On the complexities of polymorphic stream equation systems, isomorphism of finitary inductive types, and higher homotopies in univalent universes

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Sattler, Christian (2015) On the complexities of polymorphic stream equation systems, isomorphism of finitary inductive types, and higher homotopies in univalent universes. PhD thesis, University of Nottingham.

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Abstract

This thesis is composed of three separate parts.

The first part deals with definability and productivity issues of equational systems defining polymorphic stream functions. The main result consists of showing such systems composed of only unary stream functions complete with respect to specifying computable unary polymorphic stream functions.

The second part deals with syntactic and semantic notions of isomorphism of finitary inductive types and associated decidability issues. We show isomorphism of so-called guarded types decidable in the set and syntactic model, verifying that the answers coincide.

The third part deals with homotopy levels of hierarchical univalent universes in homotopy type theory, showing that the n-th universe of n-types has truncation level strictly n+1.

Item Type: Thesis (University of Nottingham only) (PhD)
Supervisors: Capretta, V.
Altenkirch, T.
Subjects: Q Science > QA Mathematics > QA 75 Electronic computers. Computer science
Faculties/Schools: UK Campuses > Faculty of Science > School of Computer Science
Item ID: 28111
Depositing User: Sattler, Christian
Date Deposited: 09 Oct 2015 14:01
Last Modified: 28 Feb 2025 11:33
URI: https://eprints.nottingham.ac.uk/id/eprint/28111

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