2009/05/16 by Jaap van Oosten, van Oosten, Jaap · 1 citation
Computer Science · Mathematics · #03B40 #68N18 #Advanced Algebra and Logic #Computability, Logic, AI Algorithms #FOS: Mathematics #Logic (math.LO) #Logic, programming, and type systems #math.LO #msc:03B40 #msc:68N18
paper · pdf · doi:10.48550/arxiv.0905.2665
17 pages
arxiv created 2009/05/16 · openalex publication_date 2009/05/16 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 J. 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 quotient of a realizability topos on a total combinatory algebra.