*** empty log message ***
authornipkow
Thu Nov 11 12:23:45 1999 +0100 (1999-11-11)
changeset 8011d14c4e9e9c8e
parent 8010 69032a618aa9
child 8012 bbdf3c51c3b8
*** empty log message ***
src/HOL/MicroJava/BV/BVSpec.ML
src/HOL/MicroJava/BV/BVSpec.thy
src/HOL/MicroJava/BV/BVSpecTypeSafe.ML
src/HOL/MicroJava/BV/BVSpecTypeSafe.thy
src/HOL/MicroJava/BV/Convert.ML
src/HOL/MicroJava/BV/Convert.thy
src/HOL/MicroJava/BV/Correct.ML
src/HOL/MicroJava/BV/Correct.thy
src/HOL/MicroJava/J/Conform.ML
src/HOL/MicroJava/J/Conform.thy
src/HOL/MicroJava/J/Decl.thy
src/HOL/MicroJava/J/Eval.ML
src/HOL/MicroJava/J/Eval.thy
src/HOL/MicroJava/J/JBasis.ML
src/HOL/MicroJava/J/JBasis.thy
src/HOL/MicroJava/J/JTypeSafe.ML
src/HOL/MicroJava/J/JTypeSafe.thy
src/HOL/MicroJava/J/Prog.ML
src/HOL/MicroJava/J/Prog.thy
src/HOL/MicroJava/J/State.ML
src/HOL/MicroJava/J/State.thy
src/HOL/MicroJava/J/Term.thy
src/HOL/MicroJava/J/Type.ML
src/HOL/MicroJava/J/Type.thy
src/HOL/MicroJava/J/TypeRel.ML
src/HOL/MicroJava/J/TypeRel.thy
src/HOL/MicroJava/J/WellForm.ML
src/HOL/MicroJava/J/WellForm.thy
src/HOL/MicroJava/J/WellType.ML
src/HOL/MicroJava/J/WellType.thy
src/HOL/MicroJava/JVM/Control.thy
src/HOL/MicroJava/JVM/JVMExec.thy
src/HOL/MicroJava/JVM/JVMState.thy
src/HOL/MicroJava/JVM/LoadAndStore.thy
src/HOL/MicroJava/JVM/Method.ML
src/HOL/MicroJava/JVM/Method.thy
src/HOL/MicroJava/JVM/Object.thy
src/HOL/MicroJava/JVM/Opstack.thy
src/HOL/MicroJava/JVM/Store.ML
src/HOL/MicroJava/JVM/Store.thy
src/HOL/MicroJava/ROOT.ML
     1.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
     1.2 +++ b/src/HOL/MicroJava/BV/BVSpec.ML	Thu Nov 11 12:23:45 1999 +0100
     1.3 @@ -0,0 +1,31 @@
     1.4 +(*  Title:      HOL/MicroJava/BV/BVSpec.ML
     1.5 +    ID:         $Id$
     1.6 +    Author:     Cornelia Pusch
     1.7 +    Copyright   1999 Technische Universitaet Muenchen
     1.8 +*)
     1.9 +
    1.10 +Addsimps [wt_MR_def];
    1.11 +
    1.12 +Goalw [wt_jvm_prog_def] "wt_jvm_prog G phi \\<Longrightarrow> (\\<exists>wt. wf_prog wt G)";
    1.13 +by(Blast_tac 1);
    1.14 +qed "wt_jvm_progD";
    1.15 +
    1.16 +
    1.17 +Goalw [wt_jvm_prog_def]
    1.18 +"\\<lbrakk> wt_jvm_prog G phi; \
    1.19 +\   cmethd (G,C) sig = Some (C,rT,maxl,ins); \
    1.20 +\   pc < length ins \\<rbrakk> \
    1.21 +\\\<Longrightarrow> wt_instr (ins!pc) G rT (phi C sig) (length ins) pc";
    1.22 +by(forward_tac [rotate_prems 2 cmethd_wf_mdecl] 1);
    1.23 + by (Asm_full_simp_tac 1);
    1.24 +by(asm_full_simp_tac (simpset() addsimps [wf_mdecl_def,wt_method_def]) 1);
    1.25 +qed "wt_jvm_prog_impl_wt_instr";
    1.26 +
    1.27 +Goalw [wt_jvm_prog_def]
    1.28 +"\\<lbrakk> wt_jvm_prog G phi; \
    1.29 +\   cmethd (G,C) sig = Some (C,rT,maxl,ins) \\<rbrakk> \\<Longrightarrow> \
    1.30 +\ 0 < (length ins) \\<and> wt_start G C (snd sig) maxl (phi C sig)";
    1.31 +by(forward_tac [rotate_prems 2 cmethd_wf_mdecl] 1);
    1.32 + by (Asm_full_simp_tac 1);
    1.33 +by(asm_full_simp_tac (simpset() addsimps [wf_mdecl_def,wt_method_def]) 1);
    1.34 +qed "wt_jvm_prog_impl_wt_start";
     2.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
     2.2 +++ b/src/HOL/MicroJava/BV/BVSpec.thy	Thu Nov 11 12:23:45 1999 +0100
     2.3 @@ -0,0 +1,201 @@
     2.4 +(*  Title:      HOL/MicroJava/BV/BVSpec.thy
     2.5 +    ID:         $Id$
     2.6 +    Author:     Cornelia Pusch
     2.7 +    Copyright   1999 Technische Universitaet Muenchen
     2.8 +
     2.9 +Specification of bytecode verifier
    2.10 +*)
    2.11 +
    2.12 +BVSpec = Convert +
    2.13 +
    2.14 +types
    2.15 + method_type 	= "state_type list"
    2.16 + class_type	= "sig \\<Rightarrow> method_type"
    2.17 + prog_type	= "cname \\<Rightarrow> class_type"
    2.18 +
    2.19 +consts
    2.20 + wt_LS	:: "[load_and_store,jvm_prog,method_type,p_count,p_count] \\<Rightarrow> bool"
    2.21 +primrec
    2.22 +"wt_LS (Load idx) G phi max_pc pc =
    2.23 +	(let (ST,LT) = phi ! pc
    2.24 +	 in
    2.25 +	 pc+1 < max_pc \\<and>
    2.26 +	 idx < length LT \\<and>
    2.27 +	 (\\<exists>ts. (LT ! idx) = Some ts \\<and> 
    2.28 +	       G \\<turnstile> phi ! (pc+1) >>>= (ts # ST , LT)))"
    2.29 +
    2.30 +"wt_LS (Store idx) G phi max_pc pc =
    2.31 +	(let (ST,LT) = phi ! pc
    2.32 +	 in
    2.33 +	 pc+1 < max_pc \\<and>
    2.34 +	 idx < length LT \\<and>
    2.35 +	 (\\<exists>ts ST'. ST = ts # ST' \\<and>
    2.36 +		   G \\<turnstile> phi ! (pc+1) >>>= (ST' , LT[idx:=Some ts])))"
    2.37 +
    2.38 +"wt_LS (Bipush i) G phi max_pc pc =
    2.39 +	(let (ST,LT) = phi ! pc
    2.40 +	 in
    2.41 +	 pc+1 < max_pc \\<and>
    2.42 +	 G \\<turnstile> phi ! (pc+1) >>>= ((PrimT Integer) # ST , LT))"
    2.43 +
    2.44 +"wt_LS (Aconst_null) G phi max_pc pc =
    2.45 +	(let (ST,LT) = phi ! pc
    2.46 +	 in
    2.47 +	 pc+1 < max_pc \\<and>
    2.48 +	 G \\<turnstile> phi ! (pc+1) >>>= (NT # ST , LT))"
    2.49 +
    2.50 +consts
    2.51 + wt_MO	:: "[manipulate_object,jvm_prog,method_type,p_count,p_count] \\<Rightarrow> bool" 
    2.52 +primrec
    2.53 +"wt_MO (Getfield F C) G phi max_pc pc =
    2.54 +	(let (ST,LT) = phi ! pc
    2.55 +	 in
    2.56 +	 pc+1 < max_pc \\<and>
    2.57 +	 is_class G C \\<and>
    2.58 +	 (\\<exists>T oT ST'. cfield (G,C) F = Some(C,T) \\<and>
    2.59 +                       ST = oT # ST' \\<and> 
    2.60 +		       G \\<turnstile> oT \\<preceq> (Class C) \\<and>
    2.61 +		       G \\<turnstile> phi ! (pc+1) >>>= (T # ST' , LT)))"
    2.62 +
    2.63 +"wt_MO (Putfield F C) G phi max_pc pc =
    2.64 +	(let (ST,LT) = phi ! pc
    2.65 +	 in
    2.66 +	 pc+1 < max_pc \\<and>
    2.67 +	 is_class G C \\<and> 
    2.68 +	 (\\<exists>T vT oT ST'.
    2.69 +             cfield (G,C) F = Some(C,T) \\<and>
    2.70 +             ST = vT # oT # ST' \\<and> 
    2.71 +             G \\<turnstile> oT \\<preceq> (Class C) \\<and>
    2.72 +	     G \\<turnstile> vT \\<preceq> T  \\<and>
    2.73 +             G \\<turnstile> phi ! (pc+1) >>>= (ST' , LT)))"
    2.74 +
    2.75 +
    2.76 +consts 
    2.77 + wt_CO	:: "[create_object,jvm_prog,method_type,p_count,p_count] \\<Rightarrow> bool" 
    2.78 +primrec
    2.79 +"wt_CO (New C) G phi max_pc pc =
    2.80 +	(let (ST,LT) = phi ! pc
    2.81 +	 in
    2.82 +	 pc+1 < max_pc \\<and>
    2.83 +	 is_class G C \\<and>
    2.84 +	 G \\<turnstile> phi ! (pc+1) >>>= ((Class C) # ST , LT))"
    2.85 +
    2.86 +consts
    2.87 + wt_CH	:: "[check_object,jvm_prog,method_type,p_count,p_count] \\<Rightarrow> bool" 
    2.88 +primrec
    2.89 +"wt_CH (Checkcast C) G phi max_pc pc = 
    2.90 +	(let (ST,LT) = phi ! pc
    2.91 +	 in
    2.92 +	 pc+1 < max_pc \\<and>
    2.93 +	 is_class G C \\<and> 
    2.94 +	 (\\<exists>rt ST'. ST = RefT rt # ST' \\<and>
    2.95 +                   G \\<turnstile> phi ! (pc+1) >>>= (Class C # ST' , LT)))"
    2.96 +
    2.97 +consts 
    2.98 + wt_OS	:: "[op_stack,jvm_prog,method_type,p_count,p_count] \\<Rightarrow> bool" 
    2.99 +primrec
   2.100 +"wt_OS Pop G phi max_pc pc =
   2.101 +	(let (ST,LT) = phi ! pc
   2.102 +	 in
   2.103 +	 \\<exists>ts ST'. pc+1 < max_pc \\<and>
   2.104 +		ST = ts # ST' \\<and> 	 
   2.105 +		G \\<turnstile> phi ! (pc+1) >>>= (ST' , LT))"
   2.106 +
   2.107 +"wt_OS Dup G phi max_pc pc =
   2.108 +	(let (ST,LT) = phi ! pc
   2.109 +	 in
   2.110 +	 pc+1 < max_pc \\<and>
   2.111 +	 (\\<exists>ts ST'. ST = ts # ST' \\<and> 	 
   2.112 +		   G \\<turnstile> phi ! (pc+1) >>>= (ts # ts # ST' , LT)))"
   2.113 +
   2.114 +"wt_OS Dup_x1 G phi max_pc pc =
   2.115 +	(let (ST,LT) = phi ! pc
   2.116 +	 in
   2.117 +	 pc+1 < max_pc \\<and>
   2.118 +	 (\\<exists>ts1 ts2 ST'. ST = ts1 # ts2 # ST' \\<and> 	 
   2.119 +		   G \\<turnstile> phi ! (pc+1) >>>= (ts1 # ts2 # ts1 # ST' , LT)))"
   2.120 +
   2.121 +"wt_OS Dup_x2 G phi max_pc pc =
   2.122 +	(let (ST,LT) = phi ! pc
   2.123 +	 in
   2.124 +	 pc+1 < max_pc \\<and>
   2.125 +	 (\\<exists>ts1 ts2 ts3 ST'. ST = ts1 # ts2 # ts3 # ST' \\<and> 	 
   2.126 +		   G \\<turnstile> phi ! (pc+1) >>>= (ts1 # ts2 # ts3 # ts1 # ST' , LT)))"
   2.127 +
   2.128 +"wt_OS Swap G phi max_pc pc =
   2.129 +	(let (ST,LT) = phi ! pc
   2.130 +	 in
   2.131 +	 pc+1 < max_pc \\<and>
   2.132 +	 (\\<exists>ts ts' ST'. ST = ts' # ts # ST' \\<and> 	 
   2.133 +		       G \\<turnstile> phi ! (pc+1) >>>= (ts # ts' # ST' , LT)))"
   2.134 +
   2.135 +consts 
   2.136 + wt_BR	:: "[branch,jvm_prog,method_type,p_count,p_count] \\<Rightarrow> bool" 
   2.137 +primrec
   2.138 +"wt_BR (Ifcmpeq branch) G phi max_pc pc =
   2.139 +	(let (ST,LT) = phi ! pc
   2.140 +	 in
   2.141 +	 pc+1 < max_pc \\<and> (nat(int pc+branch)) < max_pc \\<and> 
   2.142 +	 (\\<exists>ts ts' ST'. ST = ts # ts' # ST' \\<and>  ts = ts' \\<and>
   2.143 +		       G \\<turnstile> phi ! (pc+1) >>>= (ST' , LT) \\<and>
   2.144 +		       G \\<turnstile> phi ! (nat(int pc+branch)) >>>= (ST' , LT)))"
   2.145 +"wt_BR (Goto branch) G phi max_pc pc =
   2.146 +	(let (ST,LT) = phi ! pc
   2.147 +	 in
   2.148 +	 (nat(int pc+branch)) < max_pc \\<and> 
   2.149 +	 G \\<turnstile> phi ! (nat(int pc+branch)) >>>= (ST , LT))"
   2.150 +
   2.151 +consts
   2.152 + wt_MI :: "[meth_inv,jvm_prog,method_type,p_count,p_count] \\<Rightarrow> bool" 
   2.153 +primrec
   2.154 +"wt_MI (Invokevirtual mn fpTs) G phi max_pc pc =
   2.155 +	(let (ST,LT) = phi ! pc
   2.156 +	 in
   2.157 +         pc+1 < max_pc \\<and>
   2.158 +         (\\<exists>apTs C ST'. ST = (rev apTs) @ (Class C # ST') \\<and>
   2.159 +         length apTs = length fpTs \\<and>
   2.160 +         (\\<forall>(aT,fT)\\<in>set(zip apTs fpTs). G \\<turnstile> aT \\<preceq> fT) \\<and>
   2.161 +         (\\<exists>D rT b. cmethd (G,C) (mn,fpTs) = Some(D,rT,b) \\<and>
   2.162 +         G \\<turnstile> phi ! (pc+1) >>>= (rT # ST' , LT))))"
   2.163 +
   2.164 +constdefs
   2.165 + wt_MR	:: "[jvm_prog,ty,method_type,p_count] \\<Rightarrow> bool"
   2.166 +"wt_MR G rT phi pc \\<equiv>
   2.167 +	(let (ST,LT) = phi ! pc
   2.168 +	 in
   2.169 +	 (\\<exists>T ST'. ST = T # ST' \\<and> G \\<turnstile> T \\<preceq> rT))"
   2.170 +
   2.171 +
   2.172 +constdefs
   2.173 + wt_instr :: "[instr,jvm_prog,ty,method_type,nat,p_count] \\<Rightarrow> bool"
   2.174 + "wt_instr instr G rT phi max_pc pc \\<equiv>
   2.175 +	case instr of
   2.176 +	  LS ins \\<Rightarrow> wt_LS ins G phi max_pc pc
   2.177 +	| CO  ins \\<Rightarrow> wt_CO ins G phi max_pc pc
   2.178 +	| MO  ins \\<Rightarrow> wt_MO ins G phi max_pc pc
   2.179 +	| CH  ins \\<Rightarrow> wt_CH ins G phi max_pc pc
   2.180 +	| MI  ins \\<Rightarrow> wt_MI ins G phi max_pc pc
   2.181 +	| MR      \\<Rightarrow> wt_MR     G rT phi pc
   2.182 +	| OS  ins \\<Rightarrow> wt_OS ins G phi max_pc pc
   2.183 +	| BR  ins \\<Rightarrow> wt_BR ins G phi max_pc pc"
   2.184 +
   2.185 +
   2.186 +constdefs
   2.187 + wt_start :: "[jvm_prog,cname,ty list,nat,method_type] \\<Rightarrow> bool"
   2.188 + "wt_start G C pTs mxl phi \\<equiv> 
   2.189 +    G \\<turnstile> phi!0 >>>= ([],(Some(Class C))#((map Some pTs))@(replicate mxl None))"
   2.190 +
   2.191 +
   2.192 + wt_method :: "[jvm_prog,cname,ty list,ty,nat,instr list,method_type] \\<Rightarrow> bool"
   2.193 + "wt_method G cn pTs rT mxl ins phi \\<equiv>
   2.194 +	let max_pc = length ins
   2.195 +        in
   2.196 +	0 < max_pc \\<and> wt_start G cn pTs mxl phi \\<and> 
   2.197 +	(\\<forall>pc. pc<max_pc \\<longrightarrow> wt_instr (ins ! pc) G rT phi max_pc pc)"
   2.198 +
   2.199 + wt_jvm_prog :: "[jvm_prog,prog_type] \\<Rightarrow> bool"
   2.200 +"wt_jvm_prog G phi \\<equiv>
   2.201 +   wf_prog (\\<lambda>G C (sig,rT,maxl,b).
   2.202 +              wt_method G C (snd sig) rT maxl b (phi C sig)) G"
   2.203 +
   2.204 +end
     3.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
     3.2 +++ b/src/HOL/MicroJava/BV/BVSpecTypeSafe.ML	Thu Nov 11 12:23:45 1999 +0100
     3.3 @@ -0,0 +1,625 @@
     3.4 +(*  Title:      HOL/MicroJava/BV/BVSpecTypeSafe.ML
     3.5 +    ID:         $Id$
     3.6 +    Author:     Cornelia Pusch
     3.7 +    Copyright   1999 Technische Universitaet Muenchen
     3.8 +*)
     3.9 +
    3.10 +val defs1 = exec.rules@[split_def,sup_state_def,correct_state_def,
    3.11 +		correct_frame_def,wt_instr_def];
    3.12 +
    3.13 +Goalw [correct_state_def,Let_def,correct_frame_def,split_def]
    3.14 +"\\<lbrakk> wt_jvm_prog G phi; \
    3.15 +\   cmethd (G,C) sig = Some (C,rT,maxl,ins); \
    3.16 +\   correct_state G phi (None, hp, (stk,loc,C,sig,pc)#frs) \\<rbrakk> \
    3.17 +\\\<Longrightarrow> wt_instr (ins!pc) G rT (phi C sig) (length ins) pc";
    3.18 +by (Asm_full_simp_tac 1);
    3.19 +by(blast_tac (claset() addIs [wt_jvm_prog_impl_wt_instr]) 1);
    3.20 +qed "wt_jvm_prog_impl_wt_instr_cor";
    3.21 +
    3.22 +
    3.23 +Delsimps [split_paired_All];
    3.24 +
    3.25 +
    3.26 +(******* LS *******)
    3.27 +
    3.28 +Goal
    3.29 +"\\<lbrakk> wf_prog wt G; \
    3.30 +\  cmethd (G,C) ml = Some (C,rT,maxl,ins); \
    3.31 +\  ins!pc = LS(Load idx); \
    3.32 +\  wt_instr (ins!pc) G rT (phi C ml) (length ins) pc; \
    3.33 +\  Some (xp',hp',frs') = exec (G, None, hp, (stk,loc,C,ml,pc)#frs); \
    3.34 +\  correct_state G phi (None, hp, (stk,loc,C,ml,pc)#frs) \\<rbrakk> \
    3.35 +\\\<Longrightarrow> correct_state G phi (xp',hp',frs')";
    3.36 +by (fast_tac (claset() addIs [approx_stk_imp_approx_stk_sup,approx_loc_imp_approx_val_sup,
    3.37 +	approx_loc_imp_approx_loc_sup] 
    3.38 +	addss (simpset() addsimps [approx_stk_Cons,sup_loc_Cons,map_eq_Cons]@defs1)) 1);
    3.39 +qed "Load_correct";
    3.40 +
    3.41 +
    3.42 +Goal 
    3.43 +"\\<lbrakk> wf_prog wt G; \
    3.44 +\  cmethd (G,C) ml = Some (C,rT,maxl,ins); \
    3.45 +\  ins!pc = LS(Store idx); \
    3.46 +\  wt_instr (ins!pc) G rT (phi C ml) (length ins) pc; \
    3.47 +\  Some (xp',hp',frs') = exec (G, None, hp, (stk,loc,C,ml,pc)#frs) ; \
    3.48 +\  correct_state G phi (None, hp, (stk,loc,C,ml,pc)#frs) \\<rbrakk> \
    3.49 +\\\<Longrightarrow> correct_state G phi (xp',hp',frs')";
    3.50 +by (fast_tac (claset() addDs [approx_stk_Cons_lemma]
    3.51 +	addIs [approx_stk_imp_approx_stk_sup,approx_loc_imp_approx_loc_subst RSN(2, approx_loc_imp_approx_loc_sup)]
    3.52 +	addss (simpset() addsimps [sup_loc_Cons,map_eq_Cons]@defs1)) 1);
    3.53 +qed "Store_correct";
    3.54 +
    3.55 +Goalw [conf_def] "G,h \\<turnstile> Intg i \\<Colon>\\<preceq> PrimT Integer";
    3.56 +by(Simp_tac 1);
    3.57 +qed "conf_Intg_Integer";
    3.58 +AddIffs [conf_Intg_Integer];
    3.59 +
    3.60 +Goal
    3.61 +"\\<lbrakk> wf_prog wt G; \
    3.62 +\  cmethd (G,C) ml = Some (C,rT,maxl,ins); \
    3.63 +\  ins!pc = LS(Bipush i); \
    3.64 +\  wt_instr (ins!pc) G rT (phi C ml) (length ins) pc; \
    3.65 +\  Some (xp',hp',frs') = exec (G, None, hp, (stk,loc,C,ml,pc)#frs) ; \
    3.66 +\  correct_state G phi (None, hp, (stk,loc,C,ml,pc)#frs) \\<rbrakk> \
    3.67 +\\\<Longrightarrow> correct_state G phi (xp',hp',frs')";
    3.68 +by (fast_tac (claset()addIs [approx_stk_imp_approx_stk_sup,approx_loc_imp_approx_loc_sup]
    3.69 +	addss (simpset() addsimps [approx_val_def,sup_PTS_eq,sup_loc_Cons,map_eq_Cons,approx_stk_Cons]@defs1)) 1);
    3.70 +qed "Bipush_correct";
    3.71 +
    3.72 +Goal "G \\<turnstile> T' \\<preceq> T \\<Longrightarrow> T' = NT \\<longrightarrow> (T=NT | (\\<exists>C. T = Class C))";
    3.73 +be widen.induct 1;
    3.74 +by(Auto_tac);
    3.75 +by(rename_tac "R" 1);
    3.76 +by(exhaust_tac "R" 1);
    3.77 +by(Auto_tac);
    3.78 +val lemma = result();
    3.79 +
    3.80 +Goal "G \\<turnstile> NT \\<preceq> T = (T=NT | (\\<exists>C. T = Class C))";
    3.81 +by(force_tac (claset() addIs widen.intrs addDs [lemma],simpset()) 1);
    3.82 +qed "NT_subtype_conv";
    3.83 +
    3.84 +Goal 
    3.85 +"\\<lbrakk> wf_prog wt G; \
    3.86 +\  cmethd (G,C) ml = Some (C,rT,maxl,ins); \
    3.87 +\  ins!pc = LS Aconst_null; \
    3.88 +\  wt_instr (ins!pc) G rT (phi C ml) (length ins) pc; \
    3.89 +\  Some (xp',hp',frs') = exec (G, None, hp, (stk,loc,C,ml,pc)#frs) ; \
    3.90 +\  correct_state G phi (None, hp, (stk,loc,C,ml,pc)#frs) \\<rbrakk> \
    3.91 +\\\<Longrightarrow> correct_state G phi (xp',hp',frs')";
    3.92 +by (fast_tac (claset() addIs [approx_stk_imp_approx_stk_sup,approx_loc_imp_approx_loc_sup]
    3.93 +	addss (simpset() addsimps [approx_val_Null,NT_subtype_conv,sup_loc_Cons,map_eq_Cons,approx_stk_Cons]@defs1)) 1);
    3.94 +qed "Aconst_null_correct";
    3.95 +
    3.96 +
    3.97 +Goal
    3.98 +"\\<lbrakk> wt_jvm_prog G phi; \
    3.99 +\  cmethd (G,C) ml = Some (C,rT,maxl,ins); \
   3.100 +\  ins!pc = LS ls_com; \
   3.101 +\  Some (xp',hp',frs') = exec (G, None, hp, (stk,loc,C,ml,pc)#frs) ; \
   3.102 +\  correct_state G phi (None, hp, (stk,loc,C,ml,pc)#frs) \\<rbrakk> \
   3.103 +\\\<Longrightarrow> correct_state G phi (xp',hp',frs')";
   3.104 +by(forward_tac [wt_jvm_prog_impl_wt_instr_cor] 1);
   3.105 +  ba 1;
   3.106 + ba 1;
   3.107 +by(rewtac wt_jvm_prog_def);
   3.108 +by (exhaust_tac "ls_com" 1);
   3.109 +by (ALLGOALS (fast_tac (claset() addIs [Load_correct,Store_correct,Bipush_correct,Aconst_null_correct])));
   3.110 +qed "LS_correct";
   3.111 +
   3.112 +
   3.113 +(**** CH ****)
   3.114 +
   3.115 +Goalw [cast_ok_def]
   3.116 + "\\<lbrakk> wf_prog ok G; G,h\\<turnstile>v\\<Colon>\\<preceq>RefT rt; cast_ok G (Class C) h v ; G\\<turnstile>(Class C)\\<preceq>T'; is_class G C \\<rbrakk> \
   3.117 +\ \\<Longrightarrow> G,h\\<turnstile>v\\<Colon>\\<preceq>T'";
   3.118 +be disjE 1;
   3.119 + by (Clarify_tac 1);
   3.120 +by (forward_tac [widen_Class] 1);
   3.121 +by (Clarify_tac 1);
   3.122 +be disjE 1;
   3.123 + by (asm_full_simp_tac (simpset() addsimps [widen.null]) 1);
   3.124 +by (asm_full_simp_tac (simpset() addsimps [conf_def]) 1);
   3.125 +by (Clarify_tac 1);
   3.126 +by (asm_full_simp_tac (simpset() addsimps [obj_ty_def]) 1);
   3.127 +by (exhaust_tac "v" 1);
   3.128 +by (ALLGOALS (fast_tac  (claset() addIs [widen_trans] addss (simpset() addsimps [widen.null]))));
   3.129 +qed "Cast_conf2";
   3.130 +
   3.131 +Goal
   3.132 +"\\<lbrakk> wf_prog wt G; \
   3.133 +\  cmethd (G,C) ml = Some (C,rT,maxl,ins); \
   3.134 +\  ins!pc = CH (Checkcast D); \
   3.135 +\  wt_instr (ins!pc) G rT (phi C ml) (length ins) pc; \
   3.136 +\  Some (xp',hp',frs') = exec (G, None, hp, (stk,loc,C,ml,pc)#frs); \
   3.137 +\  correct_state G phi (None, hp, (stk,loc,C,ml,pc)#frs) \\<rbrakk> \
   3.138 +\\\<Longrightarrow> correct_state G phi (xp',hp',frs')";
   3.139 +by (asm_full_simp_tac (simpset() addsimps [sup_loc_Cons,map_eq_Cons,approx_stk_Cons,
   3.140 +		xcpt_update_def,raise_xcpt_def]@defs1 addsplits [option.split]) 1);
   3.141 +by (fast_tac (claset() addDs [approx_stk_Cons_lemma] 
   3.142 +	addIs [approx_stk_imp_approx_stk_sup,approx_loc_imp_approx_loc_sup,Cast_conf2] 
   3.143 +	addss (simpset() addsimps [sup_loc_Cons,map_eq_Cons,approx_stk_Cons,approx_val_def])) 1);
   3.144 +qed "Checkcast_correct";
   3.145 +
   3.146 +
   3.147 +Goal
   3.148 +"\\<lbrakk> wt_jvm_prog G phi; \
   3.149 +\  cmethd (G,C) ml = Some (C,rT,maxl,ins); \
   3.150 +\  ins!pc = CH ch_com; \
   3.151 +\  Some (xp',hp',frs') = exec (G, None, hp, (stk,loc,C,ml,pc)#frs) ; \
   3.152 +\  correct_state G phi (None, hp, (stk,loc,C,ml,pc)#frs) \\<rbrakk> \
   3.153 +\\\<Longrightarrow> correct_state G phi (xp',hp',frs')";
   3.154 +by(forward_tac [wt_jvm_prog_impl_wt_instr_cor] 1);
   3.155 +  ba 1;
   3.156 + ba 1;
   3.157 +by(rewtac wt_jvm_prog_def);
   3.158 +by (exhaust_tac "ch_com" 1);
   3.159 +by (ALLGOALS (fast_tac (claset() addIs [Checkcast_correct])));
   3.160 +qed "CH_correct";
   3.161 +
   3.162 +
   3.163 +(******* MO *******)
   3.164 +Goal
   3.165 +"\\<lbrakk> wf_prog wt G; \
   3.166 +\  cmethd (G,C) ml = Some (C,rT,maxl,ins); \
   3.167 +\  ins!pc = MO (Getfield F D); \
   3.168 +\  wt_instr (ins!pc) G rT (phi C ml) (length ins) pc; \
   3.169 +\  Some (xp',hp',frs') = exec (G, None, hp, (stk,loc,C,ml,pc)#frs); \
   3.170 +\  correct_state G phi (None, hp, (stk,loc,C,ml,pc)#frs) \\<rbrakk> \
   3.171 +\\\<Longrightarrow> correct_state G phi (xp',hp',frs')";
   3.172 +by (asm_full_simp_tac (simpset() addsimps [xcpt_update_def,raise_xcpt_def]@defs1 addsplits [option.split]) 1);
   3.173 +by (Clarify_tac 1);
   3.174 +by (asm_full_simp_tac (simpset() addsimps [sup_state_def,sup_loc_Cons,map_eq_Cons]) 1);
   3.175 +by (Clarify_tac 1);
   3.176 +bd approx_stk_Cons_lemma 1;
   3.177 +by (Clarify_tac 1);
   3.178 +by (asm_full_simp_tac (simpset() addsimps [approx_val_def]) 1);
   3.179 +
   3.180 +by (forward_tac [conf_widen] 1);
   3.181 +  ba 1;
   3.182 + ba 1;
   3.183 +bd conf_RefTD 1;
   3.184 +by (Clarify_tac 1);
   3.185 +by (asm_full_simp_tac (simpset() addsimps []) 1);
   3.186 +
   3.187 +(* approx_stk *)
   3.188 +br conjI 1;
   3.189 +by  (asm_full_simp_tac (simpset() addsimps [approx_stk_Cons]) 1);
   3.190 +br  conjI 1;
   3.191 +by   (fast_tac (claset() addIs [approx_stk_imp_approx_stk_sup]) 1);
   3.192 +by  (asm_full_simp_tac (simpset() addsimps [approx_val_def]) 1);
   3.193 +bd  widen_cfs_fields 1;
   3.194 +   ba 1;
   3.195 +  ba 1;
   3.196 +by  (fast_tac (claset() addIs [conf_widen] addss (simpset() addsimps [hconf_def,oconf_def,lconf_def])) 1);
   3.197 +
   3.198 +(* approx_loc *)
   3.199 +by (fast_tac (claset() addIs [approx_loc_imp_approx_loc_sup]) 1);
   3.200 +qed "Getfield_correct";
   3.201 +
   3.202 +
   3.203 +Goal
   3.204 +"\\<lbrakk> wf_prog wt G; \
   3.205 +\  cmethd (G,C) ml = Some (C,rT,maxl,ins); \
   3.206 +\  ins!pc = MO (Putfield F D); \
   3.207 +\  wt_instr (ins!pc) G rT (phi C ml) (length ins) pc; \
   3.208 +\  Some (xp',hp',frs') = exec (G, None, hp, (stk,loc,C,ml,pc)#frs); \
   3.209 +\  correct_state G phi (None, hp, (stk,loc,C,ml,pc)#frs) \\<rbrakk> \
   3.210 +\\\<Longrightarrow> correct_state G phi (xp',hp',frs')";
   3.211 +by (asm_full_simp_tac (simpset() addsimps [xcpt_update_def,raise_xcpt_def]@defs1 addsplits [option.split]) 1);
   3.212 +by (Clarify_tac 1);
   3.213 +by (asm_full_simp_tac (simpset() addsimps [sup_state_def,sup_loc_Cons,map_eq_Cons]) 1);
   3.214 +by (Clarify_tac 1);
   3.215 +bd approx_stk_Cons_lemma 1;
   3.216 +by (Clarify_tac 1);
   3.217 +bd approx_stk_Cons_lemma 1;
   3.218 +by (Clarify_tac 1);
   3.219 +by (asm_full_simp_tac (simpset() addsimps [approx_val_def]) 1);
   3.220 +
   3.221 +by (forward_tac [conf_widen] 1);
