In
relational algebra
In database theory, relational algebra is a theory that uses algebraic structures for modeling data and defining queries on it with well founded semantics (computer science), semantics. The theory was introduced by Edgar F. Codd.
The main applica ...
, a selection (sometimes called a restriction in reference to E.F. Codd's 1970 paper
and ''not'', contrary to a popular belief, to avoid confusion with
SQL's use of SELECT, since Codd's article predates the existence of SQL) is a
unary operation that denotes a
subset
In mathematics, a Set (mathematics), set ''A'' is a subset of a set ''B'' if all Element (mathematics), elements of ''A'' are also elements of ''B''; ''B'' is then a superset of ''A''. It is possible for ''A'' and ''B'' to be equal; if they a ...
of a relation.
A selection is written as
or
where:
* and are attribute names
* is a
binary operation
In mathematics, a binary operation or dyadic operation is a rule for combining two elements (called operands) to produce another element. More formally, a binary operation is an operation of arity two.
More specifically, a binary operation ...
in the set
* is a value constant
* is a relation
The selection
denotes all
tuple
In mathematics, a tuple is a finite sequence or ''ordered list'' of numbers or, more generally, mathematical objects, which are called the ''elements'' of the tuple. An -tuple is a tuple of elements, where is a non-negative integer. There is o ...
s in for which holds between the and the attribute.
The selection
denotes all tuples in for which holds between the attribute and the value .
For an example, consider the following tables where the first table gives the relation , the second table gives the result of
and the third table gives the result of
.
More formally the semantics of the selection is defined as
follows:
:
:
The result of the selection is only defined if the attribute names that it mentions are in the heading of the relation that it operates upon.
Generalized selection
A generalized selection is a
unary operation written as
where
is a
propositional formula that consists of
atom
Atoms are the basic particles of the chemical elements. An atom consists of a atomic nucleus, nucleus of protons and generally neutrons, surrounded by an electromagnetically bound swarm of electrons. The chemical elements are distinguished fr ...
s as allowed in the normal selection and, in addition, the logical operators ∧ (
and), ∨ (
or) and
(
negation
In logic, negation, also called the logical not or logical complement, is an operation (mathematics), operation that takes a Proposition (mathematics), proposition P to another proposition "not P", written \neg P, \mathord P, P^\prime or \over ...
). This selection selects all those
tuple
In mathematics, a tuple is a finite sequence or ''ordered list'' of numbers or, more generally, mathematical objects, which are called the ''elements'' of the tuple. An -tuple is a tuple of elements, where is a non-negative integer. There is o ...
s in for which
holds.
For an example, consider the following tables where the first table gives the relation and the second the result of
.
Formally the semantics of the generalized selection is defined as follows:
:
The result of the selection is only defined if the
attribute names that it mentions are in the
header of the relation that it operates upon.
The generalized selection is expressible with other basic algebraic operations. A simulation of generalized selection using the fundamental operators is defined by the following rules:
:
:
:
Computer languages
In computer languages it is expected that any
truth-value
In logic and mathematics, a truth value, sometimes called a logical value, is a value indicating the relation of a proposition to truth, which in classical logic has only two possible values ('' true'' or '' false''). Truth values are used in c ...
d expression be permitted as the selection condition rather than restricting it to be a simple comparison.
In
SQL, selections are performed by using
WHERE
definitions in
SELECT
,
UPDATE
, and
DELETE
statements, but note that the selection condition can result in any of three truth values (''true'', ''false'' and ''unknown'') instead of the usual two.
In
SQL, general selections are performed by using
WHERE
definitions with
AND
,
OR
, or
NOT
operands in
SELECT
,
UPDATE
, and
DELETE
statements.
References
External links
* http://cisnet.baruch.cuny.edu/holowczak/classes/3400/relationalalgebra/#selectionoperator
{{DEFAULTSORT:Selection (Relational Algebra)
Relational algebra