(* Title: HOL/IOA/example/Sender.thy
ID: $Id$
Author: Tobias Nipkow & Konrad Slind
Copyright 1994 TU Muenchen
The implementation: sender
*)
Sender = IOA + Action + List + Lemmas +
types
'm sender_state = "'m list * bool"
(* messages Alternating Bit *)
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"
sbit :: "'m sender_state => bool"
defs
sq_def "sq == fst"
sbit_def "sbit == snd"
sender_asig_def
"sender_asig == ((UN m. {S_msg(m)}) Un (UN b. {R_ack(b)}), \
\ UN pkt. {S_pkt(pkt)}, \
\ {})"
sender_trans_def "sender_trans == \
\ {tr. let s = fst(tr); \
\ t = snd(snd(tr)) \
\ in case fst(snd(tr)) \
\ of \
\ Next => if sq(s)=[] then t=s else False | \
\ S_msg(m) => sq(t)=sq(s)@[m] & \
\ sbit(t)=sbit(s) | \
\ R_msg(m) => False | \
\ S_pkt(pkt) => sq(s) ~= [] & \
\ hdr(pkt) = sbit(s) & \
\ msg(pkt) = hd(sq(s)) & \
\ sq(t) = sq(s) & \
\ sbit(t) = sbit(s) | \
\ R_pkt(pkt) => False | \
\ S_ack(b) => False | \
\ R_ack(b) => if b = sbit(s) then \
\ sq(t)=tl(sq(s)) & sbit(t)=(~sbit(s)) else \
\ sq(t)=sq(s) & sbit(t)=sbit(s)}"
sender_ioa_def "sender_ioa == \
\ (sender_asig, {([],True)}, sender_trans)"
end