src/HOL/Bali/DeclConcepts.thy
author wenzelm
Mon Mar 22 20:58:52 2010 +0100 (2010-03-22)
changeset 35898 c890a3835d15
parent 35547 991a6af75978
child 36366 886b94b1bed7
permissions -rw-r--r--
recovered header;
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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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definition is_public :: "prog \<Rightarrow> qtname \<Rightarrow> bool" where
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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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definition is_acc_class :: "prog \<Rightarrow> pname \<Rightarrow> qtname \<Rightarrow> bool" where
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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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definition is_acc_iface :: "prog \<Rightarrow> pname \<Rightarrow> qtname \<Rightarrow> bool" where
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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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definition is_acc_type  :: "prog \<Rightarrow> pname \<Rightarrow> ty     \<Rightarrow> bool" where
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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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definition is_acc_reftype  :: "prog \<Rightarrow> pname \<Rightarrow> ref_ty \<Rightarrow> bool" where
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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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haftmann@35416
   340
definition methdMembr :: "(qtname \<times> mdecl) \<Rightarrow> (qtname \<times> memberdecl)" where
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   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
haftmann@35416
   358
definition method :: "sig \<Rightarrow> (qtname \<times> methd) \<Rightarrow> (qtname \<times> memberdecl)" where 
schirmer@12854
   359
"method sig m \<equiv> (declclass m, mdecl (sig, mthd m))"
schirmer@12854
   360
schirmer@12854
   361
lemma method_simp[simp]: "method sig (C,m) = (C,mdecl (sig,m))"
schirmer@12854
   362
by (simp add: method_def)
schirmer@12854
   363
schirmer@12854
   364
lemma accmodi_method_simp[simp]: "accmodi (method sig m) = accmodi m"
schirmer@12854
   365
by (simp add: method_def)
schirmer@12854
   366
schirmer@12854
   367
lemma declclass_method_simp[simp]: "declclass (method sig m) = declclass m"
schirmer@12854
   368
by (simp add: method_def)
schirmer@12854
   369
schirmer@12854
   370
lemma is_static_method_simp[simp]: "is_static (method sig m) = is_static m"
schirmer@12854
   371
by (cases m) (simp add: method_def)
schirmer@12854
   372
schirmer@12854
   373
lemma mbr_method_simp[simp]: "mbr (method sig m) = mdecl (sig,mthd m)"
schirmer@12854
   374
by (simp add: mbr_def method_def)
schirmer@12854
   375
schirmer@12854
   376
lemma memberid_method_simp[simp]:  "memberid (method sig m) = mid sig"
schirmer@12854
   377
  by (simp add: method_def) 
schirmer@12854
   378
haftmann@35416
   379
definition fieldm :: "vname \<Rightarrow> (qtname \<times> field) \<Rightarrow> (qtname \<times> memberdecl)" where 
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   380
"fieldm n f \<equiv> (declclass f, fdecl (n, fld f))"
schirmer@12854
   381
schirmer@12854
   382
lemma fieldm_simp[simp]: "fieldm n (C,f) = (C,fdecl (n,f))"
schirmer@12854
   383
by (simp add: fieldm_def)
schirmer@12854
   384
schirmer@12854
   385
lemma accmodi_fieldm_simp[simp]: "accmodi (fieldm n f) = accmodi f"
schirmer@12854
   386
by (simp add: fieldm_def)
schirmer@12854
   387
schirmer@12854
   388
lemma declclass_fieldm_simp[simp]: "declclass (fieldm n f) = declclass f"
schirmer@12854
   389
by (simp add: fieldm_def)
schirmer@12854
   390
schirmer@12854
   391
lemma is_static_fieldm_simp[simp]: "is_static (fieldm n f) = is_static f"
schirmer@12854
   392
by (cases f) (simp add: fieldm_def)
schirmer@12854
   393
schirmer@12854
   394
lemma mbr_fieldm_simp[simp]: "mbr (fieldm n f) = fdecl (n,fld f)"
schirmer@12854
   395
by (simp add: mbr_def fieldm_def)
schirmer@12854
   396
schirmer@12854
   397
lemma memberid_fieldm_simp[simp]:  "memberid (fieldm n f) = fid n"
schirmer@12854
   398
by (simp add: fieldm_def) 
schirmer@12854
   399
schirmer@12854
   400
text {* Select the signature out of a qualified method declaration:
schirmer@12854
   401
 @{text msig} *}
schirmer@12854
   402
haftmann@35416
   403
definition msig :: "(qtname \<times> mdecl) \<Rightarrow> sig" where
schirmer@12854
   404
"msig m \<equiv> fst (snd m)"
schirmer@12854
   405
schirmer@12854
   406
lemma msig_simp[simp]: "msig (c,(s,m)) = s"
schirmer@12854
   407
by (simp add: msig_def)
schirmer@12854
   408
schirmer@12854
   409
text {* Convert a qualified method (qualified with its declaring 
schirmer@12854
   410
class) to a qualified method declaration:  @{text qmdecl}  *}
schirmer@12854
   411
haftmann@35416
   412
definition qmdecl :: "sig \<Rightarrow> (qtname \<times> methd) \<Rightarrow> (qtname \<times> mdecl)" where
schirmer@12854
   413
"qmdecl sig m \<equiv> (declclass m, (sig,mthd m))"
schirmer@12854
   414
schirmer@12854
   415
lemma qmdecl_simp[simp]: "qmdecl sig (C,m) = (C,(sig,m))"
schirmer@12854
   416
by (simp add: qmdecl_def)
schirmer@12854
   417
schirmer@12854
   418
lemma declclass_qmdecl_simp[simp]: "declclass (qmdecl sig m) = declclass m"
schirmer@12854
   419
by (simp add: qmdecl_def)
schirmer@12854
   420
schirmer@12854
   421
lemma accmodi_qmdecl_simp[simp]: "accmodi (qmdecl sig m) = accmodi m"
schirmer@12854
   422
by (simp add: qmdecl_def)
schirmer@12854
   423
schirmer@12854
   424
lemma is_static_qmdecl_simp[simp]: "is_static (qmdecl sig m) = is_static m"
schirmer@12854
   425
by (cases m) (simp add: qmdecl_def)
schirmer@12854
   426
schirmer@12854
   427
lemma msig_qmdecl_simp[simp]: "msig (qmdecl sig m) = sig"
schirmer@12854
   428
by (simp add: qmdecl_def)
schirmer@12854
   429
schirmer@12854
   430
lemma mdecl_qmdecl_simp[simp]:  
schirmer@12854
   431
 "mdecl (mthd (qmdecl sig new)) = mdecl (sig, mthd new)" 
schirmer@12854
   432
by (simp add: qmdecl_def) 
schirmer@12854
   433
schirmer@12854
   434
lemma methdMembr_qmdecl_simp [simp]: 
schirmer@12854
   435
 "methdMembr (qmdecl sig old) = method sig old"
schirmer@12854
   436
by (simp add: methdMembr_def qmdecl_def method_def)
schirmer@12854
   437
schirmer@12854
   438
text {* overloaded selector @{text resTy} to select the result type 
schirmer@12854
   439
out of various HOL types *}
schirmer@12854
   440
haftmann@35315
   441
class has_resTy =
haftmann@35315
   442
  fixes resTy:: "'a \<Rightarrow> ty"
haftmann@35315
   443
haftmann@35315
   444
instantiation decl_ext_type :: (has_resTy) has_resTy
haftmann@35315
   445
begin
schirmer@12854
   446
haftmann@35315
   447
instance ..
haftmann@35315
   448
haftmann@35315
   449
end
haftmann@35315
   450
haftmann@35315
   451
instantiation member_ext_type :: (has_resTy) has_resTy
haftmann@35315
   452
begin
schirmer@12854
   453
haftmann@35315
   454
instance ..
schirmer@12854
   455
haftmann@35315
   456
end
haftmann@35315
   457
haftmann@35315
   458
instantiation mhead_ext_type :: (type) has_resTy
haftmann@35315
   459
begin
schirmer@12854
   460
haftmann@35315
   461
instance ..
haftmann@35315
   462
haftmann@35315
   463
end
haftmann@35315
   464
haftmann@35315
   465
axiomatization where
haftmann@35315
   466
  mhead_ext_type_resTy_def: "resTy (m::('b mhead_scheme)) \<equiv> resT m"
schirmer@12854
   467
schirmer@12854
   468
lemma mhead_resTy_simp: "resTy (m::'a mhead_scheme) = resT m"
tsewell@32754
   469
by (simp add: mhead_ext_type_resTy_def)
schirmer@12854
   470
schirmer@12854
   471
lemma resTy_mhead [simp]:"resTy (mhead m) = resTy m"
schirmer@12854
   472
by (simp add: mhead_def mhead_resTy_simp)
schirmer@12854
   473
haftmann@35315
   474
instantiation * :: ("type","has_resTy") has_resTy
haftmann@35315
   475
begin
schirmer@12854
   476
haftmann@35315
   477
definition
haftmann@35315
   478
  pair_resTy_def: "resTy p \<equiv> resTy (snd p)"
haftmann@35315
   479
haftmann@35315
   480
instance ..
haftmann@35315
   481
haftmann@35315
   482
end
schirmer@12854
   483
schirmer@12854
   484
lemma pair_resTy_simp[simp]: "resTy (x,m) = resTy m"
schirmer@12854
   485
by (simp add: pair_resTy_def)
schirmer@12854
   486
schirmer@12854
   487
lemma qmdecl_resTy_simp [simp]: "resTy (qmdecl sig m) = resTy m"
schirmer@12854
   488
by (cases m) (simp)
schirmer@12854
   489
schirmer@12854
   490
lemma resTy_mthd [simp]:"resTy (mthd m) = resTy m"
schirmer@12854
   491
by (cases m) (simp add: mthd_def )
schirmer@12854
   492
schirmer@12854
   493
subsubsection "inheritable-in"
schirmer@12854
   494
text {*
schirmer@12854
   495
@{text "G\<turnstile>m inheritable_in P"}: m can be inherited by
schirmer@12854
   496
classes in package P if:
schirmer@12854
   497
\begin{itemize} 
schirmer@12854
   498
\item the declaration class of m is accessible in P and
schirmer@12854
   499
\item the member m is declared with protected or public access or if it is
schirmer@12854
   500
      declared with default (package) access, the package of the declaration 
schirmer@12854
   501
      class of m is also P. If the member m is declared with private access
schirmer@12854
   502
      it is not accessible for inheritance at all.
schirmer@12854
   503
\end{itemize}
schirmer@12854
   504
*}
haftmann@35416
   505
definition inheritable_in :: "prog \<Rightarrow> (qtname \<times> memberdecl) \<Rightarrow> pname \<Rightarrow> bool" ("_ \<turnstile> _ inheritable'_in _" [61,61,61] 60) where
haftmann@35416
   506
                  
schirmer@12854
   507
"G\<turnstile>membr inheritable_in pack 
schirmer@12854
   508
  \<equiv> (case (accmodi membr) of
schirmer@12854
   509
       Private   \<Rightarrow> False
schirmer@12854
   510
     | Package   \<Rightarrow> (pid (declclass membr)) = pack
schirmer@12854
   511
     | Protected \<Rightarrow> True
schirmer@12854
   512
     | Public    \<Rightarrow> True)"
schirmer@12854
   513
wenzelm@35067
   514
abbreviation
wenzelm@35067
   515
Method_inheritable_in_syntax::
schirmer@12854
   516
 "prog \<Rightarrow> (qtname \<times> mdecl) \<Rightarrow> pname \<Rightarrow> bool"
schirmer@12854
   517
                ("_ \<turnstile>Method _ inheritable'_in _ " [61,61,61] 60)
wenzelm@35067
   518
 where "G\<turnstile>Method m inheritable_in p == G\<turnstile>methdMembr m inheritable_in p"
schirmer@12854
   519
wenzelm@35067
   520
abbreviation
schirmer@12854
   521
Methd_inheritable_in::
schirmer@12854
   522
 "prog \<Rightarrow> sig \<Rightarrow> (qtname \<times> methd) \<Rightarrow> pname \<Rightarrow> bool"
schirmer@12854
   523
                ("_ \<turnstile>Methd _ _ inheritable'_in _ " [61,61,61,61] 60)
wenzelm@35067
   524
 where "G\<turnstile>Methd s m inheritable_in p == G\<turnstile>(method s m) inheritable_in p"
schirmer@12854
   525
schirmer@12854
   526
subsubsection "declared-in/undeclared-in"
schirmer@12854
   527
haftmann@35416
   528
definition cdeclaredmethd :: "prog \<Rightarrow> qtname \<Rightarrow> (sig,methd) table" where
schirmer@12854
   529
"cdeclaredmethd G C 
schirmer@12854
   530
  \<equiv> (case class G C of
schirmer@12854
   531
       None \<Rightarrow> \<lambda> sig. None
schirmer@12854
   532
     | Some c \<Rightarrow> table_of (methods c)
schirmer@12854
   533
    )"
schirmer@12854
   534
haftmann@35416
   535
definition cdeclaredfield :: "prog \<Rightarrow> qtname \<Rightarrow> (vname,field) table" where
schirmer@12854
   536
"cdeclaredfield G C 
schirmer@12854
   537
  \<equiv> (case class G C of
schirmer@12854
   538
       None \<Rightarrow> \<lambda> sig. None
schirmer@12854
   539
     | Some c \<Rightarrow> table_of (cfields c)
schirmer@12854
   540
    )"
schirmer@12854
   541
haftmann@35416
   542
definition declared_in :: "prog  \<Rightarrow> memberdecl \<Rightarrow> qtname \<Rightarrow> bool" ("_\<turnstile> _ declared'_in _" [61,61,61] 60) where
schirmer@12854
   543
"G\<turnstile>m declared_in C \<equiv> (case m of
schirmer@12854
   544
                        fdecl (fn,f ) \<Rightarrow> cdeclaredfield G C fn  = Some f
schirmer@12854
   545
                      | mdecl (sig,m) \<Rightarrow> cdeclaredmethd G C sig = Some m)"
schirmer@12854
   546
wenzelm@35067
   547
abbreviation
schirmer@12854
   548
method_declared_in:: "prog  \<Rightarrow> (qtname \<times> mdecl) \<Rightarrow> qtname \<Rightarrow> bool"
schirmer@12854
   549
                                 ("_\<turnstile>Method _ declared'_in _" [61,61,61] 60)
wenzelm@35067
   550
 where "G\<turnstile>Method m declared_in C == G\<turnstile>mdecl (mthd m) declared_in C"
schirmer@12854
   551
wenzelm@35067
   552
abbreviation
schirmer@12854
   553
methd_declared_in:: "prog  \<Rightarrow> sig  \<Rightarrow>(qtname \<times> methd) \<Rightarrow> qtname \<Rightarrow> bool"
schirmer@12854
   554
                               ("_\<turnstile>Methd _  _ declared'_in _" [61,61,61,61] 60)
wenzelm@35067
   555
 where "G\<turnstile>Methd s m declared_in C == G\<turnstile>mdecl (s,mthd m) declared_in C"
schirmer@12854
   556
schirmer@12854
   557
lemma declared_in_classD:
schirmer@12854
   558
 "G\<turnstile>m declared_in C \<Longrightarrow> is_class G C"
schirmer@12854
   559
by (cases m) 
schirmer@12854
   560
   (auto simp add: declared_in_def cdeclaredmethd_def cdeclaredfield_def)
schirmer@12854
   561
haftmann@35416
   562
definition undeclared_in :: "prog  \<Rightarrow> memberid \<Rightarrow> qtname \<Rightarrow> bool" ("_\<turnstile> _ undeclared'_in _" [61,61,61] 60) where
schirmer@12854
   563
"G\<turnstile>m undeclared_in C \<equiv> (case m of
schirmer@12854
   564
                            fid fn  \<Rightarrow> cdeclaredfield G C fn  = None
schirmer@12854
   565
                          | mid sig \<Rightarrow> cdeclaredmethd G C sig = None)"
schirmer@12854
   566
schirmer@12854
   567
schirmer@12854
   568
subsubsection "members"
schirmer@12854
   569
schirmer@12854
   570
(* Can't just take a function: prog \<Rightarrow> qtname \<Rightarrow> memberdecl set because
schirmer@12854
   571
   the class qtname changes to the superclass in the inductive definition
schirmer@12854
   572
   below
schirmer@12854
   573
*)
schirmer@12854
   574
berghofe@23747
   575
inductive
berghofe@21765
   576
  members :: "prog \<Rightarrow> (qtname \<times> memberdecl) \<Rightarrow> qtname \<Rightarrow> bool"
berghofe@21765
   577
    ("_ \<turnstile> _ member'_of _" [61,61,61] 60)
berghofe@21765
   578
  for G :: prog
berghofe@21765
   579
where
schirmer@12854
   580
berghofe@21765
   581
  Immediate: "\<lbrakk>G\<turnstile>mbr m declared_in C;declclass m = C\<rbrakk> \<Longrightarrow> G\<turnstile>m member_of C"
berghofe@21765
   582
| Inherited: "\<lbrakk>G\<turnstile>m inheritable_in (pid C); G\<turnstile>memberid m undeclared_in C; 
haftmann@35416
   583
               G\<turnstile>C \<prec>\<^sub>C1 S; G\<turnstile>(Class S) accessible_in (pid C);G\<turnstile>m member_of S 
berghofe@21765
   584
              \<rbrakk> \<Longrightarrow> G\<turnstile>m member_of C"
schirmer@12854
   585
text {* Note that in the case of an inherited member only the members of the
schirmer@12854
   586
direct superclass are concerned. If a member of a superclass of the direct
schirmer@12854
   587
superclass isn't inherited in the direct superclass (not member of the
schirmer@12854
   588
direct superclass) than it can't be a member of the class. E.g. If a
schirmer@12854
   589
member of a class A is defined with package access it isn't member of a 
schirmer@12854
   590
subclass S if S isn't in the same package as A. Any further subclasses 
schirmer@12854
   591
of S will not inherit the member, regardless if they are in the same
schirmer@12854
   592
package as A or not.*}
schirmer@12854
   593
wenzelm@35067
   594
abbreviation
schirmer@12854
   595
method_member_of:: "prog \<Rightarrow> (qtname \<times> mdecl) \<Rightarrow> qtname \<Rightarrow> bool"
schirmer@12854
   596
                           ("_ \<turnstile>Method _ member'_of _" [61,61,61] 60)
wenzelm@35067
   597
 where "G\<turnstile>Method m member_of C == G\<turnstile>(methdMembr m) member_of C"
schirmer@12854
   598
wenzelm@35067
   599
abbreviation
schirmer@12854
   600
methd_member_of:: "prog \<Rightarrow> sig \<Rightarrow> (qtname \<times> methd) \<Rightarrow> qtname \<Rightarrow> bool"
schirmer@12854
   601
                           ("_ \<turnstile>Methd _ _ member'_of _" [61,61,61,61] 60)
wenzelm@35067
   602
 where "G\<turnstile>Methd s m member_of C == G\<turnstile>(method s m) member_of C" 
schirmer@12854
   603
wenzelm@35067
   604
abbreviation
schirmer@12854
   605
fieldm_member_of:: "prog \<Rightarrow> vname \<Rightarrow> (qtname \<times> field) \<Rightarrow> qtname \<Rightarrow> bool"
schirmer@12854
   606
                           ("_ \<turnstile>Field _  _ member'_of _" [61,61,61] 60)
wenzelm@35067
   607
 where "G\<turnstile>Field n f member_of C == G\<turnstile>fieldm n f member_of C"
schirmer@12854
   608
haftmann@35416
   609
definition inherits :: "prog \<Rightarrow> qtname \<Rightarrow> (qtname \<times> memberdecl) \<Rightarrow> bool" ("_ \<turnstile> _ inherits _" [61,61,61] 60) where
schirmer@12854
   610
"G\<turnstile>C inherits m 
schirmer@12854
   611
  \<equiv> G\<turnstile>m inheritable_in (pid C) \<and> G\<turnstile>memberid m undeclared_in C \<and> 
haftmann@35416
   612
    (\<exists> S. G\<turnstile>C \<prec>\<^sub>C1 S \<and> G\<turnstile>(Class S) accessible_in (pid C) \<and> G\<turnstile>m member_of S)"
schirmer@12854
   613
schirmer@12854
   614
lemma inherits_member: "G\<turnstile>C inherits m \<Longrightarrow> G\<turnstile>m member_of C"
schirmer@12854
   615
by (auto simp add: inherits_def intro: members.Inherited)
schirmer@12854
   616
schirmer@12854
   617
haftmann@35416
   618
definition member_in :: "prog \<Rightarrow> (qtname \<times> memberdecl) \<Rightarrow> qtname \<Rightarrow> bool" ("_ \<turnstile> _ member'_in _" [61,61,61] 60) where
schirmer@12854
   619
"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
   620
text {* A member is in a class if it is member of the class or a superclass.
