RedPRL / algaett

🦠 An experimental elaborator for dependent type theory using effects and handlers

🦠 algaett’s not algaeff

This development is an experiment with the following goals:

1. Adopt smalltt and related techniques into the cubical world.
2. Show how various OCaml packages of ours fit together.
3. Write natural grammars without neccesarily conforming to LR(k).
4. Use lots of Unicode emojis.

Try It Out!

opam pin git+https://github.com/RedPRL/bantorra
opam pin git+https://github.com/RedPRL/algaett
cat tests/example.ag
algaett tests/example.ag

The last line should not have an output, which means it type checks!

Important Ideas

Ideas from Smalltt

The core NbE algorithm closely follows András Kovács’s smalltt. Here are some notable differences:

1. We intentionally do not implement unification.
2. The universe itself (as a term) is not inferable, which means that the checking might have to be redone with the type unfolded.

   📌 😄 : 🌌 🆙 2️⃣ 👉 🌌 🆙 1️⃣
   📌 _ 👉 🌌 : 😄
   

   The type inference from the universe 🌌 will fail, and then the type checking will be redone with 😄 unfolded to 🌌 🆙 1️⃣.
3. The conversion checker is generalized to handle subtyping generated by cumulativity.

Modular Development

• algaeff: reusable effects-based components
• asai: error messages (not actively used yet)
• bantorra: unit resolution (not actively used yet)
• bwd: backward lists
• mugen: universe levels
• yuujinchou: namespaces and name modifier

Parser beyond LR

We are using the Earley’s parsing algorithm which can handle all context-free grammars.

Documentation

Here is the API documentation.