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TokenTransfer10.tla
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TokenTransfer10.tla
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----------------------- MODULE TokenTransfer10 ---------------------------------
(*
* This is an example of a very simplistic token transfer
* for presentation purposes.
* Do not use it in production, as it may lead to loss of tokens.
*
* Version 10: timeouts
* Version 9: receive and send in the backward direction
* Version 8: introducing basic denominations
* Version 7: introducing basic packet receive from source
* Version 6: introducing basic packet send from source
* Version 5: introducing an inductive invariant for Apalache
* Version 4: bounding the amounts to help the model checkers
* Version 3: fixing the invariants and introducing more
* Version 2: let the banks do the local banking
* Version 1: introducing data structures
*
* Igor Konnov, 2021
*)
EXTENDS Integers, Apalache, typedefs
CONSTANT
\* A set of blockchains, i.e., their names
\* @type: Set(CHAIN);
CHAINS,
\* A set of channels, that is, pairs of chains
\* @type: Set(<<CHAIN, CHAIN>>);
CHANNELS,
\* A set of accounts, i.e., their names
\* @type: Set(ACCOUNT);
ACCOUNTS,
\* A set of all possible amounts
\* @type: Set(Int);
GENESIS_SUPPLY,
\* A set of denominations
\* @type: Set(DENOM);
DENOMS,
\* A function that produces a new denomination for a chain a denomination
\* @type: <<CHAIN, DENOM>> -> DENOM;
MK_DENOM,
\* A function that should work as an inverse of MK_DENOM
\* @type: <<CHAIN, DENOM>> -> DENOM;
UNMK_DENOM
VARIABLES
\* For every chain and account, store the amount of tokens in the account
\* for each denomination
\* @type: DADDR -> Int;
banks,
\* Packets that are sent by one chain to another (e.g., via an IBC channel)
\* @type: Set([seqno: Int, src: CHAIN, dest: CHAIN, data: [sender: ACCOUNT, receiver: ACCOUNT, denom: DENOM, amount: Int]]);
sentPackets,
\* The sequence numbers of delivered packets
\* @type: Set(Int);
deliveredNums,
\* The sequence numbers of the packets that timed out
\* @type: Set(Int);
dstTimeoutNums,
\* The sequence numbers of the packets that timed out, registered on source
\* @type: Set(Int);
srcTimeoutNums,
\* An imaginary global counter that we use to assign unique sequence numbers
\* @type: Int;
seqno
(*************************** OPERATORS ***************************************)
\* For simplicity, we fix the name of the escrow account.
\* In ICS20, one introduces one escrow account per channel.
Escrow == "escrow"
\* For simplicity, we call the coin native if it has the same name as the chain
Native(chain) == chain
\* Compute the sum of tokens over addresses.
\* @type: (DADDR -> Int, Set(DADDR)) => Int;
SumAddresses(amounts, Addrs) ==
LET Add(sum, addr) == sum + amounts[addr] IN
ApaFoldSet(Add, 0, Addrs)
\* Compute token supply in one chain.
\* @type: (DADDR -> Int, CHAIN) => Int;
ChainSupply(amounts, chain) ==
SumAddresses(amounts, {chain} \X ACCOUNTS \X { Native(chain) })
\* Compute token supply across all chains.
\* @type: (CHAIN => Int) => Int;
AllChainsSupply(GetChainSupply(_)) ==
LET Add(sum, chain) == sum + GetChainSupply(chain) IN
ApaFoldSet(Add, 0, CHAINS)
\* Compute chain supply in the genesis block.
