Filters








71 Hits in 6.0 sec

Continuation-Passing Style and Strong Normalisation for Intuitionistic Sequent Calculi

Jose Espirito Santo, Ralph Matthes, Luis Pinto, Simona Ronchi Della Rocca
2009 Logical Methods in Computer Science  
For our intuitionistic sequent calculus, we even only need "units of garbage" to be passed.  ...  Our embedding is a continuation-and-garbage-passing style translation, the inspiring idea coming from Ikeda and Nakazawa's translation of Parigot's λ_mu-calculus.  ...  The second author thanks for an invitation by that institution to Braga in October 2006 and in May 2007.  ... 
doi:10.2168/lmcs-5(2:11)2009 fatcat:33xfscvbnzgjtmvnzcioe4j3cm

Continuation-Passing Style and Strong Normalisation for Intuitionistic Sequent Calculi [chapter]

José Espírito Santo, Ralph Matthes, Luís Pinto
2007 Lecture Notes in Computer Science  
For our intuitionistic sequent calculus, we even only need "units of garbage" to be passed.  ...  Our embedding is a continuation-and-garbage-passing style translation, the inspiring idea coming from Ikeda and Nakazawa's translation of Parigot's λµ-calculus.  ...  Acknowledgements: We thank the referees for pointing out the work of Nakazawa and Tatsuta, whom we thank for an advanced copy of [19] .  ... 
doi:10.1007/978-3-540-73228-0_11 fatcat:5jyfdsaru5hhnczpjf3rvqbemq

Proving Strong Normalisation via Non-deterministic Translations into Klop's Extended lambda-Calculus

Kentaro Kikuchi, Marc Herbstritt
2013 Annual Conference for Computer Science Logic  
In the same framework we prove strong normalisation of Sørensen and Urzyczyn's cut-elimination system in intuitionistic sequent calculus.  ...  In this paper we present strong normalisation proofs using a technique of non-deterministic translations into Klop's extended λ-calculus.  ...  I would like to thank the anonymous reviewers for valuable comments. I also thank Stéphane Lengrand for valuable discussions.  ... 
doi:10.4230/lipics.csl.2013.395 dblp:conf/csl/Kikuchi13 fatcat:xspydl2wr5c5nde5ogqrbltyqa

LJQ: A Strongly Focused Calculus for Intuitionistic Logic [chapter]

Roy Dyckhoff, Stéphane Lengrand
2006 Lecture Notes in Computer Science  
LJQ is a focused sequent calculus for intuitionistic logic, with a simple restriction on the first premisss of the usual left introduction rule for implication.  ...  We discuss its history (going back to about 1950, or beyond), present the underlying theory and its applications both to terminating proof-search calculi and to call-by-value reduction in lambda calculus  ...  However, the equational theory produced by β V -conversion is shown [30] to be incomplete with respect to some canonical call-by-value semantics called Continuation Passing Style.  ... 
doi:10.1007/11780342_19 fatcat:bzzrvpy2jrhcpbpmk5lswpd4ty

Computational interpretation of classical logic with explicit structural rules [article]

Silvia Ghilezan, Pierre Lescanne, Dragisa Zunic
2012 arXiv   pre-print
From this analysis we derive strong normalisation property.  ...  We present a calculus providing a Curry-Howard correspondence to classical logic represented in the sequent calculus with explicit structural rules, namely weakening and contraction.  ...  of computational interpretations of intuitionistic and classical logic both in natural deduction and sequent-style setting.  ... 
arXiv:1203.4754v1 fatcat:ubqvhcbrx5gppeqjvbgfq66abq

Polarised Intermediate Representation of Lambda Calculus with Sums

Guillaume Munch-Maccagnoni, Gabriel Scherer
2015 2015 30th Annual ACM/IEEE Symposium on Logic in Computer Science  
We propose an untyped representation-an intermediate calculus-for thecalculus with sums, based on the following principles: 1) Computation is described as the reduction of pairs of an expression and a  ...  context; the context must be represented inside-out, 2) Operations are represented abstractly by their transition rule, 3) Positive and negative expressions are respectively eager and lazy; this polarity  ...  Many thanks to Pierre-Évariste Dagand, Olivier Danvy, Tim Griffin, Adrien Guatto, Thomas Streicher, Noam Zeilberger, and the anonymous reviewers, for their comments, criticisms and suggestions.  ... 
doi:10.1109/lics.2015.22 dblp:conf/lics/Munch-Maccagnoni15 fatcat:rsuvx3pj35ec3of7xax5nzuv4e

Monadic Translation of Intuitionistic Sequent Calculus [chapter]

José Espírito Santo, Ralph Matthes, Luís Pinto
2009 Lecture Notes in Computer Science  
Section 4 defines and proves the properties of the monadic translation and its optimized variant, and strong normalisation for λJ mse is obtained.  ...  This paper proposes and analyses a monadic translation of an intuitionistic sequent calculus.  ...  All authors were supported by the European Union FP6-2002-IST-C Coordination Action 510996 "Types for Proofs and Programs" and the first and third authors are also supported by RESCUE FCT project PTDC/  ... 
doi:10.1007/978-3-642-02444-3_7 fatcat:2mgnq6ckerftdlw7oakm4ezsha