schirmer@12854
   621
If a member is in a class we can select this member. This additional notion
schirmer@12854
   622
is necessary since not all members are inherited to subclasses. So such
schirmer@12854
   623
members are not member-of the subclass but member-in the subclass.*}
schirmer@12854
   624
wenzelm@35067
   625
abbreviation
schirmer@12854
   626
method_member_in:: "prog \<Rightarrow> (qtname \<times> mdecl) \<Rightarrow> qtname \<Rightarrow> bool"
schirmer@12854
   627
                           ("_ \<turnstile>Method _ member'_in _" [61,61,61] 60)
wenzelm@35067
   628
 where "G\<turnstile>Method m member_in C == G\<turnstile>(methdMembr m) member_in C"
schirmer@12854
   629
wenzelm@35067
   630
abbreviation
schirmer@12854
   631
methd_member_in:: "prog \<Rightarrow> sig \<Rightarrow> (qtname \<times> methd) \<Rightarrow> qtname \<Rightarrow> bool"
schirmer@12854
   632
                           ("_ \<turnstile>Methd _ _ member'_in _" [61,61,61,61] 60)
wenzelm@35067
   633
 where "G\<turnstile>Methd s m member_in C == G\<turnstile>(method s m) member_in C"
schirmer@12854
   634
schirmer@12854
   635
lemma member_inD: "G\<turnstile>m member_in C 
schirmer@12854
   636
 \<Longrightarrow> \<exists> provC. G\<turnstile> C \<preceq>\<^sub>C provC \<and> G \<turnstile> m member_of provC"
schirmer@12854
   637
by (auto simp add: member_in_def)
schirmer@12854
   638
schirmer@12854
   639
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
   640
by (auto simp add: member_in_def)
schirmer@12854
   641
schirmer@12854
   642
lemma member_of_to_member_in: "G \<turnstile> m member_of C \<Longrightarrow> G \<turnstile>m member_in C"
schirmer@12854
   643
by (auto intro: member_inI)
schirmer@12854
   644
schirmer@12854
   645
schirmer@12854
   646
subsubsection "overriding"
schirmer@12854
   647
schirmer@12854
   648
text {* Unfortunately the static notion of overriding (used during the
schirmer@12854
   649
typecheck of the compiler) and the dynamic notion of overriding (used during
schirmer@12854
   650
execution in the JVM) are not exactly the same. 
schirmer@12854
   651
*}
schirmer@12854
   652
schirmer@12854
   653
text {* Static overriding (used during the typecheck of the compiler) *}
schirmer@12854
   654
berghofe@23747
   655
inductive
berghofe@21765
   656
  stat_overridesR :: "prog \<Rightarrow> (qtname \<times> mdecl) \<Rightarrow> (qtname \<times> mdecl) \<Rightarrow> bool"
berghofe@21765
   657
    ("_ \<turnstile> _ overrides\<^sub>S _" [61,61,61] 60)
berghofe@21765
   658
  for G :: prog
berghofe@21765
   659
where
schirmer@12854
   660
berghofe@21765
   661
  Direct: "\<lbrakk>\<not> is_static new; msig new = msig old; 
berghofe@21765
   662
           G\<turnstile>Method new declared_in (declclass new);  
berghofe@21765
   663
           G\<turnstile>Method old declared_in (declclass old); 
berghofe@21765
   664
           G\<turnstile>Method old inheritable_in pid (declclass new);
haftmann@35416
   665
           G\<turnstile>(declclass new) \<prec>\<^sub>C1 superNew;
berghofe@21765
   666
           G \<turnstile>Method old member_of superNew
berghofe@21765
   667
           \<rbrakk> \<Longrightarrow> G\<turnstile>new overrides\<^sub>S old"
schirmer@12854
   668
haftmann@32134
   669
| Indirect: "\<lbrakk>G\<turnstile>new overrides\<^sub>S intr; G\<turnstile>intr overrides\<^sub>S old\<rbrakk>
berghofe@21765
   670
             \<Longrightarrow> G\<turnstile>new overrides\<^sub>S old"
schirmer@12854
   671
schirmer@12854
   672
text {* Dynamic overriding (used during the typecheck of the compiler) *}
schirmer@12854
   673
berghofe@23747
   674
inductive
berghofe@21765
   675
  overridesR :: "prog \<Rightarrow> (qtname \<times> mdecl) \<Rightarrow> (qtname \<times> mdecl) \<Rightarrow> bool"
berghofe@21765
   676
    ("_ \<turnstile> _ overrides _" [61,61,61] 60)
berghofe@21765
   677
  for G :: prog
berghofe@21765
   678
where
schirmer@12854
   679
berghofe@21765
   680
  Direct: "\<lbrakk>\<not> is_static new; \<not> is_static old; accmodi new \<noteq> Private;
berghofe@21765
   681
           msig new = msig old; 
berghofe@21765
   682
           G\<turnstile>(declclass new) \<prec>\<^sub>C (declclass old);
berghofe@21765
   683
           G\<turnstile>Method new declared_in (declclass new);  
berghofe@21765
   684
           G\<turnstile>Method old declared_in (declclass old);    
berghofe@21765
   685
           G\<turnstile>Method old inheritable_in pid (declclass new);
berghofe@21765
   686
           G\<turnstile>resTy new \<preceq> resTy old
berghofe@21765
   687
           \<rbrakk> \<Longrightarrow> G\<turnstile>new overrides old"
schirmer@12854
   688
haftmann@32134
   689
| Indirect: "\<lbrakk>G\<turnstile>new overrides intr; G\<turnstile>intr overrides old\<rbrakk>
berghofe@21765
   690
            \<Longrightarrow> G\<turnstile>new overrides old"
schirmer@12854
   691
wenzelm@35067
   692
abbreviation (input)
schirmer@12854
   693
sig_stat_overrides:: 
schirmer@12854
   694
 "prog  \<Rightarrow> sig \<Rightarrow> (qtname \<times> methd) \<Rightarrow> (qtname \<times> methd) \<Rightarrow> bool" 
schirmer@12854
   695
                                  ("_,_\<turnstile> _ overrides\<^sub>S _" [61,61,61,61] 60)
wenzelm@35067
   696
 where "G,s\<turnstile>new overrides\<^sub>S old == G\<turnstile>(qmdecl s new) overrides\<^sub>S (qmdecl s old)" 
schirmer@12854
   697
wenzelm@35067
   698
abbreviation (input)
schirmer@12854
   699
sig_overrides:: "prog  \<Rightarrow> sig \<Rightarrow> (qtname \<times> methd) \<Rightarrow> (qtname \<times> methd) \<Rightarrow> bool" 
schirmer@12854
   700
                                  ("_,_\<turnstile> _ overrides _" [61,61,61,61] 60)
wenzelm@35067
   701
 where "G,s\<turnstile>new overrides old == G\<turnstile>(qmdecl s new) overrides (qmdecl s old)"
schirmer@12854
   702
schirmer@12854
   703
subsubsection "Hiding"
schirmer@12854
   704
haftmann@35416
   705
definition hides :: "prog \<Rightarrow> (qtname \<times> mdecl) \<Rightarrow> (qtname \<times> mdecl) \<Rightarrow> bool" ("_\<turnstile> _ hides _" [61,61,61] 60) where 
schirmer@12854
   706
"G\<turnstile>new hides old
schirmer@12854
   707
  \<equiv> is_static new \<and> msig new = msig old \<and>
schirmer@12854
   708
    G\<turnstile>(declclass new) \<prec>\<^sub>C (declclass old) \<and>
schirmer@12854
   709
    G\<turnstile>Method new declared_in (declclass new) \<and>
schirmer@12854
   710
    G\<turnstile>Method old declared_in (declclass old) \<and> 
schirmer@12854
   711
    G\<turnstile>Method old inheritable_in pid (declclass new)"
schirmer@12854
   712
wenzelm@35067
   713
abbreviation
wenzelm@35067
   714
sig_hides:: "prog  \<Rightarrow> sig \<Rightarrow> (qtname \<times> methd) \<Rightarrow> (qtname \<times> methd) \<Rightarrow> bool" 
schirmer@12854
   715
                                  ("_,_\<turnstile> _ hides _" [61,61,61,61] 60)
wenzelm@35067
   716
 where "G,s\<turnstile>new hides old == G\<turnstile>(qmdecl s new) hides (qmdecl s old)"
schirmer@12854
   717
schirmer@12854
   718
lemma hidesI:
schirmer@12854
   719
"\<lbrakk>is_static new; msig new = msig old;
schirmer@12854
   720
  G\<turnstile>(declclass new) \<prec>\<^sub>C (declclass old);
schirmer@12854
   721
  G\<turnstile>Method new declared_in (declclass new);
schirmer@12854
   722
  G\<turnstile>Method old declared_in (declclass old);
schirmer@12854
   723
  G\<turnstile>Method old inheritable_in pid (declclass new)
schirmer@12854
   724
 \<rbrakk> \<Longrightarrow> G\<turnstile>new hides old"
schirmer@12854
   725
by (auto simp add: hides_def)
schirmer@12854
   726
schirmer@12854
   727
lemma hidesD:
schirmer@12854
   728
"\<lbrakk>G\<turnstile>new hides old\<rbrakk> \<Longrightarrow>  
schirmer@12854
   729
  declclass new \<noteq> Object \<and> is_static new \<and> msig new = msig old \<and> 
schirmer@12854
   730
  G\<turnstile>(declclass new) \<prec>\<^sub>C (declclass old) \<and>
schirmer@12854
   731
  G\<turnstile>Method new declared_in (declclass new) \<and>   
schirmer@12854
   732
  G\<turnstile>Method old declared_in (declclass old)"
schirmer@12854
   733
by (auto simp add: hides_def)
schirmer@12854
   734
schirmer@12854
   735
lemma overrides_commonD:
schirmer@12854
   736
"\<lbrakk>G\<turnstile>new overrides old\<rbrakk> \<Longrightarrow>  
schirmer@12854
   737
  declclass new \<noteq> Object \<and> \<not> is_static new \<and> \<not> is_static old \<and>
schirmer@12854
   738
  accmodi new \<noteq> Private \<and> 
schirmer@12854
   739
  msig new = msig old  \<and>
schirmer@12854
   740
  G\<turnstile>(declclass new) \<prec>\<^sub>C (declclass old) \<and>
schirmer@12854
   741
  G\<turnstile>Method new declared_in (declclass new) \<and>   
schirmer@12854
   742
  G\<turnstile>Method old declared_in (declclass old)"
schirmer@12854
   743
by (induct set: overridesR) (auto intro: trancl_trans)
schirmer@12854
   744
schirmer@12854
   745
lemma ws_overrides_commonD:
schirmer@12854
   746
"\<lbrakk>G\<turnstile>new overrides old;ws_prog G\<rbrakk> \<Longrightarrow>  
schirmer@12854
   747
  declclass new \<noteq> Object \<and> \<not> is_static new \<and> \<not> is_static old \<and>
schirmer@12854
   748
  accmodi new \<noteq> Private \<and> G\<turnstile>resTy new \<preceq> resTy old \<and>
schirmer@12854
   749
  msig new = msig old  \<and>
schirmer@12854
   750
  G\<turnstile>(declclass new) \<prec>\<^sub>C (declclass old) \<and>
schirmer@12854
   751
  G\<turnstile>Method new declared_in (declclass new) \<and>   
schirmer@12854
   752
  G\<turnstile>Method old declared_in (declclass old)"
schirmer@12854
   753
by (induct set: overridesR) (auto intro: trancl_trans ws_widen_trans)
schirmer@12854
   754
schirmer@12854
   755
lemma overrides_eq_sigD: 
schirmer@12854
   756
 "\<lbrakk>G\<turnstile>new overrides old\<rbrakk> \<Longrightarrow> msig old=msig new"
schirmer@12854
   757
by (auto dest: overrides_commonD)
schirmer@12854
   758
schirmer@12854
   759
lemma hides_eq_sigD: 
schirmer@12854
   760
 "\<lbrakk>G\<turnstile>new hides old\<rbrakk> \<Longrightarrow> msig old=msig new"
schirmer@12854
   761
by (auto simp add: hides_def)
schirmer@12854
   762
schirmer@12854
   763
subsubsection "permits access" 
haftmann@35416
   764
definition permits_acc :: "prog \<Rightarrow> (qtname \<times> memberdecl) \<Rightarrow> qtname \<Rightarrow> qtname \<Rightarrow> bool" ("_ \<turnstile> _ in _ permits'_acc'_from _" [61,61,61,61] 60) where
wenzelm@35067
   765
"G\<turnstile>membr in cls permits_acc_from accclass 
schirmer@12854
   766
  \<equiv> (case (accmodi membr) of
schirmer@12854
   767
       Private   \<Rightarrow> (declclass membr = accclass)
schirmer@12854
   768
     | Package   \<Rightarrow> (pid (declclass membr) = pid accclass)
schirmer@12854
   769
     | Protected \<Rightarrow> (pid (declclass membr) = pid accclass)
schirmer@12854
   770
                    \<or>
schirmer@12925
   771
                    (G\<turnstile>accclass \<prec>\<^sub>C declclass membr 
wenzelm@35067
   772
                     \<and> (G\<turnstile>cls \<preceq>\<^sub>C accclass \<or> is_static membr)) 
schirmer@12854
   773
     | Public    \<Rightarrow> True)"
schirmer@12854
   774
text {*
schirmer@12854
   775
The subcondition of the @{term "Protected"} case: 
schirmer@12854
   776
@{term "G\<turnstile>accclass \<prec>\<^sub>C declclass membr"} could also be relaxed to:
schirmer@12854
   777
@{term "G\<turnstile>accclass \<preceq>\<^sub>C declclass membr"} since in case both classes are the
schirmer@12854
   778
same the other condition @{term "(pid (declclass membr) = pid accclass)"}
schirmer@12854
   779
holds anyway.
schirmer@12854
   780
*} 
schirmer@12854
   781
schirmer@12854
   782
text {* Like in case of overriding, the static and dynamic accessibility 
schirmer@12854
   783
of members is not uniform.
schirmer@12854
   784
\begin{itemize}
schirmer@12854
   785
\item Statically the class/interface of the member must be accessible for the
schirmer@12854
   786
      member to be accessible. During runtime this is not necessary. For
schirmer@12854
   787
      Example, if a class is accessible and we are allowed to access a member
schirmer@12854
   788
      of this class (statically) we expect that we can access this member in 
schirmer@12854
   789
      an arbitrary subclass (during runtime). It's not intended to restrict
schirmer@12854
   790
      the access to accessible subclasses during runtime.
schirmer@12854
   791
\item Statically the member we want to access must be "member of" the class.
schirmer@12854
   792
      Dynamically it must only be "member in" the class.
schirmer@12854
   793
\end{itemize} 
schirmer@12854
   794
*} 
schirmer@12854
   795
berghofe@23747
   796
inductive
berghofe@21765
   797
  accessible_fromR :: "prog \<Rightarrow> qtname \<Rightarrow> (qtname \<times> memberdecl) \<Rightarrow> qtname \<Rightarrow> bool"
berghofe@21765
   798
  and accessible_from :: "prog \<Rightarrow> (qtname \<times> memberdecl) \<Rightarrow> qtname \<Rightarrow> qtname \<Rightarrow> bool"
berghofe@21765
   799
    ("_ \<turnstile> _ of _ accessible'_from _" [61,61,61,61] 60)
berghofe@21765
   800
  and method_accessible_from :: "prog \<Rightarrow> (qtname \<times> mdecl) \<Rightarrow> qtname \<Rightarrow> qtname \<Rightarrow> bool"
berghofe@21765
   801
    ("_ \<turnstile>Method _ of _ accessible'_from _" [61,61,61,61] 60)
berghofe@21765
   802
  for G :: prog and accclass :: qtname
berghofe@21765
   803
where
berghofe@21765
   804
  "G\<turnstile>membr of cls accessible_from accclass \<equiv> accessible_fromR G accclass membr cls"
schirmer@12854
   805
wenzelm@25143
   806
| "G\<turnstile>Method m of cls accessible_from accclass \<equiv> accessible_fromR G accclass (methdMembr m) cls"
schirmer@12854
   807
wenzelm@35067
   808
| Immediate:  "!!membr class.
wenzelm@35067
   809
               \<lbrakk>G\<turnstile>membr member_of class;
berghofe@21765
   810
                G\<turnstile>(Class class) accessible_in (pid accclass);
berghofe@21765
   811
                G\<turnstile>membr in class permits_acc_from accclass 
berghofe@21765
   812
               \<rbrakk> \<Longrightarrow> G\<turnstile>membr of class accessible_from accclass"
schirmer@12854
   813
wenzelm@35067
   814
| Overriding: "!!membr class C new old supr.
