Relational Algebra CMSC 461 Michael Wilson. Relational algebra Before we get into SQL, want to take a look at what exactly SQL is really modeling

Relational AlgebraCMSC 461Michael Wilson

Relational algebra Before we get into SQL, want to take a

look at what exactly SQL is really modeling Foundation for SQL and other query

languages

Base operations Union Difference Cartesian Product Projection Selection Rename

Base operations With these operations you can

accomplish everything you need in relational algebra

There are more operations, but they are for simplification

Union Say you have two relations with tuples

{a, b, c} and {d, e, f} The union of the two is {a, b, c, d, e, f}

One requirement: the two relations must have the same attributes This is called being “union-compatible”

Notation: A ∪ B

Difference Also known as the relative complement Say you have two relations

Relation A: {a, b, c} Relation B: {a, b, f}

Notation: B \ A The relative complement of A in B

B \ A results in the set of elements in B that are not in A B \ A = {f}

The two relations must be union-compatible

Cartesian product This one can get kind of ugly Requirement: the two relations involved

must have completely disjoint attributes A Cartesian product of two relations A

and B is the set of every tuple in A paired with every tuple in B

Notation: A × B

Cartesian product Two relations A and B with disjoint

attributes A has tuples {a, b, c} B has tuples {d, e, f}

Each tuple has attribute values a has a1, a2, …, an

b has b1, b2, …, bn

Etc.

Cartesian product Resulting product by tuples:

(a, d) (a, e) (a, f) (b, d) (b, e) (b, f) (c, d) (c, e) (c, f)

Cartesian product Listing out the attribute values:

(a1, a2, …, an, d1, d2, …, dn) (a1, a2, …, an, e1, e2, …, en) (a1, a2, …, an, f1, f2, …, fn) (b1, b2, …, bn, d1, d2, …, dn) (b1, b2, …, bn, e1, e2, …, en) (b1, b2, …, bn, f1, f2, …, fn) (c1, c2, …, cn, d1, d2, …, dn) (c1, c2, …, cn, e1, e2, …, en) (c1, c2, …, cn, f1, f2, …, fn)

Projection This is an operation that is used on one

relation Essentially restricts the attributes of a

relation to the ones you’re interested about

Notation: πa1,a2,…an(R) ai = attribute I R = relation to project

Projection Example (from Wikipedia):

πcontactName,contactPhoneNumber(addressBook)

Projectionaddress lastContacte

d

contactPhoneNumber

numberType contactName

111 Great Street

1 day ago 555 5555 Cell Phil

123 Not So Great Street

Last month 555 6666 Landline Henry

8 Get Out of Here Way

Last week 555 7777 Work Bob

7 RUN! Drive 2 years ago

555 8888 Cell Octavio

ProjectioncontactName contactPhoneNumber

Phil 555 5555

Henry 555 6666

Bob 555 7777

Octavio 555 8888

Selection Lists a set of tuples that match the

specified criteria Notation: σp(R)

p is a selection predicate This consists of terms that are connected

by logic operators ^ (and) v (or) ¬ (not)

Selection Terms have the following format:

<attribute> <op> <attribute/constant> <op> is =, ≠, >, ≥, <, ≤

Examples: phoneNumber=555 5555 GPA>2.0

SelectionUMBC ID Age FName LName GPA

SM11111 20 Mario Mario 4.0

SM11112 19 Luigi Mario 3.9

MT11111 21 Samus Aran 4.0

FF11113 21 Snow Villiers 0.2

SW11234 25 Snow White 3.5

Selection σGPA<4.0(R)

Select all from our relation where the attribute value for GPA is less than 4.0





Selection σage>20^fName=‘Snow’(R)

Select all from our relation where the attribute value for age is greater than 20 and the attribute value for fName is equal to ‘Snow’




Rename The result of a rename is literally the

same as the original relation, but with an attribute renamed

ρa/b(R) The b attribute in the resulting tuples is

renamed to a

RenameUMBC ID Age FName LName GPA






Rename ρMIT ID/UMBC ID(R)

Rename UMBC ID to MIT ID

RenameMIT ID Age FName LName GPA






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Relational Algebra CMSC 461 Michael Wilson. Relational algebra Before we get into SQL, want to take a look at what exactly SQL is really modeling