Database Systems - Chapter 5: Structured Query Language (SQL) - Trương Quỳnh Chi

Nội dung text: Database Systems - Chapter 5: Structured Query Language (SQL) - Trương Quỳnh Chi

1. Contents 1 Unary Relational Operations 2 Relational Algebra Operations from Set Theory 3 Binary Relational Operations 4 Additional Relational Operations 5 Brief Introduction to Relational Calculus Relational Algebra 2
2. Relational Algebra Overview £ Relational algebra is the basic set of operations for the relational model • These operations enable a user to specify basic retrieval requests (or queries) £ The result of an operation is a new relation, which may have been formed from one or more input relations • This property makes the algebra “closed” (all objects in relational algebra are relations) £ A sequence of relational algebra operations forms a relational algebra expression Relational Algebra 4
3. COMPANY Database Schema Relational Algebra 6
4. Unary Relational Operations: SELECT £ The SELECT operation (denoted by s (sigma)) is used to select a subset of the tuples from a relation based on a selection condition. £ Examples: • Select the EMPLOYEE tuples whose department number is 4: s DNO = 4 (EMPLOYEE) • Select the employee tuples whose salary is greater than $30,000: s SALARY > 30,000 (EMPLOYEE) Relational Algebra 8
5. Unary Relational Operations: SELECT £ SELECT Operation Properties • The relation S = s (R) has the same schema (same attributes) as R • SELECT s is commutative: s (s (R)) = s (s (R)) • Because of commutativity property, a cascade (sequence) of SELECT operations may be applied in any order: s (s (s (R))= s (s (s (R))) = s AND AND (R) • The number of tuples in the result of a SELECT is less than (or equal to) the number of tuples in the input relation R Relational Algebra 10
6. Unary Relational Operations: PROJECT £ The general form of the project operation is: p (R) • is the desired list of attributes from relation R £ The project operation removes any duplicate tuples because the result of the project operation must be a set of tuples and mathematical sets do not allow duplicate elements Relational Algebra 12
7. Examples of applying SELECT and PROJECT operations Relational Algebra 14
8. Single expression versus sequence of relational operations £ To retrieve the first name, last name, and salary of all employees who work in department number 5, we must apply a select and a project operation £ We can write a single relational algebra expression as follows: pFNAME, LNAME, SALARY(s DNO=5(EMPLOYEE)) £ OR We can explicitly show the sequence of operations, giving a name to each intermediate relation: • DEP5_EMPS ¬ s DNO=5(EMPLOYEE) • RESULT ¬ p FNAME, LNAME, SALARY (DEP5_EMPS) Relational Algebra 16
9. Unary Relational Operations: RENAME £ The general RENAME operation r can be expressed by any of the following forms: • rS (B1, B2, , Bn )(R) changes both: • the relation name to S, and • the column (attribute) names to B1, B1, Bn • rS(R) changes: • the relation name only to S • r(B1, B2, , Bn )(R) changes: • the column (attribute) names only to B1, B1, Bn Relational Algebra 18
10. Relational Algebra Operations from Set Theory: UNION £ Binary operation, denoted by È £ The result of R È S, is a relation that includes all tuples that are either in R or in S or in both R and S £ Duplicate tuples are eliminated £ The two operand relations R and S must be “type compatible” (or UNION compatible) • R and S must have same number of attributes • Each pair of corresponding attributes must be type compatible (have same or compatible domains) Relational Algebra 20
11. Relational Algebra Operations from Set Theory £ Type Compatibility of operands is required for the binary set operation UNION È, (also for INTERSECTION Ç, and SET DIFFERENCE –) £ The resulting relation for R1ÈR2 (also for R1ÇR2, or R1–R2) has the same attribute names as the first operand relation R1 (by convention) Relational Algebra 22
12. Relational Algebra Operations from Set Theory: SET DIFFERENCE £ SET DIFFERENCE (also called MINUS or EXCEPT) is denoted by – £ The result of R – S, is a relation that includes all tuples that are in R but not in S • The attribute names in the result will be the same as the attribute names in R £ The two operand relations R and S must be “type compatible” Relational Algebra 24
13. Some properties of UNION, INTERSECT, and DIFFERENCE £ Notice that both union and intersection are commutative operations; that is • R È S = S È R, and R Ç S = S Ç R £ Both union and intersection can be treated as n-ary operations applicable to any number of relations as both are associative operations; that is • R È (S È T) = (R È S) È T • (R Ç S) Ç T = R Ç (S Ç T) £ The minus operation is not commutative; that is, in general • R – S ≠ S – R Relational Algebra 26
14. Binary Relational Operations: JOIN £ JOIN Operation (denoted by ) • The sequence of CARTESIAN PRODECT followed by SELECT is used quite commonly to identify and select related tuples from two relations • A special operation, called JOIN combines this sequence into a single operation • This operation is very important for any relational database with more than a single relation, because it allows us combine related tuples from various relations • The general form of a join operation on two relations R(A1, A2, . . ., An) and S(B1, B2, . . ., Bm) is: R S • where R and S can be any relations that result from general relational algebra expressions. Relational Algebra 28
15. COMPANY Database Schema £ All examples discussed below refer to the COMPANY DB below: Relational Algebra 30
16. Example of applying the JOIN operation DEPT_MGR ¬ DEPARTMENT MGRSSN=SSN EMPLOYEE Relational Algebra 32
17. Some properties of JOIN £ The general case of JOIN operation is called a Theta-join: R S £ The join condition is called theta £ Theta can be any general boolean expression on the attributes of R and S; for example: • R.Ai<S.Bj AND (R.Ak=S.Bl OR R.Ap<S.Bq) Relational Algebra 34
