Partial Combinatory Algebras of Functions
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.
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