Update code in docs for style and deprecations

[WardBrian]

Submission Checklist

• Builds locally
• Declare copyright holder and open-source license: see below

Summary

Resolves #383. Fixes spacing and syntax in all examples:

array[] T syntax over T[]

Spaces following commas

Mark all stan code with ```stan

Unify format of if/for/while loops to always use {} for clarity

Some of these changes were done automatically. It's hard to be certain if I caught every outdated example, but I have checked and am reasonable certain all the changes here are valid.

Copyright and Licensing

Please list the copyright holder for the work you are submitting (this will be you or your assignee, such as a university or company):
Simons Foundation

By submitting this pull request, the copyright holder is agreeing to license the submitted work under the following licenses:

• Code: BSD 3-clause (https://opensource.org/licenses/BSD-3-Clause)
• Documentation: CC-BY 4.0 (https://creativecommons.org/licenses/by/4.0/)

[bob-carpenter]

This is fantastic, despite the fact that I need an ice pack for my forearm after all the scrolling. All the code changes look good. Only a few comments/questions.

[bob-carpenter]

These commented forms are for export to things like RStudio. Are you sure they can handle this array[] T format? If not, @bgoodri or @jgabry may know what RStudio needs.

[bgoodri]

We'll have to add signatures for that.

[WardBrian]

They were simply caught by the find-and-replace done for the formatted output. I was assuming the comments were there as a more human-readable note in the source text, that's my bad. I can change them back if it's too much of a problem?

[WardBrian]

@bob-carpenter this is ready for re-review, you should be able to look at just the diff on the most recent 3 commits

[bob-carpenter]

Looks great. Thanks for all the updates.