--- a/src/HOL/MicroJava/Comp/CorrComp.thy Tue May 26 21:58:04 2015 +0100
+++ b/src/HOL/MicroJava/Comp/CorrComp.thy Thu May 28 17:25:57 2015 +1000
@@ -16,7 +16,7 @@
"(G \<turnstile> xs -ex\<succ>val-> xs' \<longrightarrow> gx xs' = None \<longrightarrow> gx xs = None) \<and>
(G \<turnstile> xs -exs[\<succ>]vals-> xs' \<longrightarrow> gx xs' = None \<longrightarrow> gx xs = None) \<and>
(G \<turnstile> xs -st-> xs' \<longrightarrow> gx xs' = None \<longrightarrow> gx xs = None)"
-by (induct rule: eval_evals_exec.induct) auto
+ by (induct rule: eval_evals_exec.induct) auto
(* instance of eval_evals_exec_xcpt for eval *)
@@ -49,22 +49,21 @@
(**********************************************************************)
theorem exec_all_trans: "\<lbrakk>(exec_all G s0 s1); (exec_all G s1 s2)\<rbrakk> \<Longrightarrow> (exec_all G s0 s2)"
-apply (auto simp: exec_all_def elim: Transitive_Closure.rtrancl_trans)
-done
+ by (auto simp: exec_all_def elim: Transitive_Closure.rtrancl_trans)
theorem exec_all_refl: "exec_all G s s"
-by (simp only: exec_all_def)
+ by (simp only: exec_all_def)
theorem exec_instr_in_exec_all:
"\<lbrakk> exec_instr i G hp stk lvars C S pc frs = (None, hp', frs');
gis (gmb G C S) ! pc = i\<rbrakk> \<Longrightarrow>
G \<turnstile> (None, hp, (stk, lvars, C, S, pc) # frs) \<midarrow>jvm\<rightarrow> (None, hp', frs')"
-apply (simp only: exec_all_def)
-apply (rule rtrancl_refl [THEN rtrancl_into_rtrancl])
-apply (simp add: gis_def gmb_def)
-apply (case_tac frs', simp+)
-done
+ apply (simp only: exec_all_def)
+ apply (rule rtrancl_refl [THEN rtrancl_into_rtrancl])
+ apply (simp add: gis_def gmb_def)
+ apply (case_tac frs', simp+)
+ done
theorem exec_all_one_step: "
\<lbrakk> gis (gmb G C S) = pre @ (i # post); pc0 = length pre;
@@ -73,10 +72,10 @@
\<Longrightarrow>
G \<turnstile> (None, hp0, (stk0,lvars0,C,S, pc0)#frs) \<midarrow>jvm\<rightarrow>
(None, hp1, (stk1,lvars1,C,S, Suc pc0)#frs)"
-apply (unfold exec_all_def)
-apply (rule r_into_rtrancl)
-apply (simp add: gis_def gmb_def split_beta)
-done
+ apply (unfold exec_all_def)
+ apply (rule r_into_rtrancl)
+ apply (simp add: gis_def gmb_def split_beta)
+ done
(***********************************************************************)
@@ -88,7 +87,7 @@
bool"
("{_,_,_} \<turnstile> {_, _, _} >- _ \<rightarrow> {_, _, _}" [61,61,61,61,61,61,90,61,61,61]60) where
"{G,C,S} \<turnstile> {hp0, os0, lvars0} >- instrs \<rightarrow> {hp1, os1, lvars1} ==
- \<forall> pre post frs.
+ \<forall>pre post frs.
(gis (gmb G C S) = pre @ instrs @ post) \<longrightarrow>
G \<turnstile> (None,hp0,(os0,lvars0,C,S,length pre)#frs) \<midarrow>jvm\<rightarrow>
(None,hp1,(os1,lvars1,C,S,(length pre) + (length instrs))#frs)"
@@ -96,7 +95,7 @@
lemma progression_call:
- "\<lbrakk> \<forall> pc frs.
+ "\<lbrakk> \<forall>pc frs.
exec_instr instr G hp0 os0 lvars0 C S pc frs =
(None, hp', (os', lvars', C', S', 0) # (fr pc) # frs) \<and>
gis (gmb G C' S') = instrs' @ [Return] \<and>
@@ -105,22 +104,23 @@
((fr pc) # frs) =
(None, hp2, (os2, lvars2, C, S, Suc pc) # frs) \<rbrakk> \<Longrightarrow>
{G, C, S} \<turnstile> {hp0, os0, lvars0} >-[instr]\<rightarrow> {hp2,os2,lvars2}"
-apply (simp only: progression_def)
-apply (intro strip)
-apply (drule_tac x="length pre" in spec)
-apply (drule_tac x="frs" in spec)
-apply clarify
-apply (rule exec_all_trans)
-apply (rule exec_instr_in_exec_all) apply simp
-apply simp
-apply (rule exec_all_trans)
-apply (simp only: append_Nil)
-apply (drule_tac x="[]" in spec)
-apply (simp only: list.simps list.size)
-apply blast
-apply (rule exec_instr_in_exec_all)
-apply auto
-done
+ apply (simp only: progression_def)
+ apply (intro strip)
+ apply (drule_tac x="length pre" in spec)
+ apply (drule_tac x="frs" in spec)
+ apply clarify
+ apply (rule exec_all_trans)
+ apply (rule exec_instr_in_exec_all)
+ apply simp
+ apply simp
+ apply (rule exec_all_trans)
+ apply (simp only: append_Nil)
+ apply (drule_tac x="[]" in spec)
+ apply (simp only: list.simps list.size)
+ apply blast
+ apply (rule exec_instr_in_exec_all)
+ apply auto
+ done
lemma progression_transitive:
@@ -129,57 +129,57 @@
{G, C, S} \<turnstile> {hp1, os1, lvars1} >- instrs1 \<rightarrow> {hp2, os2, lvars2} \<rbrakk>
\<Longrightarrow>
{G, C, S} \<turnstile> {hp0, os0, lvars0} >- instrs_comb \<rightarrow> {hp2, os2, lvars2}"
-apply (simp only: progression_def)
-apply (intro strip)
-apply (rule_tac ?s1.0 = "Norm (hp1, (os1, lvars1, C, S,
- length pre + length instrs0) # frs)"
- in exec_all_trans)
-apply (simp only: append_assoc)
-apply (erule thin_rl, erule thin_rl)
-apply (drule_tac x="pre @ instrs0" in spec)
-apply (simp add: add.assoc)
-done
+ apply (simp only: progression_def)
+ apply (intro strip)
+ apply (rule_tac ?s1.0 = "Norm (hp1, (os1, lvars1, C, S,
+ length pre + length instrs0) # frs)"
+ in exec_all_trans)
+ apply (simp only: append_assoc)
+ apply (erule thin_rl, erule thin_rl)
+ apply (drule_tac x="pre @ instrs0" in spec)
+ apply (simp add: add.assoc)
+ done
lemma progression_refl:
"{G, C, S} \<turnstile> {hp0, os0, lvars0} >- [] \<rightarrow> {hp0, os0, lvars0}"
-apply (simp add: progression_def)
-apply (intro strip)
-apply (rule exec_all_refl)
-done
+ apply (simp add: progression_def)
+ apply (intro strip)
+ apply (rule exec_all_refl)
+ done
lemma progression_one_step: "
- \<forall> pc frs.
+ \<forall>pc frs.
(exec_instr i G hp0 os0 lvars0 C S pc frs) =
(None, hp1, (os1,lvars1,C,S, Suc pc)#frs)
\<Longrightarrow> {G, C, S} \<turnstile> {hp0, os0, lvars0} >- [i] \<rightarrow> {hp1, os1, lvars1}"
-apply (unfold progression_def)
-apply (intro strip)
-apply simp
-apply (rule exec_all_one_step)
-apply auto
-done
+ apply (unfold progression_def)
+ apply (intro strip)
+ apply simp
+ apply (rule exec_all_one_step)
+ apply auto
+ done
(*****)
definition jump_fwd :: "jvm_prog \<Rightarrow> cname \<Rightarrow> sig \<Rightarrow>
aheap \<Rightarrow> locvars \<Rightarrow> opstack \<Rightarrow> opstack \<Rightarrow>
instr \<Rightarrow> bytecode \<Rightarrow> bool" where
"jump_fwd G C S hp lvars os0 os1 instr instrs ==
- \<forall> pre post frs.
+ \<forall>pre post frs.
(gis (gmb G C S) = pre @ instr # instrs @ post) \<longrightarrow>
exec_all G (None,hp,(os0,lvars,C,S, length pre)#frs)
(None,hp,(os1,lvars,C,S,(length pre) + (length instrs) + 1)#frs)"
lemma jump_fwd_one_step:
- "\<forall> pc frs.
+ "\<forall>pc frs.
exec_instr instr G hp os0 lvars C S pc frs =
(None, hp, (os1, lvars, C, S, pc + (length instrs) + 1)#frs)
\<Longrightarrow> jump_fwd G C S hp lvars os0 os1 instr instrs"
-apply (unfold jump_fwd_def)
-apply (intro strip)
-apply (rule exec_instr_in_exec_all)
-apply auto
-done
+ apply (unfold jump_fwd_def)
+ apply (intro strip)
+ apply (rule exec_instr_in_exec_all)
+ apply auto
+ done
lemma jump_fwd_progression_aux:
@@ -187,17 +187,17 @@
jump_fwd G C S hp lvars os0 os1 instr instrs0;
{G, C, S} \<turnstile> {hp, os1, lvars} >- instrs1 \<rightarrow> {hp2, os2, lvars2} \<rbrakk>
\<Longrightarrow> {G, C, S} \<turnstile> {hp, os0, lvars} >- instrs_comb \<rightarrow> {hp2, os2, lvars2}"
-apply (simp only: progression_def jump_fwd_def)
-apply (intro strip)
-apply (rule_tac ?s1.0 = "Norm(hp, (os1, lvars, C, S, length pre + length instrs0 + 1) # frs)" in exec_all_trans)
-apply (simp only: append_assoc)
-apply (subgoal_tac "pre @ (instr # instrs0 @ instrs1) @ post = pre @ instr # instrs0 @ (instrs1 @ post)")
-apply blast
-apply simp
-apply (erule thin_rl, erule thin_rl)
-apply (drule_tac x="pre @ instr # instrs0" in spec)
-apply (simp add: add.assoc)
-done
+ apply (simp only: progression_def jump_fwd_def)
+ apply (intro strip)
+ apply (rule_tac ?s1.0 = "Norm(hp, (os1, lvars, C, S, length pre + length instrs0 + 1) # frs)" in exec_all_trans)
+ apply (simp only: append_assoc)
+ apply (subgoal_tac "pre @ (instr # instrs0 @ instrs1) @ post = pre @ instr # instrs0 @ (instrs1 @ post)")
+ apply blast
+ apply simp
+ apply (erule thin_rl, erule thin_rl)
+ apply (drule_tac x="pre @ instr # instrs0" in spec)
+ apply (simp add: add.assoc)
+ done
lemma jump_fwd_progression:
@@ -207,10 +207,10 @@
(None, hp, (os1, lvars, C, S, pc + (length instrs0) + 1)#frs);
{G, C, S} \<turnstile> {hp, os1, lvars} >- instrs1 \<rightarrow> {hp2, os2, lvars2} \<rbrakk>
\<Longrightarrow> {G, C, S} \<turnstile> {hp, os0, lvars} >- instrs_comb \<rightarrow> {hp2, os2, lvars2}"
-apply (rule jump_fwd_progression_aux)
-apply assumption
-apply (rule jump_fwd_one_step) apply assumption+
-done
+ apply (rule jump_fwd_progression_aux)
+ apply assumption
+ apply (rule jump_fwd_one_step, assumption+)
+ done
(* note: instrs and instr reversed wrt. jump_fwd *)
@@ -230,11 +230,11 @@
(None, hp, (os1, lvars, C, S, pc)#frs)
\<Longrightarrow>
jump_bwd G C S hp lvars os0 os1 instrs instr"
-apply (unfold jump_bwd_def)
-apply (intro strip)
-apply (rule exec_instr_in_exec_all)
-apply auto
-done
+ apply (unfold jump_bwd_def)
+ apply (intro strip)
+ apply (rule exec_instr_in_exec_all)
+ apply auto
+ done
lemma jump_bwd_progression:
"\<lbrakk> instrs_comb = instrs @ [instr];
@@ -242,14 +242,14 @@
jump_bwd G C S hp1 lvars1 os1 os2 instrs instr;
{G, C, S} \<turnstile> {hp1, os2, lvars1} >- instrs_comb \<rightarrow> {hp3, os3, lvars3} \<rbrakk>
\<Longrightarrow> {G, C, S} \<turnstile> {hp0, os0, lvars0} >- instrs_comb \<rightarrow> {hp3, os3, lvars3}"
-apply (simp only: progression_def jump_bwd_def)
-apply (intro strip)
-apply (rule exec_all_trans, force)
-apply (rule exec_all_trans, force)
-apply (rule exec_all_trans, force)
-apply simp
-apply (rule exec_all_refl)
-done
+ apply (simp only: progression_def jump_bwd_def)
+ apply (intro strip)
+ apply (rule exec_all_trans, force)
+ apply (rule exec_all_trans, force)
+ apply (rule exec_all_trans, force)
+ apply simp
+ apply (rule exec_all_refl)
+ done
(**********************************************************************)
@@ -281,50 +281,52 @@
\<Longrightarrow> \<forall> D.
