Dependency theory is a subfield of database theory which studies implication and optimization problems related to logical constraints, commonly called dependencies, on databases. The best known class of such dependencies are functional dependencies, which form the foundation of keys on database relations. Another important class of dependencies are the multivalued dependencies. A key algorithm in dependency theory is the chase, and much of the theory is devoted to its study.
Some recognized dependency types are:
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The relational model (RM) is an approach to managing data using a structure and language consistent with first-order predicate logic, first described in 1969 by English computer scientist Edgar F. Codd, where all data is represented in terms of tuples, grouped into relations. A database organized in terms of the relational model is a relational database.
In linguistics, syntax is the study of how words and morphemes combine to form larger units such as phrases and sentences. Central concerns of syntax include word order, grammatical relations, hierarchical sentence structure (constituency), agreement, the nature of crosslinguistic variation, and the relationship between form and meaning (semantics). There are numerous approaches to syntax that differ in their central assumptions and goals.
Phrase structure rules are a type of rewrite rule used to describe a given language's syntax and are closely associated with the early stages of transformational grammar, proposed by Noam Chomsky in 1957. They are used to break down a natural language sentence into its constituent parts, also known as syntactic categories, including both lexical categories and phrasal categories. A grammar that uses phrase structure rules is a type of phrase structure grammar. Phrase structure rules as they are commonly employed operate according to the constituency relation, and a grammar that employs phrase structure rules is therefore a constituency grammar; as such, it stands in contrast to dependency grammars, which are based on the dependency relation.
Computer science is the study of the theoretical foundations of information and computation and their implementation and application in computer systems. One well known subject classification system for computer science is the ACM Computing Classification System devised by the Association for Computing Machinery.
Second normal form (2NF) is a normal form used in database normalization. A relation is in the second normal form if it fulfills the following two requirements:
Third normal form (3NF) is a database schema design approach for relational databases which uses normalizing principles to reduce the duplication of data, avoid data anomalies, ensure referential integrity, and simplify data management. It was defined in 1971 by Edgar F. Codd, an English computer scientist who invented the relational model for database management.
Fourth normal form (4NF) is a normal form used in database normalization. Introduced by Ronald Fagin in 1977, 4NF is the next level of normalization after Boyce–Codd normal form (BCNF). Whereas the second, third, and Boyce–Codd normal forms are concerned with functional dependencies, 4NF is concerned with a more general type of dependency known as a multivalued dependency. A table is in 4NF if and only if, for every one of its non-trivial multivalued dependencies XY, X is a superkey—that is, X is either a candidate key or a superset thereof.
In relational database theory, a functional dependency is a constraint between two sets of attributes in a relation from a database. In other words, a functional dependency is a constraint between two attributes in a relation. Given a relation R and sets of attributes , X is said to functionally determineY if and only if each X value in R is associated with precisely one Y value in R; R is then said to satisfy the functional dependency X → Y. Equivalently, the projection is a function, i.e. Y is a function of X. In simple words, if the values for the X attributes are known, then the values for the Y attributes corresponding to x can be determined by looking them up in any tuple of R containing x. Customarily X is called the determinant set and Y the dependent set. A functional dependency FD: X → Y is called trivial if Y is a subset of X.
A candidate key, or simply a key, of a relational database is any set of columns that have a unique combination of values in each row, with the additional constraint that removing any column could produce duplicate combinations of values.
In software engineering, dependency injection is a programming technique in which an object or function receives other objects or functions that it requires, as opposed to creating them internally. Dependency injection aims to separate the concerns of constructing objects and using them, leading to loosely coupled programs. The pattern ensures that an object or function that wants to use a given service should not have to know how to construct those services. Instead, the receiving 'client' is provided with its dependencies by external code, which it is not aware of. Dependency injection makes implicit dependencies explicit and helps solve the following problems:
Object–relational impedance mismatch is a set of difficulties going between data in relational data stores and data in domain-driven object models. Relational Database Management Systems (RDBMS) is the standard method for storing data in a dedicated database, while object-orientated (OO) programming is the default method for business-centric design in programming languages. The problem lies in neither relational databases nor OO programming, but in the conceptual difficulty mapping between the two logic models. Both logical models are differently implementable using database servers, programming languages, design patterns, or other technologies. Issues range from application to enterprise scale, whenever stored relational data is used in domain-driven object models, and vice versa. Object-oriented data stores can trade this problem for other implementation difficulties.
Armstrong's axioms are a set of references used to infer all the functional dependencies on a relational database. They were developed by William W. Armstrong in his 1974 paper. The axioms are sound in generating only functional dependencies in the closure of a set of functional dependencies when applied to that set. They are also complete in that repeated application of these rules will generate all functional dependencies in the closure .
Boyce–Codd normal form is a normal form used in database normalization. It is a slightly stricter version of the third normal form (3NF). By using BCNF, a database will remove all redundancies based on functional dependencies.
Fifth normal form (5NF), also known as projection–join normal form (PJ/NF), is a level of database normalization designed to remove redundancy in relational databases recording multi-valued facts by isolating semantically related multiple relationships. A table is said to be in the 5NF if and only if every non-trivial join dependency in that table is implied by the candidate keys. It is the final normal form as far as removing redundancy is concerned.
In database theory, a multivalued dependency is a full constraint between two sets of attributes in a relation.
A database model is a type of data model that determines the logical structure of a database. It fundamentally determines in which manner data can be stored, organized and manipulated. The most popular example of a database model is the relational model, which uses a table-based format.
The Doctrine Project is a set of PHP libraries primarily focused on providing persistence services and related functionality. Its most commonly known projects are the object–relational mapper (ORM) and the database abstraction layer it is built on top of.
In database theory, a join dependency is a constraint on the set of legal relations over a database scheme. A table is subject to a join dependency if can always be recreated by joining multiple tables each having a subset of the attributes of . If one of the tables in the join has all the attributes of the table , the join dependency is called trivial.
Elementary key normal form (EKNF) is a subtle enhancement on third normal form, thus EKNF tables are in 3NF by definition. This happens when there is more than one unique compound key and they overlap. Such cases can cause redundant information in the overlapping column(s).
In relational database theory, an embedded dependency (ED) is a certain kind of constraint on a relational database. It is the most general type of constraint used in practice, including both tuple-generating dependencies and equality-generating dependencies. Embedded dependencies can express functional dependencies, join dependencies, multivalued dependencies, inclusion dependencies, foreign key dependencies, and many more besides.