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README.md

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@@ -11,28 +11,15 @@ You can find the proof of type safety in [Soundness.thy](./Soundness.thy), the p
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## Roadmap
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- [x] Start with a simply typed lambda calculus
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- [x] Define system
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- [x] Prove Progress
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- [x] Prove Preservation
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- [x] Add let bindings
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- [x] Extend definition
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- [x] Prove Progress
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- [x] Prove Preservation
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- [x] Use the Nominal2 framework to reason about alpha-equated terms
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- [ ] Add datatypes and `case` expressions
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- [ ] Extend definition
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- [ ] Prove Progress
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- [ ] Prove Preservation
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- [x] Extend to System F (ie introduce polymorphic variables)
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- [x] Extend definition
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- [x] Prove Progress
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- [x] Prove Preservation
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- [ ] Extend System F with Coercions
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- [ ] Extend definition
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- [ ] Prove Progress
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- [ ] Prove Preservation
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- [ ] TBD
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- [ ] Add arbitrary user-defined datatypes
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- [ ] Add `case` expressions
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- [ ] Extend to System Fc (ie introduce type equality coercions)
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## Used literature
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Up until now, I mainly used [Software Foundations: Programming Language Foundations](https://softwarefoundations.cis.upenn.edu/current/plf-current/toc.html) and the [System Fc paper](https://www.microsoft.com/en-us/research/wp-content/uploads/2007/01/tldi22-sulzmann-with-appendix.pdf?from=https%3A%2F%2Fresearch.microsoft.com%2Fen-us%2Fum%2Fpeople%2Fsimonpj%2Fpapers%2Fext-f%2Ftldi22-sulzmann-with-appendix.pdf).
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- [Software Foundations: Programming Language Foundations](https://softwarefoundations.cis.upenn.edu/current/plf-current/toc.html)
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- [System F with type equality coercions](https://www.microsoft.com/en-us/research/wp-content/uploads/2007/01/tldi22-sulzmann-with-appendix.pdf?from=https%3A%2F%2Fresearch.microsoft.com%2Fen-us%2Fum%2Fpeople%2Fsimonpj%2Fpapers%2Fext-f%2Ftldi22-sulzmann-with-appendix.pdf).
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- [Safe zero-cost coercions for Haskell](https://richarde.dev/papers/2016/coercible-jfp/coercible-jfp.pdf)

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