(* Title: HOL/IOA/example/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