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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