This tool implements a unified language for querying simulation traces of rule-based models written in Kappa about the statistical behavior of individual agents and the relative frequency of different causal patterns. This language was first described in this paper.

• Installation Instructions
• Tutorial
  • Single-event queries
  • Multi-event queries
• User Guide
  • Semantics of queries
  • Invalid queries
  • Expression language
  • Measures reference
  • Other features
    • Rule constraints
    • When-clauses
    • Every-clauses
  • The KaTie CLI
• Implementation Details
• Testing Instructions
  • Using the testing script
  • Contributing new tests
• Frequently Asked Questions

The simplest way to install KaTie is via opam:

• Install opam
• Install the Kappa Tools: opam pin add -y https://github.com/Kappa-Dev/KappaTools.git
• Install KaTie: opam pin add -y kappa-trace-queries https://github.com/jonathan-laurent/KaTie.git
• The tool can then be used as KaTie -t <trace_file> -q <query_file> [options]

To develop KaTie locally, you can do the following instead:

git clone [email protected]:jonathan-laurent/KaTie.git
cd KaTie
opam pin add -y https://github.com/Kappa-Dev/KappaTools.git
opam install . --deps-only
dune build
dune exec -- KaTie -t <trace_file> -q <query_file> [options]

We introduce the trace query language and its execution engine KaTie using a simple example involving a substrate-kinase system (see tests/large/catphos and tests/unit/catphos-mini). The example is discussed in more details in the paper.

%agent: K(d, x{u,p})
%agent: S(d, x{u,p})

'b'  K(d[./1]), S(d[./1]) @ 'on_rate'
'u'  K(d[1/.], x{u}), S(d[1/.]) @ 'off_rate_fast'
'u*' K(d[1/.], x{p}), S(d[1/.]) @ 'off_rate_slow'
'p'  K(d[1]), S(d[1], x{u/p}) @ 'phos_rate'

%init: 'C0' K(x{u}), K(x{p}), S(x{u})

In this example, a substrate of kind S can be phosphorylated by a kinase of kind K. This requires both agents to be bound together. Also, substrate-kinase complexes are more stable when the kinase is phosphorylated itself, which we model by setting off_rate_fast to be much larger than off_rate_slow.

The following query prints the current time every time a substrate binds to some kinase:

query 'binding-times.csv'
match e:{ S(d[/d.K]) } return time[e]

Some remarks:

• The match keyword introduces a pattern and the keyword return introduces a computation that is executed for every instance of the pattern in the trace.
• Here, the pattern consists in a single event named e that obeys the constraint { S(d[/d.K]) }, meaning that event e must bind a substrate to a kinase. Kappa's edit notation is used to specify transformations that a trace event must perform to match with e.
• Given a specific instance of e in the trace, the time[e] expression returns the time at which this instance happened in simulation.
• Executing the query above produces a binding-times.csv output file with as many lines as there are matchings of e in the trace, each line consisting in a floating point number.

In addition to querying the time for each matched event, we can also query the name of the corresponding rule as follows:

query 'bindings.csv'
match e:{ S(d[/d.K]) }
return time[e], rule[e]

This query outputs a CSV file with two columns. Optionally, one can provide explicit labels for those columns using the following syntax:

query 'bindings.csv'
match e:{ S(d[/d.K]) }
return {'binding-time': time[e], 'binding-rule': rule[e]}

In the rest of this document, we tend to skip the full query header for conciseness.

To estimate the probability that a substrate is bound to a phosphorylated kinase when it gets phosphorylated itself, one can use the following query:

match p:{ S(x{/p}, d[1]), k:K(d[1]) }
return int_state[.p]{k.x}

As opposed to time and rule that are event measures (measures associated to a particular event), int_state is a state measure (a measure associated to a particular mixture). As a first argument and between square brackets, it takes a state expression. For e an event identifier, the state expression .e refers to the state of the system before the triggering of event e. Similarly, e. refers to the state of the system after the triggering of e. As a second argument, int_state expects a site expression. Here, we build such an expression by introducing a name k for the kinase captured in event p.