wenzelm@35067
   815
               \<lbrakk>G\<turnstile>membr member_of class;
berghofe@21765
   816
                G\<turnstile>(Class class) accessible_in (pid accclass);
berghofe@21765
   817
                membr=(C,mdecl new);
berghofe@21765
   818
                G\<turnstile>(C,new) overrides\<^sub>S old; 
haftmann@22426
   819
                G\<turnstile>class \<prec>\<^sub>C supr;
haftmann@22426
   820
                G\<turnstile>Method old of supr accessible_from accclass
berghofe@21765
   821
               \<rbrakk>\<Longrightarrow> G\<turnstile>membr of class accessible_from accclass"
schirmer@12854
   822
wenzelm@35067
   823
abbreviation
schirmer@12854
   824
methd_accessible_from:: 
schirmer@12854
   825
 "prog \<Rightarrow> sig \<Rightarrow> (qtname \<times> methd) \<Rightarrow> qtname \<Rightarrow> qtname \<Rightarrow> bool"
schirmer@12854
   826
                 ("_ \<turnstile>Methd _ _ of _ accessible'_from _" [61,61,61,61,61] 60)
wenzelm@35067
   827
 where
wenzelm@35067
   828
 "G\<turnstile>Methd s m of cls accessible_from accclass ==
wenzelm@35067
   829
   G\<turnstile>(method s m) of cls accessible_from accclass"
schirmer@12854
   830
wenzelm@35067
   831
abbreviation
schirmer@12854
   832
field_accessible_from:: 
schirmer@12854
   833
 "prog \<Rightarrow> vname \<Rightarrow> (qtname \<times> field) \<Rightarrow> qtname \<Rightarrow> qtname \<Rightarrow> bool"
schirmer@12854
   834
                 ("_ \<turnstile>Field _  _ of _ accessible'_from _" [61,61,61,61,61] 60)
wenzelm@35067
   835
 where
wenzelm@35067
   836
 "G\<turnstile>Field fn f of C accessible_from accclass ==
wenzelm@35067
   837
  G\<turnstile>(fieldm fn f) of C accessible_from accclass"
schirmer@12854
   838
berghofe@23747
   839
inductive
berghofe@21765
   840
  dyn_accessible_fromR :: "prog \<Rightarrow> qtname \<Rightarrow> (qtname \<times> memberdecl) \<Rightarrow> qtname \<Rightarrow> bool"
berghofe@21765
   841
  and dyn_accessible_from' ::  "prog \<Rightarrow> (qtname \<times> memberdecl) \<Rightarrow> qtname \<Rightarrow> qtname \<Rightarrow> bool"
berghofe@21765
   842
    ("_ \<turnstile> _ in _ dyn'_accessible'_from _" [61,61,61,61] 60)
berghofe@21765
   843
  and method_dyn_accessible_from :: "prog \<Rightarrow> (qtname \<times> mdecl) \<Rightarrow> qtname \<Rightarrow> qtname \<Rightarrow> bool"
berghofe@21765
   844
    ("_ \<turnstile>Method _ in _ dyn'_accessible'_from _" [61,61,61,61] 60)
berghofe@21765
   845
  for G :: prog and accclass :: qtname
berghofe@21765
   846
where
berghofe@21765
   847
  "G\<turnstile>membr in C dyn_accessible_from accC \<equiv> dyn_accessible_fromR G accC membr C"
schirmer@12854
   848
wenzelm@25143
   849
| "G\<turnstile>Method m in C dyn_accessible_from accC \<equiv> dyn_accessible_fromR G accC (methdMembr m) C"
schirmer@12854
   850
wenzelm@35067
   851
| Immediate:  "!!class. \<lbrakk>G\<turnstile>membr member_in class;
berghofe@21765
   852
                G\<turnstile>membr in class permits_acc_from accclass 
berghofe@21765
   853
               \<rbrakk> \<Longrightarrow> G\<turnstile>membr in class dyn_accessible_from accclass"
schirmer@12854
   854
wenzelm@35067
   855
| Overriding: "!!class. \<lbrakk>G\<turnstile>membr member_in class;
berghofe@21765
   856
                membr=(C,mdecl new);
berghofe@21765
   857
                G\<turnstile>(C,new) overrides old; 
haftmann@22426
   858
                G\<turnstile>class \<prec>\<^sub>C supr;
haftmann@22426
   859
                G\<turnstile>Method old in supr dyn_accessible_from accclass
berghofe@21765
   860
               \<rbrakk>\<Longrightarrow> G\<turnstile>membr in class dyn_accessible_from accclass"
schirmer@12854
   861
wenzelm@35067
   862
abbreviation
schirmer@12854
   863
methd_dyn_accessible_from:: 
schirmer@12854
   864
 "prog \<Rightarrow> sig \<Rightarrow> (qtname \<times> methd) \<Rightarrow> qtname \<Rightarrow> qtname \<Rightarrow> bool"
schirmer@12854
   865
             ("_ \<turnstile>Methd _ _ in _ dyn'_accessible'_from _" [61,61,61,61,61] 60)
wenzelm@35067
   866
 where
wenzelm@35067
   867
 "G\<turnstile>Methd s m in C dyn_accessible_from accC ==
wenzelm@35067
   868
  G\<turnstile>(method s m) in C dyn_accessible_from accC"  
schirmer@12854
   869
wenzelm@35067
   870
abbreviation
schirmer@12854
   871
field_dyn_accessible_from:: 
schirmer@12854
   872
 "prog \<Rightarrow> vname \<Rightarrow> (qtname \<times> field) \<Rightarrow> qtname \<Rightarrow> qtname \<Rightarrow> bool"
schirmer@12854
   873
         ("_ \<turnstile>Field _ _ in _ dyn'_accessible'_from _" [61,61,61,61,61] 60)
wenzelm@35067
   874
 where
wenzelm@35067
   875
 "G\<turnstile>Field fn f in dynC dyn_accessible_from accC ==
wenzelm@35067
   876
  G\<turnstile>(fieldm fn f) in dynC dyn_accessible_from accC"
schirmer@12854
   877
schirmer@12854
   878
schirmer@12854
   879
lemma accessible_from_commonD: "G\<turnstile>m of C accessible_from S
schirmer@12854
   880
 \<Longrightarrow> G\<turnstile>m member_of C \<and> G\<turnstile>(Class C) accessible_in (pid S)"
schirmer@12854
   881
by (auto elim: accessible_fromR.induct)
schirmer@12854
   882
schirmer@12925
   883
lemma unique_declaration: 
schirmer@12925
   884
 "\<lbrakk>G\<turnstile>m declared_in C;  G\<turnstile>n declared_in C; memberid m = memberid n \<rbrakk> 
schirmer@12925
   885
  \<Longrightarrow> m = n"
schirmer@12925
   886
apply (cases m)
schirmer@12925
   887
apply (cases n,
schirmer@12925
   888
        auto simp add: declared_in_def cdeclaredmethd_def cdeclaredfield_def)+
schirmer@12925
   889
done
schirmer@12925
   890
schirmer@12854
   891
lemma declared_not_undeclared:
schirmer@12854
   892
  "G\<turnstile>m declared_in C \<Longrightarrow> \<not> G\<turnstile> memberid m undeclared_in C"
schirmer@12854
   893
by (cases m) (auto simp add: declared_in_def undeclared_in_def)
schirmer@12854
   894
schirmer@12925
   895
lemma undeclared_not_declared:
schirmer@12925
   896
 "G\<turnstile> memberid m undeclared_in C \<Longrightarrow> \<not> G\<turnstile> m declared_in C" 
schirmer@12925
   897
by (cases m) (auto simp add: declared_in_def undeclared_in_def)
schirmer@12925
   898
schirmer@12854
   899
lemma not_undeclared_declared:
schirmer@12854
   900
  "\<not> G\<turnstile> membr_id undeclared_in C \<Longrightarrow> (\<exists> m. G\<turnstile>m declared_in C \<and> 
schirmer@12854
   901
                                           membr_id = memberid m)"
schirmer@12854
   902
proof -
schirmer@12854
   903
  assume not_undecl:"\<not> G\<turnstile> membr_id undeclared_in C"
schirmer@12854
   904
  show ?thesis (is "?P membr_id")
schirmer@12854
   905
  proof (cases membr_id)
schirmer@12854
   906
    case (fid vname)
schirmer@12854
   907
    with not_undecl
schirmer@12854
   908
    obtain fld where
schirmer@12854
   909
      "G\<turnstile>fdecl (vname,fld) declared_in C" 
schirmer@12854
   910
      by (auto simp add: undeclared_in_def declared_in_def
schirmer@12854
   911
                         cdeclaredfield_def)
schirmer@12854
   912
    with fid show ?thesis 
schirmer@12854
   913
      by auto
schirmer@12854
   914
  next
schirmer@12854
   915
    case (mid sig)
schirmer@12854
   916
    with not_undecl
schirmer@12854
   917
    obtain mthd where
schirmer@12854
   918
      "G\<turnstile>mdecl (sig,mthd) declared_in C" 
schirmer@12854
   919
      by (auto simp add: undeclared_in_def declared_in_def
schirmer@12854
   920
                         cdeclaredmethd_def)
schirmer@12854
   921
    with mid show ?thesis 
schirmer@12854
   922
      by auto
schirmer@12854
   923
  qed
schirmer@12854
   924
qed
schirmer@12854
   925
schirmer@12854
   926
lemma unique_declared_in:
schirmer@12854
   927
 "\<lbrakk>G\<turnstile>m declared_in C; G\<turnstile>n declared_in C; memberid m = memberid n\<rbrakk>
schirmer@12854
   928
 \<Longrightarrow> m = n"
schirmer@12854
   929
by (auto simp add: declared_in_def cdeclaredmethd_def cdeclaredfield_def
schirmer@12854
   930
            split: memberdecl.splits)
schirmer@12854
   931
schirmer@12854
   932
lemma unique_member_of: 
wenzelm@12937
   933
  assumes n: "G\<turnstile>n member_of C" and  
schirmer@12854
   934
          m: "G\<turnstile>m member_of C" and
schirmer@12854
   935
       eqid: "memberid n = memberid m"
wenzelm@12937
   936
  shows "n=m"
schirmer@12854
   937
proof -
schirmer@12854
   938
  from n m eqid  
schirmer@12854
   939
  show "n=m"
schirmer@12854
   940
  proof (induct)
berghofe@21765
   941
    case (Immediate n C)
schirmer@12854
   942
    assume member_n: "G\<turnstile> mbr n declared_in C" "declclass n = C"
schirmer@12854
   943
    assume eqid: "memberid n = memberid m"
schirmer@12854
   944
    assume "G \<turnstile> m member_of C"
schirmer@12854
   945
    then show "n=m"
schirmer@12854
   946
    proof (cases)
berghofe@34990
   947
      case Immediate
berghofe@34990
   948
      with eqid member_n
schirmer@12854
   949
      show ?thesis
wenzelm@32960
   950
        by (cases n, cases m) 
schirmer@12854
   951
           (auto simp add: declared_in_def 
schirmer@12854
   952
                           cdeclaredmethd_def cdeclaredfield_def
schirmer@12854
   953
                    split: memberdecl.splits)
schirmer@12854
   954
    next
berghofe@34990
   955
      case Inherited
schirmer@12854
   956
      with eqid member_n
schirmer@12854
   957
      show ?thesis
wenzelm@32960
   958
        by (cases n) (auto dest: declared_not_undeclared)
schirmer@12854
   959
    qed
schirmer@12854
   960
  next
berghofe@21765
   961
    case (Inherited n C S)
schirmer@12854
   962
    assume undecl: "G\<turnstile> memberid n undeclared_in C"
haftmann@35416
   963
    assume  super: "G\<turnstile>C\<prec>\<^sub>C1S"
schirmer@12854
   964
    assume    hyp: "\<lbrakk>G \<turnstile> m member_of S; memberid n = memberid m\<rbrakk> \<Longrightarrow> n = m"
schirmer@12854
   965
    assume   eqid: "memberid n = memberid m"
schirmer@12854
   966
    assume "G \<turnstile> m member_of C"
schirmer@12854
   967
    then show "n=m"
schirmer@12854
   968
    proof (cases)
schirmer@12854
   969
      case Immediate
schirmer@12854
   970
      then have "G\<turnstile> mbr m declared_in C" by simp
schirmer@12854
   971
      with eqid undecl
schirmer@12854
   972
      show ?thesis
wenzelm@32960
   973
        by (cases m) (auto dest: declared_not_undeclared)
schirmer@12854
   974
    next
schirmer@12854
   975
      case Inherited 
schirmer@12854
   976
      with super have "G \<turnstile> m member_of S"
wenzelm@32960
   977
        by (auto dest!: subcls1D)
schirmer@12854
   978
      with eqid hyp
schirmer@12854
   979
      show ?thesis 
wenzelm@32960
   980
        by blast
schirmer@12854
   981
    qed
schirmer@12854
   982
  qed
schirmer@12854
   983
qed
schirmer@12854
   984
schirmer@12854
   985
lemma member_of_is_classD: "G\<turnstile>m member_of C \<Longrightarrow> is_class G C"
schirmer@12854
   986
proof (induct set: members)
berghofe@21765
   987
  case (Immediate m C)
schirmer@12854
   988
  assume "G\<turnstile> mbr m declared_in C"
schirmer@12854
   989
  then show "is_class G C"
schirmer@12854
   990
    by (cases "mbr m")
schirmer@12854
   991
       (auto simp add: declared_in_def cdeclaredmethd_def cdeclaredfield_def)
schirmer@12854
   992
next
berghofe@21765
   993
  case (Inherited m C S)  
haftmann@35416
   994
  assume "G\<turnstile>C\<prec>\<^sub>C1S" and "is_class G S"
schirmer@12854
   995
  then show "is_class G C"
schirmer@12854
   996
    by - (rule subcls_is_class2,auto)
schirmer@12854
   997
qed
schirmer@12854
   998
schirmer@12854
   999
lemma member_of_declC: 
schirmer@12854
  1000
 "G\<turnstile>m member_of C 
schirmer@12854
  1001
  \<Longrightarrow> G\<turnstile>mbr m declared_in (declclass m)"
schirmer@12854
  1002
by (induct set: members) auto
schirmer@12854
  1003
schirmer@12854
  1004
lemma member_of_member_of_declC:
schirmer@12854
  1005
 "G\<turnstile>m member_of C 
schirmer@12854
  1006
  \<Longrightarrow> G\<turnstile>m member_of (declclass m)"
schirmer@12854
  1007
by (auto dest: member_of_declC intro: members.Immediate)
schirmer@12854
  1008
schirmer@12854
  1009
lemma member_of_class_relation:
schirmer@12854
  1010
  "G\<turnstile>m member_of C \<Longrightarrow> G\<turnstile>C \<preceq>\<^sub>C declclass m"
schirmer@12854
  1011
proof (induct set: members)
berghofe@21765
  1012
  case (Immediate m C)
schirmer@12854
  1013
  then show "G\<turnstile>C \<preceq>\<^sub>C declclass m" by simp
schirmer@12854
  1014
next
berghofe@21765
  1015
  case (Inherited m C S)
schirmer@12854
  1016
  then show "G\<turnstile>C \<preceq>\<^sub>C declclass m" 
schirmer@12854
  1017
    by (auto dest: r_into_rtrancl intro: rtrancl_trans)
schirmer@12854
  1018
qed
schirmer@12854
  1019
schirmer@12854
  1020
lemma member_in_class_relation:
schirmer@12854
  1021
  "G\<turnstile>m member_in C \<Longrightarrow> G\<turnstile>C \<preceq>\<^sub>C declclass m"
schirmer@12854
  1022
by (auto dest: member_inD member_of_class_relation
schirmer@12854
  1023
        intro: rtrancl_trans)
schirmer@12854
  1024
schirmer@12962
  1025
lemma stat_override_declclasses_relation: 
haftmann@35416
  1026
"\<lbrakk>G\<turnstile>(declclass new) \<prec>\<^sub>C1 superNew; G \<turnstile>Method old member_of superNew \<rbrakk>
schirmer@12962
  1027
\<Longrightarrow> G\<turnstile>(declclass new) \<prec>\<^sub>C (declclass old)"
schirmer@12962
  1028
apply (rule trancl_rtrancl_trancl)
schirmer@12962
  1029
apply (erule r_into_trancl)
schirmer@12962
  1030
apply (cases old)
schirmer@12962
  1031
apply (auto dest: member_of_class_relation)
schirmer@12962
  1032
done
schirmer@12962
  1033
schirmer@12962
  1034
lemma stat_overrides_commonD:
schirmer@12962
  1035
"\<lbrakk>G\<turnstile>new overrides\<^sub>S old\<rbrakk> \<Longrightarrow>  
schirmer@12962
  1036
  declclass new \<noteq> Object \<and> \<not> is_static new \<and> msig new = msig old \<and> 
schirmer@12962
  1037
  G\<turnstile>(declclass new) \<prec>\<^sub>C (declclass old) \<and>
schirmer@12962
  1038
  G\<turnstile>Method new declared_in (declclass new) \<and>   
schirmer@12962
  1039
  G\<turnstile>Method old declared_in (declclass old)"
schirmer@12962
  1040
apply (induct set: stat_overridesR) 
schirmer@12962
  1041
apply (frule (1) stat_override_declclasses_relation) 
schirmer@12962
  1042
apply (auto intro: trancl_trans)
schirmer@12962
  1043
done
schirmer@12962
  1044
schirmer@12854
  1045
lemma member_of_Package: 
schirmer@12854
  1046
 "\<lbrakk>G\<turnstile>m member_of C; accmodi m = Package\<rbrakk> 
schirmer@12854
  1047
  \<Longrightarrow> pid (declclass m) = pid C" 
schirmer@12854
  1048
proof -
schirmer@12854
  1049
  assume   member: "G\<turnstile>m member_of C"
