1 / 73

Revision for Final Exam

CS157A Lecture 25. Revision for Final Exam. Prof. Sin-Min Lee Department of Computer Science. Relational Query Languages. Languages for describing queries on a relational database Structured Query Language (SQL) Predominant application-level query language Declarative Relational Algebra

tanner
Download Presentation

Revision for Final Exam

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. CS157A Lecture 25 Revision for Final Exam Prof. Sin-Min Lee Department of Computer Science

  2. Relational Query Languages • Languages for describing queries on a relational database • Structured Query Language (SQL) • Predominant application-level query language • Declarative • Relational Algebra • Intermediate language used within DBMS • Procedural

  3. What is an Algebra? • A language based on operators and a domain of values • Operators map values taken from the domain into other domain values • Hence, an expression involving operators and arguments produces a value in the domain • When the domain is a set of all relations (and the operators are as described later), we get the relational algebra • We refer to the expression as a query and the value produced as the queryresult

  4. Relational Algebra • Domain: set of relations • Basic operators: select, project, union, setdifference, Cartesianproduct • Derived operators: set intersection, division, join • Procedural: Relational expression specifies query by describing an algorithm (the sequence in which operators are applied) for determining the result of an expression

  5. The Role of Relational Algebra in a DBMS

  6. Produce table containing subset of rows of argument table satisfying condition condition (relation) Example: Person Hobby=‘stamps’(Person) Select Operator Id Name Address Hobby Id Name Address Hobby 1123 John 123 Main stamps 1123 John 123 Main coins 5556 Mary 7 Lake Dr hiking 9876 Bart 5 Pine St stamps 1123 John 123 Main stamps 9876 Bart 5 Pine St stamps

  7. Selection Condition • Operators: <, , , >, =,  • Simple selection condition: • <attribute> operator <constant> • <attribute> operator <attribute> • <condition> AND <condition> • <condition> OR <condition> • NOT <condition>

  8. Selection Condition - Examples •  Id>3000OR Hobby=‘hiking’ (Person) •  Id>3000 AND Id <3999(Person) •  NOT(Hobby=‘hiking’)(Person) •  Hobby‘hiking’(Person)

  9. Project Operator • Produces table containing subset of columns of the table taken as argument attribute list(relation) • Example: Person Name,Hobby(Person) IdName AddressHobbyNameHobby John stamps John coins Mary hiking Bart stamps 1123 John 123 Main stamps 1123 John 123 Main coins 5556 Mary 7 Lake Dr hiking 9876 Bart 5 Pine St stamps

  10. Project Operator • Example: • Person Name,Address(Person) Id Name Address Hobby Name Address John 123 Main Mary 7 Lake Dr Bart 5 Pine St 1123 John 123 Main stamps 1123 John 123 Main coins 5556 Mary 7 Lake Dr hiking 9876 Bart 5 Pine St stamps Result is a table (no duplicates); can have fewer tuples than the original

  11. Expressions Id, Name(Hobby=’stamps’OR Hobby=’coins’(Person) ) Id Name Address Hobby Id Name 1123 John 9876 Bart 1123 John 123 Main stamps 1123 John 123 Main coins 5556 Mary 7 Lake Dr hiking 9876 Bart 5 Pine St stamps Result Person

  12. Set Operators • Relation is a set of tuples, so set operations should apply: , ,  (set difference) • Result of combining two relations with a set operator is a relation; hence all its elements must be tuples having the same structure • Hence, scope of set operations limited to union compatible relations

  13. Union Compatible Relations • Two relations are union compatible if • Both have same number of columns • Names of attributes are the same in both • Attributes with the same name in both relations have the same domain • Union compatible relations can be combined using union, intersection, and setdifference

  14. Example Tables: Person(SSN, Name, Address, Hobby) Professor(Id, Name, Office, Phone) are not union compatible. But Name(Person)and Name(Professor) are union compatible so Name(Person) -Name(Professor) makes sense.

  15. Cartesian Product • If Rand Sare two relations, RS is the set of all concatenated tuples <x,y>, where x is a tuple in R and y is a tuple in S (but see naming problem next) • RS is expensive to compute: • Factor of two in the size of each row • Quadratic in the number of rows A B C D A B C D x1 x2 y1 y2 x1 x2 y1 y2 x3 x4 y3 y4 x1 x2 y3 y4 x3 x4 y1 y2 RS x3 x4 y3 y4 RS

  16. Renaming in Cartesian Product Result of expression evaluation is a relation. Attributes of relation must have distinct names. So what do we do if they don’t? E.g., suppose R(A,B) and S(A,C) and we wish to compute RS . One solution is to rename the attributes of the answer: RS( R.A, R.B, S.A, S.C) Although only A needs to be renamed, it is“cleaner” to rename them all.