method (G, C) S = Some (D, rT, mb) \<longrightarrow> (P D S (rT,mb))"
-apply (frule wf_prog_ws_prog [THEN wf_subcls1])
-apply (rule subcls1_induct, assumption, assumption)
+ apply (frule wf_prog_ws_prog [THEN wf_subcls1])
+ apply (rule subcls1_induct, assumption, assumption)
-apply (intro strip)
-apply ((drule spec)+, drule_tac x="Object" in bspec)
-apply (simp add: wf_prog_def ws_prog_def wf_syscls_def)
-apply (subgoal_tac "D=Object") apply simp
-apply (drule mp)
-apply (frule_tac C=Object in method_wf_mdecl)
- apply simp
- apply assumption apply simp apply assumption apply simp
+ apply (intro strip)
+ apply ((drule spec)+, drule_tac x="Object" in bspec)
+ apply (simp add: wf_prog_def ws_prog_def wf_syscls_def)
+ apply (subgoal_tac "D=Object") apply simp
+ apply (drule mp)
+ apply (frule_tac C=Object in method_wf_mdecl)
+ apply simp
+ apply assumption
+ apply simp
+ apply assumption
+ apply simp
-apply (simplesubst method_rec) apply simp
-apply force
-apply simp
-apply (simp only: map_add_def)
-apply (split option.split)
-apply (rule conjI)
-apply force
-apply (intro strip)
-apply (frule_tac
- ?P1.0 = "wf_mdecl wf_mb G Ca" and
- ?P2.0 = "%(S, (Da, rT, mb)). P Da S (rT, mb)" in map_of_map_prop)
-apply (force simp: wf_cdecl_def)
+ apply (simplesubst method_rec)
+ apply simp
+ apply force
+ apply simp
+ apply (simp only: map_add_def)
+ apply (split option.split)
+ apply (rule conjI)
+ apply force
+ apply (intro strip)
+ apply (frule_tac ?P1.0 = "wf_mdecl wf_mb G Ca" and
+ ?P2.0 = "%(S, (Da, rT, mb)). P Da S (rT, mb)" in map_of_map_prop)
+ apply (force simp: wf_cdecl_def)
-apply clarify
+ apply clarify
-apply (simp only: class_def)
-apply (drule map_of_SomeD)+
-apply (frule_tac A="set G" and f=fst in imageI, simp)
-apply blast
-apply simp
-done
+ apply (simp only: class_def)
+ apply (drule map_of_SomeD)+
+ apply (frule_tac A="set G" and f=fst in imageI, simp)
+ apply blast
+ apply simp
+ done
lemma method_preserves_length:
"\<lbrakk> wf_java_prog G; is_class G C;
method (G, C) (mn,pTs) = Some (D, rT, pns, lvars, blk, res)\<rbrakk>
\<Longrightarrow> length pns = length pTs"
-apply (frule_tac
- P="%D (mn,pTs) (rT, pns, lvars, blk, res). length pns = length pTs"
- in method_preserves)
-apply (auto simp: wf_mdecl_def wf_java_mdecl_def)
-done
+ apply (frule_tac P="%D (mn,pTs) (rT, pns, lvars, blk, res). length pns = length pTs"
+ in method_preserves)
+ apply (auto simp: wf_mdecl_def wf_java_mdecl_def)
+ done
(**********************************************************************)
@@ -338,91 +340,84 @@
"wtpd_stmt E c == (E\<turnstile>c \<surd>)"
lemma wtpd_expr_newc: "wtpd_expr E (NewC C) \<Longrightarrow> is_class (prg E) C"
-by (simp only: wtpd_expr_def, erule exE, erule ty_expr.cases, auto)
+ by (simp only: wtpd_expr_def, erule exE, erule ty_expr.cases, auto)
lemma wtpd_expr_cast: "wtpd_expr E (Cast cn e) \<Longrightarrow> (wtpd_expr E e)"
-by (simp only: wtpd_expr_def, erule exE, erule ty_expr.cases, auto)
+ by (simp only: wtpd_expr_def, erule exE, erule ty_expr.cases, auto)
-lemma wtpd_expr_lacc: "\<lbrakk> wtpd_expr (env_of_jmb G C S) (LAcc vn);
- class_sig_defined G C S \<rbrakk>
+lemma wtpd_expr_lacc:
+ "\<lbrakk> wtpd_expr (env_of_jmb G C S) (LAcc vn); class_sig_defined G C S \<rbrakk>
\<Longrightarrow> vn \<in> set (gjmb_plns (gmb G C S)) \<or> vn = This"
-apply (simp only: wtpd_expr_def env_of_jmb_def class_sig_defined_def galldefs)
-apply clarify
-apply (case_tac S)
-apply simp
-apply (erule ty_expr.cases)
-apply (auto dest: map_upds_SomeD map_of_SomeD fst_in_set_lemma)
-apply (drule map_upds_SomeD)
-apply (erule disjE)
- apply assumption
- apply (drule map_of_SomeD) apply (auto dest: fst_in_set_lemma)
-done
+ apply (clarsimp simp: wtpd_expr_def env_of_jmb_def class_sig_defined_def galldefs)
+ apply (case_tac S)
+ apply (erule ty_expr.cases; fastforce dest: map_upds_SomeD map_of_SomeD fst_in_set_lemma)
+ done
lemma wtpd_expr_lass: "wtpd_expr E (vn::=e)
\<Longrightarrow> (vn \<noteq> This) & (wtpd_expr E (LAcc vn)) & (wtpd_expr E e)"
-by (simp only: wtpd_expr_def, erule exE, erule ty_expr.cases, auto)
+ by (simp only: wtpd_expr_def, erule exE, erule ty_expr.cases, auto)
lemma wtpd_expr_facc: "wtpd_expr E ({fd}a..fn)
\<Longrightarrow> (wtpd_expr E a)"
-by (simp only: wtpd_expr_def, erule exE, erule ty_expr.cases, auto)
+ by (simp only: wtpd_expr_def, erule exE, erule ty_expr.cases, auto)
lemma wtpd_expr_fass: "wtpd_expr E ({fd}a..fn:=v)
\<Longrightarrow> (wtpd_expr E ({fd}a..fn)) & (wtpd_expr E v)"
-by (simp only: wtpd_expr_def, erule exE, erule ty_expr.cases, auto)
+ by (simp only: wtpd_expr_def, erule exE, erule ty_expr.cases, auto)
lemma wtpd_expr_binop: "wtpd_expr E (BinOp bop e1 e2)
\<Longrightarrow> (wtpd_expr E e1) & (wtpd_expr E e2)"
-by (simp only: wtpd_expr_def, erule exE, erule ty_expr.cases, auto)
+ by (simp only: wtpd_expr_def, erule exE, erule ty_expr.cases, auto)
lemma wtpd_exprs_cons: "wtpd_exprs E (e # es)
\<Longrightarrow> (wtpd_expr E e) & (wtpd_exprs E es)"
-by (simp only: wtpd_exprs_def wtpd_expr_def, erule exE, erule ty_exprs.cases, auto)
+ by (simp only: wtpd_exprs_def wtpd_expr_def, erule exE, erule ty_exprs.cases, auto)
lemma wtpd_stmt_expr: "wtpd_stmt E (Expr e) \<Longrightarrow> (wtpd_expr E e)"
-by (simp only: wtpd_stmt_def wtpd_expr_def, erule wt_stmt.cases, auto)
+ by (simp only: wtpd_stmt_def wtpd_expr_def, erule wt_stmt.cases, auto)
lemma wtpd_stmt_comp: "wtpd_stmt E (s1;; s2) \<Longrightarrow>
(wtpd_stmt E s1) & (wtpd_stmt E s2)"
-by (simp only: wtpd_stmt_def wtpd_expr_def, erule wt_stmt.cases, auto)
+ by (simp only: wtpd_stmt_def wtpd_expr_def, erule wt_stmt.cases, auto)
lemma wtpd_stmt_cond: "wtpd_stmt E (If(e) s1 Else s2) \<Longrightarrow>
(wtpd_expr E e) & (wtpd_stmt E s1) & (wtpd_stmt E s2)
& (E\<turnstile>e::PrimT Boolean)"
-by (simp only: wtpd_stmt_def wtpd_expr_def, erule wt_stmt.cases, auto)
+ by (simp only: wtpd_stmt_def wtpd_expr_def, erule wt_stmt.cases, auto)
lemma wtpd_stmt_loop: "wtpd_stmt E (While(e) s) \<Longrightarrow>
(wtpd_expr E e) & (wtpd_stmt E s) & (E\<turnstile>e::PrimT Boolean)"
-by (simp only: wtpd_stmt_def wtpd_expr_def, erule wt_stmt.cases, auto)
+ by (simp only: wtpd_stmt_def wtpd_expr_def, erule wt_stmt.cases, auto)
lemma wtpd_expr_call: "wtpd_expr E ({C}a..mn({pTs'}ps))
\<Longrightarrow> (wtpd_expr E a) & (wtpd_exprs E ps)
& (length ps = length pTs') & (E\<turnstile>a::Class C)
& (\<exists> pTs md rT.
