Limiting partial combinatory algebras towards infinitary lambda-calculi and classical logic

Research output: Chapter in Book/Report/Conference proceedingConference contribution

4 Citations (Scopus)

Abstract

We will construct from every partial combinatory algebra (pca, for short) A a pca a-lim(A) s.t. (1) every representable numeric function φ(n) of a-lim(A) is exactly of the form limt ξ(t, n) with ξ(t, n) being a representable numeric function of A, and (2) A can be embedded into a-lim(A) which has a synchronous application operator. Here, a-lim(A) is A equipped with a limit structure in the sense that each element of a-lim(A) is the limit of a countable sequence of A-elements. We will discuss limit structures for A in terms of Barendregt’s range property. Moreover, we will repeat the construction lim(−) transfinite times to interpret infinitary λ-calculi. Finally, we will interpret affine type-free λμ-calculus by introducing another partial applicative structure which has an asynchronous application operator and allows a parallel limit operation.

Original languageEnglish
Title of host publicationComputer Science Logic
Subtitle of host publication15th International Workshop, CSL 2001 and 10th Annual Conference of the EACSL, Proceedings
EditorsLaurent Fribourg
PublisherSpringer-Verlag
Pages399-414
Number of pages16
ISBN (Print)3540425543, 9783540425540
Publication statusPublished - 2001 Jan 1
Event15th International Workshop on Computer Science Logic, CSL 2001 and 10th Annual Conference of the European Association for Computer Science Logic, EACSL 2001 - Paris, France
Duration: 2001 Sep 102001 Sep 13

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume2142
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other15th International Workshop on Computer Science Logic, CSL 2001 and 10th Annual Conference of the European Association for Computer Science Logic, EACSL 2001
CountryFrance
CityParis
Period01/9/1001/9/13

Keywords

  • Discontinuity
  • Infinitary lambdacalculi
  • Limiting recursive functions
  • Partial combinatory algebra
  • Realizability interpretation
  • λμ-calculus

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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