author | wenzelm |
Thu, 31 Dec 2015 12:55:39 +0100 | |
changeset 62009 | ecb5212d5885 |
parent 62008 | cbedaddc9351 |
child 62116 | bc178c0fe1a1 |
permissions | -rw-r--r-- |
42151 | 1 |
(* Title: HOL/HOLCF/IOA/NTP/Receiver.thy |
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Author: Tobias Nipkow & Konrad Slind |
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*) |
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section \<open>The implementation: receiver\<close> |
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theory Receiver |
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imports "../IOA" Action |
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begin |
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type_synonym |
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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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definition rq :: "'m receiver_state => 'm list" where "rq == fst" |
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definition rsent :: "'m receiver_state => bool multiset" where "rsent == fst o snd" |
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definition rrcvd :: "'m receiver_state => 'm packet multiset" where "rrcvd == fst o snd o snd" |
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definition rbit :: "'m receiver_state => bool" where "rbit == fst o snd o snd o snd" |
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definition rsending :: "'m receiver_state => bool" where "rsending == snd o snd o snd o snd" |
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definition |
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receiver_asig :: "'m action signature" where |
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"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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definition |
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receiver_trans:: "('m action, 'm receiver_state)transition set" where |
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"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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definition |
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receiver_ioa :: "('m action, 'm receiver_state)ioa" where |
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"receiver_ioa = |
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(receiver_asig, {([],{|},{|},False,False)}, receiver_trans,{},{})" |
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lemma in_receiver_asig: |
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"S_msg(m) ~: actions(receiver_asig)" |
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"R_msg(m) : actions(receiver_asig)" |
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"S_pkt(pkt) ~: actions(receiver_asig)" |
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"R_pkt(pkt) : actions(receiver_asig)" |
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"S_ack(b) : actions(receiver_asig)" |
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"R_ack(b) ~: actions(receiver_asig)" |
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"C_m_s ~: actions(receiver_asig)" |
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"C_m_r : actions(receiver_asig)" |
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"C_r_s ~: actions(receiver_asig)" |
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"C_r_r(m) : actions(receiver_asig)" |
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by (simp_all add: receiver_asig_def actions_def asig_projections) |
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lemmas receiver_projections = rq_def rsent_def rrcvd_def rbit_def rsending_def |
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end |