E\<turnstile>ps[::]pTs & max_spec (prg E) C (mn, pTs) = {((md,rT),pTs')})"
-apply (simp only: wtpd_expr_def wtpd_exprs_def)
-apply (erule exE)
-apply (ind_cases "E \<turnstile> {C}a..mn( {pTs'}ps) :: T" for T)
-apply (auto simp: max_spec_preserves_length)
-done
+ apply (simp only: wtpd_expr_def wtpd_exprs_def)
+ apply (erule exE)
+ apply (ind_cases "E \<turnstile> {C}a..mn( {pTs'}ps) :: T" for T)
+ apply (auto simp: max_spec_preserves_length)
+ done
lemma wtpd_blk:
"\<lbrakk> method (G, D) (md, pTs) = Some (D, rT, (pns, lvars, blk, res));
wf_prog wf_java_mdecl G; is_class G D \<rbrakk>
\<Longrightarrow> wtpd_stmt (env_of_jmb G D (md, pTs)) blk"
-apply (simp add: wtpd_stmt_def env_of_jmb_def)
-apply (frule_tac P="%D (md, pTs) (rT, (pns, lvars, blk, res)). (G, map_of lvars(pns[\<mapsto>]pTs)(This\<mapsto>Class D)) \<turnstile> blk \<surd> " in method_preserves)
-apply (auto simp: wf_mdecl_def wf_java_mdecl_def)
-done
+ apply (simp add: wtpd_stmt_def env_of_jmb_def)
+ apply (frule_tac P="%D (md, pTs) (rT, (pns, lvars, blk, res)). (G, map_of lvars(pns[\<mapsto>]pTs)(This\<mapsto>Class D)) \<turnstile> blk \<surd> " in method_preserves)
+ apply (auto simp: wf_mdecl_def wf_java_mdecl_def)
+ done
lemma wtpd_res:
"\<lbrakk> method (G, D) (md, pTs) = Some (D, rT, (pns, lvars, blk, res));
wf_prog wf_java_mdecl G; is_class G D \<rbrakk>
\<Longrightarrow> wtpd_expr (env_of_jmb G D (md, pTs)) res"
-apply (simp add: wtpd_expr_def env_of_jmb_def)
-apply (frule_tac P="%D (md, pTs) (rT, (pns, lvars, blk, res)). \<exists>T. (G, map_of lvars(pns[\<mapsto>]pTs)(This\<mapsto>Class D)) \<turnstile> res :: T " in method_preserves)
-apply (auto simp: wf_mdecl_def wf_java_mdecl_def)
-done
+ apply (simp add: wtpd_expr_def env_of_jmb_def)
+ apply (frule_tac P="%D (md, pTs) (rT, (pns, lvars, blk, res)). \<exists>T. (G, map_of lvars(pns[\<mapsto>]pTs)(This\<mapsto>Class D)) \<turnstile> res :: T " in method_preserves)
+ apply (auto simp: wf_mdecl_def wf_java_mdecl_def)
+ done
(**********************************************************************)
@@ -431,16 +426,15 @@
(* Is there a more elegant proof? *)
lemma evals_preserves_length:
"G\<turnstile> xs -es[\<succ>]vs-> (None, s) \<Longrightarrow> length es = length vs"
-apply (subgoal_tac
- "\<forall> xs'. (G \<turnstile> xk -xj\<succ>xi-> xh \<longrightarrow> True) &
- (G\<turnstile> xs -es[\<succ>]vs-> xs' \<longrightarrow> (\<exists> s. (xs' = (None, s))) \<longrightarrow>
- length es = length vs) &
- (G \<turnstile> xc -xb-> xa \<longrightarrow> True)")
-apply blast
-apply (rule allI)
-apply (rule Eval.eval_evals_exec.induct)
-apply auto
-done
+ apply (subgoal_tac
+ "\<forall> xs'. (G \<turnstile> xk -xj\<succ>xi-> xh \<longrightarrow> True) &
+ (G\<turnstile> xs -es[\<succ>]vs-> xs' \<longrightarrow> (\<exists> s. (xs' = (None, s))) \<longrightarrow>
+ length es = length vs) &
+ (G \<turnstile> xc -xb-> xa \<longrightarrow> True)")
+ apply blast
+ apply (rule allI)
+ apply (rule Eval.eval_evals_exec.induct; simp)
+ done
(***********************************************************************)
@@ -451,21 +445,22 @@
{hp, (v2 # v1 # os), lvars}
>- [Ifcmpeq 3, LitPush (Bool False), Goto 2, LitPush (Bool True)] \<rightarrow>
{hp, (Bool (v1 = v2) # os), lvars}"
-apply (case_tac "v1 = v2")
+ apply (case_tac "v1 = v2")
-(* case v1 = v2 *)
-apply (rule_tac ?instrs1.0 = "[LitPush (Bool True)]" in jump_fwd_progression)
-apply (auto simp: nat_add_distrib)
-apply (rule progression_one_step) apply simp
+ (* case v1 = v2 *)
+ apply (rule_tac ?instrs1.0 = "[LitPush (Bool True)]" in jump_fwd_progression)
+ apply (auto simp: nat_add_distrib)
+ apply (rule progression_one_step)
+ apply simp
-(* case v1 \<noteq> v2 *)
-apply (rule progression_one_step [THEN HOL.refl [THEN progression_transitive], simplified])
-apply auto
-apply (rule progression_one_step [THEN HOL.refl [THEN progression_transitive], simplified])
-apply auto
-apply (rule_tac ?instrs1.0 = "[]" in jump_fwd_progression)
-apply (auto simp: nat_add_distrib intro: progression_refl)
-done
+ (* case v1 \<noteq> v2 *)
+ apply (rule progression_one_step [THEN HOL.refl [THEN progression_transitive], simplified])
+ apply auto
+ apply (rule progression_one_step [THEN HOL.refl [THEN progression_transitive], simplified])
+ apply auto
+ apply (rule_tac ?instrs1.0 = "[]" in jump_fwd_progression)
+ apply (auto simp: nat_add_distrib intro: progression_refl)
+ done
(**********************************************************************)
@@ -475,28 +470,27 @@
declare split_paired_All [simp del] split_paired_Ex [simp del]
-lemma distinct_method: "\<lbrakk> wf_java_prog G; is_class G C;
- method (G, C) S = Some (D, rT, pns, lvars, blk, res) \<rbrakk> \<Longrightarrow>
+lemma distinct_method:
+ "\<lbrakk> wf_java_prog G; is_class G C; method (G, C) S = Some (D, rT, pns, lvars, blk, res) \<rbrakk> \<Longrightarrow>
distinct (gjmb_plns (gmb G C S))"
-apply (frule method_wf_mdecl [THEN conjunct2], assumption, assumption)
-apply (case_tac S)
-apply (simp add: wf_mdecl_def wf_java_mdecl_def galldefs)
-apply (simp add: unique_def map_of_in_set)
-apply blast
-done
+ apply (frule method_wf_mdecl [THEN conjunct2], assumption, assumption)
+ apply (case_tac S)
+ apply (simp add: wf_mdecl_def wf_java_mdecl_def galldefs)
+ apply (simp add: unique_def map_of_in_set)
+ apply blast
+ done
lemma distinct_method_if_class_sig_defined :
- "\<lbrakk> wf_java_prog G; class_sig_defined G C S \<rbrakk> \<Longrightarrow>
- distinct (gjmb_plns (gmb G C S))"
-by (auto intro: distinct_method simp: class_sig_defined_def)
+ "\<lbrakk> wf_java_prog G; class_sig_defined G C S \<rbrakk> \<Longrightarrow> distinct (gjmb_plns (gmb G C S))"
+ by (auto intro: distinct_method simp: class_sig_defined_def)
lemma method_yields_wf_java_mdecl: "\<lbrakk> wf_java_prog G; is_class G C;
method (G, C) S = Some (D, rT, pns, lvars, blk, res) \<rbrakk> \<Longrightarrow>
wf_java_mdecl G D (S,rT,(pns,lvars,blk,res))"
-apply (frule method_wf_mdecl)
-apply (auto simp: wf_mdecl_def)
-done
+ apply (frule method_wf_mdecl)
+ apply (auto simp: wf_mdecl_def)
+ done
(**********************************************************************)
@@ -511,28 +505,30 @@
{h, os, (prfx @ lvals)}
>- (concat (map (compInit (pns, lvars0, blk, res)) lvars)) \<rightarrow>
{h, os, (prfx @ (map (\<lambda>p. (default_val (snd p))) lvars))}))"
-apply simp
-apply (induct lvars)
-apply (clarsimp, rule progression_refl)
-apply (intro strip)
-apply (case_tac lvals) apply simp
-apply (simp (no_asm_simp) )
+ apply simp
+ apply (induct lvars)
+ apply (clarsimp, rule progression_refl)
+ apply (intro strip)
+ apply (case_tac lvals)
+ apply simp
+ apply (simp (no_asm_simp) )
-apply (rule_tac ?lvars1.0 = "(prfx @ [default_val (snd a)]) @ list" in progression_transitive, rule HOL.refl)
-apply (case_tac a) apply (simp (no_asm_simp) add: compInit_def)
-apply (rule_tac ?instrs0.0 = "[load_default_val b]" in progression_transitive, simp)
-apply (rule progression_one_step)
-apply (simp (no_asm_simp) add: load_default_val_def)
+ apply (rule_tac ?lvars1.0 = "(prfx @ [default_val (snd a)]) @ list" in progression_transitive, rule HOL.refl)
+ apply (case_tac a)
+ apply (simp (no_asm_simp) add: compInit_def)
+ apply (rule_tac ?instrs0.0 = "[load_default_val b]" in progression_transitive, simp)
+ apply (rule progression_one_step)
+ apply (simp (no_asm_simp) add: load_default_val_def)
-apply (rule progression_one_step)
-apply (simp (no_asm_simp))
-apply (rule conjI, simp)+
-apply (simp add: index_of_var2)
-apply (drule_tac x="zs @ [a]" in spec) (* instantiate zs *)
-apply (drule mp, simp)
-apply (drule_tac x="(prfx @ [default_val (snd a)])" in spec) (* instantiate prfx *)
-apply auto
-done
+ apply (rule progression_one_step)
+ apply (simp (no_asm_simp))
+ apply (rule conjI, simp)+
+ apply (simp add: index_of_var2)
+ apply (drule_tac x="zs @ [a]" in spec) (* instantiate zs *)
+ apply (drule mp, simp)
+ apply (drule_tac x="(prfx @ [default_val (snd a)])" in spec) (* instantiate prfx *)
+ apply auto
+ done
lemma progression_lvar_init [rule_format (no_asm)]:
"\<lbrakk> wf_java_prog G; is_class G C;
@@ -544,147 +540,142 @@
{h, os, (a' # pvs @ lvals)}
>- (compInitLvars (pns, lvars, blk, res) lvars) \<rightarrow>
{h, os, (locvars_xstate G C S (Norm (h, init_vars lvars(pns[\<mapsto>]pvs)(This\<mapsto>a'))))})"
-apply (simp only: compInitLvars_def)
-apply (frule method_yields_wf_java_mdecl, assumption, assumption)
+ apply (simp only: compInitLvars_def)
+ apply (frule method_yields_wf_java_mdecl, assumption, assumption)
-apply (simp only: wf_java_mdecl_def)
-apply (subgoal_tac "(\<forall>y\<in>set pns. y \<notin> set (map fst lvars))")
-apply (simp add: init_vars_def locvars_xstate_def locvars_locals_def galldefs unique_def split_def map_of_map_as_map_upd del: map_map)
-apply (intro strip)
-apply (simp (no_asm_simp) only: append_Cons [symmetric])
-apply (rule progression_lvar_init_aux)
-apply (auto simp: unique_def map_of_in_set disjoint_varnames_def)
-done
+ apply (simp only: wf_java_mdecl_def)
