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|
; AleoBFT Library
;
; Copyright (C) 2024 Provable Inc.
;
; License: See the LICENSE file distributed with this library.
;
; Authors: Alessandro Coglio (www.alessandrocoglio.info)
; Eric McCarthy (bendyarm on GitHub)
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
(in-package "ALEOBFT-STAKE2")
(include-book "last-anchor-next")
(local (include-book "arithmetic-3/top" :dir :system))
(local (include-book "kestrel/built-ins/disable" :dir :system))
(local (acl2::disable-most-builtin-logic-defuns))
(local (acl2::disable-builtin-rewrite-rules-for-defaults))
(set-induction-depth-limit 0)
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
(defxdoc+ last-anchor-voters-def-and-init-and-next
:parents (correctness)
:short "Invariant that the last committed anchor
has at least a certain stake of successors:
definition, establishment, and preservation."
:long
(xdoc::topstring
(xdoc::p
"When the last committed round is not 0,
there is always an anchor at that round:
see @(see last-anchor-present).
Furthermore, that anchor always has successors
whose total stake is more than @($f$),
where @($f$) is introduced in @(tsee max-faulty-for-total).
This total stake provodes the votes
that are in fact necessary to commit that anchor.")
(xdoc::p
"Initially the last committed round is 0,
so the invariant holds trivially.
The only kind of events that changes the last committed anchor
is @('commit'), whose preconditions establish the invariant.
The only kinds of events that may change the successors
are @('create') and @('accept'),
which may add certificates to the DAG:
this certificate may or may not be a successor,
but if it is, it can only increase the voting stake, never decrease it.")
(xdoc::p
"Here we define the invariant,
we prove that it holds in all initial states,
and we prove that it is preserved by all transitions.
Elsewhere we prove that
the invariant holds in every reachable state."))
:order-subtopics t
:default-parent t)
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
(define validator-last-anchor-voters-p ((vstate validator-statep))
:guard (and (or (equal (validator-state->last vstate) 0)
(last-anchor vstate))
(dag-has-committees-p (validator-state->dag vstate)
(validator-state->blockchain vstate))
(dag-in-committees-p (validator-state->dag vstate)
(validator-state->blockchain vstate)))
:returns (yes/no booleanp)
:short "Check if a validator state satisfies the invariant."
:long
(xdoc::topstring
(xdoc::p
"Either the last committed round is 0,
or the committee at the next round can be calculated
and the total stake of the successors of the last anchor
is more than @($f$),
where @($f$) is the maximum stake of faulty validators in the committee.")
(xdoc::p
"The fact that the last anchor is present is in the guard,
but in @(tsee last-anchor-voters-p) it is established
from the previously proved invariant @(tsee last-anchor-present-p).
The guard also includes conditions ensuring
that the validator can calculate committees at all rounds with certificates
(and in particular the comittee at the round just after the last committed,
if the anchor has any successors),
and that the authors of all the certificates in a round
are members of the committee at that round
(and in particular the successors of the anchor, if any,
are members of the committee at their round);
these guard conditions are established, in @(tsee last-anchor-voters-p),
via previously proved invariants used as guards there."))
(b* (((validator-state vstate) vstate)
((when (equal vstate.last 0)) t)
(commtt (active-committee-at-round (1+ vstate.last) vstate.blockchain)))
(and commtt
(> (committee-members-stake (certificate-set->author-set
(successors (last-anchor vstate)
vstate.dag))
commtt)
(committee-max-faulty-stake commtt))))
:guard-hints
(("Goal"
:use ((:instance successors-subset-of-next-round
(cert (last-anchor vstate))
(dag (validator-state->dag vstate)))
(:instance set::subset-transitive
(x (certificate-set->author-set
(successors (last-anchor vstate)
(validator-state->dag vstate))))
(y (certificate-set->author-set
(certs-with-round (1+ (validator-state->last vstate))
(validator-state->dag vstate))))
(z (committee-members
(active-committee-at-round
(1+ (validator-state->last vstate))
(validator-state->blockchain vstate))))))
:in-theory (e/d (last-anchor-in-dag
certificate-set->author-set-monotone
certificate->round-of-last-anchor
round-in-committee-when-dag-in-committees-p)
(successors-subset-of-next-round))))
:hooks (:fix))
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
(define-sk last-anchor-voters-p ((systate system-statep))
:guard (and (last-anchor-present-p systate)
(signer-quorum-p systate))
:returns (yes/no booleanp)
:short "Definition of the invariant:
for each correct validator,
if the last committed round is not 0,
the last committed anchor has at least @($f+1$) successors,
where @($f$) is the maximum number of faulty validators
in the committee active at
the round just after the last committed one."
