(* Title: HOL/IOA/NTP/Sender.thy
ID: $Id$
Author: Tobias Nipkow & Konrad Slind
Copyright 1994 TU Muenchen
The implementation: sender
*)
Sender = IOA + Action + Multiset + 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