A.K. Simpson. Compositionality via cutelimination: Hennessy-Milner logic for an arbitrary GSOS. In Proc. Tenth IEEE Symp. on Logic In Computer Science, 1995.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....requirements. A desirable feature of such proof systems is that they should allow for a compositional style of proof development. Informally, a proof system is compositional if it builds a proof for a property of an LTS out of proofs for properties of certain sub LTSs. The work presented in [203] is based upon the realization that, in the context of pure first order logic, the issue of compositionality was addressed by Gentzen [93] in his work on the sequent calculus. There, compositionality is obtained via cut elimination. In [203] Simpson developed a sequent calculus for showing that ....

....properties of certain sub LTSs. The work presented in [203] is based upon the realization that, in the context of pure first order logic, the issue of compositionality was addressed by Gentzen [93] in his work on the sequent calculus. There, compositionality is obtained via cut elimination. In [203], Simpson developed a sequent calculus for showing that closed terms in a process algebra with its operational semantics specified in the GSOS format satisfy assertions of the modal logic HML (see Sect. 2.3) Such process algebras provide interesting examples, because of the well known ....

A. Simpson, Compositionality via cut-elimination: Hennessy-Milner logic for an arbitrary GSOS, in Proceedings 10th Symposium on Logic in Computer Science, San Diego, California, 1995, IEEE Computer Society Press, pp. 420--430.

....indices i k . This gives a contradiction because the ordinals are wellfounded, thus the assumption that G O D is invalid must have been false. 3.6 Rules for Context Free Processes In this section we provide rules dealing with transition judgements p q. It has been shown by Simpson [37] how such rules can be found for process algebras with an operational semantics specified in the GSOS format. The GSOS format, SOS stands for structural operational semantics [35] is very general, allowing to express most process algebras. In this dissertation we instantiate the rules of [37] to ....

....[37] how such rules can be found for process algebras with an operational semantics specified in the GSOS format. The GSOS format, SOS stands for structural operational semantics [35] is very general, allowing to express most process algebras. In this dissertation we instantiate the rules of [37] to the special case of context free processes. Let (V,Act,P, p 1 ) be a context free process. The process rules are given by: G,e G, pq G[pq x] # O D[pq x] p (p,a,p)#P O pq pq, D if (p,a, p) In this definition we are slightly sloppy with the use of p and p. Note ....

Alex K. Simpson. Compositionality via cut-elimination: Hennessy-milner logic for an arbitrary GSOS. In Logic in Computer Science, pages 420--430, 1995.

....through a term cut proof rule of the shape: # # q : #, # #, X : # # p : #, # # # p q X : #, # Technically this rule is derivable from a standard cut rule, motivating the slogan Compositionality through cut introduction as we argue, in contrast to Simp 8 Chapter 1. Introduction son [Sim95] that it is precisely the introduction, and not elimination of cuts from proofs, that allow compositional reasonings. The term cut proof rule can be used to introduce compositional reasoning on different levels of ERLANG programs. Consider for instance the function level. Let the predicate e : ....

....significant simplifications of the conditions for the discharge rule, and an improved proof, all achieved together with Dilian Gurov. Other parts of the proof system were jointly developed. For instance, the correspondence between modalities and transition relations due to an idea by Simpson [Sim95] was first implemented for ERLANG in the EVT proof assistant, and later described for CCS [DG00a] In the present thesis the condition under which discharge is sound has been made more explicit, these improvements are solely due to me. The present EVT proof assistant was jointly developed by ....

[Article contains additional citation context not shown here]

A. Simpson. Compositionality via cut-elimination: Hennessy-Milner logic for an arbitrary GSOS. In Proc. LICS, pages 420--430, 1995.

....Concerning the choice of proof rules better completeness and decidability results will give much sharper handles on the kind of rules that should be admitted. A promising approach is to embed directly into the proof system the operational semantics proof rules in the style suggested by Simpson [17] for Hennessy Milner logic (without fixed points) First investigations in this direction for CCS and the modal calculus are reported in [7] Progress in this direction would be useful to remove some apparent arbitrariness in our choice of process calculus. Really we should expect to be able to ....

A. Simpson. Compositionality via cut-elimination: Hennessy-Milner logic for an arbitrary GSOS. In Proc. LICS, pages 420--430, 26--29 1995. 51

....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. 1 Introduction In a number of recent papers [1, 2, 4, 5, 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 ....

....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 [4] the calculus [2] CHOCS [1] general GSOS definable languages [9], and even a significant core fragment of a real programming language, Erlang [5] An important precursor to the above papers is [10] which used ternary sequents to build compositional proof systems for CCS and SCCS vs. Hennessy Milner logic [7] A key idea is that the use of a general sequent ....

