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178 lines
7.9 KiB
178 lines
7.9 KiB
#lang ivy1.7
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# ---
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# layout: page
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# title: Abstract specification of Tendermint in Ivy
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# ---
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# Here we define an abstract version of the Tendermint specification. We use
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# two main forms of abstraction: a) We abstract over how information is
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# transmitted (there is no network). b) We abstract functions using relations.
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# For example, we abstract over a node's current round, instead only tracking
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# with a relation which rounds the node has left. We do something similar for
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# the `lockedRound` variable. This is in order to avoid using a function from
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# node to round, and it allows us to emit verification conditions that are
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# efficiently solvable by Z3.
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# This specification also defines the observations that are used to adjudicate
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# misbehavior. Well-behaved nodes faithfully observe every message that they
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# use to take a step, while Byzantine nodes can fake observations about
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# themselves (including withholding observations). Misbehavior is defined using
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# the collection of all observations made (in reality, those observations must
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# be collected first, but we do not model this process).
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include domain_model
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module abstract_tendermint = {
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# Protocol state
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# ##############
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relation left_round(N:node, R:round)
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relation prevoted(N:node, R:round, V:value)
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relation precommitted(N:node, R:round, V:value)
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relation decided(N:node, R:round, V:value)
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relation locked(N:node, R:round, V:value)
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# Accountability relations
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# ########################
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relation observed_prevoted(N:node, R:round, V:value)
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relation observed_precommitted(N:node, R:round, V:value)
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# relations that are defined in terms of the previous two:
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relation observed_equivocation(N:node)
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relation observed_unlawful_prevote(N:node)
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relation agreement
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relation accountability_violation
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object defs = { # we hide those definitions and use them only when needed
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private {
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definition [observed_equivocation_def] observed_equivocation(N) = exists V1,V2,R .
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V1 ~= V2 & (observed_precommitted(N,R,V1) & observed_precommitted(N,R,V2) | observed_prevoted(N,R,V1) & observed_prevoted(N,R,V2))
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definition [observed_unlawful_prevote_def] observed_unlawful_prevote(N) = exists V1,V2,R1,R2 .
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V1 ~= value.nil & V2 ~= value.nil & V1 ~= V2 & R1 < R2 & observed_precommitted(N,R1,V1) & observed_prevoted(N,R2,V2)
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& forall Q,R . R1 <= R & R < R2 & nset.is_quorum(Q) -> exists N2 . nset.member(N2,Q) & ~observed_prevoted(N2,R,V2)
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definition [agreement_def] agreement = forall N1,N2,R1,R2,V1,V2 . well_behaved(N1) & well_behaved(N2) & decided(N1,R1,V1) & decided(N2,R2,V2) -> V1 = V2
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definition [accountability_violation_def] accountability_violation = exists Q1,Q2 . nset.is_quorum(Q1) & nset.is_quorum(Q2) & (forall N . nset.member(N,Q1) & nset.member(N,Q2) -> observed_equivocation(N) | observed_unlawful_prevote(N))
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}
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}
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# Protocol transitions
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# ####################
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after init {
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left_round(N,R) := R < 0;
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prevoted(N,R,V) := false;
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precommitted(N,R,V) := false;
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decided(N,R,V) := false;
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locked(N,R,V) := false;
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observed_prevoted(N,R,V) := false;
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observed_precommitted(N,R,V) := false;
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}
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# Actions are named after the corresponding line numbers in the Tendermint
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# arXiv paper.
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action l_11(n:node, r:round) = { # start round r
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require ~left_round(n,r);
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left_round(n,R) := R < r;
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}
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action l_22(n:node, rp:round, v:value) = {
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require ~left_round(n,rp);
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require ~prevoted(n,rp,V) & ~precommitted(n,rp,V);
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require (forall R,V . locked(n,R,V) -> V = v) | v = value.nil;
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prevoted(n, rp, v) := true;
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left_round(n, R) := R < rp; # leave all lower rounds.
