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CMU SCS Carnegie Mellon Univ. Dept. of Computer Science 15-415/615 – DB Applications C. Faloutsos & A. Pavlo Lecture#5: Relational calculus.

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Presentation on theme: "CMU SCS Carnegie Mellon Univ. Dept. of Computer Science 15-415/615 – DB Applications C. Faloutsos & A. Pavlo Lecture#5: Relational calculus."— Presentation transcript:

1 CMU SCS Carnegie Mellon Univ. Dept. of Computer Science 15-415/615 – DB Applications C. Faloutsos & A. Pavlo Lecture#5: Relational calculus

2 CMU SCS Faloutsos - PavloCMU SCS 15-415/615#2 General Overview - rel. model history concepts Formal query languages –relational algebra –rel. tuple calculus –rel. domain calculus

3 CMU SCS Faloutsos - PavloCMU SCS 15-415/615#3 Overview - detailed rel. tuple calculus –why? –details –examples –equivalence with rel. algebra –more examples; ‘safety’ of expressions rel. domain calculus + QBE

4 CMU SCS Faloutsos - PavloCMU SCS 15-415/615#4 Motivation Q: weakness of rel. algebra? A: procedural –describes the steps (ie., ‘how’) –(still useful, for query optimization)

5 CMU SCS Faloutsos - PavloCMU SCS 15-415/615#5 Solution: rel. calculus –describes what we want –two equivalent flavors: ‘tuple’ and ‘domain’ calculus –basis for SQL and QBE, resp. –Useful for proofs (see query optimization, later)

6 CMU SCS Faloutsos - PavloCMU SCS 15-415/615#6 Rel. tuple calculus (RTC) first order logic ‘Give me tuples ‘t’, satisfying predicate P - eg:

7 CMU SCS Faloutsos - PavloCMU SCS 15-415/615#7 Details symbols allowed: quantifiers

8 CMU SCS Faloutsos - PavloCMU SCS 15-415/615#8 Specifically Atom

9 CMU SCS Faloutsos - PavloCMU SCS 15-415/615#9 Specifically Formula: –atom –if P1, P2 are formulas, so are –if P(s) is a formula, so are

10 CMU SCS Faloutsos - PavloCMU SCS 15-415/615#10 Specifically Reminders: –DeMorgan –implication: –double negation: ‘every human is mortal : no human is immortal’

11 CMU SCS Faloutsos - PavloCMU SCS 15-415/615#11 Reminder: our Mini-U db

12 CMU SCS Faloutsos - PavloCMU SCS 15-415/615#12 Examples find all student records output tuple of type ‘STUDENT’

13 CMU SCS (Goal: evidence that RTC = RA) Full proof: complicated We’ll just show examples of the 5 RA fundamental operators, and how RTC can handle them (Quiz: which are the 5 fundamental op’s?) Faloutsos - PavloCMU SCS 15-415/615#13

14 CMU SCS Faloutsos - PavloCMU SCS 15-415/615#14 selection projection cartesian product MALE x FEMALE set union set difference R - S FUNDAMENTAL Relational operators R U S

15 CMU SCS Faloutsos - PavloCMU SCS 15-415/615#15 Examples (selection) find student record with ssn=123

16 CMU SCS Faloutsos - PavloCMU SCS 15-415/615#16 Examples (selection) find student record with ssn=123  selection  projection X cartesian product U set union - set difference ✔

17 CMU SCS Faloutsos - PavloCMU SCS 15-415/615#17 Examples (projection) find name of student with ssn=123

18 CMU SCS Faloutsos - PavloCMU SCS 15-415/615#18 Examples (projection) find name of student with ssn=123 ‘t’ has only one column  selection  projection X cartesian product U set union - set difference ✔ ✔

19 CMU SCS Faloutsos - PavloCMU SCS 15-415/615#19 ‘Tracing’ s t

20 CMU SCS Faloutsos - PavloCMU SCS 15-415/615#20 Examples cont’d (union) get records of both PT and FT students  selection  projection X cartesian product U set union - set difference ✔ ✔ ✔

21 CMU SCS Faloutsos - PavloCMU SCS 15-415/615#21 Examples cont’d (union) get records of both PT and FT students

22 CMU SCS Faloutsos - PavloCMU SCS 15-415/615#22 Examples difference: find students that are not staff (assuming that STUDENT and STAFF are union-compatible)  selection  projection X cartesian product U set union - set difference ✔ ✔ ✔ ✔

23 CMU SCS Faloutsos - PavloCMU SCS 15-415/615#23 Examples difference: find students that are not staff

24 CMU SCS Faloutsos - PavloCMU SCS 15-415/615#24 Cartesian product eg., dog-breeding: MALE x FEMALE gives all possible couples x =

