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