https://github.com/redprl/agda-mugen
A formalization of the theory behind the mugen library
https://github.com/redprl/agda-mugen
Last synced: 2 months ago
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A formalization of the theory behind the mugen library
- Host: GitHub
- URL: https://github.com/redprl/agda-mugen
- Owner: RedPRL
- Created: 2022-09-01T04:29:04.000Z (over 3 years ago)
- Default Branch: main
- Last Pushed: 2024-06-24T01:56:08.000Z (almost 2 years ago)
- Last Synced: 2025-06-13T05:43:30.057Z (10 months ago)
- Language: Agda
- Size: 443 KB
- Stars: 19
- Watchers: 4
- Forks: 1
- Open Issues: 5
-
Metadata Files:
- Readme: README.md
Awesome Lists containing this project
README
# ♾ mugen 無限 in Agda
This is a formalization of the displacement algebras, their properties, and part of meta-theoretic analysis found in our POPL 2023 paper [“An Order-Theoretic Analysis of Universe Polymorphism”.](https://favonia.org/files/mugen.pdf) The accompanying OCaml implementation is at .
🚧 This repository is under major rewrites and cleanups. See version 0.1.0 for the code that matches the POPL 2023 paper.
## Mechanized Results
### Displacement Algebras
🚧 The links are currently broken.
| Displacements | Paper Section | Agda Module | OCaml Module(s) |
| :------------------------------------ | :--------------- | :----------------------------------------------------------------------------- | :------------------------------------------------------------------------------------------------------------------------------------------------------------------ |
| Natural numbers | 3.3.1 | [Nat](src/Mugen/Algebra/Displacement/Instances/Nat.agda) | [Nat](https://redprl.org/mugen/mugen/Mugen/Shift/Nat) and [Nat](https://redprl.org/mugen/mugen/Mugen/ShiftWithJoin/Nat) |
| Integers | 3.3.1 | [Int](src/Mugen/Algebra/Displacement/Instances/Int.agda) | [Int](https://redprl.org/mugen/mugen/Mugen/Shift/Int) and [Int](https://redprl.org/mugen/mugen/Mugen/ShiftWithJoin/Int) |
| Non-positive integers | 3.3.1 | [NonPositive](src/Mugen/Algebra/Displacement/Instances/NonPositive.agda) | [NonPositive](https://redprl.org/mugen/mugen/Mugen/Shift/NonPositive) and [NonPositive](https://redprl.org/mugen/mugen/Mugen/ShiftWithJoin/NonPositive) |
| Constant displacements | 3.3.2 | [Constant](src/Mugen/Algebra/Displacement/Instances/Constant.agda) | [Constant](https://redprl.org/mugen/mugen/Mugen/Shift/Constant) |
| Binary products | 3.3.3 | [Product](src/Mugen/Algebra/Displacement/Instances/Product.agda) | [Product](https://redprl.org/mugen/mugen/Mugen/Shift/Product) and [Product](https://redprl.org/mugen/mugen/Mugen/ShiftWithJoin/Product) |
| Lexicographic binary products | 3.3.4 | [Lexicographic](src/Mugen/Algebra/Displacement/Instances/Lexicographic.agda) | [Lexicographic](https://redprl.org/mugen/mugen/Mugen/Shift/Lexicographic) and [Lexicographic](https://redprl.org/mugen/mugen/Mugen/ShiftWithJoin/Lexicographic) |
| Indexed products | 3.3.5 | [IndexedProduct](src/Mugen/Algebra/Displacement/Instances/IndexedProduct.agda) | _(not implementable)_ |
| Nearly constant infinite products | 3.3.5 | [NearlyConstant](src/Mugen/Algebra/Displacement/Instances/NearlyConstant.agda) | [NearlyConstant](https://redprl.org/mugen/mugen/Mugen/Shift/NearlyConstant) and [NearlyConstant](https://redprl.org/mugen/mugen/Mugen/ShiftWithJoin/NearlyConstant) |
| Infinite products with finite support | 3.3.5 | [FiniteSupport](src/Mugen/Algebra/Displacement/Instances/FiniteSupport.agda) | [FiniteSupport](https://redprl.org/mugen/mugen/Mugen/Shift/FiniteSupport) and [FiniteSupport](https://redprl.org/mugen/mugen/Mugen/ShiftWithJoin/FiniteSupport) |
| Prefix order | 3.3.6 | [Prefix](src/Mugen/Algebra/Displacement/Instances/Prefix.agda) | [Prefix](https://redprl.org/mugen/mugen/Mugen/Shift/Prefix) |
| Fractal displacements | 3.3.7 | [Fractal](src/Mugen/Algebra/Displacement/Instances/Fractal.agda) | [Fractal](https://redprl.org/mugen/mugen/Mugen/Shift/Fractal) |
| Opposite displacements | 3.3.8 | [Opposite](src/Mugen/Algebra/Displacement/Instances/Opposite.agda) | [Opposite](https://redprl.org/mugen/mugen/Mugen/Shift/Opposite) |
| Weird fractal displacements | 3.3.9 (JFP only) | [WeirdFractal](src/Mugen/Algebra/Displacement/Instances/WeirdFractal.agda) | [Fractal](https://redprl.org/mugen/mugen/Mugen/Shift/Fractal) |
| Endomorphisms | 3.4 (Lemma 3.7) | [Endomorphism](src/Mugen/Algebra/Displacement/Instances/Endomorphism.agda) | _(not implementable)_ |
### Other Theorems
| Theorems | Paper Section | Agda Module |
| :------------------------------------ | :----------------- | :----------------------------------------------------------------------------------------------- |
| Traditional level polymorphism | 2.2 | [Traditional](./src/Mugen/Cat/HierarchyTheory/Traditional.agda) |
| Validity of McBride monads | 3.1 | [McBride](./src/Mugen/Cat/HierarchyTheory/McBride.agda) |
| Embedding of endomorphisms | 3.4 (Lemma 3.8) | [EndomorphismEmbedding](./src/Mugen/Cat/HierarchyTheory/Universality/EndomorphismEmbedding.agda) |
| Embedding of small hierarchy theories | 3.4 (Lemma 3.9) | [SubcategoryEmbedding](./src/Mugen/Cat/HierarchyTheory/Universality/SubcategoryEmbedding.agda) |
| Universality of McBride monads | 3.4 (Theorem 3.10) | [Universality](./src/Mugen/Cat/HierarchyTheory/Universality.agda) |
## Building
Run the following command to check formalization.
```sh
docker build -t agda-mugen:edge .
docker run agda-mugen:edge
```