Use this URL to cite or link to this record in EThOS: http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.728471
Title: Quotient inductive-inductive definitions
Author: Dijkstra, Gabe
ISNI:       0000 0004 6493 7978
Awarding Body: University of Nottingham
Current Institution: University of Nottingham
Date of Award: 2017
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Abstract:
In this thesis we present a theory of quotient inductive-inductive definitions, which are inductive-inductive definitions extended with constructors for equations. The resulting theory is an improvement over previous treatments of inductive-inductive and indexed inductive definitions in that it unifies and generalises these into a single framework. The framework can also be seen as a first approximation towards a theory of higher inductive types, but done in a set truncated setting. We give the type of specifications of quotient inductive-inductive definitions mutually with its interpretation as categories of algebras. A categorical characterisation of the induction principle is given and is shown to coincide with the property of being an initial object in the categories of algebras. From the categorical characterisation of induction, we derive a more type theoretic induction principle for our quotient inductive-inductive definitions that looks like the usual induction principles. The existence of initial objects in the categories of algebras associated to quotient inductive-inductive definitions is established for a class of definitions. This is done by a colimit construction that can be carried out in type theory itself in the presence of natural numbers, sum types and quotients or equivalently, coequalisers.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID: uk.bl.ethos.728471  DOI: Not available
Keywords: QA 75 Electronic computers. Computer science
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