Update README.md

README.md

@@ -4,27 +4,6 @@ Here I am formalizing some notions of this paper [https://arxiv.org/pdf/2102.118
 The whole project consists of literate agda files, where I add my documentation as markdown.
 A (mostly up to date) version can be found here: https://wwwcip.cs.fau.de/~hy84coky/bsc-thesis/
 
-## Running the project
-TODO
-
-## Contributions to *agda-categories*
-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.
-So far the contributions are:
-1. Kleisli triples [[merged](https://github.com/agda/agda-categories/pull/381)]
-    - `Categories.Monad.Construction.Kleisli`
-2. Distributive categories (and the relation to extensivity) [[merged](https://github.com/agda/agda-categories/pull/383)]
-    - `Categories.Category.Distributive`
-    - `Categories.Category.Extensive.Bundle`
-    - `Categories.Category.Extensive.Properties.Distributive`
-3. Parametrized (or stable) natural numbers objects [[merged](https://github.com/agda/agda-categories/pull/394)]
-    - `Categories.Object.NaturalNumbers.Parametrized`
-    - `Categories.Object.NaturalNumbers.Properties.F-Algebra`
-    - `Categories.Object.NaturalNumbers.Properties.Parametrized`
-4. Commutative monad [TODO]
-
-## TODO
-TODOs are found inside the literate agda files!
-
 ## Usage
 The project requires a new version of agda-categories (newer than some package managers ship), so the easiest way to use this project is via the provided nix flake, which fetches my fork of agda-categories that is guaranteed to work with this project.
 
@@ -39,3 +18,20 @@ There is also a Makefile for compiling every module and generating the html docu
 ```
 make
 ```
+
+## Contributions to *agda-categories*
+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.
+So far the contributions are:
+1. Kleisli triples [[merged](https://github.com/agda/agda-categories/pull/381)]
+    - `Categories.Monad.Construction.Kleisli`
+2. Distributive categories (and the relation to extensivity) [[merged](https://github.com/agda/agda-categories/pull/383)]
+    - `Categories.Category.Distributive`
+    - `Categories.Category.Extensive.Bundle`
+    - `Categories.Category.Extensive.Properties.Distributive`
+3. Parametrized (or stable) natural numbers objects [[merged](https://github.com/agda/agda-categories/pull/394)]
+    - `Categories.Object.NaturalNumbers.Parametrized`
+    - `Categories.Object.NaturalNumbers.Properties.F-Algebra`
+    - `Categories.Object.NaturalNumbers.Properties.Parametrized`
+4. Commutative monad [[merged](https://github.com/agda/agda-categories/pull/404)]
+    - `Categories.Monad.Commutative`
+    - `Categories.Monad.Strong.Properties`

