src/HOLCF/IOA/NTP/Impl.thy
changeset 3073 88366253a09a
child 3852 e694c660055b
--- /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