Effects, capabilities, and boxes: from scope-based reasoning to type-based reasoning and back

Abstract

Reasoning about the use of external resources is an important aspect of many practical applications. Effect systems enable tracking such information in types, but at the cost of complicating signatures of common functions. Capabilities coupled with escape analysis offer safety and natural signatures, but are often overly coarse grained and restrictive. We present System C, which builds on and generalizes ideas from type-based escape analysis and demonstrates that capabilities and effects can be reconciled harmoniously. By assuming that all functions are second class, we can admit natural signatures for many common programs. By introducing a notion of boxed values, we can lift the restrictions of second-class values at the cost of needing to track degree-of-impurity information in types. The system we present is expressive enough to support effect handlers in full capacity. We practically evaluate System C in an implementation and prove its soundness.

Scoped Capabilities for Polymorphic Effects

“…They present an extension of the simply typed lambda calculus that enhances function types [Γ 0 ] ( ) → with the lexical environment Γ 0 that was originally used to type the closure. Brachthäuser et al [2022] show System C, which mediates between first-and second-class values with boxes. In their system, scoped capabilities are second-class values.…”

“…This gives rise to a convenient and light-weight form of contextual effect polymorphism [Brachthäuser et al 2020a]. While this approach allows for effect polymorphism with a simple type system, it is also restrictive because it also forbids local returns and retentions of capabilities; a problem solved by adding boxing and unboxing [Brachthäuser et al 2022].…”

“…• Use reference-dependent typing, where a formal function parameter stands for the potential references captured by its argument [Brachthäuser et al 2022;Odersky et al 2021]. This avoids the need to introduce separate binders for capabilities or effects.…”

“…• Limit propagation of capabilities in instances of generic types where they cannot be accessed directly. This is achieved by boxing types when they enter a generic context and unboxing on every use site [Brachthäuser et al 2022].…”