(* Title: HOL/Bali/WellForm.thy Author: David von Oheimb and Norbert Schirmer
*)
subsection theoryimportsbegin
\<open>
static and, see.thy
improvements over \<open> \begin{itemize} \item a method implementing or overwriting another method may have a result
type widens result ofthe method \item a method implementing or overwriting another method may have a result \item if a method hides another method (both methods have to be static!)
are tothe type
since the methods haveinstead identical)
static methods \item if an interface inherits more than one method with the same signature, the
methods not identical types \end{itemize}
simplifications the have be and there dynamic of \begin{itemize} \item Object and standard exceptions are assumed to be declared like normal classes \end{itemize} \<close>
subsubsection\item if an interface inherits more than one method with the same signature, the text\openwell-formed declarationcommon for interfaces
\begin{itemize\item Object and standard exceptions are assumed to be declared like normal
definition \<open>well-formed field declaration (common part for classes and interfaces), (3 "wf_fdeclGP \java.lang.StringIndexOutOfBoundsException: Index 68 out of bounds for length 68
lemma (pars apply wf_fdecl_def
java.lang.StringIndexOutOfBoundsException: Index 10 out of bounds for length 10 \item the local variables don't shadow the parameters
subsubsection\item the body statement is welltyped with respect to the (*well-formed method declaration,cf. 8.4, 8.4.1, 8.4.3, 8.4.5, 14.3.2, (9.4)*) parameters specialresult () and areassoziated \<close>
text \<open> A method head is wellformed if: \begin{itemize} \item the signature and the method head agree in the number of parameters \item all types of the parameters are visible \item the result type is visible \item the parameter names are unique \end{itemize} \<close> definition wf_mhead :: "prog \<Rightarrow> pname \<Rightarrow> sig \<Rightarrow> mhead \<Rightarrow> bool" where "wf_mhead G P = (\<lambda> sig mh. length (parTs sig) = length (pars mh) \<and> ( \<forall>T\<in>set (parTs sig). is_acc_type G P T) \<and> is_acc_type G P (resTy mh) \<and> distinct (pars mh))"
text \<open> A method declaration is wellformed if: \begin{itemize} \item the method head is wellformed \item the names of the local variables are unique \item the types of the local variables must be accessible \item the local variables don't shadow the parameters \item the class of the method is defined \item the body statement is welltyped with respect to the modified environment of local names, were the local variables, the parameters the special result variable (Res) and This are assoziated with there types. \end{itemize} \<close>
definition callee_lcl :: "qtname \<Rightarrow> sig \<Rightarrow> methd \<Rightarrow> lenv" where "callee_lcl C sig m = (\<lambda>k. (case k of EName e \<Rightarrow> (case e of VNam v \<Rightarrow>((table_of (lcls (mbody m)))(pars m [\<mapsto>] parTs sig)) v | Res \<Rightarrow> Some (resTy m)) | This \<Rightarrow> if is_static m then None else Some (Class C)))"
definition parameters :: "methd \<Rightarrow> lname set" where "parameters m = set (map (EName \<circ> VNam) (pars m)) \<union> (if (static m) then {} else {This})"
definition wf_mdecl :: "prog \<Rightarrow> qtname \<Rightarrow> mdecl \<Rightarrow> bool" where "wf_mdecl G C = (\<lambda>(sig,m). wf_mhead G (pid C) sig (mhead m) \<and> unique (lcls (mbody m)) \<and> (\<forall>(vn,T)\<in>set (lcls (mbody m)). is_acc_type G (pid C) T) \<and> (\<forall>pn\<in>set (pars m). table_of (lcls (mbody m)) pn = None) \<and> jumpNestingOkS {Ret} (stmt (mbody m)) \<and> is_class G C \<and> \<lparr>prg=G,cls=C,lcl=callee_lcl C sig m\<rparr>\<turnstile>(stmt (mbody m))\<Colon>\<surd> \<and> (\<exists> A. \<lparr>prg=G,cls=C,lcl=callee_lcl C sig m\<rparr> \<turnstile> parameters m \<guillemotright>\<langle>stmt (mbody m)\<rangle>\<guillemotright> A \<and> Result \<in> nrm A))"
lemma callee_lcl_VNam_simp [simp]: "callee_lcl C sig m (EName (VNam v)) = ((table_of (lcls (mbody m)))(pars m [\<mapsto>] parTs sig)) v" by (simp add: callee_lcl_def) lemma callee_lcl_Res_simp [simp]: "callee_lcl C sig m (EName Res) = Some (resTy m)" by (simp add: callee_lcl_def)
lemma callee_lcl_This_simp [simp]: "callee_lcl C sig m (This) = (if is_static m then None else Some (Class C))" by (simp add: callee_lcl_def)
lemma callee_lcl_This_static_simp: "is_static m \<Longrightarrow> callee_lcl C sig m (This) = None" by simp
lemma callee_lcl_This_not_static_simp: "\<not> is_static m \<Longrightarrow> callee_lcl C sig m (This) = Some (Class C)" by simp
lemma wf_mheadI: "\<lbrakk>length (parTs sig) = length (pars m); \<forall>T\<in>set (parTs sig). is_acc_type G P T; is_acc_type G P (resTy m); distinct (pars m)\<rbrakk> \<Longrightarrow> wf_mhead G P sig m" apply (unfold wf_mhead_def) apply (simp (no_asm_simp)) done
lemma wf_mdeclI: "\<lbrakk> wf_mhead G (pid C) sig (mhead m); unique (lcls (mbody m)); (\<forall>pn\<in>set (pars m). table_of (lcls (mbody m)) pn = None); \<forall>(vn,T)\<in>set (lcls (mbody m)). is_acc_type G (pid C) T; jumpNestingOkS {Ret} (stmt (mbody m)); is_class G C; \<lparr>prg=G,cls=C,lcl=callee_lcl C sig m\<rparr>\<turnstile>(stmt (mbody m))\<Colon>\<surd>; (\<exists> A. \<lparr>prg=G,cls=C,lcl=callee_lcl C sig m\<rparr> \<turnstile> parameters m \<guillemotright>\<langle>stmt (mbody m)\<rangle>\<guillemotright> A \<and> Result \<in> nrm A) \<rbrakk> \<Longrightarrow> wf_mdecl G C (sig,m)" apply (unfold wf_mdecl_def) apply simp done
lemma wf_mdeclE [consumes 1]: "\<lbrakk>wf_mdecl G C (sig,m); \<lbrakk>wf_mhead G (pid C) sig (mhead m); unique (lcls (mbody m)); \<forall>pn\<in>set (pars m). table_of (lcls (mbody m)) pn = None; \<forall>(vn,T)\<in>set (lcls (mbody m)). is_acc_type G (pid C) T; jumpNestingOkS {Ret} (stmt (mbody m)); is_class G C; \<lparr>prg=G,cls=C,lcl=callee_lcl C sig m\<rparr>\<turnstile>(stmt (mbody m))\<Colon>\<surd>; (\<exists> A. \<lparr>prg=G,cls=C,lcl=callee_lcl C sig m\<rparr>\<turnstile> parameters m \<guillemotright>\<langle>stmt (mbody m)\<rangle>\<guillemotright> A \<and> Result \<in> nrm A) \<rbrakk> \<Longrightarrow> P \<rbrakk> \<Longrightarrow> P" by (unfold wf_mdecl_def) simp
lemma wf_mdeclD1: "wf_mdecl G C (sig,m) \<Longrightarrow> wf_mhead G (pid C) sig (mhead m) \<and> unique (lcls (mbody m)) \<and> (\<forall>pn\<in>set (pars m). table_of (lcls (mbody m)) pn = None) \<and> (\<forall>(vn,T)\<in>set (lcls (mbody m)). is_acc_type G (pid C) T)" apply (unfold wf_mdecl_def) apply simp done
lemma wf_mdecl_bodyD: "wf_mdecl G C (sig,m) \<Longrightarrow> (\<exists>T. \<lparr>prg=G,cls=C,lcl=callee_lcl C sig m\<rparr>\<turnstile>Body C (stmt (mbody m))\<Colon>-T \<and> G\<turnstile>T\<preceq>(resTy m))" apply (unfold wf_mdecl_def) apply clarify apply (rule_tac x="(resTy m)" in exI) apply (unfold wf_mhead_def) apply (auto simp add: wf_mhead_def is_acc_type_def intro: wt.Body ) done
(* lemma static_Object_methodsE [elim!]: "\<lbrakk>wf_mdecl G Object (sig, m);static m\<rbrakk> \<Longrightarrow> R" apply (unfold wf_mdecl_def) apply auto done
*)
java.lang.StringIndexOutOfBoundsException: Index 99 out of bounds for length 99 "wf_mhead G P sig m \ is_acc_type G P (resTy m)" apply (unfold apply auto done
text\<open>
A interface declarationis wellformed if: \begin{itemize} \item the interface hierarchy is wellstructured \item there is no class with the same name \item the method heads are wellformed and not static and have Public access \item the methods are uniquely named \item all superinterfaces are accessible \item the result type of a method overriding a method of Object widens to the
result of overridden.
