A First-Order Syntax for the π-Calculus in Isabelle/HOL using Permutations

Röckl, Christine

doi:10.1016/s1571-0661(04)00276-2

Cited by 7 publications

(5 citation statements)

References 23 publications

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“…Nominal formalizations of the π-calculus have been proposed so far only in variants of Isabelle [46,28,6]. We only discuss the most recent one [6], which mainly differs from our work in that it relies on tailored induction principles in the cases involving bound names, allowing to pick these bound names fresh from the context.…”

Section: Related Workmentioning

confidence: 99%

HO$$\pi $$ in Coq

2020

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We present a formalization of HOπ in Coq, a process calculus where messages carry processes. Such a higher-order calculus features two very different kinds of binder: process input, similar to λ-abstraction, and name restriction, whose scope can be expanded by communication. For the latter, we compare four approaches to represent binders: locally nameless, de Bruijn indices, nominal, and Higher-Order Abstract Syntax. In each case, we formalize strong context bisimilarity and prove it is compatible, i.e., closed under every context, using Howe's method, based on several proof schemes we developed in a previous paper.

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Section: Related Workmentioning

confidence: 99%

HO$$\pi $$ in Coq

2020

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“…Nominal Isabelle The Nominal Datatype Package extension to Isabelle/HOL [Urban 2008] supports the Gabbay-Pitts style "nominal" approach to abstract syntax modulo name-binding [Gabbay and Pitts 2002], and has been used in several formalisations. Two early contributions using similar ideas predate its development: Röckl [2001] formalised the syntax of π-calculus and α-equivalence in Isabelle/HOL. Gabbay [2003] described how to use Gabbay-Pitts nominal abstract syntax to represent the π-calculus, without giving a mechanised formalisation or proofs of properties.…”

Section: Holmentioning

confidence: 99%

Proof-relevant π-calculus: a constructive account of concurrency and causality

Perera¹,

Cheney²

2017

Math. Struct. Comp. Sci.

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We present a formalisation in Agda of the theory of concurrent transitions, residuation, and causal equivalence of traces for the π-calculus. Our formalisation employs de Bruijn indices and dependently-typed syntax, and aligns the "proved transitions" proposed by Boudol and Castellani in the context of CCS with the proof terms naturally present in Agda's representation of the labelled transition relation. Our main contributions are proofs of the "diamond lemma" for the residuals of concurrent transitions and a formal definition of equivalence of traces up to permutation of transitions.In the π-calculus transitions represent propagating binders whenever their actions involve bound names. To accommodate these cases, we require a more general diamond lemma where the target states of equivalent traces are no longer identical, but are related by a braiding that rewires the bound and free names to reflect the particular interleaving of events involving binders. Our approach may be useful for modelling concurrency in other languages where transitions carry metadata sensitive to particular interleavings, such as dynamically allocated memory addresses.

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“…Moreover, the answer to the first query is unique (up to renaming). Röckl [2001] and Gabbay [2003] have also considered encodings of the π-calculus using nominal abstract syntax. Röckl considered only modeling the syntax of terms up to α-equivalence using swapping, whereas Gabbay went further, encoding transitions and the bisimulation relation and proving basic properties thereof.…”

Section: N Omentioning

confidence: 99%

Nominal logic programming

Cheney

Urban

2008

ACM Trans. Program. Lang. Syst.

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Nominal logic is an extension of first-order logic which provides a simple foundation for formalizing and reasoning about abstract syntax modulo consistent renaming of bound names (that is, α-equivalence). This article investigates logic programming based on nominal logic. This technique is especially well-suited for prototyping type systems, proof theories, operational semantics rules, and other formal systems in which bound names are present. In many cases, nominal logic programs are essentially literal translations of "paper" specifications. As such, nominal logic programming provides an executable specification language for prototyping, communicating, and experimenting with formal systems.We describe some typical nominal logic programs, and develop the model-theoretic, prooftheoretic, and operational semantics of such programs. Besides being of interest for ensuring the correct behavior of implementations, these results provide a rigorous foundation for techniques for analysis and reasoning about nominal logic programs, as we illustrate via two examples.

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A First-Order Syntax for the π-Calculus in Isabelle/HOL using Permutations

Cited by 7 publications

References 23 publications

HO$$\pi $$ in Coq

HO$$\pi $$ in Coq

Proof-relevant π-calculus: a constructive account of concurrency and causality

Nominal logic programming

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