   3.222 +  ba 2;
   3.223 + ba 1;
   3.224 +by (fast_tac (claset() addDs [conf_RefTD,widen_cfs_fields] 
   3.225 +	addIs [sup_heap_update_value,approx_stk_imp_approx_stk_sup_heap RSN(2,approx_stk_imp_approx_stk_sup),
   3.226 +		approx_loc_imp_approx_loc_sup_heap RSN(2,approx_loc_imp_approx_loc_sup),
   3.227 +		hconf_imp_hconf_field_update,
   3.228 +		correct_frames_imp_correct_frames_field_update,conf_widen] addss (simpset())) 1);
   3.229 +qed "Putfield_correct";
   3.230 +
   3.231 +
   3.232 +Goal
   3.233 +"\\<lbrakk> wt_jvm_prog G phi; \
   3.234 +\  cmethd (G,C) ml = Some (C,rT,maxl,ins); \
   3.235 +\  ins!pc = MO mo_com; \
   3.236 +\  Some (xp',hp',frs') = exec (G, None, hp, (stk,loc,C,ml,pc)#frs) ; \
   3.237 +\  correct_state G phi (None, hp, (stk,loc,C,ml,pc)#frs) \\<rbrakk> \
   3.238 +\\\<Longrightarrow> correct_state G phi (xp',hp',frs')";
   3.239 +by(forward_tac [wt_jvm_prog_impl_wt_instr_cor] 1);
   3.240 +  ba 1;
   3.241 + ba 1;
   3.242 +by(rewtac wt_jvm_prog_def);
   3.243 +by (exhaust_tac "mo_com" 1);
   3.244 +by (ALLGOALS (fast_tac (claset() addIs [Getfield_correct,Putfield_correct])));
   3.245 +qed "MO_correct";
   3.246 +
   3.247 +
   3.248 +(****** CO ******)
   3.249 +
   3.250 +Goal "(\\<forall>x y. P(x,y)) = (\\<forall>z. P z)";
   3.251 +by(Fast_tac 1);
   3.252 +qed "collapse_paired_All";
   3.253 +
   3.254 +Goal
   3.255 +"\\<lbrakk> wf_prog wt G; \
   3.256 +\  cmethd (G,C) sig = Some (C,rT,maxl,ins); \
   3.257 +\  ins!pc = CO(New cl_idx); \
   3.258 +\  wt_instr (ins!pc) G rT (phi C sig) (length ins) pc; \
   3.259 +\  Some (xp',hp',frs') = exec (G, None, hp, (stk,loc,C,sig,pc)#frs) ; \
   3.260 +\  correct_state G phi (None, hp, (stk,loc,C,sig,pc)#frs) \\<rbrakk> \
   3.261 +\\\<Longrightarrow> correct_state G phi (xp',hp',frs')";
   3.262 +by (fast_tac (claset() addSDs [collapse_paired_All RS iffD1]addIs [sup_heap_newref,
   3.263 +		approx_stk_imp_approx_stk_sup_heap RSN(2,approx_stk_imp_approx_stk_sup),
   3.264 +		approx_loc_imp_approx_loc_sup_heap RSN(2,approx_loc_imp_approx_loc_sup),
   3.265 +		hconf_imp_hconf_newref,correct_frames_imp_correct_frames_newref,
   3.266 +		rewrite_rule [split_def] correct_init_obj]
   3.267 +	addss (simpset() addsimps [NT_subtype_conv,approx_stk_Cons,approx_val_def,conf_def,
   3.268 +		fun_upd_apply,sup_loc_Cons,map_eq_Cons,is_class_def,xcpt_update_def,raise_xcpt_def,init_vars_def]@defs1 
   3.269 +	addsplits [option.split])) 1);
   3.270 +qed "New_correct";
   3.271 +
   3.272 +Goal
   3.273 +"\\<lbrakk> wt_jvm_prog G phi; \
   3.274 +\  cmethd (G,C) ml = Some (C,rT,maxl,ins); \
   3.275 +\  ins!pc = CO co_com; \
   3.276 +\  Some (xp',hp',frs') = exec (G, None, hp, (stk,loc,C,ml,pc)#frs) ; \
   3.277 +\  correct_state G phi (None, hp, (stk,loc,C,ml,pc)#frs) \\<rbrakk> \
   3.278 +\\\<Longrightarrow> correct_state G phi (xp',hp',frs')";
   3.279 +by(forward_tac [wt_jvm_prog_impl_wt_instr_cor] 1);
   3.280 +  ba 1;
   3.281 + ba 1;
   3.282 +by(rewtac wt_jvm_prog_def);
   3.283 +by (exhaust_tac "co_com" 1);
   3.284 +by (ALLGOALS (fast_tac (claset() addIs [New_correct])));
   3.285 +qed "CO_correct";
   3.286 +
   3.287 +
   3.288 +(****** MI ******)
   3.289 +
   3.290 +Goal
   3.291 +"\\<lbrakk> wt_jvm_prog G phi; \
   3.292 +\  cmethd (G,C) ml = Some (C,rT,maxl,ins); \
   3.293 +\  ins ! pc = MI(Invokevirtual mn pTs); \
   3.294 +\  wt_instr (ins!pc) G rT (phi C ml) (length ins) pc; \
   3.295 +\  Some (xp',hp',frs') = exec (G, None, hp, (stk,loc,C,ml,pc)#frs) ; \
   3.296 +\  correct_state G phi (None, hp, (stk,loc,C,ml,pc)#frs) \\<rbrakk> \
   3.297 +\\\<Longrightarrow> correct_state G phi (xp',hp',frs')";
   3.298 +by(forward_tac [wt_jvm_progD] 1);
   3.299 +by(etac exE 1);
   3.300 +by (asm_full_simp_tac (simpset()addsimps[xcpt_update_def,raise_xcpt_def]@defs1 
   3.301 +	addsplits [option.split]) 1);
   3.302 +by (Clarify_tac 1);
   3.303 +by (asm_full_simp_tac (simpset() addsimps []@defs1) 1);
   3.304 +bd approx_stk_append_lemma 1;   
   3.305 +by (Clarify_tac 1);
   3.306 +bd approx_stk_Cons_lemma 1;
   3.307 +by (asm_full_simp_tac (simpset() addsimps []) 1);
   3.308 +by (Clarify_tac 1);
   3.309 +by (asm_full_simp_tac (simpset() addsimps [approx_val_def]) 1);
   3.310 +bd conf_RefTD 1;
   3.311 +by (Clarify_tac 1);
   3.312 +by(rename_tac "oloc oT ofs T'" 1);
   3.313 +by (asm_full_simp_tac (simpset() addsimps []@defs1) 1);
   3.314 +bd subtype_widen_methd 1;
   3.315 +  ba 1;
   3.316 + ba 1;
   3.317 +be exE 1;
   3.318 +by(rename_tac "oT'" 1);
   3.319 +by (Clarify_tac 1);
   3.320 +by(subgoal_tac "G \\<turnstile> Class oT \\<preceq> Class oT'" 1);
   3.321 + by(forw_inst_tac [("C","oT")](standard(rotate_prems 1 cmethd_wf_mdecl)) 2);
   3.322 +  ba 2;
   3.323 + by(Blast_tac 2);
   3.324 +by (asm_full_simp_tac (simpset() addsimps []@defs1) 1);
   3.325 +by(forward_tac [cmethd_in_md] 1);
   3.326 + ba 1;
   3.327 + back();
   3.328 + back();
   3.329 +by (Clarify_tac 1);
   3.330 +by (asm_full_simp_tac (simpset() addsimps []@defs1) 1);
   3.331 +by (forward_tac [wt_jvm_prog_impl_wt_start] 1);
   3.332 + ba 1;
   3.333 + back();
   3.334 +by (asm_full_simp_tac (simpset() addsimps [wt_start_def,sup_state_def]) 1);
   3.335 +by (Clarify_tac 1);
   3.336 +
   3.337 +(** approx_stk **)
   3.338 +br conjI 1;
   3.339 + by (asm_full_simp_tac (simpset() addsimps [sup_loc_Nil,approx_stk_Nil]) 1);
   3.340 +
   3.341 +
   3.342 +(** approx_loc **)
   3.343 +br conjI 1;
   3.344 + br approx_loc_imp_approx_loc_sup 1;
   3.345 +   ba 1;
   3.346 +  by (Fast_tac 2);
   3.347 + by (asm_full_simp_tac (simpset() addsimps [split_def,approx_loc_Cons,approx_val_def,approx_loc_append]) 1);
   3.348 + br conjI 1;
   3.349 +  br conf_widen 1;
   3.350 +    ba 1;
   3.351 +   by (Fast_tac 2);
   3.352 +  by (asm_full_simp_tac (simpset() addsimps [conf_def]) 1);
   3.353 + br conjI 1;
   3.354 +  by (fast_tac (claset() addIs [approx_stk_rev RS iffD2 RSN(4,assConv_approx_stk_imp_approx_loc)] 
   3.355 +	addss (simpset() addsimps [split_def,approx_loc_Cons,approx_val_def])) 1);
   3.356 + by (asm_simp_tac (simpset() addsimps [split_def,approx_loc_def,zip_replicate,approx_val_None,set_replicate_conv_if]) 1);
   3.357 +
   3.358 +br conjI 1;
   3.359 + by (asm_simp_tac (simpset() addsimps [min_def]) 1);
   3.360 +br exI 1;
   3.361 +br exI 1;
   3.362 +br conjI 1;
   3.363 + by(Blast_tac 1);
   3.364 +by (fast_tac (claset()
   3.365 +       addIs [approx_stk_imp_approx_stk_sup,approx_loc_imp_approx_loc_sup]
   3.366 +       addss (simpset()addsimps [map_eq_Cons,sup_loc_Cons])) 1);
   3.367 +qed "Invokevirtual_correct";
   3.368 +
   3.369 +Goal
   3.370 +"\\<lbrakk> wt_jvm_prog G phi; \
   3.371 +\  cmethd (G,C) ml = Some (C,rT,maxl,ins); \
   3.372 +\  ins!pc = MI mi_com; \
   3.373 +\  Some (xp',hp',frs') = exec (G, None, hp, (stk,loc,C,ml,pc)#frs) ; \
   3.374 +\  correct_state G phi (None, hp, (stk,loc,C,ml,pc)#frs) \\<rbrakk> \
   3.375 +\\\<Longrightarrow> correct_state G phi (xp',hp',frs')";
   3.376 +by(forward_tac [wt_jvm_prog_impl_wt_instr_cor] 1);
   3.377 +  ba 1;
   3.378 + ba 1;
   3.379 +by (exhaust_tac "mi_com" 1);
   3.380 +by (ALLGOALS (fast_tac (claset() addIs [Invokevirtual_correct])));
   3.381 +qed "MI_correct";
   3.382 +
   3.383 +(****** MR ******)
   3.384 +
   3.385 +Goal
   3.386 + "\\<forall>zs. (xs@ys = zs) = (xs = take (length xs) zs \\<and> ys = drop (length xs) zs)";
   3.387 +by(induct_tac "xs" 1);
   3.388 +by(Simp_tac 1);
   3.389 +by(Asm_full_simp_tac 1);
   3.390 +by(Clarify_tac 1);
   3.391 +by(exhaust_tac "zs" 1);
   3.392 +by(Auto_tac);
   3.393 +qed_spec_mp "append_eq_conv_conj";
   3.394 +
   3.395 +
   3.396 +
   3.397 +Delsimps [map_append];
   3.398 +Goal
   3.399 +"\\<lbrakk> wt_jvm_prog G phi; \
   3.400 +\  cmethd (G,C) ml = Some (C,rT,maxl,ins); \
   3.401 +\  ins ! pc = MR; \
   3.402 +\  wt_instr (ins!pc) G rT (phi C ml) (length ins) pc; \
   3.403 +\  Some (xp',hp',frs') = exec (G, None, hp, (stk,loc,C,ml,pc)#frs) ; \
   3.404 +\  correct_state G phi (None, hp, (stk,loc,C,ml,pc)#frs) \\<rbrakk> \
   3.405 +\\\<Longrightarrow> correct_state G phi (xp',hp',frs')";
   3.406 +by (asm_full_simp_tac (simpset() addsimps defs1) 1);
   3.407 +by (Clarify_tac 1);
   3.408 +by (asm_full_simp_tac (simpset() addsimps defs1) 1);
   3.409 +by (exhaust_tac "frs" 1);
   3.410 + by (asm_full_simp_tac (simpset() addsimps defs1) 1);
   3.411 +by (Clarify_tac 1);
   3.412 +by (asm_full_simp_tac (simpset() addsimps [sup_loc_Cons,map_eq_Cons]@defs1) 1);
   3.413 +by (Clarify_tac 1);
   3.414 +by (asm_full_simp_tac (simpset() addsimps defs1) 1);
   3.415 +by (forward_tac [wt_jvm_prog_impl_wt_instr] 1);
   3.416 +  by(EVERY1[atac, etac Suc_lessD]);
   3.417 +by(rewtac wt_jvm_prog_def);
   3.418 +by (fast_tac (claset()
   3.419 + addDs [approx_stk_Cons_lemma,subcls_widen_methd]
   3.420 + addEs [rotate_prems 1 widen_trans]
   3.421 + addIs [conf_widen] 
   3.422 +	addss (simpset()
   3.423 + addsimps [approx_val_def,append_eq_conv_conj,sup_loc_Cons,map_eq_Cons,approx_stk_Cons]@defs1)) 1);
   3.424 +qed "Return_correct";
   3.425 +Addsimps [map_append];
   3.426 +
   3.427 +Goal
   3.428 +"\\<lbrakk> wt_jvm_prog G phi; \
   3.429 +\  cmethd (G,C) ml = Some (C,rT,maxl,ins); \
   3.430 +\  ins!pc = MR; \
   3.431 +\  Some (xp',hp',frs') = exec (G, None, hp, (stk,loc,C,ml,pc)#frs) ; \
   3.432 +\  correct_state G phi (None, hp, (stk,loc,C,ml,pc)#frs) \\<rbrakk> \
   3.433 +\\\<Longrightarrow> correct_state G phi (xp',hp',frs')";
   3.434 +by(forward_tac [wt_jvm_prog_impl_wt_instr_cor] 1);
   3.435 +  ba 1;
   3.436 + ba 1;
   3.437 +by (ALLGOALS (fast_tac (claset() addIs [Return_correct])));
   3.438 +qed "MR_correct";
   3.439 +
   3.440 +(****** BR ******)
   3.441 +Goal 
   3.442 +"\\<lbrakk> wf_prog wt G; \
   3.443 +\  cmethd (G,C) ml = Some (C,rT,maxl,ins); \
   3.444 +\  ins ! pc = BR(Goto branch); \
   3.445 +\  wt_instr (ins!pc) G rT (phi C ml) (length ins) pc; \
   3.446 +\  Some (xp',hp',frs') = exec (G, None, hp, (stk,loc,C,ml,pc)#frs) ; \
   3.447 +\  correct_state G phi (None, hp, (stk,loc,C,ml,pc)#frs) \\<rbrakk> \
   3.448 +\\\<Longrightarrow> correct_state G phi (xp',hp',frs')";
   3.449 +by (fast_tac (claset() addIs [approx_loc_imp_approx_loc_sup,approx_stk_imp_approx_stk_sup]
   3.450 +	addss (simpset() addsimps defs1)) 1);
   3.451 +qed "Goto_correct";
   3.452 +
   3.453 +
   3.454 +Goal 
   3.455 +"\\<lbrakk> wf_prog wt G; \
   3.456 +\  cmethd (G,C) ml = Some (C,rT,maxl,ins); \
   3.457 +\  ins!pc = BR(Ifcmpeq branch); \
   3.458 +\  wt_instr (ins!pc) G rT (phi C ml) (length ins) pc; \
   3.459 +\  Some (xp',hp',frs') = exec (G, None, hp, (stk,loc,C,ml,pc)#frs) ; \
   3.460 +\  correct_state G phi (None, hp, (stk,loc,C,ml,pc)#frs) \\<rbrakk> \
   3.461 +\\\<Longrightarrow> correct_state G phi (xp',hp',frs')";
   3.462 +by (fast_tac (claset() addDs [approx_stk_Cons_lemma] 
   3.463 +	addIs [approx_stk_imp_approx_stk_sup,approx_loc_imp_approx_loc_sup] addss (simpset() addsimps defs1)) 1);
   3.464 +qed "Ifiacmpeq_correct";
   3.465 +
   3.466 +
   3.467 +Goal
   3.468 +"\\<lbrakk> wt_jvm_prog G phi; \
   3.469 +\  cmethd (G,C) ml = Some (C,rT,maxl,ins); \
   3.470 +\  ins!pc = BR br_com; \
   3.471 +\  Some (xp',hp',frs') = exec (G, None, hp, (stk,loc,C,ml,pc)#frs) ; \
   3.472 +\  correct_state G phi (None, hp, (stk,loc,C,ml,pc)#frs) \\<rbrakk> \
   3.473 +\\\<Longrightarrow> correct_state G phi (xp',hp',frs')";
   3.474 +by(forward_tac [wt_jvm_prog_impl_wt_instr_cor] 1);
   3.475 +  ba 1;
   3.476 + ba 1;
   3.477 +by(rewtac wt_jvm_prog_def);
   3.478 +by (exhaust_tac "br_com" 1);
   3.479 +by (ALLGOALS (fast_tac (claset() addIs [Goto_correct,Ifiacmpeq_correct])));
   3.480 +qed "BR_correct";
   3.481 +
   3.482 +
   3.483 +(****** OS ******)
   3.484 +
   3.485 +Goal 
   3.486 +"\\<lbrakk> wf_prog wt G; \
   3.487 +\  cmethd (G,C) ml = Some (C,rT,maxl,ins); \
   3.488 +\  ins ! pc = OS Pop; \
   3.489 +\  wt_instr (ins!pc) G rT (phi C ml) (length ins) pc; \
   3.490 +\  Some (xp',hp',frs') = exec (G, None, hp, (stk,loc,C,ml,pc)#frs); \
   3.491 +\  correct_state G phi (None, hp, (stk,loc,C,ml,pc)#frs) \\<rbrakk> \
   3.492 +\\\<Longrightarrow> correct_state G phi (xp',hp',frs')";
   3.493 +by (fast_tac (claset() addDs [approx_stk_Cons_lemma] 
   3.494 +	addIs [approx_stk_imp_approx_stk_sup,approx_loc_imp_approx_loc_sup] addss (simpset() addsimps defs1)) 1);
   3.495 +qed "Pop_correct";
   3.496 +
   3.497 +
   3.498 +Goal 
   3.499 +"\\<lbrakk> wf_prog wt G; \
   3.500 +\  cmethd (G,C) ml = Some (C,rT,maxl,ins); \
   3.501 +\  ins ! pc = OS Dup; \
   3.502 +\  wt_instr (ins!pc) G rT (phi C ml) (length ins) pc; \
   3.503 +\  Some (xp',hp',frs') = exec (G, None, hp, (stk,loc,C,ml,pc)#frs); \
   3.504 +\  correct_state G phi (None, hp, (stk,loc,C,ml,pc)#frs) \\<rbrakk> \
   3.505 +\\\<Longrightarrow> correct_state G phi (xp',hp',frs')";
   3.506 +by (fast_tac (claset() addDs [approx_stk_Cons_lemma]
   3.507 +	addIs [approx_stk_imp_approx_stk_sup,approx_val_imp_approx_val_sup,approx_loc_imp_approx_loc_sup] 
   3.508 +	addss (simpset() addsimps [approx_stk_Cons,sup_loc_Cons,map_eq_Cons]@defs1)) 1);
   3.509 +qed "Dup_correct";
   3.510 +
   3.511 +
   3.512 +Goal 
   3.513 +"\\<lbrakk> wf_prog wt G; \
   3.514 +\  cmethd (G,C) ml = Some (C,rT,maxl,ins); \
   3.515 +\  ins ! pc = OS Dup_x1; \
   3.516 +\  wt_instr (ins!pc) G rT (phi C ml) (length ins) pc; \
   3.517 +\  Some (xp',hp',frs') = exec (G, None, hp, (stk,loc,C,ml,pc)#frs); \
   3.518 +\  correct_state G phi (None, hp, (stk,loc,C,ml,pc)#frs) \\<rbrakk> \
   3.519 +\\\<Longrightarrow> correct_state G phi (xp',hp',frs')";
   3.520 +by (fast_tac (claset() addDs [approx_stk_Cons_lemma]
   3.521 +	addIs [approx_stk_imp_approx_stk_sup,approx_val_imp_approx_val_sup,approx_loc_imp_approx_loc_sup] 
   3.522 +	addss (simpset() addsimps [approx_stk_Cons,sup_loc_Cons,map_eq_Cons]@defs1)) 1);
   3.523 +qed "Dup_x1_correct";
   3.524 +
   3.525 +Goal 
   3.526 +"\\<lbrakk> wf_prog wt G; \
   3.527 +\  cmethd (G,C) ml = Some (C,rT,maxl,ins); \
   3.528 +\  ins ! pc = OS Dup_x2; \
   3.529 +\  wt_instr (ins!pc) G rT (phi C ml) (length ins) pc; \
   3.530 +\  Some (xp',hp',frs') = exec (G, None, hp, (stk,loc,C,ml,pc)#frs); \
   3.531 +\  correct_state G phi (None, hp, (stk,loc,C,ml,pc)#frs) \\<rbrakk> \
   3.532 +\\\<Longrightarrow> correct_state G phi (xp',hp',frs')";
   3.533 +by (fast_tac (claset() addDs [approx_stk_Cons_lemma]
   3.534 +	addIs [approx_stk_imp_approx_stk_sup,approx_val_imp_approx_val_sup,approx_loc_imp_approx_loc_sup] 
   3.535 +	addss (simpset() addsimps [approx_stk_Cons,sup_loc_Cons,map_eq_Cons]@defs1)) 1);
   3.536 +qed "Dup_x2_correct";
   3.537 +
   3.538 +Goal 
   3.539 +"\\<lbrakk> wf_prog wt G; \
   3.540 +\  cmethd (G,C) ml = Some (C,rT,maxl,ins); \
   3.541 +\  ins ! pc = OS Swap; \
   3.542 +\  wt_instr (ins!pc) G rT (phi C ml) (length ins) pc; \
   3.543 +\  Some (xp',hp',frs') = exec (G, None, hp, (stk,loc,C,ml,pc)#frs); \
   3.544 +\  correct_state G phi (None, hp, (stk,loc,C,ml,pc)#frs) \\<rbrakk> \
   3.545 +\\\<Longrightarrow> correct_state G phi (xp',hp',frs')";
   3.546 +by (fast_tac (claset() addDs [approx_stk_Cons_lemma] 
   3.547 +	addIs [approx_stk_imp_approx_stk_sup,approx_val_imp_approx_val_sup,approx_loc_imp_approx_loc_sup] 
   3.548 +	addss (simpset() addsimps [approx_stk_Cons,sup_loc_Cons,map_eq_Cons]@defs1)) 1);
   3.549 +qed "Swap_correct";
   3.550 +
   3.551 +Goal
   3.552 +"\\<lbrakk> wt_jvm_prog G phi; \
   3.553 +\  cmethd (G,C) ml = Some (C,rT,maxl,ins); \
   3.554 +\  ins!pc = OS os_com; \
   3.555 +\  Some (xp',hp',frs') = exec (G, None, hp, (stk,loc,C,ml,pc)#frs) ; \
   3.556 +\  correct_state G phi (None, hp, (stk,loc,C,ml,pc)#frs) \\<rbrakk> \
   3.557 +\\\<Longrightarrow> correct_state G phi (xp',hp',frs')";
   3.558 +by(forward_tac [wt_jvm_prog_impl_wt_instr_cor] 1);
   3.559 +  ba 1;
   3.560 + ba 1;
   3.561 +by(rewtac wt_jvm_prog_def);
   3.562 +by (exhaust_tac "os_com" 1);
   3.563 +by (ALLGOALS (fast_tac (claset() addIs [Pop_correct,Dup_correct,Dup_x1_correct,Dup_x2_correct,Swap_correct])));
   3.564 +qed "OS_correct";
   3.565 +
   3.566 +(** Main **)
   3.567 +
   3.568 +Goalw [correct_state_def,Let_def]
   3.569 + "correct_state G phi (None,hp,(stk,loc,C,sig,pc)#fs) \
   3.570 +\ \\<Longrightarrow> \\<exists>meth. cmethd (G,C) sig = Some(C,meth)";
   3.571 +by(Asm_full_simp_tac 1);
   3.572 +by(Blast_tac 1);
   3.573 +qed "correct_state_impl_Some_cmethd";
   3.574 +
   3.575 +Goal
   3.576 +"\\<And>state. \\<lbrakk> wt_jvm_prog G phi; correct_state G phi state\\<rbrakk> \
   3.577 +\ \\<Longrightarrow> exec (G,state) = Some state' \\<longrightarrow> correct_state G phi state'";
   3.578 +by(split_all_tac 1);
   3.579 +by(rename_tac "xp hp frs" 1);
   3.580 +by (exhaust_tac "xp" 1);
   3.581 + by (exhaust_tac "frs" 1);
   3.582 +  by (asm_full_simp_tac (simpset() addsimps exec.rules) 1);
   3.583 + by(split_all_tac 1);
   3.584 + by(hyp_subst_tac 1);
   3.585 + by(forward_tac [correct_state_impl_Some_cmethd] 1);
   3.586 + by (force_tac (claset() addIs [LS_correct,CO_correct,MO_correct,CH_correct,MI_correct,MR_correct,OS_correct,
   3.587 +	BR_correct], simpset() addsplits [instr.split,instr.split_asm] addsimps exec.rules@[split_def]) 1);
   3.588 +by (exhaust_tac "frs" 1);
   3.589 + by (asm_full_simp_tac (simpset() addsimps exec.rules) 1);
   3.590 +by (force_tac (claset(), simpset() addsimps exec.rules@[correct_state_def]) 1);
   3.591 +qed_spec_mp "BV_correct_1";
   3.592 +
   3.593 +
   3.594 +(*******)
   3.595 +Goal
   3.596 +"xp=None \\<longrightarrow> frs\\<noteq>[] \\<longrightarrow> (\\<exists>xp' hp' frs'. exec (G,xp,hp,frs) = Some (xp',hp',frs'))";
   3.597 +by (fast_tac (claset() addIs [BV_correct_1] 
   3.598 +	addss (simpset() addsplits [instr.split] addsimps [neq_Nil_conv]@defs1)) 1);
   3.599 +qed_spec_mp "exec_lemma";
   3.600 +
   3.601 +Goal
   3.602 +"\\<lbrakk> wt_jvm_prog G phi; \
   3.603 +\  correct_state G phi (xp,hp,frs); xp=None; frs\\<noteq>[] \\<rbrakk> \
   3.604 +\ \\<Longrightarrow> \\<exists>xp' hp' frs'. exec (G,xp,hp,frs) = Some (xp',hp',frs') \\<and> correct_state G phi (xp',hp',frs')";
   3.605 +by (dres_inst_tac [("G","G"),("hp","hp")]  exec_lemma 1);
   3.606 +ba 1;
   3.607 +by (fast_tac (claset() addIs [BV_correct_1]) 1);
   3.608 +qed "L1";
   3.609 +(*******)
   3.610 +
   3.611 +Goalw [exec_all_def]
   3.612 +"\\<lbrakk> wt_jvm_prog G phi; G \\<turnstile> s -jvm\\<rightarrow> t \\<rbrakk> \
   3.613 +\ \\<Longrightarrow> correct_state G phi s \\<longrightarrow> correct_state G phi t";
   3.614 +be rtrancl_induct 1;
   3.615 + by (Simp_tac 1);
   3.616 +by (fast_tac (claset() addIs [BV_correct_1] addss (simpset())) 1);
   3.617 +qed_spec_mp "BV_correct";
   3.618 +
   3.619 +
   3.620 +Goal
   3.621 +"\\<lbrakk> wt_jvm_prog G phi; G \\<turnstile> s0 -jvm\\<rightarrow> (None,hp,(stk,loc,cn,ml,pc)#frs); correct_state G phi s0 \\<rbrakk> \
   3.622 +\ \\<Longrightarrow>  approx_stk G hp stk (fst (((phi  cn)  ml) ! pc)) \\<and> approx_loc G hp loc (snd (((phi  cn)  ml) ! pc)) ";
   3.623 +bd BV_correct 1;
   3.624 +ba 1;
   3.625 +ba 1;
   3.626 +by (asm_full_simp_tac (simpset() addsimps [correct_state_def,correct_frame_def,split_def] 
   3.627 +	addsplits [option.split_asm]) 1);
   3.628 +qed_spec_mp "BV_correct_initial";
     4.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
     4.2 +++ b/src/HOL/MicroJava/BV/BVSpecTypeSafe.thy	Thu Nov 11 12:23:45 1999 +0100
     4.3 @@ -0,0 +1,10 @@
     4.4 +(*  Title:      HOL/MicroJava/BV/BVSpecTypeSafe.thy
     4.5 +    ID:         $Id$
     4.6 +    Author:     Cornelia Pusch
     4.7 +    Copyright   1999 Technische Universitaet Muenchen
     4.8 +
     4.9 +Proof that the specification of the bytecode verifier only admits type safe
    4.10 +programs.
    4.11 +*)
    4.12 +
    4.13 +BVSpecTypeSafe = Correct
     5.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
     5.2 +++ b/src/HOL/MicroJava/BV/Convert.ML	Thu Nov 11 12:23:45 1999 +0100
     5.3 @@ -0,0 +1,41 @@
     5.4 +(*  Title:      HOL/MicroJava/BV/Convert.ML
     5.5 +    ID:         $Id$
     5.6 +    Author:     Cornelia Pusch
     5.7 +    Copyright   1999 Technische Universitaet Muenchen
     5.8 +*)
     5.9 +
    5.10 +val widen_PrimT_conv1 =
    5.11 + prove_typerel "(G \\<turnstile> PrimT x \\<preceq> T) = (T = PrimT x)"
    5.12 + [ prove_widen_lemma "G\\<turnstile>S\\<preceq>T \\<Longrightarrow> S = PrimT x \\<longrightarrow> T = PrimT x"];
    5.13 +Addsimps [widen_PrimT_conv1];
    5.14 +
    5.15 +Goalw [sup_ty_opt_def] "(G \\<turnstile> any >= None) = (any = None)";
    5.16 +by(simp_tac (simpset() addsplits [option.split]) 1);
    5.17 +qed "anyConvNone";
    5.18 +Addsimps [anyConvNone];
    5.19 +
    5.20 +Goalw [sup_ty_opt_def] "(G \\<turnstile> Some ty >= Some ty') = (G \\<turnstile> ty' \\<preceq> ty)";
    5.21 +by(Simp_tac 1);
    5.22 +qed "SomeanyConvSome";
    5.23 +Addsimps [SomeanyConvSome];
    5.24 +
    5.25 +Goal
    5.26 +"(G \\<turnstile> X >= Some(PrimT Integer)) = (X=None \\<or> (X=Some(PrimT Integer)))";
    5.27 +by (simp_tac (simpset() setloop (split_tac [ty.split,option.split]) addsimps [sup_ty_opt_def]) 1);
    5.28 +qed "sup_PTS_eq";
    5.29 +
    5.30 +
    5.31 +
    5.32 +Goal
    5.33 +"CFS \\<turnstile> XT >>= [] = (XT=[])";
    5.34 +by (case_tac "XT=[]" 1);
    5.35 +by (asm_simp_tac (simpset() addsimps [sup_loc_def]) 1);
    5.36 +by (fast_tac (claset() addss (simpset() addsimps [sup_loc_def,neq_Nil_conv])) 1);
    5.37 +qed "sup_loc_Nil";
    5.38 +
    5.39 +Goal
    5.40 +"CFS \\<turnstile> XT >>= (Y#YT) = (\\<exists>X XT'. XT=X#XT' \\<and> CFS \\<turnstile> X>=Y \\<and> CFS \\<turnstile> XT'>>=YT)";
    5.41 +by (case_tac "XT=[]" 1);
    5.42 +by (asm_simp_tac (simpset() addsimps [sup_loc_def]) 1);
    5.43 +by (fast_tac (claset() addss (simpset() addsimps [sup_loc_def,neq_Nil_conv])) 1);
    5.44 +qed "sup_loc_Cons";
     6.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
     6.2 +++ b/src/HOL/MicroJava/BV/Convert.thy	Thu Nov 11 12:23:45 1999 +0100
     6.3 @@ -0,0 +1,33 @@
     6.4 +(*  Title:      HOL/MicroJava/BV/Convert.thy
     6.5 +    ID:         $Id$
     6.6 +    Author:     Cornelia Pusch
     6.7 +    Copyright   1999 Technische Universitaet Muenchen
     6.8 +
     6.9 +The supertype relation lifted to type options, type lists and state types.
