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The Scott model of PCF in univalent type theory

Published online by Cambridge University Press:  23 July 2021

Tom de Jong Open the ORCID record for Tom de Jong [Opens in a new window]
Tom de Jong*
Affiliation:
School of Computer Science, University of Birmingham, Birmingham, UK
*
Email: t.dejong@pgr.bham.ac.uk
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Abstract

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We develop the Scott model of the programming language PCF in univalent type theory. Moreover, we work constructively and predicatively. To account for the non-termination in PCF, we use the lifting monad (also known as the partial map classifier monad) from topos theory, which has been extended to univalent type theory by Escardó and Knapp. Our results show that lifting is a viable approach to partiality in univalent type theory. Moreover, we show that the Scott model can be constructed in a predicative and constructive setting. Other approaches to partiality either require some form of choice or quotient inductive-inductive types. We show that one can do without these extensions.

Keywords

Scott modelPCFunivalent mathematicstype theorylifting monadpartial map classifier
Type
Paper
Information
Mathematical Structures in Computer Science , Volume 31 , Special Issue 10: Homotopy Type Theory 2019 , November 2021 , pp. 1270 - 1300
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This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© The Author(s), 2021. Published by Cambridge University Press

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