(* Title: HOL/MicroJava/BV/BVSpec.thy
ID: $Id$
Author: Cornelia Pusch, Gerwin Klein
Copyright 1999 Technische Universitaet Muenchen
*)
header {* \isaheader{The Bytecode Verifier}\label{sec:BVSpec} *}
theory BVSpec = Effect:
text {*
This theory contains a specification of the BV. The specification
describes correct typings of method bodies; it corresponds
to type \emph{checking}.
*}
constdefs
wt_instr :: "[instr,jvm_prog,ty,method_type,nat,p_count,
exception_table,p_count] \<Rightarrow> bool"
"wt_instr i G rT phi mxs max_pc et pc ==
app i G mxs rT pc et (phi!pc) \<and>
(\<forall>(pc',s') \<in> set (eff i G pc et (phi!pc)). pc' < max_pc \<and> G \<turnstile> s' <=' phi!pc')"
wt_start :: "[jvm_prog,cname,ty list,nat,method_type] \<Rightarrow> bool"
"wt_start G C pTs mxl phi ==
G \<turnstile> Some ([],(OK (Class C))#((map OK pTs))@(replicate mxl Err)) <=' phi!0"
wt_method :: "[jvm_prog,cname,ty list,ty,nat,nat,instr list,
exception_table,method_type] \<Rightarrow> bool"
"wt_method G C pTs rT mxs mxl ins et phi ==
let max_pc = length ins in
0 < max_pc \<and> wt_start G C pTs mxl phi \<and>
(\<forall>pc. pc<max_pc \<longrightarrow> wt_instr (ins ! pc) G rT phi mxs max_pc et pc)"
wt_jvm_prog :: "[jvm_prog,prog_type] \<Rightarrow> bool"
"wt_jvm_prog G phi ==
wf_prog (\<lambda>G C (sig,rT,(maxs,maxl,b,et)).
wt_method G C (snd sig) rT maxs maxl b et (phi C sig)) G"
lemma wt_jvm_progD:
"wt_jvm_prog G phi \<Longrightarrow> (\<exists>wt. wf_prog wt G)"
by (unfold wt_jvm_prog_def, blast)
lemma wt_jvm_prog_impl_wt_instr:
"\<lbrakk> wt_jvm_prog G phi; is_class G C;
method (G,C) sig = Some (C,rT,maxs,maxl,ins,et); pc < length ins \<rbrakk>
\<Longrightarrow> wt_instr (ins!pc) G rT (phi C sig) maxs (length ins) et pc";
by (unfold wt_jvm_prog_def, drule method_wf_mdecl,
simp, simp, simp add: wf_mdecl_def wt_method_def)
lemma wt_jvm_prog_impl_wt_start:
"\<lbrakk> wt_jvm_prog G phi; is_class G C;
method (G,C) sig = Some (C,rT,maxs,maxl,ins,et) \<rbrakk> \<Longrightarrow>
0 < (length ins) \<and> wt_start G C (snd sig) maxl (phi C sig)"
by (unfold wt_jvm_prog_def, drule method_wf_mdecl,
simp, simp, simp add: wf_mdecl_def wt_method_def)
end