Functional dependency: Difference between revisions

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{{about|a concept in relational database theory|function dependencies in the Haskell programming language|type class}}

{{refimprove|date=October 2012}}

In [[relational database]] theory, a '''functional dependency''' is the following '''[[Relational database#Constraints|constraint]]''' between two attribute sets in a [[Relation (database)|relation]]: Given a relation ''R'' and setsattribute of attributessets <math>X,Y \subseteq R</math>, ''X'' is said to '''functionally determine''' ''Y'' (written ''X'' → ''Y'') if and only ififf 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 (relational algebra)|projection]] <math>\Pi_{X,Y}R</math> is a [[Function (mathematics)|function]], i.e.that is, ''Y'' is a function of ''X''.<ref name="HalpinMorgan2008">{{cite book |author1=Terry Halpin |title=Information Modeling and Relational Databases |url=https://books.google.com/books?id=puO_VlbR_x4C&pg=PA140 |year=2008 |publisher=Morgan Kaufmann |isbn=978-0-12-373568-3 |page=140 |edition=2nd}}</ref><ref name="Date2012">{{cite book |author=Chris Date |title=Database Design and Relational Theory: Normal Forms and All That Jazz |url=https://books.google.com/books?id=8jAGhpMSjAcC&pg=PA21 |year=2012 |publisher=O'Reilly Media, Inc. |isbn=978-1-4493-2801-6 |page=21}}</ref> In simple words, if the values for the ''X'' attributes are known (say they are ''x''), then the values for the ''Y'' attributes corresponding to ''x'' can be determined by looking them up in ''any'' [[Tuple#Relational model|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''.

In [[relational database]] theory, a '''functional dependency''' is a '''[[Relational database#Constraints|constraint]]''' between two sets of attributes in a [[Relation (database)|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 <math>X,Y \subseteq R</math>, ''X'' is said to '''functionally determine''' ''Y'' (written ''X'' → ''Y'') 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 (relational algebra)|projection]] <math>\Pi_{X,Y}R</math> is a [[Function (mathematics)|function]], i.e. ''Y'' is a function of ''X''.<ref name="HalpinMorgan2008">{{cite book |author1=Terry Halpin |title=Information Modeling and Relational Databases |url=https://books.google.com/books?id=puO_VlbR_x4C&pg=PA140 |year=2008 |publisher=Morgan Kaufmann |isbn=978-0-12-373568-3 |page=140 |edition=2nd}}</ref><ref name="Date2012">{{cite book |author=Chris Date |title=Database Design and Relational Theory: Normal Forms and All That Jazz |url=https://books.google.com/books?id=8jAGhpMSjAcC&pg=PA21 |year=2012 |publisher=O'Reilly Media, Inc. |isbn=978-1-4493-2801-6 |page=21}}</ref> In simple words, if the values for the ''X'' attributes are known (say they are ''x''), then the values for the ''Y'' attributes corresponding to ''x'' can be determined by looking them up in ''any'' [[Tuple#Relational model|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''.

In other words, a dependency FD: ''X'' → ''Y'' means that the values of ''Y'' are determined by the values of ''X''. Two tuples sharing the same values of ''X'' will necessarily have the same values of ''Y''.