Henry Mercer, Cameron Ramsay, and I have a new draft paper on type inference out! Check out *Implicit Polarized F: Local Type Inference for Impredicativity*.

System F, the polymorphic lambda calculus, features the principle of impredicativity: polymorphic types may be explicitly instantiated at other types, enabling many powerful idioms such as Church encoding and data abstraction. Unfortunately, type applications need to be implicit for a language to be human-usable, and the problem of inferring all type applications in System F is undecidable. As a result, language designers have historically avoided impredicative type inference.

We reformulate System F in terms of call-by-push-value, and study type inference for it. Surprisingly, this new perspective yields a novel type inference algorithm which is extremely simple to implement (not even requiring unification), infers many types, and has a simple declarative specification. Furthermore, our approach offers type theoretic explanations of how many of the heuristics used in existing algorithms for impredicative polymorphism arise.

This algorithm is *absurdly* easy to implement, too.

Because we don't need unification, it also looks like this kind of algorithm ought to play very nicely with dependent types. My PhD student Ilya Kaisin is looking at this problem now, so stay tuned for even more.

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