[nerdponx]

It's tractable in practice. That's what the Idris (2) language does, for example.

[dunham]

If anyone is interested in how this works, I've found András Kovács' "Elaboration Zoo" to be a good tutorial: https://github.com/AndrasKovacs/elaboration-zoo

It incrementally covers normalization by evaluation, bidirectional typechecking, basic pattern unification, implicit insertion (which relies on unification), and then more sophisticated variants on pattern unification.