Duplicate Tuples

• Formal query languages are based on mathematical relations. Thus no duplicates appear in relations.
• As duplicate removal is expensive, SQL allows duplicates.
• To remove duplicates, we use the distinct keyword.
• To ensure that duplicates are not removed, we use the all keyword.
• Multiset (bag) versions of relational algebra operators.
  • if there are copies of tuples in , and satisfies selection , then there are copies of in .
  • for each copy of tuple in , there is a copy of tuple in .
  • if there are copies of tuple in , and copies of tuple in , there is copies of tuple in .
• An SQL query of the form

   select   
  
  		 from   
  
  		 where P 
  

  is equivalent to the algebra expression

  

  using the multiset versions of the relational operators , and .