25 CMU SCS Faloutsos - PavloCMU SCS 15-415/615#25 Cartesian product find all the pairs of (male, female)  selection  projection X cartesian product U set union - set difference ✔ ✔ ✔ ✔ ✔

26 CMU SCS Faloutsos - PavloCMU SCS 15-415/615#26 ‘Proof’ of equivalence rel. algebra rel. tuple calculus  selection  projection X cartesian product U set union - set difference ✔ ✔ ✔ ✔ ✔

27 CMU SCS Faloutsos - PavloCMU SCS 15-415/615#27 Overview - detailed rel. tuple calculus –why? –details –examples –equivalence with rel. algebra –more examples; ‘safety’ of expressions re. domain calculus + QBE

28 CMU SCS Faloutsos - PavloCMU SCS 15-415/615#28 More examples join: find names of students taking 15-415

29 CMU SCS Faloutsos - PavloCMU SCS 15-415/615#29 Reminder: our Mini-U db

30 CMU SCS Faloutsos - PavloCMU SCS 15-415/615#30 More examples join: find names of students taking 15-415

31 CMU SCS Faloutsos - PavloCMU SCS 15-415/615#31 More examples join: find names of students taking 15-415 projection selection join (Remember: ‘SPJ’ )

32 CMU SCS Faloutsos - PavloCMU SCS 15-415/615#32 More examples 3-way join: find names of students taking a 2-unit course

33 CMU SCS Faloutsos - PavloCMU SCS 15-415/615#33 Reminder: our Mini-U db

34 CMU SCS Faloutsos - PavloCMU SCS 15-415/615#34 More examples 3-way join: find names of students taking a 2-unit course selection projection join

35 CMU SCS Faloutsos - PavloCMU SCS 15-415/615#35 More examples 3-way join: find names of students taking a 2-unit course - in rel. algebra??

36 CMU SCS Faloutsos - PavloCMU SCS 15-415/615#36 More examples 3-way join: find names of students taking a 2-unit course - in rel. algebra??

37 CMU SCS Faloutsos - PavloCMU SCS 15-415/615#37 Even more examples: self -joins: find Tom’s grandparent(s)

38 CMU SCS Faloutsos - PavloCMU SCS 15-415/615#38 Even more examples: self -joins: find Tom’s grandparent(s)

39 CMU SCS Faloutsos - PavloCMU SCS 15-415/615#39 Hard examples: DIVISION find suppliers that shipped all the ABOMB parts !

40 CMU SCS Faloutsos - PavloCMU SCS 15-415/615#40 Hard examples: DIVISION find suppliers that shipped all the ABOMB parts !

41 CMU SCS Faloutsos - PavloCMU SCS 15-415/615#41 General pattern three equivalent versions: –1) if it’s bad, he shipped it –2)either it was good, or he shipped it –3) there is no bad shipment that he missed !

42 CMU SCS Faloutsos - PavloCMU SCS 15-415/615#42 General pattern three equivalent versions: –1) if it’s bad, he shipped it –2)either it was good, or he shipped it –3) there is no bad shipment that he missed a  b  a  b !

43 CMU SCS Faloutsos - PavloCMU SCS 15-415/615#43 General pattern three equivalent versions: –1) if it’s bad, he shipped it –2)either it was good, or he shipped it –3) there is no bad shipment that he missed !

44 CMU SCS Faloutsos - PavloCMU SCS 15-415/615#44 a  b is the same as  a  b If a is true, b must be true for the implication to be true. If a is true and b is false, the implication evaluates to false. If a is not true, we don’t care about b, the expression is always true. a T F T F b T TT F

45 CMU SCS Faloutsos - PavloCMU SCS 15-415/615#45 More on division find (SSNs of) students that take all the courses that ssn=123 does (and maybe even more) find students ‘s’ so that if 123 takes a course => so does ‘s’

46 CMU SCS Faloutsos - PavloCMU SCS 15-415/615#46 More on division find students that take all the courses that ssn=123 does (and maybe even more)

47 CMU SCS Faloutsos - PavloCMU SCS 15-415/615#47 Safety of expressions FORBIDDEN: It has infinite output!! Instead, always use

48 CMU SCS Faloutsos - PavloCMU SCS 15-415/615#48 Overview - conclusions rel. tuple calculus: DECLARATIVE –dfn –details –equivalence to rel. algebra rel. domain calculus + QBE

49 CMU SCS Faloutsos - PavloCMU SCS 15-415/615#49 General Overview relational model Formal query languages –relational algebra –rel. tuple calculus –rel. domain calculus

50 CMU SCS Faloutsos - PavloCMU SCS 15-415/615#50 Rel. domain calculus (RDC) Q: why? A: slightly easier than RTC, although equivalent - basis for QBE. idea: domain variables (w/ F.O.L.) - eg: ‘find STUDENT record with ssn=123’

