The Clocks They Are Adjunctions: Denotational Semantics for Clocked Type Theory
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The Clocks They Are Adjunctions: Denotational Semantics for Clocked Type Theory. / Mannaa, Bassel; Møgelberg, Rasmus Ejlers.
3rd International Conference on Formal Structures for Computation and Deduction (FSCD 2018). Vol. 108 Schloss Dagstuhl--Leibniz-Zentrum für Informatik, 2018. 23 (Leibniz International Proceedings in Informatics (LIPIcs), Vol. 108).Research output: Conference Article in Proceeding or Book/Report chapter › Article in proceedings › Research › peer-review
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TY - GEN
T1 - The Clocks They Are Adjunctions: Denotational Semantics for Clocked Type Theory
AU - Mannaa, Bassel
AU - Møgelberg, Rasmus Ejlers
N1 - Conference code: 3
PY - 2018
Y1 - 2018
N2 - 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 semanticsfor 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.
AB - 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 semanticsfor 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.
U2 - 10.4230/LIPIcs.FSCD.2018.23
DO - 10.4230/LIPIcs.FSCD.2018.23
M3 - Article in proceedings
SN - 978-3-95977-077-4
VL - 108
T3 - Leibniz International Proceedings in Informatics (LIPIcs)
BT - 3rd International Conference on Formal Structures for Computation and Deduction (FSCD 2018)
PB - Schloss Dagstuhl--Leibniz-Zentrum für Informatik
T2 - International Conference on Formal Structures for Computation and Deduction
Y2 - 9 July 2018 through 12 July 2018
ER -
ID: 83273856