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Weighted Relational Models of Typed Lambda-Calculi

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

The category Rel

doi:10.1109/lics.2013.36
dblp:conf/lics/LairdMMP13
fatcat:5rlghyqarndr3a5lqesk2ygsru
*of*sets and*relations*yields one*of*the simplest denotational semantics*of*Linear Logic (LL). It is known that Rel is the biproduct completion*of*the Boolean ring. ... We consider the generalization*of*this construction to an arbitrary continuous semiring R, producing a cpo-enriched category which is a semantics*of*LL, and its (co)Kleisli category is an adequate*model*... We demonstrate that our*weighted**relations*correctly*model*execution in this language, and go on to use PCF R as a metalanguage for quantitative*modelling**of*the execution*of*programs in PCF or : by varying ...##
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Page 2043 of Mathematical Reviews Vol. , Issue 99c
[page]

1991
*
Mathematical Reviews
*

One

*of*these*calculi*is able to embed the*lambda*calculus extended with the “-operator, with the rewrite rule yov.t(v) > t(yev.t(x)). ... Next, the authors study some restricted*calculi*for cyclic*lambda*rewrit- ing, proving confluence for them. ...##
###
Page 4858 of Mathematical Reviews Vol. , Issue 2004f
[page]

2004
*
Mathematical Reviews
*

Our work provides a more general specification

*of**lambda*lifting (and*related*op- erations) that supports flexible translation strategies, which may result in new implementation techniques. ...*model*. ...##
###
Page 6222 of Mathematical Reviews Vol. , Issue 96j
[page]

1996
*
Mathematical Reviews
*

ISBN 0-19-853840-5
The book is an introduction to

*lambda*calculus and*related*for- malisms from a computer science perspective. ... A set*of**weighted*points in general position in R¢ defines a unique regular triangulation. When the*weights*are the same, this regular triangulation is the Delaunay triangulation. ...##
###
Page 2583 of Mathematical Reviews Vol. , Issue 96e
[page]

1996
*
Mathematical Reviews
*

Bunder (5-WLG; Wollongong)
96e:03016 03B40 03B70
Ritter, Eike (4-OX-C; Oxford)
Normalization for

*typed**lambda**calculi*with explicit substitution. ... The idea behind the functional semantics is that the usual binary*relation**of*the Kripke*models*is replaced by a family*of*functions. ...##
###
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. ... Duplication*of*subterms during reduction proceeds 'atomically', i.e. on individual constructors, similar to optimal graph reduction in the style*of*Lamping. ...*Typing*the atomic*lambda*-calculus explicit substitution*calculi*, the dynamics*of*the former is in some sense orthogonal to that*of*the latter. ...##
###
Call-by-name, Call-by-value, Call-by-need, and the Linear Lambda Calculus

1995
*
Electronical Notes in Theoretical Computer Science
*

A n umber

doi:10.1016/s1571-0661(04)00022-2
fatcat:at4imbsk3vcpxaotbrndpaxp3e
*of*di erent*lambda**calculi*based on linear logic have been proposed, including work by Lafont 16], Holmstr om 14], Wadler 34{37], Abramsky 1], Mackie 19], Lincoln and Mitchell 18], Troelstra ... The linear*lambda*calculus used in this paper is a minor re nement*of*one previously presented by W adler 36,37], which is based on Girard's successor to linear logic, the Logic*of*Unity 12]. ... For con uence, the proof is similar to our proof*of*con uence for the call-by-need*lambda*calculus 24], which uses Barendregt's technique*of*marked and*weighted*redexes with a norm for*weighted*terms 5 ...##
###
Normalization for Fitch-Style Modal Calculi
[article]

2022
*
arXiv
*
pre-print

Fitch-style modal

arXiv:2207.12807v1
fatcat:xjvcaeor5jdv5kc5o6gqpg2dcu
*lambda**calculi*enable programming with necessity modalities in a*typed**lambda*calculus by extending the*typing*context with a delimiting operator that is denoted by a lock. ... We show that NbE*models*can be constructed for*calculi*that incorporate the K, T and 4 axioms*of*modal logic, as suitable instantiations*of*the possible-world semantics. ... Acknowledgements We would like to thank Andreas Abel, Thierry Coquand, and Graham Leigh for their feedback on earlier versions*of*this work. ...##
###
Report on ICTCS 2015

