Projection (relational algebra)

In relational algebra, a projection is a unary operation written as , where is a relation and are attribute names. Its result is defined as the set obtained when the components of the tuples in are restricted to the set – it discards (or excludes) the other attributes. In practical terms, if a relation is thought of as a table, then projection can be thought of as picking a subset of its columns. For example, if the attributes are (name, age), then projection of the relation {(Alice, 5), (Bob, 8)} onto attribute list (age) yields {5,8} – we have discarded the names, and only know what ages are present. Projections may also modify attribute values. For example, if has attributes , , , where the values of are numbers, then is like , but with all -values halved. The closely related concept in set theory (see: projection (set theory)) differs from that of relational algebra in that, in set theory, one projects onto ordered components, not onto attributes. For instance, projecting onto the second component yields 7. Projection is relational algebra's counterpart of existential quantification in predicate logic. The attributes not included correspond to existentially quantified variables in the predicate whose extension the operand relation represents. The example below illustrates this point. Because of the correspondence with existential quantification, some authorities prefer to define projection in terms of the excluded attributes. In a computer language it is of course possible to provide notations for both, and that was done in ISBL and several languages that have taken their cue from ISBL. A nearly identical concept occurs in the category of monoids, called a string projection, which consists of removing all of the letters in the string that do not belong to a given alphabet. When implemented in SQL standard the "default projection" returns a multiset instead of a set, and the pi projection is obtained by the addition of the DISTINCT keyword to eliminate duplicate data.