmer@12854
  2164
apply (erule class_rec [THEN trans])
schirmer@12854
  2165
apply assumption
schirmer@12854
  2166
apply clarsimp
schirmer@12854
  2167
done
schirmer@12854
  2168
schirmer@12854
  2169
(* local lemma *)
schirmer@12854
  2170
lemma fields_norec: 
schirmer@12854
  2171
"\<lbrakk>class G fd = Some c; ws_prog G;  table_of (cfields c) fn = Some f\<rbrakk> 
schirmer@12854
  2172
 \<Longrightarrow> table_of (fields G fd) (fn,fd) = Some f"
schirmer@12854
  2173
apply (subst fields_rec)
schirmer@12854
  2174
apply assumption+
nipkow@14025
  2175
apply (subst map_of_append)
nipkow@14025
  2176
apply (rule disjI1 [THEN map_add_Some_iff [THEN iffD2]])
schirmer@12854
  2177
apply (auto elim: table_of_map2_SomeI)
schirmer@12854
  2178
done
schirmer@12854
  2179
schirmer@12854
  2180
(* local lemma *)
schirmer@12854
  2181
lemma table_of_fieldsD:
schirmer@12854
  2182
"table_of (map (\<lambda>(fn,ft). ((fn,C),ft)) (cfields c)) efn = Some f
schirmer@12854
  2183
\<Longrightarrow> (declclassf efn) = C \<and> table_of (cfields c) (fname efn) = Some f"
schirmer@12854
  2184
apply (case_tac "efn")
schirmer@12854
  2185
by auto
schirmer@12854
  2186
schirmer@12854
  2187
lemma fields_declC: 
schirmer@12854
  2188
 "\<lbrakk>table_of (fields G C) efn = Some f; ws_prog G; is_class G C\<rbrakk> \<Longrightarrow>  
schirmer@12854
  2189
  (\<exists>d. class G (declclassf efn) = Some d \<and> 
schirmer@12854
  2190
                    table_of (cfields d) (fname efn)=Some f) \<and> 
schirmer@12854
  2191
  G\<turnstile>C \<preceq>\<^sub>C (declclassf efn)  \<and> table_of (fields G (declclassf efn)) efn = Some f"
wenzelm@24038
  2192
apply (erule rev_mp)
schirmer@12854
  2193
apply (rule ws_subcls1_induct, assumption, assumption)
schirmer@12854
  2194
apply (subst fields_rec, assumption)
schirmer@12854
  2195
apply clarify
nipkow@14025
  2196
apply (simp only: map_of_append)
schirmer@12854
  2197
apply (case_tac "table_of (map (split (\<lambda>fn. Pair (fn, Ca))) (cfields c)) efn") 
nipkow@14025
  2198
apply   (force intro:rtrancl_into_rtrancl2 simp add: map_add_def)
schirmer@12854
  2199
schirmer@12854
  2200
apply   (frule_tac fd="Ca" in fields_norec)
schirmer@12854
  2201
apply     assumption
schirmer@12854
  2202
apply     blast
schirmer@12854
  2203
apply   (frule table_of_fieldsD)  
schirmer@12854
  2204
apply   (frule_tac n="table_of (map (split (\<lambda>fn. Pair (fn, Ca))) (cfields c))"
schirmer@12854
  2205
              and  m="table_of (if Ca = Object then [] else fields G (super c))"
nipkow@14025
  2206
         in map_add_find_right)
schirmer@12854
  2207
apply   (case_tac "efn")
schirmer@12854
  2208
apply   (simp)
schirmer@12854
  2209
done
schirmer@12854
  2210
schirmer@12854
  2211
lemma fields_emptyI: "\<And>y. \<lbrakk>ws_prog G; class G C = Some c;cfields c = [];  
schirmer@12854
  2212
  C \<noteq> Object \<longrightarrow> class G (super c) = Some y \<and> fields G (super c) = []\<rbrakk> \<Longrightarrow>  
schirmer@12854
  2213
  fields G C = []"
schirmer@12854
  2214
apply (subst fields_rec)
schirmer@12854
  2215
apply assumption
schirmer@12854
  2216
apply auto
schirmer@12854
  2217
done
schirmer@12854
  2218
schirmer@12854
  2219
(* easier than with table_of *)
schirmer@12854
  2220
lemma fields_mono_lemma: 
schirmer@12854
  2221
"\<lbrakk>x \<in> set (fields G C); G\<turnstile>D \<preceq>\<^sub>C C; ws_prog G\<rbrakk> 
schirmer@12854
  2222
 \<Longrightarrow> x \<in> set (fields G D)"
wenzelm@24038
  2223
apply (erule rev_mp)
schirmer@12854
  2224
apply (erule converse_rtrancl_induct)
schirmer@12854
  2225
apply  fast
schirmer@12854
  2226
apply (drule subcls1D)
schirmer@12854
  2227
apply clarsimp
schirmer@12854
  2228
apply (subst fields_rec)
schirmer@12854
  2229
apply   auto
