1. CSE-321 Programming Languages Subtyping POSTECH May 14, 2007 박성우

2. 2 Key Features of Object-Oriented Languages Multiple representation –different methods of the same name –dynamic dispatch Encapsulation –Only an object's own methods can see private data. Inheritance –classes, subclasses,... Subtyping –interface, interface extension

3. 3 Outline Overview V Principle of subtyping Subtyping relations Coercion semantics

4. 4 Principle of Subtyping

5. 5 Examples

6. 6 Basic Rules Reflexivity and transitivity Rule of subsumption

7. 7 Subset Semantics for Subtyping Example –32-bit word for nat –32-bit word for int –64-bit word for float

8. 8 Outline Overview V Principle of subtyping V Subtyping relations Coercion semantics

9. 9 Setup

10. 10 Subtyping for Product Types

11. 11 Subtyping for Sum Types

12. 12 Subtyping for Function Types

13. 13 Subtyping for Reference Types

14. You are all so gullible!

15. 15 Wrong Subtyping Rules!

16. 16

17. 17

18. 18 Subtyping for Function Types Covariant in return types B and B' Contravariant in argument types A and A'

19. 19 Dereferencing ref A

20. 20 Assigning to ref A

21. 21 Subtyping for Reference Types A · B corresponds to dereferencing. B · A corresponds to assigning a new value. Nonvariant (neither covariant nor contravariant)

22. 22 Subtyping for Array Types Array types = extension of reference types Subtyping for array types in Java –runtime overhead of dynamic tag-checks.

23. 23 Outline Overview V Principle of subtyping V Subtyping relations V Coercion semantics

24. 24 Coercion Semantics for Subtyping Example –32-bit word for int –64-bit word for float

25. 25 Coercion Subtyping Judgment

26. 26 All coercion functions for A · B ) exhibit the same behavior. Coherence