author | wenzelm |
Thu, 15 Feb 2018 12:11:00 +0100 | |
changeset 67613 | ce654b0e6d69 |
parent 66453 | cc19f7ca2ed6 |
permissions | -rw-r--r-- |
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(* Title: HOL/HOLCF/IOA/NTP/Sender.thy |
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Author: Tobias Nipkow & Konrad Slind |
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*) |
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section \<open>The implementation: sender\<close> |
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theory Sender |
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session-qualified theory imports: isabelle imports -U -i -d '~~/src/Benchmarks' -a;
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imports IOA.IOA Action |
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begin |
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type_synonym |
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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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definition sq :: "'m sender_state => 'm list" where "sq = fst" |
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definition ssent :: "'m sender_state => bool multiset" where "ssent = fst \<circ> snd" |
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definition srcvd :: "'m sender_state => bool multiset" where "srcvd = fst \<circ> snd \<circ> snd" |
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definition sbit :: "'m sender_state => bool" where "sbit = fst \<circ> snd \<circ> snd \<circ> snd" |
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definition ssending :: "'m sender_state => bool" where "ssending = snd \<circ> snd \<circ> snd \<circ> snd" |
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definition |
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sender_asig :: "'m action signature" where |
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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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definition |
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sender_trans :: "('m action, 'm sender_state)transition set" where |
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"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] \<and> |
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ssent(t)=ssent(s) \<and> |
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srcvd(t)=srcvd(s) \<and> |
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sbit(t)=sbit(s) \<and> |
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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) \<and> |
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(\<exists>Q. sq(s) = (msg(pkt)#Q)) \<and> |
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sq(t) = sq(s) \<and> |
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ssent(t) = addm (ssent s) (sbit s) \<and> |
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srcvd(t) = srcvd(s) \<and> |
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sbit(t) = sbit(s) \<and> |
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ssending(s) \<and> |
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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) \<and> |
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ssent(t)=ssent(s) \<and> |
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srcvd(t) = addm (srcvd s) b \<and> |
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sbit(t)=sbit(s) \<and> |
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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) \<and> |
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sq(t)=sq(s) \<and> |
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ssent(t)=ssent(s) \<and> |
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srcvd(t)=srcvd(s) \<and> |
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sbit(t)=sbit(s) \<and> |
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ssending(s) \<and> |
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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) \<and> |
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sq(t)=tl(sq(s)) \<and> |
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ssent(t)=ssent(s) \<and> |
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srcvd(t)=srcvd(s) \<and> |
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sbit(t) = (~sbit(s)) \<and> |
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~ssending(s) \<and> |
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ssending(t) | |
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C_r_r(m) => False}" |
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definition |
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sender_ioa :: "('m action, 'm sender_state)ioa" where |
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"sender_ioa = |
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(sender_asig, {([],{|},{|},False,True)}, sender_trans,{},{})" |
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lemma in_sender_asig: |
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"S_msg(m) \<in> actions(sender_asig)" |
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"R_msg(m) \<notin> actions(sender_asig)" |
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"S_pkt(pkt) \<in> actions(sender_asig)" |
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"R_pkt(pkt) \<notin> actions(sender_asig)" |
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"S_ack(b) \<notin> actions(sender_asig)" |
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"R_ack(b) \<in> actions(sender_asig)" |
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"C_m_s \<in> actions(sender_asig)" |
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"C_m_r \<notin> actions(sender_asig)" |
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"C_r_s \<in> actions(sender_asig)" |
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"C_r_r(m) \<notin> actions(sender_asig)" |
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by (simp_all add: sender_asig_def actions_def asig_projections) |
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lemmas sender_projections = sq_def ssent_def srcvd_def sbit_def ssending_def |
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end |