To estimate the average lifespan of a bond between a kinase and a substrate, we can run the following query:

match b:{ s:S(d[./1]), K(d[./1]) }
and first u:{ s:S(d[/.]) } after b
return time[u] - time[b]

The pattern in this query matches two events b and u. Event b must be a binding event between a substrate and a kinase and event u must match the first event in the trace after event b where the same substrate gets unbound. Note that the constraint according to which the same substrate must be involved in both events is captured by the use of a shared agent variable s.

To compute the average lifespan of a bond between a kinase and a substrate conditionned on the fact that the kinase is phosphorylated before the bond breaks, one may be tempted to use the following query:

match b:{ s:S(d[./1]), K(d[./1]) }
and first u:{ s:S(d[1/.]), K(d[1/.], x{p}) } after b
return time[u] - time[b]

This query is perfectly valid but it does not compute what we want. Indeed, suppose the following events happen in order during simulation:

1. Substrate 1 binds to unphosphorylated Kinase 1
2. Substrate 1 and Kinase 1 unbind
3. Substrate 1 binds to phosphorylated Kinase 2
4. Substrate 1 and Kinase 2 ubind

The trace pattern above would associate 1 and 4 together (along with 3 and 4 as expected), which is a unwanted. Instead, one can use one of the following queries for example:

match b:{ s:S(d[/d.K]) }
and first u:{ s:S(d[/.]) } after b
and u:{ s:S(d[1]), K(d[1], x{p}) }
return time[u] - time[b]

match b:{ s:S(d[/d.K]) }
and first u:{ s:S(d[1/.]), k:K(d[1/.]) } after b
when int_state[.u]{k.x} = 'p'
return time[u] - time[b]

match u:{ s:S(d[1/.]), K(d[1/.], x{p}) }
and last b:{ s:S(d[./_]) } before u
return time[u] - time[b]

Some comments:

• The first query adds another clause that additionally constrains s to be bound to a phosphorylated kinase in u. In general, whenever events are constrained by a first ... after or last ... before clause, another clause can be specified for performing additional checks or capturing other agents.
• The second query uses a when-clause to specify an additional condition for the computation to be performed as a boolean expression.
• The third query uses a last ... before clause instead of a first ... after clause to avoid the trap altogether.

For details on how to run KaTie concretely, you can look at the exec.sh example script. All queries mentioned in this tutorial can be found in tests/unit/catphos-mini/query.katie. More generally, the test suite is a good resource when it comes to understanding the capabilities and subtelties of the trace query language.

A query is defined by a trace pattern along with a computation. The trace pattern is a sequence of clauses, each one of them featuring an event pattern:

<query>          ::=  "match" <trace-pattern> "return" <exprs>
<trace-pattern>  ::=  <clause> | <clause> "and" <clause>
<clause>         ::=  <evar> ":" <event-pattern>
                  |   "last" <evar> ":" <event-pattern> "before" <evar>
                  |   "first" <evar> ":" <event-pattern> "after" <evar>
<event-pattern>  ::=  "{" <rule-constr>? <edit-pattern> "}"

A trace pattern contains both agent and event variables. We call matching a function that maps every event variable to an event in the trace and every agent variable to an agent in the trace. A trace pattern can be thought as a predicate (i.e. a boolean function) over matchings. For example, consider the following pattern:

b:{ s:S(x[./_]) } and first u:{ s:S(x[_/.]) } after b

This pattern evaluates to true given a matching m if and only if:

1. agent m(s) has kind S
2. agent m(s) has site x free before event m(b) and bound afterwards
3. agent m(s) has site x bound before event m(u) and free afterwards
4. event m(u) is the first event in the trace following m(b) for which (3.) is true.

The expression after the return keyword is also parametrized my a matching since it can involve both event and agent variables.

Evaluating a query on a trace consists in executing the provided computation for every choice of a matching m that makes the trace pattern true.