AllChainsGenesisSupply ==
LET Get(c) == GENESIS_SUPPLY[c] IN
AllChainsSupply(Get)
\* Compute chain supply given an "amounts" function
\* @type: (DADDR -> Int) => Int;
AllChainsAmountsSupply(amounts) ==
LET Get(c) == ChainSupply(amounts, c) IN
AllChainsSupply(Get)
(**************************** SYSTEM *****************************************)
\* Initialize the world, e.g., from the last upgrade
Init ==
/\ seqno = 0
/\ sentPackets = {}
/\ deliveredNums = {}
/\ dstTimeoutNums = {}
/\ srcTimeoutNums = {}
/\ \E b \in [ CHAINS \X ACCOUNTS \X DENOMS -> Nat ]:
/\ \A chain \in CHAINS:
/\ b[chain, "reserve", chain] > 0
/\ ChainSupply(b, chain) = GENESIS_SUPPLY[chain]
/\ \A a \in ACCOUNTS, d \in DENOMS:
\* no tokens in foreign denominations
d /= Native(chain) => b[chain, a, d] = 0
/\ banks = b
\* Transfer the tokens from on account to another (on the same chain)
LocalTransfer(chain, from, to, denom, amount) ==
/\ banks[chain, from, denom] >= amount
/\ from /= to
/\ banks' = [banks EXCEPT
![chain, from, denom] = banks[chain, from, denom] - amount,
![chain, to, denom] = banks[chain, to, denom] + amount
]
\* A computation on the local chain
LocalStep ==
/\ \E chain \in CHAINS, from, to \in ACCOUNTS,
denom \in DENOMS, amount \in Nat:
/\ from /= Escrow
/\ to /= Escrow
/\ LocalTransfer(chain, from, to, denom, amount)
/\ UNCHANGED <<seqno, sentPackets, deliveredNums,
dstTimeoutNums, srcTimeoutNums>>
\* send a packet over a channel
\* @type: (<<Str, Str>>, Str, Str, Str, Str, Int) => Bool;
SendPacket(chan, dir, sender, receiver, denom, amount) ==
LET data == [seqno |-> seqno,
sender |-> sender,
receiver |-> receiver,
denom |-> denom,
amount |-> amount]
src == IF dir = "forward" THEN chan[1] ELSE chan[2]
dst == IF dir = "forward" THEN chan[2] ELSE chan[1]
packet == [src |-> src, dest |-> dst, data |-> data]
IN
/\ sentPackets' = sentPackets \union { packet }
/\ seqno' = seqno + 1
/\ UNCHANGED <<deliveredNums, dstTimeoutNums, srcTimeoutNums>>
\* Send a packet to transfer tokens (from the source)
SendPacketFromSource ==
\E chan \in CHANNELS, sender, receiver \in ACCOUNTS,
denom \in DENOMS, amount \in Nat:
/\ sender /= Escrow /\ receiver /= Escrow
/\ amount > 0
\* the source direction: escrow source tokens
/\ LocalTransfer(chan[1], sender, Escrow, denom, amount)
/\ SendPacket(chan, "forward", sender, receiver, denom, amount)
\* Burn `amount` coins in the sender's account
BurnCoins(chain, sender, denom, amount) ==
\* do not burn native coins
/\ denom /= Native(chain)
\* do not let to burn more coins than we have
/\ LET newAmount == banks[chain, sender, denom] - amount IN
/\ newAmount >= 0
/\ banks' = [banks EXCEPT ![chain, sender, denom] = newAmount]
\* Send a packet to return tokens (to the source)
SendPacketToSource ==
\E chan \in CHANNELS, sender, receiver \in ACCOUNTS,
denom \in DENOMS, amount \in Nat:
/\ sender /= Escrow /\ receiver /= Escrow
/\ amount > 0
\* in the direction of the source: burn coins
/\ BurnCoins(chan[2], sender, denom, amount)
/\ SendPacket(chan, "backward", sender, receiver, denom, amount)
\* Produce `amount` coins in the receiver's account (out of thin air!)
MintCoins(chain, receiver, denom, amount) ==
\* do not mint native coins
/\ denom /= Native(chain)
/\ banks' = [banks EXCEPT ![chain, receiver, denom] =
banks[chain, receiver, denom] + amount]
\* Receive a packet on a non-source chain (note that ICS20 does more than that)
ReceivePacketFromSource ==
\E packet \in sentPackets:
/\ packet.seqno \notin deliveredNums
/\ packet.seqno \notin dstTimeoutNums
\* In the implementation, we produce a new denomination.
