Classifying Capabilities (Extended Version)

Abstract

Capture checking in Scala 3 enables lightweight and practical effect and resource tracking by recording capabilities in types. However, the system offers no way to reason about kinds of capabilities. Natural constraints such as "retaining only the control-flow capabilities of this closure" or "excluding all thread-local capabilities from this argument" become inexpressible. Both arise in the Scala 3 standard library: "Try" re-throws caught exceptions, so it retains only the control-flow capabilities of its body, and "Future" must not capture thread-local resources. The inability to state these constraints has kept parts of the library outside capture checking. We introduce capability classifiers: a tree-structured, user-extensible hierarchy of tags that classify capabilities by their semantic role. Projections filter capture sets by classifier, supporting both inclusion ("c.only[C]") and exclusion ("c.except[C]"). The tree structure enables decidable disjointness reasoning: classifiers on separate branches are guaranteed to be disjoint regardless of unknown extensions elsewhere in the hierarchy. We formalize classifiers as an extension of System Capless, a core calculus for capture checking, introducing a classifier kind algebra based on intersection, union, and subtraction of classifier subtrees. We extend the operational semantics to model exception interception and establish type safety, effect safety, and handler coverage via a big-step proof, fully mechanized in Lean 4. Classifiers are implemented in the Scala 3 capture checker, and we demonstrate their use on standard library types and real-world effect exclusion patterns.