Backus-Naur Description of Relation Types in Software

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Backus-Naur Description of Relation Types
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:= a collection of data elements of one domain := a collection of references to one relation := <value attribute> <value attributes>,<value attribute> := <value attributes> <reference attribute> := <value attributes> unique instances := <reference attribute unique instances := <value key> not referenced := <reference attribute> referenced := <attributes> unique within each owned set := null <attributes> := <primary entity key> := <referenced entity key> := <general ruling part> in owner relation := <quali cation>,<nest key> := <entity ruling part>,<entity ruling part> <assoc ruling part>,<entity ruling part> := <entity ruling part> <referenced ruling part> <nest ruling part> <assoc ruling part> := <entity ruling part> : <dependent part> := <referenced ruling part> : <dependent part> := <nest ruling part> : <dependent part> := <assoc ruling part> : <dependent part> := <key> : <key> := <general ruling part> : <dependent part>
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DEFINITIONS: <value attribute> <reference attribute> <value attributes> <attributes> <value key> <reference key> <primary entity key> <referenced entity key> <nest key> <dependent part> RULING PARTS: <entity ruling part> <referenced ruling part> <quali cation> <nest ruling part> <assoc ruling part> <general ruling part> RELATIONS: <entity> <referenced entity> <nest> <association> <lexicon> <subrelation>
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Sec 7-4
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It is possible to create from these basic semantic types other forms of relations which satisfy special conditions A synthesis of published material indicates that these ve types, plus the concepts of subrelations, cover the semantic possibilities controlling the structure of databases in an economic and conceptually convenient manner Combinations of ownership and reference connections, for instance, lead to four types of n m relationships among two relations Each of the four cases has distinctive semantics If we have constructed and normalized a view model in an economic fashion, that is, have kept no redundant attributes, then only attributes which implement reference, ownership, or subset linkages will be duplicated Further minimization of redundancy can be achieved by minimizing the number of relations The extent to which this is desirable depends on the further use of the view model If the view model is to become a basis for extended applications using the database it may by transformed to a database submodel
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Procedures which derive new relations by selecting from or by merging other relations can be applied to the model to formulate alternate view models Multiple view models can be combined into database models using such procedures Derived relations introduce redundancies when added to the view model When a view model has been manipulated, the result has to be reevaluated and renormalized to achieve the desired degree of redundancy Once a database model has been de ned, database submodels can be extracted which de ne the portion of the database which can be accessed by some group of users This might be a user group which has provided a view but now wishes to use elements not in its original view, or it can be a user group which is new to the database A database submodel may include derived relations, which are de ned by transformations of the database relations and its attributes Derived relations are also created when a database is manipulated to provide answers to queries Examples are found in Sec 9-2 Of the four conventional operations between sets: Union Intersection Set di erence Cartesian product set of elements of 2 or more (s) sets set of matching elements from s sets remove elements that match another set catenate all elements from s sets
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the rst three ( , , ) are easily applied when the relations involved have identical scope, that is have compatible relation-schemas as de ned in Eq 7-17 A fourth operation ( ) creates a set of all combinations of arbitrary relations These operations are de ned in Sec 7-4-1 Operations which are speci cally de ned to deal with relations are: Projection Selection Join reduce the number of attributes select speci c tuples combine attributes from two relations
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These operations are de ned in Secs 7-4-2 to 7-4-5
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