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Presentation on dbms(relational calculus)
Presentation on dbms(relational calculus)
Presentation on dbms(relational calculus)
Presentation on dbms(relational calculus)
Presentation on dbms(relational calculus)
Presentation on dbms(relational calculus)
Presentation on dbms(relational calculus)
Presentation on dbms(relational calculus)
Presentation on dbms(relational calculus)
Presentation on dbms(relational calculus)
Presentation on dbms(relational calculus)
Presentation on dbms(relational calculus)
Presentation on dbms(relational calculus)
Presentation on dbms(relational calculus)
Presentation on dbms(relational calculus)
Presentation on dbms(relational calculus)
Presentation on dbms(relational calculus)
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Presentation on dbms(relational calculus)

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  • 1.   RELATIONAL CALCULUS   www.powerpointpresentationon.blogspot.com TUSHAR GUPTA
  • 2. INTRODUCTION TO RELATIONAL MODEL <ul><ul><li>Invented by E.F. (Ted) Codd </li></ul></ul><ul><ul><li>Based on first-order predicate logic </li></ul></ul><ul><ul><li>Its core idea is to describe a database as a collection of predicates over a finite set of predicate variables, describing constraints on the possible values and combinations of values. </li></ul></ul>TUSHAR GUPTA
  • 3. THE MODEL <ul><ul><li>Data is represented as mathematical n -ary relations, an n -ary relation being a subset of the Cartesian product of n domains. </li></ul></ul><ul><ul><li>two-valued predicate logic , meaning there are two possible evaluations for each proposition : either true or false. </li></ul></ul><ul><ul><li>Data are operated upon by means of a relational calculus (procedural) or relational algebra (descriptive), these being equivalent in expressive power . </li></ul></ul>TUSHAR GUPTA
  • 4. THE MODEL <ul><ul><li>The basic relational building block is the domain or data type (or relvar). </li></ul></ul><ul><ul><li>A tuple is an set of attribute values. </li></ul></ul><ul><ul><li>An attribute is an ordered pair of attribute name and type name . </li></ul></ul>TUSHAR GUPTA
  • 5. SQL AND THE RELATIONAL MODEL <ul><ul><li>Duplicate rows </li></ul></ul><ul><ul><li>Anonymous columns </li></ul></ul><ul><ul><li>Duplicate column names </li></ul></ul><ul><ul><li>Column order significance </li></ul></ul><ul><ul><li>NULL </li></ul></ul>TUSHAR GUPTA
  • 6. RELATIONAL OPERATIONS <ul><ul><li>Join </li></ul></ul><ul><ul><li>Project - process of eliminating some of the columns </li></ul></ul><ul><ul><li>Restrict - process of eliminating some of the rows </li></ul></ul><ul><ul><li>Union - a way of combining two tables with similar structures </li></ul></ul>TUSHAR GUPTA
  • 7. RELATIONAL OPERATIONS <ul><ul><li>Difference- lists the rows in one table that are not found in the other </li></ul></ul><ul><ul><li>Intersect - lists the rows found in both tables </li></ul></ul><ul><ul><li>Product - combines each row of one table with each row of the other </li></ul></ul>TUSHAR GUPTA
  • 8. RELATIONAL CALCULUS <ul><ul><li>Comes in two flavors: Tuple relational calculus (TRC) and Domain relational calculus (DRC). </li></ul></ul><ul><ul><li>Calculus has variables, constants, comparison ops , logical connectives and quantifiers . </li></ul></ul><ul><ul><ul><li>TRC : Variables range over (i.e., get bound to) tuples . </li></ul></ul></ul><ul><ul><ul><li>DRC : Variables range over domain elements (= field values). </li></ul></ul></ul>TUSHAR GUPTA
  • 9. RELATIONAL CALCULUS <ul><ul><li>Expressions in the calculus are called formulas . </li></ul></ul><ul><ul><li>An answer tuple is essentially an assignment of constants to variables that make the formula evaluate to true . </li></ul></ul>TUSHAR GUPTA
  • 10. TUPLE RELATIONAL CALCULUS <ul><ul><li>Query: {T|P(T)} </li></ul></ul><ul><ul><ul><li>T is tuple variable </li></ul></ul></ul><ul><ul><ul><li>P(T) is a formula that describes T </li></ul></ul></ul><ul><ul><li>Result: the set of all tuples t for which P(t) evaluates True. </li></ul></ul><ul><ul><ul><li>Find all sailors with a rating above 7. </li></ul></ul></ul>TUSHAR GUPTA
  • 11. TRC <ul><ul><li>Atomic formula </li></ul></ul><ul><ul><ul><li>R.a op S.b , op is one of </li></ul></ul></ul><ul><ul><ul><li>R.a op constant </li></ul></ul></ul><ul><ul><li>Formula </li></ul></ul><ul><ul><ul><li>Any atomic formula combined: </li></ul></ul></ul>TUSHAR GUPTA
  • 12. TRC <ul><ul><li>Example </li></ul></ul><ul><ul><ul><li>Find the names and ages of sailors with a rating above 7 </li></ul></ul></ul><ul><ul><ul><li>Find the names of sailors who have reserved all boats </li></ul></ul></ul>TUSHAR GUPTA
  • 13. DOMAIN RELATIONAL CALCULUS <ul><ul><li>Query has the form: </li></ul></ul><ul><ul><li>Answer includes all tuples that make the formula be true . </li></ul></ul><ul><ul><li>Atomic formula: </li></ul></ul><ul><ul><ul><li>, Where Rname is relation specified or could be as X op Y, or X op constant </li></ul></ul></ul><ul><ul><ul><li>op is one of </li></ul></ul></ul>TUSHAR GUPTA
  • 14. DRC <ul><ul><li>Formula: </li></ul></ul><ul><ul><ul><li>an atomic formula, or </li></ul></ul></ul><ul><ul><ul><li>,               where p and q are formulas, or </li></ul></ul></ul><ul><ul><ul><li>,                 where variable X is free in p(X) </li></ul></ul></ul>TUSHAR GUPTA
  • 15. DRC <ul><ul><li>Examples </li></ul></ul><ul><ul><li>Find all sailors with a rating above 7 </li></ul></ul><ul><ul><li>Find sailors rated > 7 who’ve reserved boat #103 </li></ul></ul>TUSHAR GUPTA
  • 16. UNSAFE QUERIES, EXPRESSIVE POWER <ul><ul><li>It is possible to write syntactically correct calculus queries that have an infinite number of answers! Such queries are called unsafe . </li></ul></ul><ul><li>Eg: </li></ul><ul><ul><li>It is known that every query that can be expressed in relational algebra can be expressed as a safe query in DRC / TRC; the converse is also true. </li></ul></ul>TUSHAR GUPTA
  • 17. LIMITATIONS OF THE RELATIONAL ALGEBRA / CALCULUS <ul><li>Can not do: </li></ul><ul><ul><li>Aggregate operations </li></ul></ul><ul><ul><li>Recursive queries </li></ul></ul><ul><ul><li>Complex (non-tabular) structures </li></ul></ul><ul><ul><li>Most of these are expressible in SQL, OQL, XQuery – using other special operators </li></ul></ul>TUSHAR GUPTA

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