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Formalising the pi-calculus using nominal logic

2009
*
Logical Methods in Computer Science
*

We

doi:10.2168/lmcs-5(2:16)2009
fatcat:nccxwutgvjhe5gioo7d66vgw74
*formalise**the**pi*-*calculus**using**the**nominal*datatype package, based on ideas from*the**nominal**logic*by Pitts et al., and demonstrate an implementation in Isabelle/HOL. ... We thus provide one of*the*most extensive*formalisations*of a process*calculus*ever done inside a theorem prover. ... We would like to thank Stefan Berghofer for his generous help with*the*inner workings of Isabelle, Christian Urban for developing*the**nominal*datatype package and providing extensive support and insights ...##
###
Modal Logics for Nominal Transition Systems
[article]

2021
*
arXiv
*
pre-print

*The*main definitions and theorems have been

*formalised*in

*Nominal*Isabelle. ... A main technical novelty is

*the*

*use*of finitely supported infinite conjunctions. ... Acknowledgements We thank Andrew Pitts for enlightening discussions on

*nominal*data types with infinitary constructors, and Dmitriy Traytel for providing an Isabelle/HOL

*formalisation*of cardinality-bounded ...

##
###
Modal Logics for Nominal Transition Systems

2019
*
Logical Methods in Computer Science
*

*The*main definitions and theorems have been

*formalised*in

*Nominal*Isabelle. ... A main technical novelty is

*the*

*use*of finitely supported infinite conjunctions. ... Acknowledgements We thank Andrew Pitts for enlightening discussions on

*nominal*data types with infinitary constructors, and Dmitriy Traytel for providing an Isabelle/HOL

*formalisation*of cardinalitybounded ...

##
###
Psi-Calculi in Isabelle

2015
*
Journal of automated reasoning
*

This paper presents a mechanisation of psi-calculi, a parametric framework for modelling various dialects of process calculi including (but not limited to)

doi:10.1007/s10817-015-9336-2
fatcat:6xd44jmybzftljt2j3zc7kadzm
*the**pi*-*calculus*,*the*applied*pi*-*calculus*, and ... Psi-calculi are significantly more expressive, yet their semantics is as simple in structure as*the*semantics of*the*original*pi*-*calculus*. ... Acknowledgements We want to convey our sincere thanks to Stefan Berghofer for his hard work on enhancing*Nominal*Isabelle to include*the*features that we needed for this*formalisation*. ...##
###
Weak Nominal Modal Logic
[chapter]

2017
*
Lecture Notes in Computer Science
*

In this way we get a general framework for weak bisimulation and

doi:10.1007/978-3-319-60225-7_13
fatcat:7vggx4l5mvcitdijzsatardi24
*logic*in which formalisms such as*the**pi*-*calculus*and its many variants can be uniformly represented. ... We prove that*logical*equivalence coincides with bisimilarity and explore a few variants of*the**logic*. ... Our main results in Sects. 3 and 4, including*the*adequacy of*the*weak*logic*, have been*formalised*in*the*interactive theorem prover Isabelle/HOL*using**the**nominal*datatype package. ...##
###
Psi-calculi: a framework for mobile processes with nominal data and logic

2011
*
Logical Methods in Computer Science
*

*The*framework of psi-calculi extends

*the*

*pi*-

*calculus*with

*nominal*datatypes for data structures and for

*logical*assertions and conditions. ... Psi-calculi can capture

*the*same phenomena as other proposed extensions of

*the*

*pi*-

*calculus*such as

*the*applied

*pi*-

*calculus*,

*the*spi-

*calculus*,

*the*fusion

*calculus*,

*the*concurrent constraint

*pi*-

*calculus*, ... PSI-CALCULI: A FRAMEWORK FOR MOBILE PROCESSES WITH

*NOMINAL*DATA AND

*LOGIC*15 3.1.

*The*

*pi*-

*calculus*. In Section 2.4 we saw

*the*instance

*Pi*which corresponds to

*the*

*pi*-

*calculus*. ...

##
###
Psi-calculi in Isabelle
[chapter]

2009
*
Lecture Notes in Computer Science
*

We have

doi:10.1007/978-3-642-03359-9_9
fatcat:3nc4ftz4djg2xcpexdlbtkilc4
*formalised*psi-calculi in*the*interactive theorem prover Isabelle*using*its*nominal*datatype package. ... beyond*the*applied*pi*-*calculus*and*the*concurrent constraint picalculus. ... Acknowledgments We want to convey our sincere thanks to Stefan Berghofer for his hard work on expanding*the**nominal*package to include*the*features we have needed for this*formalisation*. ...##
###
Page 6 of Mathematical Reviews Vol. 27, Issue 1
[page]

1964
*
Mathematical Reviews
*

and induction ;

*nominalism*and platonism ;*logic*and computing machines. ... Chapter 14,*Logic*and*the*activity of thinking :*The*limitations of formal*logic*;*the**logic*of concrete thought ; inductive reasoning ;*the*elements of judgment in induction;*the**calculus*of probabilities ...##
###
Modal Logics for Nominal Transition Systems

