Theory Impl

(*  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 = (l.{Free l}  {New},
               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