Partial Combinatory Algebras of Functions
Logic
2009-05-19 v1
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 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.
Cite
@article{arxiv.0905.2665,
title = {Partial Combinatory Algebras of Functions},
author = {Jaap van Oosten},
journal= {arXiv preprint arXiv:0905.2665},
year = {2009}
}
Comments
17 pages