1

The algebra and the calculus…their correspondence and their differences

2

Some of this material was taken from

Kifer et all:http://www.amazon.com/gp/product/0321228383/ref=s9_simh_gw_p14_d1_i3?pf_rd_m=ATVPDKIKX0DER&pf_rd_s=center-2&pf_rd_r=0SF508JN5HZFRECYND6V&pf_rd_t=101&pf_rd_p=1389517282&pf_rd_i=507846

3A domain is

The set of all allowable values that a function can act on and return a meaningful result.

4A calculus is

• Any system of calculating• Apparently, the word come from Latin word for rock and

early folks did their counting with piles of rocks. • When we were in high school, it was the mathematics

that deals with the concept of change, like the slope of a curve, as opposed to the slope of a line• Line is delta-y/delta-x• Curve varies in slope depending on where you are in the

curve

5SQL

• It is a tuple calculus• Variables represent conceptual tuples from a table, derived

table, or singleton• One can also create domain calculi

6Tuple calculus

Form of query:{T | Condition(T)}

T is the target – a variable that ranges over tuples of valuesCondition is the body of the query

Involves T (and possibly other variables)Evaluates to true or false if a specific tuple is substituted for T

7Example

{T | Teaching(T) AND T.Semester = ‘F2000’}Is the same as:SELECT *FROM Teaching TWHERE T.Semester = ‘F2000’

8Domain calculus

• A domain variable is a variable whose value is drawn from the domain of an attribute • Contrast this with a tuple variable, whose value is an entire

tuple• Example: The domain of a domain variable Crs might be

the set of all possible values of the CrsCode attribute in the relation Teaching

9

Domain calculus expression

{X1 , …, Xn | condition(X1 , …, Xn) }

{Pid, Code | Teaching(Pid, Code, ‘F1997’)}

10Example

• Algebra: R – S• TRC: {T | R(T) AND NOT S(T)}• DRC: {A,B,C | R(A,B,C) AND NOT S(A,B,C) }

11

More complete example

12Another example

13A visual interface

• Declarative query language, like SQL• Based on DRC (rather than TRC)• Visual

14

In a more formal form

15The QBE interface

• Print all professors’ names in the MGT department

Professor Id Name DeptId

P._John MGT

16

Return all attributes

Professor Id Name DeptId

• MGTP.

17Joins

18Condition boxes

19Insert a tuple

20A bigger example

21

Other table based DBs: Microsoft Access

22Example

23Filemaker