1. Domains, Relations & Base RelVars (Ch
Domains, Relations & Base RelVars (Ch. 5 Overview) Relational Algebra & Calculus,, & SQL (Ch. 6,7) Preview – Design Issues & Integrity Constraints (Ch.8) A Design Review
Ch. 5?
Each attribute implies a domain (data type, set of values)
Types do not imply physical representation (encap…)
But at least one possible physical representation is suggested
Specific data types are orthogonal to the relational model.
Scalar types have visible components (non-scalars don’t).
The relational model is strongly typed.
Some operators ( selector = < > := CAST AS )

2. A table is a concrete representation of a relation.
Relations & RelVars
Relations (relation values)
A table is a concrete representation of a relation.
Tuple – a set of ordered pairs, no duplicates, unordered.
Relations have cardinality & degree.
RelVars & Views define relations
The system catalog maintains the relvars.
SQL is used to create
RelVars – CREATE DOMAIN, CREATE TABLE
Relations – INSERT, DELETE, UPDATE (tuples)

3. J.CITY = P.CITY JNAME | | PNAME QTY * 100 QTY + 100 STATUS = 5
Type Checking
J.CITY = P.CITY
JNAME | | PNAME
QTY * 100
QTY + 100
STATUS = 5
J.CITY < S.CITY
COLOR = P.CITY
J.CITY = P.CITY | | ‘burg’

4. Operates on relations, gives relations as results
Relational Algebra
Operates on relations, gives relations as results
Restrict (Select)  -- subset of tuples
Project  -- subset of columns
Product -- all possible combinations of two tuples
A X
A Y
B X
B Y A B X Y
(Natural) Join: connecting tuples
based on common value in same-named columns
A1 B1
A2 B1
A3 B2
B1 C1
B2 C2
B3 C3
A1 B1 C1
A2 B1 C1
A3 B2 C2

5. Other Joins
Theta Join -- join two relations
but not on the equality operation
((S RENAME CITY AS SCITY) TIMES
(P RENAME CITY AS PCITY) )
WHERE SCITY > PCITY
Semi Join -- (natural) join two relations,
but return only attributes of the first
((S SEMIJOIN (SP WHERE P# = # (‘P2’))

6. Standard Set Operations
Union, Intersection, Difference
treat relations as sets of tuples
old_ext(inv# ext)
rings_at(inv# ext)
(inv# ext)
(inv# ext)
(inv# ext)

7. Given 2 unary and 1 binary relation --
Division
Given 2 unary and 1 binary relation --
find tuples in the (first) unary relation
matched in the binary relation --
w/ tuples in the other unary relation
A X
A Y
A Z
B X
C Y A B C X Z A

8. Analogy Division a  b is the largest q such that b * q  a
phone_bk(person ext)
Randall 2116
Ross 2116
Ricard 2116
Randall 2218
Ross 2218
Rivers 2218
Ross 3972
Ricard 3972
Rivers 3972
 r(ext)
2116
2118
= (person)
Randall
Ross
 s(person)
Ross
Ricard
= (ext)
2116
3972
Analogy
a  b is the largest q such that b * q  a

9. Associative & Commutative -- UNION, INTERSECTION, TIMES, JOIN
Properties & Examples
Associative & Commutative --
UNION, INTERSECTION, TIMES, JOIN
((SP JOIN S) WHERE P# = P# (‘P2’)) {SNAME}
(((P WHERE COLOR = COLOR (‘Red’))
JOIN SP) {S#} JOIN S) {SNAME}
((S {S#} DIVIDEBY P {P#} PER SP {S#, P#})
JOIN S {SNAME}
S{S#} DIVIDEBY (SP WHERE S# = S# (‘S2’)) {P#}
PER SP {S#,P#}
(((S RENAME S# AS SA) {SA, CITY} JOIN
(S RENAME S# AS SB) {SB, CITY} )
WHERE SA < SB) {SA,SB}

10. the Algebra enables writing relational expressions
Retrieval
Update
Integrity constraints
Derived relvars (views)
Stability requirements (concurrency control)
Security constraints (scope of authorization)
Transformation rules -> OPTIMIZATION
((SP JOIN S) WHERE P# = P# (‘P2’)) {SNAME}
((SP WHERE P# = P# (‘P2’)) JOIN S) {SNAME}

11. Aggregates -- COUNT, SUM, AVG, MAX, MIN, ALL, ANY
Miscellaneous
Aggregates -- COUNT, SUM, AVG, MAX, MIN, ALL, ANY
SUMMARIZE SP PER SP {P#} ADD SUM (QTY) AS TOTQTY
SUMMARIZE (P JOIN SP) PER P {CITY} ADD COUNT AS NSP
Relational Comparisons
= equals
/= not equals
<= subset of (IN)
< proper subset of
>= superset
> proper superset
IS_EMPTY
GROUP, UNGROUP

12. The algebra - a language to describe how to construct a new relation.
Relational Calculus
The algebra - a language to describe how to construct a new relation.
The calculus - a language to write a definition of that new relation.
FORALL PX (PX.COLOR = COLOR (‘Red’))
EXISTS SPX (SX.S# = SX.S# AND SPX.P# = P# (‘P2’)
Procedural vs. Non-procedural
Relational Completeness

13. 6.13 Get full details of all projects.JX
SELECT * FROM J
Get supplier numbers for suppliers who supply project J1.
( SPJ WHERE J# = J# (‘J1’) ) {S#}
SPJX.S# WHERE SPJX.J# = J# (‘J1’)
SELECT DISTINCT SPJ.S#
FROM SPJ WHERE SPJ.J# = ‘J1’
6.18 Get supplier-number/part-number/project-number triples such that supplier part and project are all colocated).
(S JOIN P JOIN J) {S#, P#, J#}
(SX.S#, PX.P#, JX.J# ) WHERE SX.CITY = PX.CITY AND
PX.CITY = JX.CITY AND
JX.CITY = SX.CITY
SELECT S.S#, P.P#, J.J# FROM S,P,J
WHERE S.CITY = P.CITY AND P.CITY = J.CITY.
Query Exercises

14. An attribute value must match its type. A primary key must be unique.
Integrity Preview!
An attribute value must match its type.
A primary key must be unique.
A tuple’s foreign key must be of the same type as its “matching” primary key.
To create a record with a given foreign key, a record in the corresponding table must have that value as its primary key.
Many to many relationships cannot be modeled (directly).
Find examples to support these in SPJ!

15. Study Questions
Which of the relational algebra, tuple calculus and domain calculus is SQL based on?
Can any relational query be expressed in a single SQL statement?
To what extent do these query languages go beyond the relational model?
Why might QueryByExample languages be easier to use than SQL for someone unfamiliar with the database scheme of a database?

16. Lab Assignment for Next Week
With your partner, finish creating and populating the SPJ database.
Run the assigned queries from Chapter 6.
SQL BNF
cuiwww.unige.ch/~falquet/sdbd/langage/SQL92/BNFindex.html