Question

I need some help converting an SQL query into relational algebra.

Here is the SQL query:

SELECT * FROM Customer, Appointment
WHERE Appointment.CustomerCode = Customer.CustomerCode
    AND Appointment.ServerCode IN
    (
        SELECT ServerCode FROM Appointment WHERE CustomerCode = '102'
    )
;

I’m stuck because of the IN subquery in the above example.

Can anyone demonstrate for me how to express this SQL query in relational algebra?

Many thanks.

EDIT: Here is my proposed solution in relational algebra. Is this correct? Does it reproduce the SQL query?

Scodes ← ΠServerCode(σCustomerCode=’102′(Appointment))

Ccodes ← ΠCustomerCode(Appointment ⋉ Scodes)

Result ← (Customer ⋉ Ccodes)

Answer 1

Your SQL code will result in duplicate columns for CustomerCode and the use of SELECT [ALL] is likely to result in duplicate rows. Because the result is not a relation, it cannot be expressed in relational algebra.

These problems are easily fixed in SQL:

SELECT DISTINCT * 
  FROM Customer NATURAL JOIN Appointment
 WHERE Appointment.ServerCode IN
    (
        SELECT ServerCode FROM Appointment WHERE CustomerCode = '102'
    )
;

You didn’t specify which relational algebra you are intereted in. Date and Darwen proposed an algebra named A, specified an A language named D, and designed a D language named Tutorial D.

Tutorial D uses operators JOIN for natural join, WHERE for restriction and MATCHING for semijoin, The slight complication is the comparison in SQL:

CustomerCode = '102'

The comparison of a CustomerCode value to a CHAR value in SQL is possible because of implicit coercion. Tutorial D is stricter — type safe, if you will — requiring you to overload the equality operator or, more practically, define a selector operator for CHAR, which would typically have the same name as the type.

Therefore, the above (revised) SQL may be written in Tutorial D as:

( Customer JOIN Appointment ) 
   MATCHING ( ( Appointment WHERE CustomerCode = CustomerCode ( '102' ) ) { ServerCode } )