1(* Title: HOL/HOLCF/IOA/NTP/Receiver.thy 2 Author: Tobias Nipkow & Konrad Slind 3*) 4 5section \<open>The implementation: receiver\<close> 6 7theory Receiver 8imports IOA.IOA Action 9begin 10 11type_synonym 12 13'm receiver_state 14= "'m list * bool multiset * 'm packet multiset * bool * bool" 15(* messages #replies #received header mode *) 16 17definition rq :: "'m receiver_state => 'm list" where "rq == fst" 18definition rsent :: "'m receiver_state => bool multiset" where "rsent == fst \<circ> snd" 19definition rrcvd :: "'m receiver_state => 'm packet multiset" where "rrcvd == fst \<circ> snd \<circ> snd" 20definition rbit :: "'m receiver_state => bool" where "rbit == fst \<circ> snd \<circ> snd \<circ> snd" 21definition rsending :: "'m receiver_state => bool" where "rsending == snd \<circ> snd \<circ> snd \<circ> snd" 22 23definition 24 receiver_asig :: "'m action signature" where 25 "receiver_asig = 26 (UN pkt. {R_pkt(pkt)}, 27 (UN m. {R_msg(m)}) Un (UN b. {S_ack(b)}), 28 insert C_m_r (UN m. {C_r_r(m)}))" 29 30definition 31 receiver_trans:: "('m action, 'm receiver_state)transition set" where 32"receiver_trans = 33 {tr. let s = fst(tr); 34 t = snd(snd(tr)) 35 in 36 case fst(snd(tr)) 37 of 38 S_msg(m) => False | 39 R_msg(m) => rq(s) = (m # rq(t)) & 40 rsent(t)=rsent(s) & 41 rrcvd(t)=rrcvd(s) & 42 rbit(t)=rbit(s) & 43 rsending(t)=rsending(s) | 44 S_pkt(pkt) => False | 45 R_pkt(pkt) => rq(t) = rq(s) & 46 rsent(t) = rsent(s) & 47 rrcvd(t) = addm (rrcvd s) pkt & 48 rbit(t) = rbit(s) & 49 rsending(t) = rsending(s) | 50 S_ack(b) => b = rbit(s) & 51 rq(t) = rq(s) & 52 rsent(t) = addm (rsent s) (rbit s) & 53 rrcvd(t) = rrcvd(s) & 54 rbit(t)=rbit(s) & 55 rsending(s) & 56 rsending(t) | 57 R_ack(b) => False | 58 C_m_s => False | 59 C_m_r => count (rsent s) (~rbit s) < countm (rrcvd s) (%y. hdr(y)=rbit(s)) & 60 rq(t) = rq(s) & 61 rsent(t)=rsent(s) & 62 rrcvd(t)=rrcvd(s) & 63 rbit(t)=rbit(s) & 64 rsending(s) & 65 ~rsending(t) | 66 C_r_s => False | 67 C_r_r(m) => count (rsent s) (rbit s) <= countm (rrcvd s) (%y. hdr(y)=rbit(s)) & 68 count (rsent s) (~rbit s) < count (rrcvd s) (rbit(s),m) & 69 rq(t) = rq(s)@[m] & 70 rsent(t)=rsent(s) & 71 rrcvd(t)=rrcvd(s) & 72 rbit(t) = (~rbit(s)) & 73 ~rsending(s) & 74 rsending(t)}" 75 76definition 77 receiver_ioa :: "('m action, 'm receiver_state)ioa" where 78 "receiver_ioa = 79 (receiver_asig, {([],{|},{|},False,False)}, receiver_trans,{},{})" 80 81lemma in_receiver_asig: 82 "S_msg(m) \<notin> actions(receiver_asig)" 83 "R_msg(m) \<in> actions(receiver_asig)" 84 "S_pkt(pkt) \<notin> actions(receiver_asig)" 85 "R_pkt(pkt) \<in> actions(receiver_asig)" 86 "S_ack(b) \<in> actions(receiver_asig)" 87 "R_ack(b) \<notin> actions(receiver_asig)" 88 "C_m_s \<notin> actions(receiver_asig)" 89 "C_m_r \<in> actions(receiver_asig)" 90 "C_r_s \<notin> actions(receiver_asig)" 91 "C_r_r(m) \<in> actions(receiver_asig)" 92 by (simp_all add: receiver_asig_def actions_def asig_projections) 93 94lemmas receiver_projections = rq_def rsent_def rrcvd_def rbit_def rsending_def 95 96end 97