# Causality and Local Ledgers¶

Daml ledgers do not totally order all transactions. So different parties may observe two transactions on different Participant Nodes in different orders via the Ledger API. Moreover, different Participant Nodes may output two transactions for the same party in different orders. This document explains the ordering guarantees that Daml ledgers do provide, by example and formally via the concept of causality graphs and local ledgers.

The presentation assumes that you are familiar with the following concepts:

## Causality examples¶

A Daml Ledger need not totally order all transaction, unlike ledgers in the Daml Ledger Model. The following examples illustrate these ordering guarantees of the Ledger API. They are based on the paint counteroffer workflow from the Daml Ledger Model’s privacy section, ignoring the total ordering coming from the Daml Ledger Model. Recall that the party projections are as follows.

### Stakeholders of a contract see creation and archival in the same order.¶

Every Daml Ledger orders the creation of the CounterOffer A P Bank before the painter exercising the consuming choice on the CounterOffer. (If the Create was ordered after the Exercise, the resulting shared ledger would be inconsistent, which violates the validity guarantee of Daml ledgers.) Accordingly, Alice will see the creation before the archival on her transaction stream and so will the painter. This does not depend on whether they are hosted on the same Participant Node.

### Signatories of a contract and stakeholder actors see usages after the creation and before the archival.¶

The Fetch A (Iou Bank A) action comes after the creation of the Iou Bank A and before its archival, for both Alice and the Bank, because the Bank is a signatory of the Iou Bank A contract and Alice is a stakeholder of the Iou Bank A contract and an actor on the Fetch action.

### Commits are atomic.¶

Alice sees the Create of her Iou before the creation of the CounterOffer, because the CounterOffer is created in the same commit as the Fetch of the Iou and the Fetch commit comes after the Create of the Iou.

### Non-consuming usages in different commits may appear in different orders.¶

Suppose that the Bank exercises a non-consuming choice on the Iou Bank A without consequences while Alice creates the CounterOffer. In the ledger shown below, the Bank’s commit comes before Alice’s commit.

The Bank’s projection contains the nonconsuming Exercise and the Fetch action on the Iou. Yet, the Fetch may come before the non-consuming Exercise in the Bank’s transaction tree stream.

### Out-of-band causality is not respected.¶

The following examples assume that Alice splits up her commit into two as follows:

Counteroffer workflow with four commits.

Alice can specify in the CounterOffer the Iou that she wants to pay the painter with. In a deployed implementation, Alice’s application first observes the created Iou contract via the transaction service or active contract service before she requests to create the CounterOffer. Such application logic does not induce an ordering between commits. So the creation of the CounterOffer need not come after the creation of the Iou.

If Alice is hosted on several Participant Nodes, the Participant Nodes can therefore output the two creations in either order.

The rationale for this behaviour is that Alice could have learnt about the contract ID out of band or made it up. The Participant Nodes therefore cannot know whether there will ever be a Create event for the contract. So if Participant Nodes delayed outputting the Create action for the CounterOffer until a Create event for the Iou contract was published, this delay might last forever and liveness is lost. Daml ledgers therefore do not capture data flow through applications.

### Divulged actions do not induce order.¶

The painter witnesses the fetching of Alice’s Iou when the ShowIou contract is consumed. The painter also witnesses the Exercise of the Iou when Alice exercises the transfer choice as a consequence of the painter accepting the CounterOffer. However, as the painter is not a stakeholder of Alice’s Iou contract, he may observe Alice’s ShowIou commit after the archival of the Iou as part of accepting the CounterOffer.

In practice, this can happen in a setup where two Participant Nodes N1 and N2 host the painter. He sees the divulged Iou and the created CounterOffer through N1’s transaction tree stream and then submits the acceptance through N1. Like in the previous example, N2 does not know about the dependence of the two commits. Accordingly, N2 may output the accepting transaction before the ShowIou contract on the transaction stream.

Even though this may seem unexpected, it is in line with stakeholder-based ledgers: Since the painter is not a stakeholder of the Iou contract, he should not care about the archivals or creates of the contract. In fact, the divulged Iou contract shows up neither in the painter’s active contract service nor in the flat transaction stream. Such witnessed events are included in the transaction tree stream as a convenience: They relieve the painter from computing the consequences of the choice and enable him to check that the action conforms to the Daml model.

Similarly, being an actor of an Exercise action induces order with respect to other uses of the contract only if the actor is a contract stakeholder. This is because non-stakeholder actors of an Exercise action merely authorize the action, but they do not track whether the contract is active; this is what signatories and contract observers are for. Analogously, choice observers of an Exercise action benefit from the ordering guarantees only if they are contract stakeholders.

