--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/IOA/NTP/Impl.thy Thu Apr 13 16:57:18 1995 +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