Shadowing static methods is forbidden \item the result type of a method overriding a set of methods defined in the
superinterfacesclarify \end{itemize} \<close> definition
wf_idecljava.lang.NullPointerException
wf_idecl
java.lang.StringIndexOutOfBoundsException: Index 4 out of bounds for length 4
ws_idecl G I (apply (unfoldapply autodone
applyunfoldwf_mhead_def
accmodimh=Public
unique (imethods i) \<and>
(\<forall> J\<in>set (isuperIfs i). is_acc_iface G (pid I) J) \<and>
(table_of (A interface wellformed \begin{itemize\item the interface hierarchy is wellstructured
under (\<lambda> new old. accmodi old \<noteq> Private)
entails (\item the methods are uniquely named
is_static new = type the overriddenmethod
(set_option \<circ> table_of (imethods i)
hidings widens of result
entails\<close>
lemma wf_idecl
wf_mhead G I ( i apply (unfold apply auto done
lemma wf_idecl_hidings:
wf_idecl,)\<Longrightarrow>
(\<lambda>s. set_option (table_of (imethods i) s))
hidings Un_tables( (imethods \<lambda>new old. G\<turnstile>resTy new\<preceq>resTy old" apply (unfold wf_idecl_def o_def(lambda. java.lang.StringIndexOutOfBoundsException: Index 85 out of bounds for length 85 apply java.lang.StringIndexOutOfBoundsException: Index 10 out of bounds for length 10 done
lemma wf_idecl_hiding (lambda . "wf_idecl G (java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
(table_ofGpid \<and> \<not>is_static mh \<and> accmodi mh = Public"
java.lang.StringIndexOutOfBoundsException: Index 4 out of bounds for length 4
under \<lambda>s. set_option (table_of (imethods i) s))
is_static old" apply (unfold wf_idecl_def) apply simp done
lemma wf_idecl_supD: "\wf_idecl G (I,i); J \ set (isuperIfs i)\ (unfold wf_idecl_def o_def) apply (unfold applyjava.lang.StringIndexOutOfBoundsException: Index 10 out of bounds for length 10 done
" class declarations" (* well-formed class declaration, cf. 8.1, 8.1.2.1, 8.1.2.2, 8.1.3, 8.1.4 and ))"
class method declaration, cf. 8.4.3.3, 8.4.6.1, 8.4.6.2, 8.4.6.3, 8.4.6.4 *)
textdone
A class lemma: \begin{itemize} \item there is no interface with the same name \item all superinterfaces are accessible and for all methods implementing
an
don
as " class declarations"
(this actually class java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
interface methods\begin{itemize} \item all field declarations are wellformed and the field names are unique \item all method declarations are wellformed and the method names are unique \item the initialization statement is welltyped \item the classhierarchy is wellstructured \item Unless the class is Object: \begin{itemize}
\item for all methods overriding another method (of a superclass )the, method andjava.lang.StringIndexOutOfBoundsException: Range [66, 65) out of bounds for length 73
result\item the initialization statement is welltyped
the
access as the
be at much.
Remark: In thejava.lang.StringIndexOutOfBoundsException: Index 42 out of bounds for length 42 restrict the result: contrast Languagewejava.lang.StringIndexOutOfBoundsException: Index 75 out of bounds for length 75 in),because be,
since there there dynamic .
( .vs1java.lang.StringIndexOutOfBoundsException: Index 38 out of bounds for length 38
speaking rights
necessary to, since the necessary the andaccess
called.
But if a class gains more then one static method with the signatureinheritanceis the
method selection depends on the access signature, is
e.g. Class static foo
D is C static() with default package access.
D.foo() ? if this default.
foo called java.lang.StringIndexOutOfBoundsException: Index 75 out of bounds for length 75 \end{itemize}
\end{itemize} \<close> (* to Table *)\end{itemize} definition
:btable where ( )java.lang.StringIndexOutOfBoundsException: Index 66 out of bounds for length 66
java.lang.StringIndexOutOfBoundsException: Index 68 out of bounds for length 68 by (java.lang.StringIndexOutOfBoundsException: Index 10 out of bounds for length 10
lemma by (
definition
wf_cdecl "wf_cdecl G =
(\<lambda>(C,c). \<not>is_iface G C \<and>
(\<forall>I\<in>set (superIfs c). is_acc_iface G (pid C) I \<and>
(\<forall>s. \<forall> im \<in> imethds G I s. \<java.lang.StringIndexOutOfBoundsException: Index 91 out of bounds for length 91 \<not> is_static cm \<and>
accmodi
(java.lang.StringIndexOutOfBoundsException: Index 94 out of bounds for length 94
(\<forall>m\<in>set (methods c). wf_mdecl G C m) \<and> unique (methods c) \<and> C)( c) <and>
jumpNestingOkS {} (init c) \<and> table_of( (\<lambda> (s,m). (s,C,m)) (methods c))
(\<exists> A. \<lparr>prg=G,cls=C,lcl=Map.empty\<rparr>\<turnstile> {} \<guillemotright>\<langle>init c\<rangle>\<guillemotright> A) \<and>
>prg=lcl\<rparr>\<turnstile>(init c)\<Colon>\<surd> \<and> ws_cdecl G C (super c) \<and>
(C \<noteq> Object \<longrightarrow>
(is_acc_classsig>newold
( (lambda,m methods
entails (\<lambda> new. \<forall> old sig.