schirmer@12854
  1050
  then show " accmodi m = Package \<Longrightarrow> ?thesis" (is "PROP ?P m C")
schirmer@12854
  1051
  proof (induct rule: members.induct)
schirmer@12854
  1052
    fix C m
schirmer@12854
  1053
    assume     C: "declclass m = C"
schirmer@12854
  1054
    then show "pid (declclass m) = pid C"
schirmer@12854
  1055
      by simp
schirmer@12854
  1056
  next
schirmer@12854
  1057
    fix C S m  
schirmer@12854
  1058
    assume inheritable: "G \<turnstile> m inheritable_in pid C"
schirmer@12854
  1059
    assume         hyp: "PROP ?P m S" and
schirmer@12854
  1060
           package_acc: "accmodi m = Package" 
schirmer@12854
  1061
    with inheritable package_acc hyp
schirmer@12854
  1062
    show "pid (declclass m) = pid C" 
schirmer@12854
  1063
      by (auto simp add: inheritable_in_def)
schirmer@12854
  1064
  qed
schirmer@12854
  1065
qed
schirmer@12854
  1066
schirmer@12925
  1067
lemma member_in_declC: "G\<turnstile>m member_in C\<Longrightarrow> G\<turnstile>m member_in (declclass m)"
schirmer@12925
  1068
proof -
schirmer@12925
  1069
  assume member_in_C:  "G\<turnstile>m member_in C"
schirmer@12925
  1070
  from member_in_C
schirmer@12925
  1071
  obtain provC where
schirmer@12925
  1072
    subclseq_C_provC: "G\<turnstile> C \<preceq>\<^sub>C provC" and
schirmer@12925
  1073
     member_of_provC: "G \<turnstile> m member_of provC"
schirmer@12925
  1074
    by (auto simp add: member_in_def)
schirmer@12925
  1075
  from member_of_provC
schirmer@12925
  1076
  have "G \<turnstile> m member_of declclass m"
schirmer@12925
  1077
    by (rule member_of_member_of_declC)
schirmer@12925
  1078
  moreover
schirmer@12925
  1079
  from member_in_C
schirmer@12925
  1080
  have "G\<turnstile>C \<preceq>\<^sub>C declclass m"
schirmer@12925
  1081
    by (rule member_in_class_relation)
schirmer@12925
  1082
  ultimately
schirmer@12925
  1083
  show ?thesis
schirmer@12925
  1084
    by (auto simp add: member_in_def)
schirmer@12925
  1085
qed
schirmer@12925
  1086
schirmer@12854
  1087
lemma dyn_accessible_from_commonD: "G\<turnstile>m in C dyn_accessible_from S
schirmer@12854
  1088
 \<Longrightarrow> G\<turnstile>m member_in C"
schirmer@12854
  1089
by (auto elim: dyn_accessible_fromR.induct)
schirmer@12854
  1090
schirmer@12854
  1091
lemma no_Private_stat_override: 
schirmer@12854
  1092
 "\<lbrakk>G\<turnstile>new overrides\<^sub>S old\<rbrakk> \<Longrightarrow> accmodi old \<noteq> Private"
schirmer@12854
  1093
by (induct set:  stat_overridesR) (auto simp add: inheritable_in_def)
schirmer@12854
  1094
schirmer@12854
  1095
lemma no_Private_override: "\<lbrakk>G\<turnstile>new overrides old\<rbrakk> \<Longrightarrow> accmodi old \<noteq> Private"
schirmer@12854
  1096
by (induct set: overridesR) (auto simp add: inheritable_in_def)
schirmer@12854
  1097
schirmer@12854
  1098
lemma permits_acc_inheritance:
schirmer@14030
  1099
 "\<lbrakk>G\<turnstile>m in statC permits_acc_from accC; G\<turnstile>dynC \<preceq>\<^sub>C statC
schirmer@14030
  1100
  \<rbrakk> \<Longrightarrow> G\<turnstile>m in dynC permits_acc_from accC"
schirmer@12854
  1101
by (cases "accmodi m")
schirmer@12854
  1102
   (auto simp add: permits_acc_def
schirmer@12854
  1103
            intro: subclseq_trans) 
schirmer@12854
  1104
schirmer@12925
  1105
lemma permits_acc_static_declC:
schirmer@14030
  1106
 "\<lbrakk>G\<turnstile>m in C permits_acc_from accC; G\<turnstile>m member_in C; is_static m
schirmer@14030
  1107
  \<rbrakk> \<Longrightarrow> G\<turnstile>m in (declclass m) permits_acc_from accC"
schirmer@12925
  1108
by (cases "accmodi m") (auto simp add: permits_acc_def)
schirmer@12925
  1109
schirmer@12925
  1110
lemma dyn_accessible_from_static_declC: 
wenzelm@12937
  1111
  assumes  acc_C: "G\<turnstile>m in C dyn_accessible_from accC" and
schirmer@12925
  1112
           static: "is_static m"
wenzelm@12937
  1113
  shows "G\<turnstile>m in (declclass m) dyn_accessible_from accC"
schirmer@12925
  1114
proof -
schirmer@12925
  1115
  from acc_C static
schirmer@12925
  1116
  show "G\<turnstile>m in (declclass m) dyn_accessible_from accC"
schirmer@12925
  1117
  proof (induct)
berghofe@21765
  1118
    case (Immediate m C)
schirmer@12925
  1119
    then show ?case 
schirmer@12925
  1120
      by (auto intro!: dyn_accessible_fromR.Immediate
schirmer@12925
  1121
                 dest: member_in_declC permits_acc_static_declC) 
schirmer@12925
  1122
  next 
berghofe@21765
  1123
    case (Overriding m C declCNew new old sup)
schirmer@12925
  1124
    then have "\<not> is_static m"
schirmer@12925
  1125
      by (auto dest: overrides_commonD)
schirmer@12925
  1126
    moreover
schirmer@12925
  1127
    assume "is_static m"
schirmer@12925
  1128
    ultimately show ?case 
schirmer@12925
  1129
      by contradiction
schirmer@12925
  1130
  qed
schirmer@12925
  1131
qed
schirmer@12925
  1132
schirmer@12854
  1133
lemma field_accessible_fromD:
schirmer@12854
  1134
 "\<lbrakk>G\<turnstile>membr of C accessible_from accC;is_field membr\<rbrakk> 
schirmer@12854
  1135
  \<Longrightarrow> G\<turnstile>membr member_of C \<and>
schirmer@12854
  1136
      G\<turnstile>(Class C) accessible_in (pid accC) \<and>
schirmer@14030
  1137
      G\<turnstile>membr in C permits_acc_from accC"
schirmer@12854
  1138
by (cases set: accessible_fromR)
schirmer@12854
  1139
   (auto simp add: is_field_def split: memberdecl.splits) 
schirmer@12854
  1140
schirmer@12854
  1141
lemma field_accessible_from_permits_acc_inheritance:
schirmer@12854
  1142
"\<lbrakk>G\<turnstile>membr of statC accessible_from accC; is_field membr; G \<turnstile> dynC \<preceq>\<^sub>C statC\<rbrakk>
schirmer@14030
  1143
\<Longrightarrow> G\<turnstile>membr in dynC permits_acc_from accC"
schirmer@12854
  1144
by (auto dest: field_accessible_fromD intro: permits_acc_inheritance)
schirmer@12854
  1145
schirmer@12854
  1146
schirmer@12854
  1147
(*
schirmer@12854
  1148
lemma accessible_Package:
schirmer@12854
  1149
 "\<lbrakk>G \<turnstile> m of C accessible_from S;accmodi m = Package;
schirmer@12854
  1150
   \<And> new old. G\<turnstile>new overrides\<^sub>S old \<Longrightarrow> accmodi old \<le> accmodi new\<rbrakk>
schirmer@12854
  1151
  \<Longrightarrow> pid S = pid C \<and> pid C = pid (declclass m)"
schirmer@12854
  1152
proof -
schirmer@12854
  1153
  assume wf: "\<And> new old. G\<turnstile>new overrides\<^sub>S old \<Longrightarrow> accmodi old \<le> accmodi new"
schirmer@12854
  1154
  assume "G \<turnstile> m of C accessible_from S"
schirmer@12854
  1155
  then show "accmodi m = Package \<Longrightarrow> pid S = pid C \<and> pid C = pid (declclass m)"
schirmer@12854
  1156
    (is "?Pack m \<Longrightarrow> ?P C m")
schirmer@12854
  1157
  proof (induct rule: accessible_fromR.induct)
schirmer@12854
  1158
    fix C m
schirmer@12854
  1159
    assume "G\<turnstile>m member_of C"
schirmer@14030
  1160
           "G \<turnstile> m in C permits_acc_from S"
schirmer@12854
  1161
           "accmodi m = Package"      
schirmer@12854
  1162
    then show "?P C m"
schirmer@12854
  1163
      by (auto dest: member_of_Package simp add: permits_acc_def)
schirmer@12854
  1164
  next
schirmer@12854
  1165
    fix declC C new newm old Sup
schirmer@12854
  1166
    assume member_new: "G \<turnstile> new member_of C" and 
schirmer@12854
  1167
                acc_C: "G \<turnstile> Class C accessible_in pid S" and
schirmer@12854
  1168
                  new: "new = (declC, mdecl newm)" and
schirmer@12854
  1169
             override: "G \<turnstile> (declC, newm) overrides\<^sub>S old" and
schirmer@12854
  1170
         subcls_C_Sup: "G\<turnstile>C \<prec>\<^sub>C Sup" and
schirmer@12854
  1171
              acc_old: "G \<turnstile> methdMembr old of Sup accessible_from S" and
schirmer@12854
  1172
                  hyp: "?Pack (methdMembr old) \<Longrightarrow> ?P Sup (methdMembr old)" and
schirmer@12854
  1173
          accmodi_new: "accmodi new = Package"
schirmer@12854
  1174
    from override wf 
schirmer@12854
  1175
    have accmodi_weaken: "accmodi old \<le> accmodi newm"
schirmer@12854
  1176
      by (cases old,cases newm) auto
schirmer@12854
  1177
    from override new
schirmer@12854
  1178
    have "accmodi old \<noteq> Private"
schirmer@12854
  1179
      by (simp add: no_Private_stat_override)
schirmer@12854
  1180
    with accmodi_weaken accmodi_new new
schirmer@12854
  1181
    have accmodi_old: "accmodi old = Package"
schirmer@12854
  1182
      by (cases "accmodi old") (auto simp add: le_acc_def less_acc_def) 
schirmer@12854
  1183
    with hyp 
schirmer@12854
  1184
    have P_sup: "?P Sup (methdMembr old)"
schirmer@12854
  1185
      by (simp)
schirmer@12854
  1186
    from wf override new accmodi_old accmodi_new
schirmer@12854
  1187
    have eq_pid_new_old: "pid (declclass new) = pid (declclass old)"
schirmer@12854
  1188
      by (auto dest: stat_override_Package) 
schirmer@12854
  1189
    from member_new accmodi_new
schirmer@12854
  1190
    have "pid (declclass new) = pid C"
schirmer@12854
  1191
      by (auto dest: member_of_Package)
schirmer@12854
  1192
    with eq_pid_new_old P_sup show "?P C new"
schirmer@12854
  1193
      by auto
schirmer@12854
  1194
  qed
schirmer@12854
  1195
qed
schirmer@12854
  1196
*)
schirmer@13688
  1197
schirmer@12854
  1198
lemma accessible_fieldD: 
schirmer@12854
  1199
 "\<lbrakk>G\<turnstile>membr of C accessible_from accC; is_field membr\<rbrakk>
schirmer@12854
  1200
 \<Longrightarrow> G\<turnstile>membr member_of C \<and>
schirmer@12854
  1201
     G\<turnstile>(Class C) accessible_in (pid accC) \<and>
schirmer@14030
  1202
     G\<turnstile>membr in C permits_acc_from accC"
schirmer@12854
  1203
by (induct rule: accessible_fromR.induct) (auto dest: is_fieldD)
schirmer@12854
  1204
      
schirmer@12854
  1205
schirmer@12854
  1206
schirmer@12854
  1207
lemma member_of_Private:
schirmer@12854
  1208
"\<lbrakk>G\<turnstile>m member_of C; accmodi m = Private\<rbrakk> \<Longrightarrow> declclass m = C"
schirmer@12854
  1209
by (induct set: members) (auto simp add: inheritable_in_def)
schirmer@12854
  1210
schirmer@12854
  1211
lemma member_of_subclseq_declC:
schirmer@12854
  1212
  "G\<turnstile>m member_of C \<Longrightarrow> G\<turnstile>C \<preceq>\<^sub>C declclass m"
schirmer@12854
  1213
by (induct set: members) (auto dest: r_into_rtrancl intro: rtrancl_trans)
schirmer@12854
  1214
schirmer@12854
  1215
lemma member_of_inheritance:
wenzelm@12937
  1216
  assumes       m: "G\<turnstile>m member_of D" and
schirmer@12854
  1217
     subclseq_D_C: "G\<turnstile>D \<preceq>\<^sub>C C" and
schirmer@12854
  1218
     subclseq_C_m: "G\<turnstile>C \<preceq>\<^sub>C declclass m" and
schirmer@12854
  1219
               ws: "ws_prog G" 
wenzelm@12937
  1220
  shows "G\<turnstile>m member_of C"
schirmer@12854
  1221
proof -
schirmer@12854
  1222
  from m subclseq_D_C subclseq_C_m
schirmer@12854
  1223
  show ?thesis
schirmer@12854
  1224
  proof (induct)
berghofe@21765
  1225
    case (Immediate m D)
schirmer@12854
  1226
    assume "declclass m = D" and
schirmer@12854
  1227
           "G\<turnstile>D\<preceq>\<^sub>C C" and "G\<turnstile>C\<preceq>\<^sub>C declclass m"
schirmer@12854
  1228
    with ws have "D=C" 
schirmer@12854
  1229
      by (auto intro: subclseq_acyclic)
schirmer@12854
  1230
    with Immediate 
schirmer@12854
  1231
    show "G\<turnstile>m member_of C"
schirmer@12854
  1232
      by (auto intro: members.Immediate)
schirmer@12854
  1233
  next
berghofe@21765
  1234
    case (Inherited m D S)
schirmer@12854
  1235
    assume member_of_D_props: 
schirmer@12854
  1236
            "G \<turnstile> m inheritable_in pid D" 
schirmer@12854
  1237
            "G\<turnstile> memberid m undeclared_in D"  
schirmer@12854
  1238
            "G \<turnstile> Class S accessible_in pid D" 
schirmer@12854
  1239
            "G \<turnstile> m member_of S"
haftmann@35416
  1240
    assume super: "G\<turnstile>D\<prec>\<^sub>C1S"
schirmer@12854
  1241
    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
  1242
    assume subclseq_C_m: "G\<turnstile>C\<preceq>\<^sub>C declclass m"
schirmer@12854
  1243
    assume "G\<turnstile>D\<preceq>\<^sub>C C"
schirmer@12854
  1244
    then show "G\<turnstile>m member_of C"
schirmer@12854
  1245
    proof (cases rule: subclseq_cases)
schirmer@12854
  1246
      case Eq
schirmer@12854
  1247
      assume "D=C" 
schirmer@12854
  1248
      with super member_of_D_props 
schirmer@12854
  1249
      show ?thesis
wenzelm@32960
  1250
        by (auto intro: members.Inherited)
schirmer@12854
  1251
    next
schirmer@12854
  1252
      case Subcls
schirmer@12854
  1253
      assume "G\<turnstile>D\<prec>\<^sub>C C"
schirmer@12854
  1254
      with super 
schirmer@12854
  1255
      have "G\<turnstile>S\<preceq>\<^sub>C C"
wenzelm@32960
  1256
        by (auto dest: subcls1D subcls_superD)
schirmer@12854
  1257
      with subclseq_C_m hyp show ?thesis
wenzelm@32960
  1258
        by blast
schirmer@12854
  1259
    qed
schirmer@12854
  1260
  qed
schirmer@12854
  1261
qed
schirmer@12854
  1262
schirmer@12854
  1263
lemma member_of_subcls:
wenzelm@12937
  1264
  assumes     old: "G\<turnstile>old member_of C" and 
schirmer@12854
  1265
              new: "G\<turnstile>new member_of D" and
schirmer@12854
  1266
             eqid: "memberid new = memberid old" and
schirmer@12854
  1267
     subclseq_D_C: "G\<turnstile>D \<preceq>\<^sub>C C" and 
schirmer@12854
  1268
   subcls_new_old: "G\<turnstile>declclass new \<prec>\<^sub>C declclass old" and
schirmer@12854
  1269
               ws: "ws_prog G"
wenzelm@12937
  1270
  shows "G\<turnstile>D \<prec>\<^sub>C C"
schirmer@12854
  1271
proof -
schirmer@12854
  1272
  from old 
schirmer@12854
  1273
  have subclseq_C_old: "G\<turnstile>C \<preceq>\<^sub>C declclass old"
schirmer@12854
  1274
    by (auto dest: member_of_subclseq_declC)
schirmer@12854
  1275
  from new 
schirmer@12854
  1276
  have subclseq_D_new: "G\<turnstile>D \<preceq>\<^sub>C declclass new"
schirmer@12854
  1277
    by (auto dest: member_of_subclseq_declC)
schirmer@12854
  1278
  from subcls_new_old ws
schirmer@12854
  1279
  have neq_new_old: "new\<noteq>old"
schirmer@12854
  1280
    by (cases new,cases old) (auto dest: subcls_irrefl)
schirmer@12854
  1281
  from subclseq_D_new subclseq_D_C
schirmer@12854
  1282
  have "G\<turnstile>(declclass new) \<preceq>\<^sub>C C \<or> G\<turnstile>C \<preceq>\<^sub>C (declclass new)" 
schirmer@12854
  1283
    by (rule subcls_compareable)
schirmer@12854
  1284
  then have "G\<turnstile>(declclass new) \<preceq>\<^sub>C C"
schirmer@12854
  1285
  proof
schirmer@12854
  1286
    assume "G\<turnstile>declclass new\<preceq>\<^sub>C C" then show ?thesis .
