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A full formalisation of π-calculus theory in the calculus of constructions [chapter]

Daniel Hirschkoff
1997 Lecture Notes in Computer Science  
A formalisation of -calculus in the Coq system is presented.  ...  Based on a de Bruijn notation for names, our implementation exploits the mechanisation of some proof techniques described by Sangiorgi in San95b] to derive several results of classical -calculus theory  ...  Acknowledgments We thank Davide Sangiorgi and Ren e Lalement for enlightening discussions about this work, as well as the anonymous referees for some very useful comments.  ... 
doi:10.1007/bfb0028392 fatcat:swqe46tw65elrcwwubibrmzbwy

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  ...  To our knowledge, this is the most extensive formalisation of process calculi mechanised in a proof assistant to date.  ...  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

Proof-relevant pi-calculus

Roly Perera, James Cheney
2015 Electronic Proceedings in Theoretical Computer Science  
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  ...  Formalisations have been undertaken in a variety of systems, primarily focusing on well-studied (and challenging) properties such as the theory of process bisimulation.  ...  Prior formalisations have typically considered the syntax, semantics (usually via a variation on labelled transitions), and bisimulation theory of the π-calculus.  ... 
doi:10.4204/eptcs.185.4 fatcat:kl7uiizvcjayfn4qk2d4cutzuu

From Display Calculi to Deep Nested Sequent Calculi: Formalised for Full Intuitionistic Linear Logic [chapter]

Jeremy E. Dawson, Ranald Clouston, Rajeev Goré, Alwen Tiu
2014 Lecture Notes in Computer Science  
We present a formalisation of this methodology in the case of Full Intuitionistic Linear Logic (FILL), which is multiplicative intuitionistic linear logic extended with par.  ...  Proof theory for a logic with categorical semantics can be developed by the following methodology: define a sound and complete display calculus for an extension of the logic with additional adjunctions  ...  Formalising Display Calculi Our formalisation of the display calculus BiILLdc is very similar to that in [7] , so we shall not give full details here.  ... 
doi:10.1007/978-3-662-44602-7_20 fatcat:hb2taxk76vbitopteimhymvmyu

Inductive situation calculus

Marc Denecker, Eugenia Ternovska
2007 Artificial Intelligence  
The inductive approach allows us to solve the ramification problem for the situation calculus in a uniform and modular way.  ...  In the NMID-axiomatisation of the situation calculus, fluents and causality predicates are defined by simultaneous induction on the well-founded poset of situations.  ...  Second, we illustrate the use of our recently developed modularity techniques for NMID-logic in order to translate a theory of the inductive situation calculus into a classical logic theory of Reiter's  ... 
doi:10.1016/j.artint.2007.02.002 fatcat:eshson5fzbflvpen4gyiwjz2tm

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  
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,  ...  These can be transmitted between processes and their names can be statically scoped as in the standard pi-calculus.  ...  We have earlier [BP07] formalised a substantial part of the pi-calculus meta-theory in Isabelle. This section will cover the main extensions needed to formalise the framework for psi-calculi.  ... 
doi:10.2168/lmcs-7(1:11)2011 fatcat:u4hln7wqcrgjxa3ifoikzusr4m

Verifying Privacy-Type Properties of Electronic Voting Protocols: A Taster [chapter]

Stéphanie Delaune, Steve Kremer, Mark Ryan
2010 Lecture Notes in Computer Science  
In this paper we report on some of our recent efforts in using the applied pi calculus to model and analyse properties of electronic elections.  ...  However, protocols that were designed to satisfy privacy or receipt-freeness may not do so in the presence of corrupt officials.  ...  Thanks also to the editors of this volume for detailed comments about the presentation, which helped us improve the readability.  ... 
doi:10.1007/978-3-642-12980-3_18 fatcat:6g6q4udfvjhupopsslpoii4htm

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.  ...  We are very grateful to the anonymous referees for many constructive comments.  ... 
arXiv:1904.02564v3 fatcat:ttnxwh57grajbn7yyx2d6frxjy

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.  ...  There are several weak HMLs for variants of the pi-calculus.  ... 
doi:10.1007/978-3-319-60225-7_13 fatcat:7vggx4l5mvcitdijzsatardi24

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.  ...  We are very grateful to the anonymous referees for many constructive comments.  ... 
doi:10.23638/lmcs-17(1:6)2021 fatcat:g6xm65ck2jh7xcv4fjbzuqmfny

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

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.  ...  In the π-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  ... 
doi:10.1017/s096012951700010x fatcat:kml5dff4gvbjjbi7y63bzd7mw4

Resolution and type theory

Leen Helmink
1991 Science of Computer Programming  
Here, the method is presented for the Calculus of Constructions. To illustrate the method, a full derivation example is included.  ...  , e.g. systems in the families of AUTOMATH [6], Martin-Liif [25], the Calculus of Constructions [9], LF [16], Elf [29].  ...  Finally, the author wants to thank Henk Barendregt, for many stimulating and clarifying discussions. A previous version of this article appeared as [20] .  ... 
doi:10.1016/0167-6423(91)90038-y fatcat:7m4ktl6y7rdqxk6vyqojuygd6y

Formalising the pi-calculus using nominal logic

Jesper Bengtson, Joachim Parrow, Helmut Seidl
2009 Logical Methods in Computer Science  
We thus provide one of the most extensive formalisations of a process calculus ever done inside a theorem prover.  ...  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 would also like to thank the anonymous referees for their many helpful and constructive comments.  ... 
doi:10.2168/lmcs-5(2:16)2009 fatcat:nccxwutgvjhe5gioo7d66vgw74

Principles of Superdeduction

Paul Brauner, Clement Houtmann, Claude Kirchner
2007 22nd Annual IEEE Symposium on Logic in Computer Science (LICS 2007)  
In predicate logic, the proof that a theorem P holds in a theory Th is typically conducted in natural deduction or in the sequent calculus using all the information contained in the theory in a uniform  ...  Focusing on the sequent calculus, this paper presents and studies the dual concept where the theory is used to enrich the deduction system with new deduction rules in a systematic, correct and complete  ...  Modulo meetings and the Protheo team for many interactions.  ... 
doi:10.1109/lics.2007.37 dblp:conf/lics/BraunerHK07 fatcat:uez7vdqlbvh3jg5272onixx3rm
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