1. Trinity College
The Relational Model and
Relational Constraints
Timothy Richards
Trinity College, Hartford CT • Department of Computer Science • CPSC 372
2. Last Time
• Relational Model Concepts
• A collection of relations
• A table of values
• Each row represents a collection of related data values -
corresponds to a real-world entity
• Table/Column names interpret meaning
• Table represents facts
Trinity College, Hartford CT • Department of Computer Science • CPSC 372 2
3. Last Time
• Domains
• Each value corresponds to a domain
• Domains are associated with a datatype and a format
• Relation Schema
• Describe the facts
Trinity College, Hartford CT • Department of Computer Science • CPSC 372 3
4. Last Time
• Domains
• Each value corresponds to a domain
• Domains are associated with a datatype and a format
• Relation Schema
• Describe the facts
R(A1, A2, ..., An)
Each attribute Ai is the name of a role
played by some domain D in the relation schema R
Trinity College, Hartford CT • Department of Computer Science • CPSC 372 4
5. Last Time
R = Student(name, ssn, homephone, address, age, gpa)
R(A1, A2, ..., An)
Each attribute Ai is the name of a role
played by some domain D in the relation schema R
Trinity College, Hartford CT • Department of Computer Science • CPSC 372 5
6. Last Time
Arity/Degree: deg(R) = 6
R = Student(name, ssn, homephone, address, age, gpa)
R(A1, A2, ..., An)
Each attribute Ai is the name of a role
played by some domain D in the relation schema R
Trinity College, Hartford CT • Department of Computer Science • CPSC 372 6
7. Last Time
A relation instance r of R(A1, A2, ..., An)
is a set of n-tuples, r = {t1, t2, ..., tm,}, where
each n-tuple ti is an ordered list of
n values ti = <v1, v2, ..., vn>.
Trinity College, Hartford CT • Department of Computer Science • CPSC 372 7
8. Last Time
Important Constraint
Each value vi, 1 <= i <= n, in dom(Ai)
A relation instance r of R(A1, A2, ..., An)
is a set of n-tuples, r = {t1, t2, ..., tm,}, where
each n-tuple ti is an ordered list of
n values ti = <v1, v2, ..., vn>.
Trinity College, Hartford CT • Department of Computer Science • CPSC 372 8
9. Last Time
Relational databases are based on relations
Trinity College, Hartford CT • Department of Computer Science • CPSC 372 9
10. Last Time
Relational databases are based on relations
What characteristics make a relation
different from a file or table?
Trinity College, Hartford CT • Department of Computer Science • CPSC 372 10
11. Last Time
Relational databases are based on relations
What characteristics make a relation
different from a file or table?
Tuples have no ordering Tuples are unique
Trinity College, Hartford CT • Department of Computer Science • CPSC 372 11
12. Last Time
Relational databases are based on relations
What characteristics make a relation
different from a file or table?
Tuples have no ordering Tuples are unique
Not necessarily true at physical level!
Trinity College, Hartford CT • Department of Computer Science • CPSC 372 12
13. Last Time
Constraints are Important
Trinity College, Hartford CT • Department of Computer Science • CPSC 372 13
14. Last Time
Constraints are Important
1. model-based
2. schema-based
3. application-based
Trinity College, Hartford CT • Department of Computer Science • CPSC 372 14
15. Last Time
Constraints are Important
uniqueness,
ordering
1. model-based
2. schema-based
3. application-based
Trinity College, Hartford CT • Department of Computer Science • CPSC 372 15
16. Last Time
Constraints are Important
uniqueness,
ordering
1. model-based
Constraints we
2. schema-based
can express in a
3. application-based
relation schema
using DDL
(SQL)
Trinity College, Hartford CT • Department of Computer Science • CPSC 372 16
17. Last Time
Constraints are Important
uniqueness,
ordering
1. model-based
Constraints we
2. schema-based
can express in a
3. application-based
relation schema
using DDL
(SQL) The meaning and behavior
or attributes
Trinity College, Hartford CT • Department of Computer Science • CPSC 372 17
18. Last Time
Constraints are Important
uniqueness,
ordering
1. model-based
Constraints we
2. schema-based
can express in a
3. application-based
relation schema
using DDL
(SQL) The meaning and behavior • Difficult to express and
enforce in data model.
or attributes • Checked in application
programs
Trinity College, Hartford CT • Department of Computer Science • CPSC 372 18
19. Domain Constraints
The value of each attribute Ai
for a particular tuple
is constrained to dom(Ai)
Trinity College, Hartford CT • Department of Computer Science • CPSC 372 19
20. Domain Constraints
The value of each attribute Ai
for a particular tuple
is constrained to dom(Ai)
DDL can express this using types!
