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The Power of Linear Functions [chapter]

Sandra Alves, Maribel Fernández, Mário Florido, Ian Mackie
2006 Lecture Notes in Computer Science  
The linear lambda calculus is very weak in terms of expressive power: in particular, all functions terminate in linear time.  ...  In this paper we consider a simple extension with Booleans, natural numbers and a linear iterator.  ...  Strong normalisation for System L is a consequence of strong normalisation for System T . We start by defining a translation from System L into System T . Definition 3.  ... 
doi:10.1007/11874683_8 fatcat:w45qarlcfncefdvhpm4zzlwsxi

Gödel's system T revisited

Sandra Alves, Maribel Fernández, Mário Florido, Ian Mackie
2010 Theoretical Computer Science  
Surprisingly, this linear calculus offers a huge increase in expressive power over previous linear versions of T , which are 'closed at construction' rather than 'closed at reduction'.  ...  The linear lambda calculus, where variables are restricted to occur in terms exactly once, has a very weak expressive power: in particular, all functions terminate in linear time.  ...  Acknowledgements This work was partially supported by the British Council Treaty of Windsor Programme, Programa de Financiamento Plurianual, Fundação para a Ciência e Tecnologia and FEDER/POSI, and Programa  ... 
doi:10.1016/j.tcs.2009.11.014 fatcat:of7xz4qeezf45bkiosv3xisibq

A nonstandard standardization theorem

Beniamino Accattoli, Eduardo Bonelli, Delia Kesner, Carlos Lombardi
2014 Proceedings of the 41st ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages - POPL '14  
This paper focuses on standardization for the linear substitution calculus, a calculus with ES capable of mimicking reduction in λcalculus and linear logic proof-nets.  ...  For the latter, proof-nets can be formalized by means of a simple equational theory over the linear substitution calculus.  ...  The linear substitution calculus enjoys all the properties required of calculi with ES (including simulation of β-reduction, preservation of strong normalisation, confluence on terms and metaterms and  ... 
doi:10.1145/2535838.2535886 dblp:conf/popl/AccattoliBKL14 fatcat:gjgrgun6hbf2nguwm5tf3tyr5a

A Faithful and Quantitative Notion of Distant Reduction for Generalized Applications (Long Version) [article]

José Espírito Santo
2022 arXiv   pre-print
Our calculus relates to explicit substitution calculi by means of a translation between the two formalisms which is faithful, in the sense that it preserves strong normalization.  ...  We introduce a call-by-name lambda-calculus λ J with generalized applications which integrates a notion of distant reduction that allows to unblock β-redexes without resorting to the permutative conversions  ...  As such, we expect the dynamic behavior of our calculus to be faithful to explicit substitutions. Such translation, however, does not in general preserve strong normalization.  ... 
arXiv:2201.04156v1 fatcat:jxy6cuwxzfa5liwnqnv3uztkdq

A Light Modality for Recursion [article]

Paula Severi
2018 arXiv   pre-print
The typing discipline guarantees normalisation and can be transformed into an algorithm which infers the type of a program.  ...  This shifts the burden of controlling recursion from the programmer to the compiler. To do this, we introduce a typed lambda calculus a la Curry with a silent modality and guarded recursive types.  ...  I am grateful to Mariangiola Dezani-Ciancaglini, the anonymous reviewers of FOSSACS 2017 and LMCS for their useful suggestions, which led to substantial improvements.  ... 
arXiv:1801.00285v4 fatcat:leedclaokrbuhescocksmwgwqq

Cartesian closed bicategories: type theory and coherence [article]

Philip Saville
2020 arXiv   pre-print
Fiore's categorical analysis of normalisation-by-evaluation, I then prove a normalisation result which entails the coherence theorem for cartesian closed bicategories.  ...  For the second, which is the central preoccupation of this thesis, the proof strategy has two parts: the construction of a type theory, and the proof that it satisfies a form of normalisation I call "local  ...  On the other hand, biclones provide a categorical description of certain kinds of explicit substitution; possible connections with the categorical semantics of the simply-typed lambda calculus with explicit  ... 
arXiv:2007.00624v1 fatcat:lz5ssbkjdjamrdojhml7q3k65y

Exceptional asynchronous session types: session types without tiers

Simon Fowler, Sam Lindley, J. Garrett Morris, Sára Decova
2019 Proceedings of the ACM on Programming Languages (PACMPL)  
We define a core calculus which satisfies preservation and progress properties, is deadlock free, confluent, and terminating.  ...  Reuse of s allows a (username, password) pair to be sent along the same endpoint twice, violating the fundamental property of session fidelity, which states that in a well-typed program, communication  ...  This work was supported by EPSRC grants EP/L01503X/1 (EPSRC CDT in Pervasive Parallelism) and EP/K034413/1 (From Data Types to Session Types-A Basis for Concurrency and Distribution), and an LFCS internship  ... 
doi:10.1145/3290341 fatcat:l4rvsm5jfjfdnnnbppo5vzzotq

