(* Title: HOL/MicroJava/J/TypeRel.thy
ID: $Id$
Author: David von Oheimb
Copyright 1999 Technische Universitaet Muenchen
The relations between Java types
*)
TypeRel = Decl +
consts
subcls1 :: "'c prog \\<Rightarrow> (cname \\<times> cname) set" (* subclass *)
widen :: "'c prog \\<Rightarrow> (ty \\<times> ty ) set" (* widening *)
cast :: "'c prog \\<Rightarrow> (cname \\<times> cname) set" (* casting *)
syntax
subcls1 :: "'c prog \\<Rightarrow> [cname, cname] \\<Rightarrow> bool" ("_\\<turnstile>_\\<prec>C1_" [71,71,71] 70)
subcls :: "'c prog \\<Rightarrow> [cname, cname] \\<Rightarrow> bool" ("_\\<turnstile>_\\<preceq>C _" [71,71,71] 70)
widen :: "'c prog \\<Rightarrow> [ty , ty ] \\<Rightarrow> bool" ("_\\<turnstile>_\\<preceq>_" [71,71,71] 70)
cast :: "'c prog \\<Rightarrow> [cname, cname] \\<Rightarrow> bool" ("_\\<turnstile>_\\<preceq>? _"[71,71,71] 70)
translations
"G\\<turnstile>C \\<prec>C1 D" == "(C,D) \\<in> subcls1 G"
"G\\<turnstile>C \\<preceq>C D" == "(C,D) \\<in> (subcls1 G)^*"
"G\\<turnstile>S \\<preceq> T" == "(S,T) \\<in> widen G"
"G\\<turnstile>C \\<preceq>? D" == "(C,D) \\<in> cast G"
defs
(* direct subclass, cf. 8.1.3 *)
subcls1_def "subcls1 G \\<equiv> {(C,D). \\<exists>c. class G C = Some c \\<and> fst c = Some D}"
consts
method :: "'c prog \\<times> cname \\<Rightarrow> ( sig \\<leadsto> cname \\<times> ty \\<times> 'c)"
field :: "'c prog \\<times> cname \\<Rightarrow> ( vname \\<leadsto> cname \\<times> ty)"
fields :: "'c prog \\<times> cname \\<Rightarrow> ((vname \\<times> cname) \\<times> ty) list"
constdefs (* auxiliary relations for recursive definitions below *)
subcls1_rel :: "(('c prog \\<times> cname) \\<times> ('c prog \\<times> cname)) set"
"subcls1_rel \\<equiv> {((G,C),(G',C')). G = G' \\<and> wf ((subcls1 G)^-1) \\<and> G\\<turnstile>C'\\<prec>C1C}"
(* methods of a class, with inheritance, overriding and hiding, cf. 8.4.6 *)
recdef method "subcls1_rel"
"method (G,C) = (if wf((subcls1 G)^-1) then (case class G C of None \\<Rightarrow> empty
| Some (sc,fs,ms) \\<Rightarrow> (case sc of None \\<Rightarrow> empty | Some D \\<Rightarrow>
if is_class G D then method (G,D)
else arbitrary) \\<oplus>
map_of (map (\\<lambda>(s, m ).
(s,(C,m))) ms))
else arbitrary)"
(* list of fields of a class, including inherited and hidden ones *)
recdef fields "subcls1_rel"
"fields (G,C) = (if wf((subcls1 G)^-1) then (case class G C of None \\<Rightarrow> arbitrary
| Some (sc,fs,ms) \\<Rightarrow> map (\\<lambda>(fn,ft). ((fn,C),ft)) fs@
(case sc of None \\<Rightarrow> [] | Some D \\<Rightarrow>
if is_class G D then fields (G,D)
else arbitrary))
else arbitrary)"
defs
field_def "field \\<equiv> map_of o (map (\\<lambda>((fn,fd),ft). (fn,(fd,ft)))) o fields"
inductive "widen G" intrs (*widening, viz. method invocation conversion, cf. 5.3
i.e. sort of syntactic subtyping *)
refl "G\\<turnstile> T \\<preceq> T" (* identity conv., cf. 5.1.1 *)
subcls "G\\<turnstile>C\\<preceq>C D \\<Longrightarrow> G\\<turnstile>Class C \\<preceq> Class D"
null "G\\<turnstile> NT \\<preceq> RefT R"
inductive "cast G" intrs (* casting conversion, cf. 5.5 / 5.1.5 *)
(* left out casts on primitve types *)
widen "G\\<turnstile>C\\<preceq>C D \\<Longrightarrow> G\\<turnstile>C \\<preceq>? D"
subcls "G\\<turnstile>D\\<preceq>C C \\<Longrightarrow> G\\<turnstile>C \\<preceq>? D"
end