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str2.tla
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str2.tla
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------------- MODULE str2 --------------------
(*\* Crash fault-tolerant streamlet algorithm *)
EXTENDS Integers, Sequences, FiniteSets
CONSTANT N, EMAX
Nodes == 0..N-1
(*
--algorithm str2 {
variable Msgs=[n \in Nodes |-> {[chain|-> <<0>>, epoch|->0, sender|->0],
[chain|-> <<0>>, epoch|->0, sender|->1],
[chain|-> <<0>>, epoch|->0, sender|->2]}];
define{
ExtractMsg(e,s) == CHOOSE m \in Msgs[s]: m.epoch=e
FindMaxChain(s) == CHOOSE z \in {m.chain: m \in Msgs[s]}:
~(\E x \in {m.chain: m \in Msgs[s]}: Len(x)>Len(z))
ThreeCons(c) == Len(c)>2 /\ Head(c)= Head(Tail(c))+1 /\ Head(Tail(c))=Head(Tail(Tail(c)))+1
}
\*\* What to do with two chains with length=l
\*\* FindMaxChain returns c1, which is not notarized.
\*\* we chop off head and return it, but c2 with length l was notarized.
macro FindMaxNotarizedChain(e) {
if (2*Cardinality ({m\in Msgs[self]: m.epoch=e /\ m.chain=FindMaxChain(self)}) > N)
nChain:= FindMaxChain(self);
else
nChain:= Tail(FindMaxChain(self));
}
fair process (p \in Nodes)
variable nChain= <<>>, e=1, Q={};{
A: while (e<EMAX) {
Q:=Nodes;
if (e%N=self){
FindMaxNotarizedChain(e-1); \* \* updates nChain
AP: while (Q #{})
with (p \in Q){
Msgs[p]:= Msgs[p] \union {[chain|-> <<e>> \o nChain, epoch|->e, sender|->self]};
Q:=Q\{p};
}
}
else {
await (\E m \in Msgs[self]: m.epoch=e);
FindMaxNotarizedChain(e); \* \* updates nChain
if (Len(ExtractMsg(e,self).chain) = Len(nChain)+1)
AV: while (Q #{})
with (p \in Q){
Msgs[p]:= Msgs[p] \union {[chain|->ExtractMsg(e,self).chain, epoch|->e, sender|->self]};
Q:=Q\{p};
}
};
AZ: e:=e+1;
}
}
} \* \* end algorithm
*)
\* BEGIN TRANSLATION
VARIABLES Msgs, pc
(* define statement *)
ExtractMsg(e,s) == CHOOSE m \in Msgs[s]: m.epoch=e
FindMaxChain(s) == CHOOSE z \in {m.chain: m \in Msgs[s]}:
~(\E x \in {m.chain: m \in Msgs[s]}: Len(x)>Len(z))
ThreeCons(c) == Len(c)>2 /\ Head(c)= Head(Tail(c))+1 /\ Head(Tail(c))=Head(Tail(Tail(c)))+1
VARIABLES nChain, e, Q
vars == << Msgs, pc, nChain, e, Q >>
ProcSet == (Nodes)
Init == (* Global variables *)
/\ Msgs = [n \in Nodes |-> {[chain|-> <<0>>, epoch|->0, sender|->0],
[chain|-> <<0>>, epoch|->0, sender|->1],
[chain|-> <<0>>, epoch|->0, sender|->2]}]
(* Process p *)
/\ nChain = [self \in Nodes |-> <<>>]
/\ e = [self \in Nodes |-> 1]
/\ Q = [self \in Nodes |-> {}]
/\ pc = [self \in ProcSet |-> "A"]
A(self) == /\ pc[self] = "A"
/\ IF e[self]<EMAX
THEN /\ Q' = [Q EXCEPT ![self] = Nodes]
/\ IF e[self]%N=self
THEN /\ IF 2*Cardinality ({m\in Msgs[self]: m.epoch=(e[self]-1) /\ m.chain=FindMaxChain(self)}) > N
