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)
...