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(* Title: HOL/HOLCF/IOA/NTP/Receiver.thy
Author: Tobias Nipkow & Konrad Slind
*)
section \<open>The implementation: receiver\<close>
theory Receiver
imports IOA.IOA Action
begin
type_synonym
'm receiver_state
= "'m list * bool multiset * 'm packet multiset * bool * bool"
(* messages #replies #received header mode *)
definition rq :: "'m receiver_state => 'm list" where "rq == fst"
definition rsent :: "'m receiver_state => bool multiset" where "rsent == fst \ snd"
definition rrcvd :: "'m receiver_state => 'm packet multiset" where "rrcvd == fst \ snd \ snd"
definition rbit :: "'m receiver_state => bool" where "rbit == fst \ snd \ snd \ snd"
definition rsending :: "'m receiver_state => bool" where "rsending == snd \ snd \ snd \ snd"
definition
receiver_asig :: "'m action signature" where
"receiver_asig =
(UN pkt. {R_pkt(pkt)},
(UN m. {R_msg(m)}) Un (UN b. {S_ack(b)}),
insert C_m_r (UN m. {C_r_r(m)}))"
definition
receiver_trans:: "('m action, 'm receiver_state)transition set" where
"receiver_trans =
{tr. let s = fst(tr);
t = snd(snd(tr))
in
case fst(snd(tr))
of
S_msg(m) => False |
R_msg(m) => rq(s) = (m # rq(t)) &
rsent(t)=rsent(s) &
rrcvd(t)=rrcvd(s) &
rbit(t)=rbit(s) &
rsending(t)=rsending(s) |
S_pkt(pkt) => False |
R_pkt(pkt) => rq(t) = rq(s) &
rsent(t) = rsent(s) &
rrcvd(t) = addm (rrcvd s) pkt &
rbit(t) = rbit(s) &
rsending(t) = rsending(s) |
S_ack(b) => b = rbit(s) &
rq(t) = rq(s) &
rsent(t) = addm (rsent s) (rbit s) &
rrcvd(t) = rrcvd(s) &
rbit(t)=rbit(s) &
rsending(s) &
rsending(t) |
R_ack(b) => False |
C_m_s => False |
C_m_r => count (rsent s) (~rbit s) < countm (rrcvd s) (%y. hdr(y)=rbit(s)) &
rq(t) = rq(s) &
rsent(t)=rsent(s) &
rrcvd(t)=rrcvd(s) &
rbit(t)=rbit(s) &
rsending(s) &
~rsending(t) |
C_r_s => False |
C_r_r(m) => count (rsent s) (rbit s) <= countm (rrcvd s) (%y. hdr(y)=rbit(s)) &
count (rsent s) (~rbit s) < count (rrcvd s) (rbit(s),m) &
rq(t) = rq(s)@[m] &
rsent(t)=rsent(s) &
rrcvd(t)=rrcvd(s) &
rbit(t) = (~rbit(s)) &
~rsending(s) &
rsending(t)}"
definition
receiver_ioa :: "('m action, 'm receiver_state)ioa" where
"receiver_ioa =
(receiver_asig, {([],{|},{|},False,False)}, receiver_trans,{},{})"
lemma in_receiver_asig:
"S_msg(m) \ actions(receiver_asig)"
"R_msg(m) \ actions(receiver_asig)"
"S_pkt(pkt) \ actions(receiver_asig)"
"R_pkt(pkt) \ actions(receiver_asig)"
"S_ack(b) \ actions(receiver_asig)"
"R_ack(b) \ actions(receiver_asig)"
"C_m_s \ actions(receiver_asig)"
"C_m_r \ actions(receiver_asig)"
"C_r_s \ actions(receiver_asig)"
"C_r_r(m) \ actions(receiver_asig)"
by (simp_all add: receiver_asig_def actions_def asig_projections)
lemmas receiver_projections = rq_def rsent_def rrcvd_def rbit_def rsending_def
end
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