Relational Projection

Say you have a table:

Addresses
First-Name Last-Name Address
_______________________________________
William Underwood Somewhere
John Smith Somewhere-Else
Jane Smith Somewhere-Else


Projection lets you answer questions such as "How many unique names are there in the database?" and "What addresses are there in the database?"

For example, if we projected the above table to {First-Name Last-Name} we would be left with

Addresses.projectTo({First-Name Last-Name})
First-Name Last-Name
______________________
William Underwood
John Smith
Jane Smith


Likewise, if we projected down to {Address} we would have

Addresses.projectTo({Address})
Address
______________
Somewhere
Somewhere-Else


Note that the duplicates are eliminated from the result: in relational theory, you can't have two tuples (rows) in a table which are identical; by removing the First-Name from the table, the rows "John, Smith, Somewhere-Else" and "Jane, Smith, Somewhere-Else" become indistinguishable, and so they are collapsed into one row.

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I have not tested it, but one may be able to achieve this in SQL using something like:

select first, last, combined
from (select first, last, concat(first,' ',last) as combined
from names
)
group by first, last, combined


It's simpler than that actually, you'd just do

SELECT DISTINCT First-Name, Last-Name FROM Addresses


Not all dialects support Distinct (at least they did not used to). Then again they don't all support nested queries either.

Note though, that I'm deliberately ignoring standard SQL syntax for exactly this reason. You know SQL, but yet you don't know relational algebra, which SQL is a broken implementation of. The alternate syntax makes sure that misconceptions brought from experience in query languages are exposed.

I am just covering the practical side of things because for good or bad, we are stuck with SQL for a while.

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One of the operators in RelationalAlgebra