Reachability types: tracking aliasing and separation in higher-order functional programs

Abstract

Ownership type systems, based on the idea of enforcing unique access paths, have been primarily focused on objects and top-level classes. However, existing models do not as readily reflect the finer aspects of nested lexical scopes, capturing, or escaping closures in higher-order functional programming patterns, which are increasingly adopted even in mainstream object-oriented languages. We present a new type system, λ * , which enables expressive ownership-style reasoning across higher-order functions. It tracks sharing and separation through reachability sets, and layers additional mechanisms for selectively enforcing uniqueness on top of it. Based on reachability sets, we extend the type system with an expressive flow-sensitive effect system, which enables flavors of move semantics and ownership transfer. In addition, we present several case studies and extensions, including applications to capabilities for algebraic effects, one-shot continuations, and safe parallelization.

Scoped Capabilities for Polymorphic Effects

“…Recently, Bao et al [2021] have proposed to qualify types with reachability sets. Their reachability types allow reasoning about non-interference, scoping and uniqueness by tracking for each reference what other references it may alias or (indirectly) point to.…”

“…Technically, this means that references (but not general terms) can form part of types as members of capture sets. A similar approach is taken in the path-dependent typing discipline of DOT and by reachability types for alias checking [Bao et al 2021]. • Employ a subtyping discipline that mirrors subsetting of capabilities and that allows capabilities to be refined or abstracted.…”