Struct-as-Set @type: Multi-Context Resource Identity in CUE

Use Case Submission for the Context Graphs Community Group

Summary

apercue.ca represents resource types as CUE structs ({TypeA: true, TypeB: true}) rather than arrays or class hierarchies. This "struct-as-set" pattern gives every resource simultaneous membership in multiple contexts — data governance, provenance, scheduling, semantic web — resolved through set intersection at evaluation time.

This submission demonstrates how CUE's type system naturally models the multi-context identity that the Context Graphs CG investigates.

The Pattern: @type as a Set

Each resource declares its types as a struct with boolean values:

"sensor-dataset": {
    name:       "sensor-dataset"
    "@type":    {Dataset: true, Schedulable: true, Governed: true}
    depends_on: {"ethics-approval": true}
}

This resource exists simultaneously in three contexts: - Dataset context: subject to provenance tracking - Schedulable context: subject to critical path analysis - Governed context: subject to embargo and access policies

No context is primary. No context is added after the fact. The resource IS all of these simultaneously, and CUE unification guarantees consistency across all contexts.

How Context Resolution Works

Set Intersection as Dispatch

Providers (tools, validators, policies) declare which types they serve:

for tname, _ in provider.types
if resource["@type"][tname] != _|_ {tname}

A resource with {Dataset: true, Governed: true} matches a data repository (serves Dataset) AND an ethics board (serves Governed) simultaneously. The binding is set intersection, not registration.

Unification Guarantees Consistency

If two contexts place conflicting constraints on the same resource, CUE unification produces bottom (_|_). The graph cannot be constructed. This is not a runtime error — it is a type error caught before any output is generated.

Evidence: Multiple Projections From One Graph

The same 5-node research publication graph (defined once) produces output in 17 different W3C specifications. Each projection selects a different context:

Scheduling context (OWL-Time):

{
    "@type": "time:Interval",
    "@id": "urn:resource:analysis-code",
    "dcterms:title": "analysis-code",
    "time:hasBeginning": {
        "@type": "time:Instant",
        "time:inXSDDecimal": 150
    },
    "time:hasEnd": {
        "@type": "time:Instant",
        "time:inXSDDecimal": 195
    },
    "time:hasDuration": {
        "@type": "time:Duration",
        "time:numericDuration": 45,
        "time:unitType": {
            "@id": "time:unitDay"
        }
    },
    "apercue:slack": 0,
    "apercue:isCritical": true
}

Compliance context (SHACL):

{
    "@type": "sh:ValidationReport",
    "sh:conforms": true,
    "sh:result": []
}

Provenance context (PROV-O):

{
    "@type": "prov:Entity",
    "@id": "urn:resource:analysis-code",
    "dcterms:title": "analysis-code",
    "prov:wasAttributedTo": {
        "@id": "apercue:graph-engine"
    },
    "prov:wasDerivedFrom": [
        {
            "@id": "urn:resource:sensor-dataset"
        }
    ],
    "prov:wasGeneratedBy": {
        "@id": "apercue:graph-construction"
    }
}

Access control context (ODRL):

{
    "@type": "odrl:Set",
    "odrl:uid": "apercue:graph-policy",
    "odrl:permission": [
        {
            "odrl:action": {
                "@id": "odrl:read"
            }
        },
        {
            "odrl:action": {
                "@id": "odrl:execute"
            },
            "odrl:assignee": {
                "@id": "apercue:operator"
            }
        }
    ],
    "odrl:prohibition": []
}

Each projection is a cue export -e <expression> invocation. The resource identity is stable across all contexts because the graph is the single source of truth.

Relevance to Context Graphs

CUE's lattice semantics mean that context composition is not a graph operation — it is type unification. Adding a context to a resource is adding a key to a struct. Merging contexts is struct unification. Testing context membership is field presence.

Multi-Domain Evidence

This pattern has been validated across four domains:

The same #Graph pattern, the same set intersection dispatch. The contexts are domain-specific; the mechanism is universal.

Limitations

• Closed-world: contexts must be declared, not discovered
• Flat namespace: no hierarchical context inheritance (by design — keeps dispatch simple)
• Boolean membership only: no weighted or probabilistic context participation

References

• Core report — Full implementation evidence
• github.com/quicue/apercue — Source (Apache 2.0)