The Clocks They Are Adjunctions: Denotational Semantics for Clocked Type Theory

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Clocked Type Theory (CloTT) is a type theory for guarded recursion useful for programming with coinductive types, allowing productivity to be encoded in types, and for reasoning about advanced programming language features using an abstract form of step-indexing. CloTT has previously been shown to enjoy a number of syntactic properties including strong normalisation, canonicity and decidability of type checking. In this paper we present a denotational semantics
for CloTT useful, e.g., for studying future extensions of CloTT with constructions such as path types.
The main challenge for constructing this model is to model the notion of ticks used in CloTT for coinductive reasoning about coinductive types. We build on a category previously used to model guarded recursion, but in this category there is no object of ticks, so tick-assumptions in a context can not be modelled using standard tools. Instead we show how ticks can be modelled using adjoint functors, and how to model the tick constant using a semantic substitution.
Original languageEnglish
Title of host publication3rd International Conference on Formal Structures for Computation and Deduction (FSCD 2018)
Number of pages17
PublisherSchloss Dagstuhl--Leibniz-Zentrum für Informatik
Publication date2018
Article number23
ISBN (Print)978-3-95977-077-4
Publication statusPublished - 2018
EventInternational Conference on Formal Structures for Computation and Deduction - Oxford, United Kingdom
Duration: 9 Jul 201812 Jul 2018
Conference number: 3


ConferenceInternational Conference on Formal Structures for Computation and Deduction
LandUnited Kingdom
SeriesLeibniz International Proceedings in Informatics (LIPIcs)

ID: 83273856