src/HOLCF/IOA/NTP/Sender.thy
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(*  Title:      HOL/IOA/NTP/Sender.thy
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    ID:         $Id$
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    Author:     Tobias Nipkow & Konrad Slind
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*)
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header {* The implementation: sender *}
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theory Sender
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imports IOA Action
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begin
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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         :: "'m sender_state => bool multiset"
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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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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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ML {* use_legacy_bindings (the_context ()) *}
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end