+ apply (subgoal_tac "(\<forall>y\<in>set pns. y \<notin> set (map fst lvars))")
+ apply (simp add: init_vars_def locvars_xstate_def locvars_locals_def galldefs unique_def split_def map_of_map_as_map_upd del: map_map)
+ apply (intro strip)
+ apply (simp (no_asm_simp) only: append_Cons [symmetric])
+ apply (rule progression_lvar_init_aux)
+ apply (auto simp: unique_def map_of_in_set disjoint_varnames_def)
+ done
(**********************************************************************)
-lemma state_ok_eval: "\<lbrakk>xs::\<preceq>E; wf_java_prog (prg E); wtpd_expr E e;
- (prg E)\<turnstile>xs -e\<succ>v -> xs'\<rbrakk> \<Longrightarrow> xs'::\<preceq>E"
-apply (simp only: wtpd_expr_def)
-apply (erule exE)
-apply (case_tac xs', case_tac xs)
-apply (auto intro: eval_type_sound [THEN conjunct1])
-done
+lemma state_ok_eval:
+ "\<lbrakk>xs::\<preceq>E; wf_java_prog (prg E); wtpd_expr E e; (prg E)\<turnstile>xs -e\<succ>v -> xs'\<rbrakk> \<Longrightarrow> xs'::\<preceq>E"
+ apply (simp only: wtpd_expr_def)
+ apply (erule exE)
+ apply (case_tac xs', case_tac xs)
+ apply (auto intro: eval_type_sound [THEN conjunct1])
+ done
-lemma state_ok_evals: "\<lbrakk>xs::\<preceq>E; wf_java_prog (prg E); wtpd_exprs E es;
- prg E \<turnstile> xs -es[\<succ>]vs-> xs'\<rbrakk> \<Longrightarrow> xs'::\<preceq>E"
-apply (simp only: wtpd_exprs_def)
-apply (erule exE)
-apply (case_tac xs) apply (case_tac xs')
-apply (auto intro: evals_type_sound [THEN conjunct1])
-done
+lemma state_ok_evals:
+ "\<lbrakk>xs::\<preceq>E; wf_java_prog (prg E); wtpd_exprs E es; prg E \<turnstile> xs -es[\<succ>]vs-> xs'\<rbrakk> \<Longrightarrow> xs'::\<preceq>E"
+ apply (simp only: wtpd_exprs_def)
+ apply (erule exE)
+ apply (case_tac xs)
+ apply (case_tac xs')
+ apply (auto intro: evals_type_sound [THEN conjunct1])
+ done
-lemma state_ok_exec: "\<lbrakk>xs::\<preceq>E; wf_java_prog (prg E); wtpd_stmt E st;
- prg E \<turnstile> xs -st-> xs'\<rbrakk> \<Longrightarrow> xs'::\<preceq>E"
-apply (simp only: wtpd_stmt_def)
-apply (case_tac xs', case_tac xs)
-apply (auto dest: exec_type_sound)
-done
-
+lemma state_ok_exec:
+ "\<lbrakk>xs::\<preceq>E; wf_java_prog (prg E); wtpd_stmt E st; prg E \<turnstile> xs -st-> xs'\<rbrakk> \<Longrightarrow> xs'::\<preceq>E"
+ apply (simp only: wtpd_stmt_def)
+ apply (case_tac xs', case_tac xs)
+ apply (auto dest: exec_type_sound)
+ done
lemma state_ok_init:
"\<lbrakk> wf_java_prog G; (x, h, l)::\<preceq>(env_of_jmb G C S);
is_class G dynT;
method (G, dynT) (mn, pTs) = Some (md, rT, pns, lvars, blk, res);
list_all2 (conf G h) pvs pTs; G,h \<turnstile> a' ::\<preceq> Class md\<rbrakk>
-\<Longrightarrow>
-(np a' x, h, init_vars lvars(pns[\<mapsto>]pvs)(This\<mapsto>a'))::\<preceq>(env_of_jmb G md (mn, pTs))"
-apply (frule wf_prog_ws_prog)
-apply (frule method_in_md [THEN conjunct2], assumption+)
-apply (frule method_yields_wf_java_mdecl, assumption, assumption)
-apply (simp add: env_of_jmb_def gs_def conforms_def split_beta)
-apply (simp add: wf_java_mdecl_def)
-apply (rule conjI)
-apply (rule lconf_ext)
-apply (rule lconf_ext_list)
-apply (rule lconf_init_vars)
-apply (auto dest: Ball_set_table)
-apply (simp add: np_def xconf_raise_if)
-done
+ \<Longrightarrow>
+ (np a' x, h, init_vars lvars(pns[\<mapsto>]pvs)(This\<mapsto>a'))::\<preceq>(env_of_jmb G md (mn, pTs))"
+ apply (frule wf_prog_ws_prog)
+ apply (frule method_in_md [THEN conjunct2], assumption+)
+ apply (frule method_yields_wf_java_mdecl, assumption, assumption)
+ apply (simp add: env_of_jmb_def gs_def conforms_def split_beta)
+ apply (simp add: wf_java_mdecl_def)
+ apply (rule conjI)
+ apply (rule lconf_ext)
+ apply (rule lconf_ext_list)
+ apply (rule lconf_init_vars)
+ apply (auto dest: Ball_set_table)
+ apply (simp add: np_def xconf_raise_if)
+ done
lemma ty_exprs_list_all2 [rule_format (no_asm)]:
"(\<forall> Ts. (E \<turnstile> es [::] Ts) = list_all2 (\<lambda>e T. E \<turnstile> e :: T) es Ts)"
-apply (rule list.induct)
-apply simp
-apply (rule allI)
-apply (rule iffI)
- apply (ind_cases "E \<turnstile> [] [::] Ts" for Ts, assumption)
- apply simp apply (rule WellType.Nil)
-apply (simp add: list_all2_Cons1)
-apply (rule allI)
-apply (rule iffI)
- apply (rename_tac a exs Ts)
- apply (ind_cases "E \<turnstile> a # exs [::] Ts" for a exs Ts) apply blast
+ apply (rule list.induct)
+ apply simp
+ apply (rule allI)
+ apply (rule iffI)
+ apply (ind_cases "E \<turnstile> [] [::] Ts" for Ts, assumption)
+ apply simp apply (rule WellType.Nil)
+ apply (simp add: list_all2_Cons1)
+ apply (rule allI)
+ apply (rule iffI)
+ apply (rename_tac a exs Ts)
+ apply (ind_cases "E \<turnstile> a # exs [::] Ts" for a exs Ts) apply blast
apply (auto intro: WellType.Cons)
-done
+ done
lemma conf_bool: "G,h \<turnstile> v::\<preceq>PrimT Boolean \<Longrightarrow> \<exists> b. v = Bool b"
-apply (simp add: conf_def)
-apply (erule exE)
-apply (case_tac v)
-apply (auto elim: widen.cases)
-done
-
-
-lemma class_expr_is_class: "\<lbrakk>E \<turnstile> e :: Class C; ws_prog (prg E)\<rbrakk>
- \<Longrightarrow> is_class (prg E) C"
-by (case_tac E, auto dest: ty_expr_is_type)
+ apply (simp add: conf_def)
+ apply (erule exE)
+ apply (case_tac v)
+ apply (auto elim: widen.cases)
+ done
lemma max_spec_widen: "max_spec G C (mn, pTs) = {((md,rT),pTs')} \<Longrightarrow>
list_all2 (\<lambda> T T'. G \<turnstile> T \<preceq> T') pTs pTs'"
-by (blast dest: singleton_in_set max_spec2appl_meths appl_methsD)
+ by (blast dest: singleton_in_set max_spec2appl_meths appl_methsD)
lemma eval_conf: "\<lbrakk>G \<turnstile> s -e\<succ>v-> s'; wf_java_prog G; s::\<preceq>E;
E\<turnstile>e::T; gx s' = None; prg E = G \<rbrakk>
\<Longrightarrow> G,gh s'\<turnstile>v::\<preceq>T"
-apply (simp add: gh_def)
-apply (rule_tac x3="fst s" and s3="snd s"and x'3="fst s'"
- in eval_type_sound [THEN conjunct2 [THEN conjunct1 [THEN mp]], simplified])
-apply assumption+
-apply (simp (no_asm_use) add: surjective_pairing [symmetric])
-apply (simp only: surjective_pairing [symmetric])
-apply (auto simp add: gs_def gx_def)
-done
+ apply (simp add: gh_def)
+ apply (rule_tac x3="fst s" and s3="snd s"and x'3="fst s'"
+ in eval_type_sound [THEN conjunct2 [THEN conjunct1 [THEN mp]], simplified])
+ apply assumption+
+ apply (simp (no_asm_use))
+ apply (simp only: surjective_pairing [symmetric])
+ apply (auto simp add: gs_def gx_def)
+ done
lemma evals_preserves_conf:
"\<lbrakk> G\<turnstile> s -es[\<succ>]vs-> s'; G,gh s \<turnstile> t ::\<preceq> T; E \<turnstile>es[::]Ts;
wf_java_prog G; s::\<preceq>E;
prg E = G \<rbrakk> \<Longrightarrow> G,gh s' \<turnstile> t ::\<preceq> T"
-apply (subgoal_tac "gh s\<le>| gh s'")
-apply (frule conf_hext, assumption, assumption)
-apply (frule eval_evals_exec_type_sound [THEN conjunct2 [THEN conjunct1 [THEN mp]]])
-apply (subgoal_tac "G \<turnstile> (gx s, (gh s, gl s)) -es[\<succ>]vs-> (gx s', (gh s', gl s'))")
-apply assumption
-apply (simp add: gx_def gh_def gl_def surjective_pairing [symmetric])
-apply (case_tac E)
-apply (simp add: gx_def gs_def gh_def gl_def surjective_pairing [symmetric])
-done
+ apply (subgoal_tac "gh s\<le>| gh s'")
+ apply (frule conf_hext, assumption, assumption)
+ apply (frule eval_evals_exec_type_sound [THEN conjunct2 [THEN conjunct1 [THEN mp]]])
+ apply (subgoal_tac "G \<turnstile> (gx s, (gh s, gl s)) -es[\<succ>]vs-> (gx s', (gh s', gl s'))")
+ apply assumption
+ apply (simp add: gx_def gh_def gl_def)
+ apply (case_tac E)
+ apply (simp add: gx_def gs_def gh_def gl_def)
+ done
-lemma eval_of_class: "\<lbrakk> G \<turnstile> s -e\<succ>a'-> s'; E \<turnstile> e :: Class C;
- wf_java_prog G; s::\<preceq>E; gx s'=None; a' \<noteq> Null; G=prg E\<rbrakk>
+lemma eval_of_class:
+ "\<lbrakk> G \<turnstile> s -e\<succ>a'-> s'; E \<turnstile> e :: Class C; wf_java_prog G; s::\<preceq>E; gx s'=None; a' \<noteq> Null; G=prg E\<rbrakk>
\<Longrightarrow> (\<exists> lc. a' = Addr lc)"
-apply (case_tac s, case_tac s', simp)
-apply (frule eval_type_sound, (simp add: gs_def)+)
-apply (case_tac a')
-apply (auto simp: conf_def)
-done
+ apply (case_tac s, case_tac s', simp)
+ apply (frule eval_type_sound, (simp add: gs_def)+)
+ apply (case_tac a')
+ apply (auto simp: conf_def)
+ done
lemma dynT_subcls:
"\<lbrakk> a' \<noteq> Null; G,h\<turnstile>a'::\<preceq> Class C; dynT = fst (the (h (the_Addr a')));
is_class G dynT; ws_prog G \<rbrakk> \<Longrightarrow> G\<turnstile>dynT \<preceq>C C"
-apply (case_tac "C = Object")
-apply (simp, rule subcls_C_Object, assumption+)
-apply simp
-apply (frule non_np_objD, auto)
-done
+ apply (case_tac "C = Object")
+ apply (simp, rule subcls_C_Object, assumption+)
+ apply simp
+ apply (frule non_np_objD, auto)
+ done
lemma method_defined: "\<lbrakk>
@@ -693,15 +684,13 @@
a' \<noteq> Null; G,h\<turnstile>a'::\<preceq> Class C; a = the_Addr a';
\<exists>pTsa md rT. max_spec G C (mn, pTsa) = {((md, rT), pTs)} \<rbrakk>
\<Longrightarrow> (method (G, dynT) (mn, pTs)) = Some m"
-apply (erule exE)+
-apply (drule singleton_in_set, drule max_spec2appl_meths)
-apply (simp add: appl_methds_def)
-apply ((erule exE)+, (erule conjE)+, (erule exE)+)
