We present the first verification of full functional correctness for a range of linked data structure implementations, including mutable lists, trees, graphs, and hash tables. Specifically, we present the use of the Jahob verification system to verify formal specifications, written in classical higher-order logic, that completely capture the desired behavior of the Java data structure implementations (with the exception of properties involving execution time and/or memory consumption). Given that the desired correctness properties include intractable constructs such as quantifiers, transitive closure, and lambda abstraction, it is a challenge to successfully prove the generated verification conditions. Our Jahob verification system uses integrated reasoning to split each verification condition into a conjunction of simpler subformulas, then apply a diverse collection of specialized decision procedures,

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.

This dissertation describes an approach for automatically verifying data structures, focusing on techniques for automatically proving formulas that arise in such verification. I have implemented this approach with my colleagues in a verification system called Jahob. Jahob verifies properties of Java programs with dynamically allocated data structures. Developers write Jahob specifications in classical higher-order logic (HOL); Jahob reduces the verification problem to deciding the validity of HOL formulas. I present a new method for proving HOL formulas by combining automated reasoning techniques. My method consists of 1) splitting formulas into individual HOL conjuncts, 2) soundly approximating each HOL conjunct with a formula in a more tractable fragment and 3) proving the resulting approximation using a decision procedure or a theorem prover. I present three concrete logics; for each logic I show how to use it to approximate HOL formulas, and how to decide the validity of formulas in this logic. First, I present an approximation of HOL based on a translation to first-order logic, which enables the use of existing resolution-based theorem provers. Second, I present an approximation of HOL based on field constraint analysis, a new technique that enables

chinwn,davidcri,nguyenh2© Conventional specifications for object-oriented (OO) programs must adhere to behavioral subtyping in support of class inheritance and method overriding. However, this requirement inherently weakens the specifications of overridden methods in superclasses, leading to imprecision during program reasoning. To address this, we advocate a fresh approach to OO verification that focuses on the distinction and relation between specifications that cater to calls with static dispatching from those for calls with dynamic dispatching. We formulate a novel specification subsumption that can avoid code re-verification, where possible. Using a predicate mechanism, we propose a flexible scheme for supporting class invariant and lossless casting. Our aim is to lay the foundation for a practical verification system that is precise, concise and modular for sequential OO programs. We exploit the separation logic formalism to achieve this.

We describe a technique that enables the focused application of multiple analyses to different modules in the same program. In our approach, each module encapsulates one or more data structures and uses membership in abstract sets to characterize how objects participate in data structures. Each analysis verifies that the implementation of the module 1) preserves important internal data structure consistency properties and 2) correctly implements an interface that uses formulas in a set algebra to characterize the effects of operations on the encapsulated data structures. Collectively, the analyses use the set algebra to 1) characterize how objects participate in multiple data structures and to 2) enable the inter-analysis communication required to verify properties that depend on multiple modules analyzed by different analyses.

... In this paper, we illustrate the subtle problems any encoding of method calls in specifications has to address. We present a sound encoding that allows side-effect free methods to create and initialize objects by explicitly modeling such modifications of the heap.

Abstract. Non-interference is a semantical condition on programs that guarantees the absence of illicit information flow throughout their execution, and that can be enforced by appropriate information flow type systems. Much of previous work on type systems for non-interference has focused on calculi or high-level programming languages, and existing type systems for low-level languages typically omit objects, exceptions, and method calls, and/or do not prove formally the soundness of the type system. We define an information flow type system for a sequential JVM-like language that includes classes, objects, arrays, exceptions and method calls, and prove that it guarantees non-interference. For increased confidence, we have formalized the proof in the proof assistant Coq; an additional benefit of the formalization is that we have extracted from our proof a certified lightweight bytecode verifier for information flow. Our work provides, to our best knowledge, the first sound and implemented information flow type system for such an expressive fragment of the JVM. 1

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.

Abstract. The Java Modeling Language, JML, is an interface specification language that uses side-effect free Java expressions to describe program behavior. In particular, JML specifications can contain calls to side-effect free methods. To verify programs w.r.t. JML specifications, JML expressions have to be encoded in a program logic. This encoding is non-trivial for method calls. In this paper, we illustrate several subtle problems any program verifier for JML has to address. We present an encoding of method calls that handles abrupt termination, allows methods to create and initialize objects, and is sound, even if the JML specification is not satisfiable. 1

We present how common JAVA CARD security properties can be formalised in Dynamic Logic and verified, mostly automatically, with the KeY system. The properties we consider, are a large subset of properties that are of importance to the smart card industry. We discuss the properties one by one, illustrate them with examples of real-life, industrial size, JAVA CARD applications, and show how the properties are verified with the KeY Prover – an interactive theorem prover for JAVA CARD source code based on a version of Dynamic Logic that models the full JAVA CARD standard. We report on the experience related to formal verification of JAVA CARD programs we gained during the course of this work. Thereafter, we present the current state of the art of formal verification techniques offered by the KeY system and give an assessment of interactive theorem proving as an alternative to static analysis.