Canonicity for Cubical Type Theory · HackerPapers discussions

Canonicity for Cubical Type Theory — mentioned by YorkshireSeason

Tue, 09 Oct 2018 14:56:36 GMT

I know that this question is being asked and reseached -- indeed I do research in this direction. But it's not well understood, and it's not nearly as widely asked a question as the type-inference question which the java compiler asks every time you type something like int n = 2 + 3; Note that 2+3 needs to be type-inferred. cut elimination / normalization, I'm not sure this can be reduced to cut-elimination, because the question "What terms have this type?" can be asked for non-terminating programs as well -- indeed it becomes much more interesting. https://arxiv.org/abs/1607.04156 Aside: I'm…

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Canonicity for Cubical Type Theory — mentioned by danharaj

Tue, 09 Oct 2018 14:09:14 GMT

Oh, it's more common a question than you suggest. If I am writing a block of code and I come to some hole in context, for example `foo (bar _) baz`, and I know what type of thing has to go in that hole, then the very next thing I ask is "What term do I need there?". This is a big question for theoreticians working on new languages. The problem is called canonicity in that context. Here is an example of such a proof of "What terms have this type [in this context]?": https://arxiv.org/abs/1607.04156 And finally, compilers will ask this question if they're nice to you :) Here is GHC recently…

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