Trinity College, Hartford CT • Department of Computer Science • CPSC 372 20
21. Domain Constraints
The value of each attribute Ai
for a particular tuple
is constrained to dom(Ai)
DDL can express this using types! money
integers reals characters boolean date time
short float strings time stamp
regular double fixed length
long variable length
Trinity College, Hartford CT • Department of Computer Science • CPSC 372 21
22. Key Constraints
Tuples in a relation must be unique
Trinity College, Hartford CT • Department of Computer Science • CPSC 372 22
23. Key Constraints
Tuples in a relation must be unique
How to express in DDL?
Trinity College, Hartford CT • Department of Computer Science • CPSC 372 23
24. Key Constraints
Tuples in a relation must be unique
How to express in DDL?
For all i, j : ti[SK] != tj[SK] : i != j
Subset of attributes SK of a relation schema R
such that, no two tuples in r(R) should have
the same combination of values for SK.
Trinity College, Hartford CT • Department of Computer Science • CPSC 372 24
25. Key Constraints
Tuples in a relation must be unique
How to express in DDL?
For all i, j : ti[SK] != tj[SK] : i != j
Subset of attributes SK of a relation schema R
such that, no two tuples in r(R) should have
the same combination of values for SK.
Super Key
Trinity College, Hartford CT • Department of Computer Science • CPSC 372 25
26. Super Keys
Properties of SK:
• Distinct type can’t have duplicate values for SK.
• It is a minimal super key if we can’t remove attribute
ai in SK that breaks the first property.
Trinity College, Hartford CT • Department of Computer Science • CPSC 372 26
27. Super Keys
Properties of SK:
• Distinct type can’t have duplicate values for SK.
• It is a minimal super key if we can’t remove attribute
ai in SK that breaks the first property.
A relation schema may have more than one key
Trinity College, Hartford CT • Department of Computer Science • CPSC 372 27
28. Super Keys
Properties of SK:
• Distinct type can’t have duplicate values for SK.
• It is a minimal super key if we can’t remove attribute
ai in SK that breaks the first property.
A relation schema may have more than one key
candidate key
Trinity College, Hartford CT • Department of Computer Science • CPSC 372 28
29. Super Keys
Properties of SK:
• Distinct type can’t have duplicate values for SK.
• It is a minimal super key if we can’t remove attribute
ai in SK that breaks the first property.
A relation schema may have more than one key
candidate key
The candidate key we pick, is called the primary key
Trinity College, Hartford CT • Department of Computer Science • CPSC 372 29
30. Foreign Keys
Foreign Keys:
Values in one relations that reference
existing primary keys in other relations.
Trinity College, Hartford CT • Department of Computer Science • CPSC 372
31. Foreign Keys
Foreign Keys:
Values in one relations that reference
existing primary keys in other relations.
Also a constraint!
Trinity College, Hartford CT • Department of Computer Science • CPSC 372
32. non-Null Constraints
non-NULL is a constraint
Trinity College, Hartford CT • Department of Computer Science • CPSC 372 32
33. non-Null Constraints
non-NULL is a constraint
Certain attribute values are
required to not be null.
Trinity College, Hartford CT • Department of Computer Science • CPSC 372 33
34. non-Null Constraints
non-NULL is a constraint
Certain attribute values are
required to not be null.
Primary Keys can’t be null!
Trinity College, Hartford CT • Department of Computer Science • CPSC 372 34
35. A Relational Databases Is...
• A relation database schema S
• is a set of relation schemas: S = {R , R , ..., R }
1 2 m
• A set of integrity constraints IC
• A relational database state
• DB of S, that are a set of relation states:
DB = {r1, r2, ..., rn}
• such that for all i, r satisfies IC
i
Trinity College, Hartford CT • Department of Computer Science • CPSC 372 35
