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(* Title: HOL/IOA/example/Sender.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: sender
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*)
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Sender = IOA + Action + Multiset + List +
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156
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types
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'm sender_state = "'m list * bool multiset * bool multiset * bool * bool"
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(* messages #sent #received header mode *)
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consts
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sender_asig :: "'m action signature"
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sender_trans :: "('m action, 'm sender_state)transition set"
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sender_ioa :: "('m action, 'm sender_state)ioa"
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sq :: "'m sender_state => 'm list"
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ssent,srcvd :: "'m sender_state => bool multiset"
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sbit :: "'m sender_state => bool"
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ssending :: "'m sender_state => bool"
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168
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defs
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sq_def "sq == fst"
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ssent_def "ssent == fst o snd"
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srcvd_def "srcvd == fst o snd o snd"
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sbit_def "sbit == fst o snd o snd o snd"
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ssending_def "ssending == snd o snd o snd o snd"
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sender_asig_def
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"sender_asig == <(UN m. {S_msg(m)}) Un (UN b. {R_ack(b)}),
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UN pkt. {S_pkt(pkt)},
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{C_m_s,C_r_s}>"
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sender_trans_def "sender_trans ==
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{tr. let s = fst(tr);
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t = snd(snd(tr))
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in case fst(snd(tr))
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of
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S_msg(m) => sq(t)=sq(s)@[m] &
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ssent(t)=ssent(s) &
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srcvd(t)=srcvd(s) &
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sbit(t)=sbit(s) &
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ssending(t)=ssending(s) |
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R_msg(m) => False |
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S_pkt(pkt) => hdr(pkt) = sbit(s) &
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(? Q. sq(s) = (msg(pkt)#Q)) &
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sq(t) = sq(s) &
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ssent(t) = addm(ssent(s),sbit(s)) &
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srcvd(t) = srcvd(s) &
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sbit(t) = sbit(s) &
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ssending(s) &
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ssending(t) |
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R_pkt(pkt) => False |
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S_ack(b) => False |
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R_ack(b) => sq(t)=sq(s) &
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ssent(t)=ssent(s) &
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srcvd(t) = addm(srcvd(s),b) &
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sbit(t)=sbit(s) &
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ssending(t)=ssending(s) |
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C_m_s => count(ssent(s),~sbit(s)) < count(srcvd(s),~sbit(s)) &
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sq(t)=sq(s) &
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ssent(t)=ssent(s) &
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srcvd(t)=srcvd(s) &
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sbit(t)=sbit(s) &
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ssending(s) &
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~ssending(t) |
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C_m_r => False |
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C_r_s => count(ssent(s),sbit(s)) <= count(srcvd(s),~sbit(s)) &
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sq(t)=tl(sq(s)) &
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ssent(t)=ssent(s) &
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srcvd(t)=srcvd(s) &
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sbit(t) = (~sbit(s)) &
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~ssending(s) &
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ssending(t) |
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C_r_r(m) => False}"
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sender_ioa_def "sender_ioa ==
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<sender_asig, {<[],{|},{|},False,True>}, sender_trans>"
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end
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