FLOC 2018: FEDERATED LOGIC CONFERENCE 2018
The clocks they are adjunctions. Denotational semantics for Clocked Type Theory

Authors: Bassel Mannaa and Rasmus M√łgelberg

Paper Information

Title:The clocks they are adjunctions. Denotational semantics for Clocked Type Theory
Authors:Bassel Mannaa and Rasmus M√łgelberg
Proceedings:FSCD Presented Papers
Editor: Helene Kirchner
Keywords:Type theory, Guarded recursion, Denotational semantics
Abstract:

ABSTRACT. Clocked Type Theory (CloTT) is a type theory for guarded recursion useful for programming with coinductive types, encoding productivity 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.

Pages:17
Talk:Jul 10 09:30 (Session 52B: Types)
Paper: