Object Oriented Database Management systems evolved to address the complex objects in emerging applications that could not be effectively represented in the relational model. ODBMSs provide a direct representation of objects to the database, overcoming the impedance mismatch between application data structures and the relational model. ODBMSs take two approaches - persistent object oriented programming languages that add persistence to programming language objects, and object-relational databases that extend relational databases with object features. The Object Database Management Group developed standards including an object model, query language, and language bindings to allow portability between ODBMS systems.

1. Object Oriented Database ManagementObject Oriented Database Management

2. OutlineOutline
• Motivation
• Embedding SQL in host language
• Object Data Model
• Persistent Programming Languages
• Object Query Language
• Object-orientation in SQL

3. Motivation of ODBMSsMotivation of ODBMSs
• Complex objects in emerging DBMS applications cannot be
effectively represented as records in relational model.
• Representing information in RDBMSs requires complex and
inefficient conversion into and from the relational model to the
application programming language
• ODBMSs provide a direct representation of objects to DBMSs
overcoming the impedance mismatch problem
Application
data structures
Relational
representation
RDBMS
Copy and
translation
Transparent
ODBMS
data transfer

4. Embedded SQLEmbedded SQL
• Access to database from a general purpose programming language required since:
– Not all queries can be expressed in SQL --e.g., recursive queries cannot be written
in SQL.
– Non declarative actions -- e.g., printing reports cannot be done from SQL.
• General purpose language in which SQL is embedded called host language.
• SQL structures permitted in host language called embedded SQL.
SQL+ C
.o file
SQL library
object
code
pre-
compiler
loader
SQL library calls + C
C compiler
Embedded SQL Compilation

5. Embedded SQLEmbedded SQL
• SQL commands embedded in the host programming language
• Data exchanged between host language and DBMS using cursors
• SQL query passed from host language to DBMS which computes
the answer set
• A cursor can be viewed as a pointer into the answer set
• DBMS returns the cursor to the programming language
• Programming language can use the cursor to get a record at a
time access to materialized answer.

6. :dname = “toy”;
raise = 0.1;
EXEC SQL SELECT dnum into :dnum
FROM Department
WHERE dname= :dname;
EXEC SQL DECLARE Emp CURSOR FOR
SELECT * FROM Employee
WHERE dno = :dnum
FOR UPDATE
EXEC SQL OPEN Emp;
EXEC SQL FETCH Emp INTO :E.ssn, :E.dno, :E.name, :E.sal;
while (SQLCODE == 0) {
EXEC SQL UPDATE WHERE CURRENT OF CURSOR
SET sal = sal * (1 + ::raise);
EXEC SQL FETCH Emp INTO :E.ssn, :E.dno, :E.name, :E.sal;
}
EXEC SQL CLOSE CURSOR Emp
/* SQL embedded in C to read the list of employees who work for
the toy department and give them a 10 percent raise */
Example of Embedded SQL

7. Object Oriented Database ManagementObject Oriented Database Management
• Object Oriented databases have evolved along two different paths:
• Persistent Object Oriented Programming Languages: (pure ODBMSs)
– Start with an OO language (e.g., C++, Java, SMALLTALK) which
has a rich type system
– Add persistence to the objects in programming language where
persistent objects stored in databases
• Object Relational Database Management Systems (SQL3 Systems)
– Extend relational DBMSs with the rich type system and user-defined
functions.
– Provide a convenient path for users of relational DBMSs to migrate to
OO technology
– All major vendors (e.g., Informix, Oracle) will/are supporting
features of SQL3.

8. Object Database Management Group (ODMG)Object Database Management Group (ODMG)
• Special interest group to develop standards that allow ODBMS
customers to write portable applications
• Standards include:
– Object Model
– Object Specification Languages
• Object Definition Language (ODL) for schema definition
• Object Interchange Format (OIF) to exchange objects between databases
– Object Query Language
• declarative language to query and update database objects
– Language Bindings (C++, Java, Smalltalk)
• Object manipulation language
• Mechanisms to invoke OQL from language
• Procedures for operation on databases and transactions

9. Object ModelObject Model
• Object:
– observable entity in the world being modeled
– similar to concept to entity in the E/R model
• An object consists of:
– attributes: properties built in from primitive types
– relationships: properties whose type is a reference to some other object
or a collection of references
– methods: functions that may be applied to the object.

