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paxos.pl -- A Replicated Data Store
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This module provides a replicated data store that is coordinated using a variation on Lamport's Paxos concensus protocol. The original method is described in his paper entitled, "The Part-time Parliament", which was published in 1998. The algorithm is tolerant of non-Byzantine failure. That is late or lost delivery or reply, but not senseless delivery or reply. The present algorithm takes advantage of the convenience offered by multicast to the quorum's membership, who can remain anonymous and who can come and go as they please without effecting Liveness or Safety properties.

Paxos' quorum is a set of one or more attentive members, whose processes respond to queries within some known time limit (< 20ms), which includes roundtrip delivery delay. This property is easy to satisfy given that every coordinator is necessarily a member of the quorum as well, and a quorum of one is permitted. An inattentive member (e.g. one whose actions are late or lost) is deemed to be "not-present" for the purposes of the present transaction and consistency cannot be assured for that member. As long as there is at least one attentive member of the quorum, then persistence of the database is assured.

Each member maintains a ledger of terms along with information about when they were originally recorded. The member's ledger is deterministic. That is to say that there can only be one entry per functor/arity combination. No member will accept a new term proposal that has a line number that is equal-to or lower-than the one that is already recorded in the ledger.

Paxos is a three-phase protocol:

1: A coordinator first prepares the quorum for a new proposal by broadcasting a proposed term. The quorum responds by returning the last known line number for that functor/arity combination that is recorded in their respective ledgers.

2: The coordinator selects the highest line number it receives, increments it by one, and then asks the quorum to finally accept the new term with the new line number. The quorum checks their respective ledgers once again and if there is still no other ledger entry for that functor/arity combination that is equal-to or higher than the specified line, then each member records the term in the ledger at the specified line. The member indicates consent by returning the specified line number back to the coordinator. If consent is withheld by a member, then the member returns a nack instead. The coordinator requires unanimous consent. If it isn't achieved then the proposal fails and the coordinator must start over from the beginning.

3: Finally, the coordinator concludes the successful negotiation by broadcasting the agreement to the quorum in the form of a paxos_changed(Key,Value) event. This is the only event that should be of interest to user programs.

For practical reasons, we rely on the partially synchronous behavior (e.g. limited upper time bound for replies) of broadcast_request/1 over TIPC to ensure Progress. Perhaps more importantly, we rely on the fact that the TIPC broadcast listener state machine guarantees the atomicity of broadcast_request/1 at the process level, thus obviating the need for external mutual exclusion mechanisms.

Note that this algorithm does not guarantee the rightness of the value proposed. It only guarantees that if successful, the value proposed is identical for all attentive members of the quorum.

- Jeffrey Rosenwald (JeffRose@acm.org)
See also
- tipc_broadcast.pl, udp_broadcast.pl
- BSD-2
Source paxos_initialize(+Options) is det
Initialize this Prolog process as a paxos node. The initialization requires an initialized and configured TIPC, UDP or other broadcast protocol. Calling this initialization may be omitted, in which case the equivant of paxos_initialize([]) is executed lazily as part of the first paxos operation. Defined options:
When instantiated, this node rejoins the network with the given node id. A fixed node idea should be used if the node is configured for persistency and causes the new node to receive updates for keys that have been created or modified since the node left the network. If NodeID is a variable it is unified with the discovered NodeID.

NodeID must be a small non-negative integer as these identifiers are used in bitmaps.

