(* Title: HOL/IOA/example/Receiver.thy
ID: $Id$
Author: Tobias Nipkow & Konrad Slind
Copyright 1994 TU Muenchen
The implementation: receiver
*)
Receiver = List + IOA + Action + Lemmas +
types
'm receiver_state
= "'m list * bool"
(* messages mode *)
consts
receiver_asig :: 'm action signature
receiver_trans:: ('m action, 'm receiver_state)transition set
receiver_ioa :: ('m action, 'm receiver_state)ioa
rq :: 'm receiver_state => 'm list
rbit :: 'm receiver_state => bool
defs
rq_def "rq == fst"
rbit_def "rbit == snd"
receiver_asig_def "receiver_asig ==
(UN pkt. {R_pkt(pkt)},
(UN m. {R_msg(m)}) Un (UN b. {S_ack(b)}),
{})"
receiver_trans_def "receiver_trans ==
{tr. let s = fst(tr);
t = snd(snd(tr))
in
case fst(snd(tr))
of
Next => False |
S_msg(m) => False |
R_msg(m) => (rq(s) ~= []) &
m = hd(rq(s)) &
rq(t) = tl(rq(s)) &
rbit(t)=rbit(s) |
S_pkt(pkt) => False |
R_pkt(pkt) => if (hdr(pkt) ~= rbit(s))&rq(s)=[] then
rq(t) = (rq(s)@[msg(pkt)]) &rbit(t) = (~rbit(s)) else
rq(t) =rq(s) & rbit(t)=rbit(s) |
S_ack(b) => b = rbit(s) &
rq(t) = rq(s) &
rbit(t)=rbit(s) |
R_ack(b) => False}"
receiver_ioa_def "receiver_ioa ==
(receiver_asig, {([],False)}, receiver_trans)"
end