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Strong Normalisation for a Gentzen-like Cut-Elimination Procedure [chapter]

Christian Urban
2001 Lecture Notes in Computer Science  
In this paper we introduce a cut-elimination procedure for classical logic, which is both strongly normalising and consisting of local proof transformations.  ...  Inspired by work of Bloo and Geuvers concerning the λx-calculus, we shall show that a simple trick allows us to preserve this property in our cut-elimination procedure.  ...  In particular, strong normalisation of beta-reduction cannot be inferred from strong normalisation of cut-elimination.  ... 
doi:10.1007/3-540-45413-6_32 fatcat:nwatdcl5mbdojecblmazk7ekyu

An Algorithmic Interpretation of a Deep Inference System [chapter]

Kai Brünnler, Richard McKinley
2008 Lecture Notes in Computer Science  
simulation of beta-reduction.  ...  Starting from natural deduction for the conjunction-implication fragment of intuitionistic logic we design a corresponding deep inference system together with reduction rules on proofs that allow a fine-grained  ...  We equip these proof terms with reduction rules that allow us to simulate beta-reduction.  ... 
doi:10.1007/978-3-540-89439-1_34 fatcat:s2onuy4y3fh35avd64ngy3y67q

Extending the Explicit Substitution Paradigm [chapter]

Delia Kesner, Stéphane Lengrand
2005 Lecture Notes in Computer Science  
We establish the good operational behaviour of the language by means of some fundamental properties such as confluence, preservation of strong normalisation, strong normalisation of well-typed terms and  ...  step by step simulation.  ...  Moreover, λlxr enjoys all the nice properties that one expects such as confluence, strong normalisation of well-typed terms and step by step simulation of β-reduction.  ... 
doi:10.1007/978-3-540-32033-3_30 fatcat:n4xb3zldzveddnrsuoyn76amf4

Cut Elimination, Substitution and Normalisation [chapter]

Roy Dyckhoff
2014 Dag Prawitz on Proofs and Meaning  
No claim is made about the converse; ensuring that a cut-reduction system can simulate beta-reduction is tricky.  ...  Kikuchi [10] treats an aspect of the relationship between normalisation and cut-elimination, but only for implicational logic, and with a very different goal: the simulation of normalisation by cut-elimination  ...  Thanks are due to Jan von Plato, Peter Chapman, Jacob Howe, Stéphane Graham-Lengrand and Christian Urban for helpful comments and (to the last of these) for a copy of [21] prior to its publication, albeit  ... 
doi:10.1007/978-3-319-11041-7_7 fatcat:lowlu235ynafffes7xriz3i3ti

Call-by-Value -calculus and LJQ

R. Dyckhoff, S. Lengrand
2007 Journal of Logic and Computation  
In particular, we present an equational correspondence between these two calculi forming a bijection between the two sets of normal terms, and allowing reductions in each to be simulated by reductions  ...  in lambda calculus, establishing a connection between LJQ and the CBV calculus λ C of Moggi.  ...  , viz. strong normalisation, confluence and simulation of β-reduction).  ... 
doi:10.1093/logcom/exm037 fatcat:jcwtamfhvvfz7d3qdawgabflyy

Correlation length scaling laws in drift-Alfvén edge turbulence computations

S Konzett, D Reiser, A Kendl
2012 Plasma Physics and Controlled Fusion  
The effect of changes in plasma parameters, that are characteristic near or at an L-H transition in fusion edge plasmas, on fluctuation correlation lengths are analysed by means of drift-Alfven turbulence  ...  It is found that strongly sheared flows lead to the appearence of long-range correlations in electrostatic potential fluctuations parallel and perpendicular to the magnetic field.  ...  Y398, by a junior research grant from University of Innsbruck, and by the European Commission under the Contract of Association between EURATOM andÖAW carried out within the framework of the European Fusion  ... 
doi:10.1088/0741-3335/54/2/025011 fatcat:jxraf773ybac7kjvvcc6edvvne

Characterization of strong normalizability for a sequent lambda calculus with co-control

José Espírito Santo, Silvia Ghilezan
2017 Proceedings of the 19th International Symposium on Principles and Practice of Declarative Programming - PPDP '17  
of strong normalizability has been obtained before.  ...  lambdamu calculus -that is why our system has first-class "co-control".  ...  Ciência e a Tecnologia, within the project UID-MAT-00013/2013; by COST Action CA15123 -The European research network on types for programming and verification (EUTypes) via STSM; and by the Ministry of  ... 
doi:10.1145/3131851.3131867 dblp:conf/ppdp/SantoG17 fatcat:oidfojtapjfhpnbfhbxspaydoe

The Power of Closed Reduction Strategies

Sandra Alves, Maribel Fernández, Mario Florido, Ian Mackie
2007 Electronical Notes in Theoretical Computer Science  
Closed reduction strategies in the λ-calculus restrict the reduction rules: the idea is that reductions can only take place when certain terms are closed (i.e. do not contain free variables).  ...  We show that a linear System T with closed reduction offers a huge increase in expressive power over the usual linear systems, which are 'closed by construction' rather than 'closed at reduction'.  ...  Introduction To prove the correctness of the Geometry of Interaction [7] , Girard used a strategy for cut-elimination in linear logic [6] which restricts cut-elimination steps so that they can only  ... 
doi:10.1016/j.entcs.2007.02.047 fatcat:mag4honadbbqjdqo45w657mrrm

