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