In this paper we address the problem of writing specifications for programs that use various forms of modularity, including procedures and Java-like classes. We build on the formalism of separation logic and introduce the new notion of an abstract predicate and, more generally, abstract predicate families. This provides a flexible mechanism for reasoning about the different forms of abstraction found in modern programming languages, such as abstract datatypes and objects. As well as demonstrating the soundness of our proof system, we illustrate its utility with a series of examples.

This paper formalises a semantics for statements and expressions (in sequential imperative languages) which includes non-termination, normal termination and abrupt termination (e.g. because of an exception, break, return or continue). This extends the traditional semantics underlying e.g. Hoare logic, which only distinguishes termination and non-termination. An extension of Hoare logic is elaborated that includes means for reasoning about abrupt termination (and side-effects). It prominently involves rules for reasoning about while loops, which may contain exceptions, breaks, continues and returns. This extension applies in particular to Java. As an example, a standard pattern search algorithm in Java (involving a while loop with returns) is proven correct using the proof-tool PVS.

The state of knowledge in how to specify sequential programs in object-oriented languages such as Java and C# and the state of the art in automated verification tools for such programs have made measurable progress in the last several years. This paper describes several remaining challenges and approaches to their solution.

Abstract. This paper outlines a sound and complete Hoare logic for a sequential object-oriented language with inheritance and subtyping like Java. It describes a weakest precondition calculus for assignments and object-creation, as well as Hoare rules for reasoning about (mutually recursive) method invocations with dynamic binding. Our approach enables reasoning at an abstraction level that coincides with the general abstraction level of object-oriented languages. 1

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Object invariants describe the consistency of object-oriented data structures and are central to reasoning about the correctness of object-oriented software. But object invariants are not the only consistency conditions on which a program may depend. The data in object-oriented programs consists not just of object fields, but also of static fields, which hold data that is shared among objects. The consistency of static fields is described by static class invariants, which are enforced at the class level. Static class invariants can also mention instance fields, describing the consistency of dynamic data structures rooted in static fields. Sometimes there are even consistency conditions that relate the instance fields of many or all objects of a class; static class invariants describe these relations, too, since they cannot be enforced by any one object in isolation. This paper presents a systematic way (a methodology) for specifying and verifying static class invariants in object-oriented programs. The methodology supports the three major uses of static fields and invariants in the Java library. The methodology is amenable to static, modular verification and is sound.

Abstract. We define a compositional program logic in the style of Floyd and Hoare for a simple, typed, stack-based abstract machine with unstructured control flow, global variables and mutually recursive procedure calls. Notable features of the logic include a careful treatment of auxiliary variables and quantification and the use of substructural typing to permit local, modular reasoning about program fragments. Semantic soundness is established using an interpretation of types and assertions defined by orthogonality with respect to sets of contexts. 1

Abstract. We define NanoJava, a kernel of Java tailored to the investigation of Hoare logics. We then introduce a Hoare logic for this language featuring an elegant approach for expressing auxiliary variables: by universal quantification on the outer logical level. Furthermore, we give simple means of handling side-effecting expressions and dynamic binding within method calls. The logic is proved sound and (relatively) complete using Isabelle/HOL. Keywords: Hoare logic, Java, Isabelle/HOL, auxiliary variables, side effects, dynamic binding.

This paper presents a case study in formal specification and verification of a smart card application. The application is an electronic purse implementation, developed by the smart card producer Gemplus as a test case for formal methods for smart cards. It has been annotated (by the authors) with specifications using the Java Modeling Language (JML), a language designed to specify the functional behavior of Java classes. The reason for using JML as a specification language is that several tools are available to check (parts of) the specification w.r.t. an implementation. These tools vary in their level of automation and in the level of correctness they ensure. Several of these tools have been used for the Gemplus case study. We discuss how the usage of these di#erent tools is complementary: large parts of the specification can be checked automatically, while more precise verification methods can be used for the more intricate parts of the specification and implementation. We believe that having such a range of tools available for a single specification language is an important step towards acceptance of formal methods in industry.