    6.10 +*)
    6.11 +
    6.12 +Convert = JVMExec + 
    6.13 +
    6.14 +types
    6.15 + locvars_type = ty option list
    6.16 + opstack_type = ty list
    6.17 + state_type   = "opstack_type \\<times> locvars_type"
    6.18 +
    6.19 +constdefs
    6.20 +
    6.21 + sup_ty_opt :: "['code prog,ty option,ty option] \\<Rightarrow> bool" ("_ \\<turnstile>_ >= _")
    6.22 + "G \\<turnstile> a >= a' \\<equiv>
    6.23 +    case a of
    6.24 +      None \\<Rightarrow> True
    6.25 +    | Some t  \\<Rightarrow>  case a' of 
    6.26 +		     None \\<Rightarrow> False
    6.27 +		   | Some t' \\<Rightarrow> G \\<turnstile> t' \\<preceq> t" 
    6.28 +
    6.29 + sup_loc :: "['code prog,locvars_type,locvars_type] \\<Rightarrow> bool"	  ("_ \\<turnstile> _ >>= _"  [71,71] 70)
    6.30 + "G \\<turnstile> LT >>= LT' \\<equiv> (length LT=length LT') \\<and> (\\<forall>(t,t')\\<in>set (zip LT LT'). G \\<turnstile> t >= t')"
    6.31 +
    6.32 +
    6.33 + sup_state :: "['code prog,state_type,state_type] \\<Rightarrow> bool"	  ("_ \\<turnstile> _ >>>= _"  [71,71] 70)
    6.34 + "G \\<turnstile> s >>>= s' \\<equiv> G \\<turnstile> map Some (fst s) >>= map Some (fst s') \\<and> G \\<turnstile> snd s >>= snd s'"
    6.35 +
    6.36 +end
     7.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
     7.2 +++ b/src/HOL/MicroJava/BV/Correct.ML	Thu Nov 11 12:23:45 1999 +0100
     7.3 @@ -0,0 +1,281 @@
     7.4 +(*  Title:      HOL/MicroJava/BV/Correct.ML
     7.5 +    ID:         $Id$
     7.6 +    Author:     Cornelia Pusch
     7.7 +    Copyright   1999 Technische Universitaet Muenchen
     7.8 +*)
     7.9 +
    7.10 +(** sup_heap **)
    7.11 +
    7.12 +Goalw [hext_def]
    7.13 + "hp x = None \\<longrightarrow> hp \\<le>| (hp((newref hp) \\<mapsto> obj))";
    7.14 +by (asm_full_simp_tac (simpset() addsimps []) 1);
    7.15 +by (Clarify_tac 1);
    7.16 +bd newref_None 1;
    7.17 +back();
    7.18 +by (asm_full_simp_tac (simpset() addsimps []) 1);
    7.19 +qed_spec_mp "sup_heap_newref";
    7.20 +
    7.21 +
    7.22 +Goalw [hext_def]
    7.23 +"hp a = Some (cn,od') \\<longrightarrow> hp \\<le>| (hp(a \\<mapsto> (cn,od)))";
    7.24 +by (asm_full_simp_tac (simpset() addsimps []) 1);
    7.25 +qed_spec_mp "sup_heap_update_value";
    7.26 +
    7.27 +
    7.28 +(** approx_val **)
    7.29 +
    7.30 +Goalw [approx_val_def]
    7.31 +"approx_val G hp x None";
    7.32 +by (Asm_full_simp_tac 1);
    7.33 +qed_spec_mp "approx_val_None";
    7.34 +
    7.35 +
    7.36 +Goalw [approx_val_def]
    7.37 +"approx_val G hp Null (Some(RefT x))";
    7.38 +by(Simp_tac 1);
    7.39 +by (fast_tac (claset() addIs widen.intrs) 1);
    7.40 +qed_spec_mp "approx_val_Null";
    7.41 +
    7.42 +
    7.43 +Goal
    7.44 +"\\<lbrakk> wf_prog wt G \\<rbrakk> \
    7.45 +\\\<Longrightarrow> approx_val G hp v (Some T) \\<longrightarrow> G\\<turnstile> T\\<preceq>T' \\<longrightarrow> approx_val G hp v (Some T')";
    7.46 +by (exhaust_tac "T" 1);
    7.47 + by (Asm_simp_tac 1);
    7.48 +by (fast_tac (claset() addIs [conf_widen] addss (simpset()addsimps[approx_val_def])) 1);
    7.49 +qed_spec_mp "approx_val_imp_approx_val_assConvertible";
    7.50 +
    7.51 +
    7.52 +Goal
    7.53 +"approx_val G hp val at \\<longrightarrow> hp \\<le>| hp' \\<longrightarrow> approx_val G hp' val at";
    7.54 +by (asm_full_simp_tac (simpset() setloop (split_tac [option.split]) 
    7.55 +	addsimps [approx_val_def]) 1);
    7.56 +by(blast_tac (claset() addIs [conf_hext]) 1);
    7.57 +qed_spec_mp "approx_val_imp_approx_val_sup_heap";
    7.58 +
    7.59 +Goal
    7.60 +"\\<lbrakk> hp a = Some obj' ; G,hp\\<turnstile> v\\<Colon>\\<preceq>T ; obj_ty obj = obj_ty obj' \\<rbrakk> \
    7.61 +\\\<Longrightarrow>G,(hp(a\\<mapsto>obj))\\<turnstile> v\\<Colon>\\<preceq>T";
    7.62 +by (exhaust_tac "v" 1);
    7.63 +by (auto_tac (claset() , simpset() addsimps [obj_ty_def,conf_def] addsplits [option.split]));
    7.64 +qed_spec_mp "approx_val_imp_approx_val_heap_update";
    7.65 +
    7.66 +
    7.67 +Goal
    7.68 +"wf_prog wt G \\<Longrightarrow> approx_val G h val us \\<longrightarrow> G \\<turnstile> us' >= us \\<longrightarrow> approx_val G h val us'";
    7.69 +by (asm_simp_tac (simpset() addsimps [sup_PTS_eq,approx_val_def] addsplits [option.split,val_.split,ty.split]) 1);
    7.70 +by(blast_tac (claset() addIs [conf_widen]) 1);
    7.71 +qed_spec_mp "approx_val_imp_approx_val_sup";
    7.72 +
    7.73 +
    7.74 +Goal 
    7.75 +"\\<lbrakk> wf_prog wt G; approx_loc G hp loc LT; idx < length LT ; val = loc ! idx ; G \\<turnstile> at >= LT ! idx \\<rbrakk> \
    7.76 +\\\<Longrightarrow> approx_val G hp val at";
    7.77 +by (fast_tac (claset() addIs [approx_val_imp_approx_val_sup] addss (simpset() addsimps 
    7.78 +	[split_def,approx_loc_def,all_set_conv_all_nth])) 1);
    7.79 +qed "approx_loc_imp_approx_val_sup";
    7.80 +
    7.81 +
    7.82 +(** approx_loc **)
    7.83 +
    7.84 +Goal 
    7.85 +"approx_loc G hp (s#xs) (l#ls) = \
    7.86 +\   ((length xs = length ls) \\<and> (approx_val G hp s l) \\<and> (approx_loc G hp xs ls))";
    7.87 +by (fast_tac (claset() addss (simpset() addsimps [approx_loc_def])) 1);
    7.88 +qed "approx_loc_Cons";
    7.89 +
    7.90 +
    7.91 +Goalw [approx_stk_def,approx_loc_def]
    7.92 +"\\<lbrakk> wf_prog wt G \\<rbrakk> \
    7.93 +\\\<Longrightarrow> (\\<forall>tt'\\<in>set (zip tys_n ts). tt' \\<in> widen G) \\<longrightarrow> \
    7.94 +\     length tys_n = length ts \\<longrightarrow> approx_stk G hp s tys_n \\<longrightarrow> approx_loc G hp s (map Some ts)";
    7.95 +by (force_tac (claset() addIs [approx_val_imp_approx_val_assConvertible], simpset() 
    7.96 +	addsimps [all_set_conv_all_nth,split_def]) 1);
    7.97 +qed_spec_mp "assConv_approx_stk_imp_approx_loc";
    7.98 +
    7.99 +
   7.100 +Goalw [approx_loc_def]
   7.101 +"\\<forall> lvars. approx_loc G hp lvars lt \\<longrightarrow>  hp \\<le>| hp' \\<longrightarrow> approx_loc G hp' lvars lt";
   7.102 +by (exhaust_tac "lt" 1);
   7.103 + by (Asm_simp_tac 1);
   7.104 +by (force_tac (claset() addIs [approx_val_imp_approx_val_sup_heap],
   7.105 +	       simpset() addsimps [neq_Nil_conv]) 1);
   7.106 +qed_spec_mp "approx_loc_imp_approx_loc_sup_heap";
   7.107 +
   7.108 +
   7.109 +Goalw [sup_loc_def,approx_loc_def]
   7.110 +"wf_prog wt G \\<Longrightarrow> approx_loc G hp lvars lt \\<longrightarrow> G \\<turnstile> lt' >>= lt \\<longrightarrow> approx_loc G hp lvars lt'";
   7.111 +by (auto_tac (claset() , simpset() addsimps [all_set_conv_all_nth,split_def]));
   7.112 +by (auto_tac (claset() addEs [approx_val_imp_approx_val_sup] , simpset()));
   7.113 +qed_spec_mp "approx_loc_imp_approx_loc_sup";
   7.114 +
   7.115 +
   7.116 +Goalw  [approx_loc_def]
   7.117 +"\\<forall>loc idx x X. (approx_loc G hp loc LT) \\<longrightarrow> (approx_val G hp x X) \
   7.118 +\ \\<longrightarrow> (approx_loc G hp (loc[idx:=x]) (LT[idx:=X]))";
   7.119 +by (fast_tac (claset() addDs [set_update_subset RS subsetD]
   7.120 +              addss (simpset() addsimps [zip_update])) 1);
   7.121 +qed_spec_mp "approx_loc_imp_approx_loc_subst";
   7.122 +
   7.123 +
   7.124 +Goal 
   7.125 +"\\<forall>L1 l2 L2. length l1=length L1 \
   7.126 +\ \\<longrightarrow> approx_loc G hp (l1@l2) (L1@L2) = (approx_loc G hp l1 L1 \\<and> approx_loc G hp l2 L2)";
   7.127 +by (induct_tac "l1" 1);
   7.128 + by (fast_tac (claset() addDs [] addss (simpset() addsimps [approx_loc_def])) 1);
   7.129 +br allI 1;
   7.130 +by (exhaust_tac "L1" 1);
   7.131 + by (asm_full_simp_tac (simpset() addsimps []) 1);
   7.132 +by (asm_full_simp_tac (simpset() addsimps []) 1);
   7.133 +by (Clarify_tac 1);
   7.134 +by (asm_full_simp_tac (simpset() addsimps [approx_loc_Cons]) 1);
   7.135 +by (case_tac "length l2 = length L2" 1);
   7.136 + by (asm_full_simp_tac (simpset() addsimps []) 1);
   7.137 +by (asm_full_simp_tac (simpset() addsimps [approx_loc_def]) 1);
   7.138 +qed_spec_mp "approx_loc_append";
   7.139 +
   7.140 +
   7.141 +(** approx_stk **)
   7.142 +
   7.143 +Goalw [approx_stk_def,approx_loc_def]
   7.144 +"approx_stk G hp (rev s) (rev t) = approx_stk G hp s t";
   7.145 +by (fast_tac (claset() addss (simpset() addsimps [zip_rev,rev_map RS sym])) 1);
   7.146 +qed_spec_mp "approx_stk_rev_lem";
   7.147 +
   7.148 +Goal 
   7.149 +"approx_stk G hp (rev s) t = approx_stk G hp s (rev t)";
   7.150 +by (fast_tac (claset() addIs [approx_stk_rev_lem RS subst] addss (simpset()))  1);
   7.151 +qed_spec_mp "approx_stk_rev";
   7.152 +
   7.153 +Goalw [approx_stk_def]
   7.154 +"\\<forall> lvars. approx_stk G hp lvars lt \\<longrightarrow> hp \\<le>| hp' \\<longrightarrow> approx_stk G hp' lvars lt";
   7.155 +by (fast_tac (claset() addIs [approx_loc_imp_approx_loc_sup_heap])  1);
   7.156 +qed_spec_mp "approx_stk_imp_approx_stk_sup_heap";
   7.157 +
   7.158 +
   7.159 +Goalw [approx_stk_def]
   7.160 +"wf_prog wt G \\<Longrightarrow> approx_stk G hp lvars st \\<longrightarrow> G \\<turnstile> (map Some st') >>= (map Some st) \\<longrightarrow> approx_stk G hp lvars st'";
   7.161 +by (fast_tac (claset() addIs [approx_loc_imp_approx_loc_sup])  1);
   7.162 +qed_spec_mp "approx_stk_imp_approx_stk_sup";
   7.163 +
   7.164 +Goalw [approx_stk_def,approx_loc_def]
   7.165 +"approx_stk G hp [] []";
   7.166 +by (asm_full_simp_tac (simpset() addsimps []) 1);
   7.167 +qed "approx_stk_Nil";
   7.168 +
   7.169 +
   7.170 +Goalw [approx_stk_def,approx_loc_def]
   7.171 +"approx_stk G hp (x # stk) (S#ST) = (approx_stk G hp stk ST \\<and> approx_val G hp x (Some S))";
   7.172 +by (fast_tac (claset() addss (simpset())) 1);
   7.173 +qed "approx_stk_Cons";
   7.174 +
   7.175 +Goal 
   7.176 +"\\<lbrakk> approx_stk G hp stk (S#ST') \\<rbrakk> \
   7.177 +\ \\<Longrightarrow> \\<exists>s stk'. stk = s#stk' \\<and> approx_stk G hp stk' ST' \\<and> approx_val G hp s (Some S)";
   7.178 +by (exhaust_tac "stk" 1);
   7.179 + by (fast_tac (claset() addss (simpset() addsimps [approx_stk_def,approx_loc_def])) 1);
   7.180 +by (fast_tac (claset() addss (simpset() addsimps [approx_stk_Cons])) 1);
   7.181 +qed "approx_stk_Cons_lemma";
   7.182 +
   7.183 +Goal 
   7.184 +"\\<forall>ST' stk. approx_stk G hp stk (S@ST')   \
   7.185 +\ \\<longrightarrow> (\\<exists>s stk'. stk = s@stk' \\<and> length s = length S \\<and> length stk' = length ST' \\<and> \
   7.186 +\             approx_stk G hp s S \\<and> approx_stk G hp stk' ST')";
   7.187 +by (induct_tac "S" 1);
   7.188 + by (fast_tac (claset() addDs [] addss (simpset() addsimps [approx_stk_def,approx_loc_def])) 1);
   7.189 +by (Clarify_tac 1);
   7.190 +by (asm_full_simp_tac (simpset() addsimps []) 1);
   7.191 +bd approx_stk_Cons_lemma 1;
   7.192 +by (Clarify_tac 1);
   7.193 +by (eres_inst_tac [("x","ST'")] allE 1);
   7.194 +by (eres_inst_tac [("x","stk'")] allE 1);
   7.195 +by (Clarify_tac 1);
   7.196 +by (res_inst_tac [("x","s#sa")] exI 1);
   7.197 +by (res_inst_tac [("x","stk'a")] exI 1);
   7.198 +by (asm_full_simp_tac (simpset() addsimps [approx_stk_Cons]) 1);
   7.199 +qed_spec_mp "approx_stk_append_lemma";
   7.200 +
   7.201 +
   7.202 +(** oconf **)
   7.203 +
   7.204 +Goalw [oconf_def,lconf_def]
   7.205 +"\\<lbrakk> is_class G C; wf_prog wt G \\<rbrakk> \\<Longrightarrow> \
   7.206 +\G,h\\<turnstile> (C, map_of (map (\\<lambda>(f,fT).(f,default_val fT)) (fields(G,C))))\\<surd>";
   7.207 +by (asm_full_simp_tac (simpset() addsimps [map_of_map]) 1);
   7.208 +by (force_tac (claset() addIs [defval_conf]
   7.209 +                        addDs [map_of_SomeD,is_type_fields],simpset()) 1);
   7.210 +qed "correct_init_obj";
   7.211 +
   7.212 +
   7.213 +Goalw [oconf_def,lconf_def]
   7.214 +"\\<lbrakk> map_of (fields (G, oT)) FD = Some T ; G,hp\\<turnstile>v\\<Colon>\\<preceq>T ; \
   7.215 +\   G,hp\\<turnstile>(oT,fs)\\<surd> \\<rbrakk>  \
   7.216 +\\\<Longrightarrow> G,hp\\<turnstile>(oT, fs(FD\\<mapsto>v))\\<surd>";
   7.217 +by (asm_full_simp_tac (simpset() addsplits [ty.split]) 1);
   7.218 +qed_spec_mp "oconf_imp_oconf_field_update";
   7.219 +
   7.220 +
   7.221 +Goalw [oconf_def,lconf_def]
   7.222 +"hp x = None \\<longrightarrow> G,hp\\<turnstile>obj\\<surd>  \\<longrightarrow>  G,hp\\<turnstile>obj'\\<surd> \
   7.223 +\  \\<longrightarrow> G,(hp(newref hp\\<mapsto>obj'))\\<turnstile>obj\\<surd>";
   7.224 +by (Asm_full_simp_tac 1);
   7.225 +by (fast_tac (claset() addIs [conf_hext,sup_heap_newref]) 1);
   7.226 +qed_spec_mp "oconf_imp_oconf_heap_newref";
   7.227 +
   7.228 +Goalw [oconf_def,lconf_def]
   7.229 +"hp a = Some obj'  \\<longrightarrow> obj_ty obj' = obj_ty obj'' \\<longrightarrow> G,hp\\<turnstile>obj\\<surd> \
   7.230 +\  \\<longrightarrow> G,hp(a\\<mapsto>obj'')\\<turnstile>obj\\<surd>";
   7.231 +by (Asm_full_simp_tac 1);
   7.232 +by (fast_tac (claset() addIs [approx_val_imp_approx_val_heap_update] addss (simpset())) 1);
   7.233 +qed_spec_mp "oconf_imp_oconf_heap_update";
   7.234 +
   7.235 +
   7.236 +(** hconf **)
   7.237 +
   7.238 +
   7.239 +Goal "hp x = None \\<longrightarrow> G,hp\\<turnstile>\\<surd> \\<longrightarrow> G,hp\\<turnstile>obj\\<surd> \\<longrightarrow> G,hp(newref hp\\<mapsto>obj)\\<turnstile>\\<surd>";
   7.240 +by (asm_full_simp_tac (simpset() addsplits [split_split] 
   7.241 +				 addsimps [hconf_def]) 1);
   7.242 + by (fast_tac (claset()addIs[oconf_imp_oconf_heap_newref] addss (simpset())) 1);
   7.243 +qed_spec_mp "hconf_imp_hconf_newref";
   7.244 +
   7.245 +
   7.246 +Goal "map_of (fields (G, oT)) (F, D) = Some T \\<and> hp oloc = Some(oT,fs) \\<and> \
   7.247 +\ G,hp\\<turnstile>v\\<Colon>\\<preceq>T \\<and> G,hp\\<turnstile>\\<surd> \\<longrightarrow> G,hp(oloc \\<mapsto> (oT, fs((F,D)\\<mapsto>v)))\\<turnstile>\\<surd>";
   7.248 +by (asm_full_simp_tac (simpset() addsimps [hconf_def]) 1);
   7.249 +by (fast_tac (claset() addIs 
   7.250 +        [oconf_imp_oconf_heap_update, oconf_imp_oconf_field_update]
   7.251 +        addss (simpset() addsimps [obj_ty_def])) 1);
   7.252 +qed_spec_mp "hconf_imp_hconf_field_update";
   7.253 +
   7.254 +
   7.255 +(** correct_frames **)
   7.256 +
   7.257 +Delsimps [fun_upd_apply]; 
   7.258 +Goal
   7.259 +"\\<forall>rT C ml. correct_frames G hp phi rT C ml frs \\<longrightarrow> \
   7.260 +\    hp a = Some (cn,od) \\<longrightarrow> map_of (fields (G, cn)) fl = Some fd \\<longrightarrow> \
   7.261 +\    G,hp\\<turnstile>v\\<Colon>\\<preceq>fd \
   7.262 +\ \\<longrightarrow> correct_frames G (hp(a \\<mapsto> (cn, od(fl\\<mapsto>v)))) phi rT C ml frs";
   7.263 +by (induct_tac "frs" 1);
   7.264 + by (Asm_full_simp_tac 1);
   7.265 +by (asm_full_simp_tac (simpset() addsimps [split_def,correct_frame_def]) 1);
   7.266 +by (fast_tac (claset() addIs [approx_stk_imp_approx_stk_sup_heap,
   7.267 +				approx_loc_imp_approx_loc_sup_heap,
   7.268 +				sup_heap_update_value] addss (simpset())) 1);
   7.269 +qed_spec_mp "correct_frames_imp_correct_frames_field_update";
   7.270 +
   7.271 +
   7.272 +Goal
   7.273 +"\\<forall>rT C ml. hp x = None \\<longrightarrow> correct_frames G hp phi rT C ml frs \\<and> \
   7.274 +\    oconf G hp obj \
   7.275 +\ \\<longrightarrow> correct_frames G (hp(newref hp \\<mapsto> obj)) phi rT C ml frs";
   7.276 +by (induct_tac "frs" 1);
   7.277 +by  (asm_full_simp_tac (simpset() addsimps []) 1);
   7.278 +by (asm_full_simp_tac (simpset() addsimps [split_def,correct_frame_def]) 1);
   7.279 +by (fast_tac (claset() addIs [approx_stk_imp_approx_stk_sup_heap,
   7.280 +				approx_loc_imp_approx_loc_sup_heap,
   7.281 +				hconf_imp_hconf_newref,
   7.282 +				sup_heap_newref] addss (simpset())) 1);
   7.283 +qed_spec_mp "correct_frames_imp_correct_frames_newref";
   7.284 +
     8.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
     8.2 +++ b/src/HOL/MicroJava/BV/Correct.thy	Thu Nov 11 12:23:45 1999 +0100
     8.3 @@ -0,0 +1,65 @@
     8.4 +(*  Title:      HOL/MicroJava/BV/Correct.thy
     8.5 +    ID:         $Id$
     8.6 +    Author:     Cornelia Pusch
     8.7 +    Copyright   1999 Technische Universitaet Muenchen
     8.8 +
     8.9 +The invariant for the type safety proof.
    8.10 +*)
    8.11 +
    8.12 +Correct = BVSpec + 
    8.13 +
    8.14 +constdefs
    8.15 + approx_val :: "[jvm_prog,aheap,val,ty option] \\<Rightarrow> bool"
    8.16 +"approx_val G h v any \\<equiv> case any of None \\<Rightarrow> True | Some T \\<Rightarrow> G,h\\<turnstile>v\\<Colon>\\<preceq>T"
    8.17 +
    8.18 + approx_loc :: "[jvm_prog,aheap,val list,locvars_type] \\<Rightarrow> bool"
    8.19 +"approx_loc G hp loc LT \\<equiv> 
    8.20 +   length loc=length LT \\<and> (\\<forall>(val,any)\\<in>set (zip loc LT). approx_val G hp val any)" 
    8.21 +
    8.22 + approx_stk :: "[jvm_prog,aheap,opstack,opstack_type] \\<Rightarrow> bool"
    8.23 +"approx_stk G hp stk ST \\<equiv> approx_loc G hp stk (map Some ST)"
    8.24 +
    8.25 + correct_frame  :: "[jvm_prog,aheap,state_type,nat,bytecode] \\<Rightarrow> frame \\<Rightarrow> bool"
    8.26 +"correct_frame G hp \\<equiv> \\<lambda>(ST,LT) maxl ins (stk,loc,C,ml,pc).
    8.27 +   approx_stk G hp stk ST  \\<and> approx_loc G hp loc LT \\<and> 
    8.28 +   pc < length ins \\<and> length loc=length(snd ml)+maxl+1"
    8.29 +
    8.30 +consts
    8.31 + correct_frames  :: "[jvm_prog,aheap,prog_type,ty,cname,sig,frame list] \\<Rightarrow> bool"
    8.32 +primrec
    8.33 +"correct_frames G hp phi rT0 C0 ml0 [] = False"
    8.34 +
    8.35 +"correct_frames G hp phi rT0 C0 ml0 (f#frs) =
    8.36 +	(let (stk,loc,C,ml,pc) = f;
    8.37 +	     (ST,LT) = (phi C ml) ! pc
    8.38 +	 in
    8.39 +         (\\<exists>rT maxl ins.
    8.40 +         cmethd (G,C) ml = Some(C,rT,(maxl,ins)) \\<and>
    8.41 +	 (\\<exists>mn pTs k. pc = k+1 \\<and> ins!k = MI(Invokevirtual mn pTs) \\<and>
    8.42 +         (mn,pTs) = ml0 \\<and> 
    8.43 +         (\\<exists>apTs D ST'.
    8.44 +         fst((phi C ml)!k) = (rev apTs) @ (Class D) # ST' \\<and>
    8.45 +         length apTs = length pTs \\<and>
    8.46 +         (\\<exists>D' rT' maxl' ins'.
    8.47 +           cmethd (G,D) (mn,pTs) = Some(D',rT',(maxl',ins')) \\<and>
    8.48 +           G \\<turnstile> rT0 \\<preceq> rT') \\<and>
    8.49 +	 correct_frame G hp (tl ST, LT) maxl ins f \\<and> 
    8.50 +	 correct_frames G hp phi rT C ml frs))))"
    8.51 +
    8.52 +
    8.53 +constdefs
    8.54 + correct_state :: "[jvm_prog,prog_type,jvm_state] \\<Rightarrow> bool"
    8.55 +"correct_state G phi \\<equiv> \\<lambda>(xp,hp,frs).
    8.56 +   case xp of
    8.57 +     None \\<Rightarrow> (case frs of
    8.58 +	           [] \\<Rightarrow> True
    8.59 +             | (f#fs) \\<Rightarrow> (let (stk,loc,C,ml,pc) = f
    8.60 +		         in
    8.61 +                         \\<exists>rT maxl ins.
    8.62 +                         cmethd (G,C) ml = Some(C,rT,(maxl,ins)) \\<and>
    8.63 +		         G,hp\\<turnstile>\\<surd> \\<and> 
    8.64 +			 correct_frame G hp ((phi C ml) ! pc) maxl ins f \\<and> 
    8.65 +		         correct_frames G hp phi rT C ml fs))
    8.66 +   | Some x \\<Rightarrow> True" 
    8.67 +
    8.68 +end
     9.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
     9.2 +++ b/src/HOL/MicroJava/J/Conform.ML	Thu Nov 11 12:23:45 1999 +0100
     9.3 @@ -0,0 +1,256 @@
     9.4 +(*  Title:      HOL/MicroJava/J/Conform.ML
     9.5 +    ID:         $Id$
     9.6 +    Author:     David von Oheimb
     9.7 +    Copyright   1999 Technische Universitaet Muenchen
     9.8 +*)
     9.9 +
    9.10 +section "hext";
    9.11 +
    9.12 +val hextI = prove_goalw thy [hext_def] "\\<And>h. \
    9.13 +\ \\<forall>a C fs . h  a = Some (C,fs) \\<longrightarrow>  \
    9.14 +\     (\\<exists>fs'. h' a = Some (C,fs')) \\<Longrightarrow> h\\<le>|h'" (K [Auto_tac ]);
    9.15 +
    9.16 +val hext_objD = prove_goalw thy [hext_def] 
    9.17 +"\\<And>h. \\<lbrakk>h\\<le>|h'; h a = Some (C,fs) \\<rbrakk> \\<Longrightarrow> \\<exists>fs'. h' a = Some (C,fs')" 
    9.18 +	(K [Force_tac 1]);
    9.19 +
    9.20 +val hext_refl = prove_goal thy "h\\<le>|h" (K [
    9.21 +	rtac hextI 1,
    9.22 +	Fast_tac 1]);
    9.23 +
    9.24 +val hext_new = prove_goal thy "\\<And>h. h a = None \\<Longrightarrow> h\\<le>|h(a\\<mapsto>x)" (K [
    9.25 +	rtac hextI 1,
    9.26 +	safe_tac HOL_cs,
    9.27 +	 ALLGOALS (case_tac "aa = a"),
    9.28 +	   Auto_tac]);
    9.29 +
    9.30 +val hext_trans = prove_goal thy "\\<And>h. \\<lbrakk>h\\<le>|h'; h'\\<le>|h''\\<rbrakk> \\<Longrightarrow> h\\<le>|h''" (K [
    9.31 +	rtac hextI 1,
    9.32 +	safe_tac HOL_cs,
    9.33 +	 fast_tac (HOL_cs addDs [hext_objD]) 1]);
    9.34 +
    9.35 +Addsimps [hext_refl, hext_new];
    9.36 +
    9.37 +val hext_upd_obj = prove_goal thy 
    9.38 +"\\<And>h. h a = Some (C,fs) \\<Longrightarrow> h\\<le>|h(a\\<mapsto>(C,fs'))" (K [
    9.39 +	rtac hextI 1,
    9.40 +	safe_tac HOL_cs,
    9.41 +	 ALLGOALS (case_tac "aa = a"),
    9.42 +	   Auto_tac]);
    9.43 +
    9.44 +
    9.45 +section "conf";
    9.46 +
    9.47 +val conf_Null = prove_goalw thy [conf_def] 
    9.48 +"G,h\\<turnstile>Null\\<Colon>\\<preceq>T = G\\<turnstile>RefT NullT\\<preceq>T" (K [Simp_tac 1]);
    9.49 +Addsimps [conf_Null];
    9.50 +
    9.51 +val conf_litval = prove_goalw thy [conf_def] 
    9.52 +"typeof (\\<lambda>v. None) v = Some T \\<longrightarrow> G,h\\<turnstile>v\\<Colon>\\<preceq>T" (K [
    9.53 +	rtac val_.induct 1,
    9.54 +	    Auto_tac]) RS mp;
    9.55 +
    9.56 +val conf_AddrI = prove_goalw thy [conf_def] 
    9.57 +"\\<And>G. \\<lbrakk>h a = Some obj; G\\<turnstile>obj_ty obj\\<preceq>T\\<rbrakk> \\<Longrightarrow> G,h\\<turnstile>Addr a\\<Colon>\\<preceq>T"
    9.58 +(K [Asm_full_simp_tac 1]);
    9.59 +
    9.60 +val conf_obj_AddrI = prove_goalw thy [conf_def]
    9.61 + "\\<And>G. \\<lbrakk>h a = Some (C,fs); G\\<turnstile>Class C\\<preceq>Class D\\<rbrakk> \\<Longrightarrow> G,h\\<turnstile>Addr a\\<Colon>\\<preceq>Class D" 
    9.62 +(K [Asm_full_simp_tac 1]);
    9.63 +
    9.64 +Goalw [conf_def] "is_type G T \\<longrightarrow> G,h\\<turnstile>default_val T\\<Colon>\\<preceq>T";
    9.65 +by (Simp_tac 1);
    9.66 +by (res_inst_tac [("y","T")] ty.exhaust 1);
    9.67 +by  (etac ssubst 1);
    9.68 +by  (res_inst_tac [("y","prim_ty")] prim_ty.exhaust 1);
    9.69 +by    (auto_tac (claset(), simpset() addsimps [widen.null]));
    9.70 +qed_spec_mp "defval_conf";
    9.71 +
    9.72 +val conf_upd_obj = prove_goalw thy [conf_def] 
    9.73 +"h a = Some (C,fs) \\<longrightarrow> (G,h(a\\<mapsto>(C,fs'))\\<turnstile>x\\<Colon>\\<preceq>T) = (G,h\\<turnstile>x\\<Colon>\\<preceq>T)" (fn _ => [
    9.74 +	rtac impI 1,
    9.75 +	rtac val_.induct 1,
    9.76 +	 ALLGOALS Simp_tac,
    9.77 +	case_tac "loc = a" 1,
    9.78 +	 ALLGOALS Asm_simp_tac]) RS mp;
    9.79 +
    9.80 +val conf_widen = prove_goalw thy [conf_def] 
    9.81 +"\\<And>G. wf_prog wtm G \\<Longrightarrow> G,h\\<turnstile>x\\<Colon>\\<preceq>T \\<longrightarrow> G\\<turnstile>T\\<preceq>T' \\<longrightarrow> G,h\\<turnstile>x\\<Colon>\\<preceq>T'" (K [
    9.82 +	rtac val_.induct 1,
    9.83 +	    ALLGOALS Simp_tac,
    9.84 +	    ALLGOALS (fast_tac (HOL_cs addIs [widen_trans]))]) RS mp RS mp;
    9.85 +
    9.86 +val conf_hext' = prove_goalw thy [conf_def] 
    9.87 +	"\\<And>h. h\\<le>|h' \\<Longrightarrow> (\\<forall>v T. G,h\\<turnstile>v\\<Colon>\\<preceq>T \\<longrightarrow> G,h'\\<turnstile>v\\<Colon>\\<preceq>T)" (K [
    9.88 +	REPEAT (rtac allI 1),
    9.89 +	rtac val_.induct 1,
    9.90 +	 ALLGOALS Simp_tac,
    9.91 +	safe_tac (HOL_cs addSDs [option_map_SomeD]),
    9.92 +	rewtac option_map_def,
    9.93 +	  dtac hext_objD 1,
    9.94 +	   Auto_tac]);
    9.95 +val conf_hext = conf_hext' RS spec RS spec RS mp;
    9.96 +
    9.97 +val new_locD = prove_goalw thy [conf_def] 
    9.98 +	"\\<lbrakk>h a = None; G,h\\<turnstile>Addr t\\<Colon>\\<preceq>T\\<rbrakk> \\<Longrightarrow> t\\<noteq>a" (fn prems => [
    9.99 +	cut_facts_tac prems 1,
   9.100 +	Full_simp_tac 1,
   9.101 +	safe_tac HOL_cs,
   9.102 +	Asm_full_simp_tac 1]);
   9.103 +
   9.104 +val conf_RefTD = prove_goalw thy [conf_def] "G,h\\<turnstile>a'\\<Colon>\\<preceq>RefT T \\<longrightarrow> a' = Null |  \
   9.105 +\ (\\<exists>a obj T'. a' = Addr a \\<and>  h a = Some obj \\<and>  obj_ty obj = T' \\<and>  G\\<turnstile>T'\\<preceq>RefT T)" (K [
   9.106 +	induct_tac "a'" 1,
   9.107 +	    Auto_tac,
   9.108 +	    REPEAT (etac widen_PrimT_RefT 1)]) RS mp;
   9.109 +
   9.110 +val conf_NullTD = prove_goal thy "\\<And>G. G,h\\<turnstile>a'\\<Colon>\\<preceq>RefT NullT \\<Longrightarrow> a' = Null" (K [
   9.111 +	dtac conf_RefTD 1,
   9.112 +	Step_tac 1,
   9.113 +	 Auto_tac,
   9.114 +	 etac widen_Class_NullT 1]);
   9.115 +
   9.116 +val non_npD = prove_goal thy "\\<And>G. \\<lbrakk>a' \\<noteq> Null; G,h\\<turnstile>a'\\<Colon>\\<preceq>RefT t\\<rbrakk> \\<Longrightarrow> \
   9.117 +\ \\<exists>a C fs. a' = Addr a \\<and>  h a = Some (C,fs) \\<and>  G\\<turnstile>Class C\\<preceq>RefT t" (K [
   9.118 +	dtac conf_RefTD 1,
   9.119 +	Step_tac 1,
   9.120 +	 Auto_tac]);
   9.121 +
   9.122 +val non_np_objD = prove_goal thy "\\<And>G. \\<lbrakk>a' \\<noteq> Null; G,h\\<turnstile>a'\\<Colon>\\<preceq>Class C; C \\<noteq> Object\\<rbrakk> \\<Longrightarrow> \
   9.123 +\ (\\<exists>a C' fs. a' = Addr a \\<and>  h a = Some (C',fs) \\<and>  G\\<turnstile>Class C'\\<preceq>Class C)" 
   9.124 +	(K[fast_tac (HOL_cs addDs [non_npD]) 1]);
   9.125 +
   9.126 +Goal "a' \\<noteq> Null \\<longrightarrow> wf_prog wtm G \\<longrightarrow> G,h\\<turnstile>a'\\<Colon>\\<preceq>RefT t \\<longrightarrow>\
   9.127 +\ (\\<forall>C. t = ClassT C \\<longrightarrow> C \\<noteq> Object) \\<longrightarrow> \
   9.128 +\ (\\<exists>a C fs. a' = Addr a \\<and>  h a = Some (C,fs) \\<and>  G\\<turnstile>Class C\\<preceq>RefT t)";
   9.129 +by (rtac impI 1);
   9.130 +by (rtac impI 1);
   9.131 +by (res_inst_tac [("y","t")] ref_ty.exhaust 1);
   9.132 +by    (safe_tac HOL_cs);
   9.133 +by   (dtac conf_NullTD 1);
   9.134 +by   (contr_tac 1);
   9.135 +by  (etac non_np_objD 1);
   9.136 +by   (atac 1);
   9.137 +by  (Fast_tac 1);
   9.138 +qed_spec_mp "non_np_objD'";
   9.139 +
   9.140 +Goal "wf_prog wtm G \\<Longrightarrow> \\<forall>Ts Ts'. list_all2 (conf G h) vs Ts \\<longrightarrow> list_all2 (\\<lambda>T T'. G\\<turnstile>T\\<preceq>T') Ts Ts' \\<longrightarrow>  list_all2 (conf G h) vs Ts'";
   9.141 +by( induct_tac "vs" 1);
   9.142 +by(  ALLGOALS Clarsimp_tac);
   9.143 +by(  ALLGOALS (forward_tac [list_all2_lengthD RS sym]));
   9.144 +by(  ALLGOALS (full_simp_tac (simpset()addsimps[length_Suc_conv])));
   9.145 +by(  Safe_tac);
   9.146 +by(  rotate_tac ~1 1);
   9.147 +by(  ALLGOALS (forward_tac [list_all2_lengthD RS sym]));
   9.148 +by(  ALLGOALS (full_simp_tac (simpset()addsimps[length_Suc_conv])));
   9.149 +by(  ALLGOALS Clarify_tac);
   9.150 +by( fast_tac (claset() addEs [conf_widen]) 1);
   9.151 +qed_spec_mp "conf_list_gext_widen";
   9.152 +
   9.153 +
   9.154 +section "lconf";
   9.155 +
   9.156 +val lconfD = prove_goalw thy [lconf_def] 
   9.157 +   "\\<And>X. \\<lbrakk> G,h\\<turnstile>vs[\\<Colon>\\<preceq>]Ts; Ts n = Some T \\<rbrakk> \\<Longrightarrow> G,h\\<turnstile>(the (vs n))\\<Colon>\\<preceq>T"
   9.158 + (K [Force_tac 1]);
   9.159 +
   9.160 +val lconf_hext = prove_goalw thy [lconf_def] 
   9.161 +	"\\<And>X. \\<lbrakk> G,h\\<turnstile>l[\\<Colon>\\<preceq>]L; h\\<le>|h' \\<rbrakk> \\<Longrightarrow> G,h'\\<turnstile>l[\\<Colon>\\<preceq>]L" (K [
   9.162 +		fast_tac (claset() addEs [conf_hext]) 1]);
   9.163 +AddEs [lconf_hext];
   9.164 +
   9.165 +Goalw [lconf_def] "\\<And>X. \\<lbrakk> G,h\\<turnstile>l[\\<Colon>\\<preceq>]lT; \
   9.166 +\ G,h\\<turnstile>v\\<Colon>\\<preceq>T; lT va = Some T \\<rbrakk> \\<Longrightarrow> G,h\\<turnstile>l(va\\<mapsto>v)[\\<Colon>\\<preceq>]lT";
   9.167 +by( Clarify_tac 1);
   9.168 +by( case_tac "n = va" 1);
   9.169 + by Auto_tac;
   9.170 +qed "lconf_upd";
   9.171 +
   9.172 +Goal "\\<forall>x. P x \\<longrightarrow> R (dv x) x \\<Longrightarrow> (\\<forall>x. map_of fs f = Some x \\<longrightarrow> P x) \\<longrightarrow> \
   9.173 +\ (\\<forall>T. map_of fs f = Some T \\<longrightarrow> \
   9.174 +\ (\\<exists>v. map_of (map (\\<lambda>(f,ft). (f, dv ft)) fs) f = Some v \\<and>  R v T))";
   9.175 +by( induct_tac "fs" 1);
   9.176 +by Auto_tac;
   9.177 +qed_spec_mp "lconf_init_vars_lemma";
   9.178 +
   9.179 +Goalw [lconf_def, init_vars_def] 
   9.180 +"\\<forall>n. \\<forall>T. map_of fs n = Some T \\<longrightarrow> is_type G T \\<Longrightarrow> G,h\\<turnstile>init_vars fs[\\<Colon>\\<preceq>]map_of fs";
