(* Title: HOL/MicroJava/BV/Altern.thy ID: $Id: Altern.thy,v 1.5 2008/03/27 18:22:23 wenzelm Exp $ Author: Martin Strecker *) (* Alternative definition of well-typing of bytecode, used in compiler type correctness proof *) theory Altern imports BVSpec begin constdefs check_type :: "jvm_prog => nat => nat => JVMType.state => bool" "check_type G mxs mxr s ≡ s ∈ states G mxs mxr" wt_instr_altern :: "[instr,jvm_prog,ty,method_type,nat,nat,p_count, exception_table,p_count] => bool" "wt_instr_altern i G rT phi mxs mxr max_pc et pc ≡ app i G mxs rT pc et (phi!pc) ∧ check_type G mxs mxr (OK (phi!pc)) ∧ (∀(pc',s') ∈ set (eff i G pc et (phi!pc)). pc' < max_pc ∧ G \<turnstile> s' <=' phi!pc')" wt_method_altern :: "[jvm_prog,cname,ty list,ty,nat,nat,instr list, exception_table,method_type] => bool" "wt_method_altern G C pTs rT mxs mxl ins et phi ≡ let max_pc = length ins in 0 < max_pc ∧ length phi = length ins ∧ check_bounded ins et ∧ wt_start G C pTs mxl phi ∧ (∀pc. pc<max_pc --> wt_instr_altern (ins!pc) G rT phi mxs (1+length pTs+mxl) max_pc et pc)" lemma wt_method_wt_method_altern : "wt_method G C pTs rT mxs mxl ins et phi --> wt_method_altern G C pTs rT mxs mxl ins et phi" apply (simp add: wt_method_def wt_method_altern_def) apply (intro strip) apply clarify apply (drule spec, drule mp, assumption) apply (simp add: check_types_def wt_instr_def wt_instr_altern_def check_type_def) apply (auto intro: imageI) done lemma check_type_check_types [rule_format]: "(∀pc. pc < length phi --> check_type G mxs mxr (OK (phi ! pc))) --> check_types G mxs mxr (map OK phi)" apply (induct phi) apply (simp add: check_types_def) apply (simp add: check_types_def) apply clarify apply (frule_tac x=0 in spec) apply (simp add: check_type_def) apply auto done lemma wt_method_altern_wt_method [rule_format]: "wt_method_altern G C pTs rT mxs mxl ins et phi --> wt_method G C pTs rT mxs mxl ins et phi" apply (simp add: wt_method_def wt_method_altern_def) apply (intro strip) apply clarify apply (rule conjI) (* show check_types *) apply (rule check_type_check_types) apply (simp add: wt_instr_altern_def) (* show wt_instr *) apply (intro strip) apply (drule spec, drule mp, assumption) apply (simp add: wt_instr_def wt_instr_altern_def) done end
lemma wt_method_wt_method_altern:
wt_method G C pTs rT mxs mxl ins et phi -->
wt_method_altern G C pTs rT mxs mxl ins et phi
lemma check_type_check_types:
(!!pc. pc < length phi ==> check_type G mxs mxr (OK (phi ! pc)))
==> check_types G mxs mxr (map OK phi)
lemma wt_method_altern_wt_method:
wt_method_altern G C pTs rT mxs mxl ins et phi
==> wt_method G C pTs rT mxs mxl ins et phi