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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.  ...  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.  ...  Government and University of Edinburgh are authorized to reproduce and distribute reprints for their purposes notwithstanding any copyright notation thereon.  ... 
arXiv:1604.04575v2 fatcat:2vi7l7yt7vbdvnidsmlvrgormy

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

ROLY PERERA, JAMES CHENEY
2017 Mathematical Structures in Computer Science  
We present a formalisation in Agda of the theory of concurrent transitions, residuation and causal equivalence of traces for the π-calculus.  ...  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.  ...  Government and University of Edinburgh are authorized to reproduce and distribute reprints for their purposes notwithstanding any copyright notation thereon.  ... 
doi:10.1017/s096012951700010x fatcat:kml5dff4gvbjjbi7y63bzd7mw4

Proof-relevant pi-calculus

Roly Perera, James Cheney
2015 Electronic Proceedings in Theoretical Computer Science  
Our main contributions are proofs of the "diamond lemma" for residuation of concurrent transitions and a formal definition of equivalence of traces up to permutation of transitions.  ...  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  ...  Introduction The π-calculus [18, 19] is an expressive model of concurrent and mobile processes.  ... 
doi:10.4204/eptcs.185.4 fatcat:kl7uiizvcjayfn4qk2d4cutzuu

Reversibility in the higher-order π -calculus

Ivan Lanese, Claudio Antares Mezzina, Jean-Bernard Stefani
2016 Theoretical Computer Science  
We prove that reversibility in our calculus is causally consistent and that the causal information used to support reversibility in rhoπ is consistent with the one used in the causal semantics of the π-calculus  ...  In this paper, we continue the study undertaken by Danos and Krivine on reversible CCS by defining a reversible higher-order π-calculus, called rhoπ.  ...  While the rhoπ calculus and its reversible machinery are unchanged, the analysis in Section 3 of the relationship between our notion of causality and that provided by Boreale and Sangiorgi for the π-calculus  ... 
doi:10.1016/j.tcs.2016.02.019 fatcat:ydiureeffvelbedqtf7ce4gxoy

Modelling biochemical pathways through enhanced π-calculus

M. Curti, P. Degano, C. Priami, C.T. Baldari
2004 Theoretical Computer Science  
First, we present a reduction semantics for the -calculus from which causality and concurrency can be mechanically derived.  ...  Then, we show the applicability of our proposal on a couple of biological examples.  ...  Acknowledgements We wish to thank the referees for their precise and invaluable suggestions.  ... 
doi:10.1016/j.tcs.2004.03.066 fatcat:gmk2j7ypmffvde2iydjy3edxqm

Typed event structures and the linear π-calculus

Daniele Varacca, Nobuko Yoshida
2010 Theoretical Computer Science  
by conflict, prefix is modelled using causality, and parallel composition generates concurrent events.  ...  Various causal semantics of the π -calculus existed before [24, 9, 16, 5, 14, 10] , but none was given in terms of event structures.  ...  We acknowledge the support of the EPSRC grant GR/T04724/01 ''Program Analysis and the Typed Pi-Calculus''.  ... 
doi:10.1016/j.tcs.2010.01.024 fatcat:taorcsrcxja3zlptddnrzo64hm

Petri Net Semantics of the Finite π-Calculus [chapter]

Raymond Devillers, Hanna Klaudel, Maciej Koutny
2004 Lecture Notes in Computer Science  
In this paper we propose a translation into high level Petri nets of a finite fragment of the π-calculus.  ...  Our construction renders in a compositional way the control flow aspects present in π-calculus process expressions, by adapting the existing graph-theoretic net composition operators.  ...  to specify and reason about the causality and concurrency exhibited by a system.  ... 
doi:10.1007/978-3-540-30232-2_20 fatcat:gzalqntdenavlhhkzgbnxxpgei

Intensional and Extensional Characterisation of Global Progress in the π-Calculus [chapter]

Luca Fossati, Kohei Honda, Nobuko Yoshida
2012 Lecture Notes in Computer Science  
We introduce an observational theory of a linear π-calculus for a rigorous behavioural characterisation of global progress properties such as non-blockingness and wait-freedom.  ...  some of the representative concurrent data structures. cas(x, y, z) : if L x = v then(z L tt |Ref cas u, y )else(z L ff |Ref cas u, v )  ...  In this paper we introduce a rigorous behavioural theory of concurrent data structures based on a linear π-calculus.  ... 
doi:10.1007/978-3-642-32940-1_21 fatcat:2hwp46dpwfgy5d7fuf5na25ifm