Monadic translation of classical sequent calculus

JOSÉ ESPÍRITO SANTO, RALPH MATTHES, KOJI NAKAZAWA, LUÍS PINTO
2013 Mathematical Structures in Computer Science  
OATAO is an open access repository that collects the work of Toulouse researchers and makes it freely available over the web where possible.  ...  These embeddings are continuation-passing style (CPS) translations and, therefore, a kind of compilation.  ...  These results extend to second-order logic, with polymorphic λ-calculus as the target, giving new strong normalisation results for classical second-order logic in sequent calculus style.  ... 
doi:10.1017/s0960129512000436 fatcat:66c3hgpikrft3dyw22lbbeyeie

On Polymorphic Sessions and Functions [chapter]

Bernardo Toninho, Nobuko Yoshida
2018 Lecture Notes in Computer Science  
in System F; and (2) we extend our results to account for value and process passing, entailing strong normalisation. § 4 develops a faithful representation of inductive and coinductive session types in  ...  We show full abstraction and mutual inversion results, and derive strong normalisation of the higher-order session calculus from the encoding.  ...  The authors would like to thank the reviewers for their comments, suggestions and pointers to related works.  ... 
doi:10.1007/978-3-319-89884-1_29 fatcat:ay6ibc5edjcchjlndipak35hiy

Call-by-Value -calculus and LJQ

R. Dyckhoff, S. Lengrand
2007 Journal of Logic and Computation  
LJQ is a focused sequent calculus for intuitionistic logic, with a simple restriction on the first premiss of the usual left introduction rule for implication.  ...  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  ...  the notion of continuation and defining Continuation Passing Style translations (CPS-translations).  ... 
doi:10.1093/logcom/exm037 fatcat:jcwtamfhvvfz7d3qdawgabflyy

On Polymorphic Sessions and Functions

Bernardo Toninho, Nobuko Yoshida
2021 ACM Transactions on Programming Languages and Systems  
in System F; and (2) we extend our results to account for value and process passing, entailing strong normalisation.  ...  Leveraging the proof theoretic content of the soundness and completeness of sequent calculus and natural deduction presentations of linear logic, we develop the first mutually inverse and fully abstract  ...  We thank Domenico Ruoppolo for his detailed comments on the first version of this article; and Uwe Nestmann and Kristin Peters for their suggestions for the literature of expressiveness. The  ... 
doi:10.1145/3457884 fatcat:wfzawtubjnhp5ehhb6p2era2eu

Polarities & Focussing: a journey from Realisability to Automated Reasoning [article]

Stéphane Graham-Lengrand
2014 arXiv   pre-print
Arising from linear logic, they allow the construction of meaningful semantics for cut-elimination in classical logic, some of which relate to the Call-by-Name and Call-by-Value disciplines of functional  ...  For instance: proofs of positive formulae provide structured data, while proofs of negative formulae consume such data; focussing allows the description of the interaction between the two kinds of proofs  ...  For this we extended the focussed sequent calculus LKF into LK p (T ), equipped with the ability to polarise atoms on-the-fly and call a decision procedure specific to the background theory T .  ... 
arXiv:1412.6781v1 fatcat:sj4zl2ayu5bzfjaq76znvllsb4

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  
We study strong normalization in a lambda calculus of proof-terms with co-control for the intuitionistic sequent calculus.  ...  The characterization of strong normalization is by means of intersection types, and is obtained by analyzing the relationship with another sequent lambda calculus, without co-control, for which a characterization  ...  The authors would like to thank the anonymous referees for their valuable comments and helpful suggestions.  ... 
doi:10.1145/3131851.3131867 dblp:conf/ppdp/SantoG17 fatcat:oidfojtapjfhpnbfhbxspaydoe

A Notion of Classical Pure Type System (Preliminary version)

Gilles Barthe, John Hatcliff, Morten Heine Sørensen
1997 Electronical Notes in Theoretical Computer Science  
In classical proof theory, Girard noticed that cut-elimination in classical sequent calculus was not con uent di erent strategies for reduction gives di erent proofs in normal form, i.e. proof normalization  ...  For example, the Curry-Howard isomorphism has been exploited in the use of type theory as a framework for reasoning and computation 16, 17, 56, 68] and in the design of proof-development systems 8, 19,  ...  Section 5: Continuation-Passing Style Translation The Continuation-Passing Style (CPS) translation is a standard compilation technique for functional languages 2, 22, 83] .  ... 
doi:10.1016/s1571-0661(05)80170-7 fatcat:kugibpuzfvgcjkiasxdqeadsu4

Computation in focused intuitionistic logic

Taus Brock-Nannestad, Nicolas Guenot, Daniel Gustafsson
2015 Proceedings of the 17th International Symposium on Principles and Practice of Declarative Programming - PPDP '15  
We investigate the control of evaluation strategies in a variant of the λ-calculus derived through the Curry-Howard correspondence from LJF, a sequent calculus for intuitionistic logic implementing the  ...  In particular, standard λ-calculi as well as the call-by-push-value calculus are analysed using this framework, and we relate cut elimination for LJF to a new abstract machine subsuming well-known machines  ...  Acknowledgments This work is funded by grant 10-092309 of the Danish Council for Strategic Research to Demtech (Guenot and Gustafsson) and by the ERC Advanced Grant ProofCert (Brock-Nannestad).  ... 
doi:10.1145/2790449.2790528 dblp:conf/ppdp/Brock-Nannestad15 fatcat:4waupp7x35cltlgriy4pdo3uya
« Previous Showing results 1 — 15 out of 71 results