1. An illustrative DBMS and database
The INGRES relational database system
for a retail enterprise
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2. The Ingres Relational Database 1
A sample INGRES relational DB for a retail enterprise
Database = System Catalogue and User Relations
System Catalogue (5 standard relations)
relation
attribute
indexes
integrities
protect
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3. The Ingres Relational Database 2
A sample INGRES relational DB for a retail enterprise
User Relations (8 relations)
item
parts
store
supply
supplier
dept
employee
sale
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4. The Ingres Relational Database 3
A sample INGRES relational DB for a retail enterprise
The user relations record enterprise activity, viz.
sale of items made up of component parts ordered from suppliers.
The system catalogue records the meta-information about the user relations: their attributes, constraints, protection, relevant physical organisation
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5. The Retail Database 1 Significance of user relations
parts what parts do suppliers supply?
supply what has been supplied / is pending?
supplier who are the suppliers?
item what items do we sell / are in stock?
store what outlets do we have for sales?
dept who are dept sales managers?
employee who are our sales employees?
sale when, where & by whom are sales made?
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6. The Retail Database 2 Attributes for these relations are as follows:
item: number, name, dept, price, qoh
parts: pnum, pname, colour, weight, qoh, supplier
store: number, city, state
supply: snum, pnum, jnum, shipdate, quantity
supplier: number, name, city, state
dept: number, name, store, floor, manager
employee: number, name, salary, manager, DOB, startdate
sale: number, date, store, dept, item, quantity, employee, credit
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7. The Retail Database 3 Interpretation of relations ...
Each tuple can be interpreted as an assertion
e.g. a tuple in the sale relation:
“ on <date> salesperson <employee> sold <quantity> of the item <item> in <dept> of <store> for <credit> and this was sale number <number> ”
sale: number, date, store, dept, item,
quantity, employee, credit
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8. The Retail Database 4
The system catalogue is the Data Dictionary. Has info about all the relations in the database. For instance:
relation: relid, relowner, reltups, relwid, relatts ....
attribute: attrelid, attowner, attname, attfrmt, ....
.... content of the relation relation:
relid name of the relation
relowner who owns relation
reltups how many tuples the relation has
relwid how wide each tuple is
relatts details of attributes of relation
....
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9. The Retail Database 5
User access to data dictionary info about relations
... data dictionary info re relation presented via header:
Relation: ...
Owner: ...
Tuple width: ...
Number of Tuples: ...
Storage structure: ...
Relation type: ...
+ relation table characterising attributes of the relation.
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10. The Retail Database 6 Sample content of data dictionary ….
… suppose that current content of store relation is:
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11. The Retail Database 7
Header for the data dictionary information on store:
Relation: store
Owner: ingres
Tuple width: 23
Number of Tuples: 3
Storage structure: paged heap
Relation type: user relation
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12. The Retail Database 8
… relation table characterising the attributes of store:
Attribute name type length
number i 2
city c 15
state c 12
This means number field is up to 2 digit number, city field is up to 15 characters etc.
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13. Issues raised by relational databases 1
How do we conceive the relation scheme?
Conceptual aspect:
does relation scheme match enterprise?
how do we do the real-world modelling?
Use E-R modelling to assist here
Technical aspect:
is the scheme free of redundancy?
are there anomalies on update / deletion?
... use a theory of database design: normal forms etc
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14. Issues raised by relational databases 2
What is a suitable theoretical framework for a query language? - relational theory
What mathematical model should we use to interpret information retrieval formally?
… have logical and algebraic frameworks
- relational calculus and relational algebra
By what criterion is a query language sufficiently expressive?