Source paxos_get_admin(+Name, -Value) is semidet[private]
Source paxos_set_admin(+Name, +Value) is semidet[private]
Set administrative keys. We use a wrapper such that we can hide the key identity.
Source node(?NodeId)[private]
Source quorum(?Bitmap)[private]
Source dead(?Bitmap)[private]
Source failed(?Bitmap)[private]
Source failed(?NodeId, ?LastTried, ?Score)[private]
Track our identity as well as as the status of our peers in the network. NodeId is a small integer. Multiple NodeIds are combined in a Bitmap.
  • node/1 is our identity.
  • quorum/1 is the set of members of the quorum
  • failed/1 is the set of members for which the last message was not confirmed.
  • failed/3 tracks individual failed nodes. If accumulates failures until the node is marked dead.
  • dead/1 is the set of members that is considered dead.
Source paxos_assign_node(+Options) is det[private]
Assign a node for this paxos instance. If node is given as an option, this is the node id that is used. Otherwise the network is analysed and the system selects a new node.
Source paxos_rejoin[private]
Re-join the network. Tasks:
  • Remove myself from the dead list if I'm on there
  • Tell the replicators we lost everything.
Source paxos_leave is det[private]
Source paxos_leave(+Node) is det[private]
Leave the network. The predicate paxos_leave/0 is called from at_halt/1 to ensure the node is deleted as the process dies. The paxos_leave/1 version is called to discard other nodes if they repeatedly did not respond to queries.
Source update_failed(+Action, +Quorum, +Alive) is det[private]
We just sent the Quorum a message and got a reply from the set Alive.
is- one of set, get or replicate and indicates the intended action.
Source life_quorum(-Quorum, -LifeQuorum) is det[private]
Find the Quorum and the living nodes from the Quorum. This is the set for which we wait. If the LifeQuorum is not a majority we address the whole Quorum.
To be done
- At some point in time we must remove a node from the quorum.
Source paxos_property(?Property)
True if Property is a current property for the paxos network. Defined properties are:
  • node(?NodeID)
  • quorum(?NodeBitmap)
  • failed(?NodeBitmap)
Source paxos_message(?Message)[private]
Handle inbound actions from our peers. Defines values for Message are:
prepare(+Key, -Node, -Gen, +Value)
A request message to set Key to Value. Returns the current generation at which we have a value or 0 for Gen and the our node id for Node.
accept(+Key, -Node, +Gen, -GenA, +Value)
A request message to set Key to Value if Gen is newer than the generation we have for Key. In that case GenA is Gen. Otherwise we reject using GenA = nack.
changed(+Key, +Gen, +Value, +Acceptors)
The leader got enough accepts for setting Key to Value at Gen. Acceptors is the set of nodes that accepted this value.
learn(+Key, -Node, +Gen, -GenA, +Value)
Request message peforming phase one for replication to learner nodes.
learned(+Key, +Gen, +Value, +Acceptors)
Phase two of the replication. Confirm the newly learned knowledge.
retrieve(+Key, -Node, -Gen, -Value)
A request message to retrieve our value for Key. Also provides our node id and the generation.
Forget the existence of Nodes.
node(-Node, -Quorum, -Dead)
Get my view about the network. Node is the (integer) node id of this node, Quorum is the idea of the quorum and Dead is the idea about non-responsive nodes.
To be done
- : originally the changed was handled by a get and when not successful with a new set, named paxos_audit. I don't really see why we need this.
Source paxos_set(+Term) is semidet
Equivalent to paxos_key(Term,Key), pasox_set(Key,Term). I.e., Term is a ground compound term and its key is the name/arity pair. This version provides compatibility with older versions of this library.
Source paxos_set(+Key, +Value) is semidet
Source paxos_set(+Key, +Value, +Options) is semidet
negotiates to have Key-Value recorded in the ledger for each of the quorum's members. This predicate succeeds if the quorum unanimously accepts the proposed term. If no such entry exists in the Paxon's ledger, then one is silently created. paxos_set/1 will retry the transaction several times (default: 20) before failing. Failure is rare and is usually the result of a collision of two or more writers writing to the same term at precisely the same time. On failure, it may be useful to wait some random period of time, and then retry the transaction. By specifying a retry count of zero, paxos_set/2 will succeed iff the first ballot succeeds.

On success, paxos_set/1 will also broadcast the term paxos_changed(Key,Value), to the quorum.

Options processed:

is a non-negative integer specifying the number of retries that will be performed before a set is abandoned. Defaults to the setting max_sets (20).
Max time to wait for the forum to reply. Defaults to the setting response_timeout (0.020, 20ms).
Term- is a compound that may have unbound variables.
To be done
- If the Value is already current, should we simply do nothing?
Source collect(+Quorum, :Stop, ?Node, ?Template, ?Message, -Result, -NodeSet) is semidet[private]
Perform a broadcast request using Message. Node and Template share with Message and extract the replying node and the result value from Message. Result is the list of instantiations for Template received and NodeSet is the set (bitmask) of Node values that replies, i.e. |NodeSet| is length(Result). The transfer stops if all members of the set Quorum responded or the configured timeout passed.
Source paxos_quorum_ask(?Template, +Message, -Result, +Options)
Ask the paxos forum for their opinion. This predicate is not really part of the paxos protocol, but reuses notably the quorum maintenance mechanism of this library for asking questions to the quorum (cluster). Message is the message to be asked. Result is a list of copies of Template from the quorum. Options:
Max time to wait for a reply. Default is the setting response_timeout.
Can be used to include the replying node into Template.
Set/query the interviewed quorum as a bitmask
Source paxos_get(?Term) is semidet
Equivalent to paxos_key(Term,Key), pasox_get(Key,Term). I.e., Term is a compound term and its key is the name/arity pair. This version provides compatibility with older versions of this library.
Source paxos_get(+Key, +Value) is semidet
Source paxos_get(+Key, +Value, +Options) is semidet
unifies Term with the entry retrieved from the Paxon's ledger. If no such entry exists in the member's local cache, then the quorum is asked to provide a value, which is verified for consistency. An implied paxos_set/1 follows. This predicate succeeds if a term with the same functor and arity exists in the Paxon's ledger, and fails otherwise.

