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KVSProof.scala
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KVSProof.scala
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package distribution
import FifoNetwork._
import Networking._
import Protocol._
import stainless.lang._
import stainless.collection._
import stainless.proof._
import stainless.annotation._
import stainless.lang.synthesis._
import scala.language.postfixOps
// This object contains lemma and auxiliary functions used in the proofs
object ProtocolProof {
import Protocol._
import PrettyPrinting._
import ProtocolProof2._
import ProtocolProof3._
def subsetOf(l1: List[ActorId], l2: List[ActorId]): Boolean = {
l1 match {
case Nil() => true
case Cons(x,xs) =>
l2.contains(x) &&
subsetOf(xs, l2)
}
}
def emptyNet(): VerifiedNetwork = {
VerifiedNetwork(
Param(List(), List()),
init_states,
init_messages,
init_getActor
)
}
def areWU(list: List[(ActorId,Message)]): Boolean = {
list match {
case Cons(x,xs) if (!isWU(x._2)) => false
case Cons(_,xs) => areWU(xs)
case Nil() => true
}
}
def isWU(m: Message) = {
m match {
case WriteUser(s,i) => true
case _ => false
}
}
def isWS(m: Message) = {
m match {
case WriteSystem(s,i,id,h) => true
case _ => false
}
}
def isWW(m: Message) = {
m match {
case WriteWaiting(s,i,id,h) => true
case _ => false
}
}
def collectWUsInit(l: List[(ActorId,Message)]): Set[Message] = {
l match {
case Nil() => Set()
case Cons((id,WriteUser(s,i)), xs) => collectWUsInit(xs) ++ Set(WriteUser(s,i))
case Cons(_,xs) => collectWUsInit(xs)
}
}
def newContains(x:Message, list: List[(ActorId, Message)]): Boolean = {
list match {
case Nil() => false
case Cons(h,t) if (h._2==x) => true
case Cons(h,t) => newContains(x,t)
}
}
def differentInitMessage(list: List[(ActorId, Message)], messages: Map[(ActorId,ActorId),List[Message]]): Boolean = {
list match {
case Nil() => true
case Cons(x,xs) =>
!newContains(x._2,xs) &&
!collectWUsList(messages, channels).contains(x._2) &&
differentInitMessage(xs, messages)
}
}
def differentInitMessageWS(list: List[(ActorId, Message)], messages: Map[(ActorId,ActorId),List[Message]]): Boolean = {
list match {
case Nil() => true
case Cons(x,xs) =>
!newContains(x._2,xs) &&
!collectWSsList(messages, channels).contains(x._2) &&
differentInitMessageWS(xs, messages)
}
}
def differentInitMessageWW(list: List[(ActorId, Message)], messages: Map[(ActorId,ActorId),List[Message]]): Boolean = {
list match {
case Nil() => true
case Cons(x,xs) =>
!newContains(x._2,xs) &&
!collectWWsList(messages, channels).contains(x._2) &&
differentInitMessageWW(xs, messages)
}
}
def removeDiff(list: List[(ActorId, Message)], messages: Map[(ActorId,ActorId),List[Message]]): Boolean = {
require(
areWU(list) &&
differentInitMessage(list, messages) &&
differentInitMessageWS(list, messages) &&
differentInitMessageWW(list, messages)
)
list match {
case Nil() => true
case Cons(x,Nil())=> true
case Cons(x,xs@Cons(y,ys)) =>
!newContains(x._2, xs) &&
!newContains(y._2, ys) &&
addCollectWU(messages, (a4,x._1), x._2, channels) &&
(x._2 != y._2) &&
addCollect2(messages, (a4,x._1), x._2, channels) &&
(x._2 != y._2) &&
addCollect3(messages, (a4,x._1), x._2, channels) &&
(x._2 != y._2) &&
!collectWUsList(add(messages, (a4,x._1), x._2), channels).contains(y._2) &&
!collectWSsList(add(messages, (a4,x._1), x._2), channels).contains(y._2) &&
!collectWWsList(add(messages, (a4,x._1), x._2), channels).contains(y._2) &&
removeDiff(Cons(x,ys), messages) &&
differentInitMessage(xs, add(messages, (a4,x._1), x._2)) &&
differentInitMessageWS(xs, add(messages, (a4,x._1), x._2)) &&
differentInitMessageWW(xs, add(messages, (a4,x._1), x._2))
}
}holds
def collectContains(
messages: Map[(ActorId,ActorId),List[Message]],
c: (ActorId, ActorId),
m: Message
): Boolean = {
require(!collectWUsList(messages, channels).contains(m)&&
channels.contains(c) &&
{
m match {
case WriteUser(s,i) => true
case _ => false
}
})
!collectWUs(messages.getOrElse(c, Nil())).contains(m) &&
colLis(messages.getOrElse(c, Nil()), m) &&
!messages.getOrElse(c, Nil()).contains(m) &&
true
} holds
def colLis(l: List[Message], m: Message): Boolean = {
require(
!collectWUs(l).contains(m) && {
m match {
case WriteUser(s,i) => true
case _ => false
}
}
)
l match {
case Nil() => true
