Notre Dame Journal of Formal Logic

Partial Combinatory Algebras of Functions

Jaap van Oosten

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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

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

First available in Project Euclid: 4 November 2011

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

sequential function partial combinatory algebra preorder enriched category


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

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