SELECT   a+b AS x, c AS y   FROM   R ...

⇒    Proj_{[x←a+b, y←c]}(R)

SQL projection extends RA projection with renaming and assignment

Join:

SELECT ... FROM ... R, S ... WHERE ... R.f  op  S.g ... ,    or

SELECT ... FROM ... R JOIN S ON  (R.f op S.g) ... WHERE ...

⇒    Join_{[R.f op S.g ]}(R,S)