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Formalising the pi-calculus using nominal logic

Jesper Bengtson, Joachim Parrow, Helmut Seidl
2009 Logical Methods in Computer Science  
We 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  ... 
doi:10.2168/lmcs-5(2:16)2009 fatcat:nccxwutgvjhe5gioo7d66vgw74

Modal Logics for Nominal Transition Systems [article]

Joachim Parrow, Johannes Borgström, Lars-Henrik Eriksson, Ramūnas Forsberg Gutkovas, Tjark Weber
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  ... 
arXiv:1904.02564v3 fatcat:ttnxwh57grajbn7yyx2d6frxjy

Modal Logics for Nominal Transition Systems

Joachim Parrow, Johannes Borgström, Lars-Henrik Eriksson, Ramūnas Forsberg Gutkovas, Tjark Weber
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  ... 
doi:10.23638/lmcs-17(1:6)2021 fatcat:g6xm65ck2jh7xcv4fjbzuqmfny

Psi-Calculi in Isabelle

Jesper Bengtson, Joachim Parrow, Tjark Weber
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) 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.  ... 
doi:10.1007/s10817-015-9336-2 fatcat:6xd44jmybzftljt2j3zc7kadzm

Weak Nominal Modal Logic [chapter]

Joachim Parrow, Tjark Weber, Johannes Borgström, Lars-Henrik Eriksson
2017 Lecture Notes in Computer Science  
In this way we get a general framework for weak bisimulation and 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.  ... 
doi:10.1007/978-3-319-60225-7_13 fatcat:7vggx4l5mvcitdijzsatardi24

Psi-calculi: a framework for mobile processes with nominal data and logic

Jesper Bengtson, Magnus Johansson, Joachim Parrow, Björn Victor, Andrew Pitts
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.  ... 
doi:10.2168/lmcs-7(1:11)2011 fatcat:u4hln7wqcrgjxa3ifoikzusr4m

Psi-calculi in Isabelle [chapter]

Jesper Bengtson, Joachim Parrow
2009 Lecture Notes in Computer Science  
We have 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.  ... 
doi:10.1007/978-3-642-03359-9_9 fatcat:3nc4ftz4djg2xcpexdlbtkilc4

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

Joachim Parrow, Johannes Borgström, Lars-Henrik Eriksson, Ramunas Gutkovas, Tjark Weber, Marc Herbstritt
2015 International Conference on Concurrency Theory  
A Hennessy-Milner 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.  ... 
doi:10.4230/lipics.concur.2015.198 dblp:conf/concur/ParrowBEGW15 fatcat:ivmtvgmqsjgodef3gqcqmt6rzy

Proof-relevant pi-calculus

Roly Perera, James Cheney
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  ... 
doi:10.4204/eptcs.185.4 fatcat:kl7uiizvcjayfn4qk2d4cutzuu

Priorities Without Priorities: Representing Preemption in Psi-Calculi

Johannes Åman Pohjola, Joachim Parrow
2014 Electronic Proceedings in Theoretical Computer Science  
Psi-calculi is a parametric framework for extensions of 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 .  ... 
doi:10.4204/eptcs.160.2 fatcat:ljnbyxyglreldan6v2oxhoozgq

Psi-calculi: Mobile Processes, Nominal Data, and Logic

Jesper Bengtson, Magnus Johansson, Joachim Parrow, Björn Victor
2009 2009 24th Annual IEEE Symposium on Logic In Computer Science  
A psi-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.  ... 
doi:10.1109/lics.2009.20 dblp:conf/lics/BengtsonJPV09 fatcat:yh3f2i6langnhk4vzsessqzzve

Completeness in PVS of a Nominal Unification Algorithm

Mauricio Ayala-Rincón, Maribel Fernández, Ana Cristina Rocha-Oliveira
2016 Electronical Notes in Theoretical Computer Science  
In 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.  ... 
doi:10.1016/j.entcs.2016.06.005 fatcat:pgsndhnpbfd5nlpbjht7qo3fge

Mobile Processes: A Commented Bibliography [chapter]

Silvano Dal Zilio
2001 Lecture Notes in Computer Science  
A common characteristic of 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.  ... 
doi:10.1007/3-540-45510-8_11 fatcat:ksp2ci37rbc5jbwokvcs2ugspq

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

Roly Perera, James Cheney
2017 arXiv   pre-print
We present a 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  ... 
arXiv:1604.04575v2 fatcat:2vi7l7yt7vbdvnidsmlvrgormy
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