[wk_end]

While technically there's a relationship between category theory and substructural logics (of course there is, category theory is general enough that there's a relationship between it and everything), they don't really strike me as having that much to do with it directly - they're a fairly straightforward extension (restriction) of typical presentations of constructive logic. And I wasn't aware that e.g. Rust picked up its type system via exposure through category theory. Is there a source for that narrative?

[Loq]

> Is there a source for that narrative?

Girard mentions the connection with categories all the time.

For example in "Proofs and Types" he proves various theorems along the lines of: the sub-category of coherence spaces and stable maps (one of the main models that LL was developed for) induced by some LL fragment is cartesian closed category (IIRC). I think he developed LL in parts by fine-tuning it, until all the categories induced as models of fragments of LL have nice categorical properties. (To the extent that is possible.) When I was a PhD student, my supervisor suggested that I learn category theory to understand linear logic. (Not sure, in retrospect, that was the best course of action, but that was my trajectory)

[Loq]

> Is there a source for that narrative?

Rust's types evolved over many years. Rust used to have "typestate" for example. I had discussions with Graydon Hoare around 2011-ish about session types (which are linear). It struck me that Hoare knew exactly what I meant with the term. More generally, linear typing was just "in the air" in the early 2000s: you could not been serious in programming language design without being aware of linearity. Linearity was all over the research literature. Hoare was clearly very knowledgable in programming language research.