   9.181 +by Auto_tac;
   9.182 +by( rtac lconf_init_vars_lemma 1);
   9.183 +by(   atac 3);
   9.184 +by(  strip_tac 1);
   9.185 +by(  etac defval_conf 1);
   9.186 +by Auto_tac;
   9.187 +qed "lconf_init_vars";
   9.188 +AddSIs [lconf_init_vars];
   9.189 +
   9.190 +val lconf_ext = prove_goalw thy [lconf_def] 
   9.191 +"\\<And>X. \\<lbrakk>G,s\\<turnstile>l[\\<Colon>\\<preceq>]L; G,s\\<turnstile>v\\<Colon>\\<preceq>T\\<rbrakk> \\<Longrightarrow> G,s\\<turnstile>l(vn\\<mapsto>v)[\\<Colon>\\<preceq>]L(vn\\<mapsto>T)" 
   9.192 +	(K [Auto_tac]);
   9.193 +
   9.194 +Goalw [lconf_def] "G,h\\<turnstile>l[\\<Colon>\\<preceq>]L \\<Longrightarrow> \\<forall>vs Ts. nodups vns \\<longrightarrow> length Ts = length vns \\<longrightarrow> list_all2 (\\<lambda>v T. G,h\\<turnstile>v\\<Colon>\\<preceq>T) vs Ts \\<longrightarrow> G,h\\<turnstile>l(vns[\\<mapsto>]vs)[\\<Colon>\\<preceq>]L(vns[\\<mapsto>]Ts)";
   9.195 +by( induct_tac "vns" 1);
   9.196 +by(  ALLGOALS Clarsimp_tac);
   9.197 +by( forward_tac [list_all2_lengthD] 1);
   9.198 +by( auto_tac (claset(), simpset() addsimps [length_Suc_conv]));
   9.199 +qed_spec_mp "lconf_ext_list";
   9.200 +
   9.201 +
   9.202 +section "oconf";
   9.203 +
   9.204 +val oconf_hext = prove_goalw thy [oconf_def] 
   9.205 +"\\<And>X. G,h\\<turnstile>obj\\<surd> \\<Longrightarrow> h\\<le>|h' \\<Longrightarrow> G,h'\\<turnstile>obj\\<surd>" (K [Fast_tac 1]);
   9.206 +
   9.207 +val oconf_obj = prove_goalw thy [oconf_def,lconf_def] "G,h\\<turnstile>(C,fs)\\<surd> = \
   9.208 +\ (\\<forall>T f. map_of(fields (G,C)) f = Some T \\<longrightarrow> (\\<exists>v. fs f = Some v \\<and>  G,h\\<turnstile>v\\<Colon>\\<preceq>T))"(K [
   9.209 +	Auto_tac]);
   9.210 +
   9.211 +val oconf_objD = oconf_obj RS iffD1 RS spec RS spec RS mp;
   9.212 +
   9.213 +
   9.214 +section "hconf";
   9.215 +
   9.216 +Goalw [hconf_def] "\\<lbrakk>G,h\\<turnstile>\\<surd>; h a = Some obj\\<rbrakk> \\<Longrightarrow> G,h\\<turnstile>obj\\<surd>";
   9.217 +by (Fast_tac 1);
   9.218 +qed "hconfD";
   9.219 +
   9.220 +Goalw [hconf_def] "\\<forall>a obj. h a=Some obj \\<longrightarrow> G,h\\<turnstile>obj\\<surd> \\<Longrightarrow> G,h\\<turnstile>\\<surd>";
   9.221 +by (Fast_tac 1);
   9.222 +qed "hconfI";
   9.223 +
   9.224 +
   9.225 +section "conforms";
   9.226 +
   9.227 +val conforms_heapD = prove_goalw thy [conforms_def]
   9.228 +	"(h, l)\\<Colon>\\<preceq>(G, lT) \\<Longrightarrow> G,h\\<turnstile>\\<surd>"
   9.229 +	(fn prems => [cut_facts_tac prems 1, Asm_full_simp_tac 1]);
   9.230 +
   9.231 +val conforms_localD = prove_goalw thy [conforms_def]
   9.232 +	 "(h, l)\\<Colon>\\<preceq>(G, lT) \\<Longrightarrow> G,h\\<turnstile>l[\\<Colon>\\<preceq>]lT" (fn prems => [
   9.233 +	cut_facts_tac prems 1, Asm_full_simp_tac 1]);
   9.234 +
   9.235 +val conformsI = prove_goalw thy [conforms_def] 
   9.236 +"\\<lbrakk>G,h\\<turnstile>\\<surd>; G,h\\<turnstile>l[\\<Colon>\\<preceq>]lT\\<rbrakk> \\<Longrightarrow> (h, l)\\<Colon>\\<preceq>(G, lT)" (fn prems => [
   9.237 +	cut_facts_tac prems 1,
   9.238 +	Simp_tac 1,
   9.239 +	Auto_tac]);
   9.240 +
   9.241 +Goal "\\<lbrakk>(h,l)\\<Colon>\\<preceq>(G,lT); h\\<le>|h'; G,h'\\<turnstile>\\<surd> \\<rbrakk> \\<Longrightarrow> (h',l)\\<Colon>\\<preceq>(G,lT)";
   9.242 +by( fast_tac (HOL_cs addDs [conforms_localD] 
   9.243 +  addSEs [conformsI, lconf_hext]) 1);
   9.244 +qed "conforms_hext";
   9.245 +
   9.246 +Goal "\\<lbrakk>(h,l)\\<Colon>\\<preceq>(G, lT); G,h(a\\<mapsto>obj)\\<turnstile>obj\\<surd>; h\\<le>|h(a\\<mapsto>obj)\\<rbrakk> \\<Longrightarrow> (h(a\\<mapsto>obj),l)\\<Colon>\\<preceq>(G, lT)";
   9.247 +by( rtac conforms_hext 1);
   9.248 +by   Auto_tac;
   9.249 +by( rtac hconfI 1);
   9.250 +by( dtac conforms_heapD 1);
   9.251 +by( (auto_tac (HOL_cs addEs [oconf_hext] addDs [hconfD],
   9.252 +		simpset()delsimps[split_paired_All])));
   9.253 +qed "conforms_upd_obj";
   9.254 +
   9.255 +Goalw [conforms_def] 
   9.256 +"\\<lbrakk>(h, l)\\<Colon>\\<preceq>(G, lT); G,h\\<turnstile>v\\<Colon>\\<preceq>T; lT va = Some T\\<rbrakk> \\<Longrightarrow> \
   9.257 +\ (h, l(va\\<mapsto>v))\\<Colon>\\<preceq>(G, lT)";
   9.258 +by( auto_tac (claset() addEs [lconf_upd], simpset()));
   9.259 +qed "conforms_upd_local";
    10.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
    10.2 +++ b/src/HOL/MicroJava/J/Conform.thy	Thu Nov 11 12:23:45 1999 +0100
    10.3 @@ -0,0 +1,32 @@
    10.4 +(*  Title:      HOL/MicroJava/J/Conform.thy
    10.5 +    ID:         $Id$
    10.6 +    Author:     David von Oheimb
    10.7 +    Copyright   1999 Technische Universitaet Muenchen
    10.8 +
    10.9 +Conformity relations for type safety of Java
   10.10 +*)
   10.11 +
   10.12 +Conform = State +
   10.13 +
   10.14 +constdefs
   10.15 +
   10.16 +  hext :: "aheap \\<Rightarrow> aheap \\<Rightarrow> bool"		 (     "_\\<le>|_"  [51,51] 50)
   10.17 + "h\\<le>|h' \\<equiv> \\<forall>a C fs. h a = Some(C,fs) \\<longrightarrow> (\\<exists>fs'. h' a = Some(C,fs'))"
   10.18 +
   10.19 +  conf :: "'c prog \\<Rightarrow> aheap \\<Rightarrow> val \\<Rightarrow> ty \\<Rightarrow> bool"	 ( "_,_\\<turnstile>_\\<Colon>\\<preceq>_"  [51,51,51,51] 50)
   10.20 + "G,h\\<turnstile>v\\<Colon>\\<preceq>T \\<equiv> \\<exists>T'. typeof (option_map obj_ty o h) v = Some T' \\<and> G\\<turnstile>T'\\<preceq>T"
   10.21 +
   10.22 +  lconf :: "'c prog \\<Rightarrow> aheap \\<Rightarrow> ('a \\<leadsto> val) \\<Rightarrow> ('a \\<leadsto> ty) \\<Rightarrow> bool"
   10.23 +                                                 ("_,_\\<turnstile>_[\\<Colon>\\<preceq>]_" [51,51,51,51] 50)
   10.24 + "G,h\\<turnstile>vs[\\<Colon>\\<preceq>]Ts \\<equiv> \\<forall>n T. Ts n = Some T \\<longrightarrow> (\\<exists>v. vs n = Some v \\<and> G,h\\<turnstile>v\\<Colon>\\<preceq>T)"
   10.25 +
   10.26 +  oconf :: "'c prog \\<Rightarrow> aheap \\<Rightarrow> obj \\<Rightarrow> bool"      ("_,_\\<turnstile>_\\<surd>"     [51,51,51]    50)
   10.27 + "G,h\\<turnstile>obj\\<surd> \\<equiv> G,h\\<turnstile>snd obj[\\<Colon>\\<preceq>]map_of (fields (G,fst obj))"
   10.28 +
   10.29 +  hconf :: "'c prog \\<Rightarrow> aheap \\<Rightarrow> bool"             ("_,_\\<turnstile>\\<surd>"      [51,51]       50)
   10.30 + "G,h\\<turnstile>\\<surd>    \\<equiv> \\<forall>a obj. h a = Some obj \\<longrightarrow> G,h\\<turnstile>obj\\<surd>"
   10.31 +
   10.32 +  conforms :: "state \\<Rightarrow> javam env \\<Rightarrow> bool"	 ("_\\<Colon>\\<preceq>_"       [51,51]       50)
   10.33 + "s\\<Colon>\\<preceq>E \\<equiv> prg E,heap s\\<turnstile>\\<surd> \\<and> prg E,heap s\\<turnstile>locals s[\\<Colon>\\<preceq>]localT E"
   10.34 +
   10.35 +end
    11.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
    11.2 +++ b/src/HOL/MicroJava/J/Decl.thy	Thu Nov 11 12:23:45 1999 +0100
    11.3 @@ -0,0 +1,37 @@
    11.4 +(*  Title:      HOL/MicroJava/J/Decl.thy
    11.5 +    ID:         $Id$
    11.6 +    Author:     David von Oheimb
    11.7 +    Copyright   1997 Technische Universitaet Muenchen
    11.8 +
    11.9 +Class declarations
   11.10 +*)
   11.11 +
   11.12 +Decl = Type +
   11.13 +
   11.14 +types	fdecl		(* field declaration, cf. 8.3 (, 9.3) *)
   11.15 +	= "vname \\<times> ty"
   11.16 +
   11.17 +
   11.18 +types	sig		(* signature of a method, cf. 8.4.2 *)
   11.19 +	= "mname \\<times> ty list"
   11.20 +
   11.21 +	'c mdecl		(* method declaration in a class *)
   11.22 +	= "sig \\<times> ty \\<times> 'c"
   11.23 +
   11.24 +types	'c class		(* class *)
   11.25 +	= "cname option \\<times> fdecl list \\<times> 'c mdecl list"
   11.26 +	(* superclass, fields, methods*)
   11.27 +
   11.28 +	'c cdecl		(* class declaration, cf. 8.1 *)
   11.29 +	= "cname \\<times> 'c class"
   11.30 +
   11.31 +consts
   11.32 +
   11.33 +  Object  :: cname	(* name of root class *)
   11.34 +  ObjectC :: 'c cdecl	(* decl of root class *)
   11.35 +
   11.36 +defs 
   11.37 +
   11.38 + ObjectC_def "ObjectC \\<equiv> (Object, (None, [], []))"
   11.39 +
   11.40 +end
    12.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
    12.2 +++ b/src/HOL/MicroJava/J/Eval.ML	Thu Nov 11 12:23:45 1999 +0100
    12.3 @@ -0,0 +1,39 @@
    12.4 +(*  Title:      HOL/MicroJava/J/Eval.ML
    12.5 +    ID:         $Id$
    12.6 +    Author:     David von Oheimb
    12.7 +    Copyright   1999 Technische Universitaet Muenchen
    12.8 +*)
    12.9 +
   12.10 +Goal "\\<And>s s'. (G\\<turnstile>(x,s) -e \\<succ>  v \\<rightarrow> (x',s') \\<longrightarrow> x'=None \\<longrightarrow> x=None) \\<and> \
   12.11 +\             (G\\<turnstile>(x,s) -es[\\<succ>]vs\\<rightarrow> (x',s') \\<longrightarrow> x'=None \\<longrightarrow> x=None) \\<and> \
   12.12 +\             (G\\<turnstile>(x,s) -c       \\<rightarrow> (x',s') \\<longrightarrow> x'=None \\<longrightarrow> x=None)";
   12.13 +by(split_all_tac 1);
   12.14 +by(rtac eval_evals_exec.induct 1);
   12.15 +by(rewtac c_hupd_def);
   12.16 +by(ALLGOALS Asm_full_simp_tac);
   12.17 +qed "eval_evals_exec_no_xcpt";
   12.18 +
   12.19 +val eval_no_xcpt = prove_goal thy "\\<And>X. G\\<turnstile>(x,s) -e\\<succ>v\\<rightarrow> (None,s') \\<Longrightarrow> x=None" (K [
   12.20 +	dtac (eval_evals_exec_no_xcpt RS conjunct1 RS mp) 1,
   12.21 +	Fast_tac 1]);
   12.22 +val evals_no_xcpt = prove_goal thy "\\<And>X. G\\<turnstile>(x,s) -e[\\<succ>]v\\<rightarrow> (None,s') \\<Longrightarrow> x=None" (K [
   12.23 +	dtac (eval_evals_exec_no_xcpt RS conjunct2 RS conjunct1 RS mp) 1,
   12.24 +	Fast_tac 1]);
   12.25 +
   12.26 +val eval_evals_exec_xcpt = prove_goal thy 
   12.27 +"\\<And>s s'. (G\\<turnstile>(x,s) -e \\<succ>  v \\<rightarrow> (x',s') \\<longrightarrow> x=Some xc \\<longrightarrow> x'=Some xc \\<and> s'=s) \\<and> \
   12.28 +\        (G\\<turnstile>(x,s) -es[\\<succ>]vs\\<rightarrow> (x',s') \\<longrightarrow> x=Some xc \\<longrightarrow> x'=Some xc \\<and> s'=s) \\<and> \
   12.29 +\        (G\\<turnstile>(x,s) -c       \\<rightarrow> (x',s') \\<longrightarrow> x=Some xc \\<longrightarrow> x'=Some xc \\<and> s'=s)"
   12.30 + (K [
   12.31 +	split_all_tac 1,
   12.32 +	rtac eval_evals_exec.induct 1,
   12.33 +	rewtac c_hupd_def,
   12.34 +	ALLGOALS Asm_full_simp_tac]);
   12.35 +val eval_xcpt = prove_goal thy 
   12.36 +"\\<And>X. G\\<turnstile>(Some xc,s) -e\\<succ>v\\<rightarrow> (x',s') \\<Longrightarrow> x'=Some xc \\<and>  s'=s" (K [
   12.37 +	dtac (eval_evals_exec_xcpt RS conjunct1 RS mp) 1,
   12.38 +	Fast_tac 1]);
   12.39 +val exec_xcpt = prove_goal thy 
   12.40 +"\\<And>X. G\\<turnstile>(Some xc,s) -s0\\<rightarrow> (x',s') \\<Longrightarrow> x'=Some xc \\<and>  s'=s" (K [
   12.41 +	dtac (eval_evals_exec_xcpt RS conjunct2 RS conjunct2 RS mp) 1,
   12.42 +	Fast_tac 1]);
    13.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
    13.2 +++ b/src/HOL/MicroJava/J/Eval.thy	Thu Nov 11 12:23:45 1999 +0100
    13.3 @@ -0,0 +1,121 @@
    13.4 +(*  Title:      HOL/MicroJava/J/Eval.thy
    13.5 +    ID:         $Id$
    13.6 +    Author:     David von Oheimb
    13.7 +    Copyright   1999 Technische Universitaet Muenchen
    13.8 +
    13.9 +Operational evaluation (big-step) semantics of the 
   13.10 +execution of Java expressions and statements
   13.11 +*)
   13.12 +
   13.13 +Eval = State + 
   13.14 +
   13.15 +consts
   13.16 +  eval  :: "javam prog \\<Rightarrow> (xstate \\<times> expr      \\<times> val      \\<times> xstate) set"
   13.17 +  evals :: "javam prog \\<Rightarrow> (xstate \\<times> expr list \\<times> val list \\<times> xstate) set"
   13.18 +  exec  :: "javam prog \\<Rightarrow> (xstate \\<times> stmt                 \\<times> xstate) set"
   13.19 +
   13.20 +syntax
   13.21 +  eval :: "[javam prog,xstate,expr,val,xstate] \\<Rightarrow> bool "("_\\<turnstile>_ -_\\<succ>_\\<rightarrow> _"[51,82,82,82,82]81)
   13.22 +  evals:: "[javam prog,xstate,expr list,
   13.23 +	                      val list,xstate] \\<Rightarrow> bool "("_\\<turnstile>_ -_[\\<succ>]_\\<rightarrow> _"[51,82,51,51,82]81)
   13.24 +  exec :: "[javam prog,xstate,stmt,    xstate] \\<Rightarrow> bool "("_\\<turnstile>_ -_\\<rightarrow> _"  [51,82,82,   82]81)
   13.25 +
   13.26 +translations
   13.27 +  "G\\<turnstile>s -e \\<succ> v\\<rightarrow> (x,s')" == "(s, e, v, _args x s') \\<in> eval  G"
   13.28 +  "G\\<turnstile>s -e \\<succ> v\\<rightarrow>    s' " == "(s, e, v,         s') \\<in> eval  G"
   13.29 +  "G\\<turnstile>s -e[\\<succ>]v\\<rightarrow> (x,s')" == "(s, e, v, _args x s') \\<in> evals G"
   13.30 +  "G\\<turnstile>s -e[\\<succ>]v\\<rightarrow>    s' " == "(s, e, v,         s') \\<in> evals G"
   13.31 +  "G\\<turnstile>s -c     \\<rightarrow> (x,s')" == "(s, c,    _args x s') \\<in> exec  G"
   13.32 +  "G\\<turnstile>s -c     \\<rightarrow>    s' " == "(s, c,            s') \\<in> exec  G"
   13.33 +
   13.34 +inductive "eval G" "evals G" "exec G" intrs
   13.35 +
   13.36 +(* evaluation of expressions *)
   13.37 +
   13.38 +  (* cf. 15.5 *)
   13.39 +  XcptE				  "G\\<turnstile>(Some xc,s) -e\\<succ>arbitrary\\<rightarrow> (Some xc,s)"
   13.40 +
   13.41 +  (* cf. 15.8.1 *)
   13.42 +  NewC	"\\<lbrakk>h = heap s; (a,x) = new_Addr h;
   13.43 +	  h'= h(a\\<mapsto>(C,init_vars (fields (G,C))))\\<rbrakk> \\<Longrightarrow>
   13.44 +				   G\\<turnstile>Norm s -NewC C\\<succ>Addr a\\<rightarrow> c_hupd h' (x,s)"
   13.45 +
   13.46 +  (* cf. 15.15 *)
   13.47 +  Cast	"\\<lbrakk>G\\<turnstile>Norm s0 -e\\<succ>v\\<rightarrow> (x1,s1);
   13.48 +	  x2=raise_if (\\<not> cast_ok G T (heap s1) v) ClassCast x1\\<rbrakk> \\<Longrightarrow>
   13.49 +			        G\\<turnstile>Norm s0 -Cast T e\\<succ>v\\<rightarrow> (x2,s1)"
   13.50 +
   13.51 +  (* cf. 15.7.1 *)
   13.52 +  Lit				   "G\\<turnstile>Norm s -Lit v\\<succ>v\\<rightarrow> Norm s"
   13.53 +
   13.54 +  (* cf. 15.13.1, 15.2 *)
   13.55 +  LAcc				  "G\\<turnstile>Norm s -LAcc v\\<succ>the (locals s v)\\<rightarrow> Norm s"
   13.56 +
   13.57 +  (* cf. 15.25.1 *)
   13.58 +  LAss  "\\<lbrakk>G\\<turnstile>Norm s -e\\<succ>v\\<rightarrow>  (x,(h,l));
   13.59 +	  l' = (if x = None then l(va\\<mapsto>v) else l)\\<rbrakk> \\<Longrightarrow>
   13.60 +				   G\\<turnstile>Norm s -va\\<Colon>=e\\<succ>v\\<rightarrow> (x,(h,l'))"
   13.61 +
   13.62 +
   13.63 +  (* cf. 15.10.1, 15.2 *)
   13.64 +  FAcc	"\\<lbrakk>G\\<turnstile>Norm s0 -e\\<succ>a'\\<rightarrow> (x1,s1); 
   13.65 +	  v = the (snd (the (heap s1 (the_Addr a'))) (fn,T))\\<rbrakk> \\<Longrightarrow>
   13.66 +				 G\\<turnstile>Norm s0 -{T}e..fn\\<succ>v\\<rightarrow> (np a' x1,s1)"
   13.67 +
   13.68 +  (* cf. 15.25.1 *)
   13.69 +  FAss  "\\<lbrakk>G\\<turnstile>     Norm s0  -e1\\<succ>a'\\<rightarrow> (x1,s1); a = the_Addr a';
   13.70 +	  G\\<turnstile>(np a' x1,s1) -e2\\<succ>v \\<rightarrow> (x2,s2);
   13.71 +	  h = heap s2; (c,fs) = the (h a);
   13.72 +	  h' = h(a\\<mapsto>(c,(fs((fn,T)\\<mapsto>v))))\\<rbrakk> \\<Longrightarrow>
   13.73 +			  G\\<turnstile>Norm s0 -{T}e1..fn\\<in>=e2\\<succ>v\\<rightarrow> c_hupd h' (x2,s2)"
   13.74 +
   13.75 +  (* cf. 15.11.4.1, 15.11.4.2, 15.11.4.4, 15.11.4.5, 14.15 *)
   13.76 +  Call	"\\<lbrakk>G\\<turnstile>Norm s0 -e\\<succ>a'\\<rightarrow> s1; a = the_Addr a';
   13.77 +	   G\\<turnstile>s1 -ps[\\<succ>]pvs\\<rightarrow> (x,(h,l)); dynT = fst (the (h a));
   13.78 +	   (md,rT,pns,lvars,blk,res) = the (cmethd (G,dynT) (mn,pTs));
   13.79 +	   G\\<turnstile>(np a' x,(h,(init_vars lvars)(pns[\\<mapsto>]pvs)(This\\<mapsto>a'))) -blk\\<rightarrow> s3;
   13.80 +	   G\\<turnstile>     s3 -res\\<succ>v \\<rightarrow> (x4,s4)\\<rbrakk> \\<Longrightarrow>
   13.81 +			    G\\<turnstile>Norm s0 -e..mn({pTs}ps)\\<succ>v\\<rightarrow> (x4,(heap s4,l))"
   13.82 +
   13.83 +
   13.84 +(* evaluation of expression lists *)
   13.85 +
   13.86 +  (* cf. 15.5 *)
   13.87 +  XcptEs			  "G\\<turnstile>(Some xc,s) -e[\\<succ>]arbitrary\\<rightarrow> (Some xc,s)"
   13.88 +
   13.89 +  (* cf. 15.11.??? *)
   13.90 +  Nil
   13.91 +				    "G\\<turnstile>Norm s0 -[][\\<succ>][]\\<rightarrow> Norm s0"
   13.92 +
   13.93 +  (* cf. 15.6.4 *)
   13.94 +  Cons	"\\<lbrakk>G\\<turnstile>Norm s0 -e  \\<succ> v \\<rightarrow> s1;
   13.95 +           G\\<turnstile>     s1 -es[\\<succ>]vs\\<rightarrow> s2\\<rbrakk> \\<Longrightarrow>
   13.96 +				   G\\<turnstile>Norm s0 -e#es[\\<succ>]v#vs\\<rightarrow> s2"
   13.97 +
   13.98 +(* execution of statements *)
   13.99 +
  13.100 +  (* cf. 14.1 *)
  13.101 +  XcptS				 "G\\<turnstile>(Some xc,s) -s0\\<rightarrow> (Some xc,s)"
  13.102 +
  13.103 +  (* cf. 14.5 *)
  13.104 +  Skip	 			    "G\\<turnstile>Norm s -Skip\\<rightarrow> Norm s"
  13.105 +
  13.106 +  (* cf. 14.7 *)
  13.107 +  Expr	"\\<lbrakk>G\\<turnstile>Norm s0 -e\\<succ>v\\<rightarrow> s1\\<rbrakk> \\<Longrightarrow>
  13.108 +				  G\\<turnstile>Norm s0 -Expr e\\<rightarrow> s1"
  13.109 +
  13.110 +  (* cf. 14.2 *)
  13.111 +  Comp	"\\<lbrakk>G\\<turnstile>Norm s0 -s \\<rightarrow> s1;
  13.112 +	  G\\<turnstile>     s1 -t \\<rightarrow> s2\\<rbrakk> \\<Longrightarrow>
  13.113 +				 G\\<turnstile>Norm s0 -(s;; t)\\<rightarrow> s2"
  13.114 +
  13.115 +  (* cf. 14.8.2 *)
  13.116 +  Cond	"\\<lbrakk>G\\<turnstile>Norm s0  -e \\<succ>v\\<rightarrow> s1;
  13.117 +	  G\\<turnstile>     s1 -(if  the_Bool v then s else t)\\<rightarrow> s2\\<rbrakk> \\<Longrightarrow>
  13.118 +		        G\\<turnstile>Norm s0 -(If(e) s Else t)\\<rightarrow> s2"
  13.119 +
  13.120 +  (* cf. 14.10, 14.10.1 *)
  13.121 +  Loop	"\\<lbrakk>G\\<turnstile>Norm s0 -(If(e) (s;; While(e) s) Else Skip)\\<rightarrow> s1\\<rbrakk> \\<Longrightarrow>
  13.122 +			    G\\<turnstile>Norm s0 -(While(e) s)\\<rightarrow> s1"
  13.123 +
  13.124 +end
    14.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
    14.2 +++ b/src/HOL/MicroJava/J/JBasis.ML	Thu Nov 11 12:23:45 1999 +0100
    14.3 @@ -0,0 +1,230 @@
    14.4 +(*  Title:      HOL/MicroJava/J/JBasis.ML
    14.5 +    ID:         $Id$
    14.6 +    Author:     David von Oheimb
    14.7 +    Copyright   1999 TU Muenchen
    14.8 +*)
    14.9 +
   14.10 +val strip_tac1 = SELECT_GOAL (safe_tac (HOL_cs delrules [conjI, disjE, impCE]));
   14.11 +
   14.12 +Goalw [image_def]
   14.13 +	"x \\<in> f``A \\<Longrightarrow> \\<exists>y. y \\<in> A \\<and>  x = f y";
   14.14 +by(Auto_tac);
   14.15 +qed "image_rev";
   14.16 +
   14.17 +fun case_tac1 s i = EVERY [case_tac s i, rotate_tac ~1 i, rotate_tac ~1 (i+1)];
   14.18 +
   14.19 +val select_split = prove_goalw Prod.thy [split_def] 
   14.20 +	"(\\<epsilon>(x,y). P x y) = (\\<epsilon>xy. P (fst xy) (snd xy))" (K [rtac refl 1]);
   14.21 +	 
   14.22 +
   14.23 +val split_beta = prove_goal Prod.thy "(\\<lambda>(x,y). P x y) z = P (fst z) (snd z)"
   14.24 +	(fn _ => [stac surjective_pairing 1, stac split 1, rtac refl 1]);
   14.25 +val split_beta2 = prove_goal Prod.thy "(\\<lambda>(x,y). P x y) (w,z) = P w z"
   14.26 +	(fn _ => [Auto_tac]);
   14.27 +val splitE2 = prove_goal Prod.thy "\\<lbrakk>Q (split P z); \\<And>x y. \\<lbrakk>z = (x, y); Q (P x y)\\<rbrakk> \\<Longrightarrow> R\\<rbrakk> \\<Longrightarrow> R" (fn prems => [
   14.28 +	REPEAT (resolve_tac (prems@[surjective_pairing]) 1),
   14.29 +	rtac (split_beta RS subst) 1,
   14.30 +	rtac (hd prems) 1]);
   14.31 +val splitE2' = prove_goal Prod.thy "\\<lbrakk>((\\<lambda>(x,y). P x y) z) w; \\<And>x y. \\<lbrakk>z = (x, y); (P x y) w\\<rbrakk> \\<Longrightarrow> R\\<rbrakk> \\<Longrightarrow> R" (fn prems => [
   14.32 +	REPEAT (resolve_tac (prems@[surjective_pairing]) 1),
   14.33 +	res_inst_tac [("P1","P")] (split_beta RS subst) 1,
   14.34 +	rtac (hd prems) 1]);
   14.35 +	
   14.36 +
   14.37 +fun pair_tac s = res_inst_tac [("p",s)] PairE THEN' hyp_subst_tac;
   14.38 +
   14.39 +val BallE = prove_goal thy "\\<lbrakk>Ball A P; x \\<notin> A \\<Longrightarrow> Q; P x \\<Longrightarrow> Q \\<rbrakk> \\<Longrightarrow> Q"
   14.40 +	(fn prems => [rtac ballE 1, resolve_tac prems 1, 
   14.41 +			eresolve_tac prems 1, eresolve_tac prems 1]);
   14.42 +
   14.43 +val set_cs2 = set_cs delrules [ballE] addSEs [BallE];
   14.44 +
   14.45 +Addsimps [Let_def];
   14.46 +Addsimps [surjective_pairing RS sym];
   14.47 +
   14.48 +(* To HOL.ML *)
   14.49 +
   14.50 +val ex1_Eps_eq = prove_goal HOL.thy "\\<lbrakk> \\<exists>!x. P x; P y \\<rbrakk> \\<Longrightarrow> Eps P = y" 
   14.51 +	(fn prems => [
   14.52 +	cut_facts_tac prems 1,
   14.53 +	rtac select_equality 1,
   14.54 +	 atac 1,
   14.55 +	etac ex1E 1,
   14.56 +	etac all_dupE 1,
   14.57 +	fast_tac HOL_cs 1]);
   14.58 +
   14.59 +
   14.60 +val ball_insert = prove_goalw equalities.thy [Ball_def]
   14.61 +	"Ball (insert x A) P = (P x \\<and> Ball A P)" (fn _ => [
   14.62 +	fast_tac set_cs 1]);
   14.63 +
   14.64 +fun option_case_tac i = EVERY [
   14.65 +	etac option_caseE i,
   14.66 +	 rotate_tac ~2 (i+1), asm_full_simp_tac HOL_basic_ss (i+1), 
   14.67 +	 rotate_tac ~2  i   , asm_full_simp_tac HOL_basic_ss i];
   14.68 +
   14.69 +val not_None_tac = EVERY' [dtac (not_None_eq RS iffD1),rotate_tac ~1,etac exE,
   14.70 +		rotate_tac ~1,asm_full_simp_tac 
   14.71 +	(simpset() delsimps [split_paired_All,split_paired_Ex])];
   14.72 +
   14.73 +fun ex_ftac thm = EVERY' [forward_tac [thm], REPEAT o (etac exE), rotate_tac ~1,
   14.74 +  asm_full_simp_tac (simpset() delsimps [split_paired_All,split_paired_Ex])];
   14.75 +
   14.76 +val optionE = prove_goal thy 
   14.77 +       "\\<lbrakk> opt = None \\<Longrightarrow> P;  \\<And>x. opt = Some x \\<Longrightarrow> P \\<rbrakk> \\<Longrightarrow> P" 
   14.78 +   (fn prems => [
   14.79 +	case_tac "opt = None" 1,
   14.80 +	 eresolve_tac prems 1,
   14.81 +	not_None_tac 1,
   14.82 +	eresolve_tac prems 1]);
   14.83 +
   14.84 +fun option_case_tac2 s i = EVERY [
   14.85 +	 exhaust_tac s i,
   14.86 +	 rotate_tac ~1 (i+1), asm_full_simp_tac HOL_basic_ss (i+1), 
   14.87 +	 rotate_tac ~1  i   , asm_full_simp_tac HOL_basic_ss i];
   14.88 +
   14.89 +val option_map_SomeD = prove_goalw thy [option_map_def]
   14.90 +	"\\<And>x. option_map f x = Some y \\<Longrightarrow> \\<exists>z. x = Some z \\<and> f z = y" (K [
   14.91 +	option_case_tac2 "x" 1,
   14.92 +	 Auto_tac]);
   14.93 +
   14.94 +
   14.95 +section "unique";
   14.96 +
   14.97 +Goal "(x, y) : set l --> x : fst `` set l";
   14.98 +by (induct_tac "l" 1);
   14.99 +by  Auto_tac;
  14.100 +qed_spec_mp "fst_in_set_lemma";
  14.101 +
  14.102 +Goalw [unique_def] "unique []";
  14.103 +by (Simp_tac 1);
  14.104 +qed "unique_Nil";
  14.105 +
  14.106 +Goalw [unique_def] "unique ((x,y)#l) = (unique l \\<and> (!y. (x,y) ~: set l))";
  14.107 +by  (auto_tac (claset() addDs [fst_in_set_lemma],simpset()));
  14.108 +qed "unique_Cons";
  14.109 +
  14.110 +Addsimps [unique_Nil,unique_Cons];
  14.111 +
  14.112 +Goal "unique l' ==> unique l --> \
  14.113 +\ (!(x,y):set l. !(x',y'):set l'. x' ~= x) --> unique (l @ l')";
  14.114 +by (induct_tac "l" 1);
  14.115 +by  (auto_tac (claset() addDs [fst_in_set_lemma],simpset()));
  14.116 +qed_spec_mp "unique_append";
  14.117 +
  14.118 +Goal "unique l --> inj f --> unique (map (%(k,x). (f k, g k x)) l)";
  14.119 +by (induct_tac "l" 1);
  14.120 +by  (auto_tac (claset() addDs [fst_in_set_lemma],simpset()));
  14.121 +qed_spec_mp "unique_map_inj";
  14.122 +
  14.123 +Goal "\\<And>l. unique l \\<Longrightarrow> unique (map (split (\\<lambda>k. Pair (k, C))) l)";
  14.124 +by(etac unique_map_inj 1);
  14.125 +by(rtac injI 1);
  14.126 +by Auto_tac;
  14.127 +qed "unique_map_Pair";
  14.128 +
  14.129 +Goal "\\<lbrakk>M = N; \\<And>x. x\\<in>N \\<Longrightarrow> f x = g x\\<rbrakk> \\<Longrightarrow> f``M = g``N";
  14.130 +by(rtac set_ext 1);
  14.131 +by(simp_tac (simpset() addsimps image_def::premises()) 1);
  14.132 +qed "image_cong";
  14.133 +
  14.134 +val split_Pair_eq = prove_goal Prod.thy 
  14.135 +"\\<And>X. ((x, y), z) \\<in> split (\\<lambda>x. Pair (x, Y)) `` A \\<Longrightarrow> y = Y" (K [
  14.136 +	etac imageE 1,
  14.137 +	split_all_tac 1,
  14.138 +	auto_tac(claset_of Prod.thy,simpset_of Prod.thy)]);
  14.139 +
  14.140 +
  14.141 +section "list_all2";
  14.142 +
  14.143 +val list_all2_lengthD = prove_goalw thy [list_all2_def] 
  14.144 + "\\<And>X. list_all2 P as bs \\<Longrightarrow> length as = length bs" (K [Auto_tac]);
  14.145 +
  14.146 +val list_all2_Nil = prove_goalw thy [list_all2_def] 
  14.147 + "list_all2 P [] []" (K [Auto_tac]);
  14.148 +Addsimps[list_all2_Nil];
  14.149 +AddSIs[list_all2_Nil];
  14.150 +
  14.151 +val list_all2_Cons = prove_goalw thy [list_all2_def] 
  14.152 + "\\<And>X. list_all2 P (a#as) (b#bs) = (P a b \\<and> list_all2 P as bs)" (K [Auto_tac]);
  14.153 +AddIffs[list_all2_Cons];
  14.154 +
  14.155 +
  14.156 +(* More about Maps *)
  14.157 +
  14.158 +val override_SomeD = prove_goalw thy [override_def] "(s \\<oplus> t) k = Some x \\<Longrightarrow> \
  14.159 +\ t k = Some x |  t k = None \\<and>  s k = Some x" (fn prems => [
  14.160 +	cut_facts_tac prems 1,
  14.161 +	case_tac "\\<exists>x. t k = Some x" 1,
  14.162 +	 etac exE 1,
  14.163 +	 rotate_tac ~1 1,
  14.164 +	 Asm_full_simp_tac 1,
  14.165 +	asm_full_simp_tac (HOL_ss addsimps [not_None_eq RS sym]) 1,
  14.166 +	 rotate_tac ~1 1,
  14.167 +	 Asm_full_simp_tac 1]);
  14.168 +
  14.169 +Addsimps [fun_upd_same, fun_upd_other];
  14.170 +
  14.171 +Goal "unique xys \\<longrightarrow> (map_of xys x = Some y) = ((x,y) \\<in> set xys)";
  14.172 +by(induct_tac "xys" 1);
  14.173 + by(Simp_tac 1);
  14.174 +by(force_tac (claset(), simpset() addsimps [unique_Cons]) 1);
  14.175 +qed_spec_mp "unique_map_of_Some_conv";
  14.176 +
  14.177 +val in_set_get = unique_map_of_Some_conv RS iffD2;
  14.178 +val get_in_set = unique_map_of_Some_conv RS iffD1;
  14.179 +
  14.180 +Goal "(\\<forall>(x,y)\\<in>set l. P x y) \\<longrightarrow> (\\<forall>x. \\<forall>y. map_of l x = Some y \\<longrightarrow> P x y)";
  14.181 +by(induct_tac "l" 1);
  14.182 +by(ALLGOALS Simp_tac);
  14.183 +by Safe_tac;
  14.184 +by Auto_tac;
  14.185 +bind_thm("Ball_set_table",result() RS mp);
  14.186 +
  14.187 +val table_mono = prove_goal thy 
  14.188 +"unique l' \\<longrightarrow> (\\<forall>xy. (xy)\\<in>set l \\<longrightarrow> (xy)\\<in>set l') \\<longrightarrow>\
  14.189 +\ (\\<forall>k y. map_of l k = Some y \\<longrightarrow> map_of l' k = Some y)" (fn _ => [
  14.190 +	induct_tac "l" 1,
  14.191 +	 Auto_tac,
  14.192 + 	 fast_tac (HOL_cs addSIs [in_set_get]) 1])
  14.193 + RS mp RS mp RS spec RS spec RS mp;
  14.194 +
  14.195 +val table_map_Some' = prove_goal thy "map_of t k = Some (k', x) \\<longrightarrow> \
  14.196 +\ map_of (map (\\<lambda>u. ((fst u, fst (snd u)), snd (snd u))) t) (k, k') = Some x" (K [
  14.197 +	induct_tac "t" 1,	
  14.198 +	 ALLGOALS Simp_tac,
  14.199 +	case_tac1 "k = fst a" 1,
  14.200 +	 Auto_tac]) RS mp;
  14.201 +val table_map_Some = prove_goal thy 
  14.202 +"map_of (map (\\<lambda>((k,k'),x). (k,(k',x))) t) k = Some (k',x) \\<longrightarrow> \
  14.203 +\map_of t (k, k') = Some x" (K [
  14.204 +	induct_tac "t" 1,	
  14.205 +	Auto_tac]) RS mp;
  14.206 +
  14.207 +
  14.208 +val table_mapf_Some = prove_goal thy "\\<And>f. \\<forall>x y. f x = f y \\<longrightarrow> x = y \\<Longrightarrow> \
  14.209 +\ map_of (map (\\<lambda>(k,x). (k,f x)) t) k = Some (f x) \\<longrightarrow> map_of t k = Some x" (K [
  14.210 +	induct_tac "t" 1,	
  14.211 +	Auto_tac]) RS mp;
  14.212 +val table_mapf_SomeD = prove_goal thy 
  14.213 +"map_of (map (\\<lambda>(k,x). (k, f x)) t) k = Some z \\<longrightarrow> (\\<exists>y. (k,y)\\<in>set t \\<and>  z = f y)"(K [
  14.214 +	induct_tac "t" 1,	
  14.215 +	Auto_tac]) RS mp;
  14.216 +
  14.217 +val table_mapf_Some2 = prove_goal thy 
  14.218 +"\\<And>k. map_of (map (\\<lambda>(k,x). (k,C,x)) t) k = Some (D,x) \\<Longrightarrow> C = D \\<and> map_of t k = Some x" (K [
  14.219 +	forward_tac [table_mapf_SomeD] 1,
  14.220 +	Auto_tac,
  14.221 +	rtac table_mapf_Some 1,
  14.222 +	 atac 2,
  14.223 +	Fast_tac 1]);
  14.224 +
  14.225 +val finite_map_of = rewrite_rule [dom_def] finite_dom_map_of;
  14.226 +
  14.227 +Goal
  14.228 +"map_of (map (\\<lambda>(a,b). (a,f b)) xs) x = option_map f (map_of xs x)";
  14.229 +by (induct_tac "xs" 1);
  14.230 +auto();
  14.231 +qed "map_of_map";
  14.232 +
  14.233 +
    15.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
    15.2 +++ b/src/HOL/MicroJava/J/JBasis.thy	Thu Nov 11 12:23:45 1999 +0100
    15.3 @@ -0,0 +1,19 @@
    15.4 +(*  Title:      HOL/MicroJava/J/JBasis.thy
    15.5 +    ID:         $Id$
    15.6 +    Author:     David von Oheimb
    15.7 +    Copyright   1999 TU Muenchen
    15.8 +
    15.9 +Some auxiliary definitions.
