Partial Combinatory Algebras of Functions

Notre Dame Journal of Formal Logic 52 (4):431-448 (2011)
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
Keywords sequential function   partial combinatory algebra   preorder enriched category
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