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

2