Equivalence of Cast Calculi

This repo aims at helping people to develop new cast representations and to prove their correctness.

The package equivalence-of-cast-calculi contains necessary semantic definition and theorems. To get started, a user must pick a blame strategy. Currently only Lazy D and Lazy UD blame strategy are supported.

If a user want to prove a Lazy UD cast representation is correct, the user should

1. create an Agda module and import the equivalence-of-cast-calculi/NewLazyUDCastADT module;
2. define a Cast ADT (said c);
3. prove that c is a Lazy UD Cast ADT.

For illustration, please refer to illustration. There each file applies our framework to a known cast representation. We recommand starting with coercions in normal form if you know coercions, coercions in normal form, or canonical coercions. Otherwise, Lazy UD hypercoercions is recommanded because this cast representation is described in details in our paper.