Filters








5,846 Hits in 3.6 sec

Paths in the lambda-calculus. Three years of communications without understanding

A. Asperti, V. Danos, C. Laneve, L. Regnier
Proceedings Ninth Annual IEEE Symposium on Logic in Computer Science  
Since the rebirth of -calculus in the late sixties, three major theoretical investigations of -reduction were undertaken: 1) L evy's analysis of families of redexes (and the associated concept of labeled  ...  All these three studies happened to make crucial (if not always explicit) use of a notion of path. Namely and respectively: legal, consistent and regular paths.  ...  algebra (see 5, 14] where this is also extended to pure lambda-calculus).  ... 
doi:10.1109/lics.1994.316048 dblp:conf/lics/AspertiDLR94 fatcat:wevgcrpvmbdrjjmlut4jgaqi5m

Lambda Obfuscation [chapter]

Pengwei Lan, Pei Wang, Shuai Wang, Dinghao Wu
2018 Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering  
In this paper, we propose a novel control obfuscation technique that uses lambda calculus to hide the original computation semantics and makes the original program more obscure to understand and reverse  ...  Our obfuscator replaces the conditional instructions with lambda calculus function calls that simulate the same behavior with a more complicated execution model.  ...  This research was supported in part by the National Science Foundation (NSF) under grant CNS-1652790, and the Office of Naval Research (ONR) under grants N00014-13-1-0175, N00014-16-1-2265, and N00014-  ... 
doi:10.1007/978-3-319-78813-5_11 fatcat:rejp26s6unejblib54ck7tad2u

Graphic Lambda Calculus

Marius Buliga
2013 Complex Systems  
I hope to convince the reader that graphic lambda calculus gives a rigorous answer to this question, being a formalism that contains, in a sense, lambda calculus, emergent algebras, and tangle diagrams  ...  Graphic lambda calculus, a visual language that can be used for representing untyped lambda calculus, is introduced and studied.  ...  Acknowledgments This work was supported by a grant of the Romanian National Authority for Scientific Research, CNCS UEFISCDI, project number PN-II-ID-PCE-2011-3-0383.  ... 
doi:10.25088/complexsystems.22.4.311 fatcat:5bocqjhennekrlnmuqmpp5lqbe

Graphic lambda calculus [article]

Marius Buliga
2013 arXiv   pre-print
We introduce and study graphic lambda calculus, a visual language which can be used for representing untyped lambda calculus, but it can also be used for computations in emergent algebras or for representing  ...  We use an n-zipper in order to clip the inputs with the output. This graph is, in fact, the following one.  ...  We may interpret the graph inside the green dotted rectangle as the currying of A, let's call him Curry(A). This graph has only one output and no inputs.  ... 
arXiv:1305.5786v2 fatcat:qpxxcqjq6zfk7olk6wot35g5nu

Disjunctive Constraint Lambda Calculi [chapter]

Matthias M. Hölzl, John N. Crossley
2005 Lecture Notes in Computer Science  
We establish a limited form of confluence for the unrestricted calculus and a stronger form for the restricted one.  ...  These calculi are the Unrestricted, and the Restricted, Disjunctive Constraint-Lambda Calculi.  ...  Path-Confluence The single-valued restricted constraint-lambda calculus was proved in [8] to be confluent so we can improve Theorem 1 for terms of the Restricted Disjunctive Constraint-Lambda Calculus  ... 
doi:10.1007/11591191_6 fatcat:c7jdspgmlbb2ldo4uyzg62mvuu

Local and global moves on locally planar trivalent graphs, lambda calculus and λ-Scale [article]

Marius Buliga
2012 arXiv   pre-print
We give a description of local and global moves on a class of locally planar trivalent graphs and we show that it contains λ-Scale calculus, therefore in particular untyped lambda calculus.  ...  Surprisingly, the beta reduction rule comes from a local "sewing" transformation of trivalent locally planar graphs.  ...  It involves a λ graph (think about the λ abstraction operation in lambda calculus) and a graph (think about the application operation in lambda calculus).  ... 
arXiv:1207.0332v1 fatcat:a2iqtotphzhinfg4qdbp3d2x4a

Page 4529 of Mathematical Reviews Vol. , Issue 96h [page]

1996 Mathematical Reviews  
Summary: “We provide a new characterization of Lévy redex- families in the A-calculus as suitable paths in the initial term of the derivation.  ...  Summary: “Lambda definability is characterized in categorical models of simply typed lambda calculus with type variables.  ... 

