Psi-Calculi in Isabelle

Bengtson, Jesper; Parrow, Joachim; Weber, Tjark

doi:10.1007/s10817-015-9336-2

Cited by 14 publications

(21 citation statements)

References 48 publications

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“…Recent years have seen much work regarding the formalization of process calculi, in particular, using Nominal Isabelle. We do not have the space to discuss this line of work in detail but simply cite some of the many contributions from Parrow and his associates (Bengtson and Parrow 2009;Bengtson et al 2016;Parrow et al 2014) about various versions of the π/ψ-calculus and their congruence properties, proven without resorting to the Howe's proof strategy.…”

Section: Related Workmentioning

confidence: 99%

A case study in programming coinductive proofs: Howe’s method

Momigliano¹,

Pientka²,

Thibodeau³

2018

Math. Struct. Comp. Sci.

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Bisimulation proofs play a central role in programming languages in establishing rich properties such as contextual equivalence. They are also challenging to mechanize, since they require a combination of inductive and coinductive reasoning on open terms. In this paper, we describe mechanizing the property that similarity in the call-by-name lambda calculus is a pre-congruence using Howe’s method in the Beluga formal reasoning system. The development relies on three key ingredients: (1) we give a higher order abstract syntax (HOAS) encoding of lambda terms together with their operational semantics as intrinsically typed terms, thereby avoiding not only the need to deal with binders, renaming and substitutions, but keeping all typing invariants implicit; (2) we take advantage of Beluga’s support for representing open terms using built-in contexts and simultaneous substitutions: this allows us to directly state central definitions such as open simulation without resorting to the usual inductive closure operation and to encode very elegantly notoriously painful proofs such as the substitutivity of the Howe relation; (3) we exploit the possibility of reasoning by coinduction in Beluga’s reasoning logic. The end result is succinct and elegant, thanks to the high-level abstractions and primitives Beluga provides. We believe that this mechanization is a significant example that illustrates Beluga’s strength at mechanizing challenging (co)inductive proofs using HOAS encodings.

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Section: Related Workmentioning

confidence: 99%

A case study in programming coinductive proofs: Howe’s method

Momigliano¹,

Pientka²,

Thibodeau³

2018

Math. Struct. Comp. Sci.

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“…The key intuition is that every message m received, queued, and sent by qmsg satisfies R σ m. The proof is by induction over oreachable. The R's are preserved when the external environment acts independently (3,4), when it acts synchronously (2), and when the local process acts (1,3).…”

Section: Lemma 3 (Qmsg Lifting) Givenmentioning

confidence: 99%

“…This paper reports on both its mechanization in Isabelle/HOL [15] and the development of a compositional framework for showing invariant properties of models. 1 The techniques we describe are a response to problems encountered during the mechanization of a model and proof-presented elsewhere [4]-of an RFC-standard for routing protocols. Despite the existence of extensive research on related problems [18] and several mechanized frameworks for reactive systems [5,10,14], we are not aware of other solutions that allow the compositional statement and proof of properties relating the states of different nodes in a message-passing model-at least not within the strictures imposed by an Interactive Theorem Prover (ITP).…”

Section: Introduction and Related Workmentioning

confidence: 99%

Showing Invariance Compositionally for a Process Algebra for Network Protocols

Bourke¹,

Glabbeek²,

Höfner³

2014

Interactive Theorem Proving

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This paper presents the mechanization of a process algebra for Mobile Ad hoc Networks and Wireless Mesh Networks, and the development of a compositional framework for proving invariant properties. Mechanizing the core process algebra in Isabelle/HOL is relatively standard, but its layered structure necessitates special treatment. The control states of reactive processes, such as nodes in a network, are modelled by terms of the process algebra. We propose a technique based on these terms to streamline proofs of inductive invariance. This is not sufficient, however, to state and prove invariants that relate states across multiple processes (entire networks). To this end, we propose a novel compositional technique for lifting global invariants stated at the level of individual nodes to networks of nodes.

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“…Psi-calculi [BJPV11] is a family of applied process calculi, where standard meta-theoretical results, such as the algebraic laws and congruence properties of bisimulation, have been established once and for all through mechanised proofs [BPW16] for all members of the family. Psi-calculi generalises e.g.…”

Section: Introductionmentioning

confidence: 99%

Psi-Calculi Revisited: Connectivity and Compositionality

Pohjola

2019

Formal Techniques for Distributed Objects, Components, and Systems

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Psi-calculi is a parametric framework for process calculi similar to popular picalculus extensions such as the explicit fusion calculus, the applied pi-calculus and the spi calculus. Mechanised proofs of standard algebraic and congruence properties of bisimilarity apply to all calculi within the framework.A limitation of psi-calculi is that communication channels must be symmetric and transitive. In this paper, we give a new operational semantics to psi-calculi that allows us to lift these restrictions and simplify some of the proofs. The key technical innovation is to annotate transitions with a provenance-a description of the scope and channel they originate from.We give mechanised proofs that our extension is conservative, and that the standard algebraic and congruence properties of strong and weak bisimilarity are maintained. We show correspondence with a reduction semantics and barbed bisimulation. We show how a pi-calculus with preorders that was previously beyond the scope of psi-calculi can be captured, and how to encode mixed choice under very strong quality criteria.a(x).P | b y.Q | (a = b)

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Psi-Calculi in Isabelle

Cited by 14 publications

References 48 publications

A case study in programming coinductive proofs: Howe’s method

A case study in programming coinductive proofs: Howe’s method

Showing Invariance Compositionally for a Process Algebra for Network Protocols

Psi-Calculi Revisited: Connectivity and Compositionality

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