case Cons(x,xs) if (x==m) => collectWUs(l).contains(m)
case Cons(x,xs) => colLis(xs,m) && !l.contains(m)
}
}holds
def distinctElements[A](list: List[A]): Boolean = {
list match {
case Nil() => true
case Cons(x,xs) =>
!xs.contains(x) &&
distinctElements(xs)
}
}
def distinctElementsInit(list: List[(ActorId, Message)]): Boolean = {
list match {
case Nil() => true
case Cons(x,xs) =>
!newContains(x._2,xs) &&
distinctElementsInit(xs)
}
}
def validId(net: VerifiedNetwork, id: ActorId) = {
id == a1 || id == a2 || id == a3 || id == a4
}
def inChannels(net: VerifiedNetwork, id1:ActorId, id2:ActorId) = {
require(validId(net,id1) && validId(net,id2))
channels.contains((id1,id2))
}holds
// def makeInitMem(l: List[Variable]): List[(Variable,BigInt)] = {
// require(!l.isEmpty)
// l match {
// case Cons(x,Nil()) => List((x,0))
// case Cons(x,xs) => Cons((x,0),makeInitMem(xs))
// }
// }
//
// val init_mem = makeInitMem(correct_variables)
val init_mem = Map[Variable, BigInt](
Map[Variable, BigInt]()
)
// val init_param = Variables(correct_variables)
/*
val init_messages_list = List[((ActorId,ActorId),List[Message])](
((a1,a1),(Nil():List[Message])),
((a1,a2),(Nil():List[Message])),
((a1,a3),(Nil():List[Message])),
((a1,a4),(Nil():List[Message])),
((a2,a1),(Nil():List[Message])),
((a2,a2),(Nil():List[Message])),
((a2,a3),(Nil():List[Message])),
((a2,a4),(Nil():List[Message])),
((a3,a1),(Nil():List[Message])),
((a3,a2),(Nil():List[Message])),
((a3,a3),(Nil():List[Message])),
((a3,a4),(Nil():List[Message])),
((a4,a1),(Nil():List[Message])),
((a4,a2),(Nil():List[Message])),
((a4,a3),(Nil():List[Message])),
((a4,a4),(Nil():List[Message]))
)
val init_messages1 = Map.makeMap[(ActorId,ActorId),List[Message]](init_messages_list)
val init_messages = init_messages1.updated((a4,a4), Nil())
*/
// val init_states_list = List[(ActorId, State)](
// (a1,CommonState(Map.makeMap[Variable,BigInt](init_mem), Set())),
// (a2,CommonState(Map.makeMap[Variable,BigInt](init_mem), Set())),
// (a3,CommonState(Map.makeMap[Variable,BigInt](init_mem), Set())),
// (a4,UserState(Nil(),0))
// )
// val init_states = Map.makeMap[ActorId,State](init_states_list)
val init_states = Map[ActorId, State](
Map[ActorId, State](
(a1,CommonState(init_mem, Set())),
(a2,CommonState(init_mem, Set())),
(a3,CommonState(init_mem, Set())),
(a4,UserState(Nil(),0))
)
)
// val init_getActor_list = List[(ActorId,Actor)](
// (a1,SystemActor(a1, List(a2,a3))),
// (a2,SystemActor(a2, List(a1,a3))),
// (a3,SystemActor(a3, List(a1,a2))),
// (a4,UserActor(a4))
// )
// val init_getActor = Map.makeMap[ActorId,Actor](init_getActor_list)
val init_getActor = Map[ActorId, Actor](
Map[ActorId, Actor](
(a1,SystemActor(a1, List(a2,a3))),
(a2,SystemActor(a2, List(a1,a3))),
(a3,SystemActor(a3, List(a1,a2))),
(a4,UserActor(a4))
)
)
val init_messages = Map[(ActorId, ActorId), List[Message]](
Map[(ActorId, ActorId), List[Message]](
((a1,a1),(Nil():List[Message])),
((a1,a2),(Nil():List[Message])),
((a1,a3),(Nil():List[Message])),
((a1,a4),(Nil():List[Message])),
((a2,a1),(Nil():List[Message])),
((a2,a2),(Nil():List[Message])),
((a2,a3),(Nil():List[Message])),
((a2,a4),(Nil():List[Message])),
((a3,a1),(Nil():List[Message])),
((a3,a2),(Nil():List[Message])),
((a3,a3),(Nil():List[Message])),
((a3,a4),(Nil():List[Message])),
((a4,a1),(Nil():List[Message])),
((a4,a2),(Nil():List[Message])),
((a4,a3),(Nil():List[Message])),
((a4,a4),(Nil():List[Message]))
)
)
def checkContent[A,B](l: List[(A,B)], m: Map[A,B]): Boolean = {
l match {
case Nil() => true
case Cons((x,v), xs) => m.contains(x) && checkContent(xs, m)
}
}
def makeNetwork(p: Parameter) = {
require(validParam(p))
VerifiedNetwork(p,
init_states,
init_messages,
init_getActor
)
}ensuring(res =>
res.getActor(a1) == SystemActor(a1, List(a2,a3)) &&
res.getActor(a2) == SystemActor(a2, List(a1,a3)) &&
res.getActor(a3) == SystemActor(a3, List(a1,a2)) &&
res.getActor(a4) == UserActor(a4) &&
areInChannelsInit1() &&
areInChannelsInit2() &&
areInChannelsInit3() &&
areInChannelsBisInit1() &&
areInChannelsBisInit2() &&
areInChannelsBisInit3() &&
writeEmpty(res.states) &&
WriteHistory(res.messages, res.states) &&
initTableHistory(res.param, res.states) &&
tableHistory(res.param, res.states) &&
messagesEmpty(channels) &&
not2WriteUser(channels, res.messages) &&
res.messages == init_messages &&
