2023-06-27: Meven Lennon-Bertrand (University of Cambridge)

Tue, 14 Oct 2025 16:51:42 +0000

Meven Lennon-Bertrand (University of Cambridge)

A Shiny Hammer and Many Nails to Hit – Bidirectional typing is not only an implementation technique

Abstract

In 2000, Pierce and Turner introduced a new technique to perform type inference for ML-like languages, whose main idea was to carefully understand the local flow of information in the algorithm. This technique, which came to be referred to as bidirectional typing, did not come out of a void: similar ideas had appeared independently in many other contexts. In particular, bidirectional typing has been a part of the folklore of dependently typed languages implementers since the dawn of time.

But even in that context where it has a long history, bidirectional typing was for a long time mostly confined to implementations. Yet, its type-theoretic structure turns out to be a very versatile and powerful tool when studying (dependent) type systems and their meta-theory.

In this talk, I will try and give some of my understanding of bidirectional typing, how it is rooted in type-checker implementations but is more than just this, and how it can be used to make many facets of the infamously painful meta-theory of dependent type systems a bit less painful.

2023-06-27 16:00:00 UTC
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