Partial Combinatory Algebras of Functions

@article{Oosten2011PartialCA,
  title={Partial Combinatory Algebras of Functions},
  author={J. V. Oosten},
  journal={Notre Dame J. Formal Log.},
  year={2011},
  volume={52},
  pages={431-448}
}
  • J. V. Oosten
  • Published 2011
  • Mathematics, Computer Science
  • Notre Dame J. Formal Log.
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 geometric quotient of a realizability topos on a total… Expand
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