initMessageEmpty() &&
uniqueWriteUser(res.messages, channels) &&
prop3(res.messages, channels) &&
initProp5(init_messages, channels) &&
prop5(res.messages, channels) &&
initProp7(init_messages, channels) &&
initProp4(init_messages, channels, init_states, List(a1,a2,a3)) &&
initProp9(init_messages, channels) &&
initProp10(init_messages, channels) &&
initProp8(init_messages, channels, init_states) &&
networkInvariant(res.param,res.states, res.messages, res.getActor) &&
true
)
def validParam(p: Parameter): Boolean = {
val Param(variables, initMessages) = p
areWU(initMessages) &&
distinctElementsInit(initMessages)
}
def areInChannelsInit1(): Boolean = {
areInChannels(a1, List(a2,a3))
} holds
def areInChannelsInit2(): Boolean = {
areInChannels(a2, List(a1,a3))
} holds
def areInChannelsInit3(): Boolean = {
areInChannels(a3, List(a1,a2))
} holds
def areInChannelsBisInit1(): Boolean = {
areInChannelsBis(List(a2,a3))
} holds
def areInChannelsBisInit2(): Boolean = {
areInChannelsBis(List(a1,a3))
} holds
def areInChannelsBisInit3(): Boolean = {
areInChannelsBis(List(a1,a2))
} holds
// This is an invariant of the class VerifiedNetwork
def networkInvariant(param: Parameter, states: Map[ActorId, State], messages: Map[(ActorId,ActorId),List[Message]], getActor: Map[ActorId,Actor]) = {
getActor.contains(a1) &&
getActor.contains(a2) &&
getActor.contains(a3) &&
getActor.contains(a4) &&
states.contains(a1) &&
states.contains(a2) &&
states.contains(a3) &&
states.contains(a4) &&
//messages(a4,a4).isEmpty &&
getActor(a1) == SystemActor(a1, List(a2,a3)) &&
getActor(a2) == SystemActor(a2, List(a1,a3)) &&
getActor(a3) == SystemActor(a3, List(a1,a2)) &&
areInChannels(a1, List(a2,a3)) &&
areInChannels(a2, List(a1,a3)) &&
areInChannels(a3, List(a1,a2)) &&
areInChannelsBis(List(a2,a3)) &&
areInChannelsBis(List(a1,a3)) &&
areInChannelsBis(List(a1,a2)) &&
distinctElements[ActorId](List(a1,a2)) &&
distinctElements[ActorId](List(a1,a3)) &&
distinctElements[ActorId](List(a2,a3)) &&
distinctElements[ActorId](List(a1,a2,a3)) &&
getActor(a4) == UserActor(a4) &&
distinctChannels() &&
WriteHistory(messages, states) &&
tableHistory(param, states) &&
not2WriteUser(channels, messages)&&
uniqueWriteUser(messages, channels) &&
prop3(messages, channels) &&
prop5(messages, channels) &&
prop6(messages, channels) &&
prop7(channels, messages) &&
prop4(messages, states, channels, List(a1,a2,a3)) &&
prop9(messages, channels) &&
prop10(messages, channels) &&
prop8(messages, states, channels) &&
true
}
//basic functions
def runActorsPrecondition(p: Parameter, initialActor: Actor, schedule: List[(ActorId,ActorId,Message)]) = {
initialActor.myId == a4 &&
validParam(p)
}
def userActorReceivePre(receiver: Actor, sender: ActorId, m: Message)(implicit net: VerifiedNetwork) = {
networkInvariant(net.param, net.states, net.messages, net.getActor) &&
receiver.myId == a4 &&
{
val myId = receiver.myId
(sender, m, receiver.state) match {
case (sender, Value(v,idM,h), UserState(x,counter)) =>
val newStates = net.states.updated(myId, UserState(Cons((idM,h),x), counter))
(newStates(a4) == UserState(Cons((idM,h),x), counter)) &&
ajoutUserCheckWriteForAll(channels, net.messages, x, (idM,h)) &&
checkWriteForAll(channels, net.messages, Cons((idM,h), x)) &&
addUserCheckTable(net.param, net.states, (idM, h)) &&
updateStateUserProp4(net.messages, channels, net.states, myId, UserState(Cons((idM,h),x), counter), List(a1,a2,a3)) &&
updateStateUserProp8(net.messages, net.states, channels, myId, UserState(Cons((idM,h),x), counter)) &&
networkInvariant(net.param, newStates, net.messages, net.getActor)
case (sender, AckUser(idM,h), UserState(x,counter)) =>
val newStates = net.states.updated(myId, UserState(Cons((idM,h),x), counter))
(newStates(a4) == UserState(Cons((idM,h),x), counter)) &&
ajoutUserCheckWriteForAll(channels, net.messages, x, (idM,h)) &&
checkWriteForAll(channels, net.messages, Cons((idM,h), x)) &&
addUserCheckTable(net.param, net.states, (idM, h)) &&
updateStateUserProp4(net.messages, channels, net.states, myId, UserState(Cons((idM,h),x), counter), List(a1,a2,a3)) &&
updateStateUserProp8(net.messages, net.states, channels, myId, UserState(Cons((idM,h),x), counter)) &&
networkInvariant(net.param, newStates, net.messages, net.getActor)
case _ => true
}
} &&
