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The result of the query is the set of tuples X 1 to X n that make the DRC formula true. This language uses the same operators as tuple calculus, the logical connectives ∧ (and), ∨ (or) and ¬ (not). The existential quantifier (∃) and the universal quantifier (∀) can be used to bind the variables.
A set-valued function, also called a correspondence or set-valued relation, is a mathematical function that maps elements from one set, the domain of the function, to subsets of another set. [ 1 ] [ 2 ] Set-valued functions are used in a variety of mathematical fields, including optimization , control theory and game theory .
Query optimization consists in determining from a query the most efficient manner (or manners) to execute it. Query optimization can be formalized as translating a relational calculus expression delivering an answer A into efficient relational algebraic expressions delivering the same answer A.
[2] [3] Instead, each element is termed an attribute value. An attribute is a name paired with a domain (nowadays more commonly referred to as a type or data type ). An attribute value is an attribute name paired with an element of that attribute's domain, and a tuple is a set of attribute values in which no two distinct elements have the same ...
A relational database schema is defined as a tuple S = (D, R, h) where D is the domain of atomic values (see relational model for more on the notions of domain and atomic value), R is a finite set of relation names, and h : R → 2 C. a function that associates a header with each relation name in R. (Note that this is a simplification from the ...
A function is injective (one-to-one) if each possible element of the codomain is mapped to by at most one argument. Equivalently, a function is injective if it maps distinct arguments to distinct images. An injective function is an injection. [1] The formal definition is the following.
Queries can be nested so that the results of one query can be used in another query via a relational operator or aggregation function. A nested query is also known as a subquery. While joins and other table operations provide computationally superior (i.e. faster) alternatives in many cases, the use of subqueries introduces a hierarchy in ...
A subquery can use values from the outer query, in which case it is known as a correlated subquery. Since 1999 the SQL standard allows WITH clauses, i.e. named subqueries often called common table expressions (named and designed after the IBM DB2 version 2 implementation; Oracle calls these subquery factoring).