  17. Renaming Operator • Previous solution is used whenever possible but it won’t work when R is the same as S. • Renaming operator resolves this. It allows to assign any desired names, say A1, A2,… An , to the attributes of the n column relation produced by expression expr with the syntax expr [A1, A2, … An]

  18. Example Transcript (StudId, CrsCode, Semester, Grade) Teaching (ProfId, CrsCode, Semester) StudId, CrsCode(Transcript)[StudId, CrsCode1]  ProfId, CrsCode(Teaching) [ProfId, CrsCode2] This is a relation with 4 attributes: StudId, CrsCode1, ProfId, CrsCode2

  19. Derived Operation: Join A (general or theta) join of R and S is the expression Rjoin-conditionS where join-condition is a conjunction of terms: Ai oper Bi in which Ai is an attribute of R;Bi is an attribute of S; and oper is one of =, <, >,  , . The meaning is:  join-condition´(R  S) where join-condition and join-condition´ are the same, except for possible renamings of attributes caused by the Cartesian product.

  20. Theta Join – Example Employee(Name,Id,MngrId,Salary) Manager(Name,Id,Salary) Output the names of all employees that earn more than their managers. Employee.Name(EmployeeMngrId=Id AND Salary>SalaryManager) The join yields a table with attributes: Employee.Name, Employee.Id, Employee.Salary, Employee.MngrId Manager.Name, Manager.Id, Manager.Salary

  21. Relational Algebra • Relational algebra operations operate on relations and produce relations (“closure”) f: Relation -> Relation f: Relation x Relation -> Relation • Six basic operations: • Projection A (R) • Selection  (R) • Union R1[ R2 • Difference R1– R2 • Product R1£ R2 • (Rename) A->B (R)

  22. Equijoin Join - Example Equijoin: Join condition is a conjunction of equalities. Name,CrsCode(Student Id=StudId Grade=‘A’ (Transcript)) Student Transcript Id Name Addr Status 111 John ….. ….. 222 Mary ….. ….. 333 Bill ….. ….. 444 Joe ….. ….. StudId CrsCode Sem Grade 111 CSE305 S00 B 222 CSE306 S99 A 333 CSE304 F99 A The equijoin is used very frequently since it combines related data in different relations. Mary CSE306 Bill CSE304

  23. Natural Join • Special case of equijoin + a special projection • join condition equates all and only those attributes with the same name (condition doesn’t have to be explicitly stated) • duplicate columns eliminated (projected out) from the result Transcript (StudId, CrsCode, Sem, Grade) Teaching (ProfId, CrsCode, Sem) Teaching = Transcript StudId, Transcript.CrsCode, Transcript.Sem, Grade, ProfId (Transcript CrsCode=CrsCodeANDSem=Sem Teaching ) [StudId, CrsCode, Sem, Grade, ProfId]

  24. Natural Join (cont’d) • More generally: R S = attr-list(join-cond(R × S) ) where attr-list = attributes (R) attributes (S) (duplicates are eliminated) and join-cond has the form: A1 = A1AND … ANDAn = An where {A1 … An} = attributes(R) attributes(S)

  25. Natural Join Example • List all Ids of students who took at least two different courses: StudId( CrsCode  CrsCode2 ( Transcript Transcript[StudId, CrsCode2, Sem2, Grade2] )) We don’t want to join on CrsCode, Sem, and Grade attributes, hence renaming!

  26. Example Data Instance STUDENT COURSE Takes PROFESSOR Teaches

  27. Natural Join and Intersection Natural join: special case of join where  is implicit – attributes with same name must be equal: STUDENT ⋈ Takes ´ STUDENT ⋈STUDENT.sid = Takes.sid Takes Intersection: as with set operations, derivable from difference A  B B-A A-B A B

  28. Division • A somewhat messy operation that can be expressed in terms of the operations we have already defined • Used to express queries such as “The fid's of faculty who have taught all subjects” • Paraphrased: “The fid’s of professors for which there does not exist a subject that they haven’t taught”

  29. Division Using Our Existing Operators • All possible teaching assignments: Allpairs: • NotTaught, all (fid,subj) pairs for which professor fidhas not taught subj: • Answer is all faculty not in NotTaught: fid,subj (PROFESSOR £subj(COURSE)) Allpairs - fid,subj(Teaches ⋈ COURSE) fid(PROFESSOR) - fid(NotTaught) ´ fid(PROFESSOR) - fid( fid,subj (PROFESSOR £subj(COURSE)) - fid,subj(Teaches ⋈ COURSE))

  30. Division: R1¸ R2 • Requirement: schema(R1) ¾ schema(R2) • Result schema: schema(R1) – schema(R2) • “Professors who have taught all courses”: • What about “Courses that have been taught by all faculty”? fid (fid,subj(Teaches ⋈ COURSE) ¸subj(COURSE))