-apply (drule widen_methd)
-apply assumption
-apply (rule dynT_subcls) apply assumption+ apply simp apply simp
-apply (erule exE)+ apply simp
-done
+ apply (erule exE)+
+ apply (drule singleton_in_set, drule max_spec2appl_meths)
+ apply (simp add: appl_methds_def)
+ apply (elim exE conjE)
+ apply (drule widen_methd)
+ apply (auto intro!: dynT_subcls)
+ done
@@ -744,476 +733,515 @@
{gh xs, os, (locvars_xstate G CL S xs)}
>- (compStmt (gmb G CL S) st) \<rightarrow>
{gh xs', os, (locvars_xstate G CL S xs')})))"
-apply (rule Eval.eval_evals_exec.induct)
+ apply (rule Eval.eval_evals_exec.induct)
-(* case XcptE *)
-apply simp
+ (* case XcptE *)
+ apply simp
-(* case NewC *)
-apply clarify
-apply (frule wf_prog_ws_prog [THEN wf_subcls1]) (* establish wf ((subcls1 G)^-1) *)
-apply (simp add: c_hupd_hp_invariant)
-apply (rule progression_one_step)
-apply (rotate_tac 1, drule sym) (* reverse equation (a, None) = new_Addr (fst s) *)
-apply (simp add: locvars_xstate_def locvars_locals_def comp_fields)
+ (* case NewC *)
+ apply clarify
+ apply (frule wf_prog_ws_prog [THEN wf_subcls1]) (* establish wf ((subcls1 G)^-1) *)
+ apply (simp add: c_hupd_hp_invariant)
+ apply (rule progression_one_step)
+ apply (rotate_tac 1, drule sym) (* reverse equation (a, None) = new_Addr (fst s) *)
+ apply (simp add: locvars_xstate_def locvars_locals_def comp_fields)
-(* case Cast *)
-apply (intro allI impI)
-apply simp
-apply (frule raise_if_NoneD)
-apply (frule wtpd_expr_cast)
-apply simp
-apply (rule_tac ?instrs0.0 = "(compExpr (gmb G CL S) e)" in progression_transitive, simp)
-apply blast
-apply (rule progression_one_step)
-apply (simp add: raise_system_xcpt_def gh_def comp_cast_ok)
+ (* case Cast *)
+ apply (intro allI impI)
+ apply simp
+ apply (frule raise_if_NoneD)
+ apply (frule wtpd_expr_cast)
+ apply simp
+ apply (rule_tac ?instrs0.0 = "(compExpr (gmb G CL S) e)" in progression_transitive, simp)
+ apply blast
+ apply (rule progression_one_step)
+ apply (simp add: raise_system_xcpt_def gh_def comp_cast_ok)
-(* case Lit *)
-apply simp
-apply (intro strip)
-apply (rule progression_one_step)
-apply simp
+ (* case Lit *)
+ apply simp
+ apply (intro strip)
+ apply (rule progression_one_step)
+ apply simp
+
+
+ (* case BinOp *)
+ apply (intro allI impI)
+ apply (frule_tac xs=s1 in eval_xcpt, assumption) (* establish (gx s1 = None) *)
+ apply (frule wtpd_expr_binop)
+ (* establish (s1::\<preceq> \<dots>) *)
+ apply (frule_tac e=e1 in state_ok_eval) apply (simp (no_asm_simp))
+ apply simp
+ apply (simp (no_asm_use) only: env_of_jmb_fst)
-(* case BinOp *)
-apply (intro allI impI)
-apply (frule_tac xs=s1 in eval_xcpt, assumption) (* establish (gx s1 = None) *)
-apply (frule wtpd_expr_binop)
-(* establish (s1::\<preceq> \<dots>) *)
-apply (frule_tac e=e1 in state_ok_eval) apply (simp (no_asm_simp)) apply simp apply (simp (no_asm_use) only: env_of_jmb_fst)
-
-
-apply (simp (no_asm_use) only: compExpr.simps compExprs.simps)
-apply (rule_tac ?instrs0.0 = "compExpr (gmb G CL S) e1" in progression_transitive, simp) apply blast
-apply (rule_tac ?instrs0.0 = "compExpr (gmb G CL S) e2" in progression_transitive, simp) apply blast
-apply (case_tac bop)
- (*subcase bop = Eq *) apply simp apply (rule progression_Eq)
- (*subcase bop = Add *) apply simp apply (rule progression_one_step) apply simp
+ apply (simp (no_asm_use) only: compExpr.simps compExprs.simps)
+ apply (rule_tac ?instrs0.0 = "compExpr (gmb G CL S) e1" in progression_transitive, simp) apply blast
+ apply (rule_tac ?instrs0.0 = "compExpr (gmb G CL S) e2" in progression_transitive, simp) apply blast
+ apply (case_tac bop)
+ (*subcase bop = Eq *)
+ apply simp
+ apply (rule progression_Eq)
+ (*subcase bop = Add *)
+ apply simp
+ apply (rule progression_one_step)
+ apply simp
-(* case LAcc *)
-apply simp
-apply (intro strip)
-apply (rule progression_one_step)
-apply (simp add: locvars_xstate_def locvars_locals_def)
-apply (frule wtpd_expr_lacc)
-apply assumption
-apply (simp add: gl_def)
-apply (erule select_at_index)
+ (* case LAcc *)
+ apply simp
+ apply (intro strip)
+ apply (rule progression_one_step)
+ apply (simp add: locvars_xstate_def locvars_locals_def)
+ apply (frule wtpd_expr_lacc)
+ apply assumption
+ apply (simp add: gl_def)
+ apply (erule select_at_index)
-(* case LAss *)
-apply (intro allI impI)
-apply (frule wtpd_expr_lass, erule conjE, erule conjE)
-apply simp
+ (* case LAss *)
+ apply (intro allI impI)
+ apply (frule wtpd_expr_lass, erule conjE, erule conjE)
+ apply simp
-apply (rule_tac ?instrs0.0 = "(compExpr (gmb G CL S) e)" in progression_transitive, rule HOL.refl)
-apply blast
+ apply (rule_tac ?instrs0.0 = "(compExpr (gmb G CL S) e)" in progression_transitive, rule HOL.refl)
+ apply blast
-apply (rule_tac ?instrs0.0 = "[Dup]" in progression_transitive, simp)
-apply (rule progression_one_step)
-apply (simp add: gh_def)
-apply simp
-apply (rule progression_one_step)
-apply (simp add: gh_def)
-(* the following falls out of the general scheme *)
-apply (frule wtpd_expr_lacc) apply assumption
-apply (rule update_at_index)
-apply (rule distinct_method_if_class_sig_defined) apply assumption
-apply assumption apply simp apply assumption
+ apply (rule_tac ?instrs0.0 = "[Dup]" in progression_transitive, simp)
+ apply (rule progression_one_step)
+ apply (simp add: gh_def)
+ apply simp
+ apply (rule progression_one_step)
+ apply (simp add: gh_def)
+ (* the following falls out of the general scheme *)
+ apply (frule wtpd_expr_lacc) apply assumption
+ apply (rule update_at_index)
+ apply (rule distinct_method_if_class_sig_defined)
+ apply assumption
+ apply assumption
+ apply simp
+ apply assumption
-(* case FAcc *)
-apply (intro allI impI)
- (* establish x1 = None \<and> a' \<noteq> Null *)
-apply (simp (no_asm_use) only: gx_conv, frule np_NoneD)
-apply (frule wtpd_expr_facc)
+ (* case FAcc *)
+ apply (intro allI impI)
+ (* establish x1 = None \<and> a' \<noteq> Null *)
+ apply (simp (no_asm_use) only: gx_conv, frule np_NoneD)
+ apply (frule wtpd_expr_facc)
-apply (simp (no_asm_use) only: compExpr.simps compExprs.simps)
-apply (rule_tac ?instrs0.0 = "(compExpr (gmb G CL S) e)" in progression_transitive, rule HOL.refl)
-apply blast
-apply (rule progression_one_step)
-apply (simp add: gh_def)
-apply (case_tac "(the (fst s1 (the_Addr a')))")
-apply (simp add: raise_system_xcpt_def)
+ apply (simp (no_asm_use) only: compExpr.simps compExprs.simps)
+ apply (rule_tac ?instrs0.0 = "(compExpr (gmb G CL S) e)" in progression_transitive, rule HOL.refl)
+ apply blast
+ apply (rule progression_one_step)
+ apply (simp add: gh_def)
+ apply (case_tac "(the (fst s1 (the_Addr a')))")
+ apply (simp add: raise_system_xcpt_def)
-(* case FAss *)
-apply (intro allI impI)
-apply (frule wtpd_expr_fass) apply (erule conjE) apply (frule wtpd_expr_facc)
-apply (simp only: c_hupd_xcpt_invariant) (* establish x2 = None *)
- (* establish x1 = None and a' \<noteq> Null *)
-apply (frule_tac xs="(np a' x1, s1)" in eval_xcpt)
-apply (simp only: gx_conv, simp only: gx_conv, frule np_NoneD, erule conjE)
+ (* case FAss *)
+ apply (intro allI impI)
+ apply (frule wtpd_expr_fass) apply (erule conjE) apply (frule wtpd_expr_facc)
+ apply (simp only: c_hupd_xcpt_invariant) (* establish x2 = None *)
+ (* establish x1 = None and a' \<noteq> Null *)
+ apply (frule_tac xs="(np a' x1, s1)" in eval_xcpt)
+ apply (simp only: gx_conv, simp only: gx_conv, frule np_NoneD, erule conjE)
- (* establish ((Norm s1)::\<preceq> \<dots>) *)
-apply (frule_tac e=e1 in state_ok_eval) apply (simp (no_asm_simp) only: env_of_jmb_fst)
- apply assumption apply (simp (no_asm_use) only: env_of_jmb_fst)
+ (* establish ((Norm s1)::\<preceq> \<dots>) *)
+ apply (frule_tac e=e1 in state_ok_eval)
+ apply (simp (no_asm_simp) only: env_of_jmb_fst)
+ apply assumption
+ apply (simp (no_asm_use) only: env_of_jmb_fst)
-apply (simp only: compExpr.simps compExprs.simps)
+ apply (simp only: compExpr.simps compExprs.simps)
-apply (rule_tac ?instrs0.0 = "(compExpr (gmb G CL S) e1)" in progression_transitive, rule HOL.refl)
-apply fast (* blast does not seem to work - why? *)
-apply (rule_tac ?instrs0.0 = "(compExpr (gmb G CL S) e2)" in progression_transitive, rule HOL.refl)
-apply fast
-apply (rule_tac ?instrs0.0 = "[Dup_x1]" and ?instrs1.0 = "[Putfield fn T]" in progression_transitive, simp)
+ apply (rule_tac ?instrs0.0 = "(compExpr (gmb G CL S) e1)" in progression_transitive, rule HOL.refl)
+ apply fast (* blast does not seem to work - why? *)
+ apply (rule_tac ?instrs0.0 = "(compExpr (gmb G CL S) e2)" in progression_transitive, rule HOL.refl)
+ apply fast
+ apply (rule_tac ?instrs0.0 = "[Dup_x1]" and ?instrs1.0 = "[Putfield fn T]" in progression_transitive, simp)
- (* Dup_x1 *)
- apply (rule progression_one_step)
- apply (simp add: gh_def)
+ (* Dup_x1 *)
+ apply (rule progression_one_step)
+ apply (simp add: gh_def)
- (* Putfield \<longrightarrow> still looks nasty*)
- apply (rule progression_one_step)
- apply simp
- apply (case_tac "(the (fst s2 (the_Addr a')))")
- apply (simp add: c_hupd_hp_invariant)
- apply (case_tac s2)