   15.10 +*)
   15.11 +
   15.12 +JBasis = Main + 
   15.13 +
   15.14 +constdefs
   15.15 +
   15.16 +  unique  :: "('a \\<times> 'b) list \\<Rightarrow> bool"
   15.17 + "unique  \\<equiv> nodups \\<circ> map fst"
   15.18 +
   15.19 +  list_all2 :: "('a \\<Rightarrow> 'b \\<Rightarrow> bool) \\<Rightarrow> ('a list \\<Rightarrow> 'b list \\<Rightarrow> bool)"
   15.20 + "list_all2 P xs ys \\<equiv> length xs = length ys \\<and> (\\<forall> (x,y)\\<in>set (zip xs ys). P x y)"
   15.21 +
   15.22 +end
    16.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
    16.2 +++ b/src/HOL/MicroJava/J/JTypeSafe.ML	Thu Nov 11 12:23:45 1999 +0100
    16.3 @@ -0,0 +1,349 @@
    16.4 +(*  Title:      HOL/MicroJava/J/JTypeSafe.ML
    16.5 +    ID:         $Id$
    16.6 +    Author:     David von Oheimb
    16.7 +    Copyright   1999 Technische Universitaet Muenchen
    16.8 +
    16.9 +Type safety proof
   16.10 +*)
   16.11 +
   16.12 +Addsimps [split_beta];
   16.13 +
   16.14 +Goal "\\<lbrakk>h a = None; (h, l)\\<Colon>\\<preceq>(G, lT); wf_prog wtm G; is_class G C\\<rbrakk> \\<Longrightarrow> \
   16.15 +\ (h(a\\<mapsto>(C,(init_vars (fields (G,C))))), l)\\<Colon>\\<preceq>(G, lT)";
   16.16 +by( etac conforms_upd_obj 1);
   16.17 +by(  rewtac oconf_def);
   16.18 +by(  auto_tac (claset() addSDs [is_type_fields, map_of_SomeD], simpset()));
   16.19 +qed "NewC_conforms";
   16.20 +
   16.21 +Goalw [cast_ok_def]
   16.22 + "\\<lbrakk> wf_prog wtm G; G,h\\<turnstile>v\\<Colon>\\<preceq>Tb; G\\<turnstile>Tb\\<Rightarrow>? T'; cast_ok G T' h v\\<rbrakk> \
   16.23 +\ \\<Longrightarrow> G,h\\<turnstile>v\\<Colon>\\<preceq>T'";
   16.24 +by( case_tac1 "v = Null" 1);
   16.25 +by(  Asm_full_simp_tac 1);
   16.26 +by(  dtac widen_RefT 1);
   16.27 +by(  Clarify_tac 1);
   16.28 +by(  forward_tac [cast_RefT] 1);
   16.29 +by(  Clarify_tac 1);
   16.30 +by(  rtac widen.null 1);
   16.31 +by( case_tac1 "\\<exists>pt. T' = PrimT pt" 1);
   16.32 +by(  strip_tac1 1);
   16.33 +by(  dtac cast_PrimT2 1);
   16.34 +by(  etac conf_widen 1);
   16.35 +by(   atac 1);
   16.36 +by(  atac 1);
   16.37 +by( Asm_full_simp_tac 1);
   16.38 +by( dtac (non_PrimT RS iffD1) 1);
   16.39 +by( strip_tac1 1);
   16.40 +by( forward_tac [cast_RefT2] 1);
   16.41 +by( strip_tac1 1);
   16.42 +by( dtac non_npD 1);
   16.43 +by(  atac 1);
   16.44 +by( rewrite_goals_tac [the_Addr_def,obj_ty_def]);
   16.45 +by Auto_tac ;
   16.46 +by(  ALLGOALS (rtac conf_AddrI));
   16.47 +by     Auto_tac;
   16.48 +qed "Cast_conf";
   16.49 +
   16.50 +Goal "\\<lbrakk> wf_prog wtm G; cfield (G,C) fn = Some (fd, ft); (h,l)\\<Colon>\\<preceq>(G,lT); \
   16.51 +\    x' = None \\<longrightarrow> G,h\\<turnstile>a'\\<Colon>\\<preceq>Class C; np a' x' = None \\<rbrakk> \\<Longrightarrow> \
   16.52 +\ G,h\\<turnstile>the (snd (the (h (the_Addr a'))) (fn, fd))\\<Colon>\\<preceq>ft";
   16.53 +by( dtac np_NoneD 1);
   16.54 +by( etac conjE 1);
   16.55 +by( mp_tac 1);
   16.56 +by( dtac non_np_objD 1);
   16.57 +by   Auto_tac;
   16.58 +by( dtac (conforms_heapD RS hconfD) 1);
   16.59 +by(  atac 1);
   16.60 +by( dtac widen_cfs_fields 1);
   16.61 +by(   atac 1);
   16.62 +by(  atac 1);
   16.63 +by( dtac oconf_objD 1);
   16.64 +by(  atac 1);
   16.65 +by Auto_tac;
   16.66 +val FAcc_type_sound = result();
   16.67 +
   16.68 +Goal
   16.69 + "\\<lbrakk> wf_prog wtm G; a = the_Addr a'; (c, fs) = the (h a); \
   16.70 +\   (G, lT)\\<turnstile>v\\<Colon>T'; G\\<turnstile>T'\\<preceq>ft; \
   16.71 +\   (G, lT)\\<turnstile>aa\\<Colon>Class C; \
   16.72 +\   cfield (G,C) fn = Some (fd, ft); h''\\<le>|h'; \
   16.73 +\   x' = None \\<longrightarrow> G,h'\\<turnstile>a'\\<Colon>\\<preceq>Class C; h'\\<le>|h; \
   16.74 +\   (h, l)\\<Colon>\\<preceq>(G, lT); G,h\\<turnstile>x\\<Colon>\\<preceq>T'; np a' x' = None\\<rbrakk> \\<Longrightarrow> \
   16.75 +\ h''\\<le>|h(a\\<mapsto>(c,(fs((fn,fd)\\<mapsto>x)))) \\<and>  \
   16.76 +\ (h(a\\<mapsto>(c,(fs((fn,fd)\\<mapsto>x)))), l)\\<Colon>\\<preceq>(G, lT) \\<and>  \
   16.77 +\ G,h(a\\<mapsto>(c,(fs((fn,fd)\\<mapsto>x))))\\<turnstile>x\\<Colon>\\<preceq>T'";
   16.78 +by( dtac np_NoneD 1);
   16.79 +by( etac conjE 1);
   16.80 +by( Asm_full_simp_tac 1);
   16.81 +by( dtac non_np_objD 1);
   16.82 +by(   atac 1);
   16.83 +by(  SELECT_GOAL Auto_tac 1);
   16.84 +by( strip_tac1 1);
   16.85 +by( Full_simp_tac 1);
   16.86 +by( EVERY [forward_tac [hext_objD] 1, atac 1]);
   16.87 +by( etac exE 1);
   16.88 +by( Asm_full_simp_tac 1);
   16.89 +by( strip_tac1 1);
   16.90 +by( rtac conjI 1);
   16.91 +by(  fast_tac (HOL_cs addEs [hext_trans, hext_upd_obj]) 1);
   16.92 +by( rtac conjI 1);
   16.93 +by(  fast_tac (HOL_cs addEs [conf_upd_obj RS iffD2]) 2);
   16.94 +
   16.95 +by( rtac conforms_upd_obj 1);
   16.96 +by   Auto_tac;
   16.97 +by(  rtac hextI 2);
   16.98 +by(  Force_tac 2);
   16.99 +by( rtac oconf_hext 1);
  16.100 +by(  etac hext_upd_obj 2);
  16.101 +by( dtac widen_cfs_fields 1);
  16.102 +by(   atac 1);
  16.103 +by(  atac 1);
  16.104 +by( rtac (oconf_obj RS iffD2) 1);
  16.105 +by( Simp_tac 1);
  16.106 +by( strip_tac 1);
  16.107 +by( case_tac1 "(aaa, b) = (fn, fd)" 1);
  16.108 +by(  Asm_full_simp_tac 1);
  16.109 +by(  fast_tac (HOL_cs addIs [conf_widen]) 1);
  16.110 +by( fast_tac (HOL_cs addDs [conforms_heapD RS hconfD, oconf_objD]) 1);
  16.111 +val FAss_type_sound = result();
  16.112 +
  16.113 +Goalw [wf_mhead_def] "\\<lbrakk> wf_prog wtm G; list_all2 (conf G h) pvs pTs; \
  16.114 + \ list_all2 (\\<lambda>T T'. G\\<turnstile>T\\<preceq>T') pTs pTs'; wf_mhead G (mn,pTs') rT; \
  16.115 +\ length pTs' = length pns; nodups pns; \
  16.116 +\ Ball (set lvars) (split (\\<lambda>vn. is_type G)) \
  16.117 +\ \\<rbrakk> \\<Longrightarrow> G,h\\<turnstile>init_vars lvars(pns[\\<mapsto>]pvs)[\\<Colon>\\<preceq>]map_of lvars(pns[\\<mapsto>]pTs')";
  16.118 +by( Clarsimp_tac 1);
  16.119 +by( rtac lconf_ext_list 1);
  16.120 +by(    rtac (Ball_set_table RS lconf_init_vars) 1);
  16.121 +by(    Force_tac 1);
  16.122 +by(   atac 1);
  16.123 +by(  atac 1);
  16.124 +by( (etac conf_list_gext_widen THEN_ALL_NEW atac) 1);
  16.125 +qed "Call_lemma2";
  16.126 +
  16.127 +Goalw [wf_java_prog_def]
  16.128 + "\\<lbrakk> wf_java_prog G; a' \\<noteq> Null; (h, l)\\<Colon>\\<preceq>(G, lT); \
  16.129 +\    max_spec G T (mn,pTsa) = {((mda,rTa),pTs')}; xc\\<le>|xh; xh\\<le>|h; \
  16.130 +\    list_all2 (conf G h) pvs pTsa;\
  16.131 +\    (md, rT, pns, lvars, blk, res) = \
  16.132 +\              the (cmethd (G,fst (the (h (the_Addr a')))) (mn, pTs'));\
  16.133 +\ \\<forall>lT. (h, init_vars lvars(pns[\\<mapsto>]pvs)(This\\<mapsto>a'))\\<Colon>\\<preceq>(G, lT) \\<longrightarrow> \
  16.134 +\ (G, lT)\\<turnstile>blk\\<surd> \\<longrightarrow>  h\\<le>|xi \\<and>  (xi, xl)\\<Colon>\\<preceq>(G, lT); \
  16.135 +\ \\<forall>lT. (xi, xl)\\<Colon>\\<preceq>(G, lT) \\<longrightarrow> (\\<forall>T. (G, lT)\\<turnstile>res\\<Colon>T \\<longrightarrow> \
  16.136 +\         xi\\<le>|h' \\<and> (h', xj)\\<Colon>\\<preceq>(G, lT) \\<and> (x' = None \\<longrightarrow> G,h'\\<turnstile>v\\<Colon>\\<preceq>T)); \
  16.137 +\ G,xh\\<turnstile>a'\\<Colon>\\<preceq>RefT T \\<rbrakk> \\<Longrightarrow> \
  16.138 +\ xc\\<le>|h' \\<and> (h', l)\\<Colon>\\<preceq>(G, lT) \\<and>  (x' = None \\<longrightarrow> G,h'\\<turnstile>v\\<Colon>\\<preceq>rTa)";
  16.139 +by( dtac (insertI1 RSN (2,(equalityD2 RS subsetD))) 1);
  16.140 +by( dtac (max_spec2appl_meths RS appl_methsD) 1);
  16.141 +by( etac conjE 1);
  16.142 +by( dtac non_np_objD' 1);
  16.143 +by(    atac 1);
  16.144 +by(   atac 1);
  16.145 +by(  strip_tac1 1);
  16.146 +by(  Asm_full_simp_tac 1);
  16.147 +by( Clarsimp_tac 1);
  16.148 +by( EVERY'[forward_tac [hext_objD], atac] 1);
  16.149 +by( Clarsimp_tac 1);
  16.150 +by( EVERY'[dtac Call_lemma, atac, atac] 1);
  16.151 +by( clarsimp_tac (claset(),simpset() addsimps [wt_java_mdecl_def])1);
  16.152 +by( thin_tac "cmethd ?sig ?x = ?y" 1);
  16.153 +by( EVERY'[dtac spec, etac impE] 1);
  16.154 +by(  mp_tac 2);
  16.155 +by(  rtac conformsI 1);
  16.156 +by(   etac conforms_heapD 1);
  16.157 +by(  rtac lconf_ext 1);
  16.158 +by(   force_tac (claset() addSEs [Call_lemma2],simpset()) 1);
  16.159 +by(  EVERY'[etac conf_hext, etac conf_obj_AddrI, atac] 1);
  16.160 +by( thin_tac "?E\\<turnstile>?blk\\<surd>" 1);
  16.161 +by( etac conjE 1);
  16.162 +by( EVERY'[dtac spec, mp_tac] 1);
  16.163 +(*by( thin_tac "?E\\<Colon>\\<preceq>(G, pT')" 1);*)
  16.164 +by( EVERY'[dtac spec, mp_tac] 1);
  16.165 +by( thin_tac "?E\\<turnstile>res\\<Colon>?rT" 1);
  16.166 +by( strip_tac1 1);
  16.167 +by( rtac conjI 1);
  16.168 +by(  fast_tac (HOL_cs addIs [hext_trans]) 1);
  16.169 +by( rtac conjI 1);
  16.170 +by(  rtac impI 2);
  16.171 +by(  mp_tac 2);
  16.172 +by(  forward_tac [conf_widen] 2);
  16.173 +by(    atac 4);
  16.174 +by(   atac 2);
  16.175 +by(  fast_tac (HOL_cs addSEs [widen_trans]) 2);
  16.176 +by( etac conforms_hext 1);
  16.177 +by(  etac hext_trans 1);
  16.178 +by(  atac 1);
  16.179 +by( etac conforms_heapD 1);
  16.180 +qed "Call_type_sound";
  16.181 +
  16.182 +
  16.183 +
  16.184 +Unify.search_bound := 40;
  16.185 +Unify.trace_bound  := 40;
  16.186 +Delsplits[split_if];
  16.187 +Delsimps[fun_upd_apply];(*###*)
  16.188 +Goal
  16.189 +"wf_java_prog G \\<Longrightarrow> \
  16.190 +\ (G\\<turnstile>(x,(h,l)) -e  \\<succ>v  \\<rightarrow> (x', (h',l')) \\<longrightarrow> \
  16.191 +\     (\\<forall>lT.    (h ,l )\\<Colon>\\<preceq>(G,lT) \\<longrightarrow> (\\<forall>T . (G,lT)\\<turnstile>e  \\<Colon> T \\<longrightarrow> \
  16.192 +\     h\\<le>|h' \\<and> (h',l')\\<Colon>\\<preceq>(G,lT) \\<and> (x'=None \\<longrightarrow> G,h'\\<turnstile>v  \\<Colon>\\<preceq> T )))) \\<and> \
  16.193 +\ (G\\<turnstile>(x,(h,l)) -es[\\<succ>]vs\\<rightarrow> (x', (h',l')) \\<longrightarrow> \
  16.194 +\     (\\<forall>lT.    (h ,l )\\<Colon>\\<preceq>(G,lT) \\<longrightarrow> (\\<forall>Ts. (G,lT)\\<turnstile>es[\\<Colon>]Ts \\<longrightarrow> \
  16.195 +\     h\\<le>|h' \\<and> (h',l')\\<Colon>\\<preceq>(G,lT) \\<and> (x'=None \\<longrightarrow> list_all2 (\\<lambda>v T. G,h'\\<turnstile>v\\<Colon>\\<preceq>T) vs Ts)))) \\<and> \
  16.196 +\ (G\\<turnstile>(x,(h,l)) -c       \\<rightarrow> (x', (h',l')) \\<longrightarrow> \
  16.197 +\     (\\<forall>lT.    (h ,l )\\<Colon>\\<preceq>(G,lT) \\<longrightarrow>       (G,lT)\\<turnstile>c  \\<surd> \\<longrightarrow> \
  16.198 +\     h\\<le>|h' \\<and> (h',l')\\<Colon>\\<preceq>(G,lT)))";
  16.199 +by( rtac eval_evals_exec.induct 1);
  16.200 +by( rewtac c_hupd_def);
  16.201 +
  16.202 +(* several simplifications, XcptE, XcptEs, XcptS, Skip *)
  16.203 +by( ALLGOALS Asm_full_simp_tac);
  16.204 +by( ALLGOALS strip_tac);
  16.205 +by( ALLGOALS (eresolve_tac ty_expr_ty_exprs_wt_stmt.elims 
  16.206 +		THEN_ALL_NEW Full_simp_tac));
  16.207 +by( ALLGOALS (EVERY' [REPEAT o (etac conjE), REPEAT o hyp_subst_tac]));
  16.208 +by( rewtac wf_java_prog_def);
  16.209 +
  16.210 +(* Level 7 *)
  16.211 +
  16.212 +(* 14 NewC *)
  16.213 +by( dtac new_AddrD 1);
  16.214 +by( etac disjE 1);
  16.215 +by(  Asm_simp_tac 2);
  16.216 +by( etac conjE 1);
  16.217 +by( Asm_simp_tac 1);
  16.218 +by( rtac conjI 1);
  16.219 +by(  fast_tac (HOL_cs addSEs [NewC_conforms]) 1);
  16.220 +by( rtac conf_obj_AddrI 1);
  16.221 +by(  rtac widen.refl 2);
  16.222 +by(  Asm_simp_tac 2);
  16.223 +by( Simp_tac 1);
  16.224 +
  16.225 +(* for Cast *)
  16.226 +by( defer_tac 1);
  16.227 +
  16.228 +(* 13 Lit *)
  16.229 +by( etac conf_litval 1);
  16.230 +
  16.231 +(* 12 LAcc *)
  16.232 +by( fast_tac (claset() addEs [conforms_localD RS lconfD]) 1);
  16.233 +
  16.234 +(* 11 Nil *)
  16.235 +by( Simp_tac 5);
  16.236 +
  16.237 +(* for FAss *)
  16.238 +by( EVERY'[eresolve_tac ty_expr_ty_exprs_wt_stmt.elims THEN_ALL_NEW Full_simp_tac, 
  16.239 +			REPEAT o (etac conjE), hyp_subst_tac] 3);
  16.240 +
  16.241 +(* for if *)
  16.242 +by( (case_tac1 "the_Bool v" THEN_ALL_NEW Asm_full_simp_tac) 8);
  16.243 +
  16.244 +val forward_hyp_tac = ALLGOALS (TRY o (EVERY' [dtac spec, mp_tac,
  16.245 +	(mp_tac ORELSE' (dtac spec THEN' mp_tac)), REPEAT o (etac conjE)]));
  16.246 +by forward_hyp_tac;
  16.247 +
  16.248 +(* 10+1 if *)
  16.249 +by(  fast_tac (HOL_cs addIs [hext_trans]) 8);
  16.250 +by( fast_tac (HOL_cs addIs [hext_trans]) 8);
  16.251 +
  16.252 +(* 9 Expr *)
  16.253 +by( Fast_tac 6);
  16.254 +
  16.255 +by( ALLGOALS Asm_full_simp_tac);
  16.256 +
  16.257 +(* 8 Cast *)
  16.258 +by( EVERY'[rtac impI, dtac raise_if_NoneD, Clarsimp_tac, 
  16.259 +           fast_tac (claset() addEs [Cast_conf])] 8);
  16.260 +
  16.261 +(* 7 LAss *)
  16.262 +by( asm_simp_tac (simpset() addsplits [expand_if]) 1);
  16.263 +by( EVERY'[eresolve_tac ty_expr_ty_exprs_wt_stmt.elims THEN_ALL_NEW Full_simp_tac] 1);
  16.264 +by( blast_tac (claset() addIs [conforms_upd_local, conf_widen]) 1);
  16.265 +
  16.266 +(* 6 FAcc *)
  16.267 +by( fast_tac (claset() addSEs [FAcc_type_sound]) 1);
  16.268 +
  16.269 +(* 5 While *)
  16.270 +by( fast_tac (claset() addIs [ty_expr_ty_exprs_wt_stmt.Cond, ty_expr_ty_exprs_wt_stmt.Comp, ty_expr_ty_exprs_wt_stmt.Skip]
  16.271 +		       addEs [ty_expr_ty_exprs_wt_stmt.Loop]) 5);
  16.272 +
  16.273 +by forward_hyp_tac;
  16.274 +
  16.275 +(* 4 Cons *)
  16.276 +by( fast_tac (claset() addDs [evals_no_xcpt] addIs [conf_hext,hext_trans]) 3);
  16.277 +
  16.278 +(* 3 ;; *)
  16.279 +by( fast_tac (claset() addIs [hext_trans]) 3);
  16.280 +
  16.281 +(* 2 FAss *)
  16.282 +by( case_tac1 "x2 = None" 1);
  16.283 +by(  Asm_simp_tac 2);
  16.284 +by(  fast_tac (claset() addIs [hext_trans]) 2);
  16.285 +by( Asm_full_simp_tac 1);
  16.286 +by( dtac eval_no_xcpt 1);
  16.287 +by( SELECT_GOAL (etac FAss_type_sound 1 THEN rtac refl 1 THEN ALLGOALS atac) 1);
  16.288 +
  16.289 +by prune_params_tac;
  16.290 +(* Level 45 *)
  16.291 +
  16.292 +(* 1 Call *)
  16.293 +by( case_tac1 "x = None" 1);
  16.294 +by(  dtac (not_None_eq RS iffD1) 2);
  16.295 +by(  Clarsimp_tac 2);
  16.296 +by(  dtac exec_xcpt 2);
  16.297 +by(  Asm_full_simp_tac 2);
  16.298 +by(  dtac eval_xcpt 2);
  16.299 +by(  Asm_full_simp_tac 2);
  16.300 +by(  fast_tac (HOL_cs addEs [hext_trans]) 2);
  16.301 +by( Clarify_tac 1);
  16.302 +by( dtac evals_no_xcpt 1);
  16.303 +by( Asm_full_simp_tac 1);
  16.304 +by( case_tac1 "a' = Null" 1);
  16.305 +by(  Asm_full_simp_tac 1);
  16.306 +by(  dtac exec_xcpt 1);
  16.307 +by(  Asm_full_simp_tac 1);
  16.308 +by(  dtac eval_xcpt 1);
  16.309 +by(  Asm_full_simp_tac 1);
  16.310 +by(  fast_tac (HOL_cs addEs [hext_trans]) 1);
  16.311 +by( (rtac (rewrite_rule[wf_java_prog_def]Call_type_sound) THEN_ALL_NEW Asm_simp_tac) 1);
  16.312 +qed "eval_evals_exec_type_sound";
  16.313 +
  16.314 +Goal "\\<And>E s s'. \
  16.315 +\ \\<lbrakk> G=prg E; wf_java_prog G; G\\<turnstile>(x,s) -e\\<succ>v \\<rightarrow> (x',s'); s\\<Colon>\\<preceq>E; E\\<turnstile>e\\<Colon>T \\<rbrakk> \
  16.316 +\ \\<Longrightarrow> s'\\<Colon>\\<preceq>E \\<and> (x'=None \\<longrightarrow> G,heap s'\\<turnstile>v\\<Colon>\\<preceq>T)";
  16.317 +by( split_all_tac 1);
  16.318 +bd (eval_evals_exec_type_sound RS conjunct1 RS mp RS spec RS mp) 1;
  16.319 +by Auto_tac;
  16.320 +qed "eval_type_sound";
  16.321 +
  16.322 +Goal "\\<And>E s s'. \
  16.323 +\ \\<lbrakk> G=prg E; wf_java_prog G; G\\<turnstile>(x,s) -s0\\<rightarrow> (x',s'); s\\<Colon>\\<preceq>E; E\\<turnstile>s0\\<surd> \\<rbrakk> \
  16.324 +\ \\<Longrightarrow> s'\\<Colon>\\<preceq>E";
  16.325 +by( split_all_tac 1);
  16.326 +bd (eval_evals_exec_type_sound RS conjunct2 RS conjunct2 RS mp RS spec RS mp) 1;
  16.327 +by   Auto_tac;
  16.328 +qed "exec_type_sound";
  16.329 +
  16.330 +Goal "\\<lbrakk>G=prg E; wf_java_prog G; G\\<turnstile>(x,s) -e\\<succ>a'\\<rightarrow> Norm s'; a' \\<noteq> Null;\
  16.331 +\         s\\<Colon>\\<preceq>E; E\\<turnstile>e\\<Colon>RefT T; m_head G T sig \\<noteq> None\\<rbrakk> \\<Longrightarrow> \
  16.332 +\ cmethd (G,fst (the (heap s' (the_Addr a')))) sig \\<noteq> None";
  16.333 +by( dtac eval_type_sound 1);
  16.334 +by(     atac 1);
  16.335 +by(    atac 1);
  16.336 +by(   atac 1);
  16.337 +by(  atac 1);
  16.338 +by( not_None_tac 1);
  16.339 +by( split_all_tac 1);
  16.340 +by(rewtac wf_java_prog_def);
  16.341 +by( forward_tac [widen_methd] 1);
  16.342 +by(   atac 1);
  16.343 +by(  rtac (not_None_eq RS iffD1) 2);
  16.344 +by(  Fast_tac 2);
  16.345 +by( etac conjE 1);
  16.346 +by( dtac non_npD 1);
  16.347 +by Auto_tac;
  16.348 +qed "all_methods_understood";
  16.349 +
  16.350 +Delsimps [split_beta];
  16.351 +Addsimps[fun_upd_apply];(*###*)
  16.352 +
    17.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
    17.2 +++ b/src/HOL/MicroJava/J/JTypeSafe.thy	Thu Nov 11 12:23:45 1999 +0100
    17.3 @@ -0,0 +1,9 @@
    17.4 +(*  Title:      HOL/MicroJava/J/JTypeSafe.thy
    17.5 +    ID:         $Id$
    17.6 +    Author:     David von Oheimb
    17.7 +    Copyright   1999 Technische Universitaet Muenchen
    17.8 +
    17.9 +Type Safety of Java
   17.10 +*)
   17.11 +
   17.12 +JTypeSafe = Eval + Conform
    18.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
    18.2 +++ b/src/HOL/MicroJava/J/Prog.ML	Thu Nov 11 12:23:45 1999 +0100
    18.3 @@ -0,0 +1,15 @@
    18.4 +(*  Title:      HOL/MicroJava/J/Prog.ML
    18.5 +    ID:         $Id$
    18.6 +    Author:     David von Oheimb
    18.7 +    Copyright   1999 Technische Universitaet Muenchen
    18.8 +*)
    18.9 +
   18.10 +val finite_is_class = prove_goalw thy [is_class_def,class_def,o_def] "finite {C. is_class G C}" (K [
   18.11 +	rtac finite_map_of 1]);
   18.12 +
   18.13 +val is_classI = prove_goalw thy [is_class_def]
   18.14 +"\\<And>G. class G C = Some c \\<Longrightarrow> is_class G C" (K [Auto_tac]);
   18.15 +
   18.16 +val is_classD = prove_goalw thy [is_class_def]
   18.17 +"\\<And>G. is_class G C \\<Longrightarrow> \\<exists>sc fs ms. class G C = Some (sc,fs,ms)" (K [
   18.18 +	not_None_tac 1, pair_tac "y" 1, pair_tac "ya" 1, Auto_tac]);
    19.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
    19.2 +++ b/src/HOL/MicroJava/J/Prog.thy	Thu Nov 11 12:23:45 1999 +0100
    19.3 @@ -0,0 +1,30 @@
    19.4 +(*  Title:      HOL/MicroJava/J/Prog.thy
    19.5 +    ID:         $Id$
    19.6 +    Author:     David von Oheimb
    19.7 +    Copyright   1999 Technische Universitaet Muenchen
    19.8 +
    19.9 +Java program = list of class declarations
   19.10 +*)
   19.11 +
   19.12 +Prog = Decl +
   19.13 +
   19.14 +types 'c prog = "'c cdecl list"
   19.15 +
   19.16 +consts
   19.17 +
   19.18 +  class		:: "'c prog \\<Rightarrow> (cname \\<leadsto> 'c class)"
   19.19 +
   19.20 +  is_class	:: "'c prog \\<Rightarrow> cname \\<Rightarrow> bool"
   19.21 +  is_type	:: "'c prog \\<Rightarrow> ty    \\<Rightarrow> bool"
   19.22 +
   19.23 +defs
   19.24 +
   19.25 +  class_def	"class        \\<equiv> map_of"
   19.26 +
   19.27 +  is_class_def	"is_class G C \\<equiv> class G C \\<noteq> None"
   19.28 +
   19.29 +primrec
   19.30 +"is_type G (PrimT pt) = True"
   19.31 +"is_type G (RefT t) = (case t of NullT \\<Rightarrow> True | ClassT C \\<Rightarrow> is_class G C)"
   19.32 +
   19.33 +end
    20.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
    20.2 +++ b/src/HOL/MicroJava/J/State.ML	Thu Nov 11 12:23:45 1999 +0100
    20.3 @@ -0,0 +1,77 @@
    20.4 +(*  Title:      HOL/MicroJava/J/State.ML
    20.5 +    ID:         $Id$
    20.6 +    Author:     David von Oheimb
    20.7 +    Copyright   1999 Technische Universitaet Muenchen
    20.8 +*)
    20.9 +
   20.10 +val the_Addr_Addr = prove_goalw thy [the_Addr_def] 
   20.11 +	"the_Addr (Addr a) = a" (K [Auto_tac]);
   20.12 +
   20.13 +Addsimps [the_Addr_Addr];
   20.14 +
   20.15 +val obj_ty_def2 = prove_goalw thy [obj_ty_def] "obj_ty (C,fs) = Class C" 
   20.16 +	(K [Simp_tac 1]);
   20.17 +
   20.18 +Addsimps [obj_ty_def2];
   20.19 +
   20.20 +val new_AddrD = prove_goalw thy [new_Addr_def] 
   20.21 +"\\<And>X. (a,x) = new_Addr h \\<Longrightarrow> h a = None \\<and>  x = None |  x = Some OutOfMemory" (K[
   20.22 +	asm_full_simp_tac (simpset() addsimps [Pair_fst_snd_eq,select_split]) 1,
   20.23 +	rtac selectI 1,
   20.24 +	rtac disjI2 1,
   20.25 +	res_inst_tac [("r","snd (a,Some OutOfMemory)")] trans 1,
   20.26 +	 Auto_tac ]);
   20.27 +
   20.28 +val raise_if_True = prove_goalw thy [raise_if_def] 
   20.29 +	"raise_if True x y \\<noteq> None"
   20.30 +(K [split_tac [expand_if] 1,Auto_tac]);
   20.31 +
   20.32 +val raise_if_False = prove_goalw thy [raise_if_def] 
   20.33 +	"raise_if False x y = y"
   20.34 +(K [Auto_tac]);
   20.35 +
   20.36 +val raise_if_Some = prove_goalw thy [raise_if_def] 
   20.37 +	"raise_if c x (Some y) \\<noteq> None" (K [Auto_tac]);
   20.38 +
   20.39 +val raise_if_Some2 = prove_goalw thy [raise_if_def] 
