(*  Title:      HOLCF/IOA/meta_theory/RefMappings.thy
    ID:         $Id: RefMappings.thy,v 1.9 2005/09/02 15:24:02 wenzelm Exp $
    Author:     Olaf Müller
*)

header {* Refinement Mappings in HOLCF/IOA *}

theory RefMappings
imports Traces
begin

defaultsort type

consts
  move         ::"[('a,'s)ioa,('a,'s)pairs,'s,'a,'s] => bool"
  is_ref_map   ::"[('s1=>'s2),('a,'s1)ioa,('a,'s2)ioa] => bool"
  is_weak_ref_map ::"[('s1=>'s2),('a,'s1)ioa,('a,'s2)ioa] => bool"


defs

move_def:
  "move ioa ex s a t ==
    (is_exec_frag ioa (s,ex) &  Finite ex &
     laststate (s,ex)=t  &
     mk_trace ioa$ex = (if a:ext(ioa) then a>>nil else nil))"

is_ref_map_def:
  "is_ref_map f C A ==
   (!s:starts_of(C). f(s):starts_of(A)) &
   (!s t a. reachable C s &
            s -a--C-> t
            --> (? ex. move A ex (f s) a (f t)))"

is_weak_ref_map_def:
  "is_weak_ref_map f C A ==
   (!s:starts_of(C). f(s):starts_of(A)) &
   (!s t a. reachable C s &
            s -a--C-> t
            --> (if a:ext(C)
                 then (f s) -a--A-> (f t)
                 else (f s)=(f t)))"

ML {* use_legacy_bindings (the_context ()) *}

end