- apply (simp add: c_hupd_conv raise_system_xcpt_def)
- apply (rule locvars_xstate_par_dep, rule HOL.refl)
+ (* Putfield \<longrightarrow> still looks nasty*)
+ apply (rule progression_one_step)
+ apply simp
+ apply (case_tac "(the (fst s2 (the_Addr a')))")
+ apply (simp add: c_hupd_hp_invariant)
+ apply (case_tac s2)
+ apply (simp add: c_hupd_conv raise_system_xcpt_def)
+ apply (rule locvars_xstate_par_dep, rule HOL.refl)
-defer (* method call *)
+ defer (* method call *)
-(* case XcptEs *)
-apply simp
+ (* case XcptEs *)
+ apply simp
-(* case Nil *)
-apply simp
-apply (intro strip)
-apply (rule progression_refl)
+ (* case Nil *)
+ apply simp
+ apply (intro strip)
+ apply (rule progression_refl)
-(* case Cons *)
-apply (intro allI impI)
-apply (frule_tac xs=s1 in evals_xcpt, simp only: gx_conv) (* establish gx s1 = None *)
-apply (frule wtpd_exprs_cons)
- (* establish ((Norm s0)::\<preceq> \<dots>) *)
-apply (frule_tac e=e in state_ok_eval) apply (simp (no_asm_simp) only: env_of_jmb_fst) apply simp apply (simp (no_asm_use) only: env_of_jmb_fst)
+ (* case Cons *)
+ apply (intro allI impI)
+ apply (frule_tac xs=s1 in evals_xcpt, simp only: gx_conv) (* establish gx s1 = None *)
+ apply (frule wtpd_exprs_cons)
+ (* establish ((Norm s0)::\<preceq> \<dots>) *)
+ apply (frule_tac e=e in state_ok_eval)
+ apply (simp (no_asm_simp) only: env_of_jmb_fst)
+ apply simp
+ apply (simp (no_asm_use) only: env_of_jmb_fst)
-apply simp
-apply (rule_tac ?instrs0.0 = "(compExpr (gmb G CL S) e)" in progression_transitive, rule HOL.refl)
-apply fast
-apply fast
+ apply simp
+ apply (rule_tac ?instrs0.0 = "(compExpr (gmb G CL S) e)" in progression_transitive, rule HOL.refl)
+ apply fast
+ apply fast
-(* case Statement: exception *)
-apply simp
+ (* case Statement: exception *)
+ apply simp
-(* case Skip *)
-apply (intro allI impI)
-apply simp
-apply (rule progression_refl)
+ (* case Skip *)
+ apply (intro allI impI)
+ apply simp
+ apply (rule progression_refl)
-(* case Expr *)
-apply (intro allI impI)
-apply (frule wtpd_stmt_expr)
-apply simp
-apply (rule_tac ?instrs0.0 = "(compExpr (gmb G CL S) e)" in progression_transitive, rule HOL.refl)
-apply fast
-apply (rule progression_one_step)
-apply simp
+ (* case Expr *)
+ apply (intro allI impI)
+ apply (frule wtpd_stmt_expr)
+ apply simp
+ apply (rule_tac ?instrs0.0 = "(compExpr (gmb G CL S) e)" in progression_transitive, rule HOL.refl)
+ apply fast
+ apply (rule progression_one_step)
+ apply simp
-(* case Comp *)
-apply (intro allI impI)
-apply (frule_tac xs=s1 in exec_xcpt, assumption) (* establish (gx s1 = None) *)
-apply (frule wtpd_stmt_comp)
+ (* case Comp *)
+ apply (intro allI impI)
+ apply (frule_tac xs=s1 in exec_xcpt, assumption) (* establish (gx s1 = None) *)
+ apply (frule wtpd_stmt_comp)
- (* establish (s1::\<preceq> \<dots>) *)
-apply (frule_tac st=c1 in state_ok_exec) apply (simp (no_asm_simp) only: env_of_jmb_fst) apply simp apply (simp (no_asm_use) only: env_of_jmb_fst)
+ (* establish (s1::\<preceq> \<dots>) *)
+ apply (frule_tac st=c1 in state_ok_exec)
+ apply (simp (no_asm_simp) only: env_of_jmb_fst)
+ apply simp apply (simp (no_asm_use) only: env_of_jmb_fst)
-apply simp
-apply (rule_tac ?instrs0.0 = "(compStmt (gmb G CL S) c1)" in progression_transitive, rule HOL.refl)
-apply fast
-apply fast
+ apply simp
+ apply (rule_tac ?instrs0.0 = "(compStmt (gmb G CL S) c1)" in progression_transitive, rule HOL.refl)
+ apply fast
+ apply fast
-(* case Cond *)
-apply (intro allI impI)
-apply (frule_tac xs=s1 in exec_xcpt, assumption) (* establish (gx s1 = None) *)
-apply (frule wtpd_stmt_cond, (erule conjE)+)
-(* establish (s1::\<preceq> \<dots>) *)
-apply (frule_tac e=e in state_ok_eval)
-apply (simp (no_asm_simp) only: env_of_jmb_fst)
-apply assumption
-apply (simp (no_asm_use) only: env_of_jmb_fst)
-(* establish G,gh s1\<turnstile>v::\<preceq>PrimT Boolean *)
-apply (frule eval_conf, assumption+, rule env_of_jmb_fst)
-apply (frule conf_bool) (* establish \<exists>b. v = Bool b *)
-apply (erule exE)
+ (* case Cond *)
+ apply (intro allI impI)
+ apply (frule_tac xs=s1 in exec_xcpt, assumption) (* establish (gx s1 = None) *)
+ apply (frule wtpd_stmt_cond, (erule conjE)+)
+ (* establish (s1::\<preceq> \<dots>) *)
+ apply (frule_tac e=e in state_ok_eval)
+ apply (simp (no_asm_simp) only: env_of_jmb_fst)
+ apply assumption
+ apply (simp (no_asm_use) only: env_of_jmb_fst)
+ (* establish G,gh s1\<turnstile>v::\<preceq>PrimT Boolean *)
+ apply (frule eval_conf, assumption+, rule env_of_jmb_fst)
+ apply (frule conf_bool) (* establish \<exists>b. v = Bool b *)
+ apply (erule exE)
-apply simp
-apply (rule_tac ?instrs0.0 = "[LitPush (Bool False)]" in progression_transitive, simp (no_asm_simp))
-apply (rule progression_one_step, simp)
-
-apply (rule_tac ?instrs0.0 = "compExpr (gmb G CL S) e" in progression_transitive, rule HOL.refl)
-apply fast
+ apply simp
+ apply (rule_tac ?instrs0.0 = "[LitPush (Bool False)]" in progression_transitive, simp (no_asm_simp))
+ apply (rule progression_one_step, simp)
-apply (case_tac b)
- (* case b= True *)
-apply simp
-apply (rule_tac ?instrs0.0 = "[Ifcmpeq (2 + int (length (compStmt (gmb G CL S) c1)))]" in progression_transitive, simp)
-apply (rule progression_one_step) apply simp
-apply (rule_tac ?instrs0.0 = "(compStmt (gmb G CL S) c1)" in progression_transitive, simp)
-apply fast
-apply (rule_tac ?instrs1.0 = "[]" in jump_fwd_progression)
-apply (simp)
-apply simp apply (rule conjI, simp) apply (simp add: nat_add_distrib)
-apply (rule progression_refl)
+ apply (rule_tac ?instrs0.0 = "compExpr (gmb G CL S) e" in progression_transitive, rule HOL.refl)
+ apply fast
- (* case b= False *)
-apply simp
-apply (rule_tac ?instrs1.0 = "compStmt (gmb G CL S) c2" in jump_fwd_progression)
-apply (simp)
-apply (simp, rule conjI, rule HOL.refl, simp add: nat_add_distrib)
-apply fast
+ apply (case_tac b)
+ (* case b= True *)
+ apply simp
+ apply (rule_tac ?instrs0.0 = "[Ifcmpeq (2 + int (length (compStmt (gmb G CL S) c1)))]" in progression_transitive, simp)
+ apply (rule progression_one_step)
+ apply simp
+ apply (rule_tac ?instrs0.0 = "(compStmt (gmb G CL S) c1)" in progression_transitive, simp)
+ apply fast
+ apply (rule_tac ?instrs1.0 = "[]" in jump_fwd_progression)
+ apply (simp)
+ apply simp
+ apply (rule conjI, simp)
+ apply (simp add: nat_add_distrib)
+ apply (rule progression_refl)
-(* case exit Loop *)
-apply (intro allI impI)
-apply (frule wtpd_stmt_loop, (erule conjE)+)
-
-(* establish G,gh s1\<turnstile>v::\<preceq>PrimT Boolean *)
-apply (frule eval_conf, assumption+, rule env_of_jmb_fst)
-apply (frule conf_bool) (* establish \<exists>b. v = Bool b *)
-apply (erule exE)
-apply (case_tac b)
+ (* case b= False *)
+ apply simp
+ apply (rule_tac ?instrs1.0 = "compStmt (gmb G CL S) c2" in jump_fwd_progression)
+ apply (simp)
+ apply (simp, rule conjI, rule HOL.refl, simp add: nat_add_distrib)
+ apply fast
- (* case b= True \<longrightarrow> contradiction *)
-apply simp
+ (* case exit Loop *)
+ apply (intro allI impI)
+ apply (frule wtpd_stmt_loop, (erule conjE)+)
- (* case b= False *)
-apply simp
+ (* establish G,gh s1\<turnstile>v::\<preceq>PrimT Boolean *)
+ apply (frule eval_conf, assumption+, rule env_of_jmb_fst)
+ apply (frule conf_bool) (* establish \<exists>b. v = Bool b *)
+ apply (erule exE)
+ apply (case_tac b)
+
+ (* case b= True \<longrightarrow> contradiction *)
+ apply simp
-apply (rule_tac ?instrs0.0 = "[LitPush (Bool False)]" in progression_transitive, simp (no_asm_simp))
-apply (rule progression_one_step)
- apply simp
+ (* case b= False *)
+ apply simp
+
+ apply (rule_tac ?instrs0.0 = "[LitPush (Bool False)]" in progression_transitive, simp (no_asm_simp))
+ apply (rule progression_one_step)
+ apply simp
-apply (rule_tac ?instrs0.0 = "compExpr (gmb G CL S) e" in progression_transitive, rule HOL.refl)
-apply fast
-apply (rule_tac ?instrs1.0 = "[]" in jump_fwd_progression)
-apply (simp)
-apply (simp, rule conjI, rule HOL.refl, simp add: nat_add_distrib)
-apply (rule progression_refl)
+ apply (rule_tac ?instrs0.0 = "compExpr (gmb G CL S) e" in progression_transitive, rule HOL.refl)
+ apply fast
+ apply (rule_tac ?instrs1.0 = "[]" in jump_fwd_progression)
+ apply (simp)
+ apply (simp, rule conjI, rule HOL.refl, simp add: nat_add_distrib)
+ apply (rule progression_refl)
-(* case continue Loop *)
-apply (intro allI impI)
-apply (frule_tac xs=s2 in exec_xcpt, assumption) (* establish (gx s2 = None) *)
-apply (frule_tac xs=s1 in exec_xcpt, assumption) (* establish (gx s1 = None) *)
-apply (frule wtpd_stmt_loop, (erule conjE)+)
-
-(* establish (s1::\<preceq> \<dots>) *)
-apply (frule_tac e=e in state_ok_eval) apply (simp (no_asm_simp) only: env_of_jmb_fst) apply simp apply (simp (no_asm_use) only: env_of_jmb_fst)
-(* establish (s2::\<preceq> \<dots>) *)
-apply (frule_tac xs=s1 and st=c in state_ok_exec)
-apply (simp (no_asm_simp) only: env_of_jmb_fst) apply assumption apply (simp (no_asm_use) only: env_of_jmb_fst)
+ (* case continue Loop *)
+ apply (intro allI impI)
