Theory Decl

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(*  Title:      HOL/MicroJava/J/Decl.thy
    ID:         $Id: Decl.html,v 1.1 2002/11/28 14:17:20 kleing Exp $
    Author:     David von Oheimb
    Copyright   1999 Technische Universitaet Muenchen
*)

header {* \isaheader{Class Declarations and Programs} *}

theory Decl = Type:

types 
  fdecl    = "vname × ty"        -- "field declaration, cf. 8.3 (, 9.3)"
  sig      = "mname × ty list"   -- "signature of a method, cf. 8.4.2"
  'c mdecl = "sig × ty × 'c"     -- "method declaration in a class"
  'c class = "cname × fdecl list × 'c mdecl list" 
  -- "class = superclass, fields, methods"

  'c cdecl = "cname × 'c class"  -- "class declaration, cf. 8.1"
  'c prog  = "'c cdecl list"     -- "program"

translations
  "fdecl"   <= (type) "vname × ty"
  "sig"     <= (type) "mname × ty list"
  "mdecl c" <= (type) "sig × ty × c"
  "class c" <= (type) "cname × fdecl list × (c mdecl) list"
  "cdecl c" <= (type) "cname × (c class)"
  "prog  c" <= (type) "(c cdecl) list"


constdefs
  class :: "'c prog => (cname \<leadsto> 'c class)"
  "class \<equiv> map_of"

  is_class :: "'c prog => cname => bool"
  "is_class G C \<equiv> class G C \<noteq> None"

lemma finite_is_class: "finite {C. is_class G C}"
apply (unfold is_class_def class_def)
apply (fold dom_def)
apply (rule finite_dom_map_of)
done

consts
  is_type :: "'c prog => ty    => bool"
primrec
  "is_type G (PrimT pt) = True"
  "is_type G (RefT t) = (case t of NullT => True | ClassT C => is_class G C)"

consts
  is_RA :: "ty => bool"
recdef is_RA "{}"
  "is_RA (RA pc) = True"
  "is_RA t       = False"

end

lemma finite_is_class:

  finite (Collect (is_class G))