The Prismoid of Resources [chapter]

Delia Kesner, Fabien Renaud
2009 Lecture Notes in Computer Science  
For all the calculi in the prismoid we show simulation of β-reduction, confluence, preservation of β-strong normalisation and strong normalisation for typed terms.  ...  We define a framework called the prismoid of resources where each vertex is a λ-calculus with the possibility of having different explicit resources and/or explicit cut elimination based on a different  ...  For all calculi of the prismoid we show simulation of β-reduction, confluence, preservation of β-strong normalisation (PSN) and strong normalisation (SN) for typed terms.  ... 
doi:10.1007/978-3-642-03816-7_40 fatcat:cmiqlddgizeulhrecjpta7zlea

Towards a proof theory of rewriting: the simply typed 2λ-calculus

Barnaby P. Hilken
1996 Theoretical Computer Science  
Finally we use these properties as the basic definitions of a theory of categorical rewriting, and find that the expected relationships between confluence, strong normalisation and normal forms hold.  ...  The types and terms are those of the simply typed ).-calculus, and the rewrites are expressions denoting sequences of fl-reductions and g-expansions.  ...  The proof of Proposition 12 If F ~-YI: tl ~ t2: X,, F F-72:t2 => t3: X and F ~-73:t3 ~ t4: X are in if, then (72 t 72) t ~ : 71 t (~2 t 73).  ... 
doi:10.1016/s0304-3975(96)80713-4 fatcat:su5bylr2wjgcxbac2fcweht6ma

Preservation of Strong Normalisation modulo permutations for the structural lambda-calculus

Beniamino Accattoli, Delia Kesner, Henk Barendregt
2012 Logical Methods in Computer Science  
First, we prove some fundamental properties of lambda j such as confluence and preservation of beta-strong normalisation.  ...  We then complete this bisimulation with two more equations for (de)composition of substitutions and we prove that the resulting calculus still preserves beta-strong normalization.  ...  Normalisation of proofs (i.e. cut elimination) in MELL Proof-Nets is performed in particular by exponential and commutative rules.  ... 
doi:10.2168/lmcs-8(1:28)2012 fatcat:x57uwa2drnaspg7bouz2iwkjju

Gödel's system T revisited

Sandra Alves, Maribel Fernández, Mário Florido, Ian Mackie
2010 Theoretical Computer Science  
We show properties of this linear version of Gödel's T using a closed reduction strategy, and study the class of functions that can be represented.  ...  We show that a linear T with closed reduction is as powerful as T .  ...  Acknowledgements This work was partially supported by the British Council Treaty of Windsor Programme, Programa de Financiamento Plurianual, Fundação para a Ciência e Tecnologia and FEDER/POSI, and Programa  ... 
doi:10.1016/j.tcs.2009.11.014 fatcat:of7xz4qeezf45bkiosv3xisibq

The Permutative λ-Calculus [chapter]

Beniamino Accattoli, Delia Kesner
2012 Lecture Notes in Computer Science  
We prove confluence modulo the equations and preservation of beta-strong normalisation (PSN) by means of an auxiliary substitution calculus.  ...  A key point is that M-developments are defined and studied through the equational λsub-calculus, where the splitting of β-reduction in terms of dB and sub becomes crucial to allow a fine analysis of redex  ...  . → sub ) corresponds exactly to the multiplicative (resp. exponential) cut-elimination rule of Pure Proof-Nets.  ... 
doi:10.1007/978-3-642-28717-6_5 fatcat:xz2lvxc3obbgnmmp2utp5ppyym

The λ-context Calculus

Murdoch J. Gabbay, Stéphane Lengrand
2008 Electronical Notes in Theoretical Computer Science  
To do this requires several innovations, including a key insight in the confluence proof and a set of reduction rules which manages the complexity of a calculus of contexts over the 'vanilla' lambda-calculus  ...  This calculus remains extremely close in look and feel to a standard lambda-calculus with explicit substitutions, and good properties of the lambda-calculus are preserved.  ...  We note that the translation of possibly open terms of the untyped λ-calculus into the LCC preserves strong normalisation.  ... 
doi:10.1016/j.entcs.2007.09.015 fatcat:c62dmxiwcjhitlpvxg6mgydu3q

A Quick Overview on the Quantum Control Approach to the Lambda Calculus

Alejandro Díaz-Caro
2022 Electronic Proceedings in Theoretical Computer Science  
This is a summary of the last 10+ years of research in this area, starting from Arrighi and Dowek's seminal work until today.  ...  We give an overview of the quantum control line of research within the lambda calculus, ranging from untyped calculi up to categorical and realisability models.  ...  Acknowledgements The author wishes to thank Eduardo Bonelli and Mauricio Ayala-Rincón for the inclusion of this overview in LSFA 2021 as an invited talk, and for their useful comments.  ... 
doi:10.4204/eptcs.357.1 fatcat:rg5577pac5eorkven4cc3mnr5u
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