true
}
def addMessage(otherActor: List[ActorId], messages:Map[(ActorId, ActorId), List[Message]], m: Message, id: ActorId):Map[(ActorId, ActorId), List[Message]] = {
require{
m match {
case WriteSystem(s,i,idM,h) => true
case _ => false
}
}
val WriteSystem(s,i,idM,h) = m
otherActor match {
case Nil() =>
messages.updated((id,a4), messages.getOrElse((id,a4), Nil()) :+ AckUser(idM,h))
case Cons(x,xs) =>
val newMessages = messages.updated((id,x), messages.getOrElse((id,x), Nil()) :+ m)
addMessage(xs, newMessages, m, id)
}
}
def areInChannels(id: ActorId, l: List[ActorId]): Boolean = {
l match {
case Nil() => true
case Cons(x,xs) =>
channels.contains((id,x)) &&
areInChannels(id, xs)
}
}
def areInChannelsBis(l: List[ActorId]): Boolean = {
l match {
case Nil() => true
case Cons(x,xs) =>
channels.contains((x,x)) &&
areInChannelsBis(xs)
}
}
def broadcastAckPre(
receiver: Actor,
otherActor: List[ActorId],
m: Message,
param: Parameter,
states: Map[ActorId, State],
messages: Map[(ActorId, ActorId), List[Message]],
getActor: Map[ActorId, Actor]
): Boolean = {
(receiver.myId == a1 || receiver.myId == a2 || receiver.myId == a3) &&
networkInvariant(param, states, messages, getActor) &&
distinctElements[ActorId](otherActor) &&
{
receiver match {
case SystemActor(_,_) => true
case _ => false
}
} &&
{
val UserState(userHistory,c) = states(a4)
m match {
case WriteSystem(x,v,idM,h) =>
userHistory.contains((idM,Set())) &&
!collectWUsList(messages, channels).contains(WriteUser(x,v)) &&
collectOtherActor(receiver.myId, otherActor, messages, WriteUser(x,v)) &&
collectOtherActorProp7(otherActor, messages, WriteUser(x,v)) &&
collectOtherActorProp9(otherActor, messages, WriteUser(x,v)) &&
!collectWWsList(messages, channels).contains(WriteUser(x,v)) &&
!allHistoriesContains_aux(x, v, otherActor, states) &&
true
case _ => false
}
} &&
{
broadcastAckPreBis(receiver, otherActor, m, param, states, messages, getActor)
}
}
def broadcastAckPreBis(
receiver: Actor,
otherActor: List[ActorId],
m: Message,
param: Parameter,
states: Map[ActorId, State],
messages: Map[(ActorId, ActorId), List[Message]],
getActor: Map[ActorId, Actor]
): Boolean = {
require(
distinctElements[ActorId](otherActor) &&
(receiver.myId == a1 || receiver.myId == a2 || receiver.myId == a3) &&
networkInvariant(param, states, messages, getActor) &&
{
receiver match {
case SystemActor(_,_) => true
case _ => false
}
} &&
{
val UserState(userHistory,c) = states(a4)
m match {
case WriteSystem(x,v,idM,h) =>
userHistory.contains((idM,Set())) &&
!collectWUsList(messages, channels).contains(WriteUser(x,v)) &&
collectOtherActor(receiver.myId, otherActor, messages, WriteUser(x,v)) &&
collectOtherActorProp7(otherActor, messages, WriteUser(x,v)) &&
collectOtherActorProp9(otherActor, messages, WriteUser(x,v)) &&
!collectWWsList(messages, channels).contains(WriteUser(x,v)) &&
!allHistoriesContains_aux(x, v, otherActor, states)
case _ => false
}
}
)
val myId = receiver.myId
val UserState(userHistory,c) = states(a4)
val WriteSystem(s,i,idM,h) = m
otherActor match {
case Nil() =>
val newMessages = messages.updated((myId,a4), messages.getOrElse((myId,a4), Nil()) :+ AckUser(idM,h))
addNot2WriteUser(channels, messages, myId, a4, AckUser(idM,h)) &&
addUniqueWriteUser(messages, channels, (myId,a4), AckUser(idM,h)) &&
(ajoutCheckWriteForAll( channels, messages, userHistory, AckUser(idM,h), myId, a4)) &&
addOtherProp3(messages, channels, (myId,a4), AckUser(idM,h)) &&
addOtherprop5(messages, channels, (myId,a4), AckUser(idM,h)) &&
addOtherProp6(messages, channels, (myId,a4), AckUser(idM,h)) &&
addProp7(messages, channels, (myId, a4), AckUser(idM,h)) &&
addOtherProp4(messages, channels, states, (myId,a4), AckUser(idM,h), List(a1,a2,a3)) &&
addOtherProp9(messages, channels, (myId,a4), AckUser(idM,h)) &&
WriteHistory(newMessages, states) &&
addProp10(messages, channels, (myId, a4), AckUser(idM,h)) &&
addOtherProp8(messages, states, channels, (myId, a4), AckUser(idM,h)) &&
networkInvariant(param, states, newMessages, getActor) &&
networkInvariant(param, states, addMessage(otherActor, messages, m, myId), getActor) &&
true
case Cons(x, xs) =>
val newMessages = messages.updated((myId,x), messages.getOrElse((myId,x), Nil()) :+ m)
addNot2WriteUser(channels, messages, myId, x, m) &&
