@aspiwack

Multi-classed Software Engineer/Constructive Mathematician. Sometimes plays video games sort of fast. Puts topoi in your computer. https://xitter.cf/t.co/iFlKRVeGpN

assert-false.science/arnaud/
Joined March 2019
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This is important dl.acm.org/doi/10.1145/38286… . For instance, when you have a linear Int# in Haskell, it's the same as having an unrestricted Int#. You want the type system to understand that, that's what the authors call mode crossing. 1/2

Mode Crossing | Proceedings of the ACM on Programming Languages

OxCaml extends the OCaml type system with support for safe low-level systems programming via modes. For example, OxCaml's modal portability and contention axes ensure that concurrent OxCaml programs...

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It's more important in Ocaml because Haskell's laziness precludes most types from crossing modes. The solution deployed in the paper is pretty involved, but maybe it's as canonical as it gets. I haven't fully digested it yet. But either way, it's important. 2/2
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What I'm suggesting is that we can, and probably should, take this as the *definition* of multicategories (it's a tad more general: ordinary multicategories correspond to the case where contexts are a PROP generated by the pures).
Arnaud Spiwack@aspiwackOct 20
I noticed something the other day. If you have a monoidal category, and a subset P of objects, then arrows from arbitrary objects to objects of P form a multicategory. We'll say that this is a category of context and P are pure objects. 1/8
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Something I realised while working on sheaves (because it turns out to be relevant) is that the multicategorical definition of coproduct is stronger than the categorical one. Because in the multi case, the branches have access to the context. In the cat case they don't. 1/3
Arnaud Spiwack@aspiwackOct 20
Replying to @aspiwack
From a mathematics perspective, it may be a friendlier setting to speak about multicategories (which tend to be notationally heavy). Though I don't think it makes the definition of coproducts much less of a chore (see p92 in Shulman's tutorial). 8/8
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Hom(A+B, X) ≃ Hom(A,X)×Hom(B,X) vs Hom((Γ,A+B), X) ≃ Hom((Γ,A), X)×Hom((Γ,B), X) (assuming symmetry for simplicity) 2/3
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If you have all finite products and coproducts, then the multi case is equivalent to products distributing over coproducts (exercise), which always hold for CCCs (also exercise). But multicategories let you speak of these stronger coproducts without requiring all that. 3/3
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In June, Ocaml 5.5 was released ocaml.org/changelog/2026-06-… , whose headline change is module-dependent functions (aka modular explicits) The Ocaml mailing list is no longer online, but I found in my emails me from May 2012, trying (and failing) to garner support for this feature 1/2

Release of OCaml 5.5.0 • OCaml Changelog

Release of OCaml 5.5.0

ocaml.org
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At the time it didn't have a name. There was no paper. And it got basically no interest at all. I'm really happy now. I've been looking forward to this moment for almost 15 years.
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Someone on the butterfly network found this archive. So here is the said email inbox.ci.dev/caml-list/CAMoP… 3/2
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I noticed something the other day. If you have a monoidal category, and a subset P of objects, then arrows from arbitrary objects to objects of P form a multicategory. We'll say that this is a category of context and P are pure objects. 1/8
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From a PLT perspective, this is a friendlier re-analysis of the contextuals CCC xitter.cf/aspiwack/status/204213… . See also Shulman's multicategorical logic tutorial mikeshulman.github.io/catlog… . 7/8
Arnaud Spiwack@aspiwackApr 9
Replying to @aspiwack
Well, there's a restriction of CCC, which doesn't seem to have a standard name but Altenkirch, Hofmann, and Streicher call it “contextual CCC” in Categorical reconstruction of a reduction free normalization proof. 5/8
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From a mathematics perspective, it may be a friendlier setting to speak about multicategories (which tend to be notationally heavy). Though I don't think it makes the definition of coproducts much less of a chore (see p92 in Shulman's tutorial). 8/8
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The Ocarina of Time remake is right around the corner. And the marketing is all around me. I wanted to take the opportunity to clarify a position: it's going to be a good game. OoT is the most beloved video game of all times, and this is, for the most part, the same game. 1/3
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Some bits are going to be a little better, some are going to be a bit worse. But it's going to be good. Even if I'm not a fan of… the choices. 2/3
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Even if I'm slightly dismayed that significantly more people are going to play this game than the original (or the excellent 3DS version, which is likely to remain the highest quality version of this game). 3/3
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