### The ordering guarantees depend on the party.¶

By the previous example, for the painter, fetching the Iou is not ordered before transferring the Iou. For Alice, however, the Fetch must appear before the Exercise because Alice is a stakeholder on the Iou contract. This shows that the ordering guarantees depend on the party.

## Causality graphs¶

The above examples indicate that Daml ledgers order transactions only partially. Daml ledgers can be represented as finite directed acyclic graphs (DAG) of transactions.

Definition »causality graph«
A causality graph is a finite directed acyclic graph G of transactions that is transitively closed. Transitively closed means that whenever v1 -> v2 and v2 -> v3 are edges in G, then there is also an edge v1 -> v3 in G.
Definition »action order«

For a causality graph G, the induced action order on the actions in the transactions combines the graph-induced order between transactions with the execution order of actions inside each transaction. It is the least partial order that includes the following ordering relations between two actions act1 and act2:

• act1 and act2 belong to the same transaction and act1 precedes act2 in the transaction.

• act1 and act2 belong to different transactions in vertices tx1 and tx2 and there is a path in G from tx1 to tx2.

Note

Checking for an edge instead of a path in G from tx1 to tx2 is equivalent because causality graphs are transitively closed. The definition uses path because the figures below omit transitive edges for readability.

The action order is a partial order on the actions in a causality graph. For example, the following diagram shows such a causality graph for the ledger in the above Out-of-band causality example. Each grey box represents one transaction and the graph edges are the solid arrows between the boxes. Diagrams omit transitive edges for readability; in this graph the edge from tx1 to tx4 is not shown. The Create action of Alice’s Iou is ordered before the Create action of the ShowIou contract because there is an edge from the transaction tx1 with the Iou Create to the transaction tx3 with the ShowIou Create. Moreover, the ShowIou Create action is ordered before the Fetch of Alice’s Iou because the Create action precedes the Fetch action in the transaction. In contrast, the Create actions of the CounterOffer and Alice’s Iou are unordered: neither precedes the other because they belong to different transaction and there is no directed path between them.

Causality graph for the counteroffer workflow with four commits.

### Consistency¶

Consistency ensures that a causality graph sufficiently orders all the transactions. It generalizes ledger consistency from the Daml Ledger Model as explained below.

Definition »Causal consistency for a contract«

Let G be a causality graph and X be a set of actions on a contract c that belong to transactions in G. The graph G is causally consistent for the contract c on X if all of the following hold:

• If X is not empty, then X contains exactly one Create action. This action precedes all other actions in X in G’s action order.
• If X contains a consuming Exercise action act, then act follows all actions in X other than act in G’s action order.
Definition »Causal consistency for a key«

Let G be a causality graph and X be a set of actions on a key k that belong to transactions in G. The graph G is causally consistent for the key k on X if all of the following hold:

• All Create and consuming Exercise actions in X are totally ordered in G’s action order and Creates and consuming Exercises alternate, starting with Create. Every consecutive Create-Exercise pair acts on the same contract.
• All NoSuchKey actions in X are action-ordered with respect to all Create and consuming Exercise actions in X. No NoSuchKey action is action-ordered between a Create action and its subsequent consuming Exercise action in X.
Definition »Consistency for a causality graph«
Let X be a subset of the actions in a causality graph G. Then G is consistent on X (or X-consistent) if G is causally consistent for all contracts c on the set of actions on c in X and for all keys k on the set of actions on k in X. G is consistent if G is consistent on all the actions in G.

When edges are added to an X-consistent causality graph such that it remains acyclic and transitively closed, the resulting graph is again X-consistent. So it makes sense to consider minimal consistent causality graphs.

Definition »Minimal consistent causality graph«
An X-consistent causality graph G is X-minimal if no strict subgraph of G (same vertices, fewer edges) is an X-consistent causality graph. If X is the set of all actions in G, then X is omitted.

For example, the above causality graph for the split counteroffer workflow is consistent. This causality graph is minimal, as the following analysis shows:

Edge Justification
tx1 -> tx3 Alice’s Iou Create action of must precede the Fetch action.
tx2 -> tx4 The CounterOffer Create action of must precede the Exercise action.
tx3 -> tx4 The consuming Exercise action on Alice’s Iou must follow the Fetch action.

We can focus on parts of the causality graph by restricting the set X. If X consists of the actions on Iou contracts, this causality graph is X-consistent. Yet, it is not X-minimal since the edge tx2 -> tx4 can be removed without violating X-consistency: the edge is required only because of the CounterOffer actions, which are excluded from X. The X-minimal consistent causality graph looks as follows, where the actions in X are highlighted in red.

Minimal consistent causality graph for the highlighted actions.