\* Mint coins that are different from native.
/\ LET foreignDenom == MK_DENOM[packet.dest, packet.data.denom] IN
MintCoins(packet.dest,
packet.data.receiver, foreignDenom, packet.data.amount)
/\ deliveredNums' = deliveredNums \union { packet.seqno }
/\ UNCHANGED <<sentPackets, dstTimeoutNums, srcTimeoutNums, seqno>>
\* Receive a packet on the source chain
ReceivePacketOnSource ==
\E packet \in sentPackets:
/\ packet.seqno \notin deliveredNums
/\ packet.seqno \notin dstTimeoutNums
\* translate the coin denomination, e.g., by pruning the prefix
/\ LET sourceDenom == UNMK_DENOM[packet.denom] IN
/\ sourceDenom /= "invalid"
/\ LocalTransfer(packet.dst, packet.receiver, Escrow,
sourceDenom, packet.amount)
/\ deliveredNums' = deliveredNums \union { packet.seqno }
/\ UNCHANGED <<sentPackets, dstTimeoutNums, srcTimeoutNums, seqno>>
\* A non-determinstic timeout.
\* Note that the timeout should be registered first on the destination chain.
RegisterTimeout ==
\E packet \in sentPackets:
/\ packet.seqno \notin deliveredNums
/\ packet.seqno \notin dstTimeoutNums
/\ dstTimeoutNums' = dstTimeoutNums \union { packet.seqno }
/\ UNCHANGED <<banks, sentPackets, deliveredNums, srcTimeoutNums, seqno>>
\* Observe a timeout on the destination chain and refund the coins on the source.
\* Note that this cannot be simply done by measuring time.
\* We need a confirmation on the destination chain that the timeout has occured.
ApplyTimeout ==
\E packet \in sentPackets:
/\ packet.seqno \in dstTimeoutNums
/\ srcTimeoutNums' = srcTimeoutNums \union { packet.seqno }
/\ IF Native(packet.src) = packet.denom
THEN LocalTransfer(packet.src, packet.data.sender, Escrow,
packet.data.denom, packet.data.amount)
ELSE MintCoins(packet.dest, packet.data.receiver,
packet.data.denom, packet.data.amount)
/\ UNCHANGED <<banks, sentPackets, deliveredNums, dstTimeoutNums, seqno>>
\* Update the world
Next ==
\/ LocalStep
\/ SendPacketFromSource
\/ ReceivePacketFromSource
\/ SendPacketToSource
\/ ReceivePacketOnSource
\/ RegisterTimeout
\/ ApplyTimeout
(************************** PROPERTIES ***************************************)
\* every bank always has reserves
ReservesInv ==
\A chain \in CHAINS:
banks[chain, "reserve", Native(chain)] > 0
\* no bank account goes negative
NoNegativeAccounts ==
\A address \in DOMAIN banks:
banks[address] >= 0
\* the supply remains constant
ChainSupplyUnchanged ==
\A chain \in CHAINS:
LET supply == ChainSupply(banks, chain) IN
supply = GENESIS_SUPPLY[chain]
\* for each in-fly packet, there is enough money in the escrow account
InFlyPacketIsSecured ==
\A p \in sentPackets:
(p.seqno \notin deliveredNums /\ p.seqno \notin srcTimeoutNums)
=>
banks[p.src, Escrow, p.data.denom] >= p.data.amount
\* the supply over all chains remains constant
AllChainsSupplyUnchanged ==
AllChainsGenesisSupply = AllChainsAmountsSupply(banks)
(************* PROPERTIES TO PRODUCE COUNTEREXAMPLES *************************)
\* This property should produce a counterexample that demonstrates
\* that a foreign denomination can reach a blockchain
NoForeignCoins ==
\A chain \in CHAINS, acc \in ACCOUNTS, d \in DENOMS:
d /= Native(chain) => banks[chain, acc, d] = 0
===============================================================================