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Kraus, Nicolai (2016) Constructions with non-recursive higher inductive types. In: Thirty-First Annual ACM/IEEE Symposium on Logic in Computer Science (LICS), July 5–8, 2016, New York City, USA. (In Press)

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Abstract

Higher inductive types (HITs) in homotopy type theory are a powerful generalization of inductive types. Not only can they have ordinary constructors to define elements, but also higher constructors to define equalities (paths). We say that a HIT H is non-recursive if its constructors do not quantify over elements or paths in H. The advantage of non-recursive HITs is that their elimination principles are easier to apply than those of general HITs.

It is an open question which classes of HITs can be encoded as non-recursive HITs. One result of this paper is the construction of the propositional truncation via a sequence of approximations, yielding a representation as a non-recursive HIT. Compared to a related construction by van Doorn, ours has the advantage that the connectedness level increases in each step, yielding simplified elimination principles into n-types. As the elimination principle of our sequence has strictly lower requirements, we can then prove a similar result for van Doorn’s construction. We further derive general elimination principles of higher truncations (say, k-truncations) into n-types, generalizing a previous result by Capriotti et al. which considered the case n=k+1.

Item Type:	Conference or Workshop Item (Paper)
RIS ID:	https://nottingham-repository.worktribe.com/output/980106
Additional Information:	Permission to make digital or hard copies of part or all of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, to republish, to post on servers, or to redistribute to lists, contact the Owner/Author. Request permissions from permissions@acm.org or Publications Dept., ACM, Inc., fax +1 (212) 869-0481. Copyright 20yy held by Owner/Author. Publication Rights Licensed to ACM.
Keywords:	Homotopy type theory
Schools/Departments:	University of Nottingham, UK > Faculty of Science > School of Computer Science
Depositing User:	Kraus, Nicolai
Date Deposited:	28 Apr 2016 13:14
Last Modified:	04 May 2020 20:05
URI:	https://eprints.nottingham.ac.uk/id/eprint/33025

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