Support of Relational Algebra Knowledge ... - Hornad - TUKE

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Syntax of select operation: σ () σ - symbol of select operation condition - boolean expression specified over relation attributes relation_name – name of the relation which is processed by select operation. The result is a new relation that has the same attributes as original relation defined by relation_name. Projection Projection is vertical retrieve from relation and it selects table columns according to attribute list. Syntax of project operation: П () П - symbol of project operation attribute_list – list of attribute (comma separated) displayed in the result relation_name – name of the relation which is processed by projection The result is a new relation with attributes that is specified in the attribute list in the same order as listed. If the attribute list contains only non-key attributes of the relation, then duplicate tuples will not be displayed in the final relation. Union Set operator UNION consolidates all tuples of two relations, eliminating duplicate records. Both relations must have the same relational scheme – degrees of relations and domains of corresponding columns must be identical then the relations are union-compatible. Syntax R 3 = R 1 U R 2 U - symbol of union operation Relations R 1 (a 1 , a 2 , … , a n ) and R 2 (b 1 , b 2 , … , b n ) must be union-compatible. The degree of both relations is n. The result is R 3 (c 1 , c 2 , … , c n ) relation with degree n and each tuple of R 3 is either from R 1 or R 2. If two relations are not union-compatible UNION operator cannot be used. To overcome this problem, it can be used the project operator, to narrow the number of columns in each relation and the relations were unioncompatible. Intersect Intersection is a binary operation. The result tuples belong to both relations. Syntax R 3 = R 1 ∩ R 2 ∩ - symbol of intersect Relations R 1 (a 1 , a 2 , … , a n ) a R 2 (b 1 , b 2 , … , b n ) must be union-compatible. The degree of both relations is n. The result is R 3 (c 1 , c 2 , … , c n ) relation with degree n and each tuple from R 3 is in R 1 and also R 2 . Difference Difference operator returns all records from a single relation that are not in the second relation. Difference operator requires that both relations were unioncompatible. Syntax: R 3 = R 1 - R 2 Relations R 1 (a 1 , a 2 , … , a n ) a R 2 (b 1 , b 2 , … , b m ) must be union-compatible. The degree of both relations is n. The result is R 3 (c 1 , c 2 , … , c n ) relation with degree n. Cartesian product Syntax R 3 = R 1 X R 2 , where R 1 (a 1 , a 2 , … , a n ) is a relation with degree n and the number of tuples (the cardinality of relation) is i. R 2 (b 1 , b 2 , … , b m ) is a relation with degree m and the cardinality of relation is j. The result R 3 (a 1 , a 2 , … , a n , b 1 , b 2 , … , b m ) is a relation with degree n + m and the cardinality of result relation is i*j. Cartesian product combines tuples from two relations. The result contains many tuples that have no relationship between them. Division Syntax R 3 = R 1 ÷ R 2 R 1 (a 1 , a 2 , … , a n ) is a relation with degree n and the number of tuples (the cardinality of relation) is i. R 2 (b 1 , b 2 , … , b m ) is a relation with degree m and the cardinality of relation is j. R 3 (c 1 , c 2 , … , c k ) is a relation with degree k=n-m and the cardinality of relation is i ÷ j . The result relation contains tuples from R 1 that a combination with each tuple from R 2 is in R 1 . The result tuples has only attributes from R 1 . Join Join operation is one of the basic operations of relational algebra. It is a binary operation that combines two relations in the prescribed manner. It is one of the most important operations in relational databases, expressing the relationship between the two relations. Join R1 and R 2 is a select operation applying over Cartesian product R 1 X R 2 with particular condition. Join operation is defined over corresponding attributes both relations R 1 and R 2 . These attributes have the same domain and semantics. Syntax R 3 = R1 ⋈ R 2 ⋈ - symbol of join operation R 1 (a 1 , a 2 , … , a n ) and R 2 (b 1 , b 2 , … , b m ) - relations join_condition – boolean expression in the form AND AND … AND , where a condition has following form Ai Ө Bj. Ai is an attribute of R 1 and Bj is a attribute R 2 . Symbol Ө is one of next operators =, =, != . R 3 (a 1 , a 2 , … , a n , b 1 , b 2 , … , b m ) – a result relation with n+m attibutes The result relation contains corresponding tuples that satisfy a join condition.