A. Simpson. Compositionality via cut-elimination: Hennessy-Milner logic for an arbitrary GSOS. In Proc. LICS, pages 420--430, 26--29 1995.

....in Gamma ) this provides a very general and powerful setting for program verification which accomodates both model checking like verification based on global state space exploration, and compositional reasoning. This sort of approach has been examined in a number of recent papers, including [1 4, 7], and traces back to work by Stirling [8] and Winskel [12] Several programming or modelling languages have been considered, including CCS [3] the calculus [2] CHOCS [1] general GSOS definable languages [7] and a core fragment of the distributed functional programming language Erlang [4] ....

.... This sort of approach has been examined in a number of recent papers, including [1 4, 7] and traces back to work by Stirling [8] and Winskel [12] Several programming or modelling languages have been considered, including CCS [3] the calculus [2] CHOCS [1] general GSOS definable languages [7], and a core fragment of the distributed functional programming language Erlang [4] including features such as data types, a fairly rich sequential structure, asynchronous buffered communication, and dynamic process creation. The key idea is that the general form of sequent (1) allows correctness ....

[Article contains additional citation context not shown here]

A. Simpson. Compositionality via cut-elimination: Hennessy-Milner logic for an arbitrary GSOS. In Proc. LICS, pages 420--430, 26--29 1995.

....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 ....

....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 calculus [2] CHOCS [1] general GSOS definable languages [9], and even a significant core fragment of a real programming language, Erlang [4] An important precursor to the above papers is [10] which used ternary sequents to build compositional proof systems for CCS and SCCS vs. Hennessy Milner logic [6] A key idea is that the use of a general sequent ....

[Article contains additional citation context not shown here]

A. Simpson. Compositionality via cut-elimination: Hennessy-Milner logic for an arbitrary GSOS. In Proceedings, Tenth Annual IEEE Symposium on Logic in Computer Science, pages 420--430, San Diego, California, 26--29 1995. IEEE Computer Society Press.

....to consider the bialgebras of such distributive laws. When corresponds to some abstract operational rules ae, the bialgebras can be seen as combinations of operational and denotational models which satisfy the rules. Henceforth they are called ae models ; they specialise to the GSOS models of [25] and to models of tree rules (with an appropriate definition) The primary fact about ae models is that, from results in [15] it easily follows that the forgetful functors to each of the categories of denotational and operational models have adjoints. One adjunction implies that there exists an ....

.... bialgebras are the same as the algebras of the monad T of Theorem 7.1, and, dually, the same as the coalgebras of the comonad D : T Alg = Bialg = D Coalg Remark 7. 2 When is the distributive law induced by a finite set of concrete GSOS rules, the bialgebras are the GSOS models of [25]. 2 Given a Sigma algebra h : SigmaX X , let h : TX X be its inductive extension to a T algebra. When is induced by some abstract operational rules ae, no matter whether of type (8) or the dual (12) bialgebras are equivalent to pairs SigmaX h Gamma X k Gamma BX such that ....

A.K. Simpson. Compositionality via cutelimination: Hennessy-Milner logic for an arbitrary GSOS. In Proc. Tenth IEEE Symp. on Logic In Computer Science, 1995.

....of proof steps already exists (e.g. for the model checking fragment) but we also need to identify other classes of sequents that can be proved algorithmically. Other ongoing work focuses on integrating the operational semantics of Erlang more tightly with the proof systems (along the lines of [Sim95]) to improve the handling of process identifier scoping (but see [AD96] for an approach to this in the context of the calculus) and to handle fairness in a more elegant manner. ....

A. Simpson. Compositionality via cut-elimination: Hennessy-Milner logic for an arbitrary GSOS. In Proceedings, Tenth Annual IEEE Symposium on Logic in Computer Science, pages 420--430, San Diego, California, 26--29 1995. IEEE Computer Society Press.

....ineffective. It should be possible to remedy this by adding further reasoning principles along the lines of Hungar s box recurrences [8] Another issue is to investigate the power of our approach for general, say, GSOS definable languages (c.f. Simpson s recent work on Hennessy Milner logic [12]) For instance it is quite easy based on the present ideas to develop a sound proof system for context free processes. Is this proof system complete Acknowledgements. Thanks are due to Roberto Amadio for numerous discussions on related topics. ....

A. Simpson. Compositionality via cut-elimination: Hennessy-Milner logic for an arbitrary GSOS. Manuscript. To appear in Proc. LICS'95, 1995.