schirmer@12854
  2230
done
schirmer@12854
  2231
schirmer@12854
  2232
schirmer@12854
  2233
lemma ws_unique_fields_lemma: 
schirmer@12854
  2234
 "\<lbrakk>(efn,fd)  \<in> set (fields G (super c)); fc \<in> set (cfields c); ws_prog G;  
schirmer@12854
  2235
   fname efn = fname fc; declclassf efn = C;
schirmer@12854
  2236
   class G C = Some c; C \<noteq> Object; class G (super c) = Some d\<rbrakk> \<Longrightarrow> R"
schirmer@12854
  2237
apply (frule_tac ws_prog_cdeclD [THEN conjunct2], assumption, assumption)
schirmer@12854
  2238
apply (drule_tac weak_map_of_SomeI)
schirmer@12854
  2239
apply (frule_tac subcls1I [THEN subcls1_irrefl], assumption, assumption)
schirmer@12854
  2240
apply (auto dest: fields_declC [THEN conjunct2 [THEN conjunct1[THEN rtranclD]]])
schirmer@12854
  2241
done
schirmer@12854
  2242
schirmer@12854
  2243
lemma ws_unique_fields: "\<lbrakk>is_class G C; ws_prog G; 
schirmer@12854
  2244
       \<And>C c. \<lbrakk>class G C = Some c\<rbrakk> \<Longrightarrow> unique (cfields c) \<rbrakk> \<Longrightarrow>
schirmer@12854
  2245
      unique (fields G C)" 
schirmer@12854
  2246
apply (rule ws_subcls1_induct, assumption, assumption)
schirmer@12854
  2247
apply (subst fields_rec, assumption)            
paulson@13585
  2248
apply (auto intro!: unique_map_inj inj_onI 
paulson@13585
  2249
            elim!: unique_append ws_unique_fields_lemma fields_norec)
schirmer@12854
  2250
done
schirmer@12854
  2251
schirmer@12854
  2252
schirmer@12854
  2253
subsection "accfield"
schirmer@12854
  2254
schirmer@12854
  2255
lemma accfield_fields: 
schirmer@12854
  2256
 "accfield G S C fn = Some f 
schirmer@12854
  2257
  \<Longrightarrow> table_of (fields G C) (fn, declclass f) = Some (fld f)"
schirmer@12854
  2258
apply (simp only: accfield_def Let_def)
schirmer@12854
  2259
apply (rule table_of_remap_SomeD)
schirmer@12854
  2260
apply (auto dest: filter_tab_SomeD)
schirmer@12854
  2261
done
schirmer@12854
  2262
schirmer@12854
  2263
schirmer@12854
  2264
lemma accfield_declC_is_class: 
schirmer@12854
  2265
 "\<lbrakk>is_class G C; accfield G S C en = Some (fd, f); ws_prog G\<rbrakk> \<Longrightarrow>  
schirmer@12854
  2266
   is_class G fd"
schirmer@12854
  2267
apply (drule accfield_fields)
schirmer@12854
  2268
apply (drule fields_declC [THEN conjunct1], assumption)
schirmer@12854
  2269
apply auto
schirmer@12854
  2270
done
schirmer@12854
  2271
schirmer@12854
  2272
lemma accfield_accessibleD: 
schirmer@12854
  2273
  "accfield G S C fn = Some f \<Longrightarrow> G\<turnstile>Field fn f of C accessible_from S"
schirmer@12854
  2274
by (auto simp add: accfield_def Let_def)
schirmer@12854
  2275
schirmer@12854
  2276
subsection "is methd"
schirmer@12854
  2277
schirmer@12854
  2278
lemma is_methdI: 
schirmer@12854
  2279
"\<lbrakk>class G C = Some y; methd G C sig = Some b\<rbrakk> \<Longrightarrow> is_methd G C sig"
schirmer@12854
  2280
apply (unfold is_methd_def)
schirmer@12854
  2281
apply auto
schirmer@12854
  2282
done
schirmer@12854
  2283
schirmer@12854
  2284
lemma is_methdD: 
schirmer@12854
  2285
"is_methd G C sig \<Longrightarrow> class G C \<noteq> None \<and> methd G C sig \<noteq> None"
schirmer@12854
  2286
apply (unfold is_methd_def)
schirmer@12854
  2287
apply auto
schirmer@12854
  2288
done
schirmer@12854
  2289
schirmer@12854
  2290
lemma finite_is_methd: 
schirmer@12854
  2291
 "ws_prog G \<Longrightarrow> finite (Collect (split (is_methd G)))"
schirmer@12854
  2292
apply (unfold is_methd_def)
schirmer@12854
  2293
apply (subst SetCompr_Sigma_eq)
schirmer@12854
  2294
apply (rule finite_is_class [THEN finite_SigmaI])
schirmer@12854
  2295
apply (simp only: mem_Collect_eq)
schirmer@12854
  2296
apply (fold dom_def)
schirmer@12854
  2297
apply (erule finite_dom_methd)
