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

*
Proceedings Ninth Annual IEEE Symposium on Logic in Computer Science
*

Since

doi:10.1109/lics.1994.316048
dblp:conf/lics/AspertiDLR94
fatcat:wevgcrpvmbdrjjmlut4jgaqi5m
*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*). ...##
###
Lambda Obfuscation
[chapter]

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- ...

##
###
Graphic Lambda Calculus

2013
*
Complex Systems
*

I hope to convince

doi:10.25088/complexsystems.22.4.311
fatcat:5bocqjhennekrlnmuqmpp5lqbe
*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. ...##
###
Graphic lambda calculus
[article]

2013
*
arXiv
*
pre-print

We introduce and study graphic

arXiv:1305.5786v2
fatcat:qpxxcqjq6zfk7olk6wot35g5nu
*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. ...##
###
Disjunctive Constraint Lambda Calculi
[chapter]

2005
*
Lecture Notes in Computer Science
*

We establish a limited form of confluence for

doi:10.1007/11591191_6
fatcat:c7jdspgmlbb2ldo4uyzg62mvuu
*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*...##
###
Local and global moves on locally planar trivalent graphs, lambda calculus and λ-Scale
[article]

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

arXiv:1207.0332v1
fatcat:a2iqtotphzhinfg4qdbp3d2x4a
*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*). ...##
###
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

2013
*
2013 28th Annual ACM/IEEE Symposium on Logic in Computer Science
*

An explicit-sharing

doi:10.1109/lics.2013.37
dblp:conf/lics/GundersenHP13
fatcat:spwjke6jifasphbmqczuloxjb4
*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. ...##
###
On graphic lambda calculus and the dual of the graphic beta move
[article]

2013
*
arXiv
*
pre-print

While

arXiv:1302.0778v1
fatcat:r7tzafts65dxvn65ki6wotdnai
*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*...##
###
Topological incompleteness and order incompleteness of the lambda calculus

2003
*
ACM Transactions on Computational Logic
*

A semantics of

doi:10.1145/772062.772067
fatcat:ptvuocqvcbe5nawqmtj2ztltyu
*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. ...##
###
Term Graphs and the NP-Completeness of the Product-Free Lambek Calculus
[chapter]

2011
*
Lecture Notes in Computer Science
*

We provide a graphical representation of proofs

doi:10.1007/978-3-642-20169-1_10
fatcat:oahll5ehhje5fjypd6omobrrh4
*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. ...##
###
A Note on Confluence in Typed Probabilistic Lambda Calculi

2022
*
Electronic Proceedings in Theoretical Computer Science
*

We examine

doi:10.4204/eptcs.357.2
fatcat:qsagxymb25aobgnuanp25dl5ly
*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 . ...##
###
Lambda calculus as a workflow model

2009
*
Concurrency and Computation
*

We discuss how these can be modeled using

doi:10.1002/cpe.1448
fatcat:446xuff7lfei3aa2co6kw25hwi
*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. ...##
###
Sharing Continuations: Proofnets for Languages with Explicit Control
[chapter]

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

doi:10.1007/3-540-46425-5_16
fatcat:3jevx7qevzahhehomccscbwvum
*in*...*the*sense of Lévy. ... We prove that*the*DS transformation maintains*the*way*in*which such a*path*traverses apply and*lambda*nodes. ...##
###
Lambda Calculus as a Workflow Model

2008
*
2008 The 3rd International Conference on Grid and Pervasive Computing - Workshops
*

We discuss how these can be modeled using

doi:10.1109/gpc.workshops.2008.38
dblp:conf/gpc/KellyCW08
fatcat:usih6kyd6bhqjdsz3b5bbewcna
*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. ...
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