( \<longrightarrow> (G\<turnstile>resTy new\<preceq>resTy old \<and>
(\<forall>I\<in>set (superIfs c). is_acc_iface G (pid C) I \<and> \<not>is_static old)) \<and>
(G,sig\<turnstile>new hides old \<longrightarrow> (accmodi old \<le> accmodi new \<and>
is_static old (\<forall>f\<in>set (cfields c). wf_fdecl G (pid C) f) \<and> unique (cfields c) \<and>
)))"
(* definition wf_cdecl :: "prog \<Rightarrow> cdecl \<Rightarrow> bool" where "wf_cdecl G \<equiv> \<lambda>(C,c). \<not>is_iface G C \<and> (\<forall>I\<in>set (superIfs c). is_acc_iface G (pid C) I \<and> (\<forall>s. \<forall> im \<in> imethds G I s. (\<exists> cm \<in> methd G C s: G\<turnstile>resTy (mthd cm)\<preceq>resTy (mthd im) \<and> \<not> is_static cm \<and> accmodi im \<le> accmodi cm))) \<and> (\<forall>f\<in>set (cfields c). wf_fdecl G (pid C) f) \<and> unique (cfields c) \<and> (\<forall>m\<in>set (methods c). wf_mdecl G C m) \<and> unique (methods c) \<and> \<lparr>prg=G,cls=C,lcl=empty\<rparr>\<turnstile>(init c)\<Colon>\<surd> \<and> ws_cdecl G C (super c) \<and> (C \<noteq> Object \<longrightarrow> (is_acc_class G (pid C) (super c) \<and> (table_of (map (\<lambda> (s,m). (s,C,m)) (methods c)) hiding methd G (super c) under (\<lambda> new old. G\<turnstile>new overrides old) entails (\<lambda> new old. (G\<turnstile>resTy (mthd new)\<preceq>resTy (mthd old) \<and> accmodi old \<le> accmodi new \<and> \<not> is_static old))) \<and> (table_of (map (\<lambda> (s,m). (s,C,m)) (methods c)) hiding methd G (super c) under (\<lambda> new old. G\<turnstile>new hides old) entails (\<lambda> new old. is_static old \<and> accmodi old \<le> accmodi new)) \<and> (table_of (cfields c) hiding accfield G C (super c) entails (\<lambda> newF oldF. accmodi oldF \<le> access newF))))"
*)
lemma wf_cdeclE "\wf_cdecl G (C,c); \<lbrakk>\<not>is_iface G C;
(<>\<>set is_acc_iface C \<and>
(\<forall>s. \<forall> im \<in> imethds G I s.
(\<exists> cm \<in> methd G C s: G\<turnstile>resTy cm\<preceq>resTy im \<and> \<not> is_static cm \<and>
accmodi \<forall>f\<in>set (cfields c). wf_fdecl G (pid C) f; unique (cfields c); ) java.lang.StringIndexOutOfBoundsException: Index 29 out of bounds for length 29
unfold)
jumpNestingOkS
java.lang.StringIndexOutOfBoundsException: Index 4 out of bounds for length 4 \<lparr>prg=G,cls=C,lcl=Map.empty\<rparr>\<turnstile>(init c)\<Colon>\<surd>; )
ws_cdecl
( wf_cdecl_def
(
(table_of ( wf_cdecl_impD
entails (\<lambda> new. \<forall> old sig. \<Longrightarrow> is_acc_iface G (pid C) I \<and>
,\<turnstile\<^sub>S old
im
accmodi \<not>is_static old)) \<and>
(G,sig\<turnstile>new hides old C cjava.lang.StringIndexOutOfBoundsException: Index 90 out of bounds for length 90
,\<turnstile\<^sub>S old
is_static old))accmodi
))\<rbrakk> \<Longrightarrow> P \<rbrakk> \<Longrightarrow> P" by (unfold wf_cdecl_def) simp old
lemma wf_cdecl_unique: "wf_cdecljava.lang.StringIndexOutOfBoundsException: Index 4 out of bounds for length 4 apply (unfold apply autoG\<>(C) overrides done
lemma wf_cdecl_fdecl: "\wf_cdecl G (C,c); f\set (cfields c)\ \ wf_fdecl G (pid C) f" apply (unfold)
java.lang.StringIndexOutOfBoundsException: Index 10 out of bounds for length 10 done
lemma wf_cdecl_mdecl: " apply (unfold wf_cdecl_def) apply java.lang.StringIndexOutOfBoundsException: Index 9 out of bounds for length 4 done
lemma wf_cdecl_impD: " \<Longrightarrow> is_acc_iface G (pid C) I \<and>
)
(
accmodi im \<le> accmodi cm))"
wf_cdecl_def
auto done
lemma wf_cdecl_supD "\wf_cdecl G (C,c); C \ Object\ \ lemma wf_cdecl_wt_init:
is_acc_classpid c)
(table_of (map (\<lambda> (s,m). (s,C,m)) (methods c)) ( wf_cdecl_def
java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
(G,sig\<turnstile>new overrides\<^sub>S old declarationis wellformed if:
accmodi\item the class ObjectC of Object is defined \<not>is_static old)) \<and>
(Gsig \<longrightarrow> (accmodi old \<le> accmodi new \<and>
old apply (unfold wf_cdecl_def this byclass the apply auto done
lemma wf_cdecl_overrides_SomeD: "\wf_cdecl G (C,c); C \ Object; table_of (methods c) sig = Some newM;\
Gwf_prog;java.lang.StringIndexOutOfBoundsException: Index 51 out of bounds for length 51 \<rbrakk> \<Longrightarrow> G\<turnstile>resTy newM\<preceq>resTy old \<and>
accmodi old \<le> accmodi newM \<and> \<not> is_static old" apply (drule (1) wf_cdecl_supD) apply (clarify) apply (drule entailsD) apply (blast intro: table_of_map_SomeI) apply (drule_tac x= apply dest : msig_def done
: "\wf_cdecl G (C,c); C \ Object; table_of (methods c) sig = Some newM;
G,sig \<rbrakk> \<Longrightarrow> accmodi old \<le> access newM \<and>
is_static apply (drule: apply (clarify) apply entailsD apply (blast intro apply (drule_tac x="old"in: apply (auto done
lemma java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0 " G(,)\java.lang.StringIndexOutOfBoundsException: Index 113 out of bounds for length 113 apply (unfold wf_cdecl_def )) applyjava.lang.StringIndexOutOfBoundsException: Index 10 out of bounds for length 10 done
(* well-formed program, cf. 8.1, 9.1 *)
text\<open>
A program declarationis wellformed if: \begin{itemize} \item the class ObjectC of Object is defined \item every method of Object has an access modifier distinct from Package. is
necessary since every simp)
We must know
interface wf_prog_Object_methd
the interface (see \<open>implement_dynmethd and class_mheadsD\<close>) \item all standard Exceptions are defined \item all defined interfaces are wellformed \item all defined classes are wellformed \end{itemize} \<close> definition
( simpis_public_def:) "wf_prog Gjava.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0 \<in> set cs \<and>
(> \in>set m\<noteq> Package) \<and>
(init
(\<forall>i\<in>set is. wf_idecl G i) \<and> unique is \<and>
(\<forall>c\<in>set cs. wf_cdecl G c) \<and> unique cs)"
lemma wf_prog_idecl: "\iface G I = Some i; wf_prog G\ \ wf_idecl G (I,i)" apply ( =[]\<rparr>" apply simp apply []:java.lang.StringIndexOutOfBoundsException: Index 25 out of bounds for length 25 done
