[ccouzens]

There are other ways, like having a null with more regular semantics and better composeability (like Rust's option type).

Or imagine this data:

Students:

Name: Bob

Name: Alice

StudentsClasses

Student: Bob, class: cryptography.

Student: Bob, class: databases

If you can have arrays (or relations) as a field in your result set, then

Students left outer join StudentsClasses

Could return

Student: Bob, classes: [ cryptography, databases]

Student: Alice, classes: []

[goto11]

This violates first normal form. So if you want to query this result further you need a more complex language than relational algebra because you need to be able to query nested structures.

[emmelaich]

1nf is surprisingly tricky to define.

If you consider it as a single atomic list then it is still in 1nf.

It's only not in 1nf with respect to future queries IF you want to subselect from within the list values.

[goto11]

1NF is defined as eliminating nested relations. I assumed "[ cryptography, databases]" in the example represent a nested relation.

1NF is not defined in terms of what you want to do with the the data, it is defined in terms of domains, i.e data types. If a column allows nested tables, it violates 1NF.

"Atomic" in the context of 1NF means atomic wrt. the relational algebra.

Eg. if we have:

   Student: Bob, classes: [ cryptography, databases]
   Student: Alice, classes: [] 

Is it possible to select from this all students which has cryptography as a class, using the standard relational operators (project, filter, join)?

[emmelaich]

I think we're mostly in agreement!

You're right, it's not possible to select from this all students which has cryptography as a class. No more than if we did concat('cryptography', ',', 'databases').

[ccouzens]

The normal forms are about how data is stored, rather than how it looks after a query. After all, most joins will violate second normal form.

But yes, SQL doesn't work well with this solution.