1 (* Title: HOL/IOA/example/Receiver.thy |
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2 ID: $Id$ |
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3 Author: Tobias Nipkow & Konrad Slind |
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4 Copyright 1994 TU Muenchen |
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5 |
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6 The implementation: receiver |
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7 *) |
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8 |
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9 Receiver = List + IOA + Action + Multiset + |
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10 |
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11 types |
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12 |
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13 'm receiver_state |
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14 = "'m list * bool multiset * 'm packet multiset * bool * bool" |
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15 (* messages #replies #received header mode *) |
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16 |
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17 consts |
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18 |
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19 receiver_asig :: "'m action signature" |
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20 receiver_trans:: "('m action, 'm receiver_state)transition set" |
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21 receiver_ioa :: "('m action, 'm receiver_state)ioa" |
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22 rq :: "'m receiver_state => 'm list" |
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23 rsent :: "'m receiver_state => bool multiset" |
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24 rrcvd :: "'m receiver_state => 'm packet multiset" |
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25 rbit :: "'m receiver_state => bool" |
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26 rsending :: "'m receiver_state => bool" |
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27 |
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28 defs |
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29 |
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30 rq_def "rq == fst" |
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31 rsent_def "rsent == fst o snd" |
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32 rrcvd_def "rrcvd == fst o snd o snd" |
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33 rbit_def "rbit == fst o snd o snd o snd" |
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34 rsending_def "rsending == snd o snd o snd o snd" |
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35 |
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36 receiver_asig_def "receiver_asig == |
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37 <UN pkt. {R_pkt(pkt)}, |
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38 (UN m. {R_msg(m)}) Un (UN b. {S_ack(b)}), |
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39 insert(C_m_r, UN m. {C_r_r(m)})>" |
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40 |
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41 receiver_trans_def "receiver_trans == |
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42 {tr. let s = fst(tr); |
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43 t = snd(snd(tr)) |
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44 in |
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45 case fst(snd(tr)) |
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46 of |
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47 S_msg(m) => False | |
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48 R_msg(m) => rq(s) = (m # rq(t)) & |
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49 rsent(t)=rsent(s) & |
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50 rrcvd(t)=rrcvd(s) & |
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51 rbit(t)=rbit(s) & |
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52 rsending(t)=rsending(s) | |
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53 S_pkt(pkt) => False | |
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54 R_pkt(pkt) => rq(t) = rq(s) & |
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55 rsent(t) = rsent(s) & |
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56 rrcvd(t) = addm(rrcvd(s),pkt) & |
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57 rbit(t) = rbit(s) & |
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58 rsending(t) = rsending(s) | |
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59 S_ack(b) => b = rbit(s) & |
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60 rq(t) = rq(s) & |
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61 rsent(t) = addm(rsent(s),rbit(s)) & |
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62 rrcvd(t) = rrcvd(s) & |
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63 rbit(t)=rbit(s) & |
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64 rsending(s) & |
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65 rsending(t) | |
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66 R_ack(b) => False | |
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67 C_m_s => False | |
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68 C_m_r => count(rsent(s),~rbit(s)) < countm(rrcvd(s),%y.hdr(y)=rbit(s)) & |
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69 rq(t) = rq(s) & |
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70 rsent(t)=rsent(s) & |
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71 rrcvd(t)=rrcvd(s) & |
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72 rbit(t)=rbit(s) & |
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73 rsending(s) & |
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74 ~rsending(t) | |
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75 C_r_s => False | |
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76 C_r_r(m) => count(rsent(s),rbit(s)) <= countm(rrcvd(s),%y.hdr(y)=rbit(s)) & |
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77 count(rsent(s),~rbit(s)) < count(rrcvd(s),<rbit(s),m>) & |
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78 rq(t) = rq(s)@[m] & |
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79 rsent(t)=rsent(s) & |
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80 rrcvd(t)=rrcvd(s) & |
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81 rbit(t) = (~rbit(s)) & |
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82 ~rsending(s) & |
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83 rsending(t)}" |
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84 |
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85 |
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86 receiver_ioa_def "receiver_ioa == |
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87 <receiver_asig, {<[],{|},{|},False,False>}, receiver_trans>" |
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88 |
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89 end |
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