2015
*
Bulletin of the European Association for Theoretical Computer Science
*

In his talk, Ugo presented a survey

dblp:journals/eatcs/Aceto15g
fatcat:7xtaboqqojh5tfzxxfpwyzpuim
*of*the state*of*the art in the study*of*probabilistic*lambda*-*calculi*, focusing on some*of*his recent results on inductive and coinductive techniques for reasoning about ... In her talk, Ornela offered an accessible overview*of*the main contributions*of*her thesis, in which she developed techniques based on*types*and*type*systems for the verification*of*correctness, consistency ... One*of*the contributed papers, 'Bounds and Fixed-Parameter Algorithms for*Weighted*Improper Coloring', was authored by Bjarki Ágúst Gudmundsson, Tómas Ken Magnússon, and Björn Orri Saemundsson, who just ...##
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Page 417 of Mathematical Reviews Vol. , Issue 91A
[page]

1991
*
Mathematical Reviews
*

One

*of*Curien’s systems, CCL f, which corresponds to the*type*-free*lambda*calculus with coupling, is not confluent. ... Curien introduced rewriting systems*of*categorical combi- nators, inspired by the categorical semantics*of**lambda**calculi*[the author, Inform. and Control 69 (1986), no. 1, 188-254; MR 88f:03012]. ...##
###
The Suspension Calculus and its Relationship to Other Explicit Treatments of Substitution in Lambda Calculi
[article]

2007
*
arXiv
*
pre-print

The intrinsic treatment

arXiv:cs/0702027v1
fatcat:32j2ndyzxnciroxzn4xhwzsgea
*of*binding in the*lambda*calculus makes it an ideal data structure for representing syntactic objects with binding such as formulas, proofs,*types*, and programs. ... In this paper we present the suspension calculus, an explicit treatment*of*meta level binding in the*lambda*calculus. ... In order to balance this, we assign*lambdas*a*weight*based on the number*of*suspensions in which they are embedded. ...##
###
An abstract notion of application
[chapter]

1993
*
Lecture Notes in Computer Science
*

Many concrete notions

doi:10.1007/bfb0037102
fatcat:zbqckjr4l5c3zjvzmutexmu2r4
*of*function application, suitable for interpreting*typed**lambda**calculi*with recursive*types*, have been introduced in the literature. ... Applicative exponential structures can be used for*modeling*various forms*of*non-deterministic operators. ... More precisely these structures are rich enough to*model*the behavior*of*application in*typed*l-*calculi*with recursive*types*and appropriate constructors, destructors and fixed point operators. ...##
###
Welcome to the Jungle: A Subjective Guide to Mobile Process Calculi
[chapter]

2006
*
Lecture Notes in Computer Science
*

Almost 30 years ago, the research on process

doi:10.1007/11817949_4
fatcat:lrvgax7zcndafe64u2norsz2qu
*calculi*gained a lot*of*momentum with the invention*of*ACP, CCS and CSP. ... The original Pi Calculus arose out*of*a reformulation and extension*of*CCS. In turn, it boosted the invention and study*of*a whole zoo*of*further process*calculi*. ... Jos Baeten and Holger Hermanns for discussing*related*issues at the social event*of*CONCUR 2001. ...##
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The call-by-need lambda calculus

1998
*
Journal of functional programming
*

The call-byneed

doi:10.1017/s0956796898003037
fatcat:hzfbo4ki6bb4pjfuhxppuvqqw4
*lambda*calculus is confluent, has a notion*of*standard reduction, and entails the same observational equivalence*relation*as the call-by-name calculus. ... We present a calculus that captures the operational semantics*of*call-by-need. ... Turner and a number*of*anonymous referees for valuable comments and discussions. ...##
###
Foreword: special issue on term and graph rewriting

2018
*
Mathematical Structures in Computer Science
*

the former international conferences RTA (Rewriting Techniques and Applications) and TLCA (

doi:10.1017/s0960129518000191
fatcat:h4bmulx6wbba7mdjbnkwmhzyti
*Typed**Lambda**Calculi*and Applications). ... GCM (Graph Computation*Models*). ... Such infinite reductions can be used to*model*non-strict evaluation. ...
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