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.

Universe Types for Topology and Encapsulation

Correct mutual-exclusion is one of the key challenges in concurrent programming. Although the fine-grained locking schema can be more efficient compared with the coarse-grained techniques, it is tough to use, as well as error-prone. Here we present a static approach, based on program analysis, to automatically add fine-grained locking primitives to data structures implemented as classes. For tree-like structures, the modified class definitions are guaranteed to be thread-safe. Experiments show that the approach can successfully deal with programs which are challenging to be handled manually, and it works efficiently.

Automatic fine-grained locking generation for shared data structures

Object invariants describe the consistency of object-oriented data structures and are central to reasoning about the correctness of object-oriented software. Yet, reasoning about object invariants in the presence of object references, methods, and subclassing is difficult. This paper describes a methodology for specifying and verifying object-oriented programs, using object invariants to specify the consistency of data and using ownership to organize objects into contexts. The novelty is that contexts can be dynamic: there is no bound on the number of objects in a context and objects can be transferred between contexts. The invariant of an object is allowed to depend on the fields of the object, on the fields of all objects in transitively-owned contexts, and on fields of objects reachable via given sequences of fields. With these invariants, one can describe a large variety of properties, including properties of cyclic data structures. Object invariants can be declared in or near the classes whose fields they depend on, not necessarily in the class of an owning object. The methodology is designed to allow modular reasoning, even in the presence of subclasses, and is proved sound.

Object invariants in dynamic contexts

Object ownership is an important technique in dealing with object sharing and aliasing to support verification of OO programs. Dynamic Ownership proposes a very flexible encapsulation discipline and has been adopted in Spec#. However, to use this technique, programmers have to keep all the ownership information in mind to decide the validation for modifying one variable. This makes the approach difficult to master and use. In this paper, we apply data-flow analysis to generate most annotations of dynamic ownership automatically, thus can potentially reduce the workload of program verification. Moreover, our technique can reveal ownership topology errors and encapsulation errors. In addition, the entire analysis of our approach is static, thus is efficient.

Automatic Annotating and Checking of Dynamic Ownership

Algebraic specification is well-known in specifyingabstract data types. It could also play an important role inverifying the interrelation between methods in classes. In thispaper we develop a framework for verifying the conformanceof method implementations against an algebraic specification. Different from most existing work that perform testing atthe code level for the conformance, our approach verifies theconformance without touching the implementation details. Asanother contribution, we show that if all the inherited methods ofa subclass satisfy behavioral subtyping, then the subclass conformsto the algebraic specification of its superclass, i.e., there is no needto re-verify.

Verifying Interaction between Methods in Classes

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Automatic Annotating and Checking of Dynamic Ownership

Verifying Interaction between Methods in Classes

Automatic fine-grained locking generation for shared data structures