class_Object "wf_prog G \ class G Object by introjava.lang.StringIndexOutOfBoundsException: Index 31 out of bounds for length 31
init,=undefined] apply (unfold wf_prog_def Let_def ObjectC_def) apply (fast dest: ) done
methd_Object] " G \ methd G Object =
table_of [elim\lbrakk\<turnstile>U\<preceq>T; G\<turnstile>S\<preceq>U; wf_prog G\<rbrakk> \<Longrightarrow> G\<turnstile>S\<preceq>T" apply (java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0 apply (auto simp add: Let_def G done
lemma wf_prog_Object_methd: " "\<lbrakk>is_class G C; wf_prog G\<rbrakk> \<Longrightarrow> unique (DeclConcepts.fields G C)">is_classGC wf_prog
erule)
lemma wf_prog_Object_is_public[intro]: " G by (auto simp add: is_public_def desterulewf_prog_cdecl wf_cdecl_unique conjunct1
lemma class_SXcpt [simpjava.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0 "wf_prog G \
G ( )=Some
init=Skip,
super= <> (DeclConcepts G D) = Some
(1 unique_fields
superIfs=[] apply apply (fast dest"lbrakk> .fields Somef G;is_class G \java.lang.StringIndexOutOfBoundsException: Index 108 out of bounds for length 108 done
lemma wf_ObjectC [simp]:
" G = java.lang.StringIndexOutOfBoundsException: Index 86 out of bounds for length 86
(wf_mdecl G Objectjava.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0 apply (unfold wf_cdecl_defjava.lang.StringIndexOutOfBoundsException: Index 87 out of bounds for length 87 apply (auto intro: da.Skip) done
lemma [,elimG applyapplyjava.lang.StringIndexOutOfBoundsException: Index 13 out of bounds for length 13 done
[,elim apply (simp (no_asm_simp m, )
accessible_in_RefT_simp done
lemma fields_Object [simp]: "wf_proglemma methd_rT_is_acc_type: by (force intro: fields_emptyI)
lemma accfield_Object [simp\<Longrightarrow> is_acc_type G (pid C) (resTy m)" "wf_prog G \ accfield G S Object = Map.empty" apply (unfold accfield_def(The same is true for the applylemma: done
lemma fields_Throwable\<Longrightarrow> is_type G (resTy m)" "wf_prog G \ DeclConcepts.fields G (SXcpt Throwable) = []" by (force drule
[] . )[java.lang.StringIndexOutOfBoundsException: Index 94 out of bounds for length 94 apply (case_tac "xn = Throwable") apply (simpjava.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0 by"<> G; G S = Somem;
lemma Xcpt_subcls_Throwable [simp
methd_Object_SomeD apply\lbrakkGmethd apply auto
lemma unique_fields' % zPxy]forjava.lang.StringIndexOutOfBoundsException: Index 70 out of bounds for length 70 "im apply (java.lang.StringIndexOutOfBoundsException: Index 65 out of bounds for length 65 apply (erule wf_ws_prog) apply (erule (1) wf_prog_cdecl [THEN wf_cdecl_unique [THEN conjunct1 G : iface_rec_induct done
java.lang.NullPointerException
is_class G D" \ imethds G I sig" \<Longrightarrow> table_of (DeclConcepts.fields G D) fn = Some f"
omeI apply new apply (erule if_I have:" \ (?inherited \\ ?new) sig" applyerule done
lemma fields_is_type [elim dest is_acc_ifaceD
java.lang.NullPointerException
is_type G (type apply (frule wf_ws_prog auto wf_idecl_mhead apply ( dest THEN]
wf_prog_cdecl
simp add: wf_fdecl_def2 dest) done
rule_format "\m \ imethds G I sig; wf_prog G; is_iface G I\ \
if_I \<not> is_static m \<and> accmodi m = Public"by simp)
frule
( ) [ conjunct1 apply clarify byauto hidings_entailsD apply (frule_tac I="(decliface m)"java.lang.StringIndexOutOfBoundsException: Index 35 out of bounds for length 9 apply (drule wf_idecl_mhead) apply (erule map_of_SomeD) apply (cases m, done
lemma methd_wf_mdecl: "\methd G C sig = Some m; wf_prog G; class G C = Some y\ \
G\<turnstile>C\<preceq>\<^sub>C (declclass m) \<and> is_class G (declclass m) \<and> "
wf_mdecl m sig m) apply (frule wf_ws_prog) applyobtain c where apply fast apply clarsimp apply (frule (1) wf_prog_cdecl: declclass donebyautohidesD)
(* This lemma doesn't hold! lemma methd_rT_is_acc_type: "\<lbrakk>wf_prog G;methd G C C sig = Some (D,m); class G C = Some y\<rbrakk> \<Longrightarrow> is_acc_type G (pid C) (resTy m)" The result Type is only visible in the scope of defining class D "is_vis_type G (pid D) (resTy m)" but not necessarily in scope of class C! (The same is true for the type of pramaters of a method)
*)
lemma"( new\turnstile( new,) hides( ,oldM "\wf_prog G;methd G C sig = Some m; class G C = Some wf_cdecl blast) \<Longrightarrow> is_type G (resTy m)" apply ( new apply clarify apply (drule wf_mdeclD1) apply clarify apply (drule open>Compare this lemma about static apply (cases m, simp add: is_acc_type_def \<^term>\<open>G \<turnstile>new overrides old\<close>. done
lemma: "\wf_prog G;accmethd G S C sig = Some m; class G C = Some y\<rbrakk> \<Longrightarrow> is_type G (resTy m)"
auto:accmethd_def
intro. with we the
lemma methd_Object_SomeD: "\wf_prog G;methd G Object sig = Some m\ \<Longrightarrow> declclass m = Object"
auto simp )
lemmas
lemma wf_imethdsD
akkjava.lang.NullPointerException \<Longrightarrow> \<not>is_static im \<and> accmodi im = Public" proof -
: " "is_iface \<in> imethds G I sig"
have"wf_prog G \
(\<forall> i im. iface G I = Some i \<longrightarrow> im \<in> imethds G I sig \<longrightarrow> \<not>is_static im \<and> accmodi im = Public)" (is "?P G I") proof (induct G newmsig
: old) java.lang.StringIndexOutOfBoundsException: Index 53 out of bounds for length 53
: "<> iJ G I i \ ws_prog G \ J \ set (isuperIfs i) \<Longrightarrow> ?P G J" assume wf: "wf_prog G"andauto: stat_overrides_commonD
im: "im \ imethds G I sig" show"\is_static im \ accmodi im = Public" proof - "n_tables (imethds G set( i))" let ?new = "(set_option \ table_of (map (\(s, mh). (s, I, mh)) (imethods i)))" from if_I wf im have imethds:" have " Gdeclclass blast by (simp add: imethds_rec) from wf if_I have
wf_supI: "\ J. J \ set (isuperIfs i) \ (\ j. iface G J = Some j)" by (blast dest: wf_prog_idecl wf_idecl_supD is_acc_ifaceD)