18. Binary Relational Operations: NATURAL JOIN Operation £ NATURAL JOIN Operation • Another variation of JOIN called NATURAL JOIN — denoted by * — was created to get rid of the second (superfluous) attribute in an EQUIJOIN condition • The standard definition of natural join requires that the two join attributes, or each pair of corresponding join attributes, have the same name in both relations • If this is not the case, a renaming operation is applied first £ Example: Q ¬ R(A,B,C,D) * S(C,D,E) • The implicit join condition includes each pair of attributes with the same name, “AND”ed together: • R.C=S.C AND R.D.S.D • Result keeps only one attribute of each such pair: • Q(A,B,C,D,E) Relational Algebra 36
19. Complete Set of Relational Operations £ The set of operations {s, p , È, - , X} is called a complete set because any other relational algebra expressions can be expressed by a combination of these five operations £ For example: • R Ç S = (R È S ) – ((R - S) È (S - R)) • R S = s (R X S) Relational Algebra 38
20. The DIVISION operation (a) Dividing SSN_PNOS by SMITH_PNOS (b) T ¬ R ÷ S Relational Algebra 40
21. Notation for Query Trees £ Query tree • Represents the input relations of query as leaf nodes of the tree • Represents the relational algebra operations as internal nodes Relational Algebra 42
22. Contents 1 Unary Relational Operations 2 Relational Algebra Operations from Set Theory 3 Binary Relational Operations 4 Additional Relational Operations 5 Brief Introduction to Relational Calculus Relational Algebra 44
23. Examples of applying aggregate functions and grouping Relational Algebra 46
24. Additional Relational Operations £ Recursive Closure Operations • Another type of operation that, in general, cannot be specified in the basic original relational algebra is recursive closure. This operation is applied to a recursive relationship • An example of a recursive operation is to retrieve all SUPERVISEES of an EMPLOYEE e at all levels • Although it is possible to retrieve employees at each level and then take their union, we cannot, in general, specify a query such as “retrieve the supervisees of ‘James Borg’ at all levels” without utilizing a looping mechanism • The SQL3 standard includes syntax for recursive closure Relational Algebra 48
25. Additional Relational Operations £ The left outer join operation keeps every tuple in the first or left relation R in R S; if no matching tuple is found in S, then the attributes of S in the join result are filled or “padded” with null values. £ A similar operation, right outer join, keeps every tuple in the second or right relation S in the result of R S. £ A third operation, full outer join, denoted by keeps all tuples in both the left and the right relations when no matching tuples are found, padding them with null values as needed. Relational Algebra 50
26. The following query results refer to this database state Relational Algebra 52
27. Exercise £ Using relational algebra: retrieve the name and address of all employees who work for the ‘Research’ department RESEARCH_DEPT ¬ s DNAME=’Research’ (DEPARTMENT) RESEARCH_EMPS ¬ (RESEARCH_DEPT DNUMBER= DNOEMPLOYEE) RESULT ¬ p FNAME, LNAME, ADDRESS (RESEARCH_EMPS) Relational Algebra 54
28. Contents 1 Unary Relational Operations 2 Relational Algebra Operations from Set Theory 3 Binary Relational Operations 4 Additional Relational Operations 5 Brief Introduction to Relational Calculus Relational Algebra 56
29. Brief Introduction to Relational Calculus £ The tuple relational calculus is based on specifying a number of tuple variables. Each tuple variable usually ranges over a particular database relation, meaning that the variable may take as its value any individual tuple from that relation £ A simple tuple relational calculus query is of the form {t | COND(t)} where t is a tuple variable and COND (t) is a conditional expression involving t Example: To find the first and last names of all employees whose salary is above $50,000, we can write the following tuple calculus expression: {t.FNAME, t.LNAME | EMPLOYEE(t) AND t.SALARY>50000} The condition EMPLOYEE(t) specifies that the range relation of tuple variable t is EMPLOYEE. The first and last name (pFNAME, LNAME) of each EMPLOYEE tuple t that satisfies the condition t.SALARY>50000 (s SALARY >50000) will be retrieved Relational Algebra 58
30. Brief Introduction to Relational Calculus £ Example 1: retrieve the name and address of all employees who work for the ‘Research’ dept. {t.FNAME, t.LNAME, t.ADDRESS | EMPLOYEE(t) and ($ d) (DEPARTMENT(d) and d.DNAME=‘Research’ and d.DNUMBER=t.DNO) } Relational Algebra 60
31. Brief Introduction to Relational Calculus £ Another variation of relational calculus called the domain relational calculus, or simply, domain calculus is equivalent to tuple calculus and to relational algebra £ QBE (Query-By-Example): see Appendix D £ Domain calculus differs from tuple calculus in the type of variables used in formulas: rather than having variables range over tuples, the variables range over single values from domains of attributes. To form a relation of degree n for a query result, we must have n of these domain variables—one for each attribute £ An expression of the domain calculus is of the form {x1, x2, . . ., xn | COND(x1, x2, . . ., xn, xn+1, xn+2, . . ., xn+m)} where x1, x2, . . ., xn, xn+1, xn+2, . . ., xn+m are domain variables that range over domains (of attributes) and COND is a condition or formula of the domain relational calculus Relational Algebra 62
32. Summary 1 Unary Relational Operations 2 Relational Algebra Operations from Set Theory 3 Binary Relational Operations 4 Additional Relational Operations 5 Brief Introduction to Relational Calculus Relational Algebra 64