# pi

A dependently typed system

# Implemented

* A Basic dependent lambda calculus
  * lambda abstractions
  * variables
  * pi types
  * type of types

* let ... in ...

* Unit type

* Empty type

* Natural numbers

* Σ Types

* Martin-Löf Identity types

# TODO

* Universes (a la tarksi)

* Elaboration
  * Implicit arguments
  * Universe family application
    * Syntax level russel universes
    * Universe of all other universes? (universe polymorphism)

* Inductives
  * Indexed inductives

## Things that could be fun to do sometime eventually

* Pattern matching in elaborator

* Write down the rules

* Performence optimisation?

* Compile to scheme

# References

Some of the material I found helpful in groking dependent type checking:

* Coquand, Thierry. “An Algorithm for Type-Checking Dependent Types.” Science of Computer Programming 26, no. 1–3 (May 1996): 167–77. https://doi.org/10.1016/0167-6423(95)00021-6.

* Brady, Edwin. "SPLV20 course notes". GitHub. https://github.com/edwinb/SPLV20