1. Temple University – CIS Dept. CIS331– Principles of Database Systems V. Megalooikonomou Relational Model III (based on notes by Silberchatz,Korth, and Sudarshan and notes by C. Faloutsos at CMU)

2. Overview history concepts Formal query languages relational algebra rel. tuple calculus rel. domain calculus

3. General Overview - rel. model history concepts Formal query languages relational algebra rel. tuple calculus rel. domain calculus

4. Overview - detailed rel. tuple calculus why? details examples equivalence with rel. algebra more examples; ‘safety’ of expressions rel. domain calculus + QBE

5. Safety of expressions FORBIDDEN: It has infinite output!! Instead, always use

6. Safety of expressions Possible to write tuple calculus expressions that generate infinite relations, e.g., {t |  t  r } results in an infinite relation if the domain of any attribute of relation r is infinite To guard against the problem, we restrict the set of allowable expressions to safe expressions. An expression {t | P (t) } in the tuple relational calculus is safe if every component of t appears in one of the relations, tuples, or constants that appear in P

7. More examples: Banking example branch (branch-name, branch-city, assets) customer (customer-name, customer-street, customer-city) account (account-number, branch-name, balance) loan (loan-number, branch-name, amount) depositor (customer-name, account-number) borrower (customer-name, loan-number)

8. Example Queries Find the loan-number, branch-name, and amount for loans of over $1200 {t | t  loan  t [amount]  1200} Find the loan number for each loan of an amount greater than $1200 {t |  s  loan (t [loan-number] = s [loan-number]  s [amount]  1200} Notice that a relation on schema [loan-number] is implicitly defined by the query

9. Example Queries Find the names of all customers having a loan, an account, or both at the bank {t |  s  borrower(t[customer-name] = s[customer-name])   u  depositor(t[customer-name] = u[customer- name]) Find the names of all customers who have a loan and an account at the bank {t |  s  borrower(t[customer-name] = s[customer-name])   u  depositor(t[customer-name] = u[customer- name])

10. Example Queries Find the names of all customers having a loan at the Perryridge branch {t |  s  borrower(t[customer-name] = s[customer-name]   u  loan(u[branch-name] = “Perryridge”  u[loan-number] = s[loan-number]))} Find the names of all customers who have a loan at the Perryridge branch, but no account at any branch of the bank {t |  s  borrower(t[customer-name] = s[customer-name]   u  loan(u[branch-name] = “Perryridge”  u[loan-number] = s[loan-number]))  not  v  depositor (v[customer-name] = t[customer-name]) }

11. Example Queries Find the names of all customers having a loan from the Perryridge branch, and the cities they live in {t |  s  loan(s[branch-name] = “Perryridge”   u  borrower (u[loan-number] = s[loan-number]  t [customer-name] = u[customer-name])   v  customer (u[customer-name] = v[customer-name]  t[customer-city] = v[customer-city])))}

12. Example Queries Find the names of all customers who have an account at all branches located in Brooklyn: {t |  c  customer (t[customer.name] = c[customer-name])   s  branch(s[branch-city] = “Brooklyn”   u  account ( s[branch-name] = u[branch-name]   s  depositor ( t[customer-name] = s[customer-name]  s[account-number] = u[account-number] )) )}

13. General Overview relational model Formal query languages relational algebra rel. tuple calculus rel. domain calculus

14. Overview - detailed rel. tuple calculus dfn details equivalence to rel. algebra rel. domain calculus + QBE

15. Rel. domain calculus (RDC) Q: why? A: slightly easier than RTC, although equivalent - basis for QBE idea: domain variables (w/ F.O.L.) – e.g.: ‘find STUDENT record with ssn=123’

16. Rel. Dom. Calculus find STUDENT record with ssn=123’

17. Details Like R.T.C - symbols allowed: quantifiers

18. Details but: domain (= column) variables, as opposed to tuple variables, e.g.: ssn name address

19. Domain Relational Calculus A nonprocedural query language equivalent in power to the tuple relational calculus Each query is an expression of the form: {  x 1, x 2, …, x n  | P (x 1, x 2, …, x n )} x 1, x 2, …, x n represent domain variables P represents a formula similar to that of the predicate calculus

