Proving the validity of equations in GSOS languages using rule-matching bisimilarity

Aceto, Luca; Cimini, Matteo; Ingólfsdóttir, Anna

doi:10.1017/s0960129511000417

Cited by 3 publications

(4 citation statements)

References 37 publications

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“…In the case of GSOS on labelled transition systems, proving equations to hold at the level of a specification was considered in [2], based on rule-matching bisimulations, a refinement of De Simone's notion of FH-bisimulation. Rule-matching bisimulations are based on the syntactic notion of ruloids, while our technique is based on preservation of equations at the level of distributive laws.…”

Section: Discussionmentioning

confidence: 99%

Presenting Distributive Laws

Bonsangue¹,

Hansen²,

Kurz³

et al. 2015

Logical Methods in Computer Science

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Abstract. Distributive laws of a monad T over a functor F are categorical tools for specifying algebra-coalgebra interaction. They proved to be important for solving systems of corecursive equations, for the specification of well-behaved structural operational semantics and, more recently, also for enhancements of the bisimulation proof method. If T is a free monad, then such distributive laws correspond to simple natural transformations. However, when T is not free it can be rather difficult to prove the defining axioms of a distributive law. In this paper we describe how to obtain a distributive law for a monad with an equational presentation from a distributive law for the underlying free monad. We apply this result to show the equivalence between two different representations of context-free languages.

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Section: Discussionmentioning

confidence: 99%

Presenting Distributive Laws

Bonsangue¹,

Hansen²,

Kurz³

et al. 2015

Logical Methods in Computer Science

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“…Earlier results consider open notions of bisimilarity purely positive TSSs (e.g., [7,15,1,18,19]). We hope to use the results here to extend these results to the systems with negative premises (such as those in the (n)tyft/(n)tyxt [13], ntree [9] or PANTH [20] formats).…”

Section: Discussionmentioning

confidence: 99%

Modular Semantics for Transition System Specifications with Negative Premises

Churchill

Mosses

Mousavi

2013

CONCUR 2013 – Concurrency Theory

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Abstract. Transition rules with negative premises are needed in the structural operational semantics of programming and specification constructs such as priority and interrupt, as well as in timed extensions of specification languages. The well-known proof-theoretic semantics for transition system specifications involving such rules is based on wellsupported proofs for closed transitions. Dealing with open formulae by considering all closed instances is inherently non-modular -proofs are not necessarily preserved by disjoint extensions of the transition system specification. Here, we conservatively extend the notion of well-supported proof to open transition rules. We prove that the resulting semantics is modular, consistent, and closed under instantiation. Our results provide the foundations for modular notions of bisimulation such that equivalence can be proved with reference only to the relevant rules, without appealing to all existing closed instantiations of terms.

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“…Second, the correspondences in Theorems 5.6 and 5.10 are far from being expected. Indeed, for GSOS specifying labelled transition systems, the notions of bisimilarity of open terms proposed in literature (like the formal hypothesis in [1], the hypothesis preserving in [2], the loose and the strict in [3], the rulematching in [4]) are sound w.r.t. the semantics obtained by the interpretation of variables as closed terms, but not complete.…”

Section: Conclusion Related and Future Workmentioning

confidence: 99%

“…The main problem of such a definition is the quantification over all substitutions: one would like to have an alternative characterisation, possibly amenable to the coinduction proof principle. This issue has been investigated in several works, like [1,2,3,4,5,6,7].…”

Section: Introductionmentioning

confidence: 99%

Bisimilarity of open terms in stream GSOS

Bonchi

Bussel

Lee

et al. 2019

Science of Computer Programming

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Stream GSOS is a specification format for operations and calculi on infinite sequences. The notion of bisimilarity provides a canonical proof technique for equivalence of closed terms in such specifications. In this paper, we focus on open terms, which may contain variables, and which are equivalent whenever they denote the same stream for every possible instantiation of the variables. Our main contribution is to capture equivalence of open terms as bisimilarity on certain Mealy machines, providing a concrete proof technique. Moreover, we introduce an enhancement of this technique, called bisimulation up-to substitutions, and show how to combine it with other up-to techniques to obtain a powerful method for proving equivalence of open terms.

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Proving the validity of equations in GSOS languages using rule-matching bisimilarity

Cited by 3 publications

References 37 publications

Presenting Distributive Laws

Presenting Distributive Laws

Modular Semantics for Transition System Specifications with Negative Premises

Bisimilarity of open terms in stream GSOS

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