PPT - Relational Algebra and Relational Calculus Computer Science Engineering (CSE) Notes | EduRev

Computer Science Engineering (CSE) : PPT - Relational Algebra and Relational Calculus Computer Science Engineering (CSE) Notes | EduRev

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1
Relational Algebra & Calculus
Page 2


1
Relational Algebra & Calculus
2
Relational Query Languages
v Query languages: Allow manipulation and retrieval
of data from a database.
v Relational model supports simple, powerful QLs:
§ Strong formal foundation based on logic.
§ Allows for much optimization.
v Query Languages != programming languages!
§ QLs not expected to be “Turing complete”.
§ QLs not intended to be used for complex calculations.
§ QLs support easy, efficient access to large data sets.
Page 3


1
Relational Algebra & Calculus
2
Relational Query Languages
v Query languages: Allow manipulation and retrieval
of data from a database.
v Relational model supports simple, powerful QLs:
§ Strong formal foundation based on logic.
§ Allows for much optimization.
v Query Languages != programming languages!
§ QLs not expected to be “Turing complete”.
§ QLs not intended to be used for complex calculations.
§ QLs support easy, efficient access to large data sets.
3
Formal Relational Query Languages
v Two mathematical Query Languages form the
basis for “real” languages (e.g. SQL), and for
implementation:
§ Relational Algebra: More operational (procedural), very
useful for representing execution plans.
§ Relational Calculus: Lets users describe what they
want, rather than how to compute it: Non-operational,
declarative.
Page 4


1
Relational Algebra & Calculus
2
Relational Query Languages
v Query languages: Allow manipulation and retrieval
of data from a database.
v Relational model supports simple, powerful QLs:
§ Strong formal foundation based on logic.
§ Allows for much optimization.
v Query Languages != programming languages!
§ QLs not expected to be “Turing complete”.
§ QLs not intended to be used for complex calculations.
§ QLs support easy, efficient access to large data sets.
3
Formal Relational Query Languages
v Two mathematical Query Languages form the
basis for “real” languages (e.g. SQL), and for
implementation:
§ Relational Algebra: More operational (procedural), very
useful for representing execution plans.
§ Relational Calculus: Lets users describe what they
want, rather than how to compute it: Non-operational,
declarative.
4
Preliminaries
v A query is applied to relation instances, and the
result of a query is also a relation instance.
§ Schemas of input relations for a query are fixed.
§ The schema for the result of a given query is also
fixed! - determined by definition of query language
constructs.
v Positional vs. named-field notation:
§ Positional notation easier for formal definitions,
named-field notation more readable.
§ Both used in SQL
Page 5


1
Relational Algebra & Calculus
2
Relational Query Languages
v Query languages: Allow manipulation and retrieval
of data from a database.
v Relational model supports simple, powerful QLs:
§ Strong formal foundation based on logic.
§ Allows for much optimization.
v Query Languages != programming languages!
§ QLs not expected to be “Turing complete”.
§ QLs not intended to be used for complex calculations.
§ QLs support easy, efficient access to large data sets.
3
Formal Relational Query Languages
v Two mathematical Query Languages form the
basis for “real” languages (e.g. SQL), and for
implementation:
§ Relational Algebra: More operational (procedural), very
useful for representing execution plans.
§ Relational Calculus: Lets users describe what they
want, rather than how to compute it: Non-operational,
declarative.
4
Preliminaries
v A query is applied to relation instances, and the
result of a query is also a relation instance.
§ Schemas of input relations for a query are fixed.
§ The schema for the result of a given query is also
fixed! - determined by definition of query language
constructs.
v Positional vs. named-field notation:
§ Positional notation easier for formal definitions,
named-field notation more readable.
§ Both used in SQL
5
Example Instances
sid sname rating age
22 dustin 7 45.0
31 lubber 8 55.5
58 rusty 10 35.0
sid sname rating age
28 yuppy 9 35.0
31 lubber 8 55.5
44 guppy 5 35.0
58 rusty 10 35.0
sid bid day
22 101 10/10/96
58 103 11/12/96
R1
S1
S2
v “Sailors” and “Reserves”
relations for our examples.
v We’ll use positional or
named field notation,
assume that names of fields
in query results are
`inherited’ from names of
fields in query input
relations.
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