Results 1  10
of
15
Towards a Mathematical Operational Semantics
 In Proc. 12 th LICS Conf
, 1997
"... We present a categorical theory of `wellbehaved' operational semantics which aims at complementing the established theory of domains and denotational semantics to form a coherent whole. It is shown that, if the operational rules of a programming language can be modelled as a natural transformation ..."
Abstract

Cited by 134 (9 self)
 Add to MetaCart
We present a categorical theory of `wellbehaved' operational semantics which aims at complementing the established theory of domains and denotational semantics to form a coherent whole. It is shown that, if the operational rules of a programming language can be modelled as a natural transformation of a suitable general form, depending on functorial notions of syntax and behaviour, then one gets both an operational model and a canonical, internally fully abstract denotational model for free; moreover, both models satisfy the operational rules. The theory is based on distributive laws and bialgebras; it specialises to the known classes of wellbehaved rules for structural operational semantics, such as GSOS.
Induction and coinduction in sequent calculus
 Postproceedings of TYPES 2003, number 3085 in LNCS
, 2003
"... Abstract. Proof search has been used to specify a wide range of computation systems. In order to build a framework for reasoning about such specifications, we make use of a sequent calculus involving induction and coinduction. These proof principles are based on a proof theoretic (rather than sett ..."
Abstract

Cited by 23 (8 self)
 Add to MetaCart
Abstract. Proof search has been used to specify a wide range of computation systems. In order to build a framework for reasoning about such specifications, we make use of a sequent calculus involving induction and coinduction. These proof principles are based on a proof theoretic (rather than settheoretic) notion of definition [13, 20, 25, 51]. Definitions are akin to (stratified) logic programs, where the left and right rules for defined atoms allow one to view theories as “closed ” or defining fixed points. The use of definitions makes it possible to reason intensionally about syntax, in particular enforcing free equality via unification. We add in a consistent way rules for pre and post fixed points, thus allowing the user to reason inductively and coinductively about properties of computational system making full use of higherorder abstract syntax. Consistency is guaranteed via cutelimination, where we give the first, to our knowledge, cutelimination procedure in the presence of general inductive and coinductive definitions. 1
Toward Parametric Verification of Open Distributed Systems
 IN COMPOSITIONALITY: THE SIGNIFICANT DIFFERENCE
, 1998
"... A logic and proof system is introduced for specifying and proving properties of open distributed systems. Key problems that are addressed include the verification of process networks with a changing interconnection structure, and where new processes can be continuously spawned. To demonstrate th ..."
Abstract

Cited by 19 (7 self)
 Add to MetaCart
A logic and proof system is introduced for specifying and proving properties of open distributed systems. Key problems that are addressed include the verification of process networks with a changing interconnection structure, and where new processes can be continuously spawned. To demonstrate the results in a realistic setting we consider a core fragment of the Erlang programming language. Roughly this amounts to a firstorder actor language with data types, buffered asynchronous communication, and dynamic process spawning. Our aim is to verify quite general properties of programs in this fragment. The specification logic extends the firstorder µcalculus with Erlangspecific primitives. For verification we use an approach which combines local model checking with facilities for compositional verification. We give a specification and verification example based on a billing agent which controls and charges for user access to a given resource.
Compositional Proof Systems for Model Checking Infinite State Processes
, 1995
"... . We present the first compositional proof system for checking processes against formulas in the modal ¯calculus which is capable of handling general infinitestate processes. The proof system is obtained in a systematic way from the operational semantics of the underlying process algebra. A nontr ..."
Abstract

Cited by 15 (3 self)
 Add to MetaCart
. We present the first compositional proof system for checking processes against formulas in the modal ¯calculus which is capable of handling general infinitestate processes. The proof system is obtained in a systematic way from the operational semantics of the underlying process algebra. A nontrivial proof example is given, and the proof system is shown to be sound in general, and complete for finitestate processes. 1 Introduction In this paper we address the problem of verifying modal ¯calculus properties of general infinitestate 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 proof reuse, and it allows reasoning about partially instantiated programs, thus supporting program synthesis. Even more fundamentally it allows, at least in principle, verification...
Proof Systems for piCalculus Logics
, 2001
"... In this paper we study the problem of verifying general temporal and functional properties of mobile and dynamic process networks, cast in terms of the picalculus. Much of the expressive power of this calculus derives from the combination of name generation and communication (to handle mobility ..."
Abstract

