the relational algebra and calculus
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The relational algebra and calculus. … SQL. 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

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Presentation Transcript
the big 3
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
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
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
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
slide6
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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