1. 1 Lecture 12: Further relational algebra, further SQL www.cl.cam.ac.uk/Teaching/current/Databases/

2. 2 Today’s lecture Where does SQL differ from relational model? What are some other features of SQL? How can we extend the relational algebra to match more closely SQL?

3. 3 Duplicate rows Consider our relation instances from lecture 6, Reserves, Sailors and Boats Consider SELECT rating,age FROM Sailors; We get a relation that doesn’t satisfy our definition of a relation! RECALL: We have the keyword DISTINCT to remove duplicates

4. 4 Multiset semantics A relation in SQL is really a multiset or bag, rather than a set as in the relational model –A multiset has no order (unlike a list), but allows duplicates –E.g. {1,2,1,3} is a bag –select, project and join work for bags as well as sets Just work on a tuple-by-tuple basis

5. 5 Bag operations Bag union: –Sum the number of times that an element appears in the two bags, e.g. {1,2,1}  {1,2,3} = {1,1,1,2,2,3} Bag intersection: –Take the minimum of the number of occurrences in each bag, e.g. {1,2,1}  {1,2,3,3} = {1,2} Bag difference: –Proper-subtract the number of occurrences in the two bags, e.g. {1,2,1}-{1,2,3,3} = {1}

6. 6 Laws for bags Note that whilst some of the familiar (set- theoretic) laws continue to hold, some of them do not Example: R  (S  T) = (R  S)  (R  T) ??

7. 7 Extended relational algebra Add features needed for SQL 1.Bag semantics 2.Duplicate elimination operator,  3.Sorting operator,  4.Grouping and aggregation operator,  5.Outerjoin operators, o V, V o, o V o

8. 8 Duplicate-elimination operator  (R) = relation R with any duplicated tuples removed R=  (R)= This is used to model the DISTINCT feature of SQL AB 12 34 12 AB 12 34

9. 9 Sorting  L 1,… L n (R) returns a list of tuples of R, ordered according to the attributes L 1, …, L n Note:  does not return a relation R=  B (R)= [(5,2),(1,3),(3,4)] ORDER BY in SQL, e.g. SELECT * FROM Sailors WHERE rating>7 ORDER BY age, sname; AB 13 34 52

10. 10 Extended projection SQL allows us to use arithmetic operators SELECT age*5 FROM Sailors; We extend the projection operator to allow the columns in the projection to be functions of one or more columns in the argument relation, e.g. R=  A+B,A,A (R)= AB 12 34 A+BA.1A.2 311 733

11. 11 Arithmetic Arithmetic (and other expressions) can not be used at the top level –i.e. 2+2 is not a valid SQL query How would you get SQL to compute 2+2?

12. 12 Aggregation SQL provides us with operations to summarise a column in some way, e.g. SELECT COUNT(rating) FROM Sailors; SELECT COUNT(DISTINCT rating) FROM Sailors; SELECT COUNT(*) FROM Sailors WHERE rating>7; We also have SUM, AVG, MIN and MAX

13. 13 Grouping These aggregation operators have been applied to all qualifying tuples. Sometimes we want to apply them to each of several groups of tuples, e.g. –For each rating, find the average age of the sailors –For each rating, find the age of the youngest sailor

14. 14 GROUP BY in SQL SELECT [DISTINCT] target-list FROM relation-list WHERE qualification GROUP BY grouping-list ; The target-list contains 1.List of column names 2.Aggregate terms –NOTE: The variables in target-list must be contained in grouping-list

15. 15 GROUP BY cont. For each rating, find the average age of the sailors SELECT rating,AVG(age) FROM Sailors GROUP BY rating; For each rating find the age of the youngest sailor SELECT rating,MIN(age) FROM Sailors GROUP BY rating;

16. 16 Grouping and aggregation  L (R) where L is a list of elements that are either –Individual column names (“Grouping attributes”), or –Of the form  (A), where  is an aggregation operator (MIN, SUM, …) and A is the column it is applied to For example,  rating,AVG(age) (Sailors)

17. 17 Semantics Group R according to the grouping attributes Within each group, compute  (A) Result is the relation consisting of one tuple for each group. The components of that tuple are the values associated with each element of L for that group

18. 18 Example Let R= Compute  beer,AVG( price ) (R) barbeerprice Anchor6X2.50 AnchorAdnam’s2.40 Mill6X2.60 MillFosters2.80 EagleFosters2.90

19. 19 Example cont. 1.Group according to the grouping attribute, beer : 2.Compute average of price within groups: barbeerprice Anchor6X2.50 Mill6X2.60 AnchorAdnam’s2.40 MillFosters2.80 EagleFosters2.90 beerprice 6X2.55 Adnam’s2.40 Fosters2.85

20. 20 NULL values Sometimes field values are unknown (e.g. rating not known yet), or inapplicable (e.g. no spouse name) SQL provides a special value, NULL, for both these situations This complicates several issues –Special operators needed to check for NULL –Is NULL>8? Is (NULL OR TRUE)=TRUE? –We need a three-valued logic –Need to carefully re-define semantics

21. 21 NULL values Consider INSERT INTO Sailors (sid,sname) VALUES (101,”Julia”); SELECT * FROM Sailors; SELECT rating FROM Sailors; SELECT sname FROM Sailors WHERE rating>0;

22. 22 Entity integrity constraint An entity integrity constraint states that no primary key value can be NULL

23. 23 Outer join Note that with the usual join, a tuple that doesn’t ‘join’ with any from the other relation is removed from the resulting relation Instead, we can ‘pad out’ the columns with NULLs This operator is called an full outer join, written o V o

24. 24 Example of full outer join Let R= Let S= Then RVS = But R o V o S = AB 12 34 BC 45 67 ABC 345 ABC 12 NULL 345 67

25. 25 Outer joins in SQL SQL/92 has three variants: –LEFT OUTER JOIN (algebra: o V) –RIGHT OUTER JOIN (algebra: V o ) –FULL OUTER JOIN (algebra: o V o ) For example: SELECT * FROM Reserves r LEFT OUTER JOIN Sailors s ON r.sid=s.sid;

26. 26 Views A view is a query with a name that can be used in further SELECT statements, e.g. CREATE VIEW ExpertSailors(sid,sname,age) AS SELECT sid,sname,age FROM Sailors WHERE rating>9; Note that ExpertSailors is not a stored relation (WARNING: mysql does not support views  )

27. 27 Querying views So an example query SELECT sname FROM ExpertSailors WHERE age>27; is translated by the system to the following: SELECT sname FROM Sailors WHERE rating>9 AND age>27;

28. 28 Summary You should now understand: Multi-set semantics Conditions Aggregation GROUP BY NULLs, entity ICs and outer joins Views Extensions to the core relational algebra