Theory Impl

theory Impl
imports IOA Action
(*  Title:      HOL/HOLCF/IOA/Storage/Impl.thy
    Author:     Olaf Müller
*)

section ‹The implementation of a memory›

theory Impl
imports IOA.IOA Action
begin

definition
  impl_sig :: "action signature" where
  "impl_sig = (UN l.{Free l} Un {New},
               UN l.{Loc l},
               {})"

definition
  impl_trans :: "(action, nat  * bool)transition set" where
  "impl_trans =
    {tr. let s = fst(tr); k = fst s; b = snd s;
             t = snd(snd(tr)); k' = fst t; b' = snd t
         in
         case fst(snd(tr))
         of
         New       => k' = k & b'  |
         Loc l     => b & l= k & k'= (Suc k) & ~b' |
         Free l    => k'=k & b'=b}"

definition
  impl_ioa :: "(action, nat * bool)ioa" where
  "impl_ioa = (impl_sig, {(0,False)}, impl_trans,{},{})"

lemma in_impl_asig:
  "New : actions(impl_sig) &
    Loc l : actions(impl_sig) &
    Free l : actions(impl_sig) "
  by (simp add: impl_sig_def actions_def asig_projections)

end