Options processed:

is a non-negative integer specifying the number of retries that will be performed before a set is abandoned. Defaults to the setting max_gets (5).
Max time to wait for the forum to reply. Defaults to the setting response_timeout (0.020, 20ms).
Term- is a compound. Any unbound variables are unified with those provided in the ledger entry.
Source paxos_key(+Term, -Key) is det[private]
Compatibility to allow for paxos_get/1, paxos_set/1, etc. The key of a compound term is a term '$c'(Name,Arity). Note that we do not use Name/Arity and X/Y is naturally used to organize keys as hierachical paths.
Source start_replicator[private]
Start or signal the replicator thread that there may be outstanding replication work. This is the case if
  • The union of quorum and learners was extended, and thus all data may need to be replicated to the new members.
  • A paxos_set/3 was not fully acknowledged.
Source paxos_replicate_key(+Nodes:bitmap, ?Key, +Options) is det
Replicate a Key to Nodes. If Key is unbound, a random key is selected.
Max time to wait for the forum to reply. Defaults to the setting response_timeout (0.020, 20ms).
Source paxos_on_change(?Term, :Goal) is det
Source paxos_on_change(?Key, ?Value, :Goal) is det
Executes the specified Goal when Key changes. paxos_on_change/2 listens for paxos_changed(Key,Value) notifications for Key, which are emitted as the result of successful paxos_set/3 transactions. When one is received for Key, then Goal is executed in a separate thread of execution.
Term- is a compound, identical to that used for paxos_get/1.
Goal- is one of:
  • a callable atom or term, or
  • the atom ignore, which causes monitoring for Term to be discontinued.
Source node(-Node) is det[private]
Get the node ID for this paxos node.
Source quorum(-Quorum) is det[private]
Get the current quorum as a bitmask
Source paxos_message(+PaxOS, +TimeOut, -BroadcastMessage) is det[private]
Transform a basic PaxOS message in a message for the broadcasting service. This predicate is hooked by paxos_message_hook/3 with the same signature.
TimeOut- is one of - or a time in seconds.
 paxos_ledger_hook(+Action, ?Key, ?Gen, ?Value, ?Holders)[multifile]
Hook called for all operations on the ledger. Defined actions are:
Enumerate our ledger content.
Get a single value from our ledger.
Create a new key in our ledger.
Accept a new newly proposed value for a key. Failure causes the library to send a NACK message.
Final acceptance of Ken@Gen, providing the holders that accepted the new value.
Accept new keys in a new node or node that has been offline for some time.
Source ledger_current(?Key, ?Gen, ?Value, ?Holders) is nondet[private]
True when Key is a known key in my ledger.
Source ledger(+Key, -Gen, -Value) is semidet[private]
True if the ledger has Value associated with Key at generation Gen. Note that if the value is not yet acknowledged by the leader we should not use it.
Source ledger_create(+Key, +Gen, +Value) is det[private]
Create a new Key-Value pair at generation Gen. This is executed during the preparation phase.
Source ledger_update(+Key, +Gen, +Value) is semidet[private]
Update Key to Value if the current generation is older than Gen. This reflects the accept phase of the protocol.
Source ledger_update_holders(+Key, +Gen, +Holders) is det[private]
The leader acknowledged that Key@Gen represents a valid new
Source ledger_learn(+Key, +Gen, +Value) is semidet[private]
We received a learn event.
Source ledger_forget(+Nodes) is det[private]
Remove Nodes from all ledgers. This is executed in a background thread.
Source c_element(+NewList, +Old, -Value)[private]
A Muller c-element is a logic block used in asynchronous logic. Its output assumes the value of its input iff all of its inputs are identical. Otherwise, the output retains its original value.
Source arg_union(+Arg, +ListOfTerms, -Set) is det[private]
Get all the nth args from ListOfTerms and do a set union on the result.

Undocumented predicates

The following predicates are exported, but not or incorrectly documented.

Source paxos_admin_key(Arg1, Arg2)