# Theory Impl

Up to index of Isabelle/HOLCF/IOA/Storage

theory Impl
imports IOA Action
begin

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

    header {* The implementation of a memory *}

    theory Impl
    imports IOA Action
    begin

    consts

    impl_sig   :: "action signature"
    impl_trans :: "(action, nat  * bool)transition set"
    impl_ioa   :: "(action, nat * bool)ioa"

    defs

    sig_def: "impl_sig == (UN l.{Free l} Un {New},
                         UN l.{Loc l},
                         {})"

    trans_def: "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}"

    ioa_def: "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)

    ML {* use_legacy_bindings (the_context ()) *}

    end

lemma in_impl_asig:

      New ∈ actions impl_sig ∧ Loc l ∈ actions impl_sig ∧ Free l ∈ actions impl_sig