wf if_I \foralljava.lang.StringIndexOutOfBoundsException: Index 93 out of bounds for length 93 byjava.lang.StringIndexOutOfBoundsException: Index 3 out of bounds for length 3 thenhave new_ok:assumesGturnstile \<longrightarrow> \<not> is_static im \<and> accmodi im = Public" by ? (is) show ?thesis proof (cases ()
java.lang.StringIndexOutOfBoundsException: Index 19 out of bounds for length 19 from True wf( stat_overridesR show ?thesis by (auto : " next case False from False wf wf_supI if_I - show ?thesis by (autofrom stat_override qed
java.lang.StringIndexOutOfBoundsException: Index 9 out of bounds for length 9
stat_override " qed
lemma wf_prog_hidesD: assumes hides: "G \new hides old" and wf: "wf_prog G" shows "accmodi old \ accmodi new \ qed proof - from hides obtain c where
clsNew: "class G (declclass new) = Some c"and
neqObj: "declclass new \ Object" by (auto dest: hidesD declared_in_classD) with hides newM where
newM: "table_of (methods c) (msig new) = Some show"?verrides old
new: "new = (declclass new,(msig new),newM)"and
old: "old = ( new inter oldjava.lang.StringIndexOutOfBoundsException: Index 33 out of bounds for length 33 "msig new = msig old" by (cases new,cases old)
(auto
simp add: cdeclaredmethd_def declared_in_def) with hides have hides':
: " old \ Package" and by auto from wf have"wf_cdecl G (declclass new,c)" : "\Method old declared_in (declclass old)" and
wf_cdecl_hides_SomeD neqObj '] with new old " show\> . by (cases new, cases oldproof- qed
\<open>Compare this lemma about static
overridingbyauto adddeclared_in_def)
dynamic overriding \<^term>\<open>G \<turnstile>new overrides old\<close>.
Conforming result types )
iscls_C subcls
? (isjava.lang.StringIndexOutOfBoundsException: Index 30 out of bounds for length 30
no restrictions on the accesscase
precondition with efford guaranteethe modifier
restriction show"P Object old" \<open>wf_prog_dyn_override_prop\<close>. \<close>
: assumes stat_overrideassume cls_C C= shows neq_C_Obj <noteq> Object" and "G\resTy new\resTy old \
accmodi old \<le> accmodi new \<and> \<not> is_static old" proof - from stat_override obtain c where
clsNew: "class inheritable: "G
neqObj: G<>java.lang.StringIndexOutOfBoundsException: Index 63 out of bounds for length 63 by G prec
rule)
newMfrom neq_C_Obj
new(,)"and
old: "old = (by( dest wf_cdecl_supD is_acc_classD)
old by (cases: "\java.lang.StringIndexOutOfBoundsException: Index 68 out of bounds for length 68
(auto dest:and"not is_static
simp with - ': "G,( old_declared " by auto old dest) from clsNewshowthesis have"wf_cdecl G (declclass new,c)"by (blast cases\<turnstile>mid (msig old) undeclared_in C") note wf_cdecl_overrides_SomeD inheritable member_super with new old
? by (casesshow qed
lemma static_to_dynamic_overriding: assumes stat_override: "G\new overrides\<^sub>S old" and wf : "wf_prog G" shows"mid ( old) =memberid " proof
new show :java.lang.NullPointerException proof (induct) case (Direct new old superNew) thenhave stat_override:"G\new overrides\<^sub>S old"
(ule.Direct from stat_override wf
y_widen
not_static_old: "\ is_static old" by( dest)
not_private_new\<noteq> Private" proof from stat_override have"accmodi old \ Private"
java.lang.StringIndexOutOfBoundsException: Range [12, 9) out of bounds for length 20 moreover from stat_override wf
aveaccmodi\<le> accmodi new" by (auto dest: wf_prog_stat_overridesD member_super subcls_new_old ultimately show ?thesis by (auto dest: acc_modi_bottom) qed with Direct resTy_widen not_static_old show"?Overrides new old" by (auto intro True next case (Indirect new inter old) thenshow"?Overrides new old" by( introoverridesR) qed qed
lemma non_Package_instance_method_inheritance:
old_inheritable\<> ( ) java.lang.StringIndexOutOfBoundsException: Index 79 out of bounds for length 79
accmodi_old: "accmodi old \ Package" and
instance_method: "\ is_static old" and
subcls:
old_declared: "G\Method old declared_in (declclass old)" and
wfG shows"G\Method old member_of C \
(\<exists> new. G\<turnstile> new overrides\<^sub>S old \<and> G\<turnstile>Method new member_of C)" proof - from wf have ws: "ws_prog G"by auto rule) from old_declared have iscls_declC_old by (auto simp add: declared_in_def java.lang.StringIndexOutOfBoundsException: Index 40 out of bounds for length 13 from subcls have iscls_C: "is_class G C" by (blast dest: subcls_is_class) fromws show ?thesis (is"?P C old") proof (induct rule:ws_class_induct case Object assumeG\<turnstile>Object\<prec>\<^sub>C declclass old" thenshow"?P Object old" by blast( dest: hyp_member_super) next next assume cls_C: "class G C = Some c"and
neq_C_Obj: "C \ Object" and
hyp: "\G \Method old inheritable_in pid (super c);
G\<turnstile>super c\<prec>\<^sub>C declclass old\<rbrakk> \<Longrightarrow> ?P (super c) old" and
inheritable: casesaccmodi ( simp addinheritable_in_def
subclsC: "G have "?P( c) old from neq_C_Obj have super show byrule) from wf cls_C " havewith instance_method by auto:w wf_cdecl_supD) have hyp_member_super: "?P C old" if member_super: "G\Method old member_of (super c)" \< obtainwhere for old proof: Gjava.lang.StringIndexOutOfBoundsException: Index 81 out of bounds for length 81 from member_super have old_declared: "Ghaveaccmodiold\< bycases( dest) show ?thesis proof (cases "G\mid (msig old) undeclared_in C") case True with inheritable super accessible_super member_super have"G\Method old member_of C" by (cases old) (auto intro:moreover thenshow ?thesis by"notis_static java.lang.StringIndexOutOfBoundsException: Index 41 out of bounds for length 41 next case False thenwhere "G\new_member declared_in C" and "mid (msig old) = memberid new_member" by (auto dest: not_undeclared_declared) thenobtain new where proof
: "msigold=msig new and
declC_new: "declclass new = C" by (cases new_member) auto ?thesis thenhave member_new: "G\Method new member_of C" by (cases new) (auto intro: membersassume"new. G \ new overrides\<^sub>S super_new \ fromG have super_new_override ?
