(* Title: HOL/IOA/example/Receiver.thy
ID: $Id$
Author: Tobias Nipkow & Konrad Slind
Copyright 1994 TU Muenchen
The implementation: receiver
*)
Receiver = List + IOA + Action + Multiset +
types
'm receiver_state
= "'m list * bool multiset * 'm packet multiset * bool * bool"
(* messages #replies #received header 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"
rsent :: "'m receiver_state => bool multiset"
rrcvd :: "'m receiver_state => 'm packet multiset"
rbit :: "'m receiver_state => bool"
rsending :: "'m receiver_state => bool"
defs
rq_def "rq == fst"
rsent_def "rsent == fst o snd"
rrcvd_def "rrcvd == fst o snd o snd"
rbit_def "rbit == fst o snd o snd o snd"
rsending_def "rsending == snd o snd o snd o snd"
receiver_asig_def "receiver_asig ==
<UN pkt. {R_pkt(pkt)},
(UN m. {R_msg(m)}) Un (UN b. {S_ack(b)}),
insert(C_m_r, UN m. {C_r_r(m)})>"
receiver_trans_def "receiver_trans ==
{tr. let s = fst(tr);
t = snd(snd(tr))
in
case fst(snd(tr))
of
S_msg(m) => False |
R_msg(m) => rq(s) = (m # rq(t)) &
rsent(t)=rsent(s) &
rrcvd(t)=rrcvd(s) &
rbit(t)=rbit(s) &
rsending(t)=rsending(s) |
S_pkt(pkt) => False |
R_pkt(pkt) => rq(t) = rq(s) &
rsent(t) = rsent(s) &
rrcvd(t) = addm(rrcvd(s),pkt) &
rbit(t) = rbit(s) &
rsending(t) = rsending(s) |
S_ack(b) => b = rbit(s) &
rq(t) = rq(s) &
rsent(t) = addm(rsent(s),rbit(s)) &
rrcvd(t) = rrcvd(s) &
rbit(t)=rbit(s) &
rsending(s) &
rsending(t) |
R_ack(b) => False |
C_m_s => False |
C_m_r => count(rsent(s),~rbit(s)) < countm(rrcvd(s),%y.hdr(y)=rbit(s)) &
rq(t) = rq(s) &
rsent(t)=rsent(s) &
rrcvd(t)=rrcvd(s) &
rbit(t)=rbit(s) &
rsending(s) &
~rsending(t) |
C_r_s => False |
C_r_r(m) => count(rsent(s),rbit(s)) <= countm(rrcvd(s),%y.hdr(y)=rbit(s)) &
count(rsent(s),~rbit(s)) < count(rrcvd(s),<rbit(s),m>) &
rq(t) = rq(s)@[m] &
rsent(t)=rsent(s) &
rrcvd(t)=rrcvd(s) &
rbit(t) = (~rbit(s)) &
~rsending(s) &
rsending(t)}"
receiver_ioa_def "receiver_ioa ==
<receiver_asig, {<[],{|},{|},False,False>}, receiver_trans>"
end