Another example of a minimal causality graph is shown below. At the top, the transactions tx1 to tx4 create an Iou for Alice, exercise two non-consuming choices on it, and transfer the Iou to the painter. At the bottom, tx5 asserts that there is no key for an Account contract for the painter. Then, tx6 creates an such account with balance 0 and tx7 deposits the painter’s Iou from tx4 into the account, updating the balance to 1.

Unlike in a linearly ordered ledger, the causality graph relates the transactions of the Iou transfer workflow with the Account creation workflow only at the end, when the Iou is deposited into the account. As will be formalized below, the Bank, Alice, and the painter therefore need not observe the transactions tx1 to tx7 in the same order.

Moreover, transaction tx2 and tx3 are unordered in this causality graph even though they act on the same Iou contract. However, as both actions are non-consuming, they do not interfere with each other and could therefore be parallelized, too. Alice and the Bank accordingly may observe them in different orders.

The NoSuchKey action in tx5 must be ordered with respect to the two Account Create actions in tx6 and tx7 and the consuming Exercise on the Account contract in tx7, by the key consistency conditions. For this set of transactions, consistency allows only one such order: tx5 comes before tx6 because tx7 is atomic: tx5 cannot be interleaved with tx7, e.g., between the consuming Exercise of the Acc Bank P P 0 and the Create of the updated account Acc Bank P P 1.

NoSuchKey actions are similar to non-consuming Exercises and Fetches of contracts when it comes to causal ordering: If there were another transaction tx5’ with a NoSuchKey (Acc, Bank, P) action, then tx5 and tx5’ need not be ordered, just like tx2 and tx3 are unordered.

### From causality graphs to ledgers¶

Since causality graphs are acyclic, their vertices can be sorted topologically and the resulting list is again a causality graph, where every vertex has an outgoing edge to all later vertices. If the original causality graph is X-consistent, then so is the topological sort, as topological sorting merely adds edges. For example, the transactions on the ledger in the out-of-band causality example are a topological sort of the corresponding causality graph.

Conversely, we can reduce an X-consistent causality graph to only the causal dependencies that X-consistency imposes. This gives a minimal X-consistent causality graph.

Definition »Reduction of a consistent causality graph«
For an X-consistent causality graph G, there exists a unique minimal X-consistent causality graph reduceX(G) with the same vertices and the edges being a subset of G. reduceX(G) is called the X-reduction of G. As before, X is omitted if it contains all actions in G.

The causality graph for the split CounterOffer workflow is minimal and therefore its own reduction. It is also the reduction of the topological sort, i.e., the ledger in the out-of-band causality example.

Note

The reduction reduceX(G) of an X-consistent causality graph G can be computed as follows:

1. Set the vertices of G’ to the vertices of G.
2. The causal consistency conditions for contracts and keys demand that certain pairs of actions act1 and act2 in X must be action-ordered. For each such pair, determine the actions’ ordering in G and add an edge to G’ from the earlier action’s transaction to the later action’s transaction.
3. reduceX(G) is the transitive closure of G’.

Topological sort and reduction link causality graphs G to the ledgers L from the Daml Ledger Model. Topological sort transforms a causality graph G into a sequence of transactions; extending them with the requesters gives a sequence of commits, i.e., a ledger in the Daml Ledger Model. Conversely, a sequence of commits L yields a causality graph GL by taking the transactions as vertices and adding an edge from tx1 to tx2 whenever tx1’s commit precedes tx2’s commit in the sequence.

There are now two consistency definitions:

Fortunately, the two definitions are equivalent: If G is a consistent causality graph, then the topological sort is ledger consistent. Conversely, if the sequence of commits L is ledger consistent, GL is a consistent causality graph, and so is the reduction reduce(GL).

## Local ledgers¶

As explained in the Daml Ledger Model, parties see only a projection of the shared ledger for privacy reasons. Like consistency, projection extends to causality graphs as follows.

Definition »Stakeholder informee«

A party P is a stakeholder informee of an action act if all of the following holds:

• P is an informee of act.
• If act is an action on a contract then P is a stakeholder of the contract.

An Exercise and Fetch action acts on the input contract, a Create action on the created contract, and a NoSuchKey action does not act on a contract. So for a NoSuchKey action, the stakeholder informees are the key maintainers.

Definition »Causal consistency for a party«
A causality graph G is consistent for a party P (P-consistent) if G is consistent on all the actions that P is a stakeholder informee of.

The notions of X-minimality and X-reduction extend to parties accordingly.

For example, the split counteroffer causality graph without the edge tx2 -> tx4 is consistent for the Bank because the Bank is a stakeholder informee of exactly the highlighted actions. It is also minimal Bank-consistent and the Bank-reduction of the original split counteroffer causality graph.