  31. Division • Goal: Produce the tuples in one relation, r, that match all tuples in another relation, s • r (A1, …An, B1, …Bm) • s (B1 …Bm) • r/s, with attributes A1, …An, is the set of all tuples <a> such that for every tuple <b> ins,<a,b> is in r • Can be expressed in terms of projection, set difference, and cross-product

  32. Division (cont’d)

  33. Division - Example • List the Ids of students who have passed all courses that were taught in spring 2000 • Numerator: • StudId and CrsCode for every course passed by every student: StudId, CrsCode (Grade ‘F’ (Transcript) ) • Denominator: • CrsCode of all courses taught in spring 2000 CrsCode(Semester=‘S2000’ (Teaching) ) • Result is numerator/denominator

  34. Relational Calculus • Important features: • Declarative formal query languages for relational model • Based on the branch mathematical logic known as predicate calculus • Two types of RC: • 1) tuple relational calculus • 2) domain relational calculus • A single statement can be used to perform a query

  35. Tuple Relational Calculus • based on specifying a number of tuple variables • a tuple variable refers to any tuple

  36. Generic Form • {t | COND (t)} • where • t is a tuple variable and • COND(t) is Boolean expression involving t

  37. Simple example 1 • To find all employees whose salary is greater than $50,000 • {t| EMPLOYEE(t) and t.Salary>5000} • where • EMPLOYEE(t) specifies the range of tuple variable t • The above operation selects all the attributes

  38. Simple example 2 • To find only the names of employees whose salary is greater than $50,000 • {t.FNAME, t.NAME| EMPLOYEE(t) and t.Salary>5000} • The above is equivalent to • SELECT T.FNAME, T.LNAME • FROM EMPLOYEE T • WHERE T.SALARY > 5000

  39. Elements of a tuple calculus • In general, we need to specify the following in a tuple calculus expression: • Range Relation (I.e, R(t)) = FROM • Selected combination= WHERE • Requested attributes= SELECT

  40. More Example:Q0 • Retrieve the birthrate and address of the employee(s) whose name is ‘John B. Smith’ • {t.BDATE, t.ADDRESS| EMPLOYEE(t) AND t.FNAME=‘John’ AND t.MINIT=‘B” AND t.LNAME=‘Smith}

  41. Formal Specification of tuple Relational Calculus • A general format: • {t1.A1, t2.A2,…,tn.An |COND ( t1 ,t2 ,…, tn, tn+1, tn+2,…,tn+m)} • where • t1,…,tn+m are tuple var • Ai : attributeR(ti) • COND (formula) • Where COND corresponds to statement about the world, which can be True or False

  42. Elements of formula • A formula is made of Predicate Calculus atoms: • an atom of the from R(ti) • ti.A op tj.B op{=, <,>,..} • F1 And F2 where F1 and F2 are formulas • F1 OR F2 • Not (F1) • F’=(t) (F) or F’= (t) (F) •  Y friends (Y, John) • X likes(X, ICE_CREAM)

  43. Example Queries Using the Existential Quantifier • Retrieve the name and address of all employees who work for the ‘ Research ’ department • {t.FNAME, t.LNAME, t.ADDRESS| EMPLOYEE(t) AND ( d) (DEPARTMENT (d) AND d.DNAME=‘Research’ AND d.DNUMBER=t.DNO)}

  44. More Example • For every project located in ‘Stafford’, retrieve the project number, the controlling department number, and the last name, birthrate, and address of the manger of that department.

  45. Cont. • {p.PNUMBER,p.DNUM,m.LNAME,m.BDATE, m.ADDRESS|PROJECT(p) and EMPLOYEE(M) and P.PLOCATION=‘Stafford’ and ( d) (DEPARTMENT(D) AND P.DNUM=d.DNUMBER and d.MGRSSN=m.SSN))}

  46. Safe Expressions • A safe expression R.C: • An expression that is guaranteed to generate a finite number of rows (tuples) • Example: • {t | not EMPLOYESS(t))} results values not being in its domain (I.e., EMPLOYEE)

  47. Domain Relational Calculus (DRC) • Another type of formal predicate calculus-based language • QBE is based on DRC • The language shares a lot of similarities with the tuple calculus

  48. DRC • The only difference is the type of variables: • variables range over singles values from domains of attributes • An expression of DRC is: • {x1, x2,…,xn|COND(x1,x2,…,xn, xn+2,…,xn+m)} • where x1,x2,…,xn+m are domain var range over attributers • COND is a condition (or formula)

  49. Examples • Retrieve the birthdates and address of the employee whose name is ‘John B. Smith’ • {uv| (q)(r)(s) (EMPLOYEE(qrstuvwxyz) and q=‘John’ and r=‘B’ and s=‘Smith’

  50. Alternative notation • Ssign the constants ‘John’, ‘B’, and ‘Smith’ directly • {uv|EMPLOYEE (‘John’, ’B’, ’Smith’ ,t ,u ,v ,x ,y ,z)}

More Related