   20.40 +"raise_if c z (if x = None then Some y else x) \\<noteq> None" (K[
   20.41 +	induct_tac "x" 1,
   20.42 +	Auto_tac]);
   20.43 +val if_None_eq = prove_goal thy 
   20.44 +"(if x = None then None else x) = x" (K[
   20.45 +	induct_tac "x" 1,
   20.46 +	Auto_tac]);
   20.47 +
   20.48 +Addsimps [raise_if_True,raise_if_False,raise_if_Some,raise_if_Some2,if_None_eq];
   20.49 +
   20.50 +val raise_if_SomeD = prove_goalw thy [raise_if_def] 
   20.51 +	"raise_if c x y = Some z \\<longrightarrow> c \\<and>  Some z = Some x |  y = Some z" 
   20.52 +(K [split_tac [expand_if] 1,Auto_tac]) RS mp;
   20.53 +
   20.54 +val raise_if_NoneD = prove_goalw thy [raise_if_def] 
   20.55 +	"raise_if c x y = None \\<longrightarrow> \\<not> c \\<and>  y = None"
   20.56 +(K [split_tac [expand_if] 1,Auto_tac]) RS mp;
   20.57 +
   20.58 +
   20.59 +val np_NoneD = (prove_goalw thy [np_def, raise_if_def] 
   20.60 +	"np a' x' = None \\<longrightarrow> x' = None \\<and>  a' \\<noteq> Null" (fn _ => [
   20.61 +	split_tac [expand_if] 1,
   20.62 +	Auto_tac ])) RS mp;
   20.63 +val np_None = (prove_goalw thy [np_def, raise_if_def] 
   20.64 +	"a' \\<noteq> Null \\<longrightarrow> np a' x' = x'" (fn _ => [
   20.65 +	split_tac [expand_if] 1,
   20.66 +	Auto_tac ])) RS mp;
   20.67 +val np_Some = prove_goalw thy [np_def, raise_if_def] "np a' (Some xc) = Some xc"
   20.68 +	(fn _ => [Auto_tac ]);
   20.69 +val np_Null = prove_goalw thy [np_def, raise_if_def] 
   20.70 +	"np Null None = Some NullPointer" (fn _ => [
   20.71 +	Auto_tac ]);
   20.72 +val np_Addr = prove_goalw thy [np_def, raise_if_def] "np (Addr a) None = None" 
   20.73 +	(fn _ => [Auto_tac ]);
   20.74 +Addsimps[np_None, np_Some,np_Null,np_Addr];
   20.75 +
   20.76 +
   20.77 +
   20.78 +
   20.79 +
   20.80 +
    21.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
    21.2 +++ b/src/HOL/MicroJava/J/State.thy	Thu Nov 11 12:23:45 1999 +0100
    21.3 @@ -0,0 +1,91 @@
    21.4 +(*  Title:      HOL/MicroJava/J/State.thy
    21.5 +    ID:         $Id$
    21.6 +    Author:     David von Oheimb
    21.7 +    Copyright   1999 Technische Universitaet Muenchen
    21.8 +
    21.9 +State for evaluation of Java expressions and statements
   21.10 +*)
   21.11 +
   21.12 +State = WellType +
   21.13 +
   21.14 +constdefs
   21.15 +
   21.16 +  the_Bool	:: "val \\<Rightarrow> bool"
   21.17 + "the_Bool v  \\<equiv> \\<epsilon>b. v = Bool b"
   21.18 +
   21.19 +  the_Int	:: "val \\<Rightarrow> int"
   21.20 + "the_Int  v  \\<equiv> \\<epsilon>i. v = Intg i"
   21.21 +
   21.22 +  the_Addr	:: "val \\<Rightarrow> loc"
   21.23 + "the_Addr  v  \\<equiv> \\<epsilon>a. v = Addr a"
   21.24 +
   21.25 +consts
   21.26 +
   21.27 +  defpval	:: "prim_ty \\<Rightarrow> val"	(* default value for primitive types *)
   21.28 +  default_val	:: "ty \\<Rightarrow> val"		(* default value for all types *)
   21.29 +
   21.30 +primrec
   21.31 +	"defpval Void    = Unit"
   21.32 +	"defpval Boolean = Bool False"
   21.33 +	"defpval Integer = Intg (#0)"
   21.34 +
   21.35 +primrec
   21.36 +	"default_val (PrimT pt) = defpval pt"
   21.37 +	"default_val (RefT  r ) = Null"
   21.38 +
   21.39 +types	fields_
   21.40 +	= "(vname \\<times> cname \\<leadsto> val)" (* field name, defining class, value *)
   21.41 +
   21.42 +types obj = "cname \\<times> fields_"	(* class instance with class name and fields *)
   21.43 +
   21.44 +constdefs
   21.45 +
   21.46 +  obj_ty	:: "obj \\<Rightarrow> ty"
   21.47 + "obj_ty obj  \\<equiv> Class (fst obj)"
   21.48 +
   21.49 +  init_vars	:: "('a \\<times> ty) list \\<Rightarrow> ('a \\<leadsto> val)"
   21.50 + "init_vars	\\<equiv> map_of o map (\\<lambda>(n,T). (n,default_val T))"
   21.51 +  
   21.52 +datatype xcpt		(* exceptions *)
   21.53 +	= NullPointer
   21.54 +	| ClassCast
   21.55 +	| OutOfMemory
   21.56 +
   21.57 +types	aheap  = "loc \\<leadsto> obj" (* "heap" used in a translation below *)
   21.58 +        locals = "vname \\<leadsto> val"	
   21.59 +
   21.60 +        state		(* simple state, i.e. variable contents *)
   21.61 +	= "aheap \\<times> locals"
   21.62 +	(* heap, local parameter including This *)
   21.63 +
   21.64 +	xstate		(* state including exception information *)
   21.65 +	 = "xcpt option \\<times> state"
   21.66 +
   21.67 +syntax
   21.68 +  heap		:: "state \\<Rightarrow> aheap"
   21.69 +  locals	:: "state \\<Rightarrow> locals"
   21.70 +  Norm		:: "state \\<Rightarrow> xstate"
   21.71 +
   21.72 +translations
   21.73 +  "heap"	=> "fst"
   21.74 +  "locals"	=> "snd"
   21.75 +  "Norm s"      == "(None,s)"  
   21.76 +
   21.77 +constdefs
   21.78 +
   21.79 +  new_Addr	:: "aheap \\<Rightarrow> loc \\<times> xcpt option"
   21.80 + "new_Addr h \\<equiv> \\<epsilon>(a,x). (h a = None \\<and>  x = None) |  x = Some OutOfMemory"
   21.81 +
   21.82 +  raise_if	:: "bool \\<Rightarrow> xcpt \\<Rightarrow> xcpt option \\<Rightarrow> xcpt option"
   21.83 + "raise_if c x xo \\<equiv> if c \\<and>  (xo = None) then Some x else xo"
   21.84 +
   21.85 +  np		:: "val \\<Rightarrow> xcpt option \\<Rightarrow> xcpt option"
   21.86 + "np v \\<equiv> raise_if (v = Null) NullPointer"
   21.87 +
   21.88 +  c_hupd	:: "aheap \\<Rightarrow> xstate \\<Rightarrow> xstate"
   21.89 + "c_hupd h'\\<equiv> \\<lambda>(xo,(h,l)). if xo = None then (None,(h',l)) else (xo,(h,l))"
   21.90 +
   21.91 +  cast_ok	:: "'c prog \\<Rightarrow> ty \\<Rightarrow> aheap \\<Rightarrow> val \\<Rightarrow> bool"
   21.92 + "cast_ok G T h v \\<equiv> ((\\<exists>pt. T = PrimT pt) | (v=Null) | G\\<turnstile>obj_ty (the (h (the_Addr v)))\\<preceq>T)"
   21.93 +
   21.94 +end
    22.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
    22.2 +++ b/src/HOL/MicroJava/J/Term.thy	Thu Nov 11 12:23:45 1999 +0100
    22.3 @@ -0,0 +1,41 @@
    22.4 +(*  Title:      HOL/MicroJava/J/Term.thy
    22.5 +    ID:         $Id$
    22.6 +    Author:     David von Oheimb
    22.7 +    Copyright   1999 Technische Universitaet Muenchen
    22.8 +
    22.9 +Java expressions and statements
   22.10 +*)
   22.11 +
   22.12 +Term = Type + 
   22.13 +
   22.14 +types   loc		(* locations, i.e. abstract references on objects *)
   22.15 +arities loc :: term
   22.16 +
   22.17 +datatype val_		(* name non 'val' because of clash with ML token *)
   22.18 +	= Unit		(* dummy result value of void methods *)
   22.19 +	| Null		(* null reference *)
   22.20 +	| Bool bool	(* Boolean value *)
   22.21 +	| Intg int	(* integer value *) (* Name Intg instead of Int because
   22.22 +					       of clash with HOL/Set.thy *)
   22.23 +	| Addr loc	(* addresses, i.e. locations of objects *)
   22.24 +types	val = val_
   22.25 +translations "val" <= (type) "val_"
   22.26 +
   22.27 +datatype expr
   22.28 +	= NewC	cname		   (* class instance creation *)
   22.29 +	| Cast	ty expr		   (* type cast *)
   22.30 +	| Lit	val		   (* literal value, also references *)
   22.31 +	| LAcc vname		   (* local (incl. parameter) access *)
   22.32 +	| LAss vname expr          (* local assign *) ("_\\<Colon>=_"  [      90,90]90)
   22.33 +	| FAcc cname expr vname    (* field access *) ("{_}_.._"[10,90,99   ]90)
   22.34 +	| FAss cname expr vname 
   22.35 +	                  expr     (* field ass. *)("{_}_.._\\<in>=_"[10,90,99,90]90)
   22.36 +	| Call expr mname (ty list) (expr list)(* method call*)
   22.37 +                                    ("_.._'({_}_')" [90,99,10,10] 90)
   22.38 +and stmt
   22.39 +	= Skip			   (* empty      statement *)
   22.40 +	| Expr expr		   (* expression statement *)
   22.41 +	| Comp stmt stmt	   ("_;; _"			[      61,60]60)
   22.42 +	| Cond expr stmt stmt      ("If'(_') _ Else _"		[   80,79,79]70)
   22.43 +	| Loop expr stmt	   ("While'(_') _"		[      80,79]70)
   22.44 +end
    23.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
    23.2 +++ b/src/HOL/MicroJava/J/Type.ML	Thu Nov 11 12:23:45 1999 +0100
    23.3 @@ -0,0 +1,10 @@
    23.4 +(*  Title:      HOL/MicroJava/J/Type.ML
    23.5 +    ID:         $Id$
    23.6 +    Author:     David von Oheimb
    23.7 +    Copyright   1999 Technische Universitaet Muenchen
    23.8 +*)
    23.9 +
   23.10 +Goal "(\\<forall>pt. T \\<noteq> PrimT pt) = (\\<exists>t. T = RefT t)";
   23.11 +by(exhaust_tac "T" 1);
   23.12 +by Auto_tac;
   23.13 +qed "non_PrimT";
    24.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
    24.2 +++ b/src/HOL/MicroJava/J/Type.thy	Thu Nov 11 12:23:45 1999 +0100
    24.3 @@ -0,0 +1,39 @@
    24.4 +(*  Title:      HOL/MicroJava/J/Type.thy
    24.5 +    ID:         $Id$
    24.6 +    Author:     David von Oheimb
    24.7 +    Copyright   1999 Technische Universitaet Muenchen
    24.8 +
    24.9 +Java types
   24.10 +*)
   24.11 +
   24.12 +Type = JBasis +
   24.13 +
   24.14 +types	cname		(* class name *)
   24.15 +        vnam		(* variable or field name *)
   24.16 +	mname		(* method name *)
   24.17 +arities cname, vnam, mname :: term
   24.18 +
   24.19 +datatype vname		(* names for This pointer and local/field variables *)
   24.20 +	= This
   24.21 +	| VName   vnam
   24.22 +
   24.23 +datatype prim_ty       	(* primitive type, cf. 4.2 *)
   24.24 +	= Void    	(* 'result type' of void methods *)
   24.25 +	| Boolean
   24.26 +	| Integer
   24.27 +
   24.28 +datatype ref_ty		(* reference type, cf. 4.3 *)
   24.29 +	= NullT		(* null type, cf. 4.1 *)
   24.30 +	| ClassT cname	(* class type *)
   24.31 +and ty    		(* any type, cf. 4.1 *)
   24.32 +	= PrimT prim_ty	(* primitive type *)
   24.33 +	| RefT  ref_ty	(* reference type *)
   24.34 +
   24.35 +syntax
   24.36 +         NT     :: "          ty"
   24.37 +	 Class	:: "cname  \\<Rightarrow> ty"
   24.38 +translations
   24.39 +	"NT"      == "RefT   NullT"
   24.40 +	"Class C" == "RefT (ClassT C)"
   24.41 +
   24.42 +end
    25.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
    25.2 +++ b/src/HOL/MicroJava/J/TypeRel.ML	Thu Nov 11 12:23:45 1999 +0100
    25.3 @@ -0,0 +1,143 @@
    25.4 +(*  Title:      HOL/MicroJava/J/TypeRel.ML
    25.5 +    ID:         $Id$
    25.6 +    Author:     David von Oheimb
    25.7 +    Copyright   1999 Technische Universitaet Muenchen
    25.8 +*)
    25.9 +
   25.10 +val subcls1D = prove_goalw thy [subcls1_def] "\\<And>G. G\\<turnstile>C\\<prec>C1D \\<Longrightarrow> \
   25.11 +\ \\<exists>fs ms. class G C = Some (Some D,fs,ms)" (K [Auto_tac]);
   25.12 +
   25.13 +val subcls1I = prove_goalw  thy [subcls1_def] 
   25.14 +"\\<And>G. \\<lbrakk> class G C = Some (Some D,rest) \\<rbrakk> \\<Longrightarrow> G\\<turnstile>C\\<prec>C1D" (K [Auto_tac]);
   25.15 +
   25.16 +val subcls1_def2 = prove_goalw thy [subcls1_def,is_class_def]  "subcls1 G = \
   25.17 +\ (SIGMA C:{C. is_class G C} . {D. fst (the (class G C)) = Some D})"
   25.18 + (K [Auto_tac]);
   25.19 +
   25.20 +context Option.thy;
   25.21 +Goal "{y. x = Some y} \\<subseteq> {the x}";
   25.22 +by Auto_tac;
   25.23 +val some_subset_the = result();
   25.24 +context thy;
   25.25 +
   25.26 +Goal "finite (subcls1 G)";
   25.27 +by(stac subcls1_def2 1);
   25.28 +by( rtac finite_SigmaI 1);
   25.29 +by(  rtac finite_is_class 1);
   25.30 +by( rtac finite_subset 1);
   25.31 +by(  rtac some_subset_the 1);
   25.32 +by( Simp_tac 1);
   25.33 +qed "finite_subcls1";
   25.34 +
   25.35 +fun prove_typerel_lemma drules indrule s = prove_goal thy s (fn prems => [
   25.36 +	rtac (hd prems RS indrule) 1,
   25.37 +	auto_tac (claset() addDs drules, simpset())]);
   25.38 +
   25.39 +fun prove_typerel s lemmata = prove_goal thy s (fn prems => [
   25.40 +	cut_facts_tac prems 1,
   25.41 +	auto_tac (claset() addDs lemmata, simpset())]);
   25.42 +
   25.43 +
   25.44 +(*#### patch for Isabelle98-1*)
   25.45 +val major::prems = goal Trancl.thy
   25.46 + "\\<lbrakk> (x,y) \\<in> r^+; \
   25.47 +\    \\<And>x y. (x,y) \\<in> r \\<Longrightarrow> P x y; \
   25.48 +\    \\<And>x y z. \\<lbrakk> (x,y) \\<in> r^+; P x y; (y,z) \\<in> r^+; P y z \\<rbrakk> \\<Longrightarrow> P x z \
   25.49 +\ \\<rbrakk> \\<Longrightarrow> P x y";
   25.50 +by(blast_tac (claset() addIs ([r_into_trancl,major RS trancl_induct]@prems))1);
   25.51 +qed "trancl_trans_induct";
   25.52 +
   25.53 +Goalw [is_class_def] "G\\<turnstile>C\\<prec>C D \\<Longrightarrow> is_class G C";
   25.54 +by(etac trancl_trans_induct 1);
   25.55 +by (auto_tac (HOL_cs addSDs [subcls1D],simpset()));
   25.56 +qed "subcls_is_class";
   25.57 +
   25.58 +
   25.59 +(* A particular thm about wf;
   25.60 +   looks like it is an odd instance of something more general
   25.61 +*)
   25.62 +Goalw [wf_def] "wf{((A,x),(B,y)) . A=B \\<and> wf(R(A)) \\<and> (x,y)\\<in>R(A)}";
   25.63 +by(full_simp_tac (simpset() delcongs [imp_cong] addsimps [split_paired_All]) 1);
   25.64 +by(strip_tac 1);
   25.65 +by(rename_tac "A x" 1);
   25.66 +by(case_tac "wf(R A)" 1);
   25.67 +by (eres_inst_tac [("a","x")] wf_induct 1);
   25.68 +by (EVERY1[etac allE, etac allE, etac mp, rtac allI, rtac allI]);
   25.69 +by (Fast_tac 1);
   25.70 +by(rewrite_goals_tac [wf_def]);
   25.71 +by(Blast_tac 1);
   25.72 +val wf_rel_lemma = result();
   25.73 +
   25.74 +
   25.75 +(* Proving the termination conditions *)
   25.76 +
   25.77 +goalw thy [subcls1_rel_def] "wf subcls1_rel";
   25.78 +by(rtac (wf_rel_lemma RS wf_subset) 1);
   25.79 +by(Force_tac 1);
   25.80 +val wf_subcls1_rel = result();
   25.81 +
   25.82 +val cmethd_TC = prove_goalw_cterm [subcls1_rel_def]
   25.83 + (cterm_of (sign_of thy) (HOLogic.mk_Trueprop (hd (tl (cmethd.tcs)))))
   25.84 + (K [auto_tac (claset() addIs [subcls1I], simpset())]);
   25.85 +
   25.86 +val fields_TC = prove_goalw_cterm [subcls1_rel_def]
   25.87 + (cterm_of (sign_of thy) (HOLogic.mk_Trueprop (hd (tl (fields.tcs)))))
   25.88 + (K [auto_tac (claset() addIs [subcls1I], simpset())]);
   25.89 +
   25.90 +
   25.91 +AddSIs   [widen.refl];
   25.92 +Addsimps [widen.refl];
   25.93 +
   25.94 +val prove_widen_lemma = prove_typerel_lemma [] widen.elim;
   25.95 +
   25.96 +val widen_PrimT_RefT = prove_typerel "G\\<turnstile>PrimT x\\<preceq>RefT tname \\<Longrightarrow> R"
   25.97 + [ prove_widen_lemma "G\\<turnstile>S\\<preceq>T \\<Longrightarrow> S = PrimT x \\<longrightarrow> T = RefT tname \\<longrightarrow> R"];
   25.98 +
   25.99 +
  25.100 +val widen_RefT = prove_typerel "G\\<turnstile>RefT R\\<preceq>T \\<Longrightarrow> \\<exists>t. T=RefT t" 
  25.101 +	[prove_widen_lemma "G\\<turnstile>S\\<preceq>T \\<Longrightarrow> S=RefT R \\<longrightarrow> (\\<exists>t. T=RefT t)"];
  25.102 +
  25.103 +val widen_RefT2 = prove_typerel "G\\<turnstile>S\\<preceq>RefT R \\<Longrightarrow> \\<exists>t. S=RefT t" 
  25.104 +	[prove_widen_lemma "G\\<turnstile>S\\<preceq>T \\<Longrightarrow> T=RefT R \\<longrightarrow> (\\<exists>t. S=RefT t)"];
  25.105 +
  25.106 +val widen_Class = prove_typerel "G\\<turnstile>Class C\\<preceq>T \\<Longrightarrow> \\<exists>D. T=Class D"
  25.107 + [ prove_widen_lemma "G\\<turnstile>S\\<preceq>T \\<Longrightarrow> S = Class C \\<longrightarrow> (\\<exists>D. T=Class D)"];
  25.108 +
  25.109 +val widen_Class_RefT = prove_typerel 
  25.110 +	"G\\<turnstile>Class C\\<preceq>RefT t \\<Longrightarrow> (\\<exists>tname. t=ClassT tname)" 
  25.111 + [prove_widen_lemma 
  25.112 + "G\\<turnstile>S\\<preceq>T \\<Longrightarrow> S=Class C \\<longrightarrow> T=RefT t \\<longrightarrow> (\\<exists>tname. t=ClassT tname)"];
  25.113 +
  25.114 +val widen_Class_NullT = prove_typerel "G\\<turnstile>Class C\\<preceq>RefT NullT \\<Longrightarrow> R" 
  25.115 + [prove_widen_lemma "G\\<turnstile>S\\<preceq>T \\<Longrightarrow> S=Class C \\<longrightarrow> T=RefT NullT \\<longrightarrow> R"];
  25.116 +
  25.117 +val widen_Class_Class = prove_typerel "G\\<turnstile>Class C\\<preceq>Class cm \\<Longrightarrow> C=cm |  G\\<turnstile>C\\<prec>C cm"
  25.118 +[ prove_widen_lemma "G\\<turnstile>S\\<preceq>T \\<Longrightarrow> S = Class C \\<longrightarrow> T = Class cm \\<longrightarrow> C=cm |  G\\<turnstile>C\\<prec>C cm"];
  25.119 +
  25.120 +Goal "\\<lbrakk>G\\<turnstile>S\\<preceq>U; \\<forall>C. is_class G C \\<longrightarrow> G\\<turnstile>Class C\\<preceq>Class Object;\
  25.121 +\\\<forall>C. G\\<turnstile>Object\\<prec>C C \\<longrightarrow> False \\<rbrakk> \\<Longrightarrow> \\<forall>T. G\\<turnstile>U\\<preceq>T \\<longrightarrow> G\\<turnstile>S\\<preceq>T";
  25.122 +by( etac widen.induct 1);
  25.123 +by   Safe_tac;
  25.124 +by(  ALLGOALS (forward_tac [widen_Class, widen_RefT]));
  25.125 +by  Safe_tac;
  25.126 +by(  rtac widen.null 2);
  25.127 +by( forward_tac [widen_Class_Class] 1);
  25.128 +by Safe_tac;
  25.129 +by(  ALLGOALS(EVERY'[etac thin_rl,etac thin_rl,
  25.130 +	fast_tac (claset() addIs [widen.subcls,trancl_trans])]));
  25.131 +qed_spec_mp "widen_trans_lemma";
  25.132 +
  25.133 +
  25.134 +val prove_cast_lemma = prove_typerel_lemma [] cast.elim;
  25.135 +
  25.136 +val cast_RefT = prove_typerel "G\\<turnstile>RefT R\\<Rightarrow>? T \\<Longrightarrow> \\<exists>t. T=RefT t" 
  25.137 +	[prove_typerel_lemma [widen_RefT] cast.elim 
  25.138 +	"G\\<turnstile>S\\<Rightarrow>? T \\<Longrightarrow> S=RefT R \\<longrightarrow> (\\<exists>t. T=RefT t)"];
  25.139 +
  25.140 +val cast_RefT2 = prove_typerel "G\\<turnstile>S\\<Rightarrow>? RefT R \\<Longrightarrow> \\<exists>t. S=RefT t" 
  25.141 +	[prove_typerel_lemma [widen_RefT2] cast.elim 
  25.142 +	"G\\<turnstile>S\\<Rightarrow>? T \\<Longrightarrow> T=RefT R \\<longrightarrow> (\\<exists>t. S=RefT t)"];
  25.143 +
  25.144 +val cast_PrimT2 = prove_typerel "G\\<turnstile>S\\<Rightarrow>? PrimT pt \\<Longrightarrow> G\\<turnstile>S\\<preceq>PrimT pt" 
  25.145 + [prove_cast_lemma "G\\<turnstile>S\\<Rightarrow>? T \\<Longrightarrow> T=PrimT pt \\<longrightarrow> G\\<turnstile>S\\<preceq>PrimT pt"];
  25.146 +
    26.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
    26.2 +++ b/src/HOL/MicroJava/J/TypeRel.thy	Thu Nov 11 12:23:45 1999 +0100
    26.3 @@ -0,0 +1,76 @@
    26.4 +(*  Title:      HOL/MicroJava/J/TypeRel.thy
    26.5 +    ID:         $Id$
    26.6 +    Author:     David von Oheimb
    26.7 +    Copyright   1999 Technische Universitaet Muenchen
    26.8 +
    26.9 +The relations between Java types
   26.10 +*)
   26.11 +
   26.12 +TypeRel = Prog +
   26.13 +
   26.14 +consts
   26.15 +  subcls1	:: "'c prog \\<Rightarrow> (cname \\<times> cname) set" (*        subclass *)
   26.16 +  widen,				 	    (*        widening *)
   26.17 +  cast		:: "'c prog \\<Rightarrow> (ty \\<times> ty) set"	    (*        casting *)
   26.18 +
   26.19 +syntax
   26.20 +  subcls1	:: "'c prog \\<Rightarrow> [cname, cname] \\<Rightarrow> bool" ("_\\<turnstile>_\\<prec>C1_"	 [71,71,71] 70)
   26.21 +  subcls	:: "'c prog \\<Rightarrow> [cname, cname] \\<Rightarrow> bool" ("_\\<turnstile>_\\<prec>C _"	 [71,71,71] 70)
   26.22 +  widen		:: "'c prog \\<Rightarrow> [ty, ty] \\<Rightarrow> bool"       ("_\\<turnstile>_\\<preceq>_"  [71,71,71] 70)
   26.23 +  cast		:: "'c prog \\<Rightarrow> [ty, ty] \\<Rightarrow> bool"       ("_\\<turnstile>_\\<Rightarrow>? _"[71,71,71] 70)
   26.24 +
   26.25 +translations
   26.26 +  	"G\\<turnstile>C \\<prec>C1 D" == "(C,D) \\<in> subcls1 G"
   26.27 +	"G\\<turnstile>C \\<prec>C  D" == "(C,D) \\<in> (subcls1 G)^+"
   26.28 +	"G\\<turnstile>S \\<preceq>   T" == "(S,T) \\<in> widen   G"
   26.29 +	"G\\<turnstile>S \\<Rightarrow>?  T" == "(S,T) \\<in> cast    G"
   26.30 +
   26.31 +defs
   26.32 +
   26.33 +  (* direct subclass, cf. 8.1.3 *)
   26.34 +  subcls1_def	"subcls1 G \\<equiv> {(C,D). \\<exists>c. class G C = Some c \\<and> fst c = Some D}"
   26.35 +  
   26.36 +consts
   26.37 +
   26.38 +  cmethd	:: "'c prog \\<times> cname \\<Rightarrow> ( sig   \\<leadsto> cname \\<times> ty \\<times> 'c)"
   26.39 +  cfield	:: "'c prog \\<times> cname \\<Rightarrow> ( vname \\<leadsto> cname \\<times> ty)"
   26.40 +  fields	:: "'c prog \\<times> cname \\<Rightarrow> ((vname \\<times> cname) \\<times>  ty) list"
   26.41 +
   26.42 +constdefs       (* auxiliary relations for recursive definitions below *)
   26.43 +
   26.44 +  subcls1_rel	:: "(('c prog \\<times> cname) \\<times> ('c prog \\<times> cname)) set"
   26.45 + "subcls1_rel \\<equiv> {((G,C),(G',C')). G = G' \\<and>  wf ((subcls1 G)^-1) \\<and>  G\\<turnstile>C'\\<prec>C1C}"
   26.46 +
   26.47 +(* methods of a class, with inheritance, overriding and hiding, cf. 8.4.6 *)
   26.48 +recdef cmethd "subcls1_rel"
   26.49 + "cmethd (G,C) = (if wf((subcls1 G)^-1) then (case class G C of None \\<Rightarrow> empty
   26.50 +                   | Some (sc,fs,ms) \\<Rightarrow> (case sc of None \\<Rightarrow> empty | Some D \\<Rightarrow> 
   26.51 +                                           if is_class G D then cmethd (G,D) 
   26.52 +                                                           else arbitrary) \\<oplus>
   26.53 +                                           map_of (map (\\<lambda>(s,  m ). 