10. ClassClass
• Similar objects with the same set of properties and describing
similar real-world concepts are collected into a class.
• Class definition:
interface Employee {
attribute string name;
attribute integer salary;
attribute date date-of-birth;
attribute integer empid;
relationship Projects works-for
inverse Projects::team;
age-type age();
}
Interface Projects{
attribute string name;
attribute integer projid;
relationship Employee team
inverse Emplolyee works-for;
int number-of-employees();
}

11. Class ExtentsClass Extents
• For each ODL class, an extent may be declared.
• Extent is the current set of objects belonging to the class.
– Similar notion to the relation in the relational model.
– Queries in OQL refer to the extent of a class and not the class
directly.
interface Employee (extent Emp-set)
{ attribute string name;
attribute integer salary;
attribute date date-of-birth;
attribute integer empid;
relationship Projects works-for
inverse Projects::team;
age-type age(); }

12. Subclasses and InheritanceSubclasses and Inheritance
• A class can be declared to be a subclass of another class.
• Subclasses inherit all the properties
– attributes
– relationships
– methods
from the superclass.
Interface Married-Employee: Employees {
string spouse-name;
}
• Substitutability: any method of superclass can be invoked over
objects of any subclass (code reuse)

13. Class HierarchyClass Hierarchy
person
employee student
staff faculty
student
assistant
grad undergrad
RA TA

14. Multiple InheritanceMultiple Inheritance
• A class may have more than one superclass.
• A class inherits properties fromeach of its superclasses.
• There is a potential of ambiguity -- variable with same name
inherited from two superclasses:
– flag and error
– rename variable
– choose one

15. Object IdentityObject Identity
• Each object has an identity which it maintains even if some or all
of its attributes change.
• Object identity is a stronger notion of identity than in relational
DBMSs.
• Identity in relational DBMSs is value based (primary key).
• Identity in ODBMSs built into data model
– no user specified identifier is required
• OID is a similar notion as pointer in programming language
• Object identifier (OID) can be stored as attribute in object to refer
to another object.
• References to other objects via their OIDs can result in a
containment hierarchy
• Note: containment hierarchy different from class hierarchy

16. Containment HierarchyContainment Hierarchy
bicycle
wheel brake gear frame
rim spoketire lever pad
Links in containment hierarchy should be read as is-part-of instead of is-a

17. PersistencePersistence
• Objects created may have different lifetimes:
– transient: allocated memory managed by the programming language
run-time system.
• E.g., local variables in procedures have a lifetime of a procedure execution
• global variables have a lifetime of a program execution
– persistent: allocated memory and stored managed by ODBMS runtime
system.
• Classes are declared to be persistence-capable or transient.
• Different languages have different mechanisms to make objects
persistent:
– creation time: Object declared persistent at creation time (e.g., in C++
binding) (class must be persistent-capable)
– persistence by reachability: object is persistent if it can be reached
from a persistent object (e.g., in Java binding) (class must be
persistent-capable).

18. Persistent Object-Oriented Programming LanguagesPersistent Object-Oriented Programming Languages
• Persistent objects are stored in the database and accessed from the
programming language.
• Classes declared in ODL mapped to the programming language
type system (ODL binding).
• Single programming language for applications as well as data
management.
– Avoid having to translate data to and from application programming
language and DBMS
• efficient implementation
• less code
– Programmer does not need to write explicit code to fetch data to and
from database
• persistent objects to programmer looks exactly the same as transient
objects.
• System automatically brings the objects to and from memory to storage
device. (pointer swizzling).

