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.
"Partial Combinatory Algebras of Functions." Notre Dame J. Formal Logic 52 (4) 431 - 448, 2011. https://doi.org/10.1215/00294527-1499381