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

Yoji Akama

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

Yoji Akama

SCI - Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Conference 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 lim_t 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 language	English
Title of host publication	Computer Science Logic
Subtitle of host publication	15th International Workshop, CSL 2001 and 10th Annual Conference of the EACSL, Proceedings
Editors	Laurent Fribourg
Publisher	Springer-Verlag
Pages	399-414
Number of pages	16
ISBN (Print)	3540425543, 9783540425540
Publication status	Published - 2001 Jan 1
Event	15th 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 10 → 2001 Sep 13

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	2142
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Other

Other	15th International Workshop on Computer Science Logic, CSL 2001 and 10th Annual Conference of the European Association for Computer Science Logic, EACSL 2001
Country	France
City	Paris
Period	01/9/10 → 01/9/13

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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Cite this

Akama, Y. (2001). Limiting partial combinatory algebras towards infinitary lambda-calculi and classical logic. In L. Fribourg (Ed.), Computer Science Logic: 15th International Workshop, CSL 2001 and 10th Annual Conference of the EACSL, Proceedings (pp. 399-414). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2142). Springer-Verlag.

Limiting partial combinatory algebras towards infinitary lambda-calculi and classical logic. / Akama, Yoji.

Computer Science Logic: 15th International Workshop, CSL 2001 and 10th Annual Conference of the EACSL, Proceedings. ed. / Laurent Fribourg. Springer-Verlag, 2001. p. 399-414 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2142).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Akama, Y 2001, Limiting partial combinatory algebras towards infinitary lambda-calculi and classical logic. in L Fribourg (ed.), Computer Science Logic: 15th International Workshop, CSL 2001 and 10th Annual Conference of the EACSL, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 2142, Springer-Verlag, pp. 399-414, 15th International Workshop on Computer Science Logic, CSL 2001 and 10th Annual Conference of the European Association for Computer Science Logic, EACSL 2001, Paris, France, 01/9/10.

Akama Y. Limiting partial combinatory algebras towards infinitary lambda-calculi and classical logic. In Fribourg L, editor, Computer Science Logic: 15th International Workshop, CSL 2001 and 10th Annual Conference of the EACSL, Proceedings. Springer-Verlag. 2001. p. 399-414. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

Akama, Yoji. / Limiting partial combinatory algebras towards infinitary lambda-calculi and classical logic. Computer Science Logic: 15th International Workshop, CSL 2001 and 10th Annual Conference of the EACSL, Proceedings. editor / Laurent Fribourg. Springer-Verlag, 2001. pp. 399-414 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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