… introduce a notion of completeness
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15. Issues raised by relational databases 3
How do we make access to information efficient without disclosing physical model?
principles for storing relations: B-trees, hashing, indexes
optimisation techniques for query processing
How do we make query languages that are precise but easy to use?
commercial query language designs SQL, QBE etc
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16. Relational query languages 1
Archetypal query in Quel constructs new relation from relations R1, R2, ..., Rk.
range of t1 is R1
range of t2 is R2
....
range of tk is Rk
retrieve (ti(1).Aj(1), ...., ti(r).Aj(r))
where Y(t1, t2, ..., tk)
Y(t1, t2, ..., tk) is a (quantifier-free) logical constraint on the tuples selected by the range variables t1, t2, ..., tk in the construction process
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17. Relational query languages 2
Illustrative example of use of QUEL:
parts pnum, pname, colour, weight, qoh
supply snum, pnum, jnum, shipdate, quantity
Display supplier, partname , shipdate for all parts shipped since 1994
range of p is parts
range of s is supply
retrieve (s.snum, p.pname, s.shipdate)
where (s.pnum = p.pnum) and (s.shipdate >= 1994)
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18. Relational query languages 3
Linking example to the abstract formalism:
k= two relations used in construction
Index the relations by integers, so that
R1 is parts, R2 is supply, t1 is p, t2 is s
Index the attributes of parts and supply by integers:
e.g. t1.A3 is p.colour, t2.A3 is s.jnum etc
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19. Relational query languages 4
… linking example to abstract formalism …
i() and j() functions with domain set {1,2,3}
constructing a relation with 3-tuples
i maps onto the set {1,2}
… from which relation are new fields derived?
j maps onto the set {1, 2, ..., 5}
… from which fields are new fields derived?
Y(t1, t2) =Y(p, s) is a logical constraint on the tuples selected from parts and supply viz. "s and p must designate tuples with the same part number, and the shipdate for the supply tuple must be 1994 or later"
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20. Relational query languages 5
In general, can translate this into a logical specification for a new relation constructed from a set of source relations R1, R2, ..., Rk - express this in the form:
[The required relation is] the set of tuples of the form
u(r) = (u[1], u[2], ..., u[r])
where
ti is a tuple in the relation Ri,
u is made up of particular components of the ti's,
and
the ti's used to construct u
satisfy some additional constraint.
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21. Relational query languages 6
A suitable logical expression for the required relation is
{ u(r) | ( t1) ... ( tk)
( R1(t1)  R2(t2)  ...  Rk(tk)
 u[1] = ti(1) [ j(1) ]
 u[2] = ti(2) [j(2)]
 ...
 u[r] = ti(r) [j(r)],
 Y(t1, t2, ..., tk) ) }
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22. Relational query languages 7
This uses a Relational Calculus formalism to define the set of tuples that make up the new relation by a predicate. Here Rj(tj) is a basic predicate asserting that tj is a tuple in the relation Rj.
Need a "predicate calculus over relations" to do this.
There are two variants of this:
tuple relational calculus
domain relational calculus.
QUEL is tuple relational calculus based.
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23. The QUEL query language 1
Sample QUEL queries referring to HVFC database
MEMBERS(NAME, ADDRESS, BALANCE)
ORDERS(ORDER_NO, NAME, ITEM, QUANTITY)
SUPPLIERS(SNAME, SADDRESS, ITEM, PRICE)
Print names of members with balances < 0:
range of t is MEMBERS
retrieve (t.NAME)
where t.BALANCE<0
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24. The QUEL query language 2
Sample QUEL queries referring to HVFC database
MEMBERS(NAME, ADDRESS, BALANCE)
ORDERS(ORDER_NO, NAME, ITEM, QUANTITY)
SUPPLIERS(SNAME, SADDRESS, ITEM, PRICE)
Print supplier names, items & prices of all suppliers supplying at least one item ordered by Brooks.
range of r is ORDERS
range of s is SUPPLIERS
retrieve (s.SNAME, s.ITEM, s.PRICE)
where
r.NAME = "Brooks, B" and r.ITEM = s.ITEM
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25. The QUEL query language 3
Sample QUEL queries referring to HVFC database
MEMBERS(NAME, ADDRESS, BALANCE)
ORDERS(ORDER_NO, NAME, ITEM, QUANTITY)
SUPPLIERS(SNAME, SADDRESS, ITEM, PRICE)
Print suppliers supplying every item Brooks orders.
range of s is SUPPLIERS
range of i is SUPPLIERS
retrieve into
SUPITEM (S = s.SNAME, I = i.ITEM)
Step 1: SUPITEM now contains all (supplier, item) pairs - howsoever supplier and item related.
