(*  Title:      HOLCF/IOA/TrivEx.thy
    ID:         $Id: TrivEx.thy,v 1.4 2005/09/03 14:50:26 wenzelm Exp $
    Author:     Olaf Müller
*)

header {* Trivial Abstraction Example *}

theory TrivEx
imports Abstraction
begin

datatype action = INC

consts

C_asig   ::  "action signature"
C_trans  :: "(action, nat)transition set"
C_ioa    :: "(action, nat)ioa"

A_asig   :: "action signature"
A_trans  :: "(action, bool)transition set"
A_ioa    :: "(action, bool)ioa"

h_abs    :: "nat => bool"

defs

C_asig_def:
  "C_asig == ({},{INC},{})"

C_trans_def: "C_trans ==
 {tr. let s = fst(tr);
          t = snd(snd(tr))
      in case fst(snd(tr))
      of
      INC       => t = Suc(s)}"

C_ioa_def: "C_ioa ==
 (C_asig, {0}, C_trans,{},{})"

A_asig_def:
  "A_asig == ({},{INC},{})"

A_trans_def: "A_trans ==
 {tr. let s = fst(tr);
          t = snd(snd(tr))
      in case fst(snd(tr))
      of
      INC       => t = True}"

A_ioa_def: "A_ioa ==
 (A_asig, {False}, A_trans,{},{})"

h_abs_def:
  "h_abs n == n~=0"

axioms

MC_result:
  "validIOA A_ioa (<>[] <%(b,a,c). b>)"

ML {* use_legacy_bindings (the_context ()) *}

end