slides/bibliography.bib

@@ -81,18 +81,18 @@
 }
 
 @inproceedings{quotienting,
-author = {Chapman, James and Uustalu, Tarmo and Veltri, Niccol\`{o}},
-title = {Quotienting the Delay Monad by Weak Bisimilarity},
-year = {2015},
-isbn = {9783319251493},
-publisher = {Springer-Verlag},
-address = {Berlin, Heidelberg},
-url = {https://doi.org/10.1007/978-3-319-25150-9_8},
-doi = {10.1007/978-3-319-25150-9_8},
-abstract = {The delay datatype was introduced by Capretta [3] as a means to deal with partial functions as in computability theory in Martin-L\"{o}f type theory. It is a monad and it constitutes a constructive alternative to the maybe monad. It is often desirable to consider two delayed computations equal, if they terminate with equal values, whenever one of them terminates. The equivalence relation underlying this identification is called weak bisimilarity. In type theory, one commonly replaces quotients with setoids. In this approach, the delay monad quotiented by weak bisimilarity is still a monad. In this paper, we consider Hofmann's alternative approach [6] of extending type theory with inductive-like quotient types. In this setting, it is difficult to define the intended monad multiplication for the quotiented datatype. We give a solution where we postulate some principles, crucially proposition extensionality and the semi-classical axiom of countable choice. We have fully formalized our results in the Agda dependently typed programming language.},
-booktitle = {Proceedings of the 12th International Colloquium on Theoretical Aspects of Computing - ICTAC 2015 - Volume 9399},
-pages = {110–125},
-numpages = {16}
+  author    = {Chapman, James and Uustalu, Tarmo and Veltri, Niccol\`{o}},
+  title     = {Quotienting the Delay Monad by Weak Bisimilarity},
+  year      = {2015},
+  isbn      = {9783319251493},
+  publisher = {Springer-Verlag},
+  address   = {Berlin, Heidelberg},
+  url       = {https://doi.org/10.1007/978-3-319-25150-9_8},
+  doi       = {10.1007/978-3-319-25150-9_8},
+  abstract  = {The delay datatype was introduced by Capretta [3] as a means to deal with partial functions as in computability theory in Martin-L\"{o}f type theory. It is a monad and it constitutes a constructive alternative to the maybe monad. It is often desirable to consider two delayed computations equal, if they terminate with equal values, whenever one of them terminates. The equivalence relation underlying this identification is called weak bisimilarity. In type theory, one commonly replaces quotients with setoids. In this approach, the delay monad quotiented by weak bisimilarity is still a monad. In this paper, we consider Hofmann's alternative approach [6] of extending type theory with inductive-like quotient types. In this setting, it is difficult to define the intended monad multiplication for the quotiented datatype. We give a solution where we postulate some principles, crucially proposition extensionality and the semi-classical axiom of countable choice. We have fully formalized our results in the Agda dependently typed programming language.},
+  booktitle = {Proceedings of the 12th International Colloquium on Theoretical Aspects of Computing - ICTAC 2015 - Volume 9399},
+  pages     = {110–125},
+  numpages  = {16}
 }
 
 @article{restriction,
@@ -126,4 +126,20 @@ numpages = {16}
   timestamp  = {Fri, 26 Feb 2021 14:31:25 +0100},
   biburl     = {https://dblp.org/rec/journals/corr/abs-2102-11828.bib},
   bibsource  = {dblp computer science bibliography, https://dblp.org}
+}
+
+@article{while,
+  author     = {Sergey Goncharov and
+                Lutz Schr{\"{o}}der and
+                Christoph Rauch},
+  title      = {(Co-)Algebraic Foundations for Effect Handling and Iteration},
+  journal    = {CoRR},
+  volume     = {abs/1405.0854},
+  year       = {2014},
+  url        = {http://arxiv.org/abs/1405.0854},
+  eprinttype = {arXiv},
+  eprint     = {1405.0854},
+  timestamp  = {Mon, 13 Aug 2018 16:47:19 +0200},
+  biburl     = {https://dblp.org/rec/journals/corr/GoncharovSR14.bib},
+  bibsource  = {dblp computer science bibliography, https://dblp.org}
 }

slides/code-examples/reverse.agda

@@ -29,8 +29,8 @@ module reverse where
   fin-colist : Colist ℕ
   fin-colist = 1 ∷ ♯ (2 ∷ ♯ (3 ∷ ♯ []))
 
-  inf-colist : Colist ℕ
-  inf-colist = 1 ∷ ♯ inf-colist
+  ones : Colist ℕ
+  ones = 1 ∷ ♯ ones
 
   -- run reverse fin-colist for 5 steps
-  -- run reverse inf-colist for 1000 steps
+  -- run reverse ones for 1000 steps

slides/sections/01_abstracting.tex

@@ -170,7 +170,7 @@ The following is an adaptation of Ad\'amek, Milius and Velebil's \textit{complet
 \end{block}
 \end{frame}
 
-\begin{frame}[t, fragile]{Partiality from Iteration}{Elgot Monads~\cite{elgotmonad}}
+\begin{frame}[t, fragile]{Partiality from Iteration}{Elgot Monads~\cite{elgotmonad}~\cite{while}}
 \begin{definition}
   A monad $\mathbf{T}$ is an Elgot monad if it has an iteration operator $(f : X \rightarrow T(Y + X))^\dagger : X \rightarrow TY$ satisfying:
   \begin{itemize}