I'm trying to understand this paper and in Figure 1 page 389 there's a projection in the form of $\pi_{d.id : s.id}$. What does the colon mean? Because usually projections are simply $\pi_{name}(R)$

  • $\begingroup$ What does the paper say it means? $\endgroup$
    – philipxy
    Jan 1, 2022 at 18:30
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1 Answer 1


Colon in Π (project) seems to be attribute rename after projecting a la SQL SELECT AS, but in the order new attribute : old attribute. This is similar to its use in Γ (group by) for new attribute : value per pseudo aggregation function call.

Thus, the dependent join is executed on the projection of the students’ id only, i.e.:

. . . Π d.id:s.id ((students s ⋈ s.id=e.sid exams e) ⧑
    (Γ ∅;m:min(e2.grade)(σ d.id=e2.sid exams e2)))

This interpretation seems to be needed to make sense of Figure 1 as we follow relation attribute sets from the root down or leaves up.


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