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A Type Theory for Defining Logics and Proofs

Chapter in book
Authors B. Pientka
D. Thibodeau
Andreas Abel
F. Ferreira
R. Zucchini
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Published in 2019 34TH ANNUAL ACM/IEEE SYMPOSIUM ON LOGIC IN COMPUTER SCIENCE (LICS)
ISBN 978-1-7281-3608-0
Publisher IEEE
Publication year 2019
Published at Department of Computer Science and Engineering (GU)
Language en
Keywords framework
Subject categories Computer and Information Science

Abstract

We describe a Martin-Lof-style dependent type theory, called COCON, that allows us to mix the intensional function space that is used to represent higher-order abstract syntax (HOAS) trees with the extensional function space that describes (recursive) computations. We mediate between HOAS representations and computations using contextual modal types. Our type theory also supports an infinite hierarchy of universes and hence supports type-level computation thereby providing metaprogramming and (small-scale) reflection. Our main contribution is the development of a Kripke-style model for COCON that allows us to prove normalization. From the normalization proof, we derive subject reduction and consistency. Our work lays the foundation to incorporate the methodology of logical frameworks into systems such as Agda and bridges the longstanding gap between these two worlds.

Page Manager: Webmaster|Last update: 9/11/2012
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