Universe Types for Topology and Encapsulation

Abstract

Abstract. The Universe Type System is an ownership type system for object-oriented programming languages that hierarchically structures the object store; it is used to reason modularly about programs. We formalise Universe Types for a core subset of Java in two steps: We first define a Topological Type System that structures the object store hierarchically into an ownership tree, and demonstrate soundness of the Topological Type System by proving subject reduction. Motivated by concerns of modular verification, we then present an Encapsulation Type System that enforces the owner-as-modifier discipline; that is, that object updates are initiated by the owner of the object. The contributions of this paper are, firstly, an extensive type-theoretic account of the Universe Type System, with explanations and complete proofs, and secondly, the clean separation of the topological from the encapsulation concerns.

Inference and Checking of Object Ownership

“…We now instantiate the framework for two well-known ownership type systems, Universe Types (UT) [8,5] and Ownership Types (OT) [4]. The framework can also be instantiated for a variety of other ownership-like type systems, including EnerJ [23], a type system for energy efficiency, and AJ [27], a type system for data-centric synchronization.…”

“…Universe Types (UT) [8,5] is a lightweight ownership type system that optionally enforces the owner-as-modifier encapsulation discipline. Informally, this means Γ (x) = qx q <: qx B (tnew) (qx, q)…”

“…Qualifier lost is used only internally and users cannot annotate references as lost. In contrast to previous work [5], we type the current object this as peer and use separate rules for accesses through this, instead of adding a self qualifier. The qualifiers form the following subtyping hierarchy:…”

A Calculus for Boxes and Traits in a Java-Like Setting

“…Several different variants of ownership types exist, with varying expressiveness and flexibility. The original ownership type system by Clarke et al [8] and similar systems [6,9] enforces a so-called owners-as-dominators property, which states that all accesses from external objects to owned objects must go through the owner object. This property does not allow for multiple objects at the boundary of a component.…”

“…To guarantee encapsulation of certain objects of a box an ownership type system [8,6,15,9] is used. It defines two ownership domains [1,24,19] for each box, namely a local and a boundary domain.…”