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