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Graphic Lambda Calculus

2013
*
Complex Systems
*

Graphs

doi:10.25088/complexsystems.22.4.311
fatcat:5bocqjhennekrlnmuqmpp5lqbe
*and*Moves*An*oriented graph is*a*pair HV, EL, with V*the*set*of*nodes*and*E Õ V*ä*V*the*set*of*edges. ... 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 ... 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

arXiv:1305.5786v2
fatcat:qpxxcqjq6zfk7olk6wot35g5nu
*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 ... Reidemeister moves*of*locally planar tangle diagrams. ... 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. ...##
###
Demonstrating Lambda Calculus Reduction
[chapter]

2002
*
Lecture Notes in Computer Science
*

We show how to simply

doi:10.1007/3-540-36377-7_19
fatcat:lvhipzyr2nazjhkungdahil5fe
*and*efficiently trace such reductions,*and*use this in*a*web-based*lambda**calculus*reducer available at http://www.dina.kvl.dk/˜sestoft/lamreduce/ . ... We describe*lambda**calculus*reduction strategies, such as call-by-value, call-by-name, normal order,*and*applicative order, using big-step operational semantics. ... Landin defined*the*semantics*of*programming languages in terms*of**the**lambda**calculus*[11] ,*and*gave*a*call-by-value*interpreter*for it:*the*secd-machine [10] . ...##
###
Demonstrating Lambda Calculus Reduction

2001
*
Electronical Notes in Theoretical Computer Science
*

We show how to simply

doi:10.1016/s1571-0661(04)80973-3
fatcat:usjdjt53a5cbnkeh4g4n4qeit4
*and*efficiently trace such reductions,*and*use this in*a*web-based*lambda**calculus*reducer available at http://www.dina.kvl.dk/˜sestoft/lamreduce/ . ... We describe*lambda**calculus*reduction strategies, such as call-by-value, call-by-name, normal order,*and*applicative order, using big-step operational semantics. ... Landin defined*the*semantics*of*programming languages in terms*of**the**lambda**calculus*[11] ,*and*gave*a*call-by-value*interpreter*for it:*the*secd-machine [10] . ...##
###
The Safe Lambda Calculus

2009
*
Logical Methods in Computer Science
*

In this paper, we introduce

doi:10.2168/lmcs-5(1:3)2009
fatcat:xo2amjpnyjewhoebjgdmrkjtpe
*the*safe*lambda**calculus*, which is obtained by transposing (*and*generalizing)*the*safety condition to*the*setting*of**the*simply-typed*lambda**calculus*. ... We also propose*an*adequate notion*of**beta*-reduction that preserves safety. ... We thank Ugo dal Lago for*the*insightful discussions we had during his visit at*the*Oxford University Computing Laboratory in March 2008,*and**the*anonymous referees for helpful comments. ...##
###
Continuity and Discontinuity in Lambda Calculus
[chapter]

2005
*
Lecture Notes in Computer Science
*

As

doi:10.1007/11417170_27
fatcat:wf5s5b6r2ndfhadzfgokgrktiu
*a*first application, we prove that there is*an*injective embedding from*the*infinitary*lambda**calculus**of**the*∞η-Böhm trees in D∞. ... This paper studies continuity*of**the*normal form*and**the*context operators as functions in*the*infinitary*lambda**calculus*. ... We thank Vincent van Oostrom*and**the*referees for their useful comments, Mariangiola Dezani-Ciancaglini for her knowledge*and*inspiration, Simona Ronchi della Rocca for telling us*the*solution*of**a*key ...##
###
Categorical completeness results for the simply-typed lambda-calculus
[chapter]

1995
*
Lecture Notes in Computer Science
*

We investigate, in

doi:10.1007/bfb0014068
fatcat:dbbegn55lrhsxgmxiilddv344e
*a*categorical setting, some completeness properties*of**beta*-eta conversion between closed terms*of**the*simplytyped*lambda**calculus*. ...*A*cartesian-closed category is said to be complete if, for any two unconvertible terms, there is some*interpretation**of**the**calculus*in*the*category that distinguishes them. ... Acknowledgements I thank Aurelio Carboni, Eugenio Moggi*and*Pino Rosolini for useful feedback when I presented this work in Genoa. This research was carried out under*an*EPSRC postdoctoral fellowship. ...##
###
Strict Ideal Completions of the Lambda Calculus

2018
*
International Conference on Rewriting Techniques and Applications
*

*The*infinitary

*lambda*calculi pioneered by Kennaway et al. extend

*the*basic

*lambda*

*calculus*by metric completion to infinite terms

*and*reductions. ... In this paper we develop

*a*corresponding theory

*of*infinitary

*lambda*calculi based on ideal completion instead

*of*metric completion. ...

*the*

*Lambda*

*Calculus*from Blom [9] , which will serve as mediator between metric completion

*and*ideal completion. 1

*A*

*lambda*tree is

*a*(possibly infinite)

*labelled*tree where

*a*

*label*λ indicates abstraction ...

