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Theoretical Computer ScienceVolume 316, Issue 1-3, 28 May 2004, Pages 49-74

Behavioural inverse limit λ-models(Conference Paper)(Open Access)

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  • aDipartimento di Informatica, Università di Torino, Corso Svizzera 185, 10149 Torino, Serbia
  • bFaculty of Engineering, University of Novi Sad, Trg D. Obradovića 6, Novi Sad 21000, Serbia
  • cÉcl. Normale Sup., 46, allé d'Italie, 69364 Lyon 07, Serbia

Abstract

We construct two inverse limit λ-models which completely characterise sets of terms with similar computational behaviours: the sets of normalising, head normalising, weak head normalising λ-terms, those corresponding to the persistent versions of these notions, and the sets of closable, closable normalising, and closable head normalising λ-terms. More precisely, for each of these sets of terms there is a corresponding element in at least one of the two models such that a term belongs to the set if and only if its interpretation (in a suitable environment) is greater than or equal to that element. We use the finitary logical description of the models, obtained by defining suitable intersection type assignment systems, to prove this. © 2004 Elsevier B.V. All rights reserved.

Author keywords

Intersection typesLambda calculusModels of lambda calculusReducibility methodStone dualities

Indexed keywords

Engineering controlled terms:Computational methodsComputer scienceInverse problemsNumerical methodsSemanticsSet theory
Engineering uncontrolled termsIntersection typesLambda calculusModels of lambda calculusReducibility methodStone dualities
Engineering main heading:Mathematical models

Funding details

Funding sponsor Funding number Acronym
1630
European Commission
See opportunities by EC		DART ST-2001-33477EC

  • 1

    ∗Corresponding author. Tel.: +39-011-670-6732; fax: +39-011-751603. E-mail addresses: [email protected] (M. Dezani-Ciancaglini), [email protected] (S. Ghilezan), [email protected] (S. Likavec). 1Partially supported by EU within the FET-Global Computing initiative, project DART ST-2001-33477, and MURST Projects COMETA and McTati. The funding bodies are not responsible for any use that might be made of the results presented here. 2Partially supported by grant 1630 “Representation of proofs with applications, classi2cation of structures and in2nite combinatorics” (of the Ministry of Science, Technology, and Development of Serbia).

  • ISSN: 03043975
  • CODEN: TCSCD
  • Source Type: Journal
  • Original language: English
  • DOI: 10.1016/j.tcs.2004.01.023
  • Document Type: Conference Paper
  • Publisher: Elsevier

  Ghilezan, S.; Dipartimento di Informatica, Università di Torino, Corso Svizzera 185, Serbia;
© Copyright 2019 Elsevier B.V., All rights reserved.

Cited by 13 documents

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(2017) Logic Journal of the IGPL
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Non-idempotent intersection types and strong normalisation
(2013) Logical Methods in Computer Science
Koletsos, G.
Intersection types and termination properties
(2012) Fundamenta Informaticae
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