Type System for an Object-Oriented Database Programming Language

1. Type System for an Object-Oriented Database Programming Language Yuri Leontiev yuri@cs.ualberta.ca http://www.cs.ualberta.ca/~yuri University of Alberta Edmonton, Alberta Canada T6G 2H1

2. Persistent (Database)Programming Languages Object-OrientedDatabase Systems Object-OrientedProgramming Languages The concept of an OODBPL OODBPLs 2

3. Requirement Summary • Verifiability • Decidability • Substitutability • Multi-methods • Mutable types • Parametric types 3

4. Language Comparison Language C++JavaPizzaSatherCecilMini-CecilTransframeMLMLPolyTOILTIGUKAT Theory D/USD/USD/SD/SD/USUD?/SD/USD/SD/SD/SD/S Subst.(5) 34055555555 Multi-m.(5) 0000555n/a505 Mutable(5) 55555553355 Param.(5) 20333542325 Tests(30) 56111816272512161630 4

5. Behaviors Functions Implementationfunctions Implementationtypes Classes Types 3-Layer Design Functionality Structure 5

6. T_Shape Subtypes xCenter; yCenter;intersects(T_Shape) T_Rectangle T_Circle height;width; radius; Implements T_Point Extends C_Point C_Rectangle C_Circle _xCenter;_yCenter; _width;_height; _radius Types and Classes 6

7. Multi-methods T_Shape Subtypes xCenter; yCenterintersects(T_Shape) T_Rectangle T_Circle height; width;intersects(T_Rectangle) :: fRRintersects(T_Circle) :: fRCintersects(T_Point) :: fRP radius;intersects(T_Circle) :: fCCintersects(T_Rectangle) :: fCRintersects(T_Point) :: fCP T_Point intersects(T_Point) :: fPPintersects(T_Rectangle) :: fPRintersects(T_Circle) :: fPC T_Shape s1, s2;s1 := aRectangle1; s2 := aRectangle2; s1.intersects(s2) // fRR s1 := aRectangle; s2 := aCircle; s1.intersects(s2) // fRC s1 := aCircle; s2 := aPoint; s1.intersects(s2) // fCP 7

8. T_Person C_Person3N age :=: T_Natural; name :=: T_String; T_Natural _age; T_String _firstName, _lastName, _middleName;age implementation _age;name implementation fun() { return _firstName + ‘ ‘ + _lastName + ‘ ‘ + _middleName; }set_name implementation fun(arg) { _firstName := arg.extractToken(2,’ ’); _lastName := arg.extractToken(3,’ ’); _middleName := arg.extractToken(1,’ ’); } Implements C_Person T_Natural _age; T_String _name;age implementation _age;name implementation _name; Attributes T_Person aPerson;aPerson := new C_Person; aPerson.name := “S. John Smith”; aPerson := new C_Person3N; aPerson.name := “S. John Smith”; aPerson.name.print; 8

9. Parametric Types T_InputStream(covar X) get : X; T_OutputStream(contravar X) Subtypes put(X); T_IOStream(novar X) T_InputStream(T_Person) ip; T_InputStream(T_Student) is;ip.get.age.print; ip := is; ip.get.age.print; is.get.studentId.print; T_Person aPerson; T_Student aStudent;T_OutputStream(T_Person) op; T_OutputStream(T_Student) os;op.put(aPerson); op.put(aStudent); os.put(aStudent); os.put(aPerson) T_IOStream(T_Student) ios;ip := ios; os := ios; ios.get.studentId.print; op := ios; 9

10. Comparisons T_Ordered(T_Numeric) T_Ordered(contravar X) less(T_Ordered(X)) : T_Boolean;greater (T_Ordered(X)) : T_Boolean implementation fun(arg) { return not arg.less(self); } T_Numeric T_Real T_Ordered(T_Date) T_Integer T_Date (5.0).less(6); 3.less(3.35); ‘2/3/98’.less(‘3/4/97’); ’2/3/98’.less(3); 10

11. Constrained Types T_Set(covar X) sort() : T_List(X) where (X subtypes T_Ordered(X)); T_Set(T_Integer) iSet;T_List(T_Integer) iList;iList := iSet.sort; // If iSet was {4,3,5}, // iList will be <3,4,5> T_Set(T_Person) pSet; T_List(T_Person) pList;pList := pSet.sort; 11

12. Functional Types T_Set(covar X) sort() : T_List(X) where (X subtypes T_Ordered(X));genericSort( (X,X):T_Boolean ) : T_List(X); T_Set(T_Integer) iSet;T_List(T_Integer) iList;iList := iSet.genericSort( fun(x,y) { return x.less(y) } ); T_Set(T_Person) pSet; T_List(T_Person) pList;pList := pSet.genericSort( fun(x,y) { return x.age.less(y.age); } ); 12

13. Typechecking • Local monotonicity • Consistency of the user type graph • Constraint consistency • Global behavior consistency • Functional consistency • Dispatch consistency • coverage • unambiguity • correctness 13

14. Theory: Types • Model: regular trees •  = T_List() • Ground types • T_Integer, T_List(T_Integer), (T_Real,T_Integer)  T_Integer • Simple constrained types • (  T_Integer).(  ) • Constrained types • glb((  T_Integer).(  ),T_Date  T_Date) 14

15. Theory: Entailment • Constraint sets • C = { L1  U1, L2  U2,...,Ln  Un} • Entailment of constraint sets • C1[1,…,n] |-- C2[1,…, n,1,... ,n] iff  1,…, n : C1[1,…, n]   1,... ,n : C2[1,…, n,1,... ,n] • (T_Set(1)  T_Set(2)) |-- 1  2 15

16. Theory: Subtyping • Subtyping of simple constrained types • (C1).A1  (C2).A2 iff C2 |-- C1 & (A1  A2) • ((T_Set(T_Integer)  T_Set(1)).1) T_Integersince |-- T_Set(T_Integer)  T_Set(1) & 1  T_Integer(let 1 = T_Integer) 16

17. Contributions • Compiled a comprehensive list of OODBPL type system requirements • Designed a type system that satisfies the requirements • Developed decidable typechecking algorithms • Developed a theory capable of expressing all the type system features • Proved decidability and correctness of the resulting system 17

18. Future Research • Design issues: • Language design • Persistence model • Implementation issues: • Type checker • Compiler • Optimization • Theoretical issues: • Relaxing user type graph constraints 18

19. Questions? 19

20. Type System Features • Verifiability • Decidability • Transparency • Extensibility 20

21. OOPL Requirements • Inheritance: • interface • implementation • Method types • Method uniformity • Reflexivity 21

22. DBPL Requirements • Persistence independence • User-defined type constructors • Encapsulation • Parametric types • Partial type specification • Incremental type checking • Typability of SQL-like queries • Mutable object types 22

23. OODB Requirements • Orthogonal type constructors • Extensibility & interoperability • View mechanism • Dynamic schema evolution 23