addUniqueWriteUser(messages, channels, (myId,x), m) &&
(ajoutCheckWriteForAll(channels, messages, userHistory, m, myId, x)) &&
addWSprop3(messages, channels, (myId,x), m) &&
broadcastAckPreInduct(myId, otherActor, messages, m) &&
broadcastAckPreInductProp7(myId, otherActor, messages, m) &&
broadcastAckPreInductProp9(myId, otherActor, messages, m) &&
addCollect3(messages, (myId, x), m, channels) &&
addWSprop5(messages, channels, (myId,x), m) &&
addOtherProp6(messages, channels, (myId,x), m) &&
addProp7(messages, channels, (myId,x), m) &&
addOtherProp4(messages, channels, states, (myId,x), m, List(a1,a2,a3)) &&
addWSProp9(messages, channels, (myId,x), m) &&
addProp10(messages, channels, (myId, x), m) &&
addWSProp8(messages, states, channels, (myId,x), m, otherActor) &&
WriteHistory(newMessages, states) &&
networkInvariant(param, states, newMessages, getActor) &&
true
}
} holds
def systemActorReceivePreCase1(
receiver: Actor,
sender: ActorId,
m: Message
)(implicit net: VerifiedNetwork): Boolean = {
require{
{
receiver match {
case SystemActor(_,otherActor) =>
areInChannels(receiver.myId, otherActor) &&
areInChannelsBis(otherActor) &&
subsetOf(otherActor, List(a1,a2,a3)) &&
!otherActor.contains(receiver.myId) &&
true
case _ => false
}
} &&
(receiver.myId == a1 || receiver.myId == a2 || receiver.myId == a3) &&
networkInvariant(net.param, net.states, net.messages, net.getActor) &&
{
val UserState(userHistory,c) = net.states(a4)
(sender, m, receiver.state) match{
case (id, WriteUser(s,i), CommonState(mem,h)) =>
userHistory.contains(((true, s, i),Set())) &&
!collectWSsList(net.messages, channels).contains(WriteUser(s,i)) &&
!collectWUsList(net.messages, channels).contains(WriteUser(s,i)) &&
!collectWWsList(net.messages, channels).contains(WriteUser(s,i)) &&
!allHistoriesContains_aux(s, i, List(a1,a2,a3), net.states)
case _ => false
}
}
}
//val UserState(userHistory,c) = net.states(a4)
val myId = receiver.myId
val SystemActor(_, otherActor) = receiver
val WriteUser(s,i) = m
val CommonState(mem,h) = receiver.state
val idM = (true, s, i)
val newStates = net.states.updated(myId, CommonState(mem.updated(s,i),h++Set((true,s, i))))
val variables = extractVariables(net.param)
val UserState(newUserHistory,newc) = newStates(a4)
newUserHistory.contains((true, s, i), Set()) &&
updateCheckTable(net.param, net.states, s, i, myId) &&
tableHistory(net.param, newStates) &&
leMaprop5_2(myId, otherActor, net.messages, s, i) &&
collectOtherActor(myId, otherActor, net.messages, WriteUser(s,i)) &&
leMaprop7(myId, otherActor, net.messages, s, i) &&
collectOtherActorProp7(otherActor, net.messages, WriteUser(s,i)) &&
updateStateSystemProp4(net.messages, channels, net.states, myId, s, i, List(a1,a2,a3)) &&
lemmaReceiveProp9(otherActor, net.messages, WriteUser(s,i)) &&
collectOtherActorProp9(otherActor, net.messages, WriteUser(s,i))
leMaprop8_2(net.messages, channels, myId, WriteUser(s,i)) &&
updateStateSystemProp8(net.messages, net.states, channels, myId, s, i) &&
leMaprop8_3(s,i,otherActor, List(a1,a2,a3), net.states, CommonState(mem.updated(s,i),h++Set((true,s, i))), myId) &&
!allHistoriesContains_aux(s, i, otherActor, newStates) &&
networkInvariant(net.param, newStates, net.messages, net.getActor) &&
true
}holds
def systemActorReceivePreCase2(
receiver: Actor,
sender: ActorId,
m: Message
)(implicit net: VerifiedNetwork): Boolean = {
require{
(receiver.myId == a1 || receiver.myId == a2 || receiver.myId == a3) &&
networkInvariant(net.param, net.states, net.messages, net.getActor) &&
{
val UserState(userHistory,c) = net.states(a4)
m match {
case WriteUser(x,v) =>
userHistory.contains(((true, x, v),Set())) &&
!collectWUsList(net.messages, channels).contains(WriteUser(x,v)) &&
!collectWSsList(net.messages, channels).contains(WriteUser(x,v)) &&
!collectWWsList(net.messages, channels).contains(WriteUser(x,v))
case WriteSystem(x,v,idM,h) =>
userHistory.contains((idM,Set())) &&
!collectWUsList(net.messages, channels).contains(WriteUser(x,v)) &&
!collectNeighbour(receiver.myId, channels, net.messages).contains(WriteUser(x,v)) &&
!collectWWs(net.messages.getOrElse((receiver.myId, receiver.myId), Nil())).contains(WriteUser(x,v))
case WriteWaiting(x,v,idM,h) =>
userHistory.contains((idM,Set())) &&
!collectWUsList(net.messages, channels).contains(WriteUser(x,v)) &&
