Update to Turing 0.40

[mhauru]

No description provided.

[mhauru]

Sorry, not ready for review yet. I forgot things have actually changed in 0.40...

[penelopeysm]

I wonder if it's worth writing something in the dev docs about contexts vs accumulators and when one should use which?

[penelopeysm]

The timeout seems like it's related to a Mooncake patch bump rather than anything in Turing, given that this PR is also hanging. https://github.com/TuringLang/docs/actions/runs/17044261488/job/48317651587?pr=608

So, CI hanging on a Mooncake code block is completely misleading. It's hanging because of this error with DelayDiffEq.jl: SciML/DelayDiffEq.jl#329. The observed behaviour arises from the fact that:

1. when errors happen they don't get printed until after the entire notebook has executed.
2. the error in this case (when you attempt to sample from a Turing model with the differential equation) spits out a stack trace containing types that are something like a million characters long. (Yeahhhhhhh, just try doing quarto render tutorials/bayesian-differential-equations/index.qmd locally.)
3. GitHub Actions hangs whenever there's very long output. This is a known problem Long log lines slow down the runner actions/runner#1031

So from our perspective it looks like it's hanging after the last code block in the notebook, which is a Mooncake one.

Fixed on main now

[github-actions]

Preview the changes: https://turinglang.org/docs/pr-previews/636
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[penelopeysm]

Some minor suggestions for wording / formatting.

While it's already quite useful getting the docs to build with a version of Turing, I have a nagging feeling that we are not documenting the things that we should be documenting very well.

For one, it looks like documenting the whole accumulators / contexts thing is just being shunted until we have more stability around the interface. That's at least sort of understandable, because who knows what's going to change in upcoming releases.

However, there are also the user-facing changes that arise from that. For example, accumulators mean that chains now contain logp + its components. This is obviously worth showing somewhere, but it isn't being shown.

I don't want that to hold this PR up, but I do think that at least new issue(s) should be made for anything that needs to be added to the docs.

[penelopeysm]

(I'm otherwise happy to merge with the two changes above)

[mhauru]

I agree that we should add/improve the content. I opened these issues to track:

• Add information about what's in chains #646
• Document accumulators #644
• Update mini turing and compiler design pages #645

My goal with this PR would be to get the code examples working, and to hopefully not state anything that is plain wrong, even if it falls short of explaining all that is there.

[penelopeysm]

Feel free to merge (well, after fixing the manifest :))