To better understand the semantics of queries as defined above, let us consider a toy Kappa model where an agent A can be turned into two agents B and an agent B into two agents C (see tests/unit/cascade):

'r1' A()-, B()+, B()+  @ 1
'r2' B()-, C()+, C()+  @ 1

Simulating those rules on a mixture that starts with a single A, the following query admits four valid matchings in total:

match e1:{ +a:A }
and first e2: { -a:A, +b:B } after e1
and first e3: { -b:B, +c:C } after e2
return
    rule[e1], event_id{e1}, rule[e2], event_id{e2}, rule[e3], event_id{e3},
    agent_id{a}, agent_id{b}, agent_id{c}

More precisely, on a specific trace corresponding to a specific random seed, the query outputs the following:

"_init_", 0, "r1", 1, "r2", 2, 0, 2, 3
"_init_", 0, "r1", 1, "r2", 2, 0, 2, 4
"_init_", 0, "r1", 1, "r2", 3, 0, 1, 5
"_init_", 0, "r1", 1, "r2", 3, 0, 1, 6

As one can see, all four matchings map e1 and e2 to the same event in the trace while two mappings are possible for e3. Similarly, there are 1, 2 and 4 possible mappings for agents a, b and c respectively. Note that in this example, the agent_id function takes an agent variable as an input and returns a unique global identifier for this agent that identifies it across time. This is in contrast with simluation IDs used in KaSim, where agent IDs can be recycled once agents are deleted.

In addition to the semantics discussed above, KaTie places a number of restrictions on the queries that it can evaluate. Queries failing to meet these conditions are rejected statically before they are run.

• Trace patterns must be connected. One can define the dependency graph of a query as a graph whose nodes are event variables and where there is an edge from e1 to e2 if and only if e2 is constrained by a clause of the form last e2: {...} before e1 or first e2: {...} after e1. A pattern is said to be connected if its dependency graph is. One reason this is a requirement is that non-connected patterns can admit a number of valid matchings that is superlinear in the size of the trace. For example, the pattern e1:{} and e2:{} admits $N^2$ valid matchings on a trace with $N$ events. Causal stories are particular instances of connected patterns.
• The dependency graph of trace patterns must be a tree. Given the previous point, this is equivalent to saying that nodes in the dependency graph have either 0 or 1 predecessors. By connectedness, there has to be exactly one node without predecessors, which we call the root event of the query. A non-root event e must be introduced using a single first e:... after ... or last e:... before ... clause, which we call the defining clause for this event while other clauses of the form e:... are called auxiliary clauses. This is not as big a restriction as it may seem. Indeed, patterns such as last e:... before f and last e:... before g can be expressed as last e1:... before f and last e2:... before g when event_id{e1} = event_id{e2} using a when-clause. With this trick, KaTie can be used to match arbitrary causal DAGs.
• All event patterns must be rooted. For every event pattern, the identity of all involved agents must be fully determined by the identity of modified agents. For example, the query match e:{ s:S(x{p}) } return 1 is invalid since the pattern for e is not rooted. Rejecting such a query is once again legitimate since it would produce a huge number of matchings, of the order of $N\times E$ where $N$ is the number of events in the trace and $E$ the total number of agents in the simulation. In contrast, the event pattern { s:S(x{u/p}, d[1]), k:K(d[1]) } is rooted since the first agent in the pattern is modified and the identity of the second agent is inferrable from a bond. Importantly, this rule is relaxed for event patterns in auxiliary clauses. In this case, the identity of all agents in the pattern must be determined by the identity of modified agents taken together with the identity of all agents mentioned in the event's defining clause. Examples are provided below.

Note: the original paper for the trace query language mentions a much more stringent rigidity requirement that is no longer necessary.

match e1:{ s:S(x{u/p}) } and e2:{ s:S(x{p/u}) } return 1

match c:{ +s:S }
and first p:{ s:S(x{u/p}) } after c
and first p:{ s:S(y{u/p}) } after c
return 1

match c:{ +s:S }
and first p:{ s:S(x{u/p}) } after c
and p:{ s:S(y{u/p}) }
return 1

match c:{ +s:S }
and first p1:{ s:S(x{u/p}) } after c
and first p2:{ s:S(y{u/p}) } after c
when event_id{p1} = event_id{p2}
return 1

match e1:{ s:S(x{u/p}, d[1]), k:K(d[1]) }
and last e2:{ s:S(y{u/p}), k:K(d[.]) } before e1

match b:{ s:S(d[/d.K]) }
and first u:{ s:S(d[/.]) } after b
and u:{ s:S(d[1]), K(d[1], x{p}) }
return time[u] - time[b]

Computations can be expressed in a small language with the following types:

• int, float: numerical types. The standard arithmetic operations (e.g. +, -) and comparison operators (e.g. <, >=) are available, along with numerical constants (0, 3.14, 1.3e-7). Integers are automatically promoted to floating point numbers when doing arithmetic with both types.
• bool: boolean type. Booleans are printed as 0 or 1 in the tool's CSV output but they are represented using a distinct type internally. Boolean values can be combined using the && and || logical operators.
• string: string type. String literals are delimited by either simple or double quotes.
• agent_set: type for sets of (agent_kind, agent_id) pairs. Values of this type are returned by some measures such as component but cannot be included directly in the query's output. Functions processing agent sets include:
  • size{s: agent_set} -> int: size of a set
  • similarity{s1: agent_set}{s2: agent_set} -> float: Jaccard similarity coefficient
  • count{k: string}{s: agent_set} -> int: returns the number of agents with kind k in s. For example, if s contains 3 agents of type A and 2 agents of type B, then count{'A'}{s} = 3.

Other remarks:

• Equality = can be tested between any numerical values or between values of the same type, returning a boolean value.
• An agent variable alone does not define a valid expression (although it can be passed to some measures). To obtain a unique integer identifier from agent variable a, one can use the agent_id{a} construct. As opposed to IDs used by KaSim, such IDs can be used to compare the identity of different agents across time. The same agent IDs are also used in the output of measures such as snapshot and print_cc.
• Similarly, a unique event identifier can be obtained from an event variable e using the event_id{e} construct. The identifier of an event corresponds to its index in the trace (a trace is defined as a sequence of events). Note that this does not necessarily corresponds to KaSim's [E] variable, which does not count initialization events. The latter can be accessed using the sim_event_id measure.
• A special null value is included in the language to be returned as a failure code by measures. Any operation taking null as an input must also return null, with the exception of equality (e.g. null = null is true and null = 1 is false).
• Although KaTie's expression language is dynamically typed and type errors can be thrown at runtime, most type errors should be caught statically before queries are executed.

The expression language is not set in stone and can be easily extended. For a summary of currently allowed expressions, one can look at the examples in tests/unit/expr-basic/query.katie.

If an identical measure expression appears multiple times in a query, it is only evaluated once. In addition, sub-computations that are local to an event are evaluated as early as possible by the query engine so as to minimize the amount of data to cache in RAM while streaming through the trace. For example, consider the following query (simplified from tests/large/wnt):

match d:{-c:Cat}
and last p1:{ c:Cat(S45{un/ph}[1]), k1:CK1(c[1])} before d
and last p2:{ c:Cat(T41{un/ph}[1]), k2:GSK(c[1])} before d
return
	count{'Axn'}{component[.p1]{k1}}, count{'APC'}{component[.p1]{k1}},
	count{'Axn'}{component[.p2]{k2}}, count{'APC'}{component[.p2]{k2}}

Here, the measures component[.p1]{k1} and component[.p2]{k1} are only evaluated once. Moreover, when evaluating this query, large intermediate objects such as component[.p2]{k2} are never cached in RAM: maximal local sub-expressions such as count{'Axn'}{component[.p1]{k1}} are cached instead. In contrast, consider changing the return statement into the following:

return similarity{component[.p1]{k1}}{component[.p2]{k2}}

In this case, there is no choice but to cache the full result of component[.p1]{k1} and component[.p2]{k2} in RAM. See the implementation section for more details.

Measures are atomic expressions capturing matching-specific information. They are declined in two kinds: event measures and state measures. Event measures take as a first argument an event variable between square brackets. In contrast, state measures take as a first argument a state expression: for e an event variable, .e denotes the state before event e is triggered and e. denotes the state after event e is triggered.

Event measures:

• time[e]: float: indicates the time of event e.
• rule[e]: string: indicates the name of the rule underlying event e. Special values '_init_', '_pert_' and '_obs_' are returned for initial events, perturbation events and observation events respectively.
• sim_event_id[e]: int: returns the simulator event id for event e, which corresponds to the content of variable [E] in KaSim. This should not be confused with event_id{e}, which returns the index of event e in the trace. One particular way in which these differ is that KaSim typically assigns a single event id for all initialization steps.
• debug_event[e]: string: returns a list of all actions performed by the trace event (e.g. new(S.0) free(S.0.x) mod(S.0.x, u)). This is mostly intended for debugging.