   26.54 +                                                        (s,(C,m))) ms))
   26.55 +                  else arbitrary)"
   26.56 +
   26.57 +(* list of fields of a class, including inherited and hidden ones *)
   26.58 +recdef fields  "subcls1_rel"
   26.59 + "fields (G,C) = (if wf((subcls1 G)^-1) then (case class G C of None \\<Rightarrow> arbitrary
   26.60 +                   | Some (sc,fs,ms) \\<Rightarrow> map (\\<lambda>(fn,ft). ((fn,C),ft)) fs@
   26.61 +                                           (case sc of None \\<Rightarrow> [] | Some D \\<Rightarrow> 
   26.62 +                                           if is_class G D then fields (G,D) 
   26.63 +                                                           else arbitrary))
   26.64 +                  else arbitrary)"
   26.65 +defs
   26.66 +
   26.67 +  cfield_def "cfield \\<equiv> map_of o (map (\\<lambda>((fn,fd),ft). (fn,(fd,ft)))) o fields"
   26.68 +
   26.69 +inductive "widen G" intrs (*widening, viz. method invocation conversion, cf. 5.3
   26.70 +			     i.e. sort of syntactic subtyping *)
   26.71 +  refl	              "G\\<turnstile>      T \\<preceq> T" 	 (* identity conv., cf. 5.1.1 *)
   26.72 +  subcls "G\\<turnstile>C\\<prec>C D \\<Longrightarrow> G\\<turnstile>Class C \\<preceq> Class D"
   26.73 +  null	              "G\\<turnstile>     NT \\<preceq> RefT R"
   26.74 +
   26.75 +inductive "cast G" intrs (* casting / narr.ref. conversion, cf. 5.5 / 5.1.5 *)
   26.76 +  widen	 "G\\<turnstile>S\\<preceq>T  \\<Longrightarrow> G\\<turnstile>      S \\<Rightarrow>? T"
   26.77 +  subcls "G\\<turnstile>C\\<prec>C D \\<Longrightarrow> G\\<turnstile>Class D \\<Rightarrow>? Class C"
   26.78 +
   26.79 +end
    27.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
    27.2 +++ b/src/HOL/MicroJava/J/WellForm.ML	Thu Nov 11 12:23:45 1999 +0100
    27.3 @@ -0,0 +1,388 @@
    27.4 +(*  Title:      HOL/MicroJava/J/WellForm.ML
    27.5 +    ID:         $Id$
    27.6 +    Author:     David von Oheimb
    27.7 +    Copyright   1999 Technische Universitaet Muenchen
    27.8 +*)
    27.9 +
   27.10 +val class_wf = prove_goalw thy [wf_prog_def, Let_def, class_def]
   27.11 + "\\<And>X. \\<lbrakk>class G C = Some c; wf_prog wtm G\\<rbrakk> \\<Longrightarrow> wf_cdecl wtm G (C,c)" (K [
   27.12 +	Asm_full_simp_tac 1,
   27.13 +	fast_tac (set_cs addDs [get_in_set]) 1]);
   27.14 +
   27.15 +val class_Object = prove_goalw thy [wf_prog_def, Let_def, ObjectC_def,class_def]
   27.16 +	"\\<And>X. wf_prog wtm G \\<Longrightarrow> class G Object = Some (None, [], [])" (K [
   27.17 +	safe_tac set_cs,
   27.18 +	dtac in_set_get 1,
   27.19 +	 Auto_tac]);
   27.20 +Addsimps [class_Object];
   27.21 +
   27.22 +val is_class_Object = prove_goalw thy [is_class_def] 
   27.23 +	"\\<And>X. wf_prog wtm G \\<Longrightarrow> is_class G Object" (K [Asm_simp_tac 1]);
   27.24 +Addsimps [is_class_Object];
   27.25 +
   27.26 +Goal "\\<lbrakk>G\\<turnstile>C\\<prec>C1D; wf_prog wtm G\\<rbrakk> \\<Longrightarrow> D \\<noteq> C \\<and> \\<not>  G\\<turnstile>D\\<prec>C C";
   27.27 +by( forward_tac [r_into_trancl] 1);
   27.28 +by( dtac subcls1D 1);
   27.29 +by( strip_tac1 1);
   27.30 +by( dtac class_wf 1);
   27.31 +by(  atac 1);
   27.32 +by( rewtac wf_cdecl_def);
   27.33 +by( Clarsimp_tac 1);
   27.34 +qed "subcls1_wfD";
   27.35 +
   27.36 +val wf_cdecl_supD = prove_goalw thy [wf_cdecl_def] 
   27.37 +"\\<And>X. \\<lbrakk>wf_cdecl wtm G (C, sc, r); C \\<noteq> Object\\<rbrakk> \\<Longrightarrow> \\<exists>D. sc = Some D \\<and> is_class G D" (K [
   27.38 +	pair_tac "r" 1,
   27.39 +	Asm_full_simp_tac 1,
   27.40 +	strip_tac1 1,
   27.41 +	option_case_tac 1,
   27.42 +	Fast_tac 1]);
   27.43 +
   27.44 +local
   27.45 +val lemma = prove_goal thy "\\<And>X. \\<lbrakk>wf_prog wtm G; G\\<turnstile>C\\<prec>C D\\<rbrakk> \\<Longrightarrow> C=Object \\<longrightarrow> R" (K [
   27.46 +	etac trancl_trans_induct 1,
   27.47 +	 atac 2,
   27.48 +	rewtac subcls1_def,
   27.49 +	Auto_tac]);
   27.50 +in
   27.51 +val subcls_Object = prove_goal thy "\\<And>X. \\<lbrakk>wf_prog wtm G; G\\<turnstile>Object\\<prec>C C\\<rbrakk> \\<Longrightarrow> R" (K [
   27.52 +	etac (lemma RS mp) 1,
   27.53 +	Auto_tac]);
   27.54 +end;
   27.55 +
   27.56 +Goal "\\<lbrakk>wf_prog wt G; G\\<turnstile>C\\<prec>C D\\<rbrakk> \\<Longrightarrow> \\<not>  G\\<turnstile>D\\<prec>C C";
   27.57 +by(etac tranclE 1);
   27.58 +by(ALLGOALS(fast_tac (HOL_cs addSDs [subcls1_wfD] addIs [trancl_trans])));
   27.59 +qed "subcls_asym";
   27.60 +
   27.61 +val subcls_irrefl = prove_goal thy "\\<And>X. \\<lbrakk>wf_prog wtm G; G\\<turnstile>C\\<prec>C D\\<rbrakk> \\<Longrightarrow> C \\<noteq> D" (K [
   27.62 +	etac trancl_trans_induct 1,
   27.63 +	 fast_tac (HOL_cs addDs [subcls1_wfD]) 1,
   27.64 +	fast_tac (HOL_cs addDs [subcls_asym]) 1]);
   27.65 +
   27.66 +val acyclic_subcls1 = prove_goalw thy [acyclic_def] 
   27.67 +	"\\<And>X. wf_prog wt G \\<Longrightarrow> acyclic (subcls1 G)" (K [
   27.68 +	strip_tac1 1,
   27.69 +	fast_tac (HOL_cs addDs [subcls_irrefl]) 1]);
   27.70 +
   27.71 +val wf_subcls1 = prove_goal thy "\\<And>X. wf_prog wtm G \\<Longrightarrow> wf ((subcls1 G)^-1)" (K [
   27.72 +	rtac finite_acyclic_wf 1,
   27.73 +	 stac finite_converse 1,
   27.74 +	 rtac finite_subcls1 1,
   27.75 +	stac acyclic_converse 1,
   27.76 +	etac acyclic_subcls1 1]);
   27.77 +
   27.78 +
   27.79 +val major::prems = goal thy
   27.80 +  "\\<lbrakk>wf_prog wt G; \\<And>C. \\<forall>D. G\\<turnstile>C\\<prec>C D \\<longrightarrow> P D \\<Longrightarrow> P C\\<rbrakk> \\<Longrightarrow> P C";
   27.81 +by(cut_facts_tac [major RS wf_subcls1] 1);
   27.82 +by(dtac wf_trancl 1);
   27.83 +by(asm_full_simp_tac (HOL_ss addsimps [trancl_converse]) 1);
   27.84 +by(eres_inst_tac [("a","C")] wf_induct 1);
   27.85 +by(resolve_tac prems 1);
   27.86 +by(Auto_tac);
   27.87 +qed "subcls_induct";
   27.88 +
   27.89 +val prems = goal thy "\\<lbrakk>is_class G C; wf_prog wtm G; P Object; \
   27.90 +\\\<And>C D fs ms. \\<lbrakk>C \\<noteq> Object; is_class G C; class G C = Some (Some D,fs,ms) \\<and> \
   27.91 +\   wf_cdecl wtm G (C, Some D,fs,ms) \\<and> G\\<turnstile>C\\<prec>C1D \\<and> is_class G D \\<and> P D\\<rbrakk> \\<Longrightarrow> P C\
   27.92 +\ \\<rbrakk> \\<Longrightarrow> P C";
   27.93 +by( cut_facts_tac prems 1);
   27.94 +by( rtac impE 1);
   27.95 +by(   atac 2);
   27.96 +by(  atac 2);
   27.97 +by( etac thin_rl 1);
   27.98 +by( rtac subcls_induct 1);
   27.99 +by(  atac 1);
  27.100 +by( rtac impI 1);
  27.101 +by( case_tac "C = Object" 1);
  27.102 +by(  Fast_tac 1);
  27.103 +by( ex_ftac is_classD 1);
  27.104 +by( forward_tac [class_wf] 1);
  27.105 +by(  atac 1);
  27.106 +by( forward_tac [wf_cdecl_supD] 1);
  27.107 +by(  atac 1);
  27.108 +by( strip_tac1 1);
  27.109 +by( rtac (hd (tl (tl (tl prems)))) 1);
  27.110 +by(   atac 1);
  27.111 +by(  atac 1);
  27.112 +by( subgoal_tac "G\\<turnstile>C\\<prec>C1D" 1);
  27.113 +by(  fast_tac (HOL_cs addIs [r_into_trancl]) 1);
  27.114 +by( etac subcls1I 1);
  27.115 +qed "subcls1_induct";
  27.116 +
  27.117 +Goal "wf_prog wtm G \\<Longrightarrow> cmethd (G,C) = \
  27.118 +\ (case class G C of None \\<Rightarrow> empty | Some (sc,fs,ms) \\<Rightarrow> \
  27.119 +\ (case sc of None \\<Rightarrow> empty | Some D \\<Rightarrow> cmethd (G,D)) \\<oplus> \
  27.120 +\ map_of (map (\\<lambda>(s,m). (s,(C,m))) ms))";
  27.121 +by( stac (cmethd_TC RS (wf_subcls1_rel RS (hd cmethd.rules))) 1);
  27.122 +by( clarsimp_tac (claset(), simpset() addsimps [wf_subcls1,empty_def] 
  27.123 +		addsplits [option.split]) 1);
  27.124 +by( case_tac "C = Object" 1);
  27.125 +by(  Asm_full_simp_tac 1);
  27.126 +by( dtac class_wf 1);
  27.127 +by(  atac 1);
  27.128 +by( dtac wf_cdecl_supD 1);
  27.129 +by(  atac 1);
  27.130 +by( Asm_full_simp_tac 1);
  27.131 +val cmethd_rec = result();
  27.132 +
  27.133 +Goal "\\<lbrakk>class G C = Some (sc,fs,ms); wf_prog wtm G\\<rbrakk> \\<Longrightarrow> fields (G,C) = \
  27.134 +\ map (\\<lambda>(fn,ft). ((fn,C),ft)) fs @ \
  27.135 +\ (case sc of None \\<Rightarrow> [] | Some D \\<Rightarrow> fields (G,D))";
  27.136 +by( stac (fields_TC RS (wf_subcls1_rel RS (hd fields.rules))) 1);
  27.137 +by( asm_simp_tac (simpset() addsimps [wf_subcls1,empty_def]) 1);
  27.138 +by( option_case_tac2 "sc" 1);
  27.139 +by(  Asm_simp_tac 1);
  27.140 +by( case_tac "C = Object" 1);
  27.141 +by(  rotate_tac 2 1);
  27.142 +by(  Asm_full_simp_tac 1);
  27.143 +by( dtac class_wf 1);
  27.144 +by(  atac 1);
  27.145 +by( dtac wf_cdecl_supD 1);
  27.146 +by(  atac 1);
  27.147 +by( Asm_full_simp_tac 1);
  27.148 +val fields_rec = result();
  27.149 +
  27.150 +val cmethd_Object = prove_goal thy "\\<And>X. wf_prog wtm G \\<Longrightarrow> cmethd (G,Object) = empty"
  27.151 +	(K [stac cmethd_rec 1,Auto_tac]);
  27.152 +val fields_Object = prove_goal thy "\\<And>X. wf_prog wtm G \\<Longrightarrow> fields (G,Object) = []"(K [
  27.153 +	stac fields_rec 1,Auto_tac]);
  27.154 +Addsimps [cmethd_Object, fields_Object];
  27.155 +val cfield_Object = prove_goalw thy [cfield_def]
  27.156 + "\\<And>X. wf_prog wtm G \\<Longrightarrow> cfield (G,Object) = empty" (K [Asm_simp_tac 1]);
  27.157 +Addsimps [cfield_Object];
  27.158 +
  27.159 +val subcls_C_Object = prove_goal thy 
  27.160 +	"\\<And>X. \\<lbrakk>is_class G C; wf_prog wtm G \\<rbrakk> \\<Longrightarrow> C \\<noteq> Object \\<longrightarrow> G\\<turnstile>C\\<prec>C Object" (K [
  27.161 +	etac subcls1_induct 1,
  27.162 +	  atac 1,
  27.163 +	 Fast_tac 1,
  27.164 +	safe_tac (HOL_cs addSDs [wf_cdecl_supD] addss (simpset())),
  27.165 +	 fast_tac (HOL_cs addIs [r_into_trancl]) 1,
  27.166 +	rtac trancl_trans 1,
  27.167 +	 atac 2,
  27.168 +	rtac r_into_trancl 1,
  27.169 +	rtac subcls1I 1,
  27.170 +	ALLGOALS Asm_simp_tac]) RS mp;
  27.171 +
  27.172 +val is_type_rTI = prove_goalw thy [wf_mhead_def]
  27.173 +	"\\<And>sig. wf_mhead G sig rT \\<Longrightarrow> is_type G rT"
  27.174 +	(K [split_all_tac 1, Auto_tac]);
  27.175 +
  27.176 +val widen_Class_Object = prove_goal thy 
  27.177 +	"\\<lbrakk>wf_prog wtm G; is_class G C\\<rbrakk> \\<Longrightarrow> G\\<turnstile>Class C\\<preceq>Class Object" (fn prems => [
  27.178 +	cut_facts_tac prems 1,
  27.179 +	case_tac "C=Object" 1,
  27.180 +	 hyp_subst_tac 1,
  27.181 +	 Asm_simp_tac 1,
  27.182 +	rtac widen.subcls 1,
  27.183 +	fast_tac (HOL_cs addEs [subcls_C_Object]) 1]);
  27.184 +
  27.185 +val widen_trans = prove_goal thy "\\<lbrakk>wf_prog wtm G; G\\<turnstile>S\\<preceq>U; G\\<turnstile>U\\<preceq>T\\<rbrakk> \\<Longrightarrow> G\\<turnstile>S\\<preceq>T"
  27.186 +(fn prems=> [cut_facts_tac prems 1, 
  27.187 +	fast_tac (HOL_cs addEs [widen_trans_lemma, widen_Class_Object, 
  27.188 +				subcls_Object]) 1]);
  27.189 +
  27.190 +val fields_mono = prove_goal thy 
  27.191 +"\\<And>X. \\<lbrakk>G\\<turnstile>C'\\<prec>C C; wf_prog wtm G\\<rbrakk> \\<Longrightarrow> \
  27.192 +\ x \\<in> set (fields (G,C)) \\<longrightarrow> x \\<in> set (fields (G,C'))" (K [
  27.193 +	etac trancl_trans_induct 1,
  27.194 +	 safe_tac (HOL_cs addSDs [subcls1D]),
  27.195 +	stac fields_rec 1,
  27.196 +	  Auto_tac]) RS mp;
  27.197 +
  27.198 +Goal "\\<lbrakk>is_class G C; wf_prog wtm G\\<rbrakk> \\<Longrightarrow> \
  27.199 +\ \\<forall>((fn,fd),fT)\\<in>set (fields (G,C)). G\\<turnstile>Class C\\<preceq>Class fd";
  27.200 +by( etac subcls1_induct 1);
  27.201 +by(   atac 1);
  27.202 +by(  Asm_simp_tac 1);
  27.203 +by( safe_tac HOL_cs);
  27.204 +by( stac fields_rec 1);
  27.205 +by(   atac 1);
  27.206 +by(  atac 1);
  27.207 +by( Simp_tac 1);
  27.208 +by( rtac ballI 1);
  27.209 +by( split_all_tac 1);
  27.210 +by( Simp_tac 1);
  27.211 +by( etac UnE 1);
  27.212 +by(  dtac split_Pair_eq 1);
  27.213 +by(  SELECT_GOAL (Auto_tac) 1);
  27.214 +by( rtac widen_trans 1);
  27.215 +by(   atac 1);
  27.216 +by(  etac (r_into_trancl RS widen.subcls) 1);
  27.217 +by( etac BallE 1);
  27.218 +by(  contr_tac 1);
  27.219 +by( Asm_full_simp_tac 1);
  27.220 +val widen_fields_defpl' = result();
  27.221 +
  27.222 +Goal "\\<lbrakk>is_class G C; wf_prog wtm G; ((fn,fd),fT) \\<in> set (fields (G,C))\\<rbrakk> \\<Longrightarrow> \
  27.223 +\ G\\<turnstile>Class C\\<preceq>Class fd";
  27.224 +by( dtac widen_fields_defpl' 1);
  27.225 +by(  atac 1);
  27.226 +(*###################*)
  27.227 +by( dtac bspec 1);
  27.228 +auto();
  27.229 +val widen_fields_defpl = result();
  27.230 +
  27.231 +
  27.232 +Goal "\\<lbrakk>is_class G C; wf_prog wtm G\\<rbrakk> \\<Longrightarrow> unique (fields (G,C))";
  27.233 +by( etac subcls1_induct 1);
  27.234 +by(   atac 1);
  27.235 +by(  safe_tac (HOL_cs addSDs [wf_cdecl_supD]));
  27.236 +by(  Asm_simp_tac 1);
  27.237 +by( dtac subcls1_wfD 1);
  27.238 +by(  atac 1);
  27.239 +by( stac fields_rec 1);
  27.240 +by   Auto_tac;
  27.241 +by( rotate_tac ~1 1);
  27.242 +by( ex_ftac is_classD 1);
  27.243 +by( forward_tac [class_wf] 1);
  27.244 +by  Auto_tac;
  27.245 +by( asm_full_simp_tac (simpset() addsimps [wf_cdecl_def]) 1);
  27.246 +by( etac unique_append 1);
  27.247 +by(  rtac unique_map_Pair 1);
  27.248 +by(  Step_tac 1);
  27.249 +by (EVERY1[dtac widen_fields_defpl, atac, atac]);
  27.250 +by( Asm_full_simp_tac 1);
  27.251 +by( dtac split_Pair_eq 1);
  27.252 +by( fast_tac (HOL_cs addSDs [widen_Class_Class]) 1);
  27.253 +val unique_fields = result();
  27.254 +
  27.255 +Goal
  27.256 +"\\<lbrakk>wf_prog wtm G; G\\<turnstile>Class C'\\<preceq>Class C; map_of(fields (G,C )) f = Some ft\\<rbrakk> \\<Longrightarrow> \
  27.257 +\                          map_of (fields (G,C')) f = Some ft";
  27.258 +by( dtac widen_Class_Class 1);
  27.259 +by( etac disjE 1);
  27.260 +by(  Asm_simp_tac 1);
  27.261 +by( rtac table_mono 1);
  27.262 +by(   atac 3);
  27.263 +by(  rtac unique_fields 1);
  27.264 +by(   etac subcls_is_class 1);
  27.265 +by(  atac 1);
  27.266 +by( fast_tac (HOL_cs addEs [fields_mono]) 1);
  27.267 +val widen_fields_mono = result();
  27.268 +
  27.269 +
  27.270 +val cfs_fields_lemma = prove_goalw thy [cfield_def] 
  27.271 +"\\<And>X. cfield (G,C) fn = Some (fd, fT) \\<Longrightarrow> map_of(fields (G,C)) (fn, fd) = Some fT"
  27.272 +(K [rtac table_map_Some 1, Asm_full_simp_tac 1]);
  27.273 +
  27.274 +val widen_cfs_fields = prove_goal thy "\\<And>X. \\<lbrakk>cfield (G,C) fn = Some (fd, fT);\
  27.275 +\  G\\<turnstile>Class C'\\<preceq>Class C; wf_prog wtm G\\<rbrakk> \\<Longrightarrow> map_of (fields (G,C')) (fn, fd) = Some fT" (K[
  27.276 +fast_tac (HOL_cs addIs [widen_fields_mono, cfs_fields_lemma]) 1]);
  27.277 +
  27.278 +Goal "wf_prog wtm G \\<Longrightarrow> cmethd (G,C) sig = Some (md,mh,m)\
  27.279 +\  \\<longrightarrow> G\\<turnstile>Class C\\<preceq>Class md \\<and> wf_mdecl wtm G md (sig,(mh,m))";
  27.280 +by( case_tac "is_class G C" 1);
  27.281 +by(  forw_inst_tac [("C","C")] cmethd_rec 2);
  27.282 +by(    asm_full_simp_tac (simpset() addsimps [is_class_def] 
  27.283 +	delsimps [not_None_eq]) 2);
  27.284 +by( etac subcls1_induct 1);
  27.285 +by(   atac 1);
  27.286 +by(  Force_tac 1);
  27.287 +by( forw_inst_tac [("C","C")] cmethd_rec 1);
  27.288 +by( strip_tac1 1);
  27.289 +by( rotate_tac ~1 1);
  27.290 +by( Asm_full_simp_tac 1);
  27.291 +by( dtac override_SomeD 1);
  27.292 +by( etac disjE 1);
  27.293 +by(  thin_tac "?P \\<longrightarrow> ?Q" 1);
  27.294 +by(  Clarify_tac 2);
  27.295 +by(  rtac widen_trans 2);
  27.296 +by(    atac 2);
  27.297 +by(   atac 3);
  27.298 +by(  rtac widen.subcls 2);
  27.299 +by(  rtac r_into_trancl 2);
  27.300 +by(  fast_tac (HOL_cs addIs [subcls1I]) 2);
  27.301 +by( forward_tac [table_mapf_SomeD] 1);
  27.302 +by( strip_tac1 1);
  27.303 +by( Asm_full_simp_tac 1);
  27.304 +by( rewtac wf_cdecl_def);
  27.305 +by( Asm_full_simp_tac 1);
  27.306 +val cmethd_wf_mdecl = result() RS mp;
  27.307 +
  27.308 +Goal "\\<lbrakk>G\\<turnstile>T\\<prec>C T'; wf_prog wt G\\<rbrakk> \\<Longrightarrow> \
  27.309 +\  \\<forall>D rT b. cmethd (G,T') sig = Some (D,rT ,b) \\<longrightarrow>\
  27.310 +\ (\\<exists>D' rT' b'. cmethd (G,T) sig = Some (D',rT',b') \\<and> G\\<turnstile>rT'\\<preceq>rT)";
  27.311 +by( etac trancl_trans_induct 1);
  27.312 +by(  strip_tac1 2);
  27.313 +by(  EVERY[dtac spec 2, dtac spec 2, dtac spec 2, mp_tac 2]);
  27.314 +by(  fast_tac (HOL_cs addEs [widen_trans]) 2);
  27.315 +by( strip_tac1 1);
  27.316 +by( dtac subcls1D 1);
  27.317 +by( strip_tac1 1);
  27.318 +by( stac cmethd_rec 1);
  27.319 +by(  atac 1);
  27.320 +by( rewtac override_def);
  27.321 +by( asm_simp_tac (simpset() delsimps [split_paired_Ex]) 1);
  27.322 +by( case_tac "\\<exists>z. map_of(map (\\<lambda>(s,m). (s, ?C, m)) ms) sig = Some z" 1);
  27.323 +by(  etac exE 1);
  27.324 +by(  asm_full_simp_tac (HOL_ss addsimps [not_None_eq RS sym]) 2);
  27.325 +by(  ALLGOALS (rotate_tac ~1 THEN' forward_tac[ssubst] THEN' (fn n=>atac(n+1))));
  27.326 +by(  ALLGOALS (asm_simp_tac (simpset() delsimps [split_paired_Ex])));
  27.327 +by( dtac class_wf 1);
  27.328 +by(  atac 1);
  27.329 +by( split_all_tac 1);
  27.330 +by( rewtac wf_cdecl_def);
  27.331 +by( dtac table_mapf_Some2 1);
  27.332 +by( Clarsimp_tac 1);
  27.333 +by( dres_inst_tac [("xys1","ms")] get_in_set 1);
  27.334 +by Auto_tac;
  27.335 +qed_spec_mp "subcls_widen_methd";
  27.336 +
  27.337 +
  27.338 +Goal
  27.339 + "\\<lbrakk> G\\<turnstile>Class C\\<preceq>Class D; wf_prog wt G; \
  27.340 +\    cmethd (G,D) sig = Some (md, rT, b) \\<rbrakk> \
  27.341 +\ \\<Longrightarrow> \\<exists>mD' rT' b'. cmethd (G,C) sig= Some(mD',rT',b') \\<and> G\\<turnstile>rT'\\<preceq>rT";
  27.342 +by(auto_tac (claset() addSDs [widen_Class_Class]
  27.343 +                      addDs [subcls_widen_methd,cmethd_wf_mdecl],
  27.344 +             simpset() addsimps [wf_mdecl_def,wf_mhead_def,split_def]));
  27.345 +qed "subtype_widen_methd";
  27.346 +
  27.347 +
  27.348 +Goal "wf_prog wt G \\<Longrightarrow> \\<forall>D. cmethd (G,C) sig = Some(D,mh,code) \\<longrightarrow> is_class G D \\<and> cmethd (G,D) sig = Some(D,mh,code)";
  27.349 +by( case_tac "is_class G C" 1);
  27.350 +by(  forw_inst_tac [("C","C")] cmethd_rec 2);
  27.351 +by(    asm_full_simp_tac (simpset() addsimps [is_class_def] 
  27.352 +	delsimps [not_None_eq]) 2);
  27.353 +by (etac subcls1_induct 1);
  27.354 +  ba 1;
  27.355 + by (Asm_full_simp_tac 1);
  27.356 +by (stac cmethd_rec 1);
  27.357 + ba 1;
  27.358 +by (Clarify_tac 1);
  27.359 +by (eres_inst_tac [("x","Da")] allE 1);
  27.360 +by (Clarsimp_tac 1);
  27.361 + by (asm_full_simp_tac (simpset() addsimps [map_of_map]) 1);
  27.362 + by (Clarify_tac 1);
  27.363 + by (stac cmethd_rec 1);
  27.364 +  ba 1;
  27.365 + by (asm_full_simp_tac (simpset() addsimps [override_def,map_of_map] addsplits [option.split]) 1);
  27.366 +qed_spec_mp "cmethd_in_md";
  27.367 +
  27.368 +writeln"OK";
  27.369 +
  27.370 +Goal "\\<lbrakk>is_class G C; wf_prog wtm G\\<rbrakk> \\<Longrightarrow> \
  27.371 +\ \\<forall>f\\<in>set (fields (G,C)). is_type G (snd f)";
  27.372 +by( etac subcls1_induct 1);
  27.373 +by(   atac 1);
  27.374 +by(  Asm_simp_tac 1);
  27.375 +by( strip_tac1 1);
  27.376 +by( stac fields_rec 1);
  27.377 +by(   atac 1);
  27.378 +by(  atac 1);
  27.379 +by( Asm_simp_tac 1);
  27.380 +by( safe_tac set_cs);
  27.381 +by(  Fast_tac 2);
  27.382 +by( dtac class_wf 1);
  27.383 +by(  atac 1);
  27.384 +by( rewtac wf_cdecl_def);
  27.385 +by( Asm_full_simp_tac 1);
  27.386 +by( strip_tac1 1);
  27.387 +by( EVERY[dtac bspec 1, atac 1]);
  27.388 +by( rewtac wf_fdecl_def);
  27.389 +by( split_all_tac 1);
  27.390 +by( Asm_full_simp_tac 1);
  27.391 +val is_type_fields = result() RS bspec;
    28.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
    28.2 +++ b/src/HOL/MicroJava/J/WellForm.thy	Thu Nov 11 12:23:45 1999 +0100
    28.3 @@ -0,0 +1,47 @@
    28.4 +(*  Title:      HOL/MicroJava/J/WellForm.thy
    28.5 +    ID:         $Id$
    28.6 +    Author:     David von Oheimb
    28.7 +    Copyright   1999 Technische Universitaet Muenchen
    28.8 +
    28.9 +Well-formedness of Java programs
   28.10 +for static checks on expressions and statements, see WellType.thy
   28.11 +
   28.12 +improvements over Java Specification 1.0 (cf. 8.4.6.3, 8.4.6.4, 9.4.1):
   28.13 +* a method implementing or overwriting another method may have a result type 
   28.14 +  that widens to the result type of the other method (instead of identical type)
   28.15 +
   28.16 +simplifications:
   28.17 +* for uniformity, Object is assumed to be declared like any other class
   28.18 +*)
   28.19 +
   28.20 +WellForm = TypeRel +
   28.21 +
   28.22 +types 'c wtm = 'c prog => cname => 'c mdecl => bool
   28.23 +
   28.24 +constdefs
   28.25 +
   28.26 + wf_fdecl	:: "'c prog \\<Rightarrow>          fdecl \\<Rightarrow> bool"
   28.27 +"wf_fdecl G \\<equiv> \\<lambda>(fn,ft). is_type G ft"
   28.28 +
   28.29 + wf_mhead	:: "'c prog \\<Rightarrow> sig   \\<Rightarrow> ty \\<Rightarrow> bool"
   28.30 +"wf_mhead G \\<equiv> \\<lambda>(mn,pTs) rT. (\\<forall>T\\<in>set pTs. is_type G T) \\<and> is_type G rT"
   28.31 +
   28.32 + wf_mdecl	:: "'c wtm \\<Rightarrow> 'c wtm"
   28.33 +"wf_mdecl wtm G C \\<equiv> \\<lambda>(sig,rT,mb). wf_mhead G sig rT \\<and> wtm G C (sig,rT,mb)"
   28.34 +
   28.35 +  wf_cdecl	:: "'c wtm \\<Rightarrow> 'c prog \\<Rightarrow> 'c cdecl \\<Rightarrow> bool"
   28.36 +"wf_cdecl wtm G \\<equiv>
   28.37 +   \\<lambda>(C,(sc,fs,ms)).
   28.38 +	(\\<forall>f\\<in>set fs. wf_fdecl G   f    ) \\<and>  unique fs \\<and>
   28.39 +	(\\<forall>m\\<in>set ms. wf_mdecl wtm G C m) \\<and>  unique ms \\<and>
   28.40 +	(case sc of None \\<Rightarrow> C = Object
   28.41 +         | Some D \\<Rightarrow>
   28.42 +             is_class G D \\<and>  \\<not>  G\\<turnstile>D\\<prec>C C \\<and>
   28.43 +             (\\<forall>(sig,rT,b)\\<in>set ms. \\<forall>D' rT' b'.
   28.44 +                 cmethd(G,D) sig = Some(D',rT',b') \\<longrightarrow> G\\<turnstile>rT\\<preceq>rT'))"
   28.45 +
   28.46 + wf_prog	:: "'c wtm \\<Rightarrow> 'c prog \\<Rightarrow> bool"
   28.47 +"wf_prog wtm G \\<equiv>
   28.48 +   let cs = set G in ObjectC \\<in> cs \\<and> (\\<forall>c\\<in>cs. wf_cdecl wtm G c) \\<and> unique G"
   28.49 +
   28.50 +end
    29.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
    29.2 +++ b/src/HOL/MicroJava/J/WellType.ML	Thu Nov 11 12:23:45 1999 +0100
    29.3 @@ -0,0 +1,61 @@
    29.4 +(*  Title:      HOL/MicroJava/J/WellType.ML
    29.5 +    ID:         $Id$
    29.6 +    Author:     David von Oheimb
    29.7 +    Copyright   1999 Technische Universitaet Muenchen
    29.8 +*)
    29.9 +
   29.10 +Goalw [m_head_def]
   29.11 +"\\<lbrakk> m_head G T sig = Some (md,rT); wf_prog wtm G; G\\<turnstile>Class T''\\<preceq>RefT T\\<rbrakk> \\<Longrightarrow> \
   29.12 +\\\<exists>md' rT' b'. cmethd (G,T'') sig = Some (md',rT',b') \\<and>  G\\<turnstile>rT'\\<preceq>rT";
   29.13 +by( forward_tac [widen_Class_RefT] 1);
   29.14 +by( etac exE 1);
   29.15 +by( hyp_subst_tac 1);
   29.16 +by( asm_full_simp_tac (simpset() delsimps [split_paired_Ex]) 1);
   29.17 +by( rewtac option_map_def);
   29.18 +by( strip_tac1 1);
   29.19 +by( split_all_tac 1);
   29.20 +by( dtac widen_Class_Class 1);
   29.21 +by( etac disjE 1);
   29.22 +by(  hyp_subst_tac 1);
   29.23 +by(  asm_full_simp_tac (simpset() delsimps [split_paired_Ex]) 1);
   29.24 +by( dtac subcls_widen_methd 1);
   29.25 +by   Auto_tac;
   29.26 +qed "widen_methd";
   29.27 +
   29.28 +
   29.29 +Goal
   29.30 +"\\<lbrakk>m_head G T sig = Some (md,rT); G\\<turnstile>Class T''\\<preceq>RefT T; wf_prog wtm G\\<rbrakk> \\<Longrightarrow> \
   29.31 +\ \\<exists>T' rT' b. cmethd (G,T'') sig = Some (T',rT',b) \\<and> \
   29.32 +\ G\\<turnstile>rT'\\<preceq>rT \\<and> G\\<turnstile>Class T''\\<preceq>Class T' \\<and> wf_mhead G sig rT' \\<and> wtm G T' (sig,rT',b)";
   29.33 +by( dtac widen_methd 1);
   29.34 +by(   atac 1);
   29.35 +by(  atac 1);
   29.36 +by( Clarsimp_tac 1);
   29.37 +by( dtac cmethd_wf_mdecl 1);
   29.38 +by(  atac 1);
   29.39 +by( rewtac wf_mdecl_def);
   29.40 +by Auto_tac;
   29.41 +val Call_lemma = result();
   29.42 +
   29.43 +
   29.44 +val m_head_Object = prove_goalw thy [m_head_def]
   29.45 +"\\<And>x. wf_prog wtm G \\<Longrightarrow> m_head G (ClassT Object) sig = None" (K [Asm_simp_tac 1]);
   29.46 +
   29.47 +Addsimps [m_head_Object];
   29.48 +
   29.49 +val max_spec2appl_meths = prove_goalw thy [max_spec_def] 
   29.50 +	"x \\<in> max_spec G rT sig \\<longrightarrow> x \\<in> appl_methds G rT sig" 
   29.51 +	(fn _ => [Fast_tac 1]) RS mp;
   29.52 +
   29.53 +val appl_methsD = prove_goalw thy [appl_methds_def] 
   29.54 +"(mh,pTs')\\<in>appl_methds G rT (mn, pTs) \\<longrightarrow> \
   29.55 +\      m_head G rT (mn, pTs') = Some mh \\<and> list_all2 (\\<lambda>T T'. G\\<turnstile>T\\<preceq>T') pTs pTs'"
   29.56 +	(K [Fast_tac 1]) RS mp;
   29.57 +
   29.58 +val is_type_typeof = prove_goal thy 
   29.59 +	"(\\<forall>a. v \\<noteq> Addr a) \\<longrightarrow> (\\<exists>T. typeof t v = Some T \\<and>  is_type G T)" (K [
   29.60 +	rtac val_.induct 1,
   29.61 +	    Fast_tac 5,
   29.62 +	   ALLGOALS Simp_tac]) RS mp;
   29.63 +
   29.64 +Addsimps [is_type_typeof];
    30.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
    30.2 +++ b/src/HOL/MicroJava/J/WellType.thy	Thu Nov 11 12:23:45 1999 +0100
    30.3 @@ -0,0 +1,184 @@
    30.4 +(*  Title:      HOL/MicroJava/J/WellType.thy
    30.5 +    ID:         $Id$
    30.6 +    Author:     David von Oheimb
    30.7 +    Copyright   1999 Technische Universitaet Muenchen
    30.8 +
    30.9 +Well-typedness of Java programs
   30.10 +
   30.11 +the formulation of well-typedness of method calls given below (as well as
   30.12 +the Java Specification 1.0) is a little too restrictive: Is does not allow
   30.13 +methods of class Object to be called upon references of interface type.
