You can not select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
164 lines
6.6 KiB
164 lines
6.6 KiB
------------------------ MODULE Blockchain_003_draft -----------------------------
|
|
(*
|
|
This is a high-level specification of Tendermint blockchain
|
|
that is designed specifically for the light client.
|
|
Validators have the voting power of one. If you like to model various
|
|
voting powers, introduce multiple copies of the same validator
|
|
(do not forget to give them unique names though).
|
|
*)
|
|
EXTENDS Integers, FiniteSets
|
|
|
|
Min(a, b) == IF a < b THEN a ELSE b
|
|
|
|
CONSTANT
|
|
AllNodes,
|
|
(* a set of all nodes that can act as validators (correct and faulty) *)
|
|
ULTIMATE_HEIGHT,
|
|
(* a maximal height that can be ever reached (modelling artifact) *)
|
|
TRUSTING_PERIOD
|
|
(* the period within which the validators are trusted *)
|
|
|
|
Heights == 1..ULTIMATE_HEIGHT (* possible heights *)
|
|
|
|
(* A commit is just a set of nodes who have committed the block *)
|
|
Commits == SUBSET AllNodes
|
|
|
|
(* The set of all block headers that can be on the blockchain.
|
|
This is a simplified version of the Block data structure in the actual implementation. *)
|
|
BlockHeaders == [
|
|
height: Heights,
|
|
\* the block height
|
|
time: Int,
|
|
\* the block timestamp in some integer units
|
|
lastCommit: Commits,
|
|
\* the nodes who have voted on the previous block, the set itself instead of a hash
|
|
(* in the implementation, only the hashes of V and NextV are stored in a block,
|
|
as V and NextV are stored in the application state *)
|
|
VS: SUBSET AllNodes,
|
|
\* the validators of this bloc. We store the validators instead of the hash.
|
|
NextVS: SUBSET AllNodes
|
|
\* the validators of the next block. We store the next validators instead of the hash.
|
|
]
|
|
|
|
(* A signed header is just a header together with a set of commits *)
|
|
LightBlocks == [header: BlockHeaders, Commits: Commits]
|
|
|
|
VARIABLES
|
|
now,
|
|
(* the current global time in integer units *)
|
|
blockchain,
|
|
(* A sequence of BlockHeaders, which gives us a bird view of the blockchain. *)
|
|
Faulty
|
|
(* A set of faulty nodes, which can act as validators. We assume that the set
|
|
of faulty processes is non-decreasing. If a process has recovered, it should
|
|
connect using a different id. *)
|
|
|
|
(* all variables, to be used with UNCHANGED *)
|
|
vars == <<now, blockchain, Faulty>>
|
|
|
|
(* The set of all correct nodes in a state *)
|
|
Corr == AllNodes \ Faulty
|
|
|
|
(* APALACHE annotations *)
|
|
a <: b == a \* type annotation
|
|
|
|
NT == STRING
|
|
NodeSet(S) == S <: {NT}
|
|
EmptyNodeSet == NodeSet({})
|
|
|
|
BT == [height |-> Int, time |-> Int, lastCommit |-> {NT}, VS |-> {NT}, NextVS |-> {NT}]
|
|
|
|
LBT == [header |-> BT, Commits |-> {NT}]
|
|
(* end of APALACHE annotations *)
|
|
|
|
(****************************** BLOCKCHAIN ************************************)
|
|
|
|
(* the header is still within the trusting period *)
|
|
InTrustingPeriod(header) ==
|
|
now < header.time + TRUSTING_PERIOD
|
|
|
|
(*
|
|
Given a function pVotingPower \in D -> Powers for some D \subseteq AllNodes
|
|
and pNodes \subseteq D, test whether the set pNodes \subseteq AllNodes has
|
|
more than 2/3 of voting power among the nodes in D.
|
|
*)
|
|
TwoThirds(pVS, pNodes) ==
|
|
LET TP == Cardinality(pVS)
|
|
SP == Cardinality(pVS \intersect pNodes)
|
|
IN
|
|
3 * SP > 2 * TP \* when thinking in real numbers, not integers: SP > 2.0 / 3.0 * TP
|
|
|
|
(*
|
|
Given a set of FaultyNodes, test whether the voting power of the correct nodes in D
|
|
is more than 2/3 of the voting power of the faulty nodes in D.