!collectNeighbour(receiver.myId, channels, net.messages).contains(WriteUser(x,v)) &&
!collectWWs(net.messages.getOrElse((receiver.myId, sender), Nil())).contains(WriteUser(x,v))
case _ => true
}
} &&
{
(sender, m, receiver.state) match{
case (id, WriteSystem(s,i,idM,hs), CommonState(mem,h)) => true
case _ => false
}
}
}
val UserState(userHistory,c) = net.states(a4)
val myId = receiver.myId
val id = sender
val WriteSystem(s,i,idM,hs) = m
val CommonState(mem,h) = receiver.state
if (id != myId && (idM == (true, s, i))) {
if (checkHistory(h,hs)){
val newStates = net.states.updated(myId, CommonState(mem.updated(s,i),h++Set(idM)))
val UserState(newUserHistory,newc) = newStates(a4)
(userHistory == newUserHistory) &&
newUserHistory.contains((true, s, i), Set()) &&
updateCheckTable(net.param, net.states, s, i, myId) &&
tableHistory(net.param, newStates) &&
WriteHistory(net.messages, newStates) &&
updateStateSystemProp4(net.messages, channels, net.states, myId, s, i, List(a1,a2,a3)) &&
updateStateSystemProp8(net.messages, net.states, channels, myId, s, i) &&
networkInvariant(net.param, newStates, net.messages, net.getActor)
}
else {
val newMessages = net.messages.updated((myId,myId), net.messages.getOrElse((myId,myId), Nil()) :+ WriteWaiting(s,i,idM,hs))
(ajoutCheckWriteForAll(channels, net.messages, userHistory, WriteWaiting(s,i,idM,hs), myId, myId)) &&
WriteHistory(newMessages, net.states) &&
tableHistory(net.param, net.states) &&
addNot2WriteUser(channels, net.messages, myId, myId, WriteWaiting(s,i,idM,hs)) &&
addUniqueWriteUser(net.messages, channels, (myId, myId), WriteWaiting(s,i,idM,hs)) &&
addOtherProp3(net.messages, channels, (myId, myId), WriteWaiting(s,i,idM,hs)) &&
addOtherprop5(net.messages, channels, (myId, myId), WriteWaiting(s,i,idM,hs)) &&
addWWProp6(net.messages, channels, (myId, myId),
WriteWaiting(s,i,idM,hs)) &&
addProp7(net.messages, channels, (myId,myId), WriteWaiting(s,i,idM,hs)) &&
addOtherProp4(net.messages, channels, net.states, (myId, myId), WriteWaiting(s,i,idM,hs), List(a1,a2,a3)) &&
addWWProp9(net.messages, channels, myId, WriteWaiting(s,i,idM,hs)) &&
//theoremProp10(net.messages, channels, (myId, myId), s, i) &&
addProp10(net.messages, channels, (myId, myId), WriteWaiting(s,i,idM,hs)) &&
addOtherProp8(net.messages, net.states, channels, (myId,myId), WriteWaiting(s,i,idM,hs)) &&
networkInvariant(net.param, net.states, newMessages, net.getActor)
}
}
else {
true
}
}holds
def systemActorReceivePreCase3(
receiver: Actor,
sender: ActorId,
m: Message
)(implicit net: VerifiedNetwork): Boolean = {
require{
(receiver.myId == a1 || receiver.myId == a2 || receiver.myId == a3) &&
networkInvariant(net.param, net.states, net.messages, net.getActor) &&
{
val UserState(userHistory,c) = net.states(a4)
m match {
case WriteUser(x,v) =>
userHistory.contains(((true, x, v),Set())) &&
!collectWUsList(net.messages, channels).contains(WriteUser(x,v)) &&
!collectWSsList(net.messages, channels).contains(WriteUser(x,v)) &&
!collectWWsList(net.messages, channels).contains(WriteUser(x,v))
case WriteSystem(x,v,idM,h) =>
userHistory.contains((idM,Set())) &&
!collectWUsList(net.messages, channels).contains(WriteUser(x,v)) &&
!collectNeighbour(receiver.myId, channels, net.messages).contains(WriteUser(x,v)) &&
!collectWWs(net.messages.getOrElse((receiver.myId, receiver.myId), Nil())).contains(WriteUser(x,v))
case WriteWaiting(x,v,idM,h) if (receiver.myId == sender) =>
userHistory.contains((idM,Set())) &&
!collectWUsList(net.messages, channels).contains(WriteUser(x,v)) &&
!collectNeighbour(receiver.myId, channels, net.messages).contains(WriteUser(x,v)) &&
!collectWWs(net.messages.getOrElse((receiver.myId, sender), Nil())).contains(WriteUser(x,v))
case _ => true
}
} &&
{
(sender, m, receiver.state) match{
case (id,WriteWaiting(s,i,idM,hs), CommonState(mem,h)) => true
case _ => false
}
}
}
val UserState(userHistory,c) = net.states(a4)
val myId = receiver.myId
val id = sender
val WriteWaiting(s,i,idM,hs) = m
val CommonState(mem,h) = receiver.state
if (id==myId && idM == (true, s, i)) {
if (checkHistory(h,hs)){
val newStates = net.states.updated(myId, CommonState(mem.updated(s,i),h++Set(idM)))
val UserState(newUserHistory,newc) = newStates(a4)
(userHistory == newUserHistory) &&
newUserHistory.contains((true, s, i), Set()) &&