19. Disadvantages of ODBMS ApproachDisadvantages of ODBMS Approach
• Low protection
– since persistent objects manipulated from applications directly, more
changes that errors in applications can violate data integrity.
• Non-declarative interface:
– difficult to optimize queries
– difficult to express queries
• But …..
– Most ODBMSs offer a declarative query language OQL to overcome
the problem.
– OQL is very similar to SQL and can be optimized effectively.
– OQL can be invoked from inside ODBMS programming language.
– Objects can be manipulated both within OQL and programming
language without explicitly transferring values between the two
languages.
– OQL embedding maintains simplicity of ODBMS programming
language interface and yet provides declarative access.

20. OQL ExampleOQL Example
interface Employee {
attribute string name;
relationship
setof(Projects) works-for
inverse Projects::team;
}
Interface Projects{
attribute string name;
relationship setof(Employee) team
inverse Emplolyee works-for;
int number-of-employees();
}
Select number-of-employees()
From Employee e, e.works-for
where name = “sharad”
Find number of employees working on each project “sharad” works on

21. Migration of RDBMSs towards OO TechnologiesMigration of RDBMSs towards OO Technologies
• SQL3 standard incorporates OO concepts in the relational model.
• A row in a table considered as an object
• SQL3 allows a type to be declared for tuples (similar to class in
ODBMSs)
• Relations are collection of tuples of a row type (similar to extent in
ODBMSs)
• Rows in a relation can refer to each other using a reference type
(similar to object identity in ODBMSs)
• A reference can be dereferenced to navigate among tables
• Attributes in a relation can belong to abstract data types
• Methods and functions (expressed in SQL as well as host
programming language) can be associated with abstract data
types

22. SQL-3 ExampleSQL-3 Example
CREATE ROW TYPE Employee-type {
name CHAR(30)
works-for REF(Projects-type)
}
CREATE ROW TYPE Projects-type {
name CHAR(30)
team setof(REF(Employee-type))
}
CREATE TABLE Emp OF TYPE Employee-type
CREATE TABLE Project of TYPE Project-type
Select works-for --> name
From Emp
Where name = ‘sharad’
Return name of the project
sharad works for

23. OQLOQL
CMSC-461
Database Management Systems

24. OQL -- MotivationOQL -- Motivation
• Relational languages suffer from impedance mismatch when we
try to connect them to conventional languages like C or C++.
– The data models of C and SQL are radically different, e.g. C does not
have relations, sets, or bags as primitive types; C is tuple-at-a-time,
SQL is relation-at-a-time.

25. OQL -- Motivation (II)OQL -- Motivation (II)
• OQL is an attempt by the OO community to extend languages like
C++ with SQL-like, relation-at-a-time dictions.
• OQL is query language paired with schema-definition language
ODL.

26. OQL TypesOQL Types
• Basic types: strings, ints, reals, etc., plus class names.
• Type constructors:
– Struct for structures.
– Collection types: set, bag, list, array.
• Like ODL, but no limit on the number of times we can apply a
type constructor.
• Set(Struct()) and Bag(Struct()) play special roles akin to relations.

27. OQL Uses ODL as its Schema-Definition PortionOQL Uses ODL as its Schema-Definition Portion
• For every class we can declare an extent = name for the current
set of objects of the class.
– Remember to refer to the extent, not the class name, in queries.

28. ExampleExample
• interface Bar
(extent Bars)
{
attribute string name;
attribute string addr;
relationship Set<Sell> beersSold
inverse Sell::bar;
}

29. Example (II)Example (II)
• interface Beer
(extent Beers)
{
attribute string name;
attribute string manf;
relationship Set<Sell> soldBy
inverse Sell::beer;
}

30. Example (III)Example (III)
• interface Sell
(extent Sells)
{
attribute float price;
relationship Bar bar
inverse Bar::beersSold;
relationship Beer beer
inverse Beer::soldBy;
}

31. Path ExpressionsPath Expressions
• Let x be an object of class C.
• If a is an attribute of C, then x.a = the value of a in the x object.
• If r is a relationship of C, then x.r = the value to which x is
connected by r.
– Could be an object or a collection of objects, depending on the type of
r.
• If m is a method of C , then x.m (...) is the result of applying m to x.

