Relational Calculus Essay

Introduction Procedural Query language query specification involves giving a step by step process of obtaining the query result e.g., relational algebra usage calls for detailed knowledge of the operators involved difficult for the use of non-experts Declarative Query language query specification involves giving the logical conditions the results are required to satisfy easy for the use of non-experts Prof P Sreenivasa Kumar, Department of CS&E, IITM. 1 TRC – a declarative query language Tuple variable – associated with a relation ( called the range relation ) †¢ takes tuples from the range relation as its values †¢ t: tuple variable over relation r with scheme R(A,B,C ) t.A stands for value of column A etc TRC Query – basic form: { t1.Ai1, t2.Ai2,†¦tm.Aim | ÃŽ ¸ } predicate calculus expression involving tuple variables t1, t2,†¦, tm, tm+1,†¦,ts – specifies the condition to be satisfied Prof P Sreenivasa Kumar, Department of CS&E, IITM. 2 An example TRC query student (rollNo, name, degree, year, sex, deptNo, advisor ) department (deptId, name, hod, phone ) Obtain the rollNo, name of all girl students in the Maths Dept (deptId = 2) {s.rollNo,s.name| student(s)^ s.sex=‘F’^ s.deptNo=2} attributes required in the result This predicate is true whenever value of s is a tuple from the student relation, false otherwise In general, if t is a tuple variable with range relation r, r( t ) is taken as a predicate which is true if and only if the value of t is a tuple in r Prof P Sreenivasa Kumar, Department of CS&E, IITM. 3 General form of the condition in TRC queries Atomic expressions are the following: 1. r ( t ) -true if t is a tuple in the relation instance r 2. t1. Ai t2 .Aj compOp is one of {, ≠¥, =, ≠  } 3. t.Ai c c is a constant of appropriate type Composite expressions: 1. Any atomic expression 2. F1 ∠§ F2 ,, F1 ∠¨ F2 ,  ¬ F1 where F1 and F2 are expressions 3. (∀t) (F), (âˆÆ't) (F) where F is an expression and t is a tuple variable Free Variables Bound Variables – quantified variables Prof P Sreenivasa Kumar, Department of CS&E, IITM. 4 Interpretation of the query in TRC All possible tuple assignments to the free variables in the query are considered. For any specific assignment, if the expression to the right of the vertical bar evaluates to true, that combination of tuple values would be used to produce a tuple in the result relation. While producing the result tuple, the values of the attributes for the corresponding tuple variables as specified on the left side of the vertical bar would be used. Note: The only free variables are the ones that appear to the left of the vertical bar Prof P Sreenivasa Kumar, Department of CS&E, IITM. 5 Example TRC queries Obtain the rollNo, name of all girl students in the Maths Dept {s.rollNo,s.name | student(s) ^ s.sex=‘F’ ^ (âˆÆ' d)(department(d) ^ d.name=‘Maths’ ^ d.deptId = s.deptNo)} s: free tuple variable d: existentially bound tuple variable Existentially or universally quantified tuple variables can be used on the RHS of the vertical bar to specify query conditions Attributes of free (or unbound ) tuple variables can be used on LHS of vertical bar to specify attributes required in the results Prof P Sreenivasa Kumar, Department of CS&E, IITM. 6 Example Relational Scheme student (rollNo, name, degree, year, sex, deptNo, advisor) department (deptId, name, hod, phone) professor (empId, name, sex, startYear, deptNo, phone) course (courseId, cname, credits, deptNo) enrollment (rollNo, courseId, sem, year, grade) teaching (empId, courseId, sem, year, classRoom) preRequisite (preReqCourse, courseID) Prof P Sreenivasa Kumar, Department of CS&E, IITM. 7 Q2 Q3 Q4 Q5 Example queries in TRC (1/5) 1)Determine the departments that do not have any girl students student (rollNo, name, degree, year, sex, deptNo, advisor) department (deptId, name, hod, phone) {d.name|department(d) ^  ¬(âˆÆ' s)(student(s) ^ s.sex =‘F’ ^ s.deptNo = d.deptId) Prof P Sreenivasa Kumar, Department of CS&E, IITM. 8 Examples queries in TRC (2/5) Schema 2)Obtain the names of courses enrolled by student named Mahesh {c.name | course(c) ^ (âˆÆ's) (âˆÆ'e) ( student(s) ^ enrollment(e) ^ s.name = â€Å"Mahesh† ^ s.rollNo = e.rollNo ^ c.courseId = e.courseId } Prof P Sreenivasa Kumar, Department of CS&E, IITM. 9 Examples queries in TRC (3/5) Schema 3)Get the names of students who have scored ‘S’ in all subjects they have enrolled. Assume that every student is enrolled in at least one course. {s.name | student(s) ^ (∀e)(( enrollment(e) ^ e.rollNo = s.rollNo) → e.grade =‘S’)} person P with all S grades: for enrollment tuples not having her roll number, LHS is false for enrollment tuples having her roll number, LHS is true, RHS also true so the implication is true for all e tuples person Q with some non-S grades: for enrollment tuples not having her roll number, LHS is false for enrollment tuples having her roll number, LHS is true, but RHS is false for at least one tuple. So the implication is not true for at least one tuple. Prof P Sreenivasa Kumar, Department of CS&E, IITM. 10 Examples queries in TRC (4/5) Schema 4) Get the names of students who have taken at least one course taught by their advisor {s.name | student(s) ^ (âˆÆ'e)(âˆÆ't)(enrollment(e) ^ teaching(t) ^ e.courseId = t.courseId ^ e.rollNo = s.rollNo ^ t.empId = s.advisor} 5) Display the departments whose HODs are teaching at least one course in the current semester {d.name | department(d) ^(âˆÆ't)(teaching(t) ^ t.empid = d.hod ^ t.sem = ‘odd’ ^ t.year = ‘2008’)} Prof P Sreenivasa Kumar, Department of CS&E, IITM. 11 Examples queries in TRC (5/5) Schema 6)Determine the students who are enrolled for every course taught by Prof Ramanujam. Assume that Prof Ramanujam teaches at least one course. 1. {s.rollNo | student (s) ^ 2. (∀c)(course (c) ^ 3. ((âˆÆ't),(âˆÆ'p)( teaching(t) ^ professor(p) ^ 4. t.courseId = c.courseId ^ 5. p.name = â€Å"Ramanujam† ^ 6. p.empId = t.empId )) → 7. (âˆÆ'e) (enrollment(e) ^ 8. e.courseId = c.courseId ^ 9. e.rollNo = s.rollNo) 10. ) 11. } Prof P Sreenivasa Kumar, Department of CS&E, IITM. 12 Problem with unrestricted use of Negation What is the result of the query: {s.rollNo |  ¬ student(s)} ? Infinite answers !! Unsafe TRC expression : Any expression whose result uses â€Å"constants / values† that do not appear in the instances of any of the database relations. Unsafe expressions are to be avoided while specifying TRC queries. Prof P Sreenivasa Kumar, Department of CS&E, IITM. 13 Expressive power of TRC and Relational Algebra It can be shown that both Tuple Relational Calculus and Relational Algebra have the same expressive power A query can be formulated in (safe) TRC if and only if it can be formulated in RA Both can not be used to formulate queries involving transitive closure — find all direct or indirect pre-requisites of a course — find all subordinates of a specific employee etc. Prof P Sreenivasa Kumar, Department of CS&E, IITM.