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52 lines
2.6 KiB
52 lines
2.6 KiB
#lang ivy1.7
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include tendermint
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include abstract_tendermint
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# Here we prove the second accountability property: no well-behaved node is
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# every observed to violate the accountability properties.
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# The proof is done in two steps: first we prove the the abstract specification
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# satisfies the property, and then we show by refinement that this property
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# also holds in the concrete specification.
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# To see what is checked in the refinement proof, use `ivy_show isolate=accountable_safety_2 accountable_safety_2.ivy`
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# To see what is checked in the abstract correctness proof, use `ivy_show isolate=abstract_accountable_safety_2 accountable_safety_2.ivy`
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# To check the whole proof, use `ivy_check accountable_safety_2.ivy`.
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# Proof that the property holds in the abstract specification
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# ============================================================
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isolate abstract_accountable_safety_2 = {
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instantiate abstract_tendermint
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# the main property:
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invariant [wb_never_punished] well_behaved(N) -> ~(observed_equivocation(N) | observed_unlawful_prevote(N))
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# the main invariant for proving wb_not_punished:
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invariant well_behaved(N) & precommitted(N,R,V) & ~locked(N,R,V) & V ~= value.nil -> exists R2,V2 . V2 ~= value.nil & R < R2 & precommitted(N,R2,V2) & locked(N,R2,V2)
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invariant (exists N . well_behaved(N) & precommitted(N,R,V) & V ~= value.nil) -> exists Q . nset.is_quorum(Q) & forall N . nset.member(N,Q) -> observed_prevoted(N,R,V)
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invariant well_behaved(N) -> (observed_prevoted(N,R,V) <-> prevoted(N,R,V))
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invariant well_behaved(N) -> (observed_precommitted(N,R,V) <-> precommitted(N,R,V))
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# nodes stop prevoting or precommitting in lower rounds when doing so in a higher round:
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invariant well_behaved(N) & prevoted(N,R2,V2) & R1 < R2 -> left_round(N,R1)
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invariant well_behaved(N) & locked(N,R2,V2) & R1 < R2 -> left_round(N,R1)
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invariant [precommit_unique_per_round] well_behaved(N) & precommitted(N,R,V1) & precommitted(N,R,V2) -> V1 = V2
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} with nset, round, abstract_accountable_safety_2.defs.observed_equivocation_def, abstract_accountable_safety_2.defs.observed_unlawful_prevote_def
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# Proof that the property holds in the concrete specification
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# ===========================================================
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isolate accountable_safety_2 = {
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instantiate tendermint(abstract_accountable_safety_2)
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invariant well_behaved(N) -> ~(abstract_accountable_safety_2.observed_equivocation(N) | abstract_accountable_safety_2.observed_unlawful_prevote(N))
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} with round, value, shim, abstract_accountable_safety_2, abstract_accountable_safety_2.defs.observed_equivocation_def, abstract_accountable_safety_2.defs.observed_unlawful_prevote_def
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