jfdm / lambdadome

Lambdadome: My explorations in Lambda Calculi.

A little cage in which I explore various extensions to the STLC with things that interest me. Some of these little calculi are me looking at features in isolation for bigger projects.

This is my little project that I don’t mind sharing with the world, however, I will not accept PRs. This repository is rough and ready.

All calculi are De Bruijn indexed and intrinsically typed. I try to present them with small step operational semantics but mwah.

There are two styles of calculi here:

Classic

A classic construction as commonly seen in dependently typed programmes. I make one adjustment in that functions are explicitly annotated with their argument type.

NewWave

A style of construction I am pioneering in which types are presented as terms. Types are still stratified from values, and this is not dependently-typed constructions, more that I want to treat types as terms.

At somepoint I will add decidable type-checking procedures to show that type-checking is decidable. By that I mean I will go from an ‘un-decorated’ abstract syntax tree and construct intrinsically type terms from it. I do not intend to use `Dec` (or my personal favourite of `DecInfo`) but rather just use `Either`. At somepoint I will use `Dec`/`DecInfo`.

I will leave holes for some `DecEq` instances as they do take time to write.

Depends

• Idris2

At somepoint I will be making more detailed literate notes using Juptyer-Book. When I do, I shall depended on that and a few extra utilities.

• Jupyter-book

At somepoint I will add benchmarking of things, for that I intend to use hyperfine.

• Hyperfine