(forall (val)
(implies (set::in val (correct-addresses systate))
(validator-last-anchor-voters-p
(get-validator-state val systate))))
:guard-hints
(("Goal" :in-theory (enable last-anchor-present-p-necc
dag-has-committees-p-when-signer-quorum-p
dag-in-committees-p-when-signer-quorum-p)))
///
(fty::deffixequiv-sk last-anchor-voters-p
:args ((systate system-statep))))
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
(defruled last-anchor-voters-p-when-init
:short "Establishment of the invariant:
the invariant holds in any initial state."
:long
(xdoc::topstring
(xdoc::p
"The last committed round is initially 0, so the proof is trivial."))
(implies (system-initp systate)
(last-anchor-voters-p systate))
:enable (last-anchor-voters-p
validator-last-anchor-voters-p
system-initp
system-validators-initp-necc
validator-init))
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
(defsection last-anchor-voters-p-of-next
:short "Preservation of the invariant:
if the invariant holds in a system state,
it also holds in the next system state."
:long
(xdoc::topstring
(xdoc::p
"A @('create') or @('accept') event
does not modify the last committed anchor.
It may add certificates to the DAG,
which may be successors of the last committed anchor,
but since @(tsee successors) is monotone,
the inequality of more than @($f$) voting stake is preserved.")
(xdoc::p
"A @('commit') event changes the last committed anchor,
but its preconditions include the fact that
the new anchor has more than @($f$) voting stake.
Since our invariant is phrased in terms of successors certificates,
we need a lemma that relates the stake of successors
to the voting stake returned by @(tsee leader-stake-votes);
this needs non-equivocation because @(tsee leader-stake-votes)
would count the stake of equivocal certificates multiple times,
while @(tsee certificate-set->author-set) applied to @('successors-loop')
counts the stake of each author only once.
Since the event also extends the blockchain,
as in other proofs we need to show that the extension of the blockchain
does not modify the committee active at the round of the successors.")
(xdoc::p
"An @('advance') event does not change
the last committed anchor or the DAG,
and thus the successors of the anchor."))
;; create:
(defruled validator-last-anchor-voters-p-of-create-next
(implies (and (system-committees-fault-tolerant-p systate)
(no-self-endorsed-p systate)
(signer-records-p systate)
(signer-quorum-p systate)
(unequivocal-dags-p systate)
(same-committees-p systate)
(last-anchor-present-p systate)
(create-possiblep cert systate)
(set::in val (correct-addresses systate))
(validator-last-anchor-voters-p
(get-validator-state val systate)))
(validator-last-anchor-voters-p
(get-validator-state val (create-next cert systate))))
:use (:instance
committee-members-stake-monotone
(members1
(certificate-set->author-set
(successors
(last-anchor
(get-validator-state (certificate->author cert) systate))
(validator-state->dag
(get-validator-state (certificate->author cert) systate)))))
(members2
(certificate-set->author-set
(successors
(last-anchor
(get-validator-state (certificate->author cert)
(create-next cert systate)))
(validator-state->dag
(get-validator-state (certificate->author cert)
(create-next cert systate))))))
(commtt (active-committee-at-round
(1+ (validator-state->last
(get-validator-state (certificate->author cert)
systate)))
(validator-state->blockchain
(get-validator-state (certificate->author cert)
systate)))))
:enable (validator-last-anchor-voters-p
validator-state->dag-of-create-next
successors-monotone
certificate-set->author-set-monotone))
(defruled last-anchor-voters-p-of-create-next
(implies (and (last-anchor-voters-p systate)
(system-committees-fault-tolerant-p systate)
(no-self-endorsed-p systate)
(signer-records-p systate)
(signer-quorum-p systate)
(unequivocal-dags-p systate)
(same-committees-p systate)
(last-anchor-present-p systate)
(create-possiblep cert systate))
(last-anchor-voters-p (create-next cert systate)))
:enable (last-anchor-voters-p
last-anchor-voters-p-necc
validator-last-anchor-voters-p-of-create-next))
;; accept:
(defruled validator-last-anchor-voters-p-of-accept-next
(implies (and (system-committees-fault-tolerant-p systate)
(signer-quorum-p systate)
(unequivocal-signed-certs-p systate)
(unequivocal-dags-p systate)
(same-committees-p systate)
(last-anchor-present-p systate)
(accept-possiblep msg systate)
(messagep msg)
(set::in val (correct-addresses systate))
(validator-last-anchor-voters-p
(get-validator-state val systate)))
(validator-last-anchor-voters-p
(get-validator-state val (accept-next msg systate))))
:use (:instance
committee-members-stake-monotone
(members1
(certificate-set->author-set
(successors
(last-anchor
(get-validator-state val systate))
