(* Title: HOL/IOA/example/Spec.thy
ID: $Id$
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)
end