IOA/example/Receiver.thy

Added headers and made various small mods.

(*  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