Stream: maths

Topic: non-dependent type sheaves

Kevin Buzzard (Apr 01 2020 at 08:53):

I guess this is well-known but it's only just dawned on me. Rings are set up in a semi-bundled way in mathlib. So a sheaf of rings needs to involve a dependent type, because it's F : opens X -> Type followed by [hF : Pi (U : opens X), comm_ring (F U)]. But if rings were completely bundled then we could just have F : opens X -> CommRing and no dependent type is needed. Does this mean I should switch to Isabelle or are there dependent types under the hood in this setting?

Yury G. Kudryashov (Apr 01 2020 at 08:57):

CommRing is a dependent type

Yury G. Kudryashov (Apr 01 2020 at 08:57):

Disclaimer: I never tried Isabelle, and I don't know what it can (not) handle.

Kevin Buzzard (Apr 01 2020 at 09:13):

Yury G. Kudryashov said:

CommRing is a dependent type

I see. I thought it might well be something like this.

Yury G. Kudryashov (Apr 01 2020 at 09:48):

Another example: we have several measurable_space instances defined to be top.

Nick Chopper (Apr 02 2020 at 10:08):

I create this(cat.lean) several days ago and have some initial thoughts. I think it might possible to create one completely bundled structure and then get all sorts of things (unbundled structure, like cat/cat'/cat'/... in the file, and proof of equivalence between them or something else) automatically.

Johan Commelin (Apr 02 2020 at 10:54):

@Nick Chopper Sorry, I'm a bit dense... what exactly is your proposal?

Kevin Buzzard (Apr 02 2020 at 11:35):

bundled categories

Nick Chopper (Apr 02 2020 at 12:12):

@Johan Commelin auto coe between bundled/unbundled structure (loop?), so as to use type class fill in unbundled one and then actually get a bundled one. I find it has been solved by category_theory.bundled in the case of one-parameter class, but I wonder if it is possible to generate code like inductive type (say, unbundled structure from bundled (don't know how to avoid name confliction (instead of adding ') yet))

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Nick Chopper (Apr 02 2020 at 12:12):

sorry for poor english

Last updated: May 11 2021 at 15:12 UTC