2015
*
International Conference on Concurrency Theory
*

A Hennessy-Milner

doi:10.4230/lipics.concur.2015.198
dblp:conf/concur/ParrowBEGW15
fatcat:ivmtvgmqsjgodef3gqcqmt6rzy
*logic*for these systems is introduced, and proved adequate for bisimulation equivalence. A main novelty is*the**use*of finitely supported infinite conjunctions. ...*The*main definitions and theorems have been formalized in*Nominal*Isabelle. ... We thank Andrew Pitts for enlightening discussions on*nominal*datatypes with infinitary constructors, and Dmitriy Traytel for providing a formalization of cardinality-bounded sets. ...##
###
Proof-relevant pi-calculus

2015
*
Electronic Proceedings in Theoretical Computer Science
*

*Formalising*

*the*

*pi*-

*calculus*is an illuminating test of

*the*expressiveness of

*logical*frameworks and mechanised metatheory systems, because of

*the*presence of name binding, labelled transitions with name ... We present a

*formalisation*in Agda that instead explores

*the*theory of concurrent transitions, residuation, and causal equivalence of traces, which has not previously been

*formalised*for

*the*

*pi*-

*calculus*...

*The*π-

*calculus*has also attracted considerable attention from

*the*

*logical*frameworks and meta-languages community, and

*formalisations*of its syntax and semantics have been performed

*using*most of

*the*extant ...

##
###
Priorities Without Priorities: Representing Preemption in Psi-Calculi

2014
*
Electronic Proceedings in Theoretical Computer Science
*

Psi-calculi is a parametric framework for extensions of

doi:10.4204/eptcs.160.2
fatcat:ljnbyxyglreldan6v2oxhoozgq
*the**pi*-*calculus*with data terms and arbitrary*logics*. ... We also formally prove in*Nominal*Isabelle that*the*standard congruence and structural laws about strong bisimulation hold in psi-calculi extended with priorities. ... As a first step, it would be necessary to develop a*formalisation*of FIMMs in Isabelle, and integrate it with*the**nominal**logic*package. 0 Nil MN . P Output M(λ x)N . ...##
###
Psi-calculi: Mobile Processes, Nominal Data, and Logic

2009
*
2009 24th Annual IEEE Symposium on Logic In Computer Science
*

A psi-

doi:10.1109/lics.2009.20
dblp:conf/lics/BengtsonJPV09
fatcat:yh3f2i6langnhk4vzsessqzzve
*calculus*is an extension of*the**pi*-*calculus*with*nominal*data types for data structures and for*logical*assertions representing facts about data. ... These can be transmitted between processes and their names can be statically scoped*using**the*standard*pi*-*calculus*mechanism to allow for scope migrations. ... For example, we can*use*a higher-order*logic*for assertions and conditions, and higher-order formalisms such as*the*lambda*calculus*for data terms and channels. ...##
###
Completeness in PVS of a Nominal Unification Algorithm

2016
*
Electronical Notes in Theoretical Computer Science
*

In

doi:10.1016/j.entcs.2016.06.005
fatcat:pgsndhnpbfd5nlpbjht7qo3fge
*the**nominal*approach variable bindings are represented*using*techniques that are close to first-order*logical*techniques, instead of*using*a higher-order metalanguage. ... This*formalisation*is based on a natural notion of*nominal*α-equivalence, avoiding in this way*the**use*of*the*intermediate auxiliary weak α-relation considered in previous*formalisations*. ... For instance,*the*Substitution Lemma (well-known in*the*context of λ-*calculus*) was*formalised**using*these techniques. ...##
###
Mobile Processes: A Commented Bibliography
[chapter]

2001
*
Lecture Notes in Computer Science
*

A common characteristic of

doi:10.1007/3-540-45510-8_11
fatcat:ksp2ci37rbc5jbwokvcs2ugspq
*the*algebraic frameworks presented in this paper is*the**use*of names as first class values and*the*support for*the*dynamic generation of new, fresh names. ... π-*calculus*of Milner, Parrow and Walker for example, and motile processes, which can exhibit motion, as modelled in*the*ambient*calculus*of Cardelli and Gordon. ...*pi*-*Calculus*Processes: a Tutorial. ...##
###
Proof-relevant π-calculus: a constructive account of concurrency and causality
[article]

2017
*
arXiv
*
pre-print

We present a

arXiv:1604.04575v2
fatcat:2vi7l7yt7vbdvnidsmlvrgormy
*formalisation*in Agda of*the*theory of concurrent transitions, residuation, and causal equivalence of traces for*the**pi*-*calculus*. ... In*the**pi*-*calculus*transitions represent propagating binders whenever their actions involve bound names. ... Acknowledgements We are grateful to our colleagues in*the*Programming Languages Interest Group at Edinburgh for*useful*discussions, to Vít Šefl for assistance with*the*Agda*formalisation*, and to*the*anonymous ...
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