# toytt

this is an attempt of mine to implement a typechecker for a minimal dependent
type theory in the style of martin-löf. at the time of writing this, it has the
following features:

- type of booleans w/ dependent eliminator
- pi and sigma connectives
- universe that contains itself (lol)
- that's it

it probably has lots of bugs as well.

## example

the file `test/bool.toytt` defines some elementary functions on booleans.

```
toytt> not false
true : bool
toytt> and false
\y -> false : bool -> bool
toytt> xor true false
true : bool
toytt> or true bool
 ￫ error[E302]
 1 | or true bool
   ^ type mismatch:
     expected: bool
        found: type
```

## todo list (in descending order of importance and/or realizability)

- [x] figure out how to recover variable names in pretty-printing so we don't
  have to print de bruijn indices all the time
- [x] build a better repl
- [x] improve error messages
- [x] implement top-level definitions
- [x] implement less aggrevating syntax for non-dependent function & pair types
- [ ] add a type of natural numbers
- [ ] replace type-in-type with a proper (cumulative?) hierarchy of universes
  -> maybe use the mugen library or figure out typical ambiguity?
- [ ] implement inductive types/families
- [ ] implement axioms (probably easy)
- [ ] do HoTT stuff (maybe implement a form of cubical type theory? or stick with
  book HoTT, which is probably much easier)
- ...