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Hi Gershom, I'm not sure how useful it will be for your goals here, but my co-authored paper "Kind Inference for Datatypes <https://urldefense.com/v3/__https://dl.acm.org/doi/10.1145/3371121__;!!IBzWLUs!VLMhoiZ94plx6x0iiMBjOeUBZ-eWBZ6CG04adL5f5Awaf_cEmgvlKAhLoSuKUDSM4e1L20VY0_pWHzWibtZuSJeX-ugfLw$ >" (POPL'20) has some structure that resembles what you're looking for. It has a treatment of the surface syntax. But it focuses on inference (as the title suggests) and does not relate the surface definitions to structural isorecursive types in a core calculus. I don't believe the paper addresses type soundness. But I do remember while working on this that I was surprised there wasn't more treatment of the issues you're describing in the literature. I think it's an overlooked corner. Richard > On Jan 29, 2024, at 3:34 PM, Gershom B <[email protected]> wrote: > > [ The Types Forum, http://lists.seas.upenn.edu/mailman/listinfo/types-list ] > > Thanks all for the great responses. > > I'll give a bit more context what we're doing and what I'm looking > for, though judging from the responses thus far I don't think it > currently exists. > > We have a system with the usual type-formers and also iso-recursive > types (and of course some novel features), and a model that shows the > soundness of this system, etc. Now, what would be great is if there is > a result that lets us say "for such a system, there a related system > that also has explicit recursive datatype declarations of the form of > ML or Haskell98 [etc], and there is a simple translation such that > results done with iso-recursive types lift easily into the system with > explicit datatypes declarations." > > Extensionals / module-based approaches seem a powerful approach to the > modeling, but likely overkill what we'd like to be able to say, which > would likely be able to be done largely on a syntactic level. > > That said, it appears that most people are content to sort of > "hand-wave" that a proof in an iso-recursive setting is enough to "say > something" (even if not in a formal proof sense) about systems with > explicit datatype declarations, and given the current state of > literature, I hope an audience would find that reasonable? That is to > say -- our motivations in studying these things relate to existing > languages and implementations -- and in those, we use explicit > datatype declarations. So one hopes that limiting ourselves to instead > iso-recursive types does not undercut this motivation too drastically. > > Best, > Gershom > > > > On Sun, Jan 28, 2024 at 1:12 PM Sandro Stucki <[email protected]> wrote: >> >> Hi Gershom, >> >> That's not a naive question at all, in my opinion. :-) >> >> In addition to the many useful answers provided by others, I wanted to >> mention Christopher Stone's Chapter on "Type Definitions" (Chapter 9) >> in Advanced Topics in Types and Programming Languages (ATAPL). It >> describes a number of different approaches for adding type definitions >> in an F-omega-style type system, with calculi to illustrate them and a >> discussion of the meta-theoretic issues, TAPL-style. I found it very >> useful when I started to learn about this topic for my own research. >> >> Cheers, >> Sandro >> >> >> On Sat, Jan 27, 2024 at 3:34 AM Gershom B <[email protected]> wrote: >>> >>> [ The Types Forum, http://lists.seas.upenn.edu/mailman/listinfo/types-list ] >>> >>> In typical treatments of languages with recursive types, we present a >>> syntax with either isorecursive or equirecursive types. But we do not >>> have a syntax for introduction of type declarations. >>> >>> This is to say that we assemble types out of constructors for e.g., >>> polymorphism, recursion, sum, product, unit, exponential (give or >>> take). >>> >>> But we do not have the equivalent of a "data" declaration in Haskell >>> that lets us explicitly say >>> >>> data Bool = True | False >>> >>> or >>> >>> data List a = Nil | Cons a >>> >>> It is, I suppose, expected that readers of these papers can think >>> through how to translate any given data datatypes in languages with >>> explicit declaration into the underlying fixed type calculus. >>> >>> However, I am curious if there is any reference for *explicit* >>> treatment of the syntax for datatype declarations and semantic >>> modeling of such? >>> >>> One reason for such would be that in the calculi I described above, >>> there's of course no way to distinguish between the above `data Bool` >>> and e.g. `1 + 1`, while it might be desirable to maintain that strict >>> distinction between actual equality and merely observable isomorphism. >>> >>> Thanks, >>> Gershom
