(* Title: HOL/IOA/NTP/Sender.thy
ID: $Id$
Author: Tobias Nipkow & Konrad Slind
The implementation: sender.
*)
Sender = IOA + Action + List +
types
'm sender_state = "'m list * bool multiset * bool multiset * bool * bool"
(* messages #sent #received header mode *)
consts
sender_asig :: "'m action signature"
sender_trans :: ('m action, 'm sender_state)transition set
sender_ioa :: ('m action, 'm sender_state)ioa
sq :: 'm sender_state => 'm list
ssent,srcvd :: 'm sender_state => bool multiset
sbit :: 'm sender_state => bool
ssending :: 'm sender_state => bool
defs
sq_def "sq == fst"
ssent_def "ssent == fst o snd"
srcvd_def "srcvd == fst o snd o snd"
sbit_def "sbit == fst o snd o snd o snd"
ssending_def "ssending == snd o snd o snd o snd"
sender_asig_def
"sender_asig == ((UN m. {S_msg(m)}) Un (UN b. {R_ack(b)}),
UN pkt. {S_pkt(pkt)},
{C_m_s,C_r_s})"
sender_trans_def "sender_trans ==
{tr. let s = fst(tr);
t = snd(snd(tr))
in case fst(snd(tr))
of
S_msg(m) => sq(t)=sq(s)@[m] &
ssent(t)=ssent(s) &
srcvd(t)=srcvd(s) &
sbit(t)=sbit(s) &
ssending(t)=ssending(s) |
R_msg(m) => False |
S_pkt(pkt) => hdr(pkt) = sbit(s) &
(? Q. sq(s) = (msg(pkt)#Q)) &
sq(t) = sq(s) &
ssent(t) = addm (ssent s) (sbit s) &
srcvd(t) = srcvd(s) &
sbit(t) = sbit(s) &
ssending(s) &
ssending(t) |
R_pkt(pkt) => False |
S_ack(b) => False |
R_ack(b) => sq(t)=sq(s) &
ssent(t)=ssent(s) &
srcvd(t) = addm (srcvd s) b &
sbit(t)=sbit(s) &
ssending(t)=ssending(s) |
C_m_s => count (ssent s) (~sbit s) < count (srcvd s) (~sbit s) &
sq(t)=sq(s) &
ssent(t)=ssent(s) &
srcvd(t)=srcvd(s) &
sbit(t)=sbit(s) &
ssending(s) &
~ssending(t) |
C_m_r => False |
C_r_s => count (ssent s) (sbit s) <= count (srcvd s) (~sbit s) &
sq(t)=tl(sq(s)) &
ssent(t)=ssent(s) &
srcvd(t)=srcvd(s) &
sbit(t) = (~sbit(s)) &
~ssending(s) &
ssending(t) |
C_r_r(m) => False}"
sender_ioa_def "sender_ioa ==
(sender_asig, {([],{|},{|},False,True)}, sender_trans,{},{})"
end