Definition »Projection of a consistent causality graph«

The projection projP(G) of a consistent causality graph G to a party P is the P-reduction of the following causality graph G’:

• The vertices of G’ are the vertices of G projected to P, excluding empty projections.
• There is an edge between two vertices v1 and v2 in G’ if there is an edge from the G-vertex corresponding to v1 to the G-vertex corresponding to v2.

For the split counteroffer causality graph, the projections to Alice, the Bank, and the painter are as follows.

Alice’s projection is the same as the original minimal causality graph. The Bank sees only actions on Iou contracts, so the causality graph projection does not contain tx2 any more. Similarly, the painter is not aware of tx1, where Alice’s Iou is created. Moreover, there is no longer an edge from tx3 to tx4 in the painter’s local ledger. This is because the edge is induced by the Fetch of Alice’s Iou preceding the consuming Exercise. However, the painter is not an informee of those two actions; he merely witnesses the Fetch and Exercise actions as part of divulgence. Therefore no ordering is required from the painter’s point of view. This difference explains the divulgence causality example.

### Ledger API ordering guarantees¶

The Transaction Service provides the updates as a stream of Daml transactions and the Active Contract Service summarizes all the updates up to a given point by the contracts that are active at this point. Conceptually, both services are derived from the local ledger that the Participant Node manages for each hosted party. That is, the transaction tree stream for a party is a topological sort of the party’s local ledger. The flat transaction stream contains precisely the CreatedEvents and ArchivedEvents that correspond to Create and consuming Exercise actions in transaction trees on the transaction tree stream where the party is a stakeholder of the affected contract.

Note

The transaction trees of the Transaction Service omit Fetch and NoSuchKey actions that are part of the transactions in the local ledger. The Fetch and NoSuchKey actions are thus removed before the Transaction Service outputs the transaction trees.

Similarly, the active contract service provides the set of contracts that are active at the returned offset according to the Transaction Service streams. That is, the contract state changes of all events from the transaction event stream are taken into account in the provided set of contracts. In particular, an application can process all subsequent events from the flat transaction stream or the transaction tree stream without having to take events before the snapshot into account.

Since the topological sort of a local ledger is not unique, different Participant Nodes may pick different orders for the transaction streams of the same party. Similarly, the transaction streams for different parties may order common transactions differently, as the party’s local ledgers impose different ordering constraints. Nevertheless, Daml ledgers ensure that all local ledgers are projections of a virtual shared causality graph that connects to the Daml Ledger Model as described above. The ledger validity guarantees therefore extend via the local ledgers to the Ledger API. These guarantees are subject to the deployed Daml ledger’s trust assumptions.

Note

The virtual shared causality graph exists only as a concept, to reason about Daml ledger guarantees. A deployed Daml ledger in general does not store or even construct such a shared causality graph. The Participant Nodes merely maintain the local ledgers for their parties. They synchronize these local ledgers to the extent that they remain consistent. That is, all the local ledgers can in theory be combined into a consistent single causality graph of which they are projections.

### Explaining the causality examples¶

The causality examples can be explained in terms of causality graphs and local ledgers as follows:

1. Stakeholders of a contract see creation and archival in the same order. Causal consistency for the contract requires that the Create comes before the consuming Exercise action on the contract. As all stakeholders are informees on Create and consuming Exercise actions of their contracts, the stakeholder’s local ledgers impose this order on the actions.
2. Signatories of a contract and stakeholder actors see usages after the creation and before the archival. Causal consistency for the contract requires that the Create comes before the non-consuming Exercise and Fetch actions of a contract and that consuming Exercises follow them. Since signatories and stakeholder actors are informees of Create, Exercise, and Fetch actions, the stakeholder’s local ledgers impose this order on the actions.
3. Commits are atomic. Local ledgers are DAGs of (projected) transactions. Topologically sorting such a DAG cannot interleave one transaction with another, even if the transaction consists of several top-level actions.
4. Non-consuming usages in different commits may appear in different orders. Causal consistency does not require ordering between non-consuming usages of a contract. As there is no other action in the transaction that would prescribe an ordering, the Participant Nodes can output them in any order.
5. Out-of-band causality is not respected. Out-of-band data flow is not captured by causal consistency and therefore does not induce ordering.
6. Divulged actions do not induce order. The painter is not an informee of the Fetch and Exercise actions on Alice’s Iou; he merely witnesses them. The painter’s local ledger therefore does not order tx3 before tx4. So the painter’s transaction stream can output tx4 before tx3.
7. The ordering guarantees depend on the party. Alice is an informee of the Fetch and Exercise actions on her Iou. Unlike for the painter, her local ledger does order tx3 before tx4, so Alice is guaranteed to observe tx3 before tx4 on all Participant Nodes through which she is connect to the Daml ledger.