Atomic Lambda Calculus: A Typed Lambda-Calculus with Explicit Sharing

Tom Gundersen, Willem Heijltjes, Michel Parigot
2013 2013 28th Annual ACM/IEEE Symposium on Logic in Computer Science  
An explicit-sharing lambda-calculus is presented, based on a Curry-Howard-style interpretation of the deep inference proof formalism.  ...  The calculus preserves strong normalisation with respect to the lambdacalculus, and achieves fully lazy sharing.  ...  Acknowledgements: The authors would like to thank the anonymous referees for their helpful and insightful comments. This work was supported by the ANR-FWF project Structural.  ... 
doi:10.1109/lics.2013.37 dblp:conf/lics/GundersenHP13 fatcat:spwjke6jifasphbmqczuloxjb4

On graphic lambda calculus and the dual of the graphic beta move [article]

Marius Buliga
2013 arXiv   pre-print
While the graphic beta move corresponds to beta reduction in untyped lambda calculus, the dual graphic beta move appears in relation to emergent algebras.  ...  the graphic lambda calculus respectively.  ...  In fact, there are three important sectors of graphic lambda calculus: -untyped lambda calculus sector, which contains all graphs in GRAP H which are obtained from untyped lambda calculus terms by the  ... 
arXiv:1302.0778v1 fatcat:r7tzafts65dxvn65ki6wotdnai

Topological incompleteness and order incompleteness of the lambda calculus

Antonino Salibra
2003 ACM Transactions on Computational Logic  
A semantics of lambda calculus is (equationally) incomplete if there exists a lambda theory which is not induced by any model in the semantics.  ...  In this paper we introduce a new technique to prove in a uniform way the incompleteness of all denotational semantics of lambda calculus which have been proposed so far, including the strongly stable one  ...  ACKNOWLEDGMENTS The author wishes to thank Gordon Plotkin and the referees for helpful comments and suggestions.  ... 
doi:10.1145/772062.772067 fatcat:ptvuocqvcbe5nawqmtj2ztltyu

Term Graphs and the NP-Completeness of the Product-Free Lambek Calculus [chapter]

Timothy A. D. Fowler
2011 Lecture Notes in Computer Science  
We provide a graphical representation of proofs in the product-free Lambek calculus, called term graphs, that is related to several other proof net presentations.  ...  We use this advantage to provide an NP-completeness proof of the product-free Lambek Calculus that uses the reduction of [8] .  ...  Acknowledgements I must thank Gerald Penn for guiding this research as well as the useful comments of the three anonymous reviewers.  ... 
doi:10.1007/978-3-642-20169-1_10 fatcat:oahll5ehhje5fjypd6omobrrh4

A Note on Confluence in Typed Probabilistic Lambda Calculi

Rafael Romero, Alejandro Díaz-Caro
2022 Electronic Proceedings in Theoretical Computer Science  
We examine the effect of small modifications in probabilistic rewriting, affine variables, and strategies on the overall confluence in this strongly normalizing probabilistic calculus.  ...  While working with a lambda calculus modelling quantum computation, we found a system with probabilistic rewriting rules and strongly normalizing terms.  ...  The λ • calculus In this section we present λ • (read "lambda coin"), which is the simply typed lambda calculus extended with booleans (1 and 0), an if-then-else construction, and a coin .  ... 
doi:10.4204/eptcs.357.2 fatcat:qsagxymb25aobgnuanp25dl5ly

Lambda calculus as a workflow model

Peter M. Kelly, Paul D. Coddington, Andrew L. Wendelborn
2009 Concurrency and Computation  
We discuss how these can be modeled using lambda calculus, and how ideas from functional programming are applicable in the design of workflows.  ...  This paper explains why lambda calculus is an appropriate model for workflow representation, and how a suitably efficient implementation can provide a wide range of capabilities to developers.  ...  Lambda calculus Lambda calculus [2] is an abstract model of computation which is the theoretical foundation of functional programming.  ... 
doi:10.1002/cpe.1448 fatcat:446xuff7lfei3aa2co6kw25hwi

Sharing Continuations: Proofnets for Languages with Explicit Control [chapter]

Julia L. Lawall, Harry G. Mairson
2000 Lecture Notes in Computer Science  
introduce graph reduction technology that implements functional languages with control, such as Scheme with call/cc, where continuations can be manipulated explicitly as values, and can be optimally reduced in  ...  the sense of Lévy.  ...  We prove that the DS transformation maintains the way in which such a path traverses apply and lambda nodes.  ... 
doi:10.1007/3-540-46425-5_16 fatcat:3jevx7qevzahhehomccscbwvum

Lambda Calculus as a Workflow Model

Peter M. Kelly, Paul D. Coddington, Andrew L. Wendelborn
2008 2008 The 3rd International Conference on Grid and Pervasive Computing - Workshops  
We discuss how these can be modeled using lambda calculus, and how ideas from functional programming are applicable in the design of workflows.  ...  This paper explains why lambda calculus is an appropriate model for workflow representation, and how a suitably efficient implementation can provide a wide range of capabilities to developers.  ...  Lambda calculus Lambda calculus [2] is an abstract model of computation which is the theoretical foundation of functional programming.  ... 
doi:10.1109/gpc.workshops.2008.38 dblp:conf/gpc/KellyCW08 fatcat:usih6kyd6bhqjdsz3b5bbewcna
« Previous Showing results 1 — 15 out of 5,846 results