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)

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

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

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

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

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

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)

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

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])

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]) }

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])))}

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] )) )}

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

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

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’

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

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

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

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

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)}

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)}

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

Examples find all student records RTC:

Examples (selection) find student record with ssn=123

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

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

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

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

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

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

Examples difference: find students that are not staff RTC:

Examples difference: find students that are not staff

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

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

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

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

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

More examples join: find names of students taking cis351

Reminder: our Mini-U db

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

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

Sneak preview of QBE: TAKES SSNc-idgrade _xcis351

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Safety of expressions similar to RTC FORBIDDEN:

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 ).

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

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