We investigate proof rules for information hiding, using the recent formalism of separation logic. In essence, we use the separating conjunction to partition the internal resources of a module from those accessed by the module's clients. The use of a logical connective gives rise to a form of dynamic partitioning, where we track the transfer of ownership of portions of heap storage between program components. It also enables us to enforce separation in the presence of mutable data structures with embedded addresses that may be aliased.

Reynolds has developed a logic for reasoning about mutable data structures in which the pre- and postconditions are written in an intuitionistic logic enriched with a spatial form of conjunction. We investigate the approach from the point of view of the logic BI of bunched implications of O'Hearn and Pym. We begin by giving a model in which the law of the excluded middle holds, thus showing that the approach is compatible with classical logic. The relationship between the intuitionistic and classical versions of the system is established by a translation, analogous to a translation from intuitionistic logic into the modal logic S4. We also consider the question of completeness of the axioms. BI's spatial implication is used to express weakest preconditions for object-component assignments, and an axiom for allocating a cons cell is shown to be complete under an interpretation of triples that allows a command to be applied to states with dangling pointers. We make this latter a feature, by incorporating an operation, and axiom, for disposing of memory. Finally, we describe a local character enjoyed by specifications in the logic, and show how this enables a class of frame axioms, which say what parts of the heap don't change, to be inferred automatically.

Ownership types provide a statically enforceable notion of object-level encapsulation. We extend ownership types with computational e#ects to support reasoning about objectoriented programs. The ensuing system provides both access control and e#ects reporting. Based on this type system, we codify two formal systems for reasoning about aliasing and the disjointness of computational e#ects. The first can be used to prove that evaluation of two expressions will never lead to aliases, while the latter can be used to show the non-interference of two expressions.

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.

This paper describes a specialised logic for proving specifications in the Java Modeling Language (JML). JML is an interface specification language for Java. It allows assertions like invariants, constraints, pre- and post-conditions, and modi able clauses as annotations to Java classes, in a design-by-contract style. Within the LOOP project at the University of Nijmegen JML is used for specification and verification of Java programs. A special compiler has been developed which translates Java classes together with their JML annotations into logical theories for a theorem prover (PVS or Isabelle). The logic for JML that will be described here consists of tailor-made proof rules in the higher order logic of the back-end theorem prover for verifying translated JML specifications. The rules efficiently combine partial and total correctness (like in Hoare logic) for all possible termination modes in Java, in a single correctness formula.

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

One of the reasons for the popularity of object-oriented programming is the possibility it offers for reuse of code. Usually, the distribution of an object-oriented programming language comes together with a collection of ready-to-use classes, in a class library. Typically, these classes contain general purpose code, which can be used in many applications. Before using such classes, a programmer usually wants to know how they behave and when their methods throw exceptions. One way to do this, is to study the actual code, but since this is time-consuming and requires understanding all particular ins and outs of the implementation, this is often not the most efficient way. Another approach is to study the documentation provided. As long as the documentation is clear and concise, this works well, but otherwise one still is forced to look at the actual code.

Abstract. It is generally thought that reasoning about programs in memory safe, garbage collected languages is much easier than in languages where the programmer has more explicit control over memory. Paradoxically, existing program logics are based on a low level view of storage that is sensitive to the presence or absence of unreachable cells, and Reynolds has pointed out that the Hoare triples derivable in these logics are even incompatible with garbage collection. We present a study of a small language whose operational semantics includes a rule for reclaiming garbage. Our main results include an analysis of propositions that are garbage insensitive, and full abstraction results connecting partial and total correctness to two natural notions of observational equivalence between programs. 1 Introduction Garbage collection is an essential method used to reclaim heap-allocated objects whose lifetime cannot be easily predicted at compile time. It is most strongly associated with high-level languages such as Lisp, ML and Java, where heap allocation is the norm. It can also be used in a lower level language like C, coexisting with explicit deallocation primitives [10]. In any case, garbage collection relieves the programmer of the burden of explicitly managing dynamically allocated memory. This generally leads to simpler programs, and removes or lessens errors that result from incorrect attempts to access disposed memory, errors that are often difficult to diagnose or even reproduce.

We present a program logic for reasoning about resource consumption of programs written in Grail, an abstract fragment of the Java Virtual Machine Language. Serving as the target logic of a certifying compiler, the logic exploits Grail's dual nature of combining a functional interpretation with object-oriented features and a cost model for the JVM. We present the resource-aware operational semantics of Grail, the program logic, and prove soundness and completeness. All of the work described has been formalised in the theorem prover Isabelle/HOL, which provides us with an implementation of the logic as well as confidence in the results. We conclude with examples of using the logic for proving resource bounds on code resulting from compiling high-level functional programs.