--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOLCF/IOA/NTP/Impl.thy Wed Apr 30 11:25:31 1997 +0200
@@ -0,0 +1,71 @@
+(* 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