+ apply (frule_tac xs=s2 in exec_xcpt, assumption) (* establish (gx s2 = None) *)
+ apply (frule_tac xs=s1 in exec_xcpt, assumption) (* establish (gx s1 = None) *)
+ apply (frule wtpd_stmt_loop, (erule conjE)+)
-(* establish G,gh s1\<turnstile>v::\<preceq>PrimT Boolean *)
-apply (frule eval_conf, assumption+, rule env_of_jmb_fst)
-apply (frule conf_bool) (* establish \<exists>b. v = Bool b *)
-apply (erule exE)
+ (* establish (s1::\<preceq> \<dots>) *)
+ apply (frule_tac e=e in state_ok_eval)
+ apply (simp (no_asm_simp) only: env_of_jmb_fst)
+ apply simp
+ apply (simp (no_asm_use) only: env_of_jmb_fst)
+ (* establish (s2::\<preceq> \<dots>) *)
+ apply (frule_tac xs=s1 and st=c in state_ok_exec)
+ apply (simp (no_asm_simp) only: env_of_jmb_fst)
+ apply assumption
+ apply (simp (no_asm_use) only: env_of_jmb_fst)
-apply simp
-apply (rule jump_bwd_progression)
-apply simp
+ (* establish G,gh s1\<turnstile>v::\<preceq>PrimT Boolean *)
+ apply (frule eval_conf, assumption+, rule env_of_jmb_fst)
+ apply (frule conf_bool) (* establish \<exists>b. v = Bool b *)
+ apply (erule exE)
-apply (rule_tac ?instrs0.0 = "[LitPush (Bool False)]" in progression_transitive, simp (no_asm_simp))
-apply (rule progression_one_step)
- apply simp
+ apply simp
+ apply (rule jump_bwd_progression)
+ apply simp
+
+ apply (rule_tac ?instrs0.0 = "[LitPush (Bool False)]" in progression_transitive, simp (no_asm_simp))
+ apply (rule progression_one_step)
+ apply simp
-apply (rule_tac ?instrs0.0 = "compExpr (gmb G CL S) e" in progression_transitive, rule HOL.refl)
-apply fast
+ apply (rule_tac ?instrs0.0 = "compExpr (gmb G CL S) e" in progression_transitive, rule HOL.refl)
+ apply fast
-apply (case_tac b)
- (* case b= True *)
-apply simp
+ apply (case_tac b)
+ (* case b= True *)
+ apply simp
-apply (rule_tac ?instrs0.0 = "[Ifcmpeq (2 + int (length (compStmt (gmb G CL S) c)))]" in progression_transitive, simp)
-apply (rule progression_one_step) apply simp
-apply fast
+ apply (rule_tac ?instrs0.0 = "[Ifcmpeq (2 + int (length (compStmt (gmb G CL S) c)))]" in progression_transitive, simp)
+ apply (rule progression_one_step)
+ apply simp
+ apply fast
- (* case b= False \<longrightarrow> contradiction*)
-apply simp
+ (* case b= False \<longrightarrow> contradiction*)
+ apply simp
-apply (rule jump_bwd_one_step)
-apply simp
-apply blast
+ apply (rule jump_bwd_one_step)
+ apply simp
+ apply blast
-(*****)
-(* case method call *)
+ (*****)
+ (* case method call *)
-apply (intro allI impI)
+ apply (intro allI impI)
-apply (frule_tac xs=s3 in eval_xcpt, simp only: gx_conv) (* establish gx s3 = None *)
-apply (frule exec_xcpt, assumption, simp (no_asm_use) only: gx_conv, frule np_NoneD) (* establish x = None \<and> a' \<noteq> Null *)
-apply (frule evals_xcpt, simp only: gx_conv) (* establish gx s1 = None *)
+ apply (frule_tac xs=s3 in eval_xcpt, simp only: gx_conv) (* establish gx s3 = None *)
+ apply (frule exec_xcpt, assumption, simp (no_asm_use) only: gx_conv, frule np_NoneD) (* establish x = None \<and> a' \<noteq> Null *)
+ apply (frule evals_xcpt, simp only: gx_conv) (* establish gx s1 = None *)
-apply (frule wtpd_expr_call, (erule conjE)+)
+ apply (frule wtpd_expr_call, (erule conjE)+)
-(* assumptions about state_ok and is_class *)
+ (* assumptions about state_ok and is_class *)
-(* establish s1::\<preceq> (env_of_jmb G CL S) *)
-apply (frule_tac xs="Norm s0" and e=e in state_ok_eval)
-apply (simp (no_asm_simp) only: env_of_jmb_fst, assumption, simp (no_asm_use) only: env_of_jmb_fst)
+ (* establish s1::\<preceq> (env_of_jmb G CL S) *)
+ apply (frule_tac xs="Norm s0" and e=e in state_ok_eval)
+ apply (simp (no_asm_simp) only: env_of_jmb_fst, assumption, simp (no_asm_use) only: env_of_jmb_fst)
-(* establish (x, h, l)::\<preceq>(env_of_jmb G CL S) *)
-apply (frule_tac xs=s1 and xs'="(x, h, l)" in state_ok_evals)
-apply (simp (no_asm_simp) only: env_of_jmb_fst, assumption, simp only: env_of_jmb_fst)
+ (* establish (x, h, l)::\<preceq>(env_of_jmb G CL S) *)
+ apply (frule_tac xs=s1 and xs'="(x, h, l)" in state_ok_evals)
+ apply (simp (no_asm_simp) only: env_of_jmb_fst, assumption, simp only: env_of_jmb_fst)
-(* establish \<exists> lc. a' = Addr lc *)
-apply (frule (5) eval_of_class, rule env_of_jmb_fst [symmetric])
-apply (subgoal_tac "G,h \<turnstile> a' ::\<preceq> Class C")
-apply (subgoal_tac "is_class G dynT")
+ (* establish \<exists> lc. a' = Addr lc *)
+ apply (frule (5) eval_of_class, rule env_of_jmb_fst [symmetric])
+ apply (subgoal_tac "G,h \<turnstile> a' ::\<preceq> Class C")
+ apply (subgoal_tac "is_class G dynT")
-(* establish method (G, dynT) (mn, pTs) = Some(md, rT, pns, lvars, blk, res) *)
-apply (drule method_defined, assumption+)
-apply (simp only: env_of_jmb_fst)
-apply ((erule exE)+, erule conjE, (rule exI)+, assumption)
+ (* establish method (G, dynT) (mn, pTs) = Some(md, rT, pns, lvars, blk, res) *)
+ apply (drule method_defined, assumption+)
+ apply (simp only: env_of_jmb_fst)
+ apply ((erule exE)+, erule conjE, (rule exI)+, assumption)
-apply (subgoal_tac "is_class G md")
-apply (subgoal_tac "G\<turnstile>Class dynT \<preceq> Class md")
-apply (subgoal_tac " method (G, md) (mn, pTs) = Some (md, rT, pns, lvars, blk, res)")
-apply (subgoal_tac "list_all2 (conf G h) pvs pTs")
+ apply (subgoal_tac "is_class G md")
+ apply (subgoal_tac "G\<turnstile>Class dynT \<preceq> Class md")
+ apply (subgoal_tac " method (G, md) (mn, pTs) = Some (md, rT, pns, lvars, blk, res)")
+ apply (subgoal_tac "list_all2 (conf G h) pvs pTs")
-(* establish (np a' x, h, init_vars lvars(pns[\<mapsto>]pvs)(This\<mapsto>a'))::\<preceq>(env_of_jmb G md (mn, pTs)) *)
-apply (subgoal_tac "G,h \<turnstile> a' ::\<preceq> Class dynT")
-apply (frule (2) conf_widen)
-apply (frule state_ok_init, assumption+)
+ (* establish (np a' x, h, init_vars lvars(pns[\<mapsto>]pvs)(This\<mapsto>a'))::\<preceq>(env_of_jmb G md (mn, pTs)) *)
+ apply (subgoal_tac "G,h \<turnstile> a' ::\<preceq> Class dynT")
+ apply (frule (2) conf_widen)
+ apply (frule state_ok_init, assumption+)
-apply (subgoal_tac "class_sig_defined G md (mn, pTs)")
-apply (frule wtpd_blk, assumption, assumption)
-apply (frule wtpd_res, assumption, assumption)
-apply (subgoal_tac "s3::\<preceq>(env_of_jmb G md (mn, pTs))")
+ apply (subgoal_tac "class_sig_defined G md (mn, pTs)")
+ apply (frule wtpd_blk, assumption, assumption)
+ apply (frule wtpd_res, assumption, assumption)
+ apply (subgoal_tac "s3::\<preceq>(env_of_jmb G md (mn, pTs))")
-apply (subgoal_tac "method (TranslComp.comp G, md) (mn, pTs) =
- Some (md, rT, snd (snd (compMethod G md ((mn, pTs), rT, pns, lvars, blk, res))))")
-prefer 2 apply (simp add: wf_prog_ws_prog [THEN comp_method])
-apply (subgoal_tac "method (TranslComp.comp G, dynT) (mn, pTs) =
- Some (md, rT, snd (snd (compMethod G md ((mn, pTs), rT, pns, lvars, blk, res))))")
-prefer 2 apply (simp add: wf_prog_ws_prog [THEN comp_method])
- apply (simp only: fst_conv snd_conv)
+ apply (subgoal_tac "method (TranslComp.comp G, md) (mn, pTs) =
+ Some (md, rT, snd (snd (compMethod G md ((mn, pTs), rT, pns, lvars, blk, res))))")
+ prefer 2
+ apply (simp add: wf_prog_ws_prog [THEN comp_method])
+ apply (subgoal_tac "method (TranslComp.comp G, dynT) (mn, pTs) =
+ Some (md, rT, snd (snd (compMethod G md ((mn, pTs), rT, pns, lvars, blk, res))))")
+ prefer 2
+ apply (simp add: wf_prog_ws_prog [THEN comp_method])
+ apply (simp only: fst_conv snd_conv)
-(* establish length pns = length pTs *)
-apply (frule method_preserves_length, assumption, assumption)
-(* establish length pvs = length ps *)
-apply (frule evals_preserves_length [symmetric])
+ (* establish length pns = length pTs *)
+ apply (frule method_preserves_length, assumption, assumption)
+ (* establish length pvs = length ps *)
+ apply (frule evals_preserves_length [symmetric])
-(** start evaluating subexpressions **)
-apply (simp (no_asm_use) only: compExpr.simps compExprs.simps)
-
- (* evaluate e *)
-apply (rule_tac ?instrs0.0 = "(compExpr (gmb G CL S) e)" in progression_transitive, rule HOL.refl)
-apply fast
+ (** start evaluating subexpressions **)
+ apply (simp (no_asm_use) only: compExpr.simps compExprs.simps)
- (* evaluate parameters *)
-apply (rule_tac ?instrs0.0 = "compExprs (gmb G CL S) ps" in progression_transitive, rule HOL.refl)
-apply fast
+ (* evaluate e *)
+ apply (rule_tac ?instrs0.0 = "(compExpr (gmb G CL S) e)" in progression_transitive, rule HOL.refl)
+ apply fast
+
+ (* evaluate parameters *)
+ apply (rule_tac ?instrs0.0 = "compExprs (gmb G CL S) ps" in progression_transitive, rule HOL.refl)
+ apply fast
- (* invokation *)
-apply (rule progression_call)
-apply (intro allI impI conjI)
- (* execute Invoke statement *)
-apply (simp (no_asm_use) only: exec_instr.simps)
-apply (erule thin_rl, erule thin_rl, erule thin_rl)
-apply (simp add: compMethod_def raise_system_xcpt_def)
+ (* invokation *)
+ apply (rule progression_call)
+ apply (intro allI impI conjI)
+ (* execute Invoke statement *)
+ apply (simp (no_asm_use) only: exec_instr.simps)
+ apply (erule thin_rl, erule thin_rl, erule thin_rl)