Cited by 11 (0 self)
 Add to MetaCart
In this paper we study the problem of verifying general temporal and functional properties of mobile and dynamic process networks, cast in terms of the picalculus. Much of the expressive power of this calculus derives from the combination of name generation and communication (to handle mobility) with dynamic process creation. In the paper we introduce the calculus, an extension of the modal mucalculus with name equality, inequality, firstorder universal and existential quantification, and primitives for name input and output as an appropriate temporal logic for the picalculus. A compositional proof system is given with the scope of verifying dynamic networks of picalculus agents against properties specified in this logic. The proof system consists of a local part based, roughly, on the classical sequent calculus extended with data structures for private names, and rules to support process structure dependent reasoning. In addition the proof system contains a rule of...
Sequent Calculi for Process Verification: HennessyMilner Logic for an Arbitrary GSOS
, 2003
"... We argue that, by supporting a mixture of “compositional” and “structural” styles of proof, sequentbased proof systems provide a useful framework for the formal verification of processes. As a worked example, we present a sequent calculus for establishing that processes from a process algebra satis ..."
Abstract

Cited by 11 (1 self)
 Add to MetaCart
We argue that, by supporting a mixture of “compositional” and “structural” styles of proof, sequentbased proof systems provide a useful framework for the formal verification of processes. As a worked example, we present a sequent calculus for establishing that processes from a process algebra satisfy assertions in HennessyMilner logic. The main novelty lies in the use of the operational semantics to derive introduction rules, on the left and right of sequents, for the operators of the process calculus. This gives a generic proof system applicable to any process algebra with an operational semantics specified in the GSOS format. Using a general algebraic notion of GSOS model, we prove a completeness theorem for the cutfree fragment of the proof system, thereby establishing the admissibility of the cut rule. Under mild (and necessary) conditions on the process algebra, an ωcompleteness result, relative to the “intended” model of closed process terms, follows.
Compositional Verification of CCS Processes
, 1999
"... . 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, a ..."
Abstract

Cited by 8 (4 self)
 Add to MetaCart
. 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 [14, 9] prooftheoretical frameworks for compositional verification have been put forward based on Gentzenstyle 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 ßcalculus [2], CHOCS [1], general GSOSdefinable languages [9], and even a significant core fragment of a real programming language, Erlang [4]. An important ...
On the Verification of Open Distributed Systems
, 1998
"... A logic and proof system is introduced for specifying and proving properties of open distributed systems. Key problems that are addressed include the verification of process networks with a changing interconnection structure, and where new processes can be continuously spawned. To demonstrate the re ..."
Abstract

Cited by 6 (0 self)
 Add to MetaCart
A logic and proof system is introduced for specifying and proving properties of open distributed systems. Key problems that are addressed include the verification of process networks with a changing interconnection structure, and where new processes can be continuously spawned. To demonstrate the results in a realistic setting we consider a core fragment of the Erlang programming language. Roughly this amounts to a firstorder actor language with data types, buffered asynchronous communication, and dynamic process spawning. Our aim is to verify quite general properties of programs in this fragment. The specification logic extends the firstorder ¯calculus with Erlangspecific primitives. For verification we use an approach which combines local model checking with facilities for compositional verification. We give a specification and verification example based on a billing agent which controls and charges for user access to a given resource. 1 Introduction A central feature of open di...
μCalculus with Explicit Points and Approximations
 Journal of Logic and Computation
, 1999
"... . We present a Gentzenstyle sequent calculus for program verification which accomodates both model checkinglike verification based on global state space exploration, and compositional reasoning. To handle the complexities arrising from the presence of fixedpoint formulas, programs with dynamicall ..."
Abstract

Cited by 3 (0 self)
 Add to MetaCart
. We present a Gentzenstyle sequent calculus for program verification which accomodates both model checkinglike verification based on global state space exploration, and compositional reasoning. To handle the complexities arrising from the presence of fixedpoint formulas, programs with dynamically evolving architecture, and cut rules we use transition assertions, and introduce fixedpoint approximants explicitly into the assertion language. We address, in a gamebased 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: mucalculus, 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 ...
µCalculus with Explicit Points and Approximations
, 2000
"... We present a Gentzenstyle sequent calculus for program verification which accomodates both model checkinglike verification based on global state space exploration, and compositional reasoning. To handle the complexities arrising from the presence of fixedpoint formulas, programs with dynamically ..."
Abstract

Cited by 3 (1 self)
 Add to MetaCart
We present a Gentzenstyle sequent calculus for program verification which accomodates both model checkinglike verification based on global state space exploration, and compositional reasoning. To handle the complexities arrising from the presence of fixedpoint formulas, programs with dynamically evolving architecture, and cut rules we use transition assertions, and introduce fixedpoint approximants explicitly into the assertion language. We address, in a gamebased 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.