|
|
|
|
Parameters:
|
|
- pFaultyNodes is a set of nodes that are considered faulty
|
|
- pVS is a set of all validators, maybe including Faulty, intersecting with it, etc.
|
|
- pMaxFaultRatio is a pair <<a, b>> that limits the ratio a / b of the faulty
|
|
validators from above (exclusive)
|
|
*)
|
|
FaultyValidatorsFewerThan(pFaultyNodes, pVS, maxRatio) ==
|
|
LET FN == pFaultyNodes \intersect pVS \* faulty nodes in pNodes
|
|
CN == pVS \ pFaultyNodes \* correct nodes in pNodes
|
|
CP == Cardinality(CN) \* power of the correct nodes
|
|
FP == Cardinality(FN) \* power of the faulty nodes
|
|
IN
|
|
\* CP + FP = TP is the total voting power
|
|
LET TP == CP + FP IN
|
|
FP * maxRatio[2] < TP * maxRatio[1]
|
|
|
|
(* Can a block be produced by a correct peer, or an authenticated Byzantine peer *)
|
|
IsLightBlockAllowedByDigitalSignatures(ht, block) ==
|
|
\/ block.header = blockchain[ht] \* signed by correct and faulty (maybe)
|
|
\/ /\ block.Commits \subseteq Faulty
|
|
/\ block.header.height = ht
|
|
/\ block.header.time >= 0 \* signed only by faulty
|
|
|
|
(*
|
|
Initialize the blockchain to the ultimate height right in the initial states.
|
|
We pick the faulty validators statically, but that should not affect the light client.
|
|
|
|
Parameters:
|
|
- pMaxFaultyRatioExclusive is a pair <<a, b>> that bound the number of
|
|
faulty validators in each block by the ratio a / b (exclusive)
|
|
*)
|
|
InitToHeight(pMaxFaultyRatioExclusive) ==
|
|
/\ Faulty \in SUBSET AllNodes \* some nodes may fail
|
|
\* pick the validator sets and last commits
|
|
/\ \E vs, lastCommit \in [Heights -> SUBSET AllNodes]:
|
|
\E timestamp \in [Heights -> Int]:
|
|
\* now is at least as early as the timestamp in the last block
|
|
/\ \E tm \in Int: now = tm /\ tm >= timestamp[ULTIMATE_HEIGHT]
|
|
\* the genesis starts on day 1
|
|
/\ timestamp[1] = 1
|
|
/\ vs[1] = AllNodes
|
|
/\ lastCommit[1] = EmptyNodeSet
|
|
/\ \A h \in Heights \ {1}:
|
|
/\ lastCommit[h] \subseteq vs[h - 1] \* the non-validators cannot commit
|
|
/\ TwoThirds(vs[h - 1], lastCommit[h]) \* the commit has >2/3 of validator votes
|
|
\* the faulty validators have the power below the threshold
|
|
/\ FaultyValidatorsFewerThan(Faulty, vs[h], pMaxFaultyRatioExclusive)
|
|
/\ timestamp[h] > timestamp[h - 1] \* the time grows monotonically
|
|
/\ timestamp[h] < timestamp[h - 1] + TRUSTING_PERIOD \* but not too fast
|
|
\* form the block chain out of validator sets and commits (this makes apalache faster)
|
|
/\ blockchain = [h \in Heights |->
|
|
[height |-> h,
|
|
time |-> timestamp[h],
|
|
VS |-> vs[h],
|
|
NextVS |-> IF h < ULTIMATE_HEIGHT THEN vs[h + 1] ELSE AllNodes,
|
|
lastCommit |-> lastCommit[h]]
|
|
] \******
|
|
|
|
(********************* BLOCKCHAIN ACTIONS ********************************)
|
|
(*
|
|
Advance the clock by zero or more time units.
|
|
*)
|
|
AdvanceTime ==
|
|
\E tm \in Int: tm >= now /\ now' = tm
|
|
/\ UNCHANGED <<blockchain, Faulty>>
|
|
|
|
=============================================================================
|
|
\* Modification History
|
|
\* Last modified Wed Jun 10 14:10:54 CEST 2020 by igor
|
|
\* Created Fri Oct 11 15:45:11 CEST 2019 by igor
|