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

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. ...

##
###
Psi-Calculi in Isabelle

2015
*
Journal of automated reasoning
*

This paper presents

doi:10.1007/s10817-015-9336-2
fatcat:6xd44jmybzftljt2j3zc7kadzm
*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*. ...##
###
Proof-relevant pi-calculus

2015
*
Electronic Proceedings in Theoretical Computer Science
*

We present

doi:10.4204/eptcs.185.4
fatcat:kl7uiizvcjayfn4qk2d4cutzuu
*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*. ...##
###
From Display Calculi to Deep Nested Sequent Calculi: Formalised for Full Intuitionistic Linear Logic
[chapter]

2014
*
Lecture Notes in Computer Science
*

We present

doi:10.1007/978-3-662-44602-7_20
fatcat:hb2taxk76vbitopteimhymvmyu
*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. ...##
###
Inductive situation calculus

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 ...

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

2011
*
Logical Methods in Computer Science
*

Psi-calculi can capture

doi:10.2168/lmcs-7(1:11)2011
fatcat:u4hln7wqcrgjxa3ifoikzusr4m
*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. ...##
###
Verifying Privacy-Type Properties of Electronic Voting Protocols: A Taster
[chapter]

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. ...

##
###
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. ... We are very grateful to

*the*anonymous referees for many

*constructive*comments. ...

##
###
Weak Nominal Modal Logic
[chapter]

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*. ...

##
###
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. ... We are very grateful to

*the*anonymous referees for many

*constructive*comments. ...

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

2017
*
arXiv
*
pre-print

We present

arXiv:1604.04575v2
fatcat:2vi7l7yt7vbdvnidsmlvrgormy
*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 ...##
###
Proof-relevant π-calculus: a constructive account of concurrency and causality

2017
*
Mathematical Structures in Computer Science
*

We present

doi:10.1017/s096012951700010x
fatcat:kml5dff4gvbjjbi7y63bzd7mw4
*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 ...##
###
Resolution and type theory

1991
*
Science of Computer Programming
*

Here,

doi:10.1016/0167-6423(91)90038-y
fatcat:7m4ktl6y7rdqxk6vyqojuygd6y
*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] . ...##
###
Formalising the pi-calculus using nominal logic

2009
*
Logical Methods in Computer Science
*

We thus provide one

doi:10.2168/lmcs-5(2:16)2009
fatcat:nccxwutgvjhe5gioo7d66vgw74
*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. ...##
###
Principles of Superdeduction

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. ...

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