32. ExamplesExamples
• Let s be a variable whose type is Sell.
• s.price = the price in the object s.
• s.bar.addr = the address of the bar mentioned in s .
– Note: cascade of dots OK because s.bar is an object, not a collection.

33. Example of Illegal Use of DotExample of Illegal Use of Dot
• b.beersSold.price, where b is a Bar object.
• Why illegal? Because b.beersSold is a set of objects, not a single
object.

34. OQL Select-From-WhereOQL Select-From-Where
• SELECT < list of values >
FROM < list of collections and typical members >
WHERE < condition >

35. OQL Select-From-Where (II)OQL Select-From-Where (II)
• Collections in FROM can be:
1. Extents.
2. Expressions that evaluate to a collection.
• Following a collection is a name for a typical member, optionally
preceded by AS.

36. ExampleExample
• Get the menu at Joe's.
SELECT s.beer.name, s.price
FROM Sells s
WHERE s.bar.name = "Joe's Bar"
• Notice double-quoted strings in OQL.
• Result is of type
Bag(Struct(name: string, price: float))

37. ExampleExample
• Another way to get Joe's menu, this time focusing on the Bar objects.
SELECT s.beer.name, s.price
FROM Bars b, b.beersSold s
WHERE b.name = "Joe's Bar"
• Notice that the typical object b in the first collection of FROM is used to
help define the second collection.
– Typical usage: if x.a is an object, you can extend the path expression; if x.a is a
collection, you use it in the FROM list.

38. Tailoring the Type of the ResultTailoring the Type of the Result
• Default: bag of structs, field names taken from the ends of path
names in SELECT clause.
• Example
SELECT s.beer.name, s.price
FROM Bars b, b.beersSold s
WHERE b.name = "Joe's Bar"
has result type:
Bag(Struct( name: string, price: real))

39. Rename FieldsRename Fields
• Prefix the path with the desired name and a colon.
• Example
SELECT beer: s.beer.name, s.price
FROM Bars b, b.beersSold s
WHERE b.name = "Joe's Bar"

40. Change the Collection TypeChange the Collection Type
• Use SELECT DISTINCT to get a set of structs.

41. ExampleExample
• SELECT DISTINCT s.beer.name, s.price
FROM Bars b, b.beersSold s
WHERE b.name = "Joe's Bar"
• Use ORDER BY clause to get a list of structs.

42. ExampleExample
• joeMenu =
SELECT s.beer.name, s.price
FROM Bars b, b.beersSold s
WHERE b.name = "Joe's Bar"
ORDER BY s.price ASC
• ASC = ascending (default); DESC = descending.
• We can extract from a list as if it were an array, e.g. cheapest =
joeMenu[1].name;

43. SubqueriesSubqueries
• Used mainly in FROM clauses and with quantifiers EXISTS and
FORALL.

44. Example: Subquery in FROMExample: Subquery in FROM
• Find the manufacturers of the beers served at Joe's.
SELECT b.manf
FROM (
SELECT s.beer
FROM Sells s
WHERE s.bar.name = "Joe's Bar"
) b

45. QuantifiersQuantifiers
• Boolean-valued expressions for use in WHERE-clauses.
FOR ALL x IN < collection > :
< condition >
EXISTS x IN < collection > :
< condition >
• The expression has value TRUE if the condition is true for all
(resp. at least one) elements of the collection.

46. ExampleExample
• Find all bars that sell some beer for more than $5.
SELECT b.name
FROM Bars b
WHERE EXISTS s IN b.beersSold :
s.price > 5.00
• Problem
How would you find the bars that only sold beers for more than
$5?