20. Example queries Find the branch-name, loan-number, and amount for loans of over $1200 {  l, b, a  |  l, b, a   loan  a > 1200} Find the names of all customers who have a loan of over $1200 {  c  |  l, b, a (  c, l   borrower   l, b, a   loan  a > 1200)} Find the names of all customers who have a loan from the Perryridge branch and the loan amount: {  c, a  |  l (  c, l   borrower   b(  l, b, a   loan  b = “Perryridge”))} or {  c, a  |  l (  c, l   borrower   l, “Perryridge”, a   loan)}

21. Example Queries Find the names of all customers having a loan, an account, or both at the Perryridge branch: {  c  |  l ({  c, l   borrower   b,a (  l, b, a   loan  b = “Perryridge”))   a (  c, a   depositor   b,n (  a, b, n   account  b = “Perryridge”))} Find the names of all customers who have an account at all branches located in Brooklyn: {  c  |  n (  c, s, n   customer)   x,y,z (  x, y, z   branch  y = “Brooklyn”)   a,b (  x, y, z   account   c,a   depositor)}

22. Reminder: our Mini-U db CLASS c-idc-nameunits cis331d.b.2 cis321o.s.2 TAKES SSNc-idgrade 123cis331A 234cis331B

23. Examples find all student records RTC:

24. Examples (selection) find student record with ssn=123

25. Examples (selection) find student record with ssn=123 RTC: or

26. Examples (projection) find name of student with ssn=123

27. Examples (projection) find name of student with ssn=123 need to ‘restrict’ “a” RTC:

28. Examples (projection) find name of student with ssn=123 - RTC:

29. Examples cont’d (union) get records of both PT and FT students RTC:

30. Examples cont’d (union) get records of both PT and FT students

31. Examples difference: find students that are not staff RTC:

32. Examples difference: find students that are not staff

33. Cartesian product eg., dog-breeding: MALE x FEMALE gives all possible couples x =

34. Cartesian product find all the pairs of (male, female) - RTC:

35. Cartesian product find all the pairs of (male, female) - RDC:

36. ‘Proof’ of equivalence rel. algebra rel. domain calculus rel. tuple calculus

37. Overview - detailed rel. domain calculus why? details examples equivalence with rel. algebra more examples; ‘safety’ of expressions

38. More examples join: find names of students taking cis351

39. Reminder: our Mini-U db

40. More examples join: find names of students taking cis351 - in RTC

41. More examples join: find names of students taking cis351 - in RDC

42. Sneak preview of QBE: TAKES SSNc-idgrade _xcis351

43. Sneak preview of QBE: TAKES SSNc-idgrade _xcis351 very user friendly heavily based on RDC very similar to MS Access interface

44. More examples 3-way join: find names of students taking a 2-unit course - in RTC: selection projection join

45. Reminder: our Mini-U db CLASS c-idc-nameunits cis331d.b.2 cis321o.s.2 grade TAKES SSNc-id 123cis331A 234cis331B _x.P _x_y 2

46. More examples 3-way join: find names of students taking a 2-unit course

47. More examples 3-way join: find names of students taking a 2-unit course

48. Even more examples: self -joins: find Tom’s grandparent(s)

49. Even more examples: self -joins: find Tom’s grandparent(s)

50. Even more examples: self -joins: find Tom’s grandparent(s)

51. Even more examples: self -joins: find Tom’s grandparent(s)

52. Hard examples: DIVISION find suppliers that shipped all the ABOMB parts

53. Hard examples: DIVISION find suppliers that shipped all the ABOMB parts

54. Hard examples: DIVISION find suppliers that shipped all the ABOMB parts

55. More on division find students that take all the courses that ssn=123 does (and maybe even more)

56. More on division find students that take all the courses that ssn=123 does (and maybe even more)

57. Safety of expressions similar to RTC FORBIDDEN:

58. Safety of Expressions {  x 1, x 2, …, x n  | P(x 1, x 2, …, x n )} is safe if all of the following hold: 1. All values that appear in tuples of the expression are values from dom a(P) (that is, the values appear either in P or in a tuple of a relation mentioned in P ) 2.For every “there exists” subformula of the form  x (P 1 (x)), the subformula is true if and only if there is a value x in dom (P 1 ) such that P 1 (x) is true. 3. For every “for all” subformula of the form  x (P 1 (x)), the subformula is true if and only if P 1 (x) is true for all values x from dom (P 1 ).

59. Overview - detailed rel. domain calculus + QBE dfn details equivalence to rel. algebra

61. table