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Wed 20 Jan 2016 10:55 - 11:20 at Grand Bay South - Track 2: Types and Foundations Chair(s): Robert Atkey

We present an internal formalisation of dependent type theory in type theory using a special case of higher inductive types from Homotopy Type Theory which we call quotient inductive types (QITs). Our formalisation of type theory avoids refering to preterms or a typability relation but defines directly well typed objects by an inductive definition. We use the elimination principle to define the set-theoretic and logical predicate interpretation. The work has been formalized using the Agda system extended with QITs using postulates.

Poster (poster.pdf)113KiB

Wed 20 Jan
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10:30 - 12:10: Research Papers - Track 2: Types and Foundations at Grand Bay South
Chair(s): Robert AtkeyUniversity of Strathclyde
POPL-2016-papers10:30 - 10:55
Matt BrownUCLA, Jens PalsbergUniversity of California, Los Angeles
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POPL-2016-papers10:55 - 11:20
Thorsten AltenkirchUniversity of Nottingham, Ambrus KaposiUniversity of Nottingham
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POPL-2016-papers11:20 - 11:45
Yufei CaiUniversity of Tübingen, Germany, Paolo G. GiarrussoUniversity of Tübingen, Germany, Klaus OstermannUniversity of Tübingen, Germany
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POPL-2016-papers11:45 - 12:10
Pierre-Louis CurienUniv. Paris Diderot and INRIA Paris-Rocquencourt, Marcelo FioreComputer Laboratory, University of Cambridge, Guillaume Munch-MaccagnoniComputer Laboratory, University of Cambridge