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Proof-relevant π-calculus: a constructive account of concurrency and causality
[article]
2017
arXiv
pre-print
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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
2017
Mathematical Structures in Computer Science
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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 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
2015
Electronic Proceedings in Theoretical Computer Science
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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
2016
Theoretical Computer Science
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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
2004
Theoretical Computer Science
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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
2010
Theoretical Computer Science
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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]
2004
Lecture Notes in Computer Science
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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]
2012
Lecture Notes in Computer Science
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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
2009
The Journal of Logic and Algebraic Programming
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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
2005
Theoretical Computer Science
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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]
2016
arXiv
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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
2016
International Conference on Concurrency Theory
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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
2015
Journal of Logical and Algebraic Methods in Programming
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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]
2013
Lecture Notes in Computer Science
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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]
2016
Lecture Notes in Computer Science
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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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