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The relational algebra and calculusPowerPoint Presentation

The relational algebra and calculus

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The big 3:

- Selection and projection are unary ops
- Join is binary
- Selection is based on a formula and returns a table that contains all tuples from a given table where the formula is valid
- Projection returns a table consisting of a subset of attributes from a given table, with dupes removed
- Join creates tuples with attributes from two given tables, where a specific attribute in one matches a specific attribute in another (often a PK, FK pair)

Algebraic closure

- Any relational algebra operation returns a legal derived table
- The set operators are also part of the algebra
- From a formal perspective, the join operator is not a minimal operator, and is therefore represented as a cross product followed by a selection (where the PK equals the FK)
- Note that joins are symetric

Joins can be generalized

- Complex join conditions
- Non-equi joins
- A “natural” join is based on matching all attributes with equal names in both tables
- “Outer” join creates null-packed tuples when tuples on the left do not match any on the right; there is also a right outer join

The calculus

- It is a tuple calculus, not a domain calculus
- SQL is equivalent
- Select From Where
- The part after the Where is declarative
- A tuple calculus (SQL)
- Notice that the variables are indeed tuples
- Note that set operators often act on tables that are being created in the query

More

- IN operator is “element of”
- EXISTS
- Nesting
- FOR ALL
- FOR SOME
- Putting computations in the SELECT clause
- COUNT, SUM, AVG, MAX, MIN operators

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