1. Row Types in SQL-3 Row types define types for tuples, and they can be nested. CREATE ROW TYPE AddressType{ street CHAR(50), city CHAR(25), zipcode CHAR(10) } CREATE ROW TYPE PersonType{ name CHAR(30), address AddressType, phone phoneNumberType }

2. Relations as Row Types CREATE TABLE Person OF TYPE PersonType; Recall: row types can be nested! Accessing components of a row type: (double dots) SELECT Person.name, Person.address..city FROM Person WHERE Person.address..street LIKE ‘%Mountain%’

3. References We can define attributes of a row type to reference objects of other row types: CREATE ROW TYPE Company( name char(30), address addressType, president REF(PersonType) ); Following references: SELECT president->name FROM Company WHERE president->address..city=“Seattle”

4. Abstract Data Types in SQL3 Row types provide a lot of the functionality of objects: allow us to modify objects (unlike OQL), but do not provide encapsulation. We can modify objects arbitrarily using SQL3 commands. In OQL: we can query, but not modify only via methods. Abstract data types: are used as components of tuples. CREATE TYPE ( list of attributes and their types optional declaration of the comparison functions: =, < declaration of methods for the type );

5. Address ADT CREATE TYPE AddressADT ( street CHAR(50), city CHAR(20), EQUALS addrEq, LESS THAN addrLT FUNCTION fullAddr (a: AddressADT) RETURNS CHAR(100); :z CHAR(10); BEGIN :z = findZip(:a.street, :a.city); RETURN (….) END; DECLARE EXTERNAL findZip CHAR(50) CHAR(20) RETURNS CHAR(10) LANGUAGE C; ); Encapsulation is obtained by making methods public/private

6. Differences Between OODB Approaches Programming environment: much more closely coupled in OQL/ODL than in SQL3. Changes to objects are done via the programming language in OQL, and via SQL statements in SQL3. Role of relations: still prominent in SQL 3 Row types are really tuples, ADT’s describe attributes. In OQL: sets, bags and structures are fundamental. Encapsulation: exists in OQL; not really supported by row types in SQL3, but are supported by ADT’s.

7. Transitive Closure Suppose we are representing a graph by a relation Edge(X,Y): Edge(a,b), Edge (a,c), Edge(b,d), Edge(c,d), Edge(d,e) a b c d e I want to express the query: Find all nodes reachable from a.

8. Recursion in Datalog Path( X, Y ) :- Edge( X, Y ) Path( X, Y ) :- Path( X, Z ), Path( Z, Y ). Semantics: evaluate the rules until a fixedpoint: Iteration #0: Edge: {(a,b), (a,c), (b,d), (c,d), (d,e)} Path: {} Iteration #1: Path: {(a,b), (a,c), (b,d), (c,d), (d,e)} Iteration #2: Path gets the new tuples: (a,d), (b,e), (c,e) Iteration #3: Path gets the new tuple: (a,e) Iteration #4: Nothing changes -> We stop. Note: number of iterations depends on the data. Cannot be anticipated by only looking at the query!

9. Deductive Databases We distinguish two types of relations in our database: Extensional relations (EDB): their extent is stored in the database just like in ordinary relational databases. Intentional relations (IDB): their extension is defined by a set of possibly recursive datalog rules. Intentional relations can either be materialized or computed on demand. Note: a query and a definition of an intentional predicate look exactly the same (I.e., they’re both datalog programs). Hard problem: how do we optimize queries in the presence of recursion. Harder problem: do we really need recursion?

10. Recursion in SQL-3 Limited forms of recursion are considered important. Linear recursion: only 1 occurrence of a recursive predicate in the body Path( X, Y ) :- Edge( X, Y ) Path( X, Y ) :- Edge( X, Z ), Path( Z, Y ). WITH Pairs AS SELECT origin, dest FROM EDGE RECURSIVE Path(origin, dest) AS Pairs UNION (SELECT Pairs.origin, Path.to FROM Pairs, Path WHERE Pairs.to = Path.origin) SELECT * FROM Path;