Aggregate functions Some database queries require an application of aggregate functions to collection of data records. The aggregate functions also called group functions are COUNT, SUM, AVERAGE, MAXIMUM and MINIMUM functions. Another type of database query involves grouping the relation records according to the value of some relation attributes and subsequent use of the aggregation function independently of each group. Syntax F () group_attributes – a list of relation attributes for grouping records F – function symbol function_list – a list in form , a function is one of COUNT, SUM, AVERAGE, MAXIMUM and MINIMUM functions and attribute is one of relation attributes. relation_name – a name of relation The result relation contains a group attribute and one attribute for each item from function_list. If no group_attribute is defined the functions are applied to all tuples of specified relation. Sequences of operations The usage of relational algebra operations in sequence can be entered in two ways. The first way is one statement created by immersion of operations. The second one is implementation of operations in succession and storing intermediate results. The relations which store intermediate results must be named. ([1][3][4]) III. MODULE OF RELATIONAL ALGEBRA PERFORMANCE A query written in a relational algebra can be expressed as select statement of structured query language (SQL). Execution of select statement on the database server returns a relation. It is a way how to check the correctness of written relational algebra statements. It was developed the compiler of relational algebra statements into select statements ([5]). The check correctness of a student answer is realized by execution of translated relational algebra statement on database sever. The result relation is compared with relation which is a result of correct teacher select statement. Module of relational algebra performance based on designed grammar transforms a query written by relational algebra operations into select statement of SQL. The select statement is then processed by module of SQL statement evaluation ([6][10]). Compiler The lexical units of query are identified at the lexical level. On the basis of designated formal grammar rules it is checked syntax correctness of particular query ([8][9]). It was designed a special language for writing relational algebra queries for our solution. The special symbols (σ, П, ⋈) which are not standard keyboard input were replaced following keywords: σ = SEL П = PROJ ⋈ = JOIN The symbol of aggregate functions 'F' was replaced FUN keyword. The intermediate results are written following: MV1 = relational algebra operation MV2 = relational algebra operation ... V = relational algebra operation MVi – symbol of intermediate result V – symbol of result – resulting relation Grammar An alphabet is the foundation of every language. It is a finite set of elements called symbols ([8][9]). Alphabet of relational algebra: • { a,b,...z } – roman letters • { 0, 1, ...9 } - decimal digits • { '.' , ',' , '(', ')', '+', '-', '*', '/', '=', '=', '!=' } – special symbols • {'SEL', 'PROJ', 'JOIN', 'FUN', 'SUM', 'AVERAGE', 'MAX', 'MIN', 'COUNT', 'AND', 'OR', 'NOT'} - keywords • {'MV1', 'MV2', ….'MVi', 'V' } - reserved words Grammar of relational algebra language is G = (N, T, P, S), where N = {Program, Command, Select, Project, Join, JoinAF, Agreg, Conditions, Condition, Relation, Function, Query, Operation} – a finite set of nonterminal symbols T = { SEL, PROJ, JOIN, FUN, AND, OR, NOT, SUM, AVER, MAX, MIN, COUNT, RESULT, DOT, POINT, LOZAT, NM, POZAT, PLUS, MINUS, MULL, DIV, LT, LE, GT, GE, EQ, NE, PART, ID, KONST} - a finite set of terminal symbols (Table 1) P a set of rules S = Program – start symbol Table 1 Terminal symbols Lexical Unit Lex[[SEL]] Lex[[PROJ]] Lex[[JOIN]] Lex[[FUN]] Lex[[AND]] Lex[[OR]] Lex[[NOT]] Lex[[SUM]] Lex[[AVERAGE]] Terminal Symbol SEL PROJ JOIN FUN AND OR NOT SUM AVER
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Support of Relational Algebra Knowledge ... - Hornad - TUKE

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