State measures:

• int_state[s]{ag.x}: string: returns the internal state of site x of agent ag in state s.
• component[s]{ag}: agent_set: returns the connected component of agent ag in state s.
• print_cc[s]{ag}: string: returns the Kappa graph of the connected component of agent ag in state s. Unique identifiers are indicated for all agents (i.e. the same identifiers accessible via agent_id).
• snapshot[s]: string: performs a snapshot of the full state s, stores it into a freshly generated file in JSON format and returns a path to this file. Similarly to print_cc, snapshots are annotated with unique agent identifiers. See here for a caveat about using snapshot in the presence of when-clauses.

Whenever a measure is called on an agent that does not exist in the specified state, it returns the value null.

In addition to edit patterns, event patterns can feature a rule constraint of the form 'r1'|...|'rn', meaning that any matching event must be an instance of one of the listed rules. The special name '_init_' can be used to denote an initial event. For example, the following query matches all events e that are either initialization events or instances of rule p that additionally phosphorylate a substrate that is free on site d.

match e:{ 'p'|'_init_' S(x{u/p}, d[.]) }
return ...

A when-clause can be used right before the return statement to specify a boolean expression that must be true for the matching to be reported:

match e:{ s:S(x[/p]) }
and last b:{ s:S(d[./_]) } before e
when size{component[b.]{s}} >= 3
return snapshot[b.]

This query only reports results for which the condition size{component[b.]{s}} >= 3 evaluates to true. Note that when using measures that perform side effects such as snapshot in the return statement, our implementation provides no guarantee that the measure won't be executed for matchings that fail the when-clause. It only guarantees that the results won't be reported. In the case of snapshots, this may result in more files being created on disk than are referenced in the CSV output. The only case in which we guarantee that only reported measures are computed are for queries with a single event pattern (see here for details).

For queries with only a single event pattern, we additionally allow an every-clause to specify a minimal delay between two consecutive matchings:

match e:{ S(x{u/p}) }
every 0.2 seconds
when time[e] >= 0 && time[e] <= 10
return snapshot[.e]

The query above takes a snapshot before each phosphorylation event, from time 0 to 10, leaving at least 0.2 seconds between each snapshot. Because this query only has a single event pattern, it is additionally guaranteed that no snapshot will be taken and stored on disk that isn't referenced in the query's result.

The KaTie command-line tool can be run as follow:

KaTie -t <trace_file> -q <query_file> [options]

Here, <trace_file> must be a JSON trace file generated by KaSim using the -trace option and <query> file must be a file containing a collection of queries to evaluate on the trace. By design, queries are evaluated by batch so as to amortize the cost of streaming through the trace file while recreating intermediate simulation states across queries (see implementation details).

Here are some of KaTie's options:

• --only: only evaluate a subset of queries (expects a comma-separated list of names as an argument)`
• --output-dir: set the output directory (default: .)
• --profile: output a profile.json file with profiling info. In particular, total times spent matching the trace pattern and executing the associated computation are reported for each query. If KaTie is interrupted by the user via Ctrl+C, profiling info is reported for the time spent so far.
• --debug-level: set the debug level. Depending on this level, different files are outputted in the debug output sub-directory, which are described in the implementation section:
  • 0: output no debug information
  • 1: only output debug information that can be produced at small runtime cost (default). This includes:
    • compiled-queries.json
    • queries-ast.json
    • execution-paths.json
  • 2: output all debug information, including the following additional files:
    • trace-summary.json
    • trace-summary-long.json
    • event-cache.json
    • matchings.json
    • measurement-schedule.json
• --no-backtraces: disable exception backtraces (for better performances)
• --native-snapshots: dump snapshot using KaSim's native format (*.ka instead of *.json)
• --no-color: disable colors in the output
• --ccs-incremental: compute connected components incrementally. By default, information about connected components is not maintained when resimulating the trace. When a measure needs to extract a connected component, this component is computed from the current mixture via a graph traversal (depth-first search). With this option, a mapping of all connected components is maintained when replaying the trace and updated incrementally at each step. Querying a component is then a costless operation. However, maintaining such a mapping is going to be slower in most cases and sometimes massively so. Thus, this option should not be used by default.

built on the fly by performing a graph search on the current mixture.

