https://github.com/bryangingechen/lean-matroids

matroids in lean
https://github.com/bryangingechen/lean-matroids

formal-mathematics formal-proofs lean matroids theorem-proving

Last synced: 24 days ago
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matroids in lean

• Host: GitHub
• URL: https://github.com/bryangingechen/lean-matroids
• Owner: bryangingechen
• License: apache-2.0
• Created: 2018-09-21T05:45:25.000Z (over 6 years ago)
• Default Branch: master
• Last Pushed: 2020-12-21T03:51:54.000Z (about 4 years ago)
• Last Synced: 2024-08-10T14:12:30.552Z (4 months ago)
• Topics: formal-mathematics, formal-proofs, lean, matroids, theorem-proving
• Language: Lean
• Size: 58.6 KB
• Stars: 3
• Watchers: 2
• Forks: 1
• Open Issues: 1
• Metadata Files:
  • Readme: README.md
  • License: LICENSE

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README

        
# lean-matroids

A formalization of [matroids](https://en.wikipedia.org/wiki/Matroid) in [Lean](https://leanprover.github.io), so far following the (beginning of the) first chapter of *Matroid Theory*, by James Oxley. These files depend on and are inspired by the Lean [mathlib](https://github.com/leanprover/mathlib), and maybe someday some of this will make it in there as well.

Currently [`matroid.lean`](src/matroid.lean) contains:

* structures implementing the following formulations of matroids:

  * independent sets

  * circuits

  * bases

  * rank functions (only partially done)

* proofs that the circuit / basis formulations are equivalent to the independent set formulation, via explicit conversion functions

* proofs that the conversion functions are mutually inverse

Another file [`matroidexamples.lean`](src/matroidexamples.lean) contains:

* the independent set definitions of:

  * the loopy matroid (all subsets dependent)

  * the free matroid (all subsets independent)

  * the uniform matroid

* various explicit example computations involving the basis and circuit lemmas and functions defined in [`matroid.lean`](src/matroid.lean).

### Acknowledgements

Thanks to the denizens of the [Lean Zulip chat](https://leanprover.zulipchat.com) for patiently answering questions and providing proofs, several of which have been copied into this repository.