LFTOP: An LF-Based Approach to Domain-Specific Reasoning

Jian-Min Pang, Paul Callaghan, Zhao-Hui Luo
2005 Journal of Computer Science and Technology  
Many type theorists want to extend uses of type theory to more domains, and believe that the methods, ideas, and technology of type theory can have a beneficial effect for computer assisted reasoning in  ...  Abstract Specialized vocabulary, notations and inference rules tailored for the description, analysis and reasoning of a domain is very important for the domain.  ...  ., 1991] gave an example of a system called -Xa by using explicit substitutions. This calculus evaluates A-terms which may include unevaluated substitutions.  ... 
doi:10.1007/s11390-005-0526-y fatcat:u67u3mr4jvgjfomcepekpffl5a

Analytical Inductive Functional Programming [chapter]

Emanuel Kitzelmann
2009 Lecture Notes in Computer Science  
Acknowledgement The author would like to thank anonymous reviewers for their constructive and useful comments on the previous version of the paper.  ...  are made, which are made explicit in our formulation.  ...  ||M || t = 2 If substitutions preserve the level value of a CHR constraint, we call this constraint rigid w.r.t. the level mapping. Definition 5 (Rigidity).  ... 
doi:10.1007/978-3-642-00515-2_7 fatcat:r3xkzawlibfcpluopvlz7ukp4y

Categorical and Algebraic Aspects of the Intuitionistic Modal Logic $\operatorname{IEL}^{-}$ and its predicate extensions [article]

Daniel Rogozin
We also provide a categorical interpretation of this modal lambda calculus considering coalgebras associated with a monoidal functor on a cartesian closed category.  ...  We construct the modal lambda calculus which is Curry-Howard isomorphic to ${\bf IEL}^{-}$ as the type-theoretical representation of applicative computation widely known in functional programming.  ...  Some of the results were presented at the conference Logical Foundations of Computer Science 2020, Miami and the Computational Logic Seminar (The Graduate Centre, City University of New York).  ... 
doi:10.48550/arxiv.2005.01135 fatcat:msskvk7fmrc4vhumvl3fi7rulq

Coming to terms with modal logic : on the interpretation of modalities in typed lambda-calculus [article]

VAJ Tijn Borghuis, JCM Jos Baeten, HC Harry Bunt, RP Rob Nederpelt
Strong normalisation Using theerasure mapping 'I I' defined earlier, which preserves ,6-redexes and typeability, we can proveStrong Normalisation for MPTS13 directly from the Strong Normalis~tion of PTS13  ...  Barendregt noticed that many of the existing systems of lambda calculus with explicit typing could be uniformly reprcsented in a framework which is parametrized with respec:t to these derivation rules  ...  secoud step in proving necessity of identity for K , substitution by =-elim, also involves more work tha n its natura!  ... 
doi:10.6100/ir427575 fatcat:mj6yvuvx5neyxk4sp2psy7pjpq

Vol. 3, No. 2 (Full Issue)

2004 Journal of Modern Applied Statistical Methods  
Three areas are appropriate for JMASM: (1) development or study of new statistical tests or procedures, or the comparison of existing statistical tests or procedures, using computerintensive Monte Carlo  ...  , bootstrap, jackknife, or resampling methods, (2) development or study of nonparametric, robust, permutation, exact, and approximate randomization methods, and (3) applications of computer programming  ...  routines could be a handy addition to a practitioner's set of tools given the growing interest in R.  ... 
doi:10.22237/jmasm/1099267200 fatcat:qnwt3jqxh5cx5bzccudf7fmvyi

Machine Learning [chapter]

2014 Encyclopedia of Social Network Analysis and Mining  
Reasonable efforts have been made to publish reliable data and information, but the author and publisher cannot assume responsibility for the validity of all materials or the consequences of their use.  ...  The authors and publishers have attempted to trace the copyright holders of all material reproduced in this publication and apologize to copyright holders if permission to publish in this form has not  ...  The Curse of Dimensionality The curse of dimensionality is a very strong name, so you can probably guess that it is a bit of a problem.  ... 
doi:10.1007/978-1-4614-6170-8_100067 fatcat:dmen3wa2gzd6jnzlxgudyscbm4

Computability in constructive type theory [article]

Yannick Forster, Universität Des Saarlandes
We then identify the weak call-by-value λ-calculus L as sweet spot for programming in a model of computation.  ...  We give a formalised and machine-checked account of computability theory in the Calculus of Inductive Constructions (CIC), the constructive type theory underlying the Coq proof assistant.  ...  Weak Call-by-Value Lambda Calculus as a Model of Computation in Coq. Def. closed term Def.  ... 
doi:10.22028/d291-35758 fatcat:deb5muacebhsnnmk5p25mgc7ia

Abstract interpretation and partition refinement for model checking [article]

DR Dennis Dams, JCM Jos Baeten, W Werner Damm, RT Rob Gerth
-Eindhoven : Eindhoven University of Technology. -Ill. Thesis Technische Universiteit Eindhoven. -With index, ref. -With summary in Dutch.  ...  and existential fragments of the µ,-calculus, while for the full µ,-calculus only a strong-preservation result is given.  ...  * substituted for L).  ... 
doi:10.6100/ir462072 fatcat:3cqx6okcubajldzfnd3v5l2nv4
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