An example of using KaTie in combination with KaSim can be found in exec.sh.

One technical challenge of evaluating queries is that queries can refer to intermediate simulation states that are not explicitly represented in the trace file and often impossible to store all at once, even on disk. Queries are thus evaluated by streaming through the trace file, reconstructing intermediate states on the fly via KaSim's Replay module while caching a minimal amount of information.

More precisely, KaTie evaluates a query by replaying the trace twice: once for computing all matchings and once for evaluating measures and performing all computations. This is done to avoid the need for performing unnecessary measurements and having to store them in RAM, which can be prohibitively expensive. We detail the multi-step process of evaluating queries below.

We explain all steps of evaluating a query using a running example. This example can be run using the following command: python runtests.py tests/unit/double-phos/ run. We illustrate each step using the debug files produced by KaTie via the --debug-level 2 option.

%agent: K(d, x{u,p})
%agent: S(d, x{u,p})

'S.K'  K(d[./1]), S(d[./1])  @ 1
'S.S'  S(x[./1], d[1]), S(x[./1], d[2]), K(d[1], x{u}), K(d[2], x{p})  @ 1
'SSp'  S(x[1]{u/p}), S(x[1]{u/p})  @ 1

%init: 4 S(x{u})
%init: 2 K(x{u})
%init: 2 K(x{p})

%mod: |S(x{u})| = 0 do $STOP ;

{
  "0": [ "_init_", "new(S.0) free(S.0.x) mod(S.0.x, u) free(S.0.d)" ],
  "1": [ "_init_", "new(S.1) free(S.1.x) mod(S.1.x, u) free(S.1.d)" ],
  "2": [ "_init_", "new(S.2) free(S.2.x) mod(S.2.x, u) free(S.2.d)" ],
  "3": [ "_init_", "new(S.3) free(S.3.x) mod(S.3.x, u) free(S.3.d)" ],
  "4": [ "_init_", "new(K.4) free(K.4.x) mod(K.4.x, u) free(K.4.d)" ],
  "5": [ "_init_", "new(K.5) free(K.5.x) mod(K.5.x, u) free(K.5.d)" ],
  "6": [ "_init_", "new(K.6) free(K.6.x) mod(K.6.x, p) free(K.6.d)" ],
  "7": [ "_init_", "new(K.7) free(K.7.x) mod(K.7.x, p) free(K.7.d)" ],
  "8": [ "S.K", "bind(S.3.d, K.6.d)" ],
  "9": [ "S.K", "bind(S.1.d, K.5.d)" ],
  "10": [ "S.K", "bind(S.2.d, K.4.d)" ],
  "11": [ "S.K", "bind(S.0.d, K.7.d)" ],
  "12": [ "S.S", "bind(S.3.x, S.2.x)" ],
  "13": [ "SSp", "mod(S.2.x, p) mod(S.3.x, p)" ],
  "14": [ "S.S", "bind(S.0.x, S.1.x)" ],
  "15": [ "SSp", "mod(S.1.x, p) mod(S.0.x, p)" ]
}

query 'example.csv'
match p:{ s1:S(x{u/p}), s2:S(x{u/p}) }
and last b1:{ s1:S(d[./1]), k1:K(d[./1]) } before p
and b1:{ k1:K(x{p}) }
and last b2:{ s2:S(d[./1]), k2:K(d[./1]) } before p
return {
    'p': event_id{p}, 'b1': event_id{b1}, 'b2': event_id{b2},
    's1': agent_id{s1}, 's2': agent_id{s2}, 'k1': agent_id{k1}, 'k2': agent_id{k2} }

We now proceed to describe each of the five evaluation steps. Note that only steps 2 and 5 require replaying the trace. When queries are evaluated by batch, the underlying resimulation cost is shared across all queries.

• 1. Compiling the query
• 2. Filling in the event cache
• 3. Computing matchings
• 4. Computing a measurement schedule
• 5. Executing the measurement schedule

During the compilation step, some checks are performed to ensure that the provided query is valid. Also, an execution path is computed, which defines the order in which events in the query are tentatively matched to events in the trace. This order is topological, meaning that the root event comes first and any event comes after its predecessors in the query's dependency graph.

