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Weighted Relational Models of Typed Lambda-Calculi

Jim Laird, Giulio Manzonetto, Guy McCusker, Michele Pagani
2013 2013 28th Annual ACM/IEEE Symposium on Logic in Computer Science  
The category Rel 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  ... 
doi:10.1109/lics.2013.36 dblp:conf/lics/LairdMMP13 fatcat:5rlghyqarndr3a5lqesk2ygsru

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

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.  ...  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.  ... 
doi:10.1109/lics.2013.37 dblp:conf/lics/GundersenHP13 fatcat:spwjke6jifasphbmqczuloxjb4

Call-by-name, Call-by-value, Call-by-need, and the Linear Lambda Calculus

John Maraist, Martin Odersky, David N. Turner, Philip Wadler
1995 Electronical Notes in Theoretical Computer Science  
A n umber 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  ... 
doi:10.1016/s1571-0661(04)00022-2 fatcat:at4imbsk3vcpxaotbrndpaxp3e

Normalization for Fitch-Style Modal Calculi [article]

Nachiappan Valliappan, Fabian Ruch, Carlos Tomé Cortiñas
2022 arXiv   pre-print
Fitch-style modal 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.  ... 
arXiv:2207.12807v1 fatcat:xjvcaeor5jdv5kc5o6gqpg2dcu

Report on ICTCS 2015

Luca Aceto
2015 Bulletin of the European Association for Theoretical Computer Science  
In his talk, Ugo presented a survey 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  ... 
dblp:journals/eatcs/Aceto15g fatcat:7xtaboqqojh5tfzxxfpwyzpuim

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]

Andrew Gacek
2007 arXiv   pre-print
The intrinsic treatment 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.  ... 
arXiv:cs/0702027v1 fatcat:32j2ndyzxnciroxzn4xhwzsgea

An abstract notion of application [chapter]

Pietro Di Gianantonio, Furio Honsell
1993 Lecture Notes in Computer Science  
Many concrete notions 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.  ... 
doi:10.1007/bfb0037102 fatcat:zbqckjr4l5c3zjvzmutexmu2r4

Welcome to the Jungle: A Subjective Guide to Mobile Process Calculi [chapter]

Uwe Nestmann
2006 Lecture Notes in Computer Science  
Almost 30 years ago, the research on process 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.  ... 
doi:10.1007/11817949_4 fatcat:lrvgax7zcndafe64u2norsz2qu

The call-by-need lambda calculus

JOHN MARAIST, MARTIN ODERSKY, PHILIP WADLER
1998 Journal of functional programming  
The call-byneed 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.  ... 
doi:10.1017/s0956796898003037 fatcat:hzfbo4ki6bb4pjfuhxppuvqqw4

Foreword: special issue on term and graph rewriting

RACHID ECHAHED
2018 Mathematical Structures in Computer Science  
the former international conferences RTA (Rewriting Techniques and Applications) and TLCA (Typed Lambda Calculi and Applications).  ...  GCM (Graph Computation Models).  ...  Such infinite reductions can be used to model non-strict evaluation.  ... 
doi:10.1017/s0960129518000191 fatcat:h4bmulx6wbba7mdjbnkwmhzyti
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