47. ExampleExample
• Find the bars such that the only beers they sell for more than $5 are
manufactured by Pete's.
SELECT b.name
FROM Bars b
WHERE FOR ALL be IN (
SELECT s.beer
FROM b.beersSold s
WHERE s.price > 5.00
) :
be.manf = "Pete's"

48. Extraction of Collection ElementsExtraction of Collection Elements
• a) A collection with a single member: Extract
the member with ELEMENT.

49. ExampleExample
• Find the price Joe charges for Bud and put the result in a variable
p.
• p = ELEMENT(
SELECT s.price
FROM Sells s
WHERE s.bar.name = "Joe's Bar"
AND s.beer.name = "Bud"
)

50. Extraction of Collection Elements (II)Extraction of Collection Elements (II)
• b) Extracting all elements of a collection, one at a time:
– 1. Turn the collection into a list.
– 2. Extract elements of a list with <list name>[i].

51. ExampleExample
• Print Joe's menu, in order of price, with beers of the same price
listed alphabetically.

52. Example (II)Example (II)
• L =
SELECT s.beer.name, s.price
FROM Sells s
WHERE s.bar.name = "Joe's Bar"
ORDER BY s.price, s.beer.name;
printf("BeertPricenn");
for(I = 1; I <= COUNT(L); i++)
printf("%st%fn", L[i].name, L[i].price );

53. AggregationAggregation
• The five operators avg, min, max, sum, count apply to any
collection, as long as the operators make sense for the element
type.

54. ExampleExample
• Find the average price of beer at Joe's.
• x = AVG(
SELECT s.price
FROM Sells s
WHERE s.bar.name = "Joe's Bar"
);
• Note coercion: result of SELECT is technically a bag of 1-field structs,
which is identified with the bag of the values of that field.

55. GroupingGrouping
• Recall SQL grouping, for example:
SELECT bar, AVG(price)
FROM Sells
GROUP BY bar;
• Is the bar value the "name" of the group, or the common value for
the bar component of all tuples in the group?

56. Grouping (II)Grouping (II)
• In SQL it doesn't matter, but in OQL, you can create groups from
the values of any function(s), not just attributes.
– Thus, groups are identified by common values, not name."
– Example: group by first letter of bar names (method needed).

57. Outline of OQL Group-ByOutline of OQL Group-By
Collection Defined
by FROM, WHERE
Collection with
function values and
partition
Output collection
Group by values
of function(s)
Terms from
SELECT clause

58. ExampleExample
Find the average price of beer at each
bar.
SELECT barName, avgPrice: AVG(
SELECT p.s.price
FROM partition p
)
FROM Sells s
GROUP BY barName: s.bar.name

59. Example (II)Example (II)
1. Initial collection = Sells.
» But technically, it is a bag of structs of the
form
Struct(s: s1)
Where s1 is a Sells object. Note, the lone
field is named s; in general, there are fields
for all of the tuple variables in the FROM
clause.

60. Example (II)Example (II)
2. Intermediate collection:
» One function: s.bar.name maps Sells
objects s to the value of the name of the
bar referred to by s.
» Collection is a set of structs of type:
Struct{barName: string, partition: Set<
Struct{s: Sell} >
}

61. Example (III)Example (III)
» For example:
Struct(barName = "Joe's Bar", partition = {s1,…, sn})
where s1,…, sn are all the structs with one field,
named s, whose value is one of the Sells objects
that represent Joe's Bar selling some beer.

62. Example (IV)Example (IV)
3. Output collection: consists of beer-
average price pairs, one for each struct
in the intermediate collection.
» Type of structures in the output:
Struct{barName: string, avgPrice: real}

63. Example (V)Example (V)
» Note that in the subquery of the SELECT clause:
SELECT barName, avgPrice: AVG(
SELECT p.s.price
FROM partition p
)
We let p range over all structs in partition. Each of these
structs contains a single field named s and has a Sells object
as its value. Thus, p.s.price extracts the price from one of
the Sells tuples.
» Typical output struct:
Struct(barName = "Joe's Bar", avgPrice = 2.83)

64. Another, Less Typical ExampleAnother, Less Typical Example
Find, for each beer, the number of bars
that charge a "low" price ( 2.00) and a
"high" price ( 4.00) for that beer.
Strategy: group by three things:
» 1. The beer name,
» 2. A boolean function that is true iff the
price is low.
» 3. A boolean function that is true iff the
price is high.