Distributed semantics for the π-calculus based on Petri nets with inhibitor arcs

Nadia Busi, Roberto Gorrieri
2009 The Journal of Logic and Algebraic Programming  
Such a class of nets is equipped with a step and a causal semantics, hence allowing to study non-interleaving semantics for the π -calculus.  ...  A distributed model for the π-calculus is presented in terms of Place/Transition Petri nets with inhibitor arcs (PTI for short).  ...  The second author has collected that material after first author's premature death in September 2007, and updated the paper with relevant, more recent, related work.  ... 
doi:10.1016/j.jlap.2008.08.002 fatcat:7d3ndzhobrdm3gcdqk3cxhb6au

Structured coalgebras and minimal HD-automata for the π-calculus

Ugo Montanari, Marco Pistore
2005 Theoretical Computer Science  
In this paper we propose to model the transition system of the -calculus as a coalgebra on a category of name permutation algebras and to define its abstract semantics as the final coalgebra of such a  ...  HD-automata associated with agents with a bounded number of threads in their derivatives are finite and can be actually minimized.  ...  Acknowledgements We thank Andrea Corradini for the helpful comments and suggestions on the application of structured coalgebras in our framework.  ... 
doi:10.1016/j.tcs.2005.03.014 fatcat:plbpj3opczgihfkklwkgtk7cqm

Causally consistent dynamic slicing [article]

Roly Perera, Deepak Garg, James Cheney
2016 arXiv   pre-print
We offer a lattice-theoretic account of dynamic slicing for π-calculus, building on prior work in the sequential setting.  ...  For any run of a concurrent program, we exhibit a Galois connection relating forward slices of the start configuration to backward slices of the end configuration.  ...  We build on an earlier "proof-relevant" formalisation of causal equivalence for π-calculus in Agda [15] .  ... 
arXiv:1610.02327v1 fatcat:aneukckdvjepjoldg2t5hkswwa

Causally Consistent Dynamic Slicing

Roly Perera, Deepak Garg, James Cheney, Marc Herbstritt
2016 International Conference on Concurrency Theory  
We offer a lattice-theoretic account of dynamic slicing for π-calculus, building on prior work in the sequential setting.  ...  For any run of a concurrent program, we exhibit a Galois connection relating forward slices of the start configuration to backward slices of the end configuration.  ...  Government and University of Edinburgh are authorized to reproduce and distribute reprints for their purposes notwithstanding any copyright notation thereon.  ... 
doi:10.4230/lipics.concur.2016.18 dblp:conf/concur/PereraGC16 fatcat:2rp6egrfojh2fbhfbhiyczeimi

Reversible session-based pi-calculus

Francesco Tiezzi, Nobuko Yoshida
2015 Journal of Logical and Algebraic Methods in Programming  
Concerning the session type discipline, ReSπ inherits the notion of types and the typing system from π -calculus. Thus, the related results are mainly based on the ones stated for π -calculus.  ...  If we would consider only a single session, due to linearity, a causal-consistent form of reversibility would not be necessary, i.e. concurrent interactions along the same session are forbidden and, hence  ...  We formalise below the notions of independent (i.e., concurrent) actions and of causal consistency.  ... 
doi:10.1016/j.jlamp.2015.03.004 fatcat:ch4cm6hoc5aptchiup7dk7kl24

Concurrent Flexible Reversibility [chapter]

Ivan Lanese, Michael Lienhardt, Claudio Antares Mezzina, Alan Schmitt, Jean-Bernard Stefani
2013 Lecture Notes in Computer Science  
In this paper, we present croll-π, a concurrent calculus featuring flexible reversibility, allowing the specification of alternatives to a computation to be used upon rollback.  ...  We show the robustness of this mechanism by encoding more complex idioms for specifying flexible reversibility, and we illustrate the benefits of our approach by encoding a calculus of communicating transactions  ...  The croll-π calculus is a conservative extension of the roll-π calculus introduced in [19] . 5 We briefly review the roll-π constructs before presenting the extension added by croll-π.  ... 
doi:10.1007/978-3-642-37036-6_21 fatcat:tp2wbjgupbfodkhz37oxwfjv54

The Challenge of Typed Expressiveness in Concurrency [chapter]

Jorge A. Pérez
2016 Lecture Notes in Computer Science  
I would like to thank Ilaria Castellani, Ornela Dardha, Mariangiola Dezani-Ciancaglini, Dimitrios Kouzapas, Hugo A. López, and Camilo Rueda for their useful feedback on previous drafts of this paper.  ...  Introduction Communication and types are increasingly relevant in (concurrent) programming.  ...  Orchard and Yoshida [46] encode PCF with an effect type system into a session π-calculus; a reverse encoding that embeds the session π-calculus into PCF with concurrency primitives is used to offer a  ... 
doi:10.1007/978-3-319-39570-8_16 fatcat:y6mx3k2dejdephkuwksc64n2ai
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