CODEWITHSUNDEEP
relational-databaserelational-algebra
Tim
Tim

Reputation: 99468

Why does this cascade of projection not change the projecton result?

From Database System Concept:

Only the final operations in a sequence of projection operations are needed; the others can be omitted. This transformation can also be referred to as a cascade of projection.

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Why does the above equation hold?

If L2 isn't a super set of L1, doesn't the left hand side have less columns than the right hand side?

Thanks.

Upvotes: 1

Views: 580

Answers (1)

philipxy
philipxy

Reputation: 15148

Why does the above equation hold?

A projection's attribute set must be a subset of its argument's. So each left hand side set is a subset of the set to its right. Each projection keeps some of its argument's columns. Finally only the leftmost set is left. That gives the right hand side.

If you wrote out the equation clearly saying what E & the Ls are then the restrictions would be apparent.

If L2 isn't a super set of L1, doesn't the left hand side have less columns than the right hand side?

L2 must be a superset of L1. Otherwise the left hand side is undefined.

Upvotes: 1

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