51 CMU SCS Faloutsos - PavloCMU SCS 15-415/615#51 Rel. Dom. Calculus find STUDENT record with ssn=123’

52 CMU SCS Faloutsos - PavloCMU SCS 15-415/615#52 Details Like R.T.C - symbols allowed: quantifiers

53 CMU SCS Faloutsos - PavloCMU SCS 15-415/615#53 Details but: domain (= column) variables, as opposed to tuple variables, eg: ssn name address

54 CMU SCS Faloutsos - PavloCMU SCS 15-415/615#54 Reminder: our Mini-U db

55 CMU SCS Faloutsos - PavloCMU SCS 15-415/615#55 Examples find all student records RTC:

56 CMU SCS Faloutsos - PavloCMU SCS 15-415/615#56 Examples (selection) find student record with ssn=123

57 CMU SCS (‘Proof’ of RDC = RA) Again, we show examples of the 5 fundamental operators, in RDC Faloutsos - PavloCMU SCS 15-415/615#57

58 CMU SCS Faloutsos - PavloCMU SCS 15-415/615#58 Examples (selection) find student record with ssn=123 RTC:

59 CMU SCS Faloutsos - PavloCMU SCS 15-415/615#59 Examples (selection) find student record with ssn=123 RTC: or

60 CMU SCS Faloutsos - PavloCMU SCS 15-415/615#60 Examples (projection) find name of student with ssn=123

61 CMU SCS Faloutsos - PavloCMU SCS 15-415/615#61 Examples (projection) find name of student with ssn=123 need to ‘restrict’ “a” RTC:

62 CMU SCS Faloutsos - PavloCMU SCS 15-415/615#62 Examples cont’d (union) get records of both PT and FT students RTC:

63 CMU SCS Faloutsos - PavloCMU SCS 15-415/615#63 Examples cont’d (union) get records of both PT and FT students

64 CMU SCS Faloutsos - PavloCMU SCS 15-415/615#64 Examples difference: find students that are not staff RTC:

65 CMU SCS Faloutsos - PavloCMU SCS 15-415/615#65 Examples difference: find students that are not staff

66 CMU SCS Faloutsos - PavloCMU SCS 15-415/615#66 Cartesian product eg., dog-breeding: MALE x FEMALE gives all possible couples x =

67 CMU SCS Faloutsos - PavloCMU SCS 15-415/615#67 Cartesian product find all the pairs of (male, female) - RTC:

68 CMU SCS Faloutsos - PavloCMU SCS 15-415/615#68 Cartesian product find all the pairs of (male, female) - RDC:

69 CMU SCS Faloutsos - PavloCMU SCS 15-415/615#69 Cartesian product find all the pairs of (male, female) - RDC:

70 CMU SCS Faloutsos - PavloCMU SCS 15-415/615#70 ‘Proof’ of equivalence rel. algebra rel. domain calculus rel. tuple calculus

71 CMU SCS Faloutsos - PavloCMU SCS 15-415/615#71 Overview - detailed rel. domain calculus –why? –details –examples –equivalence with rel. algebra –more examples; ‘safety’ of expressions

72 CMU SCS Faloutsos - PavloCMU SCS 15-415/615#72 More examples join: find names of students taking 15-415

73 CMU SCS Faloutsos - PavloCMU SCS 15-415/615#73 Reminder: our Mini-U db

74 CMU SCS Faloutsos - PavloCMU SCS 15-415/615#74 More examples join: find names of students taking 15-415 - in RTC

75 CMU SCS Faloutsos - PavloCMU SCS 15-415/615#75 More examples join: find names of students taking 15-415 - in RDC

76 CMU SCS Faloutsos - PavloCMU SCS 15-415/615#76 Sneak preview of QBE:

77 CMU SCS Faloutsos - PavloCMU SCS 15-415/615#77 Glimpse of QBE: very user friendly heavily based on RDC very similar to MS Access interface and pgAdminIII

78 CMU SCS Faloutsos - PavloCMU SCS 15-415/615#78 More examples 3-way join: find names of students taking a 2-unit course - in RTC: selection projection join

79 CMU SCS Faloutsos - PavloCMU SCS 15-415/615#79 Reminder: our Mini-U db _x.P _x_y 2

80 CMU SCS Faloutsos - PavloCMU SCS 15-415/615#80 More examples 3-way join: find names of students taking a 2-unit course

81 CMU SCS Faloutsos - PavloCMU SCS 15-415/615#81 More examples 3-way join: find names of students taking a 2-unit course