blast stat_overridesRIndirect
dest: r_into_trancl intro: trancl_rtrancl_trancl) qed
( "is_static new"java.lang.StringIndexOutOfBoundsException: Index 37 out of bounds for length 37 case False with eq_sig declC_new new >Method inheritable_in )java.lang.StringIndexOutOfBoundsException: Index 79 out of bounds for length 79
super: \<not> is_static old" and havejava.lang.NullPointerException by (auto intro!old_declared
member_new ?thesis by blast next casejava.lang.StringIndexOutOfBoundsException: Index 19 out of bounds for length 19 with accmodi_old subcls wf have" byshowthesis with wf have"is_static old" by (blast dest
instance_method showassumes: "G\ new overrides old" and
(contradiction qed qed qed from cls_C have"G\(super c)\\<^sub>C declclass old" by (rule subcls_superD) then show?Cold proof : "G<>Method new declared_in declclass new" case Eq : "msig = msig old" assume"superc " with" turnstileMethod old inheritable_in pid declclassnew"and have accmodi by (cases old) (auto intro: members.Immediate) with inheritable instance_method G<> declared_in show by (blast "? new old" next case SubclscaseInheritance assume moreover from inheritable accmodi_old have"G \Method old inheritable_in pid (super c)" by subcls_new_old show ultimately have"?P (super c) old"
Inherited then ? proof assume"\turnstile> superc" with inheritable instance_method showjava.lang.StringIndexOutOfBoundsException: Index 9 out of bounds for length 9 by (blast dest: hyp_member_super ?thesis
assume"\new. G \ new overrides\<^sub>S old \ G \Method new member_of super c" then super_new
super_new_override: "G assume stat_override_new': "G \ new' overrides\<^sub>S old"
super_new_member " new' = msig " by dest:stat_overrides_commonD
wf have"accmodi old \ accmodi super_new" byGjava.lang.NullPointerException
inheritable have"G \Method super_new inheritable_in pid C" by (auto simp case Immediate
split: acc_modi.splits
dest: acc_modi_le_Dests) moreover fromsuper_new_override have"\ is_static super_new" by (auto dest: stat_overrides_commonD) moreover note super_new_member ultimately new_declared' by (auto dest: hyp_member_super)
thesis proof assume"G \Method super_new member_of C" with super_new_override show ?thesis by blast next assume"\new. G \ new overrides\<^sub>S super_new \
G \<turnstile>Method new member_of C" eq_sig_new_new with super_new_override show ?thesis by (blast intro: stat_overridesR.Indirect) qed qed qed qed qed
lemma non_Package_instance_method_inheritance_cases:accmodi assume old
accmodi_old accmodi_old
:"not is_staticold and
subcls
old_declared: "G\Method old declared_in (declclass old)" and
wf: "wf_prog G" obtains (Inheritance) "G\Method old member_of C"
| (Overriding stat_override_inter_old proof - from old_inheritable accmodi_old instance_method subcls old_declared wfby( dest wf_prog_stat_overridesD)
Inheritance show thesis by (auto dest: non_Package_instance_method_inheritance) qed
lemma dynamic_to_static_overriding: assumes dyn_override: "G\ new overrides old" and
accmodi_old: "accmodi old \ Package" and
wf: "wf_prog G" shows"G\ new overrides\<^sub>S old" proof - from dyn_override
?thesis "? new old"java.lang.StringIndexOutOfBoundsException: Range [40, 41) out of bounds for length 40
wf case (Direct new "accmodi old \ accmodi new" assume new_declared: "G\Method new declared_in declclass new" proofcases Package assume subcls_new_old: "G\declclass new \\<^sub>C declclass old" assume"G \Method old inheritable_in pid (declclass new)" and case True "\ is_static old" and "G\declclass new\\<^sub>C declclass old" and "G\Method old declared_in declclass old" from this wf show"?Overrides new old" proof (cases rule: non_Package_instance_method_inheritance_cases) case Inheritance assume"G \Method old member_of declclass new" thenhave"G\mid (msig old) undeclared_in declclass new" proof cases case Immediate with subcls_new_old wf showwith by auto: subcls_irrefl next case ( "accmodi new") (auto add le_acc_def ) thenshow ?thesis by (cases old) auto ( dest) qed with eq_sig_new_old new_declared show ?thesis by (cases old,cases" <>new\<^sub>S old"
java.lang.StringIndexOutOfBoundsException: Index 8 out of bounds for length 8 case ? ': G\ new' overrides\<^sub>S old" thenhave"msig by (auto dest: have'"msig = new' by simp assume"Gshows " old" thenshow ?thesis proof (cases) case Immediate thenhave declC_new: "declclass new' = declclass new" by auto from Immediate have"G\Method new' declared_in declclass new" by (cases new') have G\java.lang.StringIndexOutOfBoundsException: Index 49 out of bounds for length 49 witheq_sig_new_new have wf by (cases new, cases new') (auto dest: unique_declared_in) with' show ?thesis by simp next case Inherited wf thenhave"G\mid (msig new') undeclared_in declclass new"
with wf with eq_sig_new_new' new_declared show ?thesis by (cases new,cases new') (auto dest!: declared_not_undeclared) qed qed next case (Indirect
accmodi_old assume dyn_override
accmodi_old
: " new = "and by blast moreover assume hyp_inter accmodi_old
java.lang.StringIndexOutOfBoundsException: Index 12 out of bounds for length 12 have"accmodi inter \ Package" proof -"\turnstileMethod old pid ( new)java.lang.StringIndexOutOfBoundsException: Index 72 out of bounds for length 72 fromby addjava.lang.StringIndexOutOfBoundsException: Index 44 out of bounds for length 44 have"accmodi old \ accmodi inter" by (auto dest: wf_prog_stat_overridesD: " with stat_override_inter_old accmodi_old wf show ?thesis by (auto dest!: no_Private_stat_override
: acc_modi
dest: acc_modi_le_Dests) qed ultimatelyshow"?Overrides new old dyn_override_Package_escape: by (blast intro: stat_overridesR.Indirect)accmodi_old
qed:G
lemma wf_prog_dyn_override_prop: assumes dyn_override: "G \ new overrides old" and
wf: "wf_prog G" shows proof (cases "accmodi old = Package") case True note old_Package = this show ?thesis
accmodi case True thenshow ?thesis . next case False withturnstile>Method old inheritable_in pid (declclass new)" have"accmodi new = Private" by (cases "accmodi new") (auto" (declclassold) = (declclass new)" with dyn_override show ?java.lang.StringIndexOutOfBoundsException: Index 21 out of bounds for length 21 by (auto dest: overrides_commonDIndirect ) qed next case False with dyn_override: \<turnstile> new overrides inter" have"G \ new overrides\<^sub>S old" by (blast intro: dynamic_to_static_overriding) with wf show ?thesis
: ) qed old
lemma overrides_Package_old: assumes dyn_override: "G \ new overrides old" and
