Deterministic operators

Relate

Recover labeled relationships within one Space using deterministic code.

Relate evaluates pairs from one Space and emits declared relationship labels.

Worked example

Relate(
    name="map-package-dependencies",
    input_spaces=("packages",),
    output_space="package-relations",
    primary_key="package",
    evidence=("dependencies", "conflicts"),
    labels=("depends_on", "conflicts_with"),
    fn=lambda left, right: (
        "depends_on" if right["package"] in left["dependencies"]
        else "conflicts_with" if right["package"] in left["conflicts"]
        else None
    ),
)

Callable contract

fn(left, right) -> label | labels | None. Every emitted label must be declared.

Rows available to the callable

Each row argument contains the declared primary-key fields and the declared evidence fields available for that input role. If the callable reads a field that is not part of the primary key, declare it as evidence.

Parameter	Default	Meaning
`input_spaces`	required	The Space or Spaces read by the task.
`output_space`	required	The Space that receives the task output.
`name`	required	A stable task name used in sessions, reviews, and metrics.
`primary_key`	id	The field, or tuple of fields, that identifies one task input. Duplicate primary-key values are evaluated once.
`evidence`	none	Optional fields made available to the callable in addition to the primary key.
`fn`	required	A deterministic callable that completely defines the operation's decision. Use an importable named function from your package, or PythonFunction(name=..., source=...) when authoring through the hosted API or node editor. Pairwise endomorphic functions may declare an exact indexed candidate_gate.
`function_parameters`	registered defaults	Typed values bound to parameters declared by the registered function. Finite candidate sets let reviewed evidence support parameter advice.

Parameter	Default	Meaning
`labels`	required	The complete allowed relationship vocabulary.
`closure_rules`	label defaults	Optional valid implications among labels.
`min_labels_per_pair`	0	Require at least this many labels on every admitted pair after closure.
`max_labels_per_pair`	unlimited	Require no pair to carry more than this many labels after closure.

Output

Known labeled relationships among input values.

Design guidance

Cardinality fields validate authoritative function and closure truth. A violation fails the task; Relate never drops true labels or invents absent labels.