schirmer@12854
  1287
  next
schirmer@12854
  1288
    assume "G\<turnstile>C \<preceq>\<^sub>C (declclass new)"
schirmer@12854
  1289
    with new subclseq_D_C ws 
schirmer@12854
  1290
    have "G\<turnstile>new member_of C"
schirmer@12854
  1291
      by (blast intro: member_of_inheritance)
schirmer@12854
  1292
    with eqid old 
schirmer@12854
  1293
    have "new=old"
schirmer@12854
  1294
      by (blast intro: unique_member_of)
schirmer@12854
  1295
    with neq_new_old 
schirmer@12854
  1296
    show ?thesis
schirmer@12854
  1297
      by contradiction
schirmer@12854
  1298
  qed
schirmer@12854
  1299
  then show ?thesis
schirmer@12854
  1300
  proof (cases rule: subclseq_cases)
schirmer@12854
  1301
    case Eq
schirmer@12854
  1302
    assume "declclass new = C"
schirmer@12854
  1303
    with new have "G\<turnstile>new member_of C"
schirmer@12854
  1304
      by (auto dest: member_of_member_of_declC)
schirmer@12854
  1305
    with eqid old 
schirmer@12854
  1306
    have "new=old"
schirmer@12854
  1307
      by (blast intro: unique_member_of)
schirmer@12854
  1308
    with neq_new_old 
schirmer@12854
  1309
    show ?thesis
schirmer@12854
  1310
      by contradiction
schirmer@12854
  1311
  next
schirmer@12854
  1312
    case Subcls
schirmer@12854
  1313
    assume "G\<turnstile>declclass new\<prec>\<^sub>C C"
schirmer@12854
  1314
    with subclseq_D_new
schirmer@12854
  1315
    show "G\<turnstile>D\<prec>\<^sub>C C"
schirmer@12854
  1316
      by (rule rtrancl_trancl_trancl)
schirmer@12854
  1317
  qed
schirmer@12854
  1318
qed
schirmer@12854
  1319
schirmer@12854
  1320
corollary member_of_overrides_subcls:
schirmer@12854
  1321
 "\<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
  1322
   G,sig\<turnstile>new overrides old; ws_prog G\<rbrakk>
schirmer@12854
  1323
 \<Longrightarrow> G\<turnstile>D \<prec>\<^sub>C C"
schirmer@12854
  1324
by (drule overrides_commonD) (auto intro: member_of_subcls)    
schirmer@12854
  1325
schirmer@12854
  1326
corollary member_of_stat_overrides_subcls:
schirmer@12854
  1327
 "\<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
  1328
   G,sig\<turnstile>new overrides\<^sub>S old; ws_prog G\<rbrakk>
schirmer@12854
  1329
 \<Longrightarrow> G\<turnstile>D \<prec>\<^sub>C C"
schirmer@12854
  1330
by (drule stat_overrides_commonD) (auto intro: member_of_subcls)    
schirmer@12854
  1331
schirmer@12854
  1332
schirmer@12854
  1333
schirmer@12854
  1334
lemma inherited_field_access: 
wenzelm@12937
  1335
  assumes stat_acc: "G\<turnstile>membr of statC accessible_from accC" and
schirmer@12854
  1336
          is_field: "is_field membr" and 
schirmer@12854
  1337
          subclseq: "G \<turnstile> dynC \<preceq>\<^sub>C statC"
wenzelm@12937
  1338
  shows "G\<turnstile>membr in dynC dyn_accessible_from accC"
schirmer@12854
  1339
proof -
schirmer@12854
  1340
  from stat_acc is_field subclseq 
schirmer@12854
  1341
  show ?thesis
schirmer@12854
  1342
    by (auto dest: accessible_fieldD 
schirmer@12925
  1343
            intro: dyn_accessible_fromR.Immediate 
schirmer@12854
  1344
                   member_inI 
schirmer@12854
  1345
                   permits_acc_inheritance)
schirmer@12854
  1346
qed
schirmer@12854
  1347
schirmer@12854
  1348
lemma accessible_inheritance:
wenzelm@12937
  1349
  assumes stat_acc: "G\<turnstile>m of statC accessible_from accC" and
schirmer@12854
  1350
          subclseq: "G\<turnstile>dynC \<preceq>\<^sub>C statC" and
schirmer@12854
  1351
       member_dynC: "G\<turnstile>m member_of dynC" and
schirmer@12854
  1352
          dynC_acc: "G\<turnstile>(Class dynC) accessible_in (pid accC)"
wenzelm@12937
  1353
  shows "G\<turnstile>m of dynC accessible_from accC"
schirmer@12854
  1354
proof -
schirmer@12854
  1355
  from stat_acc
schirmer@12854
  1356
  have member_statC: "G\<turnstile>m member_of statC" 
schirmer@12854
  1357
    by (auto dest: accessible_from_commonD)
schirmer@12854
  1358
  from stat_acc
schirmer@12854
  1359
  show ?thesis
schirmer@12854
  1360
  proof (cases)
schirmer@12925
  1361
    case Immediate
schirmer@12854
  1362
    with member_dynC member_statC subclseq dynC_acc
schirmer@12854
  1363
    show ?thesis
schirmer@12925
  1364
      by (auto intro: accessible_fromR.Immediate permits_acc_inheritance)
schirmer@12854
  1365
  next
schirmer@12925
  1366
    case Overriding
schirmer@12854
  1367
    with member_dynC subclseq dynC_acc
schirmer@12854
  1368
    show ?thesis
schirmer@12925
  1369
      by (auto intro: accessible_fromR.Overriding rtrancl_trancl_trancl)
schirmer@12854
  1370
  qed
schirmer@12854
  1371
qed
schirmer@12854
  1372
schirmer@12854
  1373
section "fields and methods"
schirmer@12854
  1374
schirmer@12854
  1375
schirmer@12854
  1376
types
schirmer@12854
  1377
  fspec = "vname \<times> qtname"
schirmer@12854
  1378
schirmer@12854
  1379
translations 
wenzelm@35431
  1380
  (type) "fspec" <= (type) "vname \<times> qtname" 
schirmer@12854
  1381
haftmann@35416
  1382
definition imethds :: "prog \<Rightarrow> qtname \<Rightarrow> (sig,qtname \<times> mhead) tables" where
schirmer@12854
  1383
"imethds G I 
krauss@35440
  1384
  \<equiv> iface_rec G I  
schirmer@12854
  1385
              (\<lambda>I i ts. (Un_tables ts) \<oplus>\<oplus> 
nipkow@30235
  1386
                        (Option.set \<circ> table_of (map (\<lambda>(s,m). (s,I,m)) (imethods i))))"
schirmer@12854
  1387
text {* methods of an interface, with overriding and inheritance, cf. 9.2 *}
schirmer@12854
  1388
haftmann@35416
  1389
definition accimethds :: "prog \<Rightarrow> pname \<Rightarrow> qtname \<Rightarrow> (sig,qtname \<times> mhead) tables" where
schirmer@12854
  1390
"accimethds G pack I
schirmer@12854
  1391
  \<equiv> if G\<turnstile>Iface I accessible_in pack 
schirmer@12854
  1392
       then imethds G I
schirmer@12854
  1393
       else \<lambda> k. {}"
schirmer@12854
  1394
text {* only returns imethds if the interface is accessible *}
schirmer@12854
  1395
haftmann@35416
  1396
definition methd :: "prog \<Rightarrow> qtname  \<Rightarrow> (sig,qtname \<times> methd) table" where
schirmer@12854
  1397
schirmer@12854
  1398
"methd G C 
krauss@35440
  1399
 \<equiv> class_rec G C empty
schirmer@12854
  1400
             (\<lambda>C c subcls_mthds. 
schirmer@12854
  1401
               filter_tab (\<lambda>sig m. G\<turnstile>C inherits method sig m)
schirmer@12854
  1402
                          subcls_mthds 
schirmer@12854
  1403
               ++ 
schirmer@12854
  1404
               table_of (map (\<lambda>(s,m). (s,C,m)) (methods c)))"
schirmer@12854
  1405
text {* @{term "methd G C"}: methods of a class C (statically visible from C), 
schirmer@12854
  1406
     with inheritance and hiding cf. 8.4.6;
schirmer@12854
  1407
     Overriding is captured by @{text dynmethd}.
schirmer@12854
  1408
     Every new method with the same signature coalesces the
schirmer@12854
  1409
     method of a superclass. *}
schirmer@12854
  1410
haftmann@35416
  1411
definition accmethd :: "prog \<Rightarrow> qtname \<Rightarrow> qtname  \<Rightarrow> (sig,qtname \<times> methd) table" where
schirmer@12854
  1412
"accmethd G S C 
schirmer@12854
  1413
 \<equiv> filter_tab (\<lambda>sig m. G\<turnstile>method sig m of C accessible_from S) 
schirmer@12854
  1414
              (methd G C)"
schirmer@12854
  1415
text {* @{term "accmethd G S C"}: only those methods of @{term "methd G C"}, 
schirmer@12854
  1416
        accessible from S *}
schirmer@12854
  1417
schirmer@12854
  1418
text {* Note the class component in the accessibility filter. The class where
schirmer@12854
  1419
    method @{term m} is declared (@{term declC}) isn't necessarily accessible 
schirmer@12854
  1420
    from the current scope @{term S}. The method can be made accessible 
schirmer@12854
  1421
    through inheritance, too.
schirmer@12854
  1422
    So we must test accessibility of method @{term m} of class @{term C} 
schirmer@12854
  1423
    (not @{term "declclass m"}) *}
schirmer@12854
  1424
haftmann@35416
  1425
definition dynmethd :: "prog  \<Rightarrow> qtname \<Rightarrow> qtname \<Rightarrow> (sig,qtname \<times> methd) table" where
schirmer@12854
  1426
"dynmethd G statC dynC  
schirmer@12854
  1427
  \<equiv> \<lambda> sig. 
schirmer@12854
  1428
     (if G\<turnstile>dynC \<preceq>\<^sub>C statC
schirmer@12854
  1429
        then (case methd G statC sig of
schirmer@12854
  1430
                None \<Rightarrow> None
schirmer@12854
  1431
              | Some statM 
krauss@35440
  1432
                  \<Rightarrow> (class_rec G dynC empty
schirmer@12854
  1433
                       (\<lambda>C c subcls_mthds. 
schirmer@12854
  1434
                          subcls_mthds
schirmer@12854
  1435
                          ++
schirmer@12854
  1436
                          (filter_tab 
schirmer@12854
  1437
                            (\<lambda> _ dynM. G,sig\<turnstile>dynM overrides statM \<or> dynM=statM)
schirmer@12854
  1438
                            (methd G C) ))
schirmer@12854
  1439
                      ) sig
schirmer@12854
  1440
              )
schirmer@12854
  1441
        else None)"
schirmer@13688
  1442
schirmer@12854
  1443
text {* @{term "dynmethd G statC dynC"}: dynamic method lookup of a reference 
schirmer@12854
  1444
        with dynamic class @{term dynC} and static class @{term statC} *}
schirmer@12854
  1445
text {* Note some kind of duality between @{term methd} and @{term dynmethd} 
schirmer@12854
  1446
        in the @{term class_rec} arguments. Whereas @{term methd} filters the 
schirmer@12854
  1447
        subclass methods (to get only the inherited ones), @{term dynmethd} 
schirmer@12854
  1448
        filters the new methods (to get only those methods which actually
schirmer@12854
  1449
        override the methods of the static class) *}
schirmer@12854
  1450
haftmann@35416
  1451
definition dynimethd :: "prog \<Rightarrow> qtname \<Rightarrow> qtname \<Rightarrow> (sig,qtname \<times> methd) table" where
schirmer@12854
  1452
"dynimethd G I dynC 
schirmer@12854
  1453
  \<equiv> \<lambda> sig. if imethds G I sig \<noteq> {}
schirmer@12854
  1454
               then methd G dynC sig
schirmer@12854
  1455
               else dynmethd G Object dynC sig"
schirmer@12854
  1456
text {* @{term "dynimethd G I dynC"}: dynamic method lookup of a reference with 
schirmer@12854
  1457
        dynamic class dynC and static interface type I *}
schirmer@12854
  1458
text {* 
schirmer@12854
  1459
   When calling an interface method, we must distinguish if the method signature
schirmer@12854
  1460
   was defined in the interface or if it must be an Object method in the other
schirmer@12854
  1461
   case. If it was an interface method we search the class hierarchy
schirmer@12854
  1462
   starting at the dynamic class of the object up to Object to find the 
schirmer@12854
  1463
   first matching method (@{term methd}). Since all interface methods have 
schirmer@12854
  1464
   public access the method can't be coalesced due to some odd visibility 
schirmer@12854
  1465
   effects like in case of dynmethd. The method will be inherited or 
schirmer@12854
  1466
   overridden in all classes from the first class implementing the interface 
schirmer@12854
  1467
   down to the actual dynamic class.
schirmer@12854
  1468
 *}
schirmer@12854
  1469
haftmann@35416
  1470
definition dynlookup :: "prog  \<Rightarrow> ref_ty \<Rightarrow> qtname \<Rightarrow> (sig,qtname \<times> methd) table" where
schirmer@12854
  1471
"dynlookup G statT dynC
schirmer@12854
  1472
  \<equiv> (case statT of
schirmer@12854
  1473
       NullT        \<Rightarrow> empty
schirmer@12854
  1474
     | IfaceT I     \<Rightarrow> dynimethd G I      dynC
schirmer@12854
  1475
     | ClassT statC \<Rightarrow> dynmethd  G statC  dynC
schirmer@12854
  1476
     | ArrayT ty    \<Rightarrow> dynmethd  G Object dynC)"
schirmer@12854
  1477
text {* @{term "dynlookup G statT dynC"}: dynamic lookup of a method within the 
schirmer@12854
  1478
    static reference type statT and the dynamic class dynC. 
schirmer@12854
  1479
    In a wellformd context statT will not be NullT and in case
schirmer@12854
  1480
    statT is an array type, dynC=Object *}
schirmer@12854
  1481
haftmann@35416
  1482
definition fields :: "prog \<Rightarrow> qtname \<Rightarrow> ((vname \<times> qtname) \<times> field) list" where
schirmer@12854
  1483
"fields G C 
krauss@35440
  1484
  \<equiv> class_rec G C [] (\<lambda>C c ts. map (\<lambda>(n,t). ((n,C),t)) (cfields c) @ ts)"
schirmer@12854
  1485
text {* @{term "fields G C"} 
schirmer@12854
  1486
     list of fields of a class, including all the fields of the superclasses
schirmer@12854
  1487
     (private, inherited and hidden ones) not only the accessible ones
schirmer@12854
  1488
     (an instance of a object allocates all these fields *}
schirmer@12854
  1489
haftmann@35416
  1490
definition accfield :: "prog \<Rightarrow> qtname \<Rightarrow> qtname \<Rightarrow> (vname, qtname  \<times>  field) table" where
schirmer@12854
  1491
"accfield G S C
schirmer@12854
  1492
  \<equiv> let field_tab = table_of((map (\<lambda>((n,d),f).(n,(d,f)))) (fields G C))
schirmer@12854
  1493
    in filter_tab (\<lambda>n (declC,f). G\<turnstile> (declC,fdecl (n,f)) of C accessible_from S)
schirmer@12854
  1494
                  field_tab"
schirmer@12854
  1495
text  {* @{term "accfield G C S"}: fields of a class @{term C} which are 
schirmer@12854
  1496
         accessible from scope of class
schirmer@12854
  1497
         @{term S} with inheritance and hiding, cf. 8.3 *}
schirmer@12854
  1498
text {* note the class component in the accessibility filter (see also 
schirmer@12854
  1499
        @{term methd}).
