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A next-gen functional language
dependent-typesformalityfunctional-programminglambda-calculusmoonadproof-languageproof-languagesstarred-higherorderco-repostarred-repotheorem-provertype-theory
f9a5bdb963
on the `infer` function, we usually have something like this:
infer (App f x) ctx =
infer <- infer f ctx
case infer of
All a b -> do
check x a ctx
return $ out arg
otherwise ->
fail
this causes `x : a` to be happen before `infer (f x)` returns `b x`.
this is generally fine, but, in situations such as dependent
eliminations:
λx (bool-elim ?A x t f) : (P x)
we really want `(elim ...)` to return `P x` BEFORE we check `t : ?A
true` and `t : ?A false`. that would allow the unification problem `?A x
== P x` to generate the solution `?A = λx (P x)` **before** the `t : ?A
true` check possibly fails.
being able to fill that metavar is very important for Kind2, since that
would allow us to omit motives in pattern-matches. because of that, I
think that the more sensible order is for infer to return its result
first, and then its inner checks occur. this is via a very lightweight
mechanism that consists of a list of suspended checks (`susp`), which we
push to inside `infer`, and fully consume inside `check`.
this is a middle-ground between checking in order (from left-to-right)
and a more complex suspension mechanism (involving dependency graphs).
with this simple solution, we're able to use metavars inside the motive
of dependent eliminations, greatly reducing the need for annotations in
practical code.
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| kind2.ts | ||
| package.json | ||
| README.md | ||
Kind2 WIP
Kind1 has been developed in JavaScript, which wasn't meant to be a long-term
solution, but allowed us to explore self-types. Recently, we started developing
Kind2 for HVM1, but it has been
discontinued when we started working on HVM2. In this repository, we'll remake
and continue Kind2's development, now targetting HVM2. Kind2 will be fully
implemented in itself. Temporarily, we're using TypeScript+HVM1 to aid on the
bootstrapping process.