(* Title: HOL/IOA/NTP/Receiver.thy
ID: $Id$
Author: Tobias Nipkow & Konrad Slind
Copyright 1994 TU Muenchen
The implementation: receiver
*)
Receiver = List + IOA + Action +
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