User-defined densities allowed over nested and complex values.

[WardBrian]

Closes #1045. The is_int_type and is_real_types now check the type recursively to handle nesting, and lpdf is defined not by 'takes a real as the first argument' but (properly) as 'does not take an int as the first argument'

Submission Checklist

• Run unit tests
• Documentation
  • OR, no user-facing changes were made
    This is consistent with the final paragraph given here already

Release notes

Allow user-defined densities over complex arguments and deeply nested arguments.

Copyright and Licensing

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license the submitted work under the BSD 3-clause license (https://opensource.org/licenses/BSD-3-Clause)

[nhuurre]

Oh cool, I forgot about the complex type.
I'm going to point out that technically we also have function types and I don't think they should be allowed in _lpdfs. It's not possible to name them at the moment so it doesn't really matter until Stan gets closures.

[WardBrian]

Yeah, we can cross that bridge once a user could actually try to write a function type as an argument declaration. Something like UnsizedType.is_numeric_type && not UnsizedType.is_int_type (we'd have to define the first function if we haven't already, but it's easy)

[nhuurre]

Ok.