Coalgebras for Named Sets

1. IFIP WG1.3, Udine, September 12, 2009 Coalgebras for Named Sets Ugo Montanari Dipartimento di Informatica Università di Pisa Work in collaboration with Vincenzo Ciancia Universidad Complutense Madrid

2. Roadmap • Models for nominal process description languages • The basic idea of named sets • Permutation algebras • Named sets • Operations on named sets • Generating fresh names and garbage collecting unused ones • Product in named sets • Inputting names • Generalizing MIHDA • Conclusion

3. Roadmap • Models for nominal process description languages • The basic idea of named sets • Permutation algebras • Named sets • Operations on named sets • Generating fresh names and garbage collecting unused ones • Product in named sets • Inputting names • Generalizing MIHDA • Conclusion

9. Roadmap • Models for nominal process description languages • The basic idea of named sets • Permutation algebras • Named sets • Operations on named sets • Generating fresh names and garbage collecting unused ones • Product in named sets • Inputting names • Generalizing MIHDA • Conclusion

12. : states with name symmetries

13. Roadmap • Models for nominal process description languages • The basic idea of named sets • Permutation algebras • Named sets • Operations on named sets • Generating fresh names and garbage collecting unused ones • Product in named sets • Inputting names • Generalizing MIHDA • Conclusion

14. Axioms:  (’(x)= o’(x) id(x)=x

19. ((A,{A})) = (a,{A+1}) (f) = f

21. Roadmap • Models for nominal process description languages • The basic idea of named sets • Permutation algebras • Named sets • Operations on named sets • Generating fresh names and garbage collecting unused ones • Product in named sets • Inputting names • Generalizing MIHDA • Conclusion

25. Roadmap • Models for nominal process description languages • The basic idea of named sets • Permutation algebras • Named sets • Operations on named sets • Generating fresh names and garbage collecting unused ones • Product in named sets • Inputting names • Generalizing MIHDA • Conclusion

27. Generating fresh names

28. Exactly corresponds to ((A,{A})) = (a,{A+1}) (f) = f

30. Garbage collecting unused names

33. Product in named sets

39. Inputting names

43. Roadmap • Models for nominal process description languages • The basic idea of named sets • Permutation algebras • Named sets • Operations on named sets • Generating fresh names and garbage collecting unused ones • Product in named sets • Inputting names • Generalizing MIHDA • Conclusion

46. Roadmap • Models for nominal process description languages • The basic idea of named sets • Permutation algebras • Named sets • Operations on named sets • Generating fresh names and garbage collecting unused ones • Product in named sets • Inputting names • Generalizing MIHDA • Conclusion