schirmer@12854
  2298
apply assumption
schirmer@12854
  2299
done
schirmer@12854
  2300
schirmer@12854
  2301
section "calculation of the superclasses of a class"
schirmer@12854
  2302
schirmer@12854
  2303
constdefs 
schirmer@12854
  2304
 superclasses:: "prog \<Rightarrow> qtname \<Rightarrow> qtname set"
schirmer@12854
  2305
 "superclasses G C \<equiv> class_rec (G,C) {} 
schirmer@12854
  2306
                       (\<lambda> C c superclss. (if C=Object 
schirmer@12854
  2307
                                            then {} 
schirmer@12854
  2308
                                            else insert (super c) superclss))"
schirmer@12854
  2309
   
schirmer@12854
  2310
lemma superclasses_rec: "\<lbrakk>class G C = Some c; ws_prog G\<rbrakk> \<Longrightarrow>  
schirmer@12854
  2311
 superclasses G C 
schirmer@12854
  2312
 = (if (C=Object) 
schirmer@12854
  2313
       then {}
schirmer@12854
  2314
       else insert (super c) (superclasses G (super c)))"
schirmer@12854
  2315
apply (unfold superclasses_def)
schirmer@12854
  2316
apply (erule class_rec [THEN trans], assumption)
schirmer@12854
  2317
apply (simp)
schirmer@12854
  2318
done
schirmer@12854
  2319
schirmer@12854
  2320
lemma superclasses_mono:
berghofe@34915
  2321
  assumes clsrel: "G\<turnstile>C\<prec>\<^sub>C D"
berghofe@34915
  2322
  and ws: "ws_prog G"
berghofe@34915
  2323
  and cls_C: "class G C = Some c"
berghofe@34915
  2324
  and wf: "\<And>C c. \<lbrakk>class G C = Some c; C \<noteq> Object\<rbrakk>
berghofe@34915
  2325
    \<Longrightarrow> \<exists>sc. class G (super c) = Some sc"
berghofe@34915
  2326
  and x: "x\<in>superclasses G D"
berghofe@34915
  2327
  shows "x\<in>superclasses G C" using clsrel cls_C x
berghofe@34915
  2328
proof (induct arbitrary: c rule: converse_trancl_induct)
berghofe@34915
  2329
  case (base C)
berghofe@34915
  2330
  with wf ws show ?case
berghofe@34915
  2331
    by (auto    intro: no_subcls1_Object 
berghofe@34915
  2332
             simp add: superclasses_rec subcls1_def)
berghofe@34915
  2333
next
berghofe@34915
  2334
  case (step C S)
berghofe@34915
  2335
  moreover note wf ws
berghofe@34915
  2336
  moreover from calculation 
berghofe@34915
  2337
  have "x\<in>superclasses G S"
berghofe@34915
  2338
    by (force intro: no_subcls1_Object simp add: subcls1_def)
berghofe@34915
  2339
  moreover from calculation 
berghofe@34915
  2340
  have "super c = S" 
berghofe@34915
  2341
    by (auto intro: no_subcls1_Object simp add: subcls1_def)
berghofe@34915
  2342
  ultimately show ?case 
berghofe@34915
  2343
    by (auto intro: no_subcls1_Object simp add: superclasses_rec)
schirmer@12854
  2344
qed
schirmer@12854
  2345
schirmer@12854
  2346
lemma subclsEval:
berghofe@34915
  2347
  assumes clsrel: "G\<turnstile>C\<prec>\<^sub>C D"
berghofe@34915
  2348
  and ws: "ws_prog G"
berghofe@34915
  2349
  and cls_C: "class G C = Some c"
berghofe@34915
  2350
  and wf: "\<And>C c. \<lbrakk>class G C = Some c; C \<noteq> Object\<rbrakk>
berghofe@34915
  2351
    \<Longrightarrow> \<exists>sc. class G (super c) = Some sc"
berghofe@34915
  2352
  shows "D\<in>superclasses G C" using clsrel cls_C
berghofe@34915
  2353
proof (induct arbitrary: c rule: converse_trancl_induct)
berghofe@34915
  2354
  case (base C)
berghofe@34915
  2355
  with ws wf show ?case
berghofe@34915
  2356
    by (auto intro: no_subcls1_Object simp add: superclasses_rec subcls1_def)
berghofe@34915
  2357
next
berghofe@34915
  2358
  case (step C S)
berghofe@34915
  2359
  with ws wf show ?case
berghofe@34915
  2360
    by - (rule superclasses_mono,
berghofe@34915
  2361
          auto dest: no_subcls1_Object simp add: subcls1_def )
schirmer@12854
  2362
qed
schirmer@12854
  2363
kleing@14981
  2364
end