Notre Dame Journal of Formal Logic

Partial Combinatory Algebras of Functions

Jaap van Oosten

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Abstract

We employ the notions of "sequential function" and "interrogation" (dialogue) in order to define new partial combinatory algebra structures on sets of functions. These structures are analyzed using Longley's preorder-enriched category of partial combinatory algebras and decidable applicative structures. We also investigate total combinatory algebras of partial functions. One of the results is that every realizability topos is a geometric quotient of a realizability topos on a total combinatory algebra.

Article information

Source
Notre Dame J. Formal Logic Volume 52, Number 4 (2011), 431-448.

Dates
First available in Project Euclid: 4 November 2011

Permanent link to this document
http://projecteuclid.org/euclid.ndjfl/1320427647

Digital Object Identifier
doi:10.1215/00294527-1499381

Zentralblatt MATH identifier
05991009

Mathematical Reviews number (MathSciNet)
MR2855881

Subjects
Primary: 03B40: Combinatory logic and lambda-calculus [See also 68N18]
Secondary: 68N18: Functional programming and lambda calculus [See also 03B40]

Keywords
sequential function partial combinatory algebra preorder enriched category

Citation

van Oosten, Jaap. Partial Combinatory Algebras of Functions. Notre Dame J. Formal Logic 52 (2011), no. 4, 431--448. doi:10.1215/00294527-1499381. http://projecteuclid.org/euclid.ndjfl/1320427647.


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