For each non-root event, we call link agent an agent constrained by both the defining clause of this event and at least one prior event in the execution path. Given these definitions, all matchings of the trace pattern can be enumerated using the following algorithm:

For every matching of the root event in the trace, determine the identity of all non-root events in the order they appear in the execution path. Given a partial matching m of previously constrained events and agents, the only possible matching for an event e with defining clause first e:P after e' is the first event in the trace after m(e') that matches event pattern P after constraining the identity of the link agents of e with m (and similarly for defining clauses of the form last e:P before e').

{ "example.csv": "p(->s1,s2) b1(s1->k1) b2(s2->k2)" }

As previously mentioned, enumerating all the matchings of the trace pattern requires answering questions of the kind: "what is the first event in the trace with index more than $k$ that matches the defining pattern of event $e$, provided a fixed mapping for the link agents of $e$ ?". The second step of evaluating a query consists in replaying the trace to build a data structure capable of efficiently answering such queries. We call this data structure the event cache.

The event cache maps any pair $(e, m)$ consisting in an event variable $e$ and a mapping $m$ of the link agents of $e$ to the sequence of all $(i, M')$ pairs such that:

• $i$ is the index of a trace event that matches the defining pattern of $e$ given $m$
• $M'$ is the set of all possible mappings $m'$ for the other agents constrained by $e$ such that trace event $i$ matches both the defining pattern of $e$ and all auxiliary patterns of $e$ given $m$ and $m'$.

The event cache can be filled by performing the following actions, for every index $i$ in the trace and every event variable $e$ with defining pattern $p$ in the query:

• Compute the set of all mappings $m'$ for the agents in $p$ such that $p$ matches trace event $i$ given $m'$:
  • Since trace event $i$ performs a finite (and typically small) number of actions, use those to enumerate possible mappings for the agents modified in $p$.
  • Since $p$ is assumed to be rooted, extend those mappings to cover all agents in $p$.
• Group those mappings according to the values assigned to link agents of $e$. Add one entry to the event cache for each resulting group, taking auxiliary patterns into account.

{
  "example.csv": {
    "p": {
      "": {
        "13": [ "s1:3 s2:2", "s1:2 s2:3" ],
        "15": [ "s1:0 s2:1", "s1:1 s2:0" ]
      }
    },
    "b1": {
      "s1:0": { "11": [ "k1:7" ] },
      "s1:1": { "9": [] },
      "s1:2": { "10": [] },
      "s1:3": { "8": [ "k1:6" ] }
    },
    "b2": {
      "s2:0": { "11": [ "k2:7" ] },
      "s2:1": { "9": [ "k2:5" ] },
      "s2:2": { "10": [ "k2:4" ] },
      "s2:3": { "8": [ "k2:6" ] }
    }
  }
}

Once the event cache is filled, all matchings of the query's trace pattern can be enumerated without further access to the trace. For every matching of the root event, non-root events are instantiated in the order specified by the execution path, using the current mapping of link agents to index the event cache.

{
  "example.csv": [
    "p:13 b1:8 b2:10 | s1:3 s2:2 k1:6 k2:4",
    "p:15 b1:11 b2:9 | s1:0 s2:1 k1:7 k2:5"
  ]
}

Once all matchings are determined, one can compute a measurement schedule that specifies the exact order in which measures must be taken and computation results must be printed during a second and final replaying of the trace. The measurement schedule consists in a sequence of $(i, j, k)$ integer triples sorted by increasing value of $i$. Such an $(i, j, k)$ triple can be interpreted as: "while replaying event $i$ from the trace, compute all measures related to event variable number $k$ in matching number $j$".

{
  "example.csv": [
    { "ev_gid": 8, "matching_id": 0, "ev_lid": 1 },
    { "ev_gid": 9, "matching_id": 1, "ev_lid": 2 },
    { "ev_gid": 10, "matching_id": 0, "ev_lid": 2 },
    { "ev_gid": 11, "matching_id": 1, "ev_lid": 1 },
    { "ev_gid": 13, "matching_id": 0, "ev_lid": 0 },
    { "ev_gid": 15, "matching_id": 1, "ev_lid": 0 }
  ]
}

Once a measurement schedule is computed, it can be executed in order as the trace is replayed a second and final time. For each matching, the query's computation is executed and printed as soon as the last triple associated with this matching is processed, thereby allowing all cached measure values associated with it to be released from memory.

