We present the first compositional proof system for checking processes against formulas in the modal ¯-calculus which is capable of handling dynamic process networks. The proof system is obtained in a systematic way from the operational semantics of the underlying process algebra. A non-trivial proof example is given, and the proof system is shown to be sound in general, and complete for finite-state processes. 1 Introduction In this paper we address the problem of verifying modal ¯-calculus properties of general infinite-state processes, and we present what we believe to be the first genuinely compositional solution to this problem. The value of compositionality in program logics is well established. Compositionality allows better structuring and decomposition of the verification task, it allows reuse of proofs, and it allows reasoning about partially instantiated programs, thus supporting program synthesis. Even more fundamentally it allows, at least in principle, verification exe...

We consider the problem of proving correctness properties for concurrent systems with features such as higher-order communication and dynamic resource generation. As examples we consider operational models of security and authentication protocols based on the higher-order -calculus. In the setting we propose key features such as nonces/time stamps, encryption /decryption, and key generation can be modelled in a simple and abstract fashion using channel name generation and second-order process communication. A temporal logic is proposed as an appropriate logic to express crucial correctness properties such as secrecy and authenticity. The logic is based on the modal -calculus with only greatest fixed points and universal next-state quantification, extended with first-order features to deal with names, and second-order features including function space constructions to deal with process input and output. A difficulty is that formulas need recursion in both covariant and contravariant po...

. We present a proof system for verifying CCS processes in the modal ¯-calculus. Its novelty lies in the generality of the proof judgements allowing parametric and compositional reasoning in this complex setting. This is achieved, in part, by the use of explicit fixed point ordinal approximations, and in part by a complete separation, following an approach by Simpson, of rules concerning the logic from the rules encoding the operational semantics of the process language. 1 Introduction In a number of recent papers [1--4, 9] proof-theoretical frameworks for compositional verification have been put forward based on Gentzen-style sequents of the shape \Gamma ` \Delta, where the components of \Gamma and \Delta are correctness assertions P : OE. Several programming or modelling languages have been considered, including CCS [3], the ß-calculus [2], CHOCS [1], general GSOS-definable languages [9], and even a significant core fragment of a real programming language, Erlang [4]. An important ...

Context bisimulation [13, 1] has become an important notion of behavioral equivalence for higher-order processes. Weak forms of context bisimulation are particularly interesting, because of their high level of abstraction. We present a modal logic for this setting and provide a characterization of a variant of weak context bisimulation on second-order processes. We show how the logic permits compositional reasoning. In comparison to previous work by Amadio and Dam [2] on the strong case, our modal logic supports derived operators through a complete duality and thus constitutes an appealing extension of Hennessy-Milner logic.

. We present a Gentzen-style sequent calculus for program verification which accomodates both model checking-like verification based on global state space exploration, and compositional reasoning. To handle the complexities arrising from the presence of fixed-point formulas, programs with dynamically evolving architecture, and cut rules we use transition assertions, and introduce fixed-point approximants explicitly into the assertion language. We address, in a game-based manner, the semantical basis of this approach, as it applies to the entailment subproblem. Soundness and completeness results are obtained, and examples are shown illustrating some of the concepts. Keywords: mu-calculus, sequent calculus, program verification, compositionality. 1 Introduction In this paper we study program verification in terms of provability of general sequents of the shape \Gamma ` \Delta; (1) where the components of \Gamma and \Delta can be temporal correctness assertions P : OE. Since program ...

Abstract. In this paper, we present a formal verification framework for higherorder value-passing process algebra. This framework stems from an established synergy between type inference and model-checking. The language considered here is based on a sugared version of an implicitly typed λ-calculus extended with higher-order synchronous concurrency primitives. First, we endow such a syntax with a semantic theory made of a static semantics together with a dynamic semantics. The static semantics consists of an annotated type system. The dynamic semantics is operational and comes as a two-layered labeled transition system. The dynamic semantics is abstracted into a transitional semantics so as to make finite some infinite-state processes. We describe the syntax and the semantics of a verification logic that allows one to specify properties. The logic is an extension of the modal µ-calculus for handling higher-order processes, value-passing and return of results. 1

We present a Gentzen-style sequent calculus for program verification which accomodates both model checking-like verification based on global state space exploration, and compositional reasoning. To handle the complexities arrising from the presence of fixed-point formulas, programs with dynamically evolving architecture, and cut rules we use transition assertions, and introduce fixed-point approximants explicitly into the assertion language. We address, in a game-based manner, the semantical basis of this approach, as it applies to the entailment subproblem. Soundness and completeness results are obtained, and examples are shown illustrating some of the concepts.

Abstract. Higher-order process calculi have been receiving much attention in recent years for its significance in both theorey and practice. Work on bisimulations has never ceased evolving, typically represented by Thomsen and Sangiorgi for their work on bisimulation theory and encoding to and from first-order process calculi. Fu puts forth linear higher-order π-calculus, and makes improvement to previous work on bisimulation and builds a sound and complete equation system by exploitng linearity of processes, which takes resource sensitiveness into account. In this paper, we establish some recent result on bisimulation theory in linear higher-order π-calculus. By exploiting the properties of linear high-order processes, we work out two simpler variants than local bisimulation, which is an intuitive observational equivalence, and they both coincide with local bisimilarity. The first variant, called local linear bisimulation, simplifies the matching of higher-order input and higher-order output based on the feature of checking equivalence with some special processes (in input or output) instead of general ones. The second variant, called local linear variant bisimulation, rewrites the first-order bound output clause in local bisimulation in some more suitable form for some application on it, by harnessing the congruence properties. We also mention some future work in the conclusion. Key words: Bisimulation, Linear, Higher-order, π-Calculus, Process calculi 1

Interpretation [25], Modalities in Analysis and Verification [30], and Enhanced Operational Semantics [35]. Each section below begins with a presentation of our view of the state-of-the-art within the area, and ends with a brief explanation of how the papers in these proceedings enhance our knowledge of the area. Integration of Programming Paradigms Programming notions can be expressed in many di erent paradigms - imperative, object-oriented, concurrent, functional, logic-programming, constraint, etc. It is widely agreed that each programming paradigm has its own merits and is particularly appropriate for expressing certain classes of computation, thus the choice of paradigm can greatly affect the ease of programming. Traditionally, when constructing large scale systems, in particular distributed systems, it is often necessary to use multiple programming styles with disparate programming models, and very often it is necessary to resolve conflicts by low level methods reverting to the lowest...

Higher-order process calculi, for its abstraction capability and theoretical significance, have constantly been receiving much attention in the field of process calculi, and stand as a mathematical tool for describing and analyzing mobile systems with dynamically changing inter-connection structures. In this thesis we contribute to the higher-order paradigm in several aspects. • Higher-order π-calculus with mismatch: the bisimulation theory. Linear fragment of higherorder π-calculus with mismatch: the axiomatization. The problem of the axiomatization of higher-order process calculi, such as higher-order πcalculus, is always a non-trivial one. However, it is important, both in theory and practice, to be able to decide whether two higher-order processes are equivalent with respect to some bisimulation, which needs an algorithm that can effectively analyze and give an answer efficiently. We further the available work by considering the higher-order π-calculus with mismatch, which is a useful operator in bisimulation theory and especially the axiomatization, from algorithmic point of view. We first formulate the bisimulation theory, where the bisimulation we define is called open weak higher-order bisimulation, which is a non-delayed