## Composition

### January 11, 2010

New term for this month, borrowed from Algebra of Binary Relations: *composition* operation. Composition of two binary relations can be interpreted in Codd’s Relational Algebra (aka Algebra of Relations with Named Attributes) by taking their join, leading to a ternary relation, followed by a projection that removes the middle component. The less concise synonym for it is *set intersection join*. Renaming operation can be simulated as composition of the input relation with binary identity relation, which should convince the reader that composition is as frequent and important as *natural join*.

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