updateCheckTable(net.param, net.states, s, i, myId) &&
tableHistory(net.param, newStates) &&
WriteHistory(net.messages, newStates) &&
updateStateSystemProp4(net.messages, channels, net.states, myId, s, i, List(a1,a2,a3)) &&
updateStateSystemProp8(net.messages, net.states, channels, myId, s, i) &&
networkInvariant(net.param, newStates, net.messages, net.getActor)
}
else {
val newMessages = net.messages.updated((myId,myId), net.messages.getOrElse((myId,myId), Nil()) :+ WriteWaiting(s,i,idM,hs))
(ajoutCheckWriteForAll(channels, net.messages, userHistory, WriteWaiting(s,i,idM,hs), myId, myId)) &&
WriteHistory(newMessages, net.states) &&
tableHistory(net.param, net.states) &&
addNot2WriteUser(channels, net.messages, myId, myId, WriteWaiting(s,i,idM,hs)) &&
addUniqueWriteUser(net.messages, channels, (myId, myId), WriteWaiting(s,i,idM,hs)) &&
addOtherProp3(net.messages, channels, (myId, myId),
WriteWaiting(s,i,idM,hs)) &&
addOtherprop5(net.messages, channels, (myId, myId), WriteWaiting(s,i,idM,hs)) &&
addWWProp6(net.messages, channels, (myId, myId), WriteWaiting(s,i,idM,hs)) &&
addProp7(net.messages, channels, (myId,myId), WriteWaiting(s,i,idM,hs)) &&
addOtherProp4(net.messages, channels, net.states, (myId, myId), WriteWaiting(s,i,idM,hs), List(a1,a2,a3)) &&
addWWProp9(net.messages, channels, myId, WriteWaiting(s,i,idM,hs)) &&
//theoremProp10(net.messages, channels, (myId, myId), s, i) &&
addProp10(net.messages, channels, (myId, myId), WriteWaiting(s,i,idM,hs)) &&
addOtherProp8(net.messages, net.states, channels, (myId,myId), WriteWaiting(s,i,idM,hs)) &&
networkInvariant(net.param, net.states, newMessages, net.getActor)
}
}
else true
}holds
def systemActorReceivePreCase4(
receiver: Actor,
sender: ActorId,
m: Message
)(implicit net: VerifiedNetwork): Boolean = {
require{
(receiver.myId == a1 || receiver.myId == a2 || receiver.myId == a3) &&
networkInvariant(net.param, net.states, net.messages, net.getActor) &&
{
val UserState(userHistory,c) = net.states(a4)
m match {
case WriteUser(x,v) =>
userHistory.contains(((true, x, v),Set())) &&
!collectWUsList(net.messages, channels).contains(WriteUser(x,v)) &&
!collectWSsList(net.messages, channels).contains(WriteUser(x,v)) &&
!collectWWsList(net.messages, channels).contains(WriteUser(x,v))
case WriteSystem(x,v,idM,h) =>
userHistory.contains((idM,Set())) &&
!collectWUsList(net.messages, channels).contains(WriteUser(x,v)) &&
!collectNeighbour(receiver.myId, channels, net.messages).contains(WriteUser(x,v)) &&
!collectWWs(net.messages.getOrElse((receiver.myId, receiver.myId), Nil())).contains(WriteUser(x,v))
case WriteWaiting(x,v,idM,h) =>
userHistory.contains((idM,Set())) &&
!collectWUsList(net.messages, channels).contains(WriteUser(x,v)) &&
!collectNeighbour(receiver.myId, channels, net.messages).contains(WriteUser(x,v)) &&
!collectWWs(net.messages.getOrElse((receiver.myId, sender), Nil())).contains(WriteUser(x,v))
case _ => true
}
} &&
{
(sender, m, receiver.state) match{
case (id,Read(s), CommonState(mem,h)) => true
case _ => false
}
}
}
val UserState(userHistory,c) = net.states(a4)
val myId = receiver.myId
val id = sender
val Read(s) = m
val CommonState(mem,h) = receiver.state
val variables = extractVariables(net.param)
if (id == a4 && {
val variables = extractVariables(net.param)
variables.contains(s)
}) {
val newMessages = net.messages.updated((myId,a4), net.messages.getOrElse((myId,a4), Nil()) :+ Value(mem.getOrElse(s,0),(false, s, mem.getOrElse(s,0)),h))
tableHistory(net.param, net.states) &&
tableToValue(s, variables, receiver.state, userHistory) &&
ajoutCheckWriteForAll(channels, net.messages, userHistory, Value(mem.getOrElse(s,0), (false, s, mem.getOrElse(s,0)), h), myId, id) &&
addNot2WriteUser(channels, net.messages, myId, id, Value(mem.getOrElse(s,0), (false, s, mem.getOrElse(s,0)), h)) &&
WriteHistory(newMessages, net.states) &&
addUniqueWriteUser(net.messages, channels, (myId, id), Value(mem.getOrElse(s,0), (false, s, mem.getOrElse(s,0)), h)) &&
addOtherProp3(net.messages, channels, (myId, id), Value(mem.getOrElse(s,0), (false, s, mem.getOrElse(s,0)), h)) &&
addOtherprop5(net.messages, channels, (myId, id), Value(mem.getOrElse(s,0), (false, s, mem.getOrElse(s,0)), h)) &&
addOtherProp6(net.messages, channels, (myId, id), Value(mem.getOrElse(s,0), (false, s, mem.getOrElse(s,0)), h)) &&
