24 lines
1.3 KiB
TeX
24 lines
1.3 KiB
TeX
\chapter*{Abstract}
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The usual notion of propositional equality in intensional type-theory
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is restrictive. For instance it does not admit functional
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extensionality or univalence. This poses a severe limitation on both
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what is \emph{provable} and the \emph{re-usability} of proofs. Recent
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developments have, however, resulted in cubical type theory which
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permits a constructive proof of these two important notions. The
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programming language Agda has been extended with capabilities for
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working in such a cubical setting. This thesis will explore the
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usefulness of this extension in the context of category theory.
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The thesis will motivate and explain why propositional equality in
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cubical Agda is more expressive than in standard Agda. Alternative
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approaches to Cubical Agda will be presented and their pros and cons
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will be explained. It will emphasize why it is useful to have a
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constructive interpretation of univalence. As an example of this two
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formulations of monads will be presented: Namely monads in the
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monoidal form and monads in the Kleisli form.
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Finally the thesis will explain the challenges that a developer will
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face when working with cubical Agda and give some techniques to
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overcome these difficulties. It will also try to suggest how further
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work can help alleviate some of these challenges.
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