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26. The QUEL query language 4
Sample QUEL queries referring to HVFC database
MEMBERS(NAME, ADDRESS, BALANCE)
ORDERS(ORDER_NO, NAME, ITEM, QUANTITY)
SUPPLIERS(SNAME, SADDRESS, ITEM, PRICE)
Print suppliers supplying every item Brooks orders.
range of s is SUPPLIERS
range of t is SUPITEM
delete t where
t.S = s.SNAME and t.I = s.ITEM
Step 2: Find all tuples (S, I) where S does not supply I.
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27. The QUEL query language 5
Sample QUEL queries referring to HVFC database
MEMBERS(NAME, ADDRESS, BALANCE)
ORDERS(ORDER_NO, NAME, ITEM, QUANTITY)
SUPPLIERS(SNAME, SADDRESS, ITEM, PRICE)
Print suppliers supplying every item Brooks orders.
range of r is ORDERS
range of t is SUPITEM
retrieve into SUPFAIL (S = t.S, I = t.I)
where r.NAME = "Brooks, B" and r.ITEM = t.I
Step 3: Construct list of suppliers who don't supply some item ordered by Brooks.
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28. The QUEL query language 6
Sample QUEL queries referring to HVFC database
MEMBERS(NAME, ADDRESS, BALANCE)
ORDERS(ORDER_NO, NAME, ITEM, QUANTITY)
SUPPLIERS(SNAME, SADDRESS, ITEM, PRICE)
Print suppliers supplying every item Brooks orders.
range of s is SUPPLIERS
retrieve into SNAMES (S = s.SNAME)
constructs list of supplier names. Finally
range of n is SNAMES
range of f is SUPFAIL
delete n where n.S = f.S
Step 4: SNAMES is the now required relation
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29. The QUEL query language 7
Print suppliers supplying every item Brooks orders:
range of s is SUPPLIERS
range of i is SUPPLIERS
retrieve into SUPITEM (S = s.SNAME, I = i.ITEM)
range of t is SUPITEM
delete t where t.S = s.SNAME and t.I = s.ITEM
range of r is ORDERS
retrieve into SUPFAIL (S = t.S, I = t.I)
where r.NAME = "Brooks, B" and r.ITEM = t.I
retrieve into SNAMES (S = s.SNAME)
range of n is SNAMES
range of f is SUPFAIL
delete n where n.S = f.S
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30. The QUEL query language 7
Completeness of QUEL
Must represent 5 primitive relational algebra operations:
1. Union T(n) = R(n) È S(n)
range of r is R
append to T(C1 = r.A1, ..., Cn = r.An)
range of s is S
append to T(C1 = s.B1, ..., Cn = s.Bn)
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31. The QUEL query language 8
Completeness of QUEL (cont.)
2. Set Difference T(n) = R(n) - S(n)
range of r is R
append to T (C1 = r.A1, ..., Cn = r.An)
range of t is T
range of s is S
delete t
where t.C1 = s.B1 and ... and t.Cn = s.Bn)
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32. The QUEL query language 9
Completeness of QUEL
3. Cartesian Product T(m+n) = R(m) ´ S(n)
range of r is R
range of s is S
append to T(C1 = r.A1, ..., Cm = r.Am,
Cm+1 = s.B1, ..., Cm+n = s.Bn)
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33. The QUEL query language 10
Completeness of QUEL
4. Projection T = Õ i(1), i(2), ..., i(k) (R)
range of r is R
append to T(C1 = r.Ai(1), ..., Ck = r.Ai(k) )
5. Selection sF(R), where F condition on tuples in R
append to T(C1 = r.A1, ..., Cn = r.An) where F'
[ F' º condition F transformed to QUEL syntax ]
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34. To follow … Review of Relational Database Systems
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