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Coalgebras for Named Sets

Explore models for nominal process description languages, permutation algebras, operations on named sets, and more. Learn about generating fresh names and garbage collecting unused ones. Discover how inputting names and product operations play a role in generalizing MIHDA.

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Coalgebras for Named Sets

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  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

  4. 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

  5. : states with name symmetries

  6. 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

  7. Axioms:  (’(x)= o’(x) id(x)=x

  8. ((A,{A})) = (a,{A+1}) (f) = f

  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

  10. 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

  11. Generating fresh names

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

  13. Garbage collecting unused names

  14. Product in named sets

  15. Inputting names

  16. 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

  17. 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

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