....the above lines already exists (e.g. for some model checking analyses) but we also need to identify other classes of sequents that can be solved algorithmically. Other ongoing work focuses on integrating the operational semantics of Erlang more tightly with the proof systems (along the lines of [Sim95]) and to improve the handling of process identifier scoping (but see [AD96] for an approach to this in the context of the calculus) Acknowledgements Many thanks are due to Fredrik Orava of the department of Teleinformatics at the Royal Institute of Technology, and Thomas Arts, Tony Rogvall and ....

A. Simpson. Compositionality via cut-elimination: Hennessy-Milner logic for an arbitrary GSOS. In Proceedings, Tenth Annual IEEE Symposium on Logic in Computer Science, pages 420--430, San Diego, California, 26--29 June 1995. IEEE Computer Society Press.

No context found.

Alex K. Simpson. Compositionality via cut-elimination: Hennessy-Milner logic for an arbitrary GSOS. In Proceedings, Tenth Annual IEEE Symposium on Logic in Computer Science, pages 420--430, San Diego, California, 26--29 June 1995. IEEE Computer Society Press.

....decompose logical connectives on the left and right of sequents in the familiar Gentzen style, allowing the construction of a derivation to be guided by the form of the goal sequent. Such a sequent based approach to process verification was proposed independently by Dam [4] and the second author [17], as a way of uniformly accounting for many specialist techniques for compositional reasoning that had appeared in the earlier literature, especially [18] The paper [17] presents a sequent calculus, for establishing properties expressed in Hennessy Milner logic [12] in which sequents contain a ....

....sequent. Such a sequent based approach to process verification was proposed independently by Dam [4] and the second author [17] as a way of uniformly accounting for many specialist techniques for compositional reasoning that had appeared in the earlier literature, especially [18] The paper [17] presents a sequent calculus, for establishing properties expressed in Hennessy Milner logic [12] in which sequents contain a second form of assertion, transition assertions p q, expressing that process p evolves to process q under action a. This device allows the proof system to be adapted to ....

[Article contains additional citation context not shown here]

A.K. Simpson. Compositionality via cut-elimination: Hennessy-Milner logic for an arbitrary GSOS. In Logic in Computer Science, pages 420--430, 1995.

....a proof system for establishing correctness assertions p #, where # is a formula in the modal calculus [13] We prove the soundness of the system, Theorem 1, and illustrate its workings with an example derivation of a calculus property with non trivial fixed point alternation. Following [16] the proof system can be adapted to processes in any process algebra with a GSOS specified operational semantics [1] Our main result, Theorem 2, is a restricted completeness result: the proof system is complete for establishing arbitrary calculus properties of context free processes, see e.g. ....

....decompose logical connectives on the left and right of sequents in the familiar Gentzen style, allowing the construction of a derivation to be guided by the form of the goal sequent. Such a sequent based approach to process verification was proposed independently by Dam [4] and the second author [16] as a way of uniformly accounting for many specialist techniques for compositional reasoning that had appeared in the earlier literature, especially [17] The approach has since been further developed in a series of papers by Dam and his co workers [5] 10] We now discuss this previous ....

[Article contains additional citation context not shown here]

A.K. Simpson. Compositionality via cut-elimination: Hennessy-Milner logic for an arbitrary GSOS. In Logic in Computer Science, pages 420--430, 1995.

No context found.

A.K. Simpson. Compositionality via cutelimination: Hennessy-Milner logic for an arbitrary GSOS. In Proc. Tenth IEEE Symp. on Logic In Computer Science, 1995.

No context found.

A. Simpson. Compositionality via cut-elimination: HennessyMilner logic for an arbitrary GSOS. In Proc. LICS, pages 420-430, 1995.

No context found.

A. Simpson. Compositionality via cut-elimination: Hennessy--Milner logic for an arbitrary GSOS. In Proc. LICS, pp. 420--430, 26--29, 1995.

No context found.

A. K. Simpson. Compositionality via cut-elimination: Hennessy-Milner logic for an arbitrary GSOS. In D. Kozen, editor, Proceedings of LICS'95, pp 420--430, San Diego, California, June 1995. IEEE Computer Society Press.

No context found.

A. Simpson. Compositionality via cut-elimination: Hennessy-Milner logic for an arbitrary GSOS. In Proc. LICS, pages 420-430. IEEE Computer Society Press, 1995.

No context found.

Alex Simpson. Compositionality via cut-elimination: Hennessy-Milner logic for an arbitrary GSOS. In Proc. Tenth IEEE Symp. on Logic In Computer Science, 1995.

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC