(* Title: HOL/IOA/NTP/Impl.thy
ID: $Id$
Author: Tobias Nipkow & Konrad Slind
Copyright 1994 TU Muenchen
The implementation
*)
Impl = Sender + Receiver + Abschannel +
types
'm impl_state
= "'m sender_state * 'm receiver_state * 'm packet multiset * bool multiset"
(* sender_state * receiver_state * srch_state * rsch_state *)
consts
impl_ioa :: ('m action, 'm impl_state)ioa
sen :: 'm impl_state => 'm sender_state
rec :: 'm impl_state => 'm receiver_state
srch :: 'm impl_state => 'm packet multiset
rsch :: 'm impl_state => bool multiset
inv1, inv2,
inv3, inv4 :: 'm impl_state => bool
hdr_sum :: 'm packet multiset => bool => nat
defs
impl_def
"impl_ioa == (sender_ioa || receiver_ioa || srch_ioa || rsch_ioa)"
sen_def "sen == fst"
rec_def "rec == fst o snd"
srch_def "srch == fst o snd o snd"
rsch_def "rsch == snd o snd o snd"
hdr_sum_def
"hdr_sum M b == countm M (%pkt. hdr(pkt) = b)"
(* Lemma 5.1 *)
inv1_def
"inv1(s) ==
(!b. count (rsent(rec s)) b = count (srcvd(sen s)) b + count (rsch s) b)
& (!b. count (ssent(sen s)) b
= hdr_sum (rrcvd(rec s)) b + hdr_sum (srch s) b)"
(* Lemma 5.2 *)
inv2_def "inv2(s) ==
(rbit(rec(s)) = sbit(sen(s)) &
ssending(sen(s)) &
count (rsent(rec s)) (~sbit(sen s)) <= count (ssent(sen s)) (~sbit(sen s)) &
count (ssent(sen s)) (~sbit(sen s)) <= count (rsent(rec s)) (sbit(sen s)))
|
(rbit(rec(s)) = (~sbit(sen(s))) &
rsending(rec(s)) &
count (ssent(sen s)) (~sbit(sen s)) <= count (rsent(rec s)) (sbit(sen s)) &
count (rsent(rec s)) (sbit(sen s)) <= count (ssent(sen s)) (sbit(sen s)))"
(* Lemma 5.3 *)
inv3_def "inv3(s) ==
rbit(rec(s)) = sbit(sen(s))
--> (!m. sq(sen(s))=[] | m ~= hd(sq(sen(s)))
--> count (rrcvd(rec s)) (sbit(sen(s)),m)
+ count (srch s) (sbit(sen(s)),m)
<= count (rsent(rec s)) (~sbit(sen s)))"
(* Lemma 5.4 *)
inv4_def "inv4(s) == rbit(rec(s)) = (~sbit(sen(s))) --> sq(sen(s)) ~= []"
end