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