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observed_prevoted(n, rp, v) := observed_prevoted(n, rp, v) | well_behaved(n); # the node observes itself
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}
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action l_28(n:node, rp:round, v:value, vr:round, q:nset) = {
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require ~left_round(n,rp) & ~prevoted(n,rp,V);
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require ~prevoted(n,rp,V) & ~precommitted(n,rp,V);
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require vr < rp;
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require nset.is_quorum(q) & (forall N . nset.member(N,q) -> (prevoted(N,vr,v) | ~well_behaved(N)));
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var proposal:value;
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if value.valid(v) & ((forall R0,V0 . locked(n,R0,V0) -> R0 <= vr) | (forall R,V . locked(n,R,V) -> V = v)) {
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proposal := v;
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}
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else {
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proposal := value.nil;
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};
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prevoted(n, rp, proposal) := true;
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left_round(n, R) := R < rp; # leave all lower rounds
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observed_prevoted(N, vr, v) := observed_prevoted(N, vr, v) | (well_behaved(n) & nset.member(N,q)); # the node observes the prevotes of quorum q
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observed_prevoted(n, rp, proposal) := observed_prevoted(n, rp, proposal) | well_behaved(n); # the node observes itself
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}
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action l_36(n:node, rp:round, v:value, q:nset) = {
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require v ~= value.nil;
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require ~left_round(n,rp);
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require exists V . prevoted(n,rp,V);
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require ~precommitted(n,rp,V);
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require nset.is_quorum(q) & (forall N . nset.member(N,q) -> (prevoted(N,rp,v) | ~well_behaved(N)));
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precommitted(n, rp, v) := true;
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left_round(n, R) := R < rp; # leave all lower rounds
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locked(n,R,V) := R <= rp & V = v;
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observed_prevoted(N, rp, v) := observed_prevoted(N, rp, v) | (well_behaved(n) & nset.member(N,q)); # the node observes the prevotes of quorum q
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observed_precommitted(n, rp, v) := observed_precommitted(n, rp, v) | well_behaved(n); # the node observes itself
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}
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action l_44(n:node, rp:round, q:nset) = {
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require ~left_round(n,rp);
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require ~precommitted(n,rp,V);
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require nset.is_quorum(q) & (forall N .nset.member(N,q) -> (prevoted(N,rp,value.nil) | ~well_behaved(N)));
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precommitted(n, rp, value.nil) := true;
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left_round(n, R) := R < rp; # leave all lower rounds
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observed_prevoted(N, rp, value.nil) := observed_prevoted(N, rp, value.nil) | (well_behaved(n) & nset.member(N,q)); # the node observes the prevotes of quorum q
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observed_precommitted(n, rp, value.nil) := observed_precommitted(n, rp, value.nil) | well_behaved(n); # the node observes itself
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}
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action l_57(n:node, rp:round) = {
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require ~left_round(n,rp);
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require ~prevoted(n,rp,V);
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prevoted(n, rp, value.nil) := true;
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left_round(n, R) := R < rp; # leave all lower rounds
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observed_prevoted(n, rp, value.nil) := observed_prevoted(n, rp, value.nil) | well_behaved(n); # the node observes itself
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}
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action l_61(n:node, rp:round) = {
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require ~left_round(n,rp);
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require ~precommitted(n,rp,V);
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precommitted(n, rp, value.nil) := true;
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left_round(n, R) := R < rp; # leave all lower rounds
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observed_precommitted(n, rp, value.nil) := observed_precommitted(n, rp, value.nil) | well_behaved(n); # the node observes itself
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}
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action decide(n:node, r:round, v:value, q:nset) = {
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require v ~= value.nil;
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require nset.is_quorum(q) & (forall N . nset.member(N, q) -> (precommitted(N, r, v) | ~well_behaved(N)));
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decided(n, r, v) := true;
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observed_precommitted(N, r, v) := observed_precommitted(N, r, v) | (well_behaved(n) & nset.member(N,q)); # the node observes the precommits of quorum q
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}
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action misbehave = {
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# Byzantine nodes can claim they observed whatever they want about themselves,
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# but they cannot remove observations. Note that we use assume because we don't
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# want those to be checked; we just want them to be true (that's the model of
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# Byzantine behavior).
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observed_prevoted(N,R,V) := *;
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assume (old observed_prevoted(N,R,V)) -> observed_prevoted(N,R,V);
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assume well_behaved(N) -> old observed_prevoted(N,R,V) = observed_prevoted(N,R,V);
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observed_precommitted(N,R,V) := *;
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assume (old observed_precommitted(N,R,V)) -> observed_precommitted(N,R,V);
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assume well_behaved(N) -> old observed_precommitted(N,R,V) = observed_precommitted(N,R,V);
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}
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}
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