   30.14 +
   30.15 +simplifications:
   30.16 +* the type rules include all static checks on expressions and statements, e.g.
   30.17 +  definedness of names (of parameters, locals, fields, methods)
   30.18 +
   30.19 +*)
   30.20 +
   30.21 +WellType = Term + WellForm +
   30.22 +
   30.23 +types	lenv (* local variables, including method parameters and This *)
   30.24 +	= "vname \\<leadsto> ty"
   30.25 +        'c env
   30.26 +	= "'c prog \\<times> lenv"
   30.27 +
   30.28 +syntax
   30.29 +
   30.30 +  prg		:: "'c env \\<Rightarrow> 'c prog"
   30.31 +  localT	:: "'c env \\<Rightarrow> (vname \\<leadsto> ty)"
   30.32 +
   30.33 +translations	
   30.34 +
   30.35 +  "prg"		=> "fst"
   30.36 +  "localT"	=> "snd"
   30.37 +
   30.38 +consts
   30.39 +
   30.40 +  more_spec	:: "'c prog \\<Rightarrow> (ty \\<times> 'x) \\<times> ty list \\<Rightarrow>
   30.41 +		               (ty \\<times> 'x) \\<times> ty list \\<Rightarrow> bool"
   30.42 +  m_head	:: "'c prog \\<Rightarrow>  ref_ty \\<Rightarrow> sig \\<Rightarrow>  (ty \\<times> ty) option"
   30.43 +  appl_methds	:: "'c prog \\<Rightarrow>  ref_ty \\<Rightarrow> sig \\<Rightarrow> ((ty \\<times> ty) \\<times> ty list) set"
   30.44 +  max_spec	:: "'c prog \\<Rightarrow>  ref_ty \\<Rightarrow> sig \\<Rightarrow> ((ty \\<times> ty) \\<times> ty list) set"
   30.45 +
   30.46 +defs
   30.47 +
   30.48 +  m_head_def  "m_head G t sig \\<equiv> case t of NullT \\<Rightarrow> None | ClassT C \\<Rightarrow>
   30.49 +		 option_map (\\<lambda>(md,(rT,mb)). (Class md,rT)) (cmethd (G,C) sig)"
   30.50 +                                                               
   30.51 +  more_spec_def	  "more_spec G \\<equiv> \\<lambda>((d,h),pTs). \\<lambda>((d',h'),pTs'). G\\<turnstile>d\\<preceq>d' \\<and>
   30.52 +		                  list_all2 (\\<lambda>T T'. G\\<turnstile>T\\<preceq>T') pTs pTs'"
   30.53 +  
   30.54 +  (* applicable methods, cf. 15.11.2.1 *)
   30.55 +  appl_methds_def "appl_methds G T \\<equiv> \\<lambda>(mn, pTs). {(mh,pTs') |mh pTs'.
   30.56 +		                  m_head G T (mn, pTs') = Some mh \\<and>
   30.57 +		                  list_all2 (\\<lambda>T T'. G\\<turnstile>T\\<preceq>T') pTs pTs'}"
   30.58 +
   30.59 +  (* maximally specific methods, cf. 15.11.2.2 *)
   30.60 +   max_spec_def	  "max_spec G rT sig \\<equiv> {m. m \\<in>appl_methds G rT sig \\<and> 
   30.61 +				          (\\<forall>m'\\<in>appl_methds G rT sig.
   30.62 +				                   more_spec G m' m \\<longrightarrow> m' = m)}"
   30.63 +consts
   30.64 +
   30.65 +  typeof :: "(loc \\<Rightarrow> ty option) \\<Rightarrow> val \\<Rightarrow> ty option"
   30.66 +
   30.67 +primrec
   30.68 +	"typeof dt  Unit    = Some (PrimT Void)"
   30.69 +	"typeof dt  Null    = Some NT"
   30.70 +	"typeof dt (Bool b) = Some (PrimT Boolean)"
   30.71 +	"typeof dt (Intg i) = Some (PrimT Integer)"
   30.72 +	"typeof dt (Addr a) = dt a"
   30.73 +
   30.74 +types
   30.75 +	javam = "vname list \\<times> (vname \\<times> ty) list \\<times> stmt \\<times> expr"
   30.76 +	(* method body with parameter names, local variables, block, result expression *)
   30.77 +
   30.78 +consts
   30.79 +
   30.80 +  ty_expr :: "javam env \\<Rightarrow> (expr      \\<times> ty     ) set"
   30.81 +  ty_exprs:: "javam env \\<Rightarrow> (expr list \\<times> ty list) set"
   30.82 +  wt_stmt :: "javam env \\<Rightarrow>  stmt                 set"
   30.83 +
   30.84 +syntax
   30.85 +
   30.86 +ty_expr :: "javam env \\<Rightarrow> [expr     , ty     ] \\<Rightarrow> bool" ("_\\<turnstile>_\\<Colon>_"  [51,51,51]50)
   30.87 +ty_exprs:: "javam env \\<Rightarrow> [expr list, ty list] \\<Rightarrow> bool" ("_\\<turnstile>_[\\<Colon>]_"[51,51,51]50)
   30.88 +wt_stmt :: "javam env \\<Rightarrow>  stmt                \\<Rightarrow> bool" ("_\\<turnstile>_ \\<surd>" [51,51   ]50)
   30.89 +
   30.90 +translations
   30.91 +	"E\\<turnstile>e \\<Colon> T" == "(e,T) \\<in> ty_expr  E"
   30.92 +	"E\\<turnstile>e[\\<Colon>]T" == "(e,T) \\<in> ty_exprs E"
   30.93 +	"E\\<turnstile>c \\<surd>"    == "c     \\<in> wt_stmt  E"
   30.94 +  
   30.95 +inductive "ty_expr E" "ty_exprs E" "wt_stmt E" intrs
   30.96 +
   30.97 +(* well-typed expressions *)
   30.98 +
   30.99 +  (* cf. 15.8 *)
  30.100 +  NewC	"\\<lbrakk>is_class (prg E) C\\<rbrakk> \\<Longrightarrow>
  30.101 +						 E\\<turnstile>NewC C\\<Colon>Class C"
  30.102 +
  30.103 +  (* cf. 15.15 *)
  30.104 +  Cast	"\\<lbrakk>E\\<turnstile>e\\<Colon>T;
  30.105 +	  prg E\\<turnstile>T\\<Rightarrow>? T'\\<rbrakk> \\<Longrightarrow>
  30.106 +						 E\\<turnstile>Cast T' e\\<Colon>T'"
  30.107 +
  30.108 +  (* cf. 15.7.1 *)
  30.109 +  Lit	"\\<lbrakk>typeof (\\<lambda>v. None) x = Some T\\<rbrakk> \\<Longrightarrow>
  30.110 +						 E\\<turnstile>Lit x\\<Colon>T"
  30.111 +
  30.112 +  (* cf. 15.13.1 *)
  30.113 +  LAcc	"\\<lbrakk>localT E v = Some T; is_type (prg E) T\\<rbrakk> \\<Longrightarrow>
  30.114 +						 E\\<turnstile>LAcc v\\<Colon>T"
  30.115 +  
  30.116 +  (* cf. 15.25, 15.25.1 *)
  30.117 +  LAss  "\\<lbrakk>E\\<turnstile>LAcc v\\<Colon>T;
  30.118 +	   E\\<turnstile>e\\<Colon>T';
  30.119 +	   prg E\\<turnstile>T'\\<preceq>T\\<rbrakk> \\<Longrightarrow>
  30.120 +						 E\\<turnstile>v\\<Colon>=e\\<Colon>T'"
  30.121 +
  30.122 +  (* cf. 15.10.1 *)
  30.123 +  FAcc	"\\<lbrakk>E\\<turnstile>a\\<Colon>Class C; 
  30.124 +	  cfield (prg E,C) fn = Some (fd,fT)\\<rbrakk> \\<Longrightarrow>
  30.125 +						 E\\<turnstile>{fd}a..fn\\<Colon>fT"
  30.126 +
  30.127 +  (* cf. 15.25, 15.25.1 *)
  30.128 +  FAss  "\\<lbrakk>E\\<turnstile>{fd}a..fn\\<Colon>T;
  30.129 +	  E\\<turnstile>v       \\<Colon>T';
  30.130 +	  prg E\\<turnstile>T'\\<preceq>T\\<rbrakk> \\<Longrightarrow>
  30.131 +					 	 E\\<turnstile>{fd}a..fn\\<in>=v\\<Colon>T'"
  30.132 +
  30.133 +
  30.134 +  (* cf. 15.11.1, 15.11.2, 15.11.3 *)
  30.135 +  Call	"\\<lbrakk>E\\<turnstile>a\\<Colon>RefT t;
  30.136 +	  E\\<turnstile>ps[\\<Colon>]pTs;
  30.137 +	  max_spec (prg E) t (mn, pTs) = {((md,rT),pTs')}\\<rbrakk> \\<Longrightarrow>
  30.138 +						 E\\<turnstile>a..mn({pTs'}ps)\\<Colon>rT"
  30.139 +
  30.140 +(* well-typed expression lists *)
  30.141 +
  30.142 +  (* cf. 15.11.??? *)
  30.143 +  Nil						"E\\<turnstile>[][\\<Colon>][]"
  30.144 +
  30.145 +  (* cf. 15.11.??? *)
  30.146 +  Cons	"\\<lbrakk>E\\<turnstile>e\\<Colon>T;
  30.147 +	   E\\<turnstile>es[\\<Colon>]Ts\\<rbrakk> \\<Longrightarrow>
  30.148 +						 E\\<turnstile>e#es[\\<Colon>]T#Ts"
  30.149 +
  30.150 +(* well-typed statements *)
  30.151 +
  30.152 +  Skip					"E\\<turnstile>Skip\\<surd>"
  30.153 +
  30.154 +  Expr	"\\<lbrakk>E\\<turnstile>e\\<Colon>T\\<rbrakk> \\<Longrightarrow>
  30.155 +					 E\\<turnstile>Expr e\\<surd>"
  30.156 +
  30.157 + Comp	"\\<lbrakk>E\\<turnstile>s1\\<surd>; 
  30.158 +	  E\\<turnstile>s2\\<surd>\\<rbrakk> \\<Longrightarrow>
  30.159 +					 E\\<turnstile>s1;; s2\\<surd>"
  30.160 +
  30.161 +  (* cf. 14.8 *)
  30.162 +  Cond	"\\<lbrakk>E\\<turnstile>e\\<Colon>PrimT Boolean;
  30.163 +	  E\\<turnstile>s1\\<surd>;
  30.164 +	  E\\<turnstile>s2\\<surd>\\<rbrakk> \\<Longrightarrow>
  30.165 +					 E\\<turnstile>If(e) s1 Else s2\\<surd>"
  30.166 +
  30.167 +  (* cf. 14.10 *)
  30.168 +  Loop "\\<lbrakk>E\\<turnstile>e\\<Colon>PrimT Boolean;
  30.169 +	 E\\<turnstile>s\\<surd>\\<rbrakk> \\<Longrightarrow>
  30.170 +					 E\\<turnstile>While(e) s\\<surd>"
  30.171 +
  30.172 +constdefs
  30.173 +
  30.174 + wt_java_mdecl :: javam prog => cname => javam mdecl => bool
  30.175 +"wt_java_mdecl G C \\<equiv> \\<lambda>((mn,pTs),rT,(pns,lvars,blk,res)).
  30.176 +	length pTs = length pns \\<and>
  30.177 +	nodups pns \\<and>
  30.178 +	unique lvars \\<and>
  30.179 +	(\\<forall>pn\\<in>set pns. map_of lvars pn = None) \\<and>
  30.180 +	(\\<forall>(vn,T)\\<in>set lvars. is_type G T) &
  30.181 +	(let E = (G,map_of lvars(pns[\\<mapsto>]pTs)(This\\<mapsto>Class C)) in
  30.182 +	 E\\<turnstile>blk\\<surd> \\<and> (\\<exists>T. E\\<turnstile>res\\<Colon>T \\<and> G\\<turnstile>T\\<preceq>rT))"
  30.183 +
  30.184 + wf_java_prog :: javam prog => bool
  30.185 +"wf_java_prog G \\<equiv> wf_prog wt_java_mdecl G"
  30.186 +
  30.187 +end
    31.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
    31.2 +++ b/src/HOL/MicroJava/JVM/Control.thy	Thu Nov 11 12:23:45 1999 +0100
    31.3 @@ -0,0 +1,26 @@
    31.4 +(*  Title:      HOL/MicroJava/JVM/Control.thy
    31.5 +    ID:         $Id$
    31.6 +    Author:     Cornelia Pusch
    31.7 +    Copyright   1999 Technische Universitaet Muenchen
    31.8 +
    31.9 +(Un)conditional branch instructions
   31.10 +*)
   31.11 +
   31.12 +Control = JVMState +
   31.13 +
   31.14 +datatype branch = Goto int
   31.15 +                | Ifcmpeq int	(** Branch if int/ref comparison succeeds **)
   31.16 +
   31.17 +
   31.18 +consts
   31.19 + exec_br :: "[branch,opstack,p_count] \\<Rightarrow> (opstack \\<times> p_count)" 
   31.20 +
   31.21 +primrec
   31.22 +  "exec_br (Ifcmpeq i) stk pc =
   31.23 +	(let (val1,val2) = (hd stk, hd (tl stk));
   31.24 +	     pc'	 = if val1 = val2 then nat(int pc+i) else pc+1
   31.25 +	 in
   31.26 +	 (tl (tl stk),pc'))"				
   31.27 +  "exec_br (Goto i) stk pc = (stk, nat(int pc+i))"
   31.28 +
   31.29 +end
    32.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
    32.2 +++ b/src/HOL/MicroJava/JVM/JVMExec.thy	Thu Nov 11 12:23:45 1999 +0100
    32.3 @@ -0,0 +1,72 @@
    32.4 +(*  Title:      HOL/MicroJava/JVM/JVMExec.thy
    32.5 +    ID:         $Id$
    32.6 +    Author:     Cornelia Pusch
    32.7 +    Copyright   1999 Technische Universitaet Muenchen
    32.8 +
    32.9 +Execution of the JVM
   32.10 +*)
   32.11 +
   32.12 +JVMExec = LoadAndStore + Object + Method + Opstack + Control + 
   32.13 +
   32.14 +datatype
   32.15 + instr	= LS load_and_store	
   32.16 +        | CO create_object	
   32.17 +        | MO manipulate_object	
   32.18 +	| CH check_object	
   32.19 +	| MI meth_inv		
   32.20 +	| MR
   32.21 +	| OS op_stack		
   32.22 +	| BR branch
   32.23 +
   32.24 +types
   32.25 + bytecode = instr list
   32.26 + jvm_prog = "(nat \\<times> bytecode)prog"
   32.27 +
   32.28 +consts
   32.29 + exec :: "jvm_prog \\<times> jvm_state \\<Rightarrow> jvm_state option"
   32.30 +
   32.31 +(** exec is not recursive. recdef is just used because for pattern matching **)
   32.32 +recdef exec "{}"
   32.33 + "exec (G, xp, hp, []) = None"
   32.34 +
   32.35 + "exec (G, None, hp, (stk,loc,cn,ml,pc)#frs) = 
   32.36 +   Some (case snd(snd(snd(the(cmethd (G,cn) ml)))) ! pc of
   32.37 +      LS ins \\<Rightarrow> (let (stk',loc',pc') = exec_las ins stk loc pc
   32.38 +		in
   32.39 +		(None,hp,(stk',loc',cn,ml,pc')#frs))
   32.40 +
   32.41 +    | CO ins \\<Rightarrow> (let (xp',hp',stk',pc') = exec_co ins G hp stk pc
   32.42 +		in
   32.43 +		(xp',hp',(stk',loc,cn,ml,pc')#frs))	    
   32.44 +
   32.45 +    | MO ins \\<Rightarrow> (let (xp',hp',stk',pc') = exec_mo ins hp stk pc
   32.46 +		in
   32.47 +		(xp',hp',(stk',loc,cn,ml,pc')#frs))	
   32.48 +
   32.49 +    | CH ins \\<Rightarrow> (let (xp',stk',pc') = exec_ch ins G hp stk pc
   32.50 +		in
   32.51 +		(xp',hp,(stk',loc,cn,ml,pc')#frs))
   32.52 +
   32.53 +    | MI ins \\<Rightarrow> (let (xp',frs',stk',pc') = exec_mi ins G hp stk pc 
   32.54 +		in
   32.55 +		(xp',hp,frs'@(stk',loc,cn,ml,pc')#frs))
   32.56 +
   32.57 +    | MR     \\<Rightarrow> (let frs' = exec_mr stk frs in
   32.58 +		(None,hp,frs'))
   32.59 +
   32.60 +    | OS ins \\<Rightarrow> (let (stk',pc') = exec_os ins stk pc
   32.61 +		in
   32.62 +		(None,hp,(stk',loc,cn,ml,pc')#frs))
   32.63 +
   32.64 +    | BR ins \\<Rightarrow> (let (stk',pc') = exec_br ins stk pc
   32.65 +		in
   32.66 +		(None,hp,(stk',loc,cn,ml,pc')#frs)))"
   32.67 +
   32.68 + "exec (G, Some xp, hp, f#frs) = Some (Some xp, hp, [])"
   32.69 +
   32.70 +
   32.71 +constdefs
   32.72 + exec_all :: "[jvm_prog,jvm_state,jvm_state] \\<Rightarrow> bool"  ("_ \\<turnstile> _ -jvm\\<rightarrow> _" [61,61,61]60)
   32.73 + "G \\<turnstile> s -jvm\\<rightarrow> t \\<equiv> (s,t) \\<in> {(s,t). exec(G,s) = Some t}^*"
   32.74 +
   32.75 +end
    33.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
    33.2 +++ b/src/HOL/MicroJava/JVM/JVMState.thy	Thu Nov 11 12:23:45 1999 +0100
    33.3 @@ -0,0 +1,61 @@
    33.4 +(*  Title:      HOL/MicroJava/JVM/JVMState.thy
    33.5 +    ID:         $Id$
    33.6 +    Author:     Cornelia Pusch
    33.7 +    Copyright   1999 Technische Universitaet Muenchen
    33.8 +
    33.9 +State of the JVM
   33.10 +*)
   33.11 +
   33.12 +JVMState = Store +
   33.13 +
   33.14 +
   33.15 +(** frame stack **)
   33.16 +
   33.17 +types
   33.18 + opstack 	 = "val list"
   33.19 + locvars 	 = "val list" 
   33.20 + p_count 	 = nat
   33.21 +
   33.22 + frame = "opstack \\<times>			
   33.23 +	  locvars \\<times>		
   33.24 +	  cname \\<times>			
   33.25 +	  sig \\<times>			
   33.26 +	  p_count"
   33.27 +
   33.28 +	(* operand stack *)
   33.29 +	(* local variables *)
   33.30 +	(* name of def. class defined *)
   33.31 +	(* meth name+param_desc *)
   33.32 +	(* program counter within frame *)
   33.33 +
   33.34 +
   33.35 +(** exceptions **)
   33.36 +
   33.37 +constdefs
   33.38 + raise_xcpt :: "bool \\<Rightarrow> xcpt \\<Rightarrow> xcpt option"
   33.39 +"raise_xcpt c x \\<equiv> (if c then Some x else None)"
   33.40 +
   33.41 + heap_update :: "[xcpt option,aheap,aheap] \\<Rightarrow> aheap"
   33.42 +"heap_update xp hp' hp \\<equiv> if xp=None then hp' else hp"
   33.43 +
   33.44 + stk_update :: "[xcpt option,opstack,opstack] \\<Rightarrow> opstack"
   33.45 +"stk_update xp stk' stk \\<equiv> if xp=None then stk' else stk"
   33.46 +
   33.47 + xcpt_update :: "[xcpt option,'a,'a] \\<Rightarrow> 'a"
   33.48 +"xcpt_update xp y' y \\<equiv> if xp=None then y' else y"
   33.49 +
   33.50 +(** runtime state **)
   33.51 +
   33.52 +types
   33.53 + jvm_state = "xcpt option \\<times>		
   33.54 +	      aheap \\<times>				
   33.55 +	      frame list"	
   33.56 +
   33.57 +
   33.58 +
   33.59 +(** dynamic method lookup **)
   33.60 +
   33.61 +constdefs
   33.62 + dyn_class	:: "'code prog \\<times> sig \\<times> cname \\<Rightarrow> cname"
   33.63 +"dyn_class \\<equiv> \\<lambda>(G,sig,C). fst(the(cmethd(G,C) sig))"
   33.64 +end
    34.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
    34.2 +++ b/src/HOL/MicroJava/JVM/LoadAndStore.thy	Thu Nov 11 12:23:45 1999 +0100
    34.3 @@ -0,0 +1,32 @@
    34.4 +(*  Title:      HOL/MicroJava/JVM/LoadAndStore.thy
    34.5 +    ID:         $Id$
    34.6 +    Author:     Cornelia Pusch
    34.7 +    Copyright   1999 Technische Universitaet Muenchen
    34.8 +
    34.9 +Load and store instructions
   34.10 +*)
   34.11 +
   34.12 +LoadAndStore = JVMState +
   34.13 +
   34.14 +(** load and store instructions transfer values between local variables 
   34.15 +    and operand stack. Values must all be of the same size (or tagged) **)
   34.16 +
   34.17 +datatype load_and_store =
   34.18 +  Load  nat  	(* load from local variable *)
   34.19 +| Store nat	(* store into local variable *)
   34.20 +| Bipush int	(* push int *)
   34.21 +| Aconst_null	(* push null *)
   34.22 +
   34.23 +
   34.24 +consts
   34.25 + exec_las :: "[load_and_store,opstack,locvars,p_count] \\<Rightarrow> (opstack \\<times> locvars \\<times> p_count)" 
   34.26 +primrec
   34.27 + "exec_las (Load idx) stk vars pc = ((vars ! idx) # stk , vars , pc+1)"
   34.28 +
   34.29 + "exec_las (Store idx) stk vars pc = (tl stk , vars[idx:=hd stk] , pc+1)"	
   34.30 +
   34.31 + "exec_las (Bipush ival) stk vars pc = (Intg ival # stk , vars , pc+1)"
   34.32 +
   34.33 + "exec_las Aconst_null stk vars pc = (Null # stk , vars , pc+1)"
   34.34 +
   34.35 +end
    35.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
    35.2 +++ b/src/HOL/MicroJava/JVM/Method.ML	Thu Nov 11 12:23:45 1999 +0100
    35.3 @@ -0,0 +1,7 @@
    35.4 +(*  Title:      HOL/MicroJava/JVM/Method.ML
    35.5 +    ID:         $Id$
    35.6 +    Author:     Cornelia Pusch
    35.7 +    Copyright   1999 Technische Universitaet Muenchen
    35.8 +*)
    35.9 +
   35.10 +Addsimps [exec_mr_def];
    36.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
    36.2 +++ b/src/HOL/MicroJava/JVM/Method.thy	Thu Nov 11 12:23:45 1999 +0100
    36.3 @@ -0,0 +1,41 @@
    36.4 +(*  Title:      HOL/MicroJava/JVM/Method.thy
    36.5 +    ID:         $Id$
    36.6 +    Author:     Cornelia Pusch
    36.7 +    Copyright   1999 Technische Universitaet Muenchen
    36.8 +
    36.9 +Method invocation
   36.10 +*)
   36.11 +
   36.12 +Method = JVMState +
   36.13 +
   36.14 +(** method invocation and return instructions **)
   36.15 +
   36.16 +datatype 
   36.17 + meth_inv = 
   36.18 +   Invokevirtual   mname (ty list)      (** inv. instance meth of an object **)
   36.19 + 
   36.20 +consts
   36.21 + exec_mi :: "[meth_inv,(nat \\<times> 'c)prog,aheap,opstack,p_count] 
   36.22 +		\\<Rightarrow> (xcpt option \\<times> frame list \\<times> opstack \\<times> p_count)" 
   36.23 +primrec
   36.24 + "exec_mi (Invokevirtual mn ps) G hp stk pc =
   36.25 +	(let n		= length ps;
   36.26 +	     argsoref	= take (n+1) stk;
   36.27 +	     oref	= last argsoref;
   36.28 +	     xp'	= raise_xcpt (oref=Null) NullPointer;
   36.29 +	     dynT	= fst(hp \\<And> (the_Addr oref));
   36.30 +	     (dc,mh,mxl,c)= the (cmethd (G,dynT) (mn,ps));
   36.31 +	     frs'	= xcpt_update xp' [([],rev argsoref@replicate mxl arbitrary,dc,(mn,ps),0)] []
   36.32 +	 in
   36.33 +	 (xp' , frs' , drop (n+1) stk , pc+1))"
   36.34 +
   36.35 +
   36.36 +constdefs
   36.37 + exec_mr :: "[opstack,frame list] \\<Rightarrow> frame list"
   36.38 +"exec_mr stk0 frs \\<equiv>
   36.39 +	 (let val			= hd stk0;
   36.40 +	      (stk,loc,cn,met,pc) = hd frs
   36.41 +	  in
   36.42 +	  (val#stk,loc,cn,met,pc)#tl frs)"
   36.43 +
   36.44 +end
    37.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
    37.2 +++ b/src/HOL/MicroJava/JVM/Object.thy	Thu Nov 11 12:23:45 1999 +0100
    37.3 @@ -0,0 +1,73 @@
    37.4 +(*  Title:      HOL/MicroJava/JVM/Object.thy
    37.5 +    ID:         $Id$
    37.6 +    Author:     Cornelia Pusch
    37.7 +    Copyright   1999 Technische Universitaet Muenchen
    37.8 +
    37.9 +Get and putfield instructions
   37.10 +*)
   37.11 +
   37.12 +Object = JVMState +
   37.13 +
   37.14 +datatype 
   37.15 + create_object = New cname
   37.16 +
   37.17 +consts
   37.18 + exec_co :: "[create_object,'code prog,aheap,opstack,p_count] \\<Rightarrow> 
   37.19 +		(xcpt option \\<times> aheap \\<times> opstack \\<times> p_count)"
   37.20 +
   37.21 +
   37.22 +primrec
   37.23 +  "exec_co (New C) G hp stk pc = 
   37.24 +	(let xp'	= raise_xcpt (\\<forall>x. hp x \\<noteq> None) OutOfMemory;
   37.25 +	     oref	= newref hp;
   37.26 +             fs		= init_vars (fields(G,C));
   37.27 +	     hp'	= xcpt_update xp' (hp(oref \\<mapsto> (C,fs))) hp;
   37.28 +	     stk'	= xcpt_update xp' ((Addr oref)#stk) stk
   37.29 +	 in (xp' , hp' , stk' , pc+1))"	
   37.30 +
   37.31 +
   37.32 +datatype
   37.33 + manipulate_object = 
   37.34 +   Getfield vname cname		(* Fetch field from object *)
   37.35 + | Putfield vname cname		(* Set field in object     *)
   37.36 +
   37.37 +consts
   37.38 + exec_mo :: "[manipulate_object,aheap,opstack,p_count] \\<Rightarrow> 
   37.39 +		(xcpt option \\<times> aheap \\<times> opstack \\<times> p_count)"
   37.40 +
   37.41 +primrec
   37.42 + "exec_mo (Getfield F C) hp stk pc = 
   37.43 +	(let oref	= hd stk;
   37.44 +	     xp'	= raise_xcpt (oref=Null) NullPointer;
   37.45 +	     (oc,fs)	= hp \\<And> (the_Addr oref);
   37.46 +	     stk'	= xcpt_update xp' ((fs\\<And>(F,C))#(tl stk)) (tl stk)
   37.47 +	 in
   37.48 +         (xp' , hp , stk' , pc+1))"
   37.49 +
   37.50 + "exec_mo (Putfield F C) hp stk pc = 
   37.51 +	(let (fval,oref)= (hd stk, hd(tl stk));
   37.52 +	     xp'	= raise_xcpt (oref=Null) NullPointer;
   37.53 +	     a		= the_Addr oref;
   37.54 +	     (oc,fs)	= hp \\<And> a;
   37.55 +	     hp'	= xcpt_update xp' (hp(a \\<mapsto> (oc, fs((F,C) \\<mapsto> fval)))) hp
   37.56 +	 in
   37.57 +         (xp' , hp' , tl (tl stk), pc+1))"				
   37.58 +
   37.59 +
   37.60 +datatype
   37.61 + check_object =
   37.62 +    Checkcast cname	(* Check whether object is of given type *)
   37.63 +
   37.64 +consts
   37.65 + exec_ch :: "[check_object,'code prog,aheap,opstack,p_count] 
   37.66 +		\\<Rightarrow> (xcpt option \\<times> opstack \\<times> p_count)"
   37.67 +
   37.68 +primrec
   37.69 +  "exec_ch (Checkcast C) G hp stk pc =
   37.70 +	(let oref	= hd stk;
   37.71 +	     xp'	= raise_xcpt (\\<not> cast_ok G (Class C) hp oref) ClassCast;
   37.72 +	     stk'	= xcpt_update xp' stk (tl stk)
   37.73 +	 in
   37.74 +	 (xp' , stk' , pc+1))"
   37.75 +
   37.76 +end
    38.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
    38.2 +++ b/src/HOL/MicroJava/JVM/Opstack.thy	Thu Nov 11 12:23:45 1999 +0100
    38.3 @@ -0,0 +1,38 @@
    38.4 +(*  Title:      HOL/MicroJava/JVM/Opstack.thy
    38.5 +    ID:         $Id$
    38.6 +    Author:     Cornelia Pusch
    38.7 +    Copyright   1999 Technische Universitaet Muenchen
    38.8 +
    38.9 +Manipulation of operand stack
   38.10 +*)
   38.11 +
   38.12 +Opstack = JVMState +
   38.13 +
   38.14 +(** instructions for the direct manipulation of the operand stack **)
   38.15 +
   38.16 +datatype 
   38.17 + op_stack = 
   38.18 +   Pop
   38.19 + | Dup
   38.20 + | Dup_x1
   38.21 + | Dup_x2
   38.22 + | Swap
   38.23 +	  
   38.24 +consts
   38.25 + exec_os :: "[op_stack,opstack,p_count] \\<Rightarrow> (opstack \\<times> p_count)" 
   38.26 +
   38.27 +primrec 
   38.28 +  "exec_os Pop stk pc = (tl stk , pc+1)"
   38.29 +
   38.30 +  "exec_os Dup stk pc = (hd stk # stk , pc+1)"
   38.31 +
   38.32 +  "exec_os Dup_x1 stk pc = (hd stk # hd (tl stk) # hd stk # (tl (tl stk)) , pc+1)"
   38.33 +
   38.34 +  "exec_os Dup_x2 stk pc = (hd stk # hd (tl stk) # (hd (tl (tl stk))) # hd stk # (tl (tl (tl stk))) , pc+1)"
   38.35 +
   38.36 +  "exec_os Swap stk pc = 
   38.37 +	(let (val1,val2) = (hd stk,hd (tl stk))
   38.38 +	 in
   38.39 +	 (val2#val1#(tl (tl stk)) , pc+1))"
   38.40 +
   38.41 +end
    39.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
    39.2 +++ b/src/HOL/MicroJava/JVM/Store.ML	Thu Nov 11 12:23:45 1999 +0100
    39.3 @@ -0,0 +1,10 @@
    39.4 +(*  Title:      HOL/MicroJava/JVM/Store.thy
    39.5 +    ID:         $Id$
    39.6 +    Author:     Cornelia Pusch
    39.7 +    Copyright   1999 Technische Universitaet Muenchen
    39.8 +*)
    39.9 +
   39.10 +Goalw [newref_def]
   39.11 + "hp x = None \\<longrightarrow> hp (newref hp) = None";
   39.12 +by (fast_tac (claset() addIs [selectI2EX] addss (simpset())) 1);
   39.13 +qed_spec_mp "newref_None";
    40.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
    40.2 +++ b/src/HOL/MicroJava/JVM/Store.thy	Thu Nov 11 12:23:45 1999 +0100
    40.3 @@ -0,0 +1,23 @@
    40.4 +(*  Title:      HOL/MicroJava/JVM/Store.thy
    40.5 +    ID:         $Id$
    40.6 +    Author:     Cornelia Pusch
    40.7 +    Copyright   1999 Technische Universitaet Muenchen
    40.8 +
    40.9 +The store.
   40.10 +
   40.11 +The JVM builds on many notions already defined in Java.
   40.12 +Conform provides notions for the type safety proof of the Bytecode Verifier.
   40.13 +*)
   40.14 +
   40.15 +Store = Conform +  
   40.16 +
   40.17 +syntax
   40.18 + value	:: "['a \\<leadsto> 'b,'a] \\<Rightarrow> 'b"			("_ \\<And> _")		
   40.19 +translations
   40.20 + "t \\<And> x"  == "the (t x)"
   40.21 +
   40.22 +constdefs
   40.23 + newref :: "('a \\<leadsto> 'b) \\<Rightarrow> 'a"
   40.24 + "newref s \\<equiv> \\<epsilon>v. s v = None"
   40.25 +
   40.26 +end
    41.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
    41.2 +++ b/src/HOL/MicroJava/ROOT.ML	Thu Nov 11 12:23:45 1999 +0100
    41.3 @@ -0,0 +1,12 @@
    41.4 +goals_limit:=1;
    41.5 +
    41.6 +Unify.search_bound := 40;
    41.7 +Unify.trace_bound  := 40;
    41.8 +
    41.9 +add_path "J";
   41.10 +add_path "JVM";
   41.11 +add_path "BV";
   41.12 +
   41.13 +
   41.14 +use_thy "JTypeSafe";
   41.15 +use_thy "BVSpecTypeSafe";