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1 Sender = IOA + Action + Multiset + List + "Lemmas" + |
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2 |
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3 types |
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4 |
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5 'm sender_state = "'m list * bool multiset * bool multiset * bool * bool" |
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6 (* messages #sent #received header mode *) |
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7 |
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8 consts |
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9 |
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10 sender_asig :: "'m action signature" |
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11 sender_trans :: "('m action, 'm sender_state)transition set" |
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12 sender_ioa :: "('m action, 'm sender_state)ioa" |
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13 sq :: "'m sender_state => 'm list" |
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14 ssent,srcvd :: "'m sender_state => bool multiset" |
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15 sbit :: "'m sender_state => bool" |
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16 ssending :: "'m sender_state => bool" |
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17 |
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18 rules |
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19 |
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20 sq_def "sq == fst" |
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21 ssent_def "ssent == fst o snd" |
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22 srcvd_def "srcvd == fst o snd o snd" |
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23 sbit_def "sbit == fst o snd o snd o snd" |
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24 ssending_def "ssending == snd o snd o snd o snd" |
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25 |
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26 sender_asig_def |
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27 "sender_asig == <(UN m. {S_msg(m)}) Un (UN b. {R_ack(b)}), \ |
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28 \ UN pkt. {S_pkt(pkt)}, \ |
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29 \ {C_m_s,C_r_s}>" |
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30 |
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31 sender_trans_def "sender_trans == \ |
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32 \ {tr. let s = fst(tr); \ |
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33 \ t = snd(snd(tr)) \ |
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34 \ in case fst(snd(tr)) \ |
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35 \ of \ |
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36 \ S_msg(m) => sq(t)=sq(s)@[m] & \ |
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37 \ ssent(t)=ssent(s) & \ |
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38 \ srcvd(t)=srcvd(s) & \ |
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39 \ sbit(t)=sbit(s) & \ |
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40 \ ssending(t)=ssending(s) | \ |
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41 \ R_msg(m) => False | \ |
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42 \ S_pkt(pkt) => hdr(pkt) = sbit(s) & \ |
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43 \ (? Q. sq(s) = (msg(pkt)#Q)) & \ |
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44 \ sq(t) = sq(s) & \ |
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45 \ ssent(t) = addm(ssent(s),sbit(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(s) & \ |
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49 \ ssending(t) | \ |
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50 \ R_pkt(pkt) => False | \ |
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51 \ S_ack(b) => False | \ |
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52 \ R_ack(b) => sq(t)=sq(s) & \ |
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53 \ ssent(t)=ssent(s) & \ |
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54 \ srcvd(t) = addm(srcvd(s),b) & \ |
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55 \ sbit(t)=sbit(s) & \ |
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56 \ ssending(t)=ssending(s) | \ |
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57 \ C_m_s => count(ssent(s),~sbit(s)) < count(srcvd(s),~sbit(s)) & \ |
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58 \ sq(t)=sq(s) & \ |
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59 \ ssent(t)=ssent(s) & \ |
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60 \ srcvd(t)=srcvd(s) & \ |
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61 \ sbit(t)=sbit(s) & \ |
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62 \ ssending(s) & \ |
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63 \ ~ssending(t) | \ |
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64 \ C_m_r => False | \ |
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65 \ C_r_s => count(ssent(s),sbit(s)) <= count(srcvd(s),~sbit(s)) & \ |
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66 \ sq(t)=tl(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_r_r(m) => False}" |
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73 |
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74 sender_ioa_def "sender_ioa == \ |
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75 \ <sender_asig, {<[],{|},{|},False,True>}, sender_trans>" |
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76 |
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77 end |