schirmer@12854
  1500
   The class declaring field @{term f} (@{term declC}) isn't necessarily 
schirmer@12854
  1501
   accessible from scope @{term S}. The field can be made visible through 
schirmer@12854
  1502
   inheritance, too. So we must test accessibility of field @{term f} of class 
schirmer@12854
  1503
   @{term C} (not @{term "declclass f"}) *} 
schirmer@12854
  1504
haftmann@35416
  1505
definition is_methd :: "prog \<Rightarrow> qtname  \<Rightarrow> sig \<Rightarrow> bool" where
schirmer@12854
  1506
 "is_methd G \<equiv> \<lambda>C sig. is_class G C \<and> methd G C sig \<noteq> None"
schirmer@12854
  1507
haftmann@35416
  1508
definition efname :: "((vname \<times> qtname) \<times> field) \<Rightarrow> (vname \<times> qtname)" where
schirmer@12854
  1509
"efname \<equiv> fst"
schirmer@12854
  1510
schirmer@12854
  1511
lemma efname_simp[simp]:"efname (n,f) = n"
schirmer@12854
  1512
by (simp add: efname_def) 
schirmer@12854
  1513
schirmer@12854
  1514
schirmer@12854
  1515
subsection "imethds"
schirmer@12854
  1516
schirmer@12854
  1517
lemma imethds_rec: "\<lbrakk>iface G I = Some i; ws_prog G\<rbrakk> \<Longrightarrow>  
schirmer@12854
  1518
  imethds G I = Un_tables ((\<lambda>J. imethds  G J)`set (isuperIfs i)) \<oplus>\<oplus>  
nipkow@30235
  1519
                      (Option.set \<circ> table_of (map (\<lambda>(s,mh). (s,I,mh)) (imethods i)))"
schirmer@12854
  1520
apply (unfold imethds_def)
schirmer@12854
  1521
apply (rule iface_rec [THEN trans])
schirmer@12854
  1522
apply auto
schirmer@12854
  1523
done
schirmer@12854
  1524
schirmer@12854
  1525
schirmer@12854
  1526
(* local lemma *)
schirmer@12854
  1527
lemma imethds_norec:
schirmer@12854
  1528
  "\<lbrakk>iface G md = Some i; ws_prog G; table_of (imethods i) sig = Some mh\<rbrakk> \<Longrightarrow>  
schirmer@12854
  1529
  (md, mh) \<in> imethds G md sig"
schirmer@12854
  1530
apply (subst imethds_rec)
schirmer@12854
  1531
apply assumption+
schirmer@12854
  1532
apply (rule iffD2)
schirmer@12854
  1533
apply (rule overrides_t_Some_iff)
schirmer@12854
  1534
apply (rule disjI1)
schirmer@12854
  1535
apply (auto elim: table_of_map_SomeI)
schirmer@12854
  1536
done
schirmer@12854
  1537
schirmer@12854
  1538
lemma imethds_declI: "\<lbrakk>m \<in> imethds G I sig; ws_prog G; is_iface G I\<rbrakk> \<Longrightarrow> 
schirmer@12854
  1539
  (\<exists>i. iface G (decliface m) = Some i \<and> 
schirmer@12854
  1540
  table_of (imethods i) sig = Some (mthd m)) \<and>  
schirmer@12854
  1541
  (I,decliface m) \<in> (subint1 G)^* \<and> m \<in> imethds G (decliface m) sig"
wenzelm@24038
  1542
apply (erule rev_mp)
schirmer@12854
  1543
apply (rule ws_subint1_induct, assumption, assumption)
schirmer@12854
  1544
apply (subst imethds_rec, erule conjunct1, assumption)
schirmer@12854
  1545
apply (force elim: imethds_norec intro: rtrancl_into_rtrancl2)
schirmer@12854
  1546
done
schirmer@12854
  1547
schirmer@12854
  1548
lemma imethds_cases [consumes 3, case_names NewMethod InheritedMethod]:
wenzelm@12937
  1549
  assumes im: "im \<in> imethds G I sig" and  
schirmer@12854
  1550
         ifI: "iface G I = Some i" and
schirmer@12854
  1551
          ws: "ws_prog G" and
schirmer@12854
  1552
     hyp_new:  "table_of (map (\<lambda>(s, mh). (s, I, mh)) (imethods i)) sig 
schirmer@12854
  1553
                = Some im \<Longrightarrow> P" and
schirmer@12854
  1554
     hyp_inh: "\<And> J. \<lbrakk>J \<in> set (isuperIfs i); im \<in> imethds G J sig\<rbrakk> \<Longrightarrow> P"
wenzelm@12937
  1555
  shows P
schirmer@12854
  1556
proof -
schirmer@12854
  1557
  from ifI ws im hyp_new hyp_inh
schirmer@12854
  1558
  show "P"
schirmer@12854
  1559
    by (auto simp add: imethds_rec)
schirmer@12854
  1560
qed
schirmer@12854
  1561
schirmer@12854
  1562
subsection "accimethd"
schirmer@12854
  1563
schirmer@12854
  1564
lemma accimethds_simp [simp]: 
schirmer@12854
  1565
"G\<turnstile>Iface I accessible_in pack \<Longrightarrow> accimethds G pack I = imethds G I"
schirmer@12854
  1566
by (simp add: accimethds_def)
schirmer@12854
  1567
schirmer@12854
  1568
lemma accimethdsD:
schirmer@12854
  1569
 "im \<in> accimethds G pack I sig 
schirmer@12854
  1570
  \<Longrightarrow> im \<in> imethds G I sig \<and> G\<turnstile>Iface I accessible_in pack"
schirmer@12854
  1571
by (auto simp add: accimethds_def)
schirmer@12854
  1572
schirmer@12854
  1573
lemma accimethdsI: 
schirmer@12854
  1574
"\<lbrakk>im \<in> imethds G I sig;G\<turnstile>Iface I accessible_in pack\<rbrakk>
schirmer@12854
  1575
 \<Longrightarrow> im \<in> accimethds G pack I sig"
schirmer@12854
  1576
by simp
schirmer@12854
  1577
schirmer@12854
  1578
subsection "methd"
schirmer@12854
  1579
schirmer@12854
  1580
lemma methd_rec: "\<lbrakk>class G C = Some c; ws_prog G\<rbrakk> \<Longrightarrow>  
schirmer@12854
  1581
  methd G C 
schirmer@12854
  1582
    = (if C = Object 
schirmer@12854
  1583
          then empty 
schirmer@12854
  1584
          else filter_tab (\<lambda>sig m. G\<turnstile>C inherits method sig m)
schirmer@12854
  1585
                          (methd G (super c))) 
schirmer@12854
  1586
      ++ table_of (map (\<lambda>(s,m). (s,C,m)) (methods c))"
schirmer@12854
  1587
apply (unfold methd_def)
schirmer@12854
  1588
apply (erule class_rec [THEN trans], assumption)
schirmer@12854
  1589
apply (simp)
schirmer@12854
  1590
done
schirmer@12854
  1591
schirmer@12854
  1592
(* local lemma *)
schirmer@12854
  1593
lemma methd_norec: 
schirmer@12854
  1594
 "\<lbrakk>class G declC = Some c; ws_prog G;table_of (methods c) sig = Some m\<rbrakk> 
schirmer@12854
  1595
  \<Longrightarrow> methd G declC sig = Some (declC, m)"
schirmer@12854
  1596
apply (simp only: methd_rec)
nipkow@14025
  1597
apply (rule disjI1 [THEN map_add_Some_iff [THEN iffD2]])
schirmer@12854
  1598
apply (auto elim: table_of_map_SomeI)
schirmer@12854
  1599
done
schirmer@12854
  1600
schirmer@12854
  1601
schirmer@12854
  1602
lemma methd_declC: 
schirmer@12854
  1603
"\<lbrakk>methd G C sig = Some m; ws_prog G;is_class G C\<rbrakk> \<Longrightarrow>
schirmer@12854
  1604
 (\<exists>d. class G (declclass m)=Some d \<and> table_of (methods d) sig=Some (mthd m)) \<and> 
schirmer@12854
  1605
 G\<turnstile>C \<preceq>\<^sub>C (declclass m) \<and> methd G (declclass m) sig = Some m"   
wenzelm@24038
  1606
apply (erule rev_mp)
schirmer@12854
  1607
apply (rule ws_subcls1_induct, assumption, assumption)
schirmer@12854
  1608
apply (subst methd_rec, assumption)
schirmer@12854
  1609
apply (case_tac "Ca=Object")
schirmer@12854
  1610
apply   (force elim: methd_norec )
schirmer@12854
  1611
schirmer@12854
  1612
apply   simp
schirmer@12854
  1613
apply   (case_tac "table_of (map (\<lambda>(s, m). (s, Ca, m)) (methods c)) sig")
schirmer@12854
  1614
apply     (force intro: rtrancl_into_rtrancl2)
schirmer@12854
  1615
schirmer@12854
  1616
apply     (auto intro: methd_norec)
schirmer@12854
  1617
done
schirmer@12854
  1618
schirmer@12854
  1619
lemma methd_inheritedD:
schirmer@12854
  1620
  "\<lbrakk>class G C = Some c; ws_prog G;methd G C sig = Some m\<rbrakk>
schirmer@12854
  1621
  \<Longrightarrow>  (declclass m \<noteq> C \<longrightarrow> G \<turnstile>C inherits method sig m)"
schirmer@12854
  1622
by (auto simp add: methd_rec)
schirmer@12854
  1623
schirmer@12854
  1624
lemma methd_diff_cls:
schirmer@12854
  1625
"\<lbrakk>ws_prog G; is_class G C; is_class G D;
schirmer@12854
  1626
 methd G C sig = m; methd G D sig = n; m\<noteq>n
schirmer@12854
  1627
\<rbrakk> \<Longrightarrow> C\<noteq>D"
schirmer@12854
  1628
by (auto simp add: methd_rec)
schirmer@12854
  1629
schirmer@12854
  1630
lemma method_declared_inI: 
schirmer@12854
  1631
 "\<lbrakk>table_of (methods c) sig = Some m; class G C = Some c\<rbrakk>
schirmer@12854
  1632
  \<Longrightarrow> G\<turnstile>mdecl (sig,m) declared_in C"
schirmer@12854
  1633
by (auto simp add: cdeclaredmethd_def declared_in_def)
schirmer@12854
  1634
schirmer@12854
  1635
lemma methd_declared_in_declclass: 
schirmer@12854
  1636
 "\<lbrakk>methd G C sig = Some m; ws_prog G;is_class G C\<rbrakk> 
schirmer@12854
  1637
 \<Longrightarrow> G\<turnstile>Methd sig m declared_in (declclass m)"
schirmer@12854
  1638
by (auto dest: methd_declC method_declared_inI)
schirmer@12854
  1639
schirmer@12854
  1640
lemma member_methd:
wenzelm@12937
  1641
  assumes member_of: "G\<turnstile>Methd sig m member_of C" and
schirmer@12854
  1642
                 ws: "ws_prog G"
wenzelm@12937
  1643
  shows "methd G C sig = Some m"
schirmer@12854
  1644
proof -
schirmer@12854
  1645
  from member_of 
schirmer@12854
  1646
  have iscls_C: "is_class G C" 
schirmer@12854
  1647
    by (rule member_of_is_classD)
schirmer@12854
  1648
  from iscls_C ws member_of
schirmer@12854
  1649
  show ?thesis (is "?Methd C")
schirmer@12854
  1650
  proof (induct rule: ws_class_induct')
schirmer@12854
  1651
    case (Object co)
schirmer@12854
  1652
    assume "G \<turnstile>Methd sig m member_of Object"
schirmer@12854
  1653
    then have "G\<turnstile>Methd sig m declared_in Object \<and> declclass m = Object"
schirmer@12854
  1654
      by (cases set: members) (cases m, auto dest: subcls1D)
schirmer@12854
  1655
    with ws Object 
schirmer@12854
  1656
    show "?Methd Object"
schirmer@12854
  1657
      by (cases m)
schirmer@12854
  1658
         (auto simp add: declared_in_def cdeclaredmethd_def methd_rec
schirmer@12854
  1659
                  intro:  table_of_mapconst_SomeI)
schirmer@12854
  1660
  next
schirmer@12854
  1661
    case (Subcls C c)
schirmer@12854
  1662
    assume clsC: "class G C = Some c" and
schirmer@12854
  1663
      neq_C_Obj: "C \<noteq> Object" and
schirmer@12854
  1664
            hyp: "G \<turnstile>Methd sig m member_of super c \<Longrightarrow> ?Methd (super c)" and
schirmer@12854
  1665
      member_of: "G \<turnstile>Methd sig m member_of C"
schirmer@12854
  1666
    from member_of
schirmer@12854
  1667
    show "?Methd C"
schirmer@12854
  1668
    proof (cases)
berghofe@34990
  1669
      case Immediate
schirmer@12854
  1670
      with clsC 
schirmer@12854
  1671
      have "table_of (map (\<lambda>(s, m). (s, C, m)) (methods c)) sig = Some m"
wenzelm@32960
  1672
        by (cases m)
wenzelm@32960
  1673
           (auto simp add: declared_in_def cdeclaredmethd_def
wenzelm@32960
  1674
                    intro: table_of_mapconst_SomeI)
schirmer@12854
  1675
      with clsC neq_C_Obj ws 
schirmer@12854
  1676
      show ?thesis
wenzelm@32960
  1677
        by (simp add: methd_rec)
schirmer@12854
  1678
    next
berghofe@34990
  1679
      case (Inherited S)
schirmer@12854
  1680
      with clsC
berghofe@34990
  1681
      have  undecl: "G\<turnstile>mid sig undeclared_in C" and
schirmer@12854
  1682
             super: "G \<turnstile>Methd sig m member_of (super c)"
wenzelm@32960
  1683
        by (auto dest: subcls1D)
berghofe@34990
  1684
      from clsC undecl 
schirmer@12854
  1685
      have "table_of (map (\<lambda>(s, m). (s, C, m)) (methods c)) sig = None"
wenzelm@32960
  1686
        by (auto simp add: undeclared_in_def cdeclaredmethd_def
wenzelm@32960
  1687
                    intro: table_of_mapconst_NoneI)
schirmer@12854
  1688
      moreover
schirmer@12854
  1689
      from Inherited have "G \<turnstile> C inherits (method sig m)"
wenzelm@32960
  1690
        by (auto simp add: inherits_def)
schirmer@12854
  1691
      moreover
schirmer@12854
  1692
      note clsC neq_C_Obj ws super hyp 
schirmer@12854
  1693
      ultimately
schirmer@12854
  1694
      show ?thesis
wenzelm@32960
  1695
        by (auto simp add: methd_rec intro: filter_tab_SomeI)
schirmer@12854
  1696
    qed
schirmer@12854
  1697
  qed
schirmer@12854
  1698
qed
schirmer@12854
  1699
schirmer@12854
  1700
(*unused*)
schirmer@12854
  1701
lemma finite_methd:"ws_prog G \<Longrightarrow> finite {methd G C sig |sig C. is_class G C}"
schirmer@12854
  1702
apply (rule finite_is_class [THEN finite_SetCompr2])
schirmer@12854
  1703
apply (intro strip)
schirmer@12854
  1704
apply (erule_tac ws_subcls1_induct, assumption)
schirmer@12854
  1705
apply (subst methd_rec)
schirmer@12854
  1706
apply (assumption)
nipkow@14025
  1707
apply (auto intro!: finite_range_map_of finite_range_filter_tab finite_range_map_of_map_add)
schirmer@12854
  1708
done
schirmer@12854
  1709
schirmer@12854
  1710
lemma finite_dom_methd:
schirmer@12854
  1711
 "\<lbrakk>ws_prog G; is_class G C\<rbrakk> \<Longrightarrow> finite (dom (methd G C))"
schirmer@12854
  1712
apply (erule_tac ws_subcls1_induct)
schirmer@12854
  1713
apply assumption
schirmer@12854
  1714
apply (subst methd_rec)
schirmer@12854
  1715
apply (assumption)
schirmer@12854
  1716
apply (auto intro!: finite_dom_map_of finite_dom_filter_tab)
schirmer@12854
  1717
done
schirmer@12854
  1718
schirmer@12854
  1719
schirmer@12854
  1720
subsection "accmethd"
schirmer@12854
  1721
schirmer@12854
  1722
lemma accmethd_SomeD:
schirmer@12854
  1723
"accmethd G S C sig = Some m
schirmer@12854
  1724
 \<Longrightarrow> methd G C sig = Some m \<and> G\<turnstile>method sig m of C accessible_from S"
schirmer@12854
  1725
by (auto simp add: accmethd_def dest: filter_tab_SomeD)
schirmer@12854
  1726
schirmer@12854
  1727
lemma accmethd_SomeI:
schirmer@12854
  1728
"\<lbrakk>methd G C sig = Some m; G\<turnstile>method sig m of C accessible_from S\<rbrakk> 
schirmer@12854
  1729
 \<Longrightarrow> accmethd G S C sig = Some m"
schirmer@12854
  1730
by (auto simp add: accmethd_def intro: filter_tab_SomeI)
schirmer@12854
  1731
schirmer@12854
  1732
lemma accmethd_declC: 
schirmer@12854
  1733
"\<lbrakk>accmethd G S C sig = Some m; ws_prog G; is_class G C\<rbrakk> \<Longrightarrow>
schirmer@12854
  1734
 (\<exists>d. class G (declclass m)=Some d \<and> 
schirmer@12854
  1735
  table_of (methods d) sig=Some (mthd m)) \<and> 
schirmer@12854
  1736
 G\<turnstile>C \<preceq>\<^sub>C (declclass m) \<and> methd G (declclass m) sig = Some m \<and> 
schirmer@12854
  1737
 G\<turnstile>method sig m of C accessible_from S"
schirmer@12854
  1738
by (auto dest: accmethd_SomeD methd_declC accmethd_SomeI)
schirmer@12854
  1739
schirmer@12854
  1740
schirmer@12854
  1741
lemma finite_dom_accmethd:
schirmer@12854
  1742
 "\<lbrakk>ws_prog G; is_class G C\<rbrakk> \<Longrightarrow> finite (dom (accmethd G S C))"
schirmer@12854
  1743
by (auto simp add: accmethd_def intro: finite_dom_filter_tab finite_dom_methd)
schirmer@12854
  1744
schirmer@12854
  1745
schirmer@12854
  1746
subsection "dynmethd"
schirmer@12854
  1747
schirmer@12854
  1748
lemma dynmethd_rec:
schirmer@12854
  1749
"\<lbrakk>class G dynC = Some c; ws_prog G\<rbrakk> \<Longrightarrow>  
schirmer@12854
  1750
 dynmethd G statC dynC sig
schirmer@12854
  1751
   = (if G\<turnstile>dynC \<preceq>\<^sub>C statC
schirmer@12854
  1752
        then (case methd G statC sig of
schirmer@12854
  1753
                None \<Rightarrow> None
schirmer@12854
  1754
              | Some statM 
schirmer@12854
  1755
                  \<Rightarrow> (case methd G dynC sig of
schirmer@12854
  1756
                        None \<Rightarrow> dynmethd G statC (super c) sig
schirmer@12854
  1757
                      | Some dynM \<Rightarrow> 
schirmer@12854
  1758
                          (if G,sig\<turnstile> dynM overrides statM \<or> dynM = statM 
schirmer@12854
  1759
                              then Some dynM
schirmer@12854
  1760
                              else (dynmethd G statC (super c) sig)
schirmer@12854
  1761
                      )))
schirmer@12854
  1762
         else None)" 
schirmer@12854
  1763
   (is "_ \<Longrightarrow> _ \<Longrightarrow> ?Dynmethd_def dynC sig  = ?Dynmethd_rec dynC c sig") 
schirmer@12854
  1764
proof -
schirmer@12854
  1765
  assume clsDynC: "class G dynC = Some c" and 
schirmer@12854
  1766
              ws: "ws_prog G"
schirmer@12854
  1767
  then show "?Dynmethd_def dynC sig  = ?Dynmethd_rec dynC c sig" 
schirmer@12854
  1768
  proof (induct rule: ws_class_induct'')
schirmer@12854
  1769
    case (Object co)
schirmer@12854
  1770
    show "?Dynmethd_def Object sig = ?Dynmethd_rec Object co sig"
schirmer@12854
  1771
    proof (cases "G\<turnstile>Object \<preceq>\<^sub>C statC") 
schirmer@12854
  1772
      case False
schirmer@12854
  1773
      then show ?thesis by (simp add: dynmethd_def)
schirmer@12854
  1774
    next
schirmer@12854
  1775
      case True
schirmer@12854
  1776
      then have eq_statC_Obj: "statC = Object" ..