82 CMU SCS Faloutsos - PavloCMU SCS 15-415/615#82 Even more examples: self -joins: find Tom’s grandparent(s)

83 CMU SCS Faloutsos - PavloCMU SCS 15-415/615#83 Even more examples: self -joins: find Tom’s grandparent(s)

84 CMU SCS Faloutsos - PavloCMU SCS 15-415/615#84 Even more examples: self -joins: find Tom’s grandparent(s)

85 CMU SCS Faloutsos - PavloCMU SCS 15-415/615#85 Even more examples: self -joins: find Tom’s grandparent(s)

86 CMU SCS Faloutsos - PavloCMU SCS 15-415/615#86 Hard examples: DIVISION find suppliers that shipped all the ABOMB parts

87 CMU SCS Faloutsos - PavloCMU SCS 15-415/615#87 Hard examples: DIVISION find suppliers that shipped all the ABOMB parts

88 CMU SCS Faloutsos - PavloCMU SCS 15-415/615#88 Hard examples: DIVISION find suppliers that shipped all the ABOMB parts

89 CMU SCS Faloutsos - PavloCMU SCS 15-415/615#89 More on division find students that take all the courses that ssn=123 does (and maybe even more)

90 CMU SCS Faloutsos - PavloCMU SCS 15-415/615#90 More on division find students that take all the courses that ssn=123 does (and maybe even more)

91 CMU SCS Faloutsos - PavloCMU SCS 15-415/615#91 Safety of expressions similar to RTC FORBIDDEN:

92 CMU SCS Faloutsos - PavloCMU SCS 15-415/615#92 Overview - detailed rel. domain calculus + QBE –dfn –details –equivalence to rel. algebra

93 CMU SCS Faloutsos - PavloCMU SCS 15-415/615#93 Fun Drill:Your turn … Schema: Movie(title, year, studioName) ActsIn(movieTitle, starName) Star(name, gender, birthdate, salary)

94 CMU SCS Faloutsos - PavloCMU SCS 15-415/615#94 Your turn … Queries to write in TRC: –Find all movies by Paramount studio –… movies starring Kevin Bacon –Find stars who have been in a film w/Kevin Bacon –Stars within six degrees of Kevin Bacon* –Stars connected to K. Bacon via any number of films** * Try two degrees for starters ** Good luck with this one!

95 CMU SCS Faloutsos - PavloCMU SCS 15-415/615#95 Answers … Find all movies by Paramount studio {M | M  Movie  M.studioName = ‘Paramount’}

96 CMU SCS Faloutsos - PavloCMU SCS 15-415/615#96 Answers … Movies starring Kevin Bacon {M | M  Movie   A  ActsIn(A.movieTitle = M.title  A.starName = ‘Bacon’))}

97 CMU SCS Faloutsos - PavloCMU SCS 15-415/615#97 Answers … Stars who have been in a film w/Kevin Bacon {S | S  Star   A  ActsIn(A.starName = S.name   A2  ActsIn(A2.movieTitle = A.movieTitle  A2.starName = ‘Bacon’))} moviestar A2: S: name… ‘Bacon’ moviestar A:

98 CMU SCS Faloutsos - PavloCMU SCS 15-415/615#98 Answers … Stars within six degrees of Kevin Bacon {S | S  Star   A  ActsIn(A.starName = S.name   A2  ActsIn(A2.movieTitle = A.movieTitle   A3  ActsIn(A3.starName = A2.starName   A4  ActsIn(A4.movieTitle = A3.movieTitle  A4.starName = ‘Bacon’))} two

99 CMU SCS Faloutsos - PavloCMU SCS 15-415/615#99 Two degrees: S: name… ‘Bacon’ moviestar A4: moviestar A3:

100 CMU SCS Faloutsos - PavloCMU SCS 15-415/615#100 Two degrees: S: name… ‘Bacon’ moviestar A2: moviestar A: moviestar A4: moviestar A3:

101 CMU SCS Faloutsos - PavloCMU SCS 15-415/615#101 Answers … Stars connected to K. Bacon via any number of films Sorry … that was a trick question –Not expressible in relational calculus!! What about in relational algebra? –No – RA, RTC, RDC are equivalent

102 CMU SCS Faloutsos - PavloCMU SCS 15-415/615#102 Expressive Power Expressive Power (Theorem due to Codd): –Every query that can be expressed in relational algebra can be expressed as a safe query in RDC / RTC; the converse is also true. Relational Completeness: Query language (e.g., SQL) can express every query that is expressible in relational algebra/calculus. (actually, SQL is more powerful, as we will see…)

103 CMU SCS Faloutsos - PavloCMU SCS 15-415/615#103 Summary The relational model has rigorously defined query languages — simple and powerful. Relational algebra is more operational/procedural –useful as internal representation for query evaluation plans Relational calculus is declarative –users define queries in terms of what they want, not in terms of how to compute it.

104 CMU SCS Faloutsos - PavloCMU SCS 15-415/615#104 Summary - cnt’d Several ways of expressing a given query –a query optimizer chooses best plan. Algebra and safe calculus: same expressive power => relational completeness.

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