Relational Calculus and QBEThe Relational CalculusTuple Relational CalculusJoin ExampleRelational Calculus vs. Predicate CalculusDomain Relational CalculusDomain R.C. Join ExampleNot so abstract, really...10/26/97 I-1Relational Calculus and QBEChapter 8 (skim)10/26/97 I-2The Relational Calculus•Like the Relational Algebra...–An abstract DB language–No aggregate operators–R.A. and R.C. can accomplish the same results•"relationally complete"•"Queries" describe sets { | } with desired properties–More declarative than RA: no operations!•Two flavors: "tuple" and "domain"10/26/97 I-3Tuple Relational Calculus•Set elements are tuples from relations•'Find employees named John'{t | EMPLOYEE (t) and t.FNAME = "John"}–Read as: "The set of all t such that t is an element (member) of the relation EMPLOYEE, and the NAME attribute of t has the value John."•QUEL (Ingres) and to some extent SQL are base on tuple R.C. model10/26/97 I-4Join Example•"Find names of employees who work for the Research department"{e.FNAME, e.LNAME | EMPLOYEE (e) and (( d) (DEPARTMENT(d) and e.DNO = d.DNUMBER and d.DNAME = "Research") )}10/26/97 I-5Relational Calculus vs. Predicate Calculus•Both flavors of R.C. are extensions of the predicate calculus•Can give formal definitions of terms, formulas, scoping and binding of variables, etc.–can build a model theory with TRUE, FALSE•P.C. quantifiers like , and operators like (not) can be used–Care must be taken with and 10/26/97 I-6Domain Relational Calculus•The variables represent individual domain values (rather than whole tuples)"Find employees whose pay is over $25,000"{f,n | ( p) EMPLOYEE (f,m,n,s,b,a,x,p,u,d) and p > 25000}•This is already a shorthand: should say f exists and belongs to the domain "string", etc. etc. for each variable.10/26/97 I-7Domain R.C. Join Example•"Find employees of the Research dept. whose pay is over $25,000"{fn,ln | ( p) ( d1) (EMPLOYEE (fn,m,ln,s,b,a,x,p,u,d1) and p > 25000) and ( d2) ( dn) DEPARTMENT (dn,d2,mg,ms) and d1= d2 and dn="Research"}Many of the variables are just placeholders. In Prolog you could use "anonymous variables" (_).10/26/97 I-8Not so abstract, really...•"Query by Example" uses this framework•User see 2-dimensional layout of schema•Can select which tables are involved, which columns (variables) appear in output (i.e., what vars are to the left of |), what conditions apply between columns, etc. etc.•This is the predominant paradigm in direct end-user query systems (e.g. Microsoft
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