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Set operations in SQL is a type of operations which allow the results of multiple queries to be combined into a single result set. [1] Set operators in SQL include UNION, INTERSECT, and EXCEPT, which mathematically correspond to the concepts of union, intersection and set difference.
See MSDN documentation [2] or IBM documentation [13] [14] for tutorial examples. The RECURSIVE keyword is not usually needed after WITH in systems other than PostgreSQL. [15] In SQL:1999 a recursive (CTE) query may appear anywhere a query is allowed. It's possible, for example, to name the result using CREATE [RECURSIVE] VIEW. [16]
The relational algebra uses set union, set difference, and Cartesian product from set theory, and adds additional constraints to these operators to create new ones.. For set union and set difference, the two relations involved must be union-compatible—that is, the two relations must have the same set of attributes.
The union operator (υ) combines the tuples of two relations and removes all duplicate tuples from the result. The relational union operator is equivalent to the SQL UNION operator. The intersection operator (∩) produces the set of tuples that two relations share in common. Intersection is implemented in SQL in the form of the INTERSECT operator.
Actual SQL implementations normally use other approaches, such as hash joins or sort-merge joins, since computing the Cartesian product is slower and would often require a prohibitively large amount of memory to store. SQL specifies two different syntactical ways to express joins: the "explicit join notation" and the "implicit join notation".
If an element lies in both, there will be two effectively distinct copies of the value in A + B, one from A and one from B. In type theory, a tagged union is called a sum type. Sum types are the dual of product types. Notations vary, but usually the sum type A + B comes with two introduction forms inj 1: A → A + B and inj 2: B → A + B.
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SQL was initially developed at IBM by Donald D. Chamberlin and Raymond F. Boyce after learning about the relational model from Edgar F. Codd [12] in the early 1970s. [13] This version, initially called SEQUEL (Structured English Query Language), was designed to manipulate and retrieve data stored in IBM's original quasirelational database management system, System R, which a group at IBM San ...