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45 lines
2 KiB
Markdown
45 lines
2 KiB
Markdown
# BSc Leon Vatthauer
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Here I am formalizing some notions of this paper [https://arxiv.org/pdf/2102.11828.pdf](https://arxiv.org/pdf/2102.11828.pdf) in agda.
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## Running the project
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TODO
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## Contributions to *agda-categories*
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This project uses the awesome category theory library for agda ([agda-categories](https://github.com/agda/agda-categories)), it is already very extensive, but some notions needed here are missing, so I contribute them to the library.
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So far the contributions are:
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1. Kleisli triples [[merged](https://github.com/agda/agda-categories/pull/381)]
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- `Categories.Monad.Construction.Kleisli`
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2. Distributive categories (and the relation to extensivity) [[merged](https://github.com/agda/agda-categories/pull/383)]
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- `Categories.Category.Distributive`
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- `Categories.Category.Extensive.Bundle`
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- `Categories.Category.Extensive.Properties.Distributive`
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3. Commutative categories [TODO]
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## Goals
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- [ ] `Monad.Instance.Delay`
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- [X] Formalize the delay monad (as kleisli triple)
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- [ ] Show that a strong delay monad is commutative (also needs formalization of strong delay monad)
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- [X] `ElgotAlgebra.agda`
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- [X] Formalize (un-)guarded elgot-algebra.
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- [X] Show the equivalence of `#-Folding` and `#-Compositionality` in the unguarded case. (*Proposition 10*)
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- [ ] `ElgotAlgebras.agda`
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- [X] Formalize the category of elgot algebras for a given carrier.
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- [X] Show existence of products in this category
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- [ ] Show existence of exponentials (if carrier has exponentials)
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- [ ] `ElgotMonad.agda` [TODO]
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- [ ] Formalize (strong) (pre) elgot monad
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- [ ] Show ElgotMonad->PreElgotMonat
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- [ ] Monad K [TODO]
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- [ ] Definitions using free uniform iteration algebras
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- [ ] strength
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- [ ] stable free uniform iteration algebras (and the relation to CCC carriers)
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- [ ] ...
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- [ ] Theorem 37 [TODO] (final goal)
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## Roadmap
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TODO
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## TODOs
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- [ ] Create Roadmap (find what theorem 37 depends on and then create a game plan)
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- [X] Refactor `ElgotAlgebras.agda` using `Categories.Morphism.Reasoning` (nicer proofs)
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