(* Title: HOL/MicroJava/J/Conform.thy
ID: $Id$
Author: David von Oheimb
Copyright 1999 Technische Universitaet Muenchen
Conformity relations for type safety of Java
*)
Conform = State + WellType +
types 'c env_ = "'c prog \\<times> (vname \\<leadsto> ty)" (* same as env of WellType.thy *)
constdefs
hext :: "aheap \\<Rightarrow> aheap \\<Rightarrow> bool" ( "_\\<le>|_" [51,51] 50)
"h\\<le>|h' \\<equiv> \\<forall>a C fs. h a = Some(C,fs) \\<longrightarrow> (\\<exists>fs'. h' a = Some(C,fs'))"
conf :: "'c prog \\<Rightarrow> aheap \\<Rightarrow> val \\<Rightarrow> ty \\<Rightarrow> bool" ( "_,_\\<turnstile>_\\<Colon>\\<preceq>_" [51,51,51,51] 50)
"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"
lconf :: "'c prog \\<Rightarrow> aheap \\<Rightarrow> ('a \\<leadsto> val) \\<Rightarrow> ('a \\<leadsto> ty) \\<Rightarrow> bool"
("_,_\\<turnstile>_[\\<Colon>\\<preceq>]_" [51,51,51,51] 50)
"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)"
oconf :: "'c prog \\<Rightarrow> aheap \\<Rightarrow> obj \\<Rightarrow> bool" ("_,_\\<turnstile>_\\<surd>" [51,51,51] 50)
"G,h\\<turnstile>obj\\<surd> \\<equiv> G,h\\<turnstile>snd obj[\\<Colon>\\<preceq>]map_of (fields (G,fst obj))"
hconf :: "'c prog \\<Rightarrow> aheap \\<Rightarrow> bool" ("_\\<turnstile>h _\\<surd>" [51,51] 50)
"G\\<turnstile>h h\\<surd> \\<equiv> \\<forall>a obj. h a = Some obj \\<longrightarrow> G,h\\<turnstile>obj\\<surd>"
conforms :: "state \\<Rightarrow> java_mb env_ \\<Rightarrow> bool" ("_\\<Colon>\\<preceq>_" [51,51] 50)
"s\\<Colon>\\<preceq>E \\<equiv> prg E\\<turnstile>h heap s\\<surd> \\<and> prg E,heap s\\<turnstile>locals s[\\<Colon>\\<preceq>]localT E"
end