accmodi_new:
wf: "wf_prog G " shows"accmodi old = Package" proof (cases "accmodi old") case Private with dyn_override show ?thesis
( : ) next case thenshow =java.lang.StringIndexOutOfBoundsException: Index 39 out of bounds for length 39 next case Protected
diff_pack_inter_new have"G \ new overrides\<^sub>S old" by (auto intro: dynamic_to_static_overriding) with wf have old by (auto dest: wf_prog_stat_overridesD) with Protected accmodi_new show ?thesis by (simp add: less_acc_def le_acc_def) next case Public with dyn_override wfjava.lang.StringIndexOutOfBoundsException: Index 18 out of bounds for length 18 have"G \ new overrides\<^sub>S old" by (auto intro: dynamic_to_static_overriding) with wf have"accmodi old \ accmodi new" by (auto dest: wf_prog_stat_overridesD) with Public accmodi_new show ?thesis by (simp add: less_acc_def le_acc_def) qed
lemma Protected assumes dyn_override: "G \ new overrides old" and
accmodi_old: "accmodi old = Package"and
accmodi_new: "accmodi new = Package"and
wf blast shows"pid (declclass old) = pid (declclass new)" proof - from dyn_override accmodi_old accmodi_new show hyp_inter_old obtainwhere case (Direct new old) assume"accmodi old = Package" "G \Method old inheritable_in pid (declclass new)" thenshow"pid (declclass old) = pid (declclass new)" by (auto simp add: inheritable_in_def) next case (Indirect new inter old) assume accmodi_old: " by (rule overridesRIndirect)
: "accmodi new = Package assume"G \ new overrides inter" by have"accmodi inter = Package" by (auto intro:qed with Indirect show"pid (declclass old) = java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0 by auto qed qed
lemma dyn_override_Package_escape: assumes dyn_override: "G \ new overrides old" and
accmodi_old: "accmodi old = Package"and
outside_pack: "pid (declclass old) \ pid (declclass new)" and
wf: "wf_prog G" shows"\ inter. G \ new overrides inter \ G \ inter overrides old \
(declclass) = (declclass) \<and>
Protected \<le> accmodi inter" proof - from dyn_override accmodi_old outside_pack show ?thesis (is"?P new old") proof (induct rule: overridesR.induct) case (Direct new old) assume accmodi_old: "accmodi old = Package" assume outside_pack: "pid (declclass old) \ pid (declclass new)" assume" next with accmodi_old
pid) by (simp? = " (map( with show"?P new old" by (contradiction) next caseIndirect old
? assume outside_pack: "pid (declclass old) proof (cases "?table sig") assume override_new_inter: "G \ new overrides inter"
: " assume hyp_new_inter: "\accmodi inter = Package;
" assume hyp_inter_old: "\accmodi old = Package;
pid (declclass old) \<noteq> pid (declclass inter)\<rbrakk> \<Longrightarrow> ?P inter old"
( : Hyp "piddeclclass old) = (declclass )") case True note same_pack_old_inter = this show ?thesis proof (cases "pid (declclass inter) = pid (declclass new)") case True with same_pack_old_inter outside_pack show ?thesis by auto next case False note diff_pack_inter_new = this\lbrakk methd \<rbrakk> show ?thesis proof: " G" case True with diff_pack_inter_new hyp_new_inter obtain newinter where
over_new_newinter: "G \ new overrides newinter" and
over_newinter_inter: "G \ newinter overrides inter" and
eq_pidpid= declclass
accmodi_newintercaseObject by auto fromjava.lang.StringIndexOutOfBoundsException: Index 53 out of bounds for length 53 have"G\newinter overrides old" by (rule overridesR.Indirect) moreover from eq_pid same_pack_old_inter havepid ( old)= pid newinter by simp moreover note accmodi_newinter ultimatelyshow ?thesis by blast next case False caseNone fromNone clsC m hyp have"Protected \ accmodi inter"show ? by (auto: method_declared_inI : methd_rec by (cases "accmodi inter") (auto dest java.lang.StringIndexOutOfBoundsException: Index 15 out of bounds for length 15 with override_new_inter override_inter_old same_pack_old_inter showthesis by blast qed qed next case False with accmodi_old hyp_inter_old obtain newinter where
over_inter_newinter: "G \ inter overrides newinter" and
over_newinter_old: "G \ newinter overrides old" and
eq_piddeclclass
accmodi_newinter: "Protected \ accmodi newinter" by auto from override_new_inter - have by (( Gsuper with eq_pid ?new"table_of ( \lambda(,m) , m)(methods )" show ?thesis
have meti ) Some qed qed qed
lemmas class_rec_induct' = class_rec.induct [of "%x y z w. P x y"] for P
lemma declclass_widen[ InheritedMethod byjava.lang.StringIndexOutOfBoundsException: Index 46 out of bounds for length 46 "wf_prog G \<longrightarrow> (\<forall>c m. class G C = Some c \<longrightarrow> methd G C sig = Some m \<longrightarrow> G\<turnstile>C \<preceq>\<^sub>C declclass m)" (is "?P G C") proof (induct G C rule: class_rec_induct', intro allI impI) fix G C c m assume Hyp: "\c. class G C = Some c \ ws_prog G \ C \ Object \<Longrightarrow> ?P G (super c)" assume wf: "wf_prog G"and cls_C shows
m: "methd G C sig = Some m" show proof"=") casejava.lang.StringIndexOutOfBoundsException: Index 14 out of bounds for length 14 with" Longrightarrow next let ?filter="filter_tab (\sig m. G\C inherits method sig m)" let wf:=" case False with cls_C wf m have methd_C: "(?filter (methd G (super c)) wf Gturnstile>Methd sig m declared_in Object" by (simp add: methd_rec) show?thesis proof (cases " declC
java.lang.StringIndexOutOfBoundsException: Index 15 out of bounds for length 15 from this methd_C have"?filterjava.lang.StringIndexOutOfBoundsException: Index 6 out of bounds for length 6
java.lang.StringIndexOutOfBoundsException: Index 15 out of bounds for length 15 moreover from wf cls_C False obtainfrom methd neq_C_Obj by (blast( rule) moreovernote wf False cls_C ultimately auto intro) by (auto intro moreoverfrom cls_C False have"G\C \\<^sub>C1 super c" by (rule subcls1I) ultimately next case Some from this wf False cls_C methd_Clemma: qed qed qed
lemma declclass_methd_Object: " \ methd G C sig = Some (C,new)" by auto
lemma methd_declaredD: " \<Longrightarrow> G\<turnstile>(mdecl (sig,mthd m)) declared_in (declclass m)" proof -
: "wf_prog Gjava.lang.StringIndexOutOfBoundsException: Index 27 out of bounds for length 27 thenhave ws: "ws_prog neq_C_Obj: "C \ Object" assume:is_class from clsC ws show"methd G C sig = Some m \<Longrightarrow> G\<turnstile>(mdecl (sig,mthd m)) declared_in (declclass m)"
