Did you write down this recipe anywhere?

Oh, guess I was too busy touching grass to notice.

Not enough people are talking about this

But what IS the right order of solving them?

Hmmm, I agree that bidirectional systems make precise where to put the unification constraints, but are unification constraints the only kind of constraint that's needed? What about ie generalisation/instantiation constraints for type schemes?

Eh, this is nowhere near as cool as alpha fold. the article is just hype and overinflation of capabilities.

(fun fact: this system is unable to express the *strict* (tensor) product, the same way that the lambda calculus has no way to express 'par'

In CBPV terminology, Times is the 'lazy product', aka 'With' from linear logic

And, of course, the language in that paper subsumes both lambda and co-lambda calculus.

This system flips natural deduction inside out.

So it has left-introduction and left-elimination.

And just as natural deduction limits judgements to have one output, this limits them to have one input (but a whole context of possible outputs).

Oh yes, very much so!

So the sequent calculus is all about introduction rules, you have left-introduction and right-introduction.

Meanwhile, natural deduction is all about working on the right-hand-side of the turnstile: you have right-intro like with sequents, but also right-*elimination*.

This system is *alien*. The rules don't do justice to how bizzaro-world it feels to reason with this

Ok I am *very* impressed :D

Cool! I'm definitely a fan of parser combinators, and the TS-macros project looks 🤯

this is sort of what i'm thinking for functions, for example. still fixing the inference for return types but once i'm done with this, i'll have a really expressive and type-safe way to do macros for TS!

Oh yes? :D Tell me more! Do you have anything written that I can look at!

I'm currently working on a project in this space that could spark your interest, but it's not public yet. I could give you a ping in a few weeks though with more details if you're interested >:D