+ apply (simp add: compMethod_def raise_system_xcpt_def)
- (* get instructions of invoked method *)
-apply (simp (no_asm_simp) add: gis_def gmb_def compMethod_def)
+ (* get instructions of invoked method *)
+ apply (simp (no_asm_simp) add: gis_def gmb_def compMethod_def)
- (* var. initialization *)
-apply (rule_tac ?instrs0.0 = "(compInitLvars (pns, lvars, blk, res) lvars)" in progression_transitive, rule HOL.refl)
-apply (rule_tac C=md in progression_lvar_init, assumption, assumption, assumption)
-apply (simp (no_asm_simp)) (* length pns = length pvs *)
-apply (simp (no_asm_simp)) (* length lvars = length (replicate (length lvars) undefined) *)
+ (* var. initialization *)
+ apply (rule_tac ?instrs0.0 = "(compInitLvars (pns, lvars, blk, res) lvars)" in progression_transitive, rule HOL.refl)
+ apply (rule_tac C=md in progression_lvar_init, assumption, assumption, assumption)
+ apply (simp (no_asm_simp)) (* length pns = length pvs *)
+ apply (simp (no_asm_simp)) (* length lvars = length (replicate (length lvars) undefined) *)
- (* body statement *)
-apply (rule_tac ?instrs0.0 = "compStmt (pns, lvars, blk, res) blk" in progression_transitive, rule HOL.refl)
-apply (subgoal_tac "(pns, lvars, blk, res) = gmb G md (mn, pTs)")
-apply (simp (no_asm_simp))
-apply (simp only: gh_conv)
-apply (drule mp [OF _ TrueI])+
-apply (erule allE, erule allE, erule allE, erule impE, assumption)+
-apply ((erule impE, assumption)+, assumption)
+ (* body statement *)
+ apply (rule_tac ?instrs0.0 = "compStmt (pns, lvars, blk, res) blk" in progression_transitive, rule HOL.refl)
+ apply (subgoal_tac "(pns, lvars, blk, res) = gmb G md (mn, pTs)")
+ apply (simp (no_asm_simp))
+ apply (simp only: gh_conv)
+ apply (drule mp [OF _ TrueI])+
+ apply (erule allE, erule allE, erule allE, erule impE, assumption)+
+ apply ((erule impE, assumption)+, assumption)
-apply (simp (no_asm_use))
-apply (simp (no_asm_simp) add: gmb_def)
+ apply (simp (no_asm_use))
+ apply (simp (no_asm_simp) add: gmb_def)
- (* return expression *)
-apply (subgoal_tac "(pns, lvars, blk, res) = gmb G md (mn, pTs)")
-apply (simp (no_asm_simp))
-apply (simp only: gh_conv)
-apply ((drule mp, rule TrueI)+, (drule spec)+, (drule mp, assumption)+, assumption)
-apply (simp (no_asm_use))
-apply (simp (no_asm_simp) add: gmb_def)
+ (* return expression *)
+ apply (subgoal_tac "(pns, lvars, blk, res) = gmb G md (mn, pTs)")
+ apply (simp (no_asm_simp))
+ apply (simp only: gh_conv)
+ apply ((drule mp, rule TrueI)+, (drule spec)+, (drule mp, assumption)+, assumption)
+ apply (simp (no_asm_use))
+ apply (simp (no_asm_simp) add: gmb_def)
- (* execute return statement *)
-apply (simp (no_asm_use) add: gh_def locvars_xstate_def gl_def del: drop_append)
-apply (subgoal_tac "rev pvs @ a' # os = (rev (a' # pvs)) @ os")
-apply (simp only: drop_append)
-apply (simp (no_asm_simp))
-apply (simp (no_asm_simp))
+ (* execute return statement *)
+ apply (simp (no_asm_use) add: gh_def locvars_xstate_def gl_def del: drop_append)
+ apply (subgoal_tac "rev pvs @ a' # os = (rev (a' # pvs)) @ os")
+ apply (simp only: drop_append)
+ apply (simp (no_asm_simp))
+ apply (simp (no_asm_simp))
-(* show s3::\<preceq>\<dots> *)
-apply (rule_tac xs = "(np a' x, h, init_vars lvars(pns[\<mapsto>]pvs)(This\<mapsto>a'))" and st=blk in state_ok_exec)
-apply assumption apply (simp (no_asm_simp) only: env_of_jmb_fst)
-apply assumption apply (simp (no_asm_use) only: env_of_jmb_fst)
+ (* show s3::\<preceq>\<dots> *)
+ apply (rule_tac xs = "(np a' x, h, init_vars lvars(pns[\<mapsto>]pvs)(This\<mapsto>a'))" and st=blk in state_ok_exec)
+ apply assumption
+ apply (simp (no_asm_simp) only: env_of_jmb_fst)
+ apply assumption
+ apply (simp (no_asm_use) only: env_of_jmb_fst)
-(* show class_sig_defined G md (mn, pTs) *)
-apply (simp (no_asm_simp) add: class_sig_defined_def)
+ (* show class_sig_defined G md (mn, pTs) *)
+ apply (simp (no_asm_simp) add: class_sig_defined_def)
-(* show G,h \<turnstile> a' ::\<preceq> Class dynT *)
-apply (frule non_npD) apply assumption
-apply (erule exE)+ apply simp
-apply (rule conf_obj_AddrI) apply simp
-apply (rule widen_Class_Class [THEN iffD1], rule widen.refl)
+ (* show G,h \<turnstile> a' ::\<preceq> Class dynT *)
+ apply (frule non_npD)
+ apply assumption
+ apply (erule exE)+
+ apply simp
+ apply (rule conf_obj_AddrI)
+ apply simp
+ apply (rule widen_Class_Class [THEN iffD1], rule widen.refl)
- (* show list_all2 (conf G h) pvs pTs *)
-apply (erule exE)+ apply (erule conjE)+
-apply (rule_tac Ts="pTsa" in conf_list_gext_widen) apply assumption
-apply (subgoal_tac "G \<turnstile> (gx s1, gs s1) -ps[\<succ>]pvs-> (x, h, l)")
-apply (frule_tac E="env_of_jmb G CL S" in evals_type_sound)
-apply assumption+
-apply (simp only: env_of_jmb_fst)
-apply (simp add: conforms_def xconf_def gs_def)
-apply simp
-apply (simp (no_asm_use) only: gx_def gs_def surjective_pairing [symmetric])
-apply (simp (no_asm_use) only: ty_exprs_list_all2) apply simp
-apply simp
-apply (simp (no_asm_use) only: gx_def gs_def surjective_pairing [symmetric])
- (* list_all2 (\<lambda>T T'. G \<turnstile> T \<preceq> T') pTsa pTs *)
- apply (rule max_spec_widen, simp only: env_of_jmb_fst)
+ (* show list_all2 (conf G h) pvs pTs *)
+ apply (erule exE)+ apply (erule conjE)+
+ apply (rule_tac Ts="pTsa" in conf_list_gext_widen)
+ apply assumption
+ apply (subgoal_tac "G \<turnstile> (gx s1, gs s1) -ps[\<succ>]pvs-> (x, h, l)")
+ apply (frule_tac E="env_of_jmb G CL S" in evals_type_sound)
+ apply assumption+
+ apply (simp only: env_of_jmb_fst)
+ apply (simp add: conforms_def xconf_def gs_def)
+ apply simp
+ apply (simp (no_asm_use) only: gx_def gs_def surjective_pairing [symmetric])
+ apply (simp (no_asm_use) only: ty_exprs_list_all2)
+ apply simp
+ apply simp
+ apply (simp (no_asm_use) only: gx_def gs_def surjective_pairing [symmetric])
+ (* list_all2 (\<lambda>T T'. G \<turnstile> T \<preceq> T') pTsa pTs *)
+ apply (rule max_spec_widen, simp only: env_of_jmb_fst)
-(* show method (G, md) (mn, pTs) = Some (md, rT, pns, lvars, blk, res) *)
-apply (frule wf_prog_ws_prog [THEN method_in_md [THEN conjunct2]], assumption+)
+ (* show method (G, md) (mn, pTs) = Some (md, rT, pns, lvars, blk, res) *)
+ apply (frule wf_prog_ws_prog [THEN method_in_md [THEN conjunct2]], assumption+)
- (* show G\<turnstile>Class dynT \<preceq> Class md *)
-apply (simp (no_asm_use) only: widen_Class_Class)
-apply (rule method_wf_mdecl [THEN conjunct1], assumption+)
+ (* show G\<turnstile>Class dynT \<preceq> Class md *)
+ apply (simp (no_asm_use) only: widen_Class_Class)
+ apply (rule method_wf_mdecl [THEN conjunct1], assumption+)
- (* is_class G md *)
-apply (rule wf_prog_ws_prog [THEN method_in_md [THEN conjunct1]], assumption+)
+ (* is_class G md *)
+ apply (rule wf_prog_ws_prog [THEN method_in_md [THEN conjunct1]], assumption+)
- (* show is_class G dynT *)
-apply (frule non_npD) apply assumption
-apply (erule exE)+ apply (erule conjE)+
-apply simp
-apply (rule subcls_is_class2) apply assumption
-apply (frule class_expr_is_class) apply (simp only: env_of_jmb_fst)
-apply (rule wf_prog_ws_prog, assumption)
-apply (simp only: env_of_jmb_fst)
+ (* show is_class G dynT *)
+ apply (frule non_npD)
+ apply assumption
+ apply (erule exE)+
+ apply (erule conjE)+
+ apply simp
+ apply (rule subcls_is_class2)
+ apply assumption
+ apply (frule expr_class_is_class [rotated])
+ apply (simp only: env_of_jmb_fst)
+ apply (rule wf_prog_ws_prog, assumption)
+ apply (simp only: env_of_jmb_fst)
- (* show G,h \<turnstile> a' ::\<preceq> Class C *)
-apply (simp only: wtpd_exprs_def, erule exE)
-apply (frule evals_preserves_conf)
-apply (rule eval_conf, assumption+)
-apply (rule env_of_jmb_fst, assumption+)
-apply (rule env_of_jmb_fst)
-apply (simp only: gh_conv)
-done
+ (* show G,h \<turnstile> a' ::\<preceq> Class C *)
+ apply (simp only: wtpd_exprs_def, erule exE)
+ apply (frule evals_preserves_conf)
+ apply (rule eval_conf, assumption+)
+ apply (rule env_of_jmb_fst, assumption+)
+ apply (rule env_of_jmb_fst)
+ apply (simp only: gh_conv)
+ done
theorem compiler_correctness_eval: "
@@ -1226,9 +1254,9 @@
{hp, os, (locvars_locals G C S loc)}
>- (compExpr (gmb G C S) ex) \<rightarrow>
{hp', val#os, (locvars_locals G C S loc')}"
-apply (frule compiler_correctness [THEN conjunct1])
-apply (auto simp: gh_def gx_def gs_def gl_def locvars_xstate_def)
-done
+ apply (frule compiler_correctness [THEN conjunct1])
+ apply (auto simp: gh_def gx_def gs_def gl_def locvars_xstate_def)
+ done
theorem compiler_correctness_exec: "
\<lbrakk> G \<turnstile> Norm (hp, loc) -st-> Norm (hp', loc');
@@ -1240,9 +1268,9 @@
{hp, os, (locvars_locals G C S loc)}
>- (compStmt (gmb G C S) st) \<rightarrow>
{hp', os, (locvars_locals G C S loc')}"
-apply (frule compiler_correctness [THEN conjunct2 [THEN conjunct2]])
-apply (auto simp: gh_def gx_def gs_def gl_def locvars_xstate_def)
-done
+ apply (frule compiler_correctness [THEN conjunct2 [THEN conjunct2]])
+ apply (auto simp: gh_def gx_def gs_def gl_def locvars_xstate_def)
+ done
(**********************************************************************)