THEN /\ nChain' = [nChain EXCEPT ![self] = FindMaxChain(self)]
ELSE /\ nChain' = [nChain EXCEPT ![self] = Tail(FindMaxChain(self))]
/\ pc' = [pc EXCEPT ![self] = "AP"]
ELSE /\ (\E m \in Msgs[self]: m.epoch=e[self])
/\ IF 2*Cardinality ({m\in Msgs[self]: m.epoch=e[self] /\ m.chain=FindMaxChain(self)}) > N
THEN /\ nChain' = [nChain EXCEPT ![self] = FindMaxChain(self)]
ELSE /\ nChain' = [nChain EXCEPT ![self] = Tail(FindMaxChain(self))]
/\ IF Len(ExtractMsg(e[self],self).chain) = Len(nChain'[self])+1
THEN /\ pc' = [pc EXCEPT ![self] = "AV"]
ELSE /\ pc' = [pc EXCEPT ![self] = "AZ"]
ELSE /\ pc' = [pc EXCEPT ![self] = "Done"]
/\ UNCHANGED << nChain, Q >>
/\ UNCHANGED << Msgs, e >>
AZ(self) == /\ pc[self] = "AZ"
/\ e' = [e EXCEPT ![self] = e[self]+1]
/\ pc' = [pc EXCEPT ![self] = "A"]
/\ UNCHANGED << Msgs, nChain, Q >>
AP(self) == /\ pc[self] = "AP"
/\ IF Q[self] #{}
THEN /\ \E p \in Q[self]:
/\ Msgs' = [Msgs EXCEPT ![p] = Msgs[p] \union {[chain|-> <<e[self]>> \o nChain[self], epoch|->e[self], sender|->self]}]
/\ Q' = [Q EXCEPT ![self] = Q[self]\{p}]
/\ pc' = [pc EXCEPT ![self] = "AP"]
ELSE /\ pc' = [pc EXCEPT ![self] = "AZ"]
/\ UNCHANGED << Msgs, Q >>
/\ UNCHANGED << nChain, e >>
AV(self) == /\ pc[self] = "AV"
/\ IF Q[self] #{}
THEN /\ \E p \in Q[self]:
/\ Msgs' = [Msgs EXCEPT ![p] = Msgs[p] \union {[chain|->ExtractMsg(e[self],self).chain, epoch|->e[self], sender|->self]}]
/\ Q' = [Q EXCEPT ![self] = Q[self]\{p}]
/\ pc' = [pc EXCEPT ![self] = "AV"]
ELSE /\ pc' = [pc EXCEPT ![self] = "AZ"]
/\ UNCHANGED << Msgs, Q >>
/\ UNCHANGED << nChain, e >>
p(self) == A(self) \/ AZ(self) \/ AP(self) \/ AV(self)
(* Allow infinite stuttering to prevent deadlock on termination. *)
Terminating == /\ \A self \in ProcSet: pc[self] = "Done"
/\ UNCHANGED vars
Next == (\E self \in Nodes: p(self))
\/ Terminating
Spec == /\ Init /\ [][Next]_vars
/\ \A self \in Nodes : WF_vars(p(self))
Termination == <>(\A self \in ProcSet: pc[self] = "Done")
\* END TRANSLATION
---------------------------------------------------------
\* Invariants
\* Check three finality rule!!
Consistency == \A i,j \in Nodes: ThreeCons(nChain[i]) /\ ThreeCons(nChain[j]) /\ Len(nChain[i])=< Len(nChain[j])
=> \A k \in 1..Len(nChain[i]): nChain[i][k]=nChain[j][Len(nChain[j])-Len(nChain[i])+k]
Bait2 == ~( \E i \in Nodes: Len(nChain[i])>1 /\ Head(nChain[i])= Head(Tail(nChain[i]))+1 )
Bait3 == ~( \E i \in Nodes: Len(nChain[i])>2 /\ Head(nChain[i])= Head(Tail(nChain[i]))+1
/\ Head(Tail(nChain[i]))=Head(Tail(Tail(nChain[i])))+1 )
BaitLength == \A i \in Nodes: Len (nChain[i]) <5
BaitWidth == \A ep \in 1..EMAX : Cardinality({m \in Msgs: m.epoch=ep}) < 2
BaitSet == Cardinality(Msgs) <9
=========================================================