##
###
On Constructor Rewrite Systems and the Lambda Calculus

2012
*
Logical Methods in Computer Science
*

We prove that orthogonal constructor term rewrite systems

doi:10.2168/lmcs-8(3:12)2012
fatcat:b6jjp5g6nvcirmndn4i7iy3iru
*and**lambda*-*calculus*with weak (i.e., no reduction is allowed under*the*scope*of**a**lambda*-abstraction) call-by-value reduction can simulate each ... In particular, weak call-by- value*beta*-reduction can be simulated by*an*orthogonal constructor term rewrite system in*the*same number*of*reduction steps. ... Given*a*signature Σ,*a**labelled*graph over Σ consists*of**a*directed acyclic graph together with*an*ordering on*the*outgoing edges*of*each node*and**a*(partial)*labelling**of*nodes with symbols from Σ such ...##
###
An Infinitary Affine Lambda-Calculus Isomorphic to the Full Lambda-Calculus

2012
*
2012 27th Annual IEEE Symposium on Logic in Computer Science
*

This paper proposes

doi:10.1109/lics.2012.57
dblp:conf/lics/Mazza12
fatcat:ldqkg5sxyzb75lfgmanlhbwsl4
*a*technical realization*of*this idea:*an*affine*lambda*-*calculus*is introduced, based on*a*fragment*of*intuitionistic multiplicative linear logic;*the**calculus*is endowed with*a*notion ...*of*distance making*the*set*of*terms*an*incomplete metric space;*the*completion*of*this space is shown to yield*an*infinitary affine*lambda*-*calculus*, whose quotient under*a*suitable partial equivalence ... Acknowledgments We are thankful to Michele Pagani*and*Rune Bak for interesting discussions on*the*subject*of*this paper. ...##
###
Polymorphic lambda calculus and subtyping

2002
*
Theoretical Computer Science
*

We present

doi:10.1016/s0304-3975(00)00333-9
fatcat:ubfrfxrhr5dudpgcutqaauhj2i
*a*denotational model for F ,*the*extension*of*second-order*lambda**calculus*with subtyping deÿned in Cardelli*and*Wegner (ACM Comput. Surveys 17(4) (1985) 471-522.) ... Types are*interpreted*as arbitrary cpos*and*elements*of*types as natural transformations. We prove*the*soundness*of*our model with respect to*the*equational theory*of*F (Cardelli et al. ... is*the*at cpo*of*record*labels*. ...##
###
Normalization by Evaluation for Call-By-Push-Value and Polarized Lambda Calculus

2019
*
Proceedings of the 21st International Symposium on Principles and Practice of Programming Languages 2019 - PPDP '19
*

We further discuss different implementations

doi:10.1145/3354166.3354168
dblp:conf/ppdp/0001S19
fatcat:hyx7bh5jebgdrirboktvpxxoeu
*of**the*monad*and*their relation to existing normalization proofs for*lambda*-*calculus*with sums. ... We observe that normalization by evaluation for simply-typed*lambda*-*calculus*with weak coproducts can be carried out in*a*weak bi-cartesian closed category*of*presheaves equipped with*a*monad that allows ... Moggi's studies were continued by Levy [19] who designed*the*call-by-push-value (CBPV)*lambda*-*calculus*to embed both*the*CBN*and*CBV*lambda**calculus*. ...##
###
A Calculus for Modeling Software Components
[chapter]

2003
*
Lecture Notes in Computer Science
*

We have identified

doi:10.1007/978-3-540-39656-7_14
fatcat:tw7cbheuvnetrhe3eeytzxeifi
*a*number*of*key features*and*mechanisms for expressing composable software,*and*propose*a**calculus*for modeling components, based on*the*asynchronous π*calculus*extended with explicit ... This*calculus*serves as*a*semantic foundation*and**an*executable abstract machine for Piccola,*an*experimental composition language. ... Acknowledgments We gratefully acknowledge*the*financial support*of**the*Swiss National Science Foundation for projects No. 20-61655.00, "Meta-models*and*Tools for Evolution Towards Component Systems",*and*...##
###
Algebras and coalgebras in the light affine Lambda calculus

2015
*
SIGPLAN notices
*

Their use permits to better structure

doi:10.1145/2858949.2784759
fatcat:ezlynnzdxrepfpxnj3qtddwj2q
*the*computations*and*also to enhance*the*expressivity*of**a*language or*of**a*proof system. ...*Algebra**and*coalgebra are widely used to model data types in functional programming languages*and*proof assistants. ...*The*Light Affine*Lambda**Calculus**The*Light Affine*Lambda**Calculus*is*the*affine version*of**the*Light Linear*Lambda**Calculus*[39]*and*provide*a*concrete syntax for Intuitionistic Light Affine Logic [ ...##
###
The λ-calculus in the π-calculus

2011
*
Mathematical Structures in Computer Science
*

*The*power

*of*

*the*approach is demonstrated by applying it to generate

*an*encoding

*of*

*the*full

*lambda*

*calculus*in

*the*π-

*calculus*. ... -

*The*intensional equalities

*of*source models are

*interpreted*by

*the*observational equivalence

*of*

*the*π-

*calculus*.

*The*quality

*of*

*an*

*interpretation*is judged by

*a*full abstraction property. ... We are also grateful to

*the*two anonymous referees for their detailed comments on

*a*previous version

*of*this paper. ...

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