65. The QueryThe Query
SELECT beerName, low, high, count:
COUNT(partition)
FROM Beers b, b.soldBy s
GROUP BY beerName: b.name, low:
s.price <= 2.00, high: s.price >= 4.00

66. The Query (II)The Query (II)
1. Initial collection: Pairs (b; s), where b
is a beer, and s is a Sells object
representing the sale of that beer at
some bar.
» Type of collection members: Struct{b:
Beer, s: Sell}

67. 2. Intermediate collection2. Intermediate collection
Quadruples consisting of a beer name,
booleans telling whether this group is
for high, low, or neither prices for that
beer, and the partition for that group.
The partition is a set of structs of the
type:
Struct{b: Beer, s: Sell}
A typical value:
Struct(b: "Bud" object, s: a Sells object
involving Bud)

68. 2. Intermediate collection (II)2. Intermediate collection (II)
» Type of quadruples in the intermediate
collection:
Struct{
beerName: string,
low: boolean,
high: boolean,
partition: Set<Struct{
b: Beer,
s: Sell
}>
}

69. 2. Intermediate collection (III)2. Intermediate collection (III)
» BeerName low high partition
» Bud TRUE FALSE Slow
Bud FALSE TRUE Shigh
Bud FALSE FALSE Smid
» where Slow Shigh, and Smid are the sets of beer-sells pairs (b;
s) where the beer is Bud and s has, respectively, a low
( 2:00), high ( 4:00) and medium (between 2.00 and 4.00)
price.
» Note the partition with low = high = TRUE must be empty
and will not appear.

70. 3. Output collection:3. Output collection:
The first three components of each
group's struct are copied to the output,
and the last (partition) is counted.
The result:
beerName low high count
Bud TRUE FALSE 27
Bud FALSE TRUE 14
Bud FALSE FALSE 36

71. SQL3 ObjectsSQL3 Objects

72. Objects in SQL3Objects in SQL3
• OQL extends C++ with database concepts, while SQL3 extends
SQL with OO concepts.

73. Objects in SQL3 (II)Objects in SQL3 (II)
• Ullman's personal opinion: the relation is so fundamental to data
manipulation that retaining it as the core, as SQL3 does, is
"right."
• Systems using the SQL3 philosophy are called object-relational.

74. Objects in SQL3 (III)Objects in SQL3 (III)
– All the major relational vendors have something of this kind, allowing
any class to become the type of a column.
• Informix Data Blades
• Oracle Cartridges
• Sybase Plug-Ins
• IBM/DB2 Extenders

75. Two Levels of SQL3 ObjectsTwo Levels of SQL3 Objects
• 1. For tuples of relations = "row types."
• 2. For columns of relations = "types."
– But row types can also be used as column types.

76. ReferencesReferences
• Row types can have references.
• If T is a row type, then REF(T) is the type of a reference to a T
object.
• Unlike OO systems, refs are values that can be seen by queries.

77. Example of Row TypesExample of Row Types
• CREATE ROW TYPE BarType (
name CHAR(20) UNIQUE,
addr CHAR(20)
);
• CREATE ROW TYPE BeerType (
name CHAR(20) UNIQUE,
manf CHAR(20)
);

78. Example of Row Types (II)Example of Row Types (II)
• CREATE ROW TYPE MenuType (
bar REF(BarType),
beer REF(BeerType),
price FLOAT
);

79. Creating TablesCreating Tables
• Row-type declarations do not create tables.
– They are used in place of element lists in CREATE TABLE
statements.
• Example
– CREATE TABLE Bars OF TYPE BarType
– CREATE TABLE Beers OF TYPE BeerType
– CREATE TABLE Sells OF TYPE MenuType

