603 Database Systems Senior Lecturer: Laurie Webster II, M.S.S.E.,M.S.E.E., M.S.BME, Ph.D., P.E. Lecture 16 A First Course in Database Systems

Relational Calculus DRC Select: { |  p  a =  } Query: Retrieve the birthdate and address of the employee whose name is ‘John B. Smith’. Free variables Bound variables {uv | (  q) (  r) (  s) (  t) (  w) (  x) (  y) (  z) (EMPLOYEE (qrstuvwxyz) and q = ‘John’ and r = ‘B’ and s = ‘Smith’) } FNAME MINIT LNAME SSN BDATE ADDRESS SEX SALARY SUPERSSN DNO EMPLOYEE u v

Relational Calculus Free variables Bound variables {uv | (  q) (  r) (  s) (  t) (  w) (  x) (  y) (  z) (EMPLOYEE (qrstuvwxyz) and q = ‘John’ and r = ‘B’ and s = ‘Smith’) } - We need ten variables for the EMPLOYEE relation, one to range over the domain of each attribute in order. Very Important!!!! - Of the ten variables q, r. s, ……, z, only u and v are free.

Relational Calculus Free variables Bound variables {uv | (  q) (  r) (  s) (  t) (  w) (  x) (  y) (  z) (EMPLOYEE (qrstuvwxyz) and q = ‘John’ and r = ‘B’ and s = ‘Smith’) } We first specify the requested attributes, BDATE, and ADDRESS, by domain variables u for BDATE and v for ADDRESS.

Relational Calculus Free variables Bound variables {uv | (  q) (  r) (  s) (  t) (  w) (  x) (  y) (  z) (EMPLOYEE (qrstuvwxyz) and q = ‘John’ and r = ‘B’ and s = ‘Smith’) } Secondly, we specify the condition for selecting a tuple following the bar ( | ) - qrs…..z be a tuple of EMPLOYEE with values for q(FNAME) and s(LNAME) be q=‘John’, r=‘B’ and s=‘Smith’

Relational Calculus Alternatively: { uv | EMPLOYEE (‘John’, ‘B’, ‘Smith’, t, u, v, w, x, y, z)}

Relational Calculus Q1: Retrieve the name and address of all employees who work for the ‘Research’ department. Q1: {qrs | (  z) (  l) (  m) (EMPLOYEE (qrstuvwxyz) DEPARTMENT (lmno) and l = ‘Research’ and m = z) }

Relational Calculus Queries in DRC DEPARTMENT DNAME DNUMBER MGRSSN MGRSTARTDATE l m n o FNAME MINIT LNAME SSN BDATE ADDRESS SEX SALARY SUPERSSN DNO EMPLOYEE q r s t u v w x y z

Relational Calculus Q1: {qrs | (  z) (  l) (  m) (EMPLOYEE (qrstuvwxyz) DEPARTMENT (lmno) and l = ‘Research’ and m = z) }selection condition z = DNO join condition m = z l = ‘Research’ relate two domain variables from two m = DNUMBER relations. selection condition relates a domain variable to a constant

Relational Calculus Note: SQL does not include a universal quantifier. SELECT… FROM…. WHERE EXISTS (SELECT * FROM R AS X WHERE P(X) not (  x ) => NOT EXISTS is how SQL supports universal quantification.

Relational Calculus DOMAIN RELATIONAL CALCULUS (DRC): Domain relational calculus (DRC) differs from the tuple calculus in the type of variables used in the formulas: rather than having variables range over the tuples, the variables range over single values from domains of attributes.

Relational Calculus Query: For every project located in ‘Stafford’, list the project number, the controlling department number, and the department manager’s last name, birthdate, and address. Query(DRC): {iksuv | (  j ) (PROJECT(hijk) and (  t ) (EMPLOYEE(qrstuvwxyz) and (  m ) (  n ) (DEPARTMENT (lmno) and k=m and n=t and j=‘Stafford’)))} PNAMEPNUMBERPLOCATIONDNUM PROJECT h i j k

Relational Calculus Query(DRC): {iksuv | (  j ) (PROJECT(hijk) and (  t ) (EMPLOYEE(qrstuvwxyz) and (  m ) (  n ) (DEPARTMENT (lmno) and k=m and n=t and j=‘Stafford’)))} i = project number (PNUMBER) k = department number (DNUM) s = last name (LNAME) u = birthdate (BDATE) v = address (ADDRESS) m = department number (DNUMBER) n = manager’s SSN (MGRSSN) t = employee SSN (SSN)

Relational Calculus Query: For every project located in ‘Stafford’, list the project number, the controlling department number, and the department manager’s last name, birthdate, and address. i = project number (PNUMBER) k = department number (DNUM) s = last name (LNAME) u = birthdate (BDATE) v = address (ADDRESS) List iksuv ==> left of bar ( | )

Relational Calculus Query(DRC): {iksuv| (  j ) (PROJECT(hijk) and (  t ) (EMPLOYEE(qrstuvwxyz) and (  m ) (  n ) (DEPARTMENT (lmno) and k=m and n=t and j=‘Stafford’)))} i = project number (PNUMBER) k = department number (DNUM) s = last name (LNAME) u = birthdate (BDATE) v = address (ADDRESS) List iksuv ==> left of bar ( | )

Relational Calculus Query:Find the names of employees who have no dependents. Query(DRC): {qs|  t ) EMPLOYEE(qrstuvwxyz) and (not (  l ) (DEPENDENT(lmnop) and t = l)))} ESSNDEPENDENT_NAMES SEX BDATERELATIONSHIP DEPENDENT l m n o p SSN ESSN