Enhancements of the bisimulation proof method

Pous, Damien; Sangiorgi, Davide

doi:10.1017/cbo9780511792588.007

Cited by 65 publications

(189 citation statements)

References 19 publications

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“…Like the interpretation of a GSOS specification with assignment rules, we construct this latter specification by fixed point induction. As a direct consequence of this alternative representation of the interpretation, we obtain that bisimilarity is a congruence and that bisimulation up to context is sound and even compatibleproperties that do not follow from bisimilarity being a congruence [32]. As an example, we obtain the compatibility of bisimulation up to context for CCS with replication, which was shown earlier with an ad-hoc argument (see, e.g., [32]).…”

Section: Introductionsupporting

confidence: 67%

“…By the above Corollary, we obtain once more that bisimilarity is a congruence and the contextual closure is compatible, for CCS with replication. This compatibility result is known (see, e.g., [32]), but contrary to previous proofs, here we obtain it directly from the fact that the specification is expressed in terms of GSOS and assignment rules, by the above results.…”

Section: Abstract Gsos Specifications For Assignment Rulesmentioning

confidence: 61%

“…To state and prove the applications of our main results to the proof technique of bisimulation-up-to, we recall here a few of the elements of its (coalgebraic) theory from [32,33]. We only mention those definitions and results that are strictly necessary, and refer the reader to the aforementioned papers for the full theory, motivation and examples.…”

Section: Bisimulation Up-tomentioning

confidence: 99%

“…We say f is g-compatible if for any two relations R and S: R ⊆ g(S) implies f (R) ⊆ g(f (S)). Compatibility implies soundness, that is, if R ⊆ g(f (R)), then R ⊆ S for some relation S satisfying S ⊆ g(S) [32].…”

Section: Bisimulation Up-tomentioning

confidence: 99%

“…By instantiating the theory to concrete instances, one can then obtain congruence formats for systems such as probabilistic automata, weighted transition systems and streams-see [23] for an overview. Another advantage of abstract GSOS is that bisimulation up to context is "compatible" [34,33], providing a sound enhancement of the bisimulation proof method which can be combined with other compatible enhancements such as bisimulation up to bisimilarity [39,32].…”

Section: Introductionmentioning

confidence: 99%

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Structural congruence for bialgebraic semantics

Rot¹,

Bonsangue²

2016

Journal of Logical and Algebraic Methods in Programming

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It was observed by Turi and Plotkin that structural operational semantics can be studied at the level of universal coalgebra, providing specification formats for well-behaved operations on many different types of systems. We extend this framework with non-structural assignment rules which can express, for example, the syntactic format for structural congruences proposed by Mousavi and Reniers. Our main result is that the operational model of such an extended specification is well-behaved, in the sense that bisimilarity is a congruence and that bisimulation-up-to techniques are sound.

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Section: Introductionsupporting

confidence: 67%

Section: Abstract Gsos Specifications For Assignment Rulesmentioning

confidence: 61%

Section: Bisimulation Up-tomentioning

confidence: 99%

Section: Bisimulation Up-tomentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Structural congruence for bialgebraic semantics

Rot¹,

Bonsangue²

2016

Journal of Logical and Algebraic Methods in Programming

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Effectful Normal Form Bisimulation

Lago

Gavazzo

2019

Programming Languages and Systems

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Normal form bisimulation, also known as open bisimulation, is a coinductive technique for higher-order program equivalence in which programs are compared by looking at their essentially infinitary tree-like normal forms, i.e. at their Böhm or Lévy-Longo trees. The technique has been shown to be useful not only when proving metatheorems about λ-calculi and their semantics, but also when looking at concrete examples of terms. In this paper, we show that there is a way to generalise normal form bisimulation to calculi with algebraic effects,à la Plotkin and Power. We show that some mild conditions on monads and relators, which have already been shown to guarantee effectful applicative bisimilarity to be a congruence relation, are enough to prove that the obtained notion of bisimilarity, which we call effectful normal form bisimilarity, is a congruence relation, and thus sound for contextual equivalence. Additionally, contrary to applicative bisimilarity, normal form bisimilarity allows for enhancements of the bisimulation proof method, hence proving a powerful reasoning principle for effectful programming languages.

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Up-to Techniques for Branching Bisimilarity

Erkens

Rot

Luttik

2020

SOFSEM 2020: Theory and Practice of Computer Science

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Ever since the introduction of behavioral equivalences on processes one has been searching for efficient proof techniques that accompany those equivalences. Both strong bisimilarity and weak bisimilarity are accompanied by an arsenal of up-to techniques: enhancements of their proof methods. For branching bisimilarity, these results have not been established yet. We show that a powerful proof technique is sound for branching bisimilarity by combining the three techniques of up to union, up to expansion and up to context for Bloom's BB cool format. We then make an initial proposal for casting the correctness proof of the up to context technique in an abstract coalgebraic setting, covering branching but also η, delay and weak bisimilarity. ⋆ The research of the second author was supported by a Marie Curie Fellowship (grant code 795119). An extended abstract has been published in the proceedings of SOF-SEM 2020, see https://doi.

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Enhancements of the bisimulation proof method

Cited by 65 publications

References 19 publications

Structural congruence for bialgebraic semantics

Structural congruence for bialgebraic semantics

Effectful Normal Form Bisimulation

Up-to Techniques for Branching Bisimilarity

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