schirmer@12854
  1777
      show ?thesis 
schirmer@12854
  1778
      proof (cases "methd G statC sig")
wenzelm@32960
  1779
        case None then show ?thesis by (simp add: dynmethd_def)
schirmer@12854
  1780
      next
wenzelm@32960
  1781
        case Some
wenzelm@32960
  1782
        with True Object ws eq_statC_Obj 
wenzelm@32960
  1783
        show ?thesis
wenzelm@32960
  1784
          by (auto simp add: dynmethd_def class_rec
schirmer@12854
  1785
                      intro: filter_tab_SomeI)
schirmer@12854
  1786
      qed
schirmer@12854
  1787
    qed
schirmer@12854
  1788
  next  
schirmer@12854
  1789
    case (Subcls dynC c sc)
schirmer@12854
  1790
    show "?Dynmethd_def dynC sig = ?Dynmethd_rec dynC c sig"
schirmer@12854
  1791
    proof (cases "G\<turnstile>dynC \<preceq>\<^sub>C statC") 
schirmer@12854
  1792
      case False
schirmer@12854
  1793
      then show ?thesis by (simp add: dynmethd_def)
schirmer@12854
  1794
    next
schirmer@12854
  1795
      case True
schirmer@12854
  1796
      note subclseq_dynC_statC = True
schirmer@12854
  1797
      show ?thesis
schirmer@12854
  1798
      proof (cases "methd G statC sig")
wenzelm@32960
  1799
        case None then show ?thesis by (simp add: dynmethd_def)
schirmer@12854
  1800
      next
wenzelm@32960
  1801
        case (Some statM)
wenzelm@32960
  1802
        note statM = Some
wenzelm@32960
  1803
        let "?filter C" = 
schirmer@12854
  1804
              "filter_tab
schirmer@12854
  1805
                (\<lambda>_ dynM. G,sig \<turnstile> dynM overrides statM \<or> dynM = statM)
schirmer@12854
  1806
                (methd G C)"
schirmer@12854
  1807
        let "?class_rec C" =
krauss@35440
  1808
              "(class_rec G C empty
schirmer@12854
  1809
                           (\<lambda>C c subcls_mthds. subcls_mthds ++ (?filter C)))"
wenzelm@32960
  1810
        from statM Subcls ws subclseq_dynC_statC
wenzelm@32960
  1811
        have dynmethd_dynC_def:
schirmer@12854
  1812
             "?Dynmethd_def dynC sig =
schirmer@12854
  1813
                ((?class_rec (super c)) 
schirmer@12854
  1814
                 ++
schirmer@12854
  1815
                (?filter dynC)) sig"
schirmer@12854
  1816
         by (simp (no_asm_simp) only: dynmethd_def class_rec)
wenzelm@32960
  1817
            auto
schirmer@12854
  1818
       show ?thesis
schirmer@12854
  1819
       proof (cases "dynC = statC")
wenzelm@32960
  1820
         case True
wenzelm@32960
  1821
         with subclseq_dynC_statC statM dynmethd_dynC_def
wenzelm@32960
  1822
         have "?Dynmethd_def dynC sig = Some statM"
wenzelm@32960
  1823
           by (auto intro: map_add_find_right filter_tab_SomeI)
wenzelm@32960
  1824
         with subclseq_dynC_statC True Some 
wenzelm@32960
  1825
         show ?thesis
wenzelm@32960
  1826
           by auto
schirmer@12854
  1827
       next
wenzelm@32960
  1828
         case False
wenzelm@32960
  1829
         with subclseq_dynC_statC Subcls 
wenzelm@32960
  1830
         have subclseq_super_statC: "G\<turnstile>(super c) \<preceq>\<^sub>C statC"
wenzelm@32960
  1831
           by (blast dest: subclseq_superD)
wenzelm@32960
  1832
         show ?thesis
wenzelm@32960
  1833
         proof (cases "methd G dynC sig") 
wenzelm@32960
  1834
           case None
wenzelm@32960
  1835
           then have "?filter dynC sig = None"
wenzelm@32960
  1836
             by (rule filter_tab_None)
schirmer@12854
  1837
           then have "?Dynmethd_def dynC sig=?class_rec (super c) sig"
wenzelm@32960
  1838
             by (simp add: dynmethd_dynC_def)
wenzelm@32960
  1839
           with  subclseq_super_statC statM None
wenzelm@32960
  1840
           have "?Dynmethd_def dynC sig = ?Dynmethd_def (super c) sig"
wenzelm@32960
  1841
             by (auto simp add: empty_def dynmethd_def)
schirmer@12854
  1842
           with None subclseq_dynC_statC statM
wenzelm@32960
  1843
           show ?thesis 
wenzelm@32960
  1844
             by simp
wenzelm@32960
  1845
         next
wenzelm@32960
  1846
           case (Some dynM)
wenzelm@32960
  1847
           note dynM = Some
wenzelm@32960
  1848
           let ?Termination = "G \<turnstile> qmdecl sig dynM overrides qmdecl sig statM \<or>
schirmer@12854
  1849
                               dynM = statM"
wenzelm@32960
  1850
           show ?thesis
wenzelm@32960
  1851
           proof (cases "?filter dynC sig")
wenzelm@32960
  1852
             case None
wenzelm@32960
  1853
             with dynM 
wenzelm@32960
  1854
             have no_termination: "\<not> ?Termination"
wenzelm@32960
  1855
               by (simp add: filter_tab_def)
wenzelm@32960
  1856
             from None 
wenzelm@32960
  1857
             have "?Dynmethd_def dynC sig=?class_rec (super c) sig"
wenzelm@32960
  1858
               by (simp add: dynmethd_dynC_def)
wenzelm@32960
  1859
             with subclseq_super_statC statM dynM no_termination
wenzelm@32960
  1860
             show ?thesis
wenzelm@32960
  1861
               by (auto simp add: empty_def dynmethd_def)
wenzelm@32960
  1862
           next
wenzelm@32960
  1863
             case Some
wenzelm@32960
  1864
             with dynM
wenzelm@32960
  1865
             have "termination": "?Termination"
wenzelm@32960
  1866
               by (auto)
wenzelm@32960
  1867
             with Some dynM
wenzelm@32960
  1868
             have "?Dynmethd_def dynC sig=Some dynM"
wenzelm@32960
  1869
              by (auto simp add: dynmethd_dynC_def)
wenzelm@32960
  1870
             with subclseq_super_statC statM dynM "termination"
wenzelm@32960
  1871
             show ?thesis
wenzelm@32960
  1872
               by (auto simp add: dynmethd_def)
wenzelm@32960
  1873
           qed
wenzelm@32960
  1874
         qed
schirmer@12854
  1875
       qed
schirmer@12854
  1876
     qed
schirmer@12854
  1877
   qed
schirmer@12854
  1878
 qed
schirmer@12854
  1879
qed
wenzelm@32960
  1880
               
schirmer@12854
  1881
lemma dynmethd_C_C:"\<lbrakk>is_class G C; ws_prog G\<rbrakk> 
schirmer@12854
  1882
\<Longrightarrow> dynmethd G C C sig = methd G C sig"          
schirmer@12854
  1883
apply (auto simp add: dynmethd_rec)
schirmer@12854
  1884
done
schirmer@12854
  1885
 
schirmer@12854
  1886
lemma dynmethdSomeD: 
schirmer@12854
  1887
 "\<lbrakk>dynmethd G statC dynC sig = Some dynM; is_class G dynC; ws_prog G\<rbrakk> 
schirmer@12854
  1888
  \<Longrightarrow> G\<turnstile>dynC \<preceq>\<^sub>C statC \<and> (\<exists> statM. methd G statC sig = Some statM)"
schirmer@12854
  1889
by (auto simp add: dynmethd_rec)
schirmer@12854
  1890
 
schirmer@12854
  1891
lemma dynmethd_Some_cases [consumes 3, case_names Static Overrides]:
wenzelm@12937
  1892
  assumes      dynM: "dynmethd G statC dynC sig = Some dynM" and
schirmer@12854
  1893
        is_cls_dynC: "is_class G dynC" and
schirmer@12854
  1894
                 ws: "ws_prog G" and
schirmer@12854
  1895
         hyp_static: "methd G statC sig = Some dynM \<Longrightarrow> P" and
schirmer@12854
  1896
       hyp_override: "\<And> statM. \<lbrakk>methd G statC sig = Some statM;dynM\<noteq>statM;
schirmer@12854
  1897
                       G,sig\<turnstile>dynM overrides statM\<rbrakk> \<Longrightarrow> P"
wenzelm@12937
  1898
  shows P
schirmer@12854
  1899
proof -
schirmer@12854
  1900
  from is_cls_dynC obtain dc where clsDynC: "class G dynC = Some dc" by blast
schirmer@12854
  1901
  from clsDynC ws dynM hyp_static hyp_override
schirmer@12854
  1902
  show "P"
schirmer@12854
  1903
  proof (induct rule: ws_class_induct)
schirmer@12854
  1904
    case (Object co)
schirmer@12854
  1905
    with ws  have "statC = Object" 
schirmer@12854
  1906
      by (auto simp add: dynmethd_rec)
schirmer@12854
  1907
    with ws Object show ?thesis by (auto simp add: dynmethd_C_C)
schirmer@12854
  1908
  next
schirmer@12854
  1909
    case (Subcls C c)
schirmer@12854
  1910
    with ws show ?thesis
schirmer@12854
  1911
      by (auto simp add: dynmethd_rec)
schirmer@12854
  1912
  qed
schirmer@12854
  1913
qed
schirmer@12854
  1914
schirmer@12854
  1915
lemma no_override_in_Object:
wenzelm@12937
  1916
  assumes          dynM: "dynmethd G statC dynC sig = Some dynM" and
schirmer@12854
  1917
            is_cls_dynC: "is_class G dynC" and
schirmer@12854
  1918
                     ws: "ws_prog G" and
schirmer@12854
  1919
                  statM: "methd G statC sig = Some statM" and
schirmer@12854
  1920
         neq_dynM_statM: "dynM\<noteq>statM"
wenzelm@12937
  1921
  shows "dynC \<noteq> Object"
schirmer@12854
  1922
proof -
schirmer@12854
  1923
  from is_cls_dynC obtain dc where clsDynC: "class G dynC = Some dc" by blast
schirmer@12854
  1924
  from clsDynC ws dynM statM neq_dynM_statM 
schirmer@12854
  1925
  show ?thesis (is "?P dynC")
schirmer@12854
  1926
  proof (induct rule: ws_class_induct)
schirmer@12854
  1927
    case (Object co)
schirmer@12854
  1928
    with ws  have "statC = Object" 
schirmer@12854
  1929
      by (auto simp add: dynmethd_rec)
schirmer@12854
  1930
    with ws Object show "?P Object" by (auto simp add: dynmethd_C_C)
schirmer@12854
  1931
  next
schirmer@12854
  1932
    case (Subcls dynC c)
schirmer@12854
  1933
    with ws show "?P dynC"
schirmer@12854
  1934
      by (auto simp add: dynmethd_rec)
schirmer@12854
  1935
  qed
schirmer@12854
  1936
qed
schirmer@12854
  1937
schirmer@12854
  1938
schirmer@12854
  1939
lemma dynmethd_Some_rec_cases [consumes 3, 
schirmer@12854
  1940
                               case_names Static Override  Recursion]:
wenzelm@12937
  1941
  assumes          dynM: "dynmethd G statC dynC sig = Some dynM" and
schirmer@12854
  1942
                clsDynC: "class G dynC = Some c" and
schirmer@12854
  1943
                     ws: "ws_prog G" and
schirmer@12854
  1944
             hyp_static: "methd G statC sig = Some dynM \<Longrightarrow> P" and
schirmer@12854
  1945
           hyp_override: "\<And> statM. \<lbrakk>methd G statC sig = Some statM;
schirmer@12854
  1946
                                     methd G dynC sig = Some dynM; statM\<noteq>dynM;
schirmer@12854
  1947
                                     G,sig\<turnstile> dynM overrides statM\<rbrakk> \<Longrightarrow> P" and
schirmer@12854
  1948
schirmer@12854
  1949
          hyp_recursion: "\<lbrakk>dynC\<noteq>Object;
wenzelm@12937
  1950
                           dynmethd G statC (super c) sig = Some dynM\<rbrakk> \<Longrightarrow> P"
wenzelm@12937
  1951
  shows P
schirmer@12854
  1952
proof -
schirmer@12854
  1953
  from clsDynC have "is_class G dynC" by simp
schirmer@12854
  1954
  note no_override_in_Object' = no_override_in_Object [OF dynM this ws]
schirmer@12854
  1955
  from ws clsDynC dynM hyp_static hyp_override hyp_recursion
schirmer@12854
  1956
  show ?thesis
schirmer@12854
  1957
    by (auto simp add: dynmethd_rec dest: no_override_in_Object')
schirmer@12854
  1958
qed
schirmer@12854
  1959
schirmer@12854
  1960
lemma dynmethd_declC: 
schirmer@12854
  1961
"\<lbrakk>dynmethd G statC dynC sig = Some m;
schirmer@12854
  1962
  is_class G statC;ws_prog G
schirmer@12854
  1963
 \<rbrakk> \<Longrightarrow>
schirmer@12854
  1964
  (\<exists>d. class G (declclass m)=Some d \<and> table_of (methods d) sig=Some (mthd m)) \<and>
schirmer@12854
  1965
  G\<turnstile>dynC \<preceq>\<^sub>C (declclass m) \<and> methd G (declclass m) sig = Some m"
schirmer@12854
  1966
proof - 
schirmer@12854
  1967
  assume  is_cls_statC: "is_class G statC" 
schirmer@12854
  1968
  assume            ws: "ws_prog G"  
schirmer@12854
  1969
  assume             m: "dynmethd G statC dynC sig = Some m"
schirmer@12854
  1970
  from m 
schirmer@12854
  1971
  have "G\<turnstile>dynC \<preceq>\<^sub>C statC" by (auto simp add: dynmethd_def)
schirmer@12854
  1972
  from this is_cls_statC 
schirmer@12854
  1973
  have is_cls_dynC: "is_class G dynC" by (rule subcls_is_class2)
schirmer@12854
  1974
  from is_cls_dynC ws m  
schirmer@12854
  1975
  show ?thesis (is "?P dynC") 
schirmer@12854
  1976
  proof (induct rule: ws_class_induct')
schirmer@12854
  1977
    case (Object co)
schirmer@12854
  1978
    with ws have "statC=Object" by (auto simp add: dynmethd_rec)
schirmer@12854
  1979
    with ws Object  
schirmer@12854
  1980
    show "?P Object" 
schirmer@12854
  1981
      by (auto simp add: dynmethd_C_C dest: methd_declC)
schirmer@12854
  1982
  next
schirmer@12854
  1983
    case (Subcls dynC c)
schirmer@12854
  1984
    assume   hyp: "dynmethd G statC (super c) sig = Some m \<Longrightarrow> ?P (super c)" and
schirmer@12854
  1985
         clsDynC: "class G dynC = Some c"  and
schirmer@12854
  1986
              m': "dynmethd G statC dynC sig = Some m" and
schirmer@12854
  1987
    neq_dynC_Obj: "dynC \<noteq> Object"
schirmer@12854
  1988
    from ws this obtain statM where
schirmer@12854
  1989
      subclseq_dynC_statC: "G\<turnstile>dynC \<preceq>\<^sub>C statC" and 
schirmer@12854
  1990
                     statM: "methd G statC sig = Some statM"
schirmer@12854
  1991
      by (blast dest: dynmethdSomeD)
schirmer@12854
  1992
    from clsDynC neq_dynC_Obj 
schirmer@12854
  1993
    have subclseq_dynC_super: "G\<turnstile>dynC \<preceq>\<^sub>C (super c)" 
schirmer@12854
  1994
      by (auto intro: subcls1I) 
schirmer@12854
  1995
    from m' clsDynC ws 
schirmer@12854
  1996
    show "?P dynC"
schirmer@12854
  1997
    proof (cases rule: dynmethd_Some_rec_cases) 
schirmer@12854
  1998
      case Static
schirmer@12854
  1999
      with is_cls_statC ws subclseq_dynC_statC 
schirmer@12854
  2000
      show ?thesis 
wenzelm@32960
  2001
        by (auto intro: rtrancl_trans dest: methd_declC)
schirmer@12854
  2002
    next
schirmer@12854
  2003
      case Override
schirmer@12854
  2004
      with clsDynC ws 
schirmer@12854
  2005
      show ?thesis 
wenzelm@32960
  2006
        by (auto dest: methd_declC)
schirmer@12854
  2007
    next
schirmer@12854
  2008
      case Recursion
schirmer@12854
  2009
      with hyp subclseq_dynC_super 
schirmer@12854
  2010
      show ?thesis 
wenzelm@32960
  2011
        by (auto intro: rtrancl_trans) 
schirmer@12854
  2012
    qed
schirmer@12854
  2013
  qed
schirmer@12854
  2014
qed
schirmer@12854
  2015
schirmer@12854
  2016
lemma methd_Some_dynmethd_Some:
wenzelm@12937
  2017
  assumes     statM: "methd G statC sig = Some statM" and
schirmer@12854
  2018
           subclseq: "G\<turnstile>dynC \<preceq>\<^sub>C statC" and
schirmer@12854
  2019
       is_cls_statC: "is_class G statC" and
schirmer@12854
  2020
                 ws: "ws_prog G"
wenzelm@12937
  2021
  shows "\<exists> dynM. dynmethd G statC dynC sig = Some dynM"
wenzelm@12937
  2022
    (is "?P dynC")
schirmer@12854
  2023
proof -
schirmer@12854
  2024
  from subclseq is_cls_statC 
schirmer@12854
  2025
  have is_cls_dynC: "is_class G dynC" by (rule subcls_is_class2)
schirmer@12854
  2026
  then obtain dc where
schirmer@12854
  2027
    clsDynC: "class G dynC = Some dc" by blast
schirmer@12854
  2028
  from clsDynC ws subclseq 
schirmer@12854
  2029
  show "?thesis"
schirmer@12854
  2030
  proof (induct rule: ws_class_induct)
schirmer@12854
  2031
    case (Object co)
schirmer@12854
  2032
    with ws  have "statC = Object" 
schirmer@12854
  2033
      by (auto)
schirmer@12854
  2034
    with ws Object statM
schirmer@12854
  2035
    show "?P Object"  
schirmer@12854
  2036
      by (auto simp add: dynmethd_C_C)
schirmer@12854
  2037
  next
schirmer@12854
  2038
    case (Subcls dynC dc)
schirmer@12854
  2039
    assume clsDynC': "class G dynC = Some dc"
schirmer@12854
  2040
    assume neq_dynC_Obj: "dynC \<noteq> Object"
schirmer@12854
  2041
    assume hyp: "G\<turnstile>super dc\<preceq>\<^sub>C statC \<Longrightarrow> ?P (super dc)"
schirmer@12854
  2042
    assume subclseq': "G\<turnstile>dynC\<preceq>\<^sub>C statC"
schirmer@12854
  2043
    then
schirmer@12854
  2044
    show "?P dynC"
schirmer@12854
  2045
    proof (cases rule: subclseq_cases)
schirmer@12854
  2046
      case Eq
schirmer@12854
  2047
      with ws statM clsDynC' 
schirmer@12854
  2048
      show ?thesis
wenzelm@32960
  2049
        by (auto simp add: dynmethd_rec)
schirmer@12854
  2050
    next
schirmer@12854
  2051
      case Subcls
schirmer@12854
  2052
      assume "G\<turnstile>dynC\<prec>\<^sub>C statC"
schirmer@12854
  2053
      from this clsDynC' 
schirmer@12854
  2054
      have "G\<turnstile>super dc\<preceq>\<^sub>C statC" by (rule subcls_superD)
schirmer@12854
  2055
      with hyp ws clsDynC' subclseq' statM
schirmer@12854
  2056
      show ?thesis
wenzelm@32960
  2057
        by (auto simp add: dynmethd_rec)
schirmer@12854
  2058
    qed
schirmer@12854
  2059
  qed
schirmer@12854
  2060
qed
schirmer@12854
  2061
schirmer@12854
  2062
lemma dynmethd_cases [consumes 4, case_names Static Overrides]:
wenzelm@12937
  2063
  assumes     statM: "methd G statC sig = Some statM" and 
schirmer@12854
  2064
           subclseq: "G\<turnstile>dynC \<preceq>\<^sub>C statC" and
schirmer@12854
  2065
       is_cls_statC: "is_class G statC" and
schirmer@12854
  2066
                 ws: "ws_prog G" and
schirmer@12854
  2067
         hyp_static: "dynmethd G statC dynC sig = Some statM \<Longrightarrow> P" and
schirmer@12854
  2068
       hyp_override: "\<And> dynM. \<lbrakk>dynmethd G statC dynC sig = Some dynM;
schirmer@12854
  2069
                                 dynM\<noteq>statM;
schirmer@12854
  2070
                           G,sig\<turnstile>dynM overrides statM\<rbrakk> \<Longrightarrow> P"
wenzelm@12937
  2071
  shows P
schirmer@12854
  2072
proof -
schirmer@12854
  2073
  from subclseq is_cls_statC 
schirmer@12854
  2074
  have is_cls_dynC: "is_class G dynC" by (rule subcls_is_class2)
schirmer@12854
  2075
  then obtain dc where
schirmer@12854
  2076
    clsDynC: "class G dynC = Some dc" by blast
schirmer@12854
  2077
  from statM subclseq is_cls_statC ws 
schirmer@12854
  2078
  obtain dynM
schirmer@12854
  2079
    where dynM: "dynmethd G statC dynC sig = Some dynM"
schirmer@12854
  2080
    by (blast dest: methd_Some_dynmethd_Some)
schirmer@12854
  2081
  from dynM is_cls_dynC ws 
schirmer@12854
  2082
  show ?thesis
schirmer@12854
  2083
  proof (cases rule: dynmethd_Some_cases)
schirmer@12854
  2084
    case Static
schirmer@12854
  2085
    with hyp_static dynM statM show ?thesis by simp
schirmer@12854
  2086
  next
schirmer@12854
  2087
    case Overrides
schirmer@12854
  2088
    with hyp_override dynM statM show ?thesis by simp
schirmer@12854
  2089
  qed
schirmer@12854
  2090
qed
schirmer@12854
  2091
schirmer@12854
  2092
lemma ws_dynmethd:
wenzelm@12937
  2093
  assumes  statM: "methd G statC sig = Some statM" and
schirmer@12854
  2094
        subclseq: "G\<turnstile>dynC \<preceq>\<^sub>C statC" and
schirmer@12854
  2095
    is_cls_statC: "is_class G statC" and
schirmer@12854
  2096
              ws: "ws_prog G"
wenzelm@12937
  2097
  shows
wenzelm@12937
  2098
    "\<exists> dynM. dynmethd G statC dynC sig = Some dynM \<and>
wenzelm@12937
  2099
             is_static dynM = is_static statM \<and> G\<turnstile>resTy dynM\<preceq>resTy statM"
schirmer@12854
  2100
proof - 
schirmer@12854
  2101
  from statM subclseq is_cls_statC ws
schirmer@12854
  2102
  show ?thesis
schirmer@12854
  2103
  proof (cases rule: dynmethd_cases)
schirmer@12854
  2104
    case Static
schirmer@12854
  2105
    with statM 
schirmer@12854
  2106
    show ?thesis
schirmer@12854
  2107
      by simp
schirmer@12854
  2108
  next
schirmer@12854
  2109
    case Overrides
schirmer@12854
  2110
    with ws
schirmer@12854
  2111
    show ?thesis
schirmer@12854
  2112
      by (auto dest: ws_overrides_commonD)
schirmer@12854
  2113
  qed
schirmer@12854
  2114
qed
schirmer@12854
  2115
schirmer@12854
  2116
subsection "dynlookup"
schirmer@12854
  2117
schirmer@12854
  2118
lemma dynlookup_cases [consumes 1, case_names NullT IfaceT ClassT ArrayT]:
schirmer@12854
  2119
"\<lbrakk>dynlookup G statT dynC sig = x;
schirmer@12854
  2120
           \<lbrakk>statT = NullT       ; empty sig = x                  \<rbrakk> \<Longrightarrow> P;
schirmer@12854
  2121
  \<And> I.    \<lbrakk>statT = IfaceT I    ; dynimethd G I      dynC sig = x\<rbrakk> \<Longrightarrow> P;
schirmer@12854
  2122
  \<And> statC.\<lbrakk>statT = ClassT statC; dynmethd  G statC  dynC sig = x\<rbrakk> \<Longrightarrow> P;
schirmer@12854
  2123
  \<And> ty.   \<lbrakk>statT = ArrayT ty   ; dynmethd  G Object dynC sig = x\<rbrakk> \<Longrightarrow> P
schirmer@12854
  2124
 \<rbrakk> \<Longrightarrow> P"
schirmer@12854
  2125
by (cases statT) (auto simp add: dynlookup_def)
schirmer@12854
  2126
schirmer@12854
  2127
subsection "fields"
schirmer@12854
  2128
schirmer@12854
  2129
lemma fields_rec: "\<lbrakk>class G C = Some c; ws_prog G\<rbrakk> \<Longrightarrow>  
schirmer@12854
  2130
  fields G C = map (\<lambda>(fn,ft). ((fn,C),ft)) (cfields c) @  
schirmer@12854
  2131
  (if C = Object then [] else fields G (super c))"
schirmer@12854
  2132
apply (simp only: fields_def)
schirmer@12854
  2133
apply (erule class_rec [THEN trans])
schirmer@12854
  2134
apply assumption
schirmer@12854
  2135
apply clarsimp
schirmer@12854
  2136
done
schirmer@12854
  2137
schirmer@12854
  2138
(* local lemma *)
schirmer@12854
  2139
lemma fields_norec: 
schirmer@12854
  2140
"\<lbrakk>class G fd = Some c; ws_prog G;  table_of (cfields c) fn = Some f\<rbrakk> 
schirmer@12854
  2141
 \<Longrightarrow> table_of (fields G fd) (fn,fd) = Some f"
schirmer@12854
  2142
apply (subst fields_rec)
schirmer@12854
  2143
apply assumption+
nipkow@14025
  2144
apply (subst map_of_append)
nipkow@14025
  2145
apply (rule disjI1 [THEN map_add_Some_iff [THEN iffD2]])
schirmer@12854
  2146
apply (auto elim: table_of_map2_SomeI)
schirmer@12854
  2147
done
schirmer@12854
  2148
schirmer@12854
  2149
(* local lemma *)
schirmer@12854
  2150
lemma table_of_fieldsD:
schirmer@12854
  2151
"table_of (map (\<lambda>(fn,ft). ((fn,C),ft)) (cfields c)) efn = Some f
schirmer@12854
  2152
\<Longrightarrow> (declclassf efn) = C \<and> table_of (cfields c) (fname efn) = Some f"
schirmer@12854
  2153
apply (case_tac "efn")
schirmer@12854
  2154
by auto
schirmer@12854
  2155
schirmer@12854
  2156
lemma fields_declC: 
schirmer@12854
  2157
 "\<lbrakk>table_of (fields G C) efn = Some f; ws_prog G; is_class G C\<rbrakk> \<Longrightarrow>  
schirmer@12854
  2158
  (\<exists>d. class G (declclassf efn) = Some d \<and> 
schirmer@12854
  2159
                    table_of (cfields d) (fname efn)=Some f) \<and> 
schirmer@12854
  2160
  G\<turnstile>C \<preceq>\<^sub>C (declclassf efn)  \<and> table_of (fields G (declclassf efn)) efn = Some f"
wenzelm@24038
  2161
apply (erule rev_mp)
schirmer@12854
  2162
apply (rule ws_subcls1_induct, assumption, assumption)
schirmer@12854
  2163
apply (subst fields_rec, assumption)
schirmer@12854
  2164
apply clarify
nipkow@14025
  2165
apply (simp only: map_of_append)
schirmer@12854
  2166
apply (case_tac "table_of (map (split (\<lambda>fn. Pair (fn, Ca))) (cfields c)) efn") 
nipkow@14025
  2167
apply   (force intro:rtrancl_into_rtrancl2 simp add: map_add_def)
schirmer@12854
  2168
schirmer@12854
  2169
apply   (frule_tac fd="Ca" in fields_norec)
schirmer@12854
  2170
apply     assumption
schirmer@12854
  2171
apply     blast
schirmer@12854
  2172
apply   (frule table_of_fieldsD)  
schirmer@12854
  2173
apply   (frule_tac n="table_of (map (split (\<lambda>fn. Pair (fn, Ca))) (cfields c))"
schirmer@12854
  2174
              and  m="table_of (if Ca = Object then [] else fields G (super c))"
nipkow@14025
  2175
         in map_add_find_right)
schirmer@12854
  2176
apply   (case_tac "efn")
schirmer@12854
  2177
apply   (simp)
schirmer@12854
  2178
done
schirmer@12854
  2179
schirmer@12854
  2180
lemma fields_emptyI: "\<And>y. \<lbrakk>ws_prog G; class G C = Some c;cfields c = [];  
schirmer@12854
  2181
  C \<noteq> Object \<longrightarrow> class G (super c) = Some y \<and> fields G (super c) = []\<rbrakk> \<Longrightarrow>  
schirmer@12854
  2182
  fields G C = []"
schirmer@12854
  2183
apply (subst fields_rec)
schirmer@12854
  2184
apply assumption
schirmer@12854
  2185
apply auto
schirmer@12854
  2186
done
schirmer@12854
  2187
schirmer@12854
  2188
(* easier than with table_of *)
schirmer@12854
  2189
lemma fields_mono_lemma: 
schirmer@12854
  2190
"\<lbrakk>x \<in> set (fields G C); G\<turnstile>D \<preceq>\<^sub>C C; ws_prog G\<rbrakk> 
schirmer@12854
  2191
 \<Longrightarrow> x \<in> set (fields G D)"
wenzelm@24038
  2192
apply (erule rev_mp)
schirmer@12854
  2193
apply (erule converse_rtrancl_induct)
schirmer@12854
  2194
apply  fast
schirmer@12854
  2195
apply (drule subcls1D)
schirmer@12854
  2196
apply clarsimp
schirmer@12854
  2197
apply (subst fields_rec)
schirmer@12854
  2198
apply   auto
schirmer@12854
  2199
done
schirmer@12854
  2200
schirmer@12854
  2201
schirmer@12854
  2202
lemma ws_unique_fields_lemma: 
schirmer@12854
  2203
 "\<lbrakk>(efn,fd)  \<in> set (fields G (super c)); fc \<in> set (cfields c); ws_prog G;  
schirmer@12854
  2204
   fname efn = fname fc; declclassf efn = C;
schirmer@12854
  2205
   class G C = Some c; C \<noteq> Object; class G (super c) = Some d\<rbrakk> \<Longrightarrow> R"
schirmer@12854
  2206
apply (frule_tac ws_prog_cdeclD [THEN conjunct2], assumption, assumption)
schirmer@12854
  2207
apply (drule_tac weak_map_of_SomeI)
schirmer@12854
  2208
apply (frule_tac subcls1I [THEN subcls1_irrefl], assumption, assumption)
schirmer@12854
  2209
apply (auto dest: fields_declC [THEN conjunct2 [THEN conjunct1[THEN rtranclD]]])
schirmer@12854
  2210
done
schirmer@12854
  2211
schirmer@12854
  2212
lemma ws_unique_fields: "\<lbrakk>is_class G C; ws_prog G; 
schirmer@12854
  2213
       \<And>C c. \<lbrakk>class G C = Some c\<rbrakk> \<Longrightarrow> unique (cfields c) \<rbrakk> \<Longrightarrow>
schirmer@12854
  2214
      unique (fields G C)" 
schirmer@12854
  2215
apply (rule ws_subcls1_induct, assumption, assumption)
schirmer@12854
  2216
apply (subst fields_rec, assumption)            
paulson@13585
  2217
apply (auto intro!: unique_map_inj inj_onI 
paulson@13585
  2218
            elim!: unique_append ws_unique_fields_lemma fields_norec)
schirmer@12854
  2219
done
schirmer@12854
  2220
schirmer@12854
  2221
schirmer@12854
  2222
subsection "accfield"
schirmer@12854
  2223
schirmer@12854
  2224
lemma accfield_fields: 
schirmer@12854
  2225
 "accfield G S C fn = Some f 
schirmer@12854
  2226
  \<Longrightarrow> table_of (fields G C) (fn, declclass f) = Some (fld f)"
schirmer@12854
  2227
apply (simp only: accfield_def Let_def)
schirmer@12854
  2228
apply (rule table_of_remap_SomeD)
schirmer@12854
  2229
apply (auto dest: filter_tab_SomeD)
schirmer@12854
  2230
done
schirmer@12854
  2231
schirmer@12854
  2232
schirmer@12854
  2233
lemma accfield_declC_is_class: 
schirmer@12854
  2234
 "\<lbrakk>is_class G C; accfield G S C en = Some (fd, f); ws_prog G\<rbrakk> \<Longrightarrow>  
schirmer@12854
  2235
   is_class G fd"
schirmer@12854
  2236
apply (drule accfield_fields)
schirmer@12854
  2237
apply (drule fields_declC [THEN conjunct1], assumption)
schirmer@12854
  2238
apply auto
schirmer@12854
  2239
done
schirmer@12854
  2240
schirmer@12854
  2241
lemma accfield_accessibleD: 
schirmer@12854
  2242
  "accfield G S C fn = Some f \<Longrightarrow> G\<turnstile>Field fn f of C accessible_from S"
schirmer@12854
  2243
by (auto simp add: accfield_def Let_def)
schirmer@12854
  2244
schirmer@12854
  2245
subsection "is methd"
schirmer@12854
  2246
schirmer@12854
  2247
lemma is_methdI: 
schirmer@12854
  2248
"\<lbrakk>class G C = Some y; methd G C sig = Some b\<rbrakk> \<Longrightarrow> is_methd G C sig"
schirmer@12854
  2249
apply (unfold is_methd_def)
schirmer@12854
  2250
apply auto
schirmer@12854
  2251
done
schirmer@12854
  2252
schirmer@12854
  2253
lemma is_methdD: 
schirmer@12854
  2254
"is_methd G C sig \<Longrightarrow> class G C \<noteq> None \<and> methd G C sig \<noteq> None"
schirmer@12854
  2255
apply (unfold is_methd_def)
schirmer@12854
  2256
apply auto
schirmer@12854
  2257
done
schirmer@12854
  2258
schirmer@12854
  2259
lemma finite_is_methd: 
schirmer@12854
  2260
 "ws_prog G \<Longrightarrow> finite (Collect (split (is_methd G)))"
schirmer@12854
  2261
apply (unfold is_methd_def)
schirmer@12854
  2262
apply (subst SetCompr_Sigma_eq)
schirmer@12854
  2263
apply (rule finite_is_class [THEN finite_SigmaI])
schirmer@12854
  2264
apply (simp only: mem_Collect_eq)
schirmer@12854
  2265
apply (fold dom_def)
schirmer@12854
  2266
apply (erule finite_dom_methd)
schirmer@12854
  2267
apply assumption
schirmer@12854
  2268
done
schirmer@12854
  2269
schirmer@12854
  2270
section "calculation of the superclasses of a class"
schirmer@12854
  2271
haftmann@35416
  2272
definition superclasses :: "prog \<Rightarrow> qtname \<Rightarrow> qtname set" where
krauss@35440
  2273
 "superclasses G C \<equiv> class_rec G C {} 
schirmer@12854
  2274
                       (\<lambda> C c superclss. (if C=Object 
schirmer@12854
  2275
                                            then {} 
schirmer@12854
  2276
                                            else insert (super c) superclss))"
schirmer@12854
  2277
   
schirmer@12854
  2278
lemma superclasses_rec: "\<lbrakk>class G C = Some c; ws_prog G\<rbrakk> \<Longrightarrow>  
schirmer@12854
  2279
 superclasses G C 
schirmer@12854
  2280
 = (if (C=Object) 
schirmer@12854
  2281
       then {}
schirmer@12854
  2282
       else insert (super c) (superclasses G (super c)))"
schirmer@12854
  2283
apply (unfold superclasses_def)
schirmer@12854
  2284
apply (erule class_rec [THEN trans], assumption)
schirmer@12854
  2285
apply (simp)
schirmer@12854
  2286
done
schirmer@12854
  2287
schirmer@12854
  2288
lemma superclasses_mono:
berghofe@34915
  2289
  assumes clsrel: "G\<turnstile>C\<prec>\<^sub>C D"
berghofe@34915
  2290
  and ws: "ws_prog G"
berghofe@34915
  2291
  and cls_C: "class G C = Some c"
berghofe@34915
  2292
  and wf: "\<And>C c. \<lbrakk>class G C = Some c; C \<noteq> Object\<rbrakk>
berghofe@34915
  2293
    \<Longrightarrow> \<exists>sc. class G (super c) = Some sc"
berghofe@34915
  2294
  and x: "x\<in>superclasses G D"
berghofe@34915
  2295
  shows "x\<in>superclasses G C" using clsrel cls_C x
berghofe@34915
  2296
proof (induct arbitrary: c rule: converse_trancl_induct)
berghofe@34915
  2297
  case (base C)
berghofe@34915
  2298
  with wf ws show ?case
berghofe@34915
  2299
    by (auto    intro: no_subcls1_Object 
berghofe@34915
  2300
             simp add: superclasses_rec subcls1_def)
berghofe@34915
  2301
next
berghofe@34915
  2302
  case (step C S)
berghofe@34915
  2303
  moreover note wf ws
berghofe@34915
  2304
  moreover from calculation 
berghofe@34915
  2305
  have "x\<in>superclasses G S"
berghofe@34915
  2306
    by (force intro: no_subcls1_Object simp add: subcls1_def)
berghofe@34915
  2307
  moreover from calculation 
berghofe@34915
  2308
  have "super c = S" 
berghofe@34915
  2309
    by (auto intro: no_subcls1_Object simp add: subcls1_def)
berghofe@34915
  2310
  ultimately show ?case 
berghofe@34915
  2311
    by (auto intro: no_subcls1_Object simp add: superclasses_rec)
schirmer@12854
  2312
qed
schirmer@12854
  2313
schirmer@12854
  2314
lemma subclsEval:
berghofe@34915
  2315
  assumes clsrel: "G\<turnstile>C\<prec>\<^sub>C D"
berghofe@34915
  2316
  and ws: "ws_prog G"
berghofe@34915
  2317
  and cls_C: "class G C = Some c"
berghofe@34915
  2318
  and wf: "\<And>C c. \<lbrakk>class G C = Some c; C \<noteq> Object\<rbrakk>
berghofe@34915
  2319
    \<Longrightarrow> \<exists>sc. class G (super c) = Some sc"
berghofe@34915
  2320
  shows "D\<in>superclasses G C" using clsrel cls_C
berghofe@34915
  2321
proof (induct arbitrary: c rule: converse_trancl_induct)
berghofe@34915
  2322
  case (base C)
berghofe@34915
  2323
  with ws wf show ?case
berghofe@34915
  2324
    by (auto intro: no_subcls1_Object simp add: superclasses_rec subcls1_def)
berghofe@34915
  2325
next
berghofe@34915
  2326
  case (step C S)
berghofe@34915
  2327
  with ws wf show ?case
berghofe@34915
  2328
    by - (rule superclasses_mono,
berghofe@34915
  2329
          auto dest: no_subcls1_Object simp add: subcls1_def )
schirmer@12854
  2330
qed
schirmer@12854
  2331
kleing@14981
  2332
end