Download relationalcalculus

Relational Calculus
Database Management Systems,
1
Tuple Relational Calculus(TRC)


Tuple variable is a variable that takes on the tuples of
a particular relation schema as values
It has the form {T|p(T)}
– Where T is the tuple variable and p(.) is the formula that
describe T.
– The result of the query is the set of all tuples for which the
formula is true…



The formula is constructed using the tuples and
relational operators: >, <, =, not equal, less than or
equal, greater than or equal.
The formulas may be atomic: composed of tuple
variables, operators, and constants
Formula may also be recursively defined in terms of
other sub-formulas.
Database Management Systems,
2
Examples

Find all sailors with rating above 7:(Q11)
{S|SSailors  S.rating>7}
– S is instantiated for each tuple of Sailor and the test is applied
to it. The answer is the set of those instances passing the test.

Find the names and ages of the sailors with rating
above 7:(Q12)
{P|SSailors (S.rating>7  P.sname=S.sname  P.age=S.age)}

Find the sailor names, boat id, and reservation dates
for each reservation:(Q13)
{P|RReserves S  Sailors
(R.sid=S.sid P.bid=R.bid P.day=R.day P.sname=S.sname)}
Database Management Systems,
3
Examples (cont.)

Find the name of the sailors who have reserved boat
103:(Q1)
{P|SSailors R  Reserves
(R.sid=S.sid R.bid=103P.sname=S.sname )}

Find the name of the sailors who have reserved a red
boat:(Q2)
{P|SSailors R  Reserves  B Boats
(R.sid=S.sid  B.bid=R.bid B.color=‘red’  P.sname=S.sname)}

Find the name of the sailors who have reserved a at
least two boats:(Q7)
{P|SSailors R1  Reserves  R2 Reserves
(S.sid=R1.sid  R1.sid=R2.sid  R1.bidR2.bid 
P.sname=S.sname)}
Database Management Systems,
4
Examples (cont.)

Find the name of the sailors who have reserved all boats:(Q9)
{P|SSailors  B Boats
R  Reserves(S.sid=R.sid  R.bid=B.bid  P.sname=S.sname)}
– English statement for this query is “find sailors S such that for all boats
B there is a Reserves tuple…”

Find the name of the sailors who have reserved all red boats:(Q14)
{P|SSailors   B Boats (B.color =‘red’
(R  Reserves(S.sid=R.sid  R.bid=B.bid  P.sname=S.sname)))} or
replacing implication by NOT and OR:
{P|SSailors   B Boats (B.color ‘red’
(R  Reserves(S.sid=R.sid  R.bid=B.bid  P.sname=S.sname)))}
– Find sailors S such that for all boats B, either the boat is not red or the
sailor S has reserved boat B.
Database Management Systems,
5
Aggregate Functions



Aggregate functions and grouping are not included as
basic algebraic operations. However, they are useful,
like division and join operation. Count and Average,
Minimum, Maximum, and Sum are aggregate functions.
Example for Count and Average:
Number of sailors reserving each boat:
bid₣count sid

(Reserves)
Total number of students and the average rating:
₣count sid, Average rating (Sailors)
Database Management Systems,
6
Review

Major problem with calculus: unsafe queries
(P|SSailors) is syntactically correct but it is an unsafe query.




If a query language can express all the queries that can
be expresses in relational algebra it is called a
relationally complete language
Relational algebra query describe a procedure to
compute output relation from input relations, using
RelAlg operators
Relational calculus describe the tuples in output
relation, using a subset of first order predicate logic
All relational algebra queries can be expresses in
relational calculus, the converse is true only for
restricted relational calculus
Database Management Systems,
7