80. DereferencingDereferencing
• A → B = the B attribute of the object referred to by reference A.
• Example
– Find the beers served by Joe.
SELECT beer -> name
FROM Sells
WHERE bar -> name = 'Joe''s Bar';

81. OID's as ValuesOID's as Values
• A row type can have a reference to itself.
– Serves as the OID for tuples of that type.
• Example
CREATE ROW TYPE BarType (
name CHAR(20),
addr CHAR(20),
barID REF(BarType)
);
CREATE TABLE Bars OF TYPE BarType
VALUES FOR barID ARE SYSTEM GENERATED

82. OID's as Values (II)OID's as Values (II)
• VALUES... clause forces the barID of each tuple to refer to the
tuple itself.
Name addr barID
Joe'sMaple St.

83. Example: Using References as ValuesExample: Using References as Values
• Find the menu at Joe's.
SELECT Sells.beer->name, Sells.price
FROM Bars, Sells
WHERE Bars.name = 'Joe''s Bar' AND
Bars.barID = Sells.bar;

84. ADT's in SQL3ADT's in SQL3
• Allows a column of a relation to have a type that is a "class,"
including methods.
• Intended application: data that doesn't fit relational model well,
e.g., locations, signals, images, etc.
• The type itself is usually a multi-attribute tuple.

85. ADT's in SQL3 (II)ADT's in SQL3 (II)
• Type declaration:
CREATE TYPE <name> (
attributes
method declarations or definitions
);
• Methods defined in a PL/SQL-like language.

86. ExampleExample
CREATE TYPE BeerADT ( name CHAR(20), manf CHAR(20),
FUNCTION newBeer( :n CHAR(20), :m CHAR(20))
RETURNS BeerADT;
:b BeerADT; /* local decl. */
BEGIN
:b := BeerADT(); /* built-in constructor */
:b.name := :n;
:b.manf := :m;
RETURN :b;
END;
FUNCTION getMinPrice(:b BeerADT) RETURNS FLOAT; );

87. Example (II)Example (II)
• getMinPrice is declaration only; newBeer is definition.
• getMinPrice must be defined somewhere where relation Sells is
available.

88. Example (III)Example (III)
• FUNCTION getMinPrice(:b BeerADT)
RETURNS FLOAT;
:p FLOAT;
BEGIN
SELECT MIN(price) INTO :p
FROM Sells
WHERE beer->name = :b.name;
RETURN :p;
END;

89. Built-In Comparison FunctionsBuilt-In Comparison Functions
• We can define for each ADT two functions EQUAL and
LESSTHAN that allow values of this ADT to participate in
WHERE clauses involving =, <=, etc.

90. Example: AExample: A ""Point" ADTPoint" ADT
• CREATE TYPE Point ( x FLOAT, y FLOAT,
FUNCTION EQUALS( :p Point, :q Point )
RETURNS BOOLEAN;
BEGIN
IF :p.x = :q.x AND :p.y = :q.y THEN
RETURN TRUE
ELSE
RETURN FALSE;
END;

91. Example: AExample: A ""Point" ADT (II)Point" ADT (II)
• FUNCTION LESSTHAN( :p Point, :q Point )
RETURNS BOOLEAN;
BEGIN
IF :p.x > :q.x THEN
RETURN FALSE
ELSIF :p.x < :q.x THEN
IF :p.y <= :q.y THEN
RETURN TRUE
ELSE RETURN FALSE
ELSE /* :p.x = :q.x
IF :p.y < :q.y THEN
RETURN TRUE
ELSE RETURN FALSE
END;
);

92. Using the Comparison FunctionsUsing the Comparison Functions
• Here is a query that computes the lower convex hull of a set of
points.
• Assumes MyPoints(p) is a relation with a single column p of type
Point.
– SELECT p
FROM MyPoints
WHERE NOT p > ANY MyPoints;

93. Using the Comparison Functions (II)Using the Comparison Functions (II)