Theory Receiver

theory Receiver
imports IOA Action Lemmas
(*  Title:      HOL/HOLCF/IOA/ABP/Receiver.thy
    Author:     Olaf Müller
*)

section ‹The implementation: receiver›

theory Receiver
imports IOA.IOA Action Lemmas
begin

type_synonym
  'm receiver_state = "'m list * bool"  ― ‹messages, mode›

definition
  rq :: "'m receiver_state => 'm list" where
  "rq = fst"

definition
  rbit :: "'m receiver_state => bool" where
  "rbit = 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)}),
    {})"

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
        Next    =>  False |
        S_msg(m) => False |
        R_msg(m) => (rq(s) ~= [])  &
                     m = hd(rq(s))  &
                     rq(t) = tl(rq(s))   &
                    rbit(t)=rbit(s)  |
        S_pkt(pkt) => False |
        R_pkt(pkt) => if (hdr(pkt) ~= rbit(s))&rq(s)=[] then
                           rq(t) = (rq(s)@[msg(pkt)]) &rbit(t) = (~rbit(s)) else
                           rq(t) =rq(s) & rbit(t)=rbit(s)  |
        S_ack(b) => b = rbit(s)                        &
                        rq(t) = rq(s)                    &
                        rbit(t)=rbit(s) |
        R_ack(b) => False}"

definition
  receiver_ioa :: "('m action, 'm receiver_state)ioa" where
  "receiver_ioa =
   (receiver_asig, {([],False)}, receiver_trans,{},{})"

end