(validator-state->dag
(get-validator-state val systate)))))
(members2
(certificate-set->author-set
(successors
(last-anchor
(get-validator-state val (accept-next msg systate)))
(validator-state->dag
(get-validator-state val (accept-next msg systate))))))
(commtt (active-committee-at-round
(1+ (validator-state->last
(get-validator-state val systate)))
(validator-state->blockchain
(get-validator-state val systate)))))
:enable (validator-last-anchor-voters-p
validator-state->dag-of-accept-next
successors-monotone
certificate-set->author-set-monotone))
(defruled last-anchor-voters-p-of-accept-next
(implies (and (last-anchor-voters-p systate)
(system-committees-fault-tolerant-p systate)
(signer-quorum-p systate)
(unequivocal-signed-certs-p systate)
(unequivocal-dags-p systate)
(same-committees-p systate)
(last-anchor-present-p systate)
(accept-possiblep msg systate)
(messagep msg))
(last-anchor-voters-p (accept-next msg systate)))
:enable (last-anchor-voters-p
last-anchor-voters-p-necc
validator-last-anchor-voters-p-of-accept-next))
;; advance:
(defruled validator-last-anchor-voters-p-of-advance-next
(implies (and (advance-possiblep val systate)
(set::in val1 (correct-addresses systate))
(validator-last-anchor-voters-p
(get-validator-state val1 systate)))
(validator-last-anchor-voters-p
(get-validator-state val1 (advance-next val systate))))
:enable validator-last-anchor-voters-p)
(defruled last-anchor-voters-p-of-advance-next
(implies (and (last-anchor-voters-p systate)
(advance-possiblep val systate))
(last-anchor-voters-p (advance-next val systate)))
:enable (last-anchor-voters-p
last-anchor-voters-p-necc
validator-last-anchor-voters-p-of-advance-next))
;; commit
(defruled stake-of-successors-loop-to-leader-stake-votes
(implies (and (certificate-setp certs)
(certificate-set-unequivocalp certs)
(addressp prev)
(<= (set::cardinality (certificate-set->round-set certs)) 1))
(equal (committee-members-stake
(certificate-set->author-set
(successors-loop certs prev))
commtt)
(leader-stake-votes prev certs commtt)))
:induct t
:enable (leader-stake-votes
successors-loop
in-of-successors-loop
certificate-set->author-set-of-insert
committee-members-stake-of-insert
certificate-set-unequivocalp-when-subset
set::expensive-rules
certificate-set->author-set-monotone)
:hints ('(:use
(head-author-not-in-tail-authors-when-unequiv-and-all-same-round
(:instance certificate-set->round-set-monotone
(certs1 (set::tail certs))
(certs2 certs))))))
(defruled stake-of-successors-to-leader-stake-votes
(implies (and (certificate-setp dag)
(certificate-set-unequivocalp dag))
(equal (committee-members-stake
(certificate-set->author-set (successors cert dag))
commtt)
(leader-stake-votes
(certificate->author cert)
(certs-with-round
(1+ (certificate->round cert))
dag)
commtt)))
:enable (successors
stake-of-successors-loop-to-leader-stake-votes
certificate-set-unequivocalp-when-subset
cardinality-of-round-set-of-certs-with-round-leq-1))
(defruled validator-last-anchor-voters-p-of-commit-next
(implies (and (last-blockchain-round-p systate)
(ordered-even-p systate)
(unequivocal-dags-p systate)
(commit-possiblep val systate)
(addressp val)
(set::in val1 (correct-addresses systate))
(validator-last-anchor-voters-p
(get-validator-state val1 systate)))
(validator-last-anchor-voters-p
(get-validator-state val1 (commit-next val systate))))
:enable (unequivocal-dags-p-necc-single
active-committee-at-previous-round-when-at-round
validator-last-anchor-voters-p
commit-possiblep
commit-next
last-anchor
get-validator-state-of-update-validator-state
nfix
active-committee-at-round-of-extend-blockchain-no-change
blocks-ordered-even-p-of-extend-blockchain
certificates-ordered-even-p-of-collect-anchors
ordered-even-p-necc-fixing
collect-anchors-above-last-committed-round
last-blockchain-round-p-necc-fixing
posp
evenp
stake-of-successors-to-leader-stake-votes))
(defruled last-anchor-voters-p-of-commit-next
(implies (and (last-anchor-voters-p systate)
(last-blockchain-round-p systate)
(ordered-even-p systate)
(unequivocal-dags-p systate)
(commit-possiblep val systate)
(addressp val))
(last-anchor-voters-p (commit-next val systate)))
:enable (last-anchor-voters-p
last-anchor-voters-p-necc
validator-last-anchor-voters-p-of-commit-next))
;; all events:
(defruled last-anchor-voters-p-of-event-next
(implies (and (last-anchor-voters-p systate)
(system-committees-fault-tolerant-p systate)
(last-blockchain-round-p systate)
(ordered-even-p systate)
(no-self-endorsed-p systate)
(signer-records-p systate)
(signer-quorum-p systate)
(unequivocal-signed-certs-p systate)
(unequivocal-dags-p systate)
(same-committees-p systate)
(last-anchor-present-p systate)
(event-possiblep event systate))
(last-anchor-voters-p (event-next event systate)))
:enable (event-possiblep
event-next)))
|
