Removed theory NatDef.
(* Title: HOLCF/IOA/ABP/Correctness.thy
ID: $Id$
Author: Olaf Müller
License: GPL (GNU GENERAL PUBLIC LICENSE)
The main correctness proof: System_fin implements System.
*)
Correctness = IOA + Env + Impl + Impl_finite +
consts
reduce :: 'a list => 'a list
abs :: 'c
system_ioa :: "('m action, bool * 'm impl_state)ioa"
system_fin_ioa :: "('m action, bool * 'm impl_state)ioa"
primrec
reduce_Nil "reduce [] = []"
reduce_Cons "reduce(x#xs) =
(case xs of
[] => [x]
| y#ys => (if (x=y)
then reduce xs
else (x#(reduce xs))))"
defs
system_def
"system_ioa == (env_ioa || impl_ioa)"
system_fin_def
"system_fin_ioa == (env_ioa || impl_fin_ioa)"
abs_def "abs ==
(%p.(fst(p),(fst(snd(p)),(fst(snd(snd(p))),
(reduce(fst(snd(snd(snd(p))))),reduce(snd(snd(snd(snd(p))))))))))"
rules
sys_IOA "IOA system_ioa"
sys_fin_IOA "IOA system_fin_ioa"
end