addProp7(net.messages, channels, (myId,id), Value(mem.getOrElse(s,0), (false, s, mem.getOrElse(s,0)), h)) &&
addOtherProp4(net.messages, channels, net.states, (myId, id), Value(mem.getOrElse(s,0), (false, s, mem.getOrElse(s,0)), h), List(a1,a2,a3)) &&
addOtherProp9(net.messages, channels, (myId, id), Value(mem.getOrElse(s,0), (false, s, mem.getOrElse(s,0)), h)) &&
addProp10(net.messages, channels, (myId,id), Value(mem.getOrElse(s,0), (false, s, mem.getOrElse(s,0)), h)) &&
addOtherProp8(net.messages, net.states, channels, (myId,id), Value(mem.getOrElse(s,0), (false, s, mem.getOrElse(s,0)), h)) &&
networkInvariant(net.param, net.states, newMessages, net.getActor) &&
true
}
else true
}holds
def systemActorReceivePre(receiver: Actor, sender: ActorId, m: Message)(implicit net: VerifiedNetwork) = {
require{
receiver match {
case SystemActor(_,otherActor) =>
areInChannels(receiver.myId, otherActor) &&
areInChannelsBis(otherActor) &&
subsetOf(otherActor, List(a1,a2,a3)) &&
!otherActor.contains(receiver.myId) &&
true
case _ => false
}
}
val SystemActor(myId, otherActor) = receiver
(receiver.myId == a1 || receiver.myId == a2 || receiver.myId == a3) &&
networkInvariant(net.param, net.states, net.messages, net.getActor) &&
{
val UserState(userHistory,c) = net.states(a4)
m match {
case WriteUser(x,v) =>
userHistory.contains(((true, x, v),Set())) &&
!collectWUsList(net.messages, channels).contains(WriteUser(x,v)) &&
!collectWSsList(net.messages, channels).contains(WriteUser(x,v)) &&
!collectWWsList(net.messages, channels).contains(WriteUser(x,v)) &&
!allHistoriesContains_aux(x, v, List(a1,a2,a3), net.states)
case WriteSystem(x,v,idM,h) =>
userHistory.contains((idM,Set())) &&
!collectWUsList(net.messages, channels).contains(WriteUser(x,v)) &&
!collectNeighbour(receiver.myId, channels, net.messages).contains(WriteUser(x,v)) &&
!collectWWs(net.messages.getOrElse((receiver.myId, receiver.myId), Nil())).contains(WriteUser(x,v))
case WriteWaiting(x,v,idM,h) if (receiver.myId == sender) =>
userHistory.contains((idM,Set())) &&
!collectWUsList(net.messages, channels).contains(WriteUser(x,v)) &&
!collectNeighbour(receiver.myId, channels, net.messages).contains(WriteUser(x,v)) &&
!collectWWs(net.messages.getOrElse((receiver.myId, sender), Nil())).contains(WriteUser(x,v))
case _ => true
}} && {
val UserState(userHistory,c) = net.states(a4)
(sender, m, receiver.state) match {
case (id, WriteUser(s,i), CommonState(mem,h)) =>
!collectWUsList(net.messages, channels).contains(WriteUser(s,i)) &&
!collectWSsList(net.messages, channels).contains(WriteUser(s,i)) &&
systemActorReceivePreCase1(receiver, sender, m)
case (id, WriteSystem(s,i,idM,hs), CommonState(mem,h)) =>
systemActorReceivePreCase2(receiver, sender, m)
case (id,WriteWaiting(s,i,idM,hs), CommonState(mem,h)) =>
systemActorReceivePreCase3(receiver, sender, m)
case (id,Read(s), CommonState(mem,h)) =>
systemActorReceivePreCase4(receiver, sender, m)
case _ => true
}
}
}
def receivePre(a: Actor, sender: ActorId, m: Message)(implicit net: VerifiedNetwork) = {
validId(net, sender) &&
validId(net, a.myId) &&
net.states.contains(sender) &&
net.states.contains(a.myId) &&
networkInvariant(net.param, net.states, net.messages, net.getActor) &&
{
val UserState(userHistory,c) = net.states(a4)
m match {
case WriteUser(x,v) =>
userHistory.contains(((true, x, v),Set())) &&
!collectWUsList(net.messages, channels).contains(WriteUser(x,v)) &&
!collectWSsList(net.messages, channels).contains(WriteUser(x,v)) &&
!collectWWsList(net.messages, channels).contains(WriteUser(x,v)) &&
!allHistoriesContains_aux(x, v, List(a1,a2,a3), net.states)
case WriteSystem(x,v,idM,h) =>
userHistory.contains((idM,Set())) &&
!collectWUsList(net.messages, channels).contains(WriteUser(x,v)) &&
!collectNeighbour(a.myId, channels, net.messages).contains(WriteUser(x,v)) &&
!collectWWs(net.messages.getOrElse((a.myId, a.myId), Nil())).contains(WriteUser(x,v))
case WriteWaiting(x,v,idM,h) if (a.myId == sender) =>
userHistory.contains((idM,Set())) &&
!collectWUsList(net.messages, channels).contains(WriteUser(x,v)) &&
!collectNeighbour(a.myId, channels, net.messages).contains(WriteUser(x,v)) &&
!collectWWs(net.messages.getOrElse((a.myId, sender), Nil())).contains(WriteUser(x,v))
case _ => true
}} && (