( C rule') case Object show ?thesis if" clsCwf byrule)use that auto next case Subcls fix java.lang.StringIndexOutOfBoundsException: Index 11 out of bounds for length 11 assume clsC: "class G C = Some c" andm methd=m" and hyp: "methd G (super c) sig = Some m \ ?thesis" let ?newMethodshave: "G\Methd sig old declared_in (declclass old)"
?thesis proof (cases " newclsC
java.lang.StringIndexOutOfBoundsException: Index 15 out of bounds for length 15 from None ws clsC m hyp show ?thesis by (auto intro: method_declared_inI notetrancl_rtrancl_tranc [trans next case Some by( subcls1I) showthesis byautomethod_declared_inI qed qed qed
:
simp
Gand
clsC: "class G C = Some c"and
neq_C_Obj
java.lang.StringIndexOutOfBoundsException: Range [8, 5) out of bounds for length 59
| (InheritedMethod) "G\C inherits (method sig m)" and "methd G (super c) sig = Some m" proof - let dest
let ?new old_declared fromjava.lang.StringIndexOutOfBoundsException: Index 22 out of bounds for length 22 haveby intro) by (simp add: methd_rec) show thesis:) proof (cases "?new sig") case None with methd_unfold
()
subclseq_C_D next case Some with : "wf_progG andjava.lang.StringIndexOutOfBoundsException: Index 40 out of bounds for length 40 by auto with NewMethod show ?thesis by blast qed qed
lemma methd_member_of: assumes wf: "wf_prog G" shows "\is_class G C; methd G C sig = Some m\ \ G\Methd sig m member_of C"
(is"?Class C \ ?Method C \ ?MemberOf C") proof -
wf: "ws_progG . assume defC: "is_class G C" from defC ws show"?Class C \ ?Method C \ ?MemberOf C" proof (induct rule: ws_class_induct') case Object with wf have declC: "Object = declclass m" by (simp add: declclass_methd_Object old
Object " by (auto intro: methd_declaredD simp eq_D_Obj with declC
java.lang.StringIndexOutOfBoundsException: Index 6 out of bounds for length 6 by (auto intro!: members.Immediate
simp del: methd_Object) next case (Subcls C c) assume clsCfromclsC
neq_C_Obj: "C \ Object" assume methd: "?Method C" from methd ws clsC neq_C_Obj showMemberOf proof (cases rule: is_cls_super: "is_class c)" case NewMethod
auto ) by (autoclsC neq_C_Obj
java.lang.StringIndexOutOfBoundsException: Index 8 out of bounds for length 8 case InheritedMethod thenshow"?thesis" by (blast dest: inherits_member qed qed qed
: "\table_of (methods c) sig = Some new;
ws_prog G; class G C = Some old
methd G (super c) sig = Some old\<rbrakk> \<Longrightarrow> methd G C sig = Some (C,new)" by (auto simp "
intro: filter_tab_SomeI
lemma wf_prog_staticD: assumes wf: "wf_prog G"and
clsCC=c java.lang.StringIndexOutOfBoundsException: Index 42 out of bounds for length 42
neq_C_Obj: "C \ Object" and
old: "methd havenot_static_super "<not>is_static
accmodi_old <le> accmodi old" and"and
new: "table_of (methods c) sig = Some new" shows"is_static new = is_static old" proof - from clsC wf have wf_cdecl: "wf_cdecl G inheritable "\<turnstile>Methd sig super_method inheritable_in (pid C)" from wf clsC neq_C_Obj have is_cls_super: "is_class G (super c)" by (blast dest: wf_prog_acc_superD is_acc_classD) from wf is_cls_super old have old_member_of: "G\Methd sig old member_of (super c)" by (rule methd_member_of) from old wf is_cls_super have old_declared: "G\Methd sig old declared_in (declclass old)" by (auto dest: methd_declared_in_declclass) from new clsC have new_declared: "G\Methd sig (C,new) declared_in C" by (auto intro: method_declared_inI) note trancl_rtrancl_tranc = trancl_rtrancl_trancl [trans] (* ### in Basis *) from clsC neq_C_Obj have subcls1_C_super: "G\C \\<^sub>C1 super c" by (rule subcls1I) thenhave"G\C \\<^sub>C super c" .. alsofrom old wf is_cls_super have"G\super c \\<^sub>C (declclass old)" by (auto dest: methd_declC) finallyhave subcls_C_old: "G\C \\<^sub>C (declclass old)" . from accmodi_old have inheritable: "G\Methd sig old inheritable_in pid C" by (auto simp add: inheritable_in_def
dest: acc_modi_le_Dests) show ?thesis proof (cases "is_static new") case True with subcls_C_old new_declared old_declared inheritable have"G,sig\(C,new) hides old" by (auto intro: hidesI) with True wf_cdecl neq_C_Obj new show ?thesis by (auto dest: wf_cdecl_hides_SomeD) next case False with subcls_C_old new_declared old_declared inheritable subcls1_C_super
old_member_of have"G,sig\(C,new) overrides\<^sub>S old" by (auto intro: stat_overridesR.Direct) with False wf_cdecl neq_C_Obj new show ?thesis by (auto dest: wf_cdecl_overrides_SomeD) qed qed
lemma inheritable_instance_methd: assumes subclseq_C_D: "G\C \\<^sub>C D" and
is_cls_D: "is_class G D"and
wf: "wf_prog G"and
old: "methd G D sig = Some old"and
accmodi_old: "Protected \ accmodi old" and
not_static_old: "\ is_static old" shows "\new. methd G C sig = Some new \
(new = old \<or> G,sig\<turnstile>new overrides\<^sub>S old)"
(is"(\new. (?Constraint C new old))") proof - from subclseq_C_D is_cls_D have is_cls_C: "is_class G C"by (rule subcls_is_class2) from wf have ws: "ws_prog G" .. from is_cls_C ws subclseq_C_D show"\new. ?Constraint C new old" proof (induct rule: ws_class_induct') case (Object co) thenhave eq_D_Obj: "D=Object"by auto with old have"?Constraint Object old old" by auto with eq_D_Obj show"\ new. ?Constraint Object new old" by auto next case (Subcls C c) assume hyp: "G\super c\\<^sub>C D \ \new. ?Constraint (super c) new old" assume clsC: "class G C = Some c" assume neq_C_Obj: "C\Object" from clsC wf have wf_cdecl: "wf_cdecl G (C,c)" by (rule wf_prog_cdecl) from ws clsC neq_C_Obj have is_cls_super: "is_class G (super c)" by (auto dest: ws_prog_cdeclD) from clsC wf neq_C_Obj have superAccessible: "G\(Class (super c)) accessible_in (pid C)" and
subcls1_C_super: "G\C \\<^sub>C1 super c" by (auto dest: wf_prog_cdecl wf_cdecl_supD is_acc_classD
intro: subcls1I) show"\new. ?Constraint C new old" proof (cases "G\super c\\<^sub>C D") case False from False Subcls have eq_C_D: "C=D" by (auto dest: subclseq_superD) with old have"?Constraint C old old" by auto with eq_C_D show"\ new. ?Constraint C new old" by auto next case True with hyp obtain super_method where super: "?Constraint (super c) super_method old"by blast from super not_static_old have not_static_super: "\ is_static super_method" by (auto dest!: stat_overrides_commonD) from super old wf accmodi_old have accmodi_super_method: "Protected \ accmodi super_method" by (auto dest!: wf_prog_stat_overridesD) from super accmodi_old wf have inheritable: "G\Methd sig super_method inheritable_in (pid C)" by (auto dest!: wf_prog_stat_overridesD
acc_modi_le_Dests
simp add: inheritable_in_def) from super wf is_cls_super
--> --------------------
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