'p', 'b1', 'b2', 's1', 's2', 'k1', 'k2'
13, 8, 10, 3, 2, 6, 4
15, 11, 9, 0, 1, 7, 5

Compared to multi-event queries, single-event queries are straightforward to evaluate in a single replaying of the trace and without caching any data in memory. Thus, KaTie uses a separate, optimized execution engine for those.

The tests directory contains a collection of example models and queries. A subdirectory is considered as defining a valid test if it features a model.ka and a query.katie file. The exec.sh script can be used to run KaSim and KaTie in sequence on a test.

There are two ways to specify the expected outcome of running a test:

1. An expected/results folder can be placed in the test directory. The testing script checks that the content of katie-output matches the content of expected/results.
2. The expected behavior of a query can be encoded in the name of the query itself. If a query's name contains the substring __matches_N with N a nonnegative integer, then it is expected to produce N matches exactly. In addition, if it contains the substring __all_true, then every element of the resulting CSV output must be equal to 1. Finally, if it contains the substring errors__, then the query must be detected as invalid statically (before execution starts).

The testing script runtests.py can be used as follows:

python runtests.py [TEST_SUBDIRS] {run,clean,diff,promote}.

Here, TEST_SUBDIRS is a list of sub-directories indicating which tests must be targeted by the command that follows. If no tests are provided, all tests in the tests hierarchy are implicitely included. The following commands are available:

• run: run a test. KaTie's output is stored in katie-output. The stdout and stderr channels are captured and their content stored into katie-output too. Test failures are shown in red.
• clean: clean up a test's directory of all non-versioned auto-generated files.
• diff: whenever run indicates an unexpected output, this command can be used to show a diff.
• promote: update the expected folder with the current content of katie-output.

Here are some example commands:

python runtests.py run  # run the full test suite
python runtests.py clean  # clean-up everything
python runtests.py tests/large/catphos run  # run the 'catphos' test
python runtests.py tests/large/catphos diff  # show a diff for 'catphos'

Remark: some tests rely on the stability of OCaml's random number generator. The current test suite is optimized to run with OCaml 4.14 and some tests may fail when using OCaml 5 since this version breaks backwards compatibility for the random number generator. When using the test suite, users are therefore encouraged to use OCaml 4.14: opam switch create ocaml4 4.14.1.

Users are encouraged to contribute new tests via pull-requests. To add a new test, just add a sub-directory in the tests hierarchy and make sure that it works with runtests.py.

Here are some tips for debugging and inspecting tests:

• The runtests.py script captures the standard output and uses specific KaTie options that must not be changed. To explore running the test with other options or just have the standard output printed on your terminal, you can use the exec.sh script instead.
• The runtests.py script runs KaTie with a maximal debug level, meaning that a lot of useful files are generated in the katie-output/debug directory to help understanding how the trace was processed. In particular, trace-summary.json contains a summary of the trace that is friendlier than the original trace.json file and matchings.json enumerates all found matchings. Other debug files are discussed in the implementation section.

In addition to ensuring that valid queries are correctly executed, it is also important to ensure that invalid queries are detected as such statically (i.e. before they are executed) to avoid having them failing at runtime, possibly wasting weeks of computation. Users are therefore encouraged to add invalid queries to the test suite with the errors__ substring included in their name. Note that KaTie's return code can be used to determine whether or not errors were detected statically: a return code of 0 means that all queries ran fine, 1 means that errors were detected statically, 2 means that at least one user error was detected dynamically and 3 indicates an internal error. Users should consider filing issues when encountering return codes 2 or 3, even for invalid queries.

Both KaTie and the underlying KaSim API make a heavy use of recursive functions on lists, which may result in stack overflows on some systems. This is particularly likely to arise when querying traces that were created using KaSim's -mixture option, in which case the trace may contain events initializing a very high number of agents at once. A simple workaround is to raise the stack size limit. On Linux, this can be done for the current shell with the following command:

ulimit -s 1000000  # set the stack size limit to 1GB