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1. Lecture 2 - Relational Model
1
Fall 2001 Database Systems 1
Relational Model
• In the relational data model
– a database is a set of tables (with additional constraints,
programs and interfaces)
– a schema is the description of tables in a database
– a relation or a table is a “set” of tuples
– a tuple or a record is a mapping from a set of attributes to their
values
– an attribute is a slot for recording data, it has a name and a
domain of applicable values
– the schema of a table contains the table’s name and the
attributes and the domain of the attributes
Fall 2001 Database Systems 2
Example Database - Auction
• OWNERS - people who sell items
– Oid unique identifier given to them
– Name their name
– Email their e-mail address
• ITEMS - the items sold by “owners”
– Iid unique identifier of an item being sold
– Oid the owner of the item
– Name description of the item
– Location location of the item
• BUYERS - registered buyers allowed to bid on items
– Buyid buyer identifier
– Name buyer’s name
– Email buyer’s e-mail address
3. Lecture 2 - Relational Model
3
Fall 2001 Database Systems 5
Attributes and Domains
• Let D1 = the letter “O” followed by the set of all
integers
D2 = the set of all strings up to 30 characters
that contain only letters A-Z,a-z
D3 = the set of all strings that contain a single
@ symbol, and a combination of
Alphanumeric characters and “.”.
Then, owners relation has schema
Owners(OID:D1, Name:D2, Email:D3)
Fall 2001 Database Systems 6
Attributes - Domains
• All tuples in Owners come from
– D1 × D2 × D3
– An example tuple: OID:O1, Name: ’Smith’,
Email: ‘smith@aol.com’
– For any tuple: OID:v1, Name: v2, Email: v3
we have the property that v1 ∈ D1, v2 ∈ D2, v3 ∈ D3
• We usually abuse notation and assume an ordering
for the attribute/domain pairs, and write the relation
schema as:
Owners(OID, Name, Email)
and a tuple as:
O1,’Smith’,’smith@aol.com ∈ Owners
4. Lecture 2 - Relational Model
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Fall 2001 Database Systems 7
More on domains
• A domain is a type in the programming language sense
• Domain values is a set of acceptable values for a
variable of a given type.
– Zipcode: zipcodeDomain = {11111, … ,99999},
– Grants: availableGrants = {50,000, … ,1,000,000}
– Simple/Composite domains
• Address = Street name+street number+city+province+ postal code
• Domain compatibility
– Binary operations (e.g., comparison to one another, addition, etc)
can be performed on them.
• Full support for domains is not provided in many current
relational DBMSs
Fall 2001 Database Systems 8
Relation Instances
• A relation/table instance is a set of tuples with a
specific schema (attribute/domain pairs)
List form:
OWNERS(OID,Name,Email) = { O1, Smith, smith@aol.com,
O2, Johns, johns@geocities.com, O3, Brown,
Brown@netmail.com, O4, Gray, Gray@microsoft.com }
Tabular form: Ô Õ¤Ö¦×uب٠ÔÚ Û ÖÜiÝIÞ ×¨ÝqÜ!Ú ß
à%á âäã¦åæAç Smith@aol.com
à¦è é6êeç9ëTì Johns@geocities.com
àí î!ïEêeðië Brown@netmail.com
àIñ òQïEóAô Gray@microsoft.com
5. Lecture 2 - Relational Model
5
Fall 2001 Database Systems 9
Relational Model
Based on finite set theory:
• First Normal Form Rule: all attributes take simple
values - no set values are allowed.
• Rows are accessed only by their content. The order of
tuples does not have any meaning.
• The order of columns does not have any specific
meaning either.
• No two tuples can have the same values for all the
attributes, i.e. relations are sets.
• Commercial systems allow duplicates (so bag
semantics)
Fall 2001 Database Systems 10
Keys
• A superkey is a set of attributes that help uniquely
identify a specific tuple
– if no two owners may have the same Oid, then Oid
is a superkey
– if no two owners may have the same email
address, then Email is a superkey
• How about:
– Oid + Name (together) for Owners?
– Oid + Name (together) for ITEMS?
– Iid + Oid (together) for ITEMS?
6. Lecture 2 - Relational Model
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Fall 2001 Database Systems 11
Keys
• Given relation T, we use t[A1,…,Ak] to denote tuples with only
attributes A1,…,Ak
– for example, if t = O1, Smith, smith@aol.com then
t[oid,name] = O1, Smith
• Given a relation T with attributes {A1,…,Ak}, a key is a set of
attributes {B1,…,Bm} ⊆ {A1,…,Ak} such that
– if u and v are distinct tuples in relation T, then u[B1,…,Bm] and
v[B1,…,Bm] are necessarily different from each other by user
design!
– no proper subset of {B1,…,Bm} has this property
• Every table must have a unique primary key
– Primary key is a key designated by the user and managed by
the system
Fall 2001 Database Systems 12
Null values
• Attributes may be allowed to have null values because
– a value does not exist for a tuple
– a value exists, but it is not known
– it is not known whether a value exists or not
• Integrity rule: No column in a primary key can have null
values
