1 (* Title: HOL/IOA/example/Sender.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: sender |
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7 *) |
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8 |
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9 Sender = IOA + Action + Multiset + List + |
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10 |
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11 types |
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12 |
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13 'm sender_state = "'m list * bool multiset * bool multiset * bool * bool" |
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14 (* messages #sent #received header mode *) |
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15 |
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16 consts |
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17 |
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18 sender_asig :: "'m action signature" |
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19 sender_trans :: "('m action, 'm sender_state)transition set" |
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20 sender_ioa :: "('m action, 'm sender_state)ioa" |
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21 sq :: "'m sender_state => 'm list" |
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22 ssent,srcvd :: "'m sender_state => bool multiset" |
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23 sbit :: "'m sender_state => bool" |
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24 ssending :: "'m sender_state => bool" |
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25 |
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26 defs |
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27 |
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28 sq_def "sq == fst" |
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29 ssent_def "ssent == fst o snd" |
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30 srcvd_def "srcvd == fst o snd o snd" |
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31 sbit_def "sbit == fst o snd o snd o snd" |
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32 ssending_def "ssending == snd o snd o snd o snd" |
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33 |
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34 sender_asig_def |
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35 "sender_asig == <(UN m. {S_msg(m)}) Un (UN b. {R_ack(b)}), |
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36 UN pkt. {S_pkt(pkt)}, |
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37 {C_m_s,C_r_s}>" |
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38 |
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39 sender_trans_def "sender_trans == |
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40 {tr. let s = fst(tr); |
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41 t = snd(snd(tr)) |
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42 in case fst(snd(tr)) |
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43 of |
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44 S_msg(m) => sq(t)=sq(s)@[m] & |
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45 ssent(t)=ssent(s) & |
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46 srcvd(t)=srcvd(s) & |
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47 sbit(t)=sbit(s) & |
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48 ssending(t)=ssending(s) | |
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49 R_msg(m) => False | |
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50 S_pkt(pkt) => hdr(pkt) = sbit(s) & |
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51 (? Q. sq(s) = (msg(pkt)#Q)) & |
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52 sq(t) = sq(s) & |
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53 ssent(t) = addm(ssent(s),sbit(s)) & |
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54 srcvd(t) = srcvd(s) & |
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55 sbit(t) = sbit(s) & |
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56 ssending(s) & |
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57 ssending(t) | |
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58 R_pkt(pkt) => False | |
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59 S_ack(b) => False | |
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60 R_ack(b) => sq(t)=sq(s) & |
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61 ssent(t)=ssent(s) & |
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62 srcvd(t) = addm(srcvd(s),b) & |
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63 sbit(t)=sbit(s) & |
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64 ssending(t)=ssending(s) | |
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65 C_m_s => count(ssent(s),~sbit(s)) < count(srcvd(s),~sbit(s)) & |
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66 sq(t)=sq(s) & |
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67 ssent(t)=ssent(s) & |
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68 srcvd(t)=srcvd(s) & |
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69 sbit(t)=sbit(s) & |
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70 ssending(s) & |
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71 ~ssending(t) | |
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72 C_m_r => False | |
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73 C_r_s => count(ssent(s),sbit(s)) <= count(srcvd(s),~sbit(s)) & |
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74 sq(t)=tl(sq(s)) & |
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75 ssent(t)=ssent(s) & |
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76 srcvd(t)=srcvd(s) & |
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77 sbit(t) = (~sbit(s)) & |
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78 ~ssending(s) & |
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79 ssending(t) | |
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80 C_r_r(m) => False}" |
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81 |
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82 sender_ioa_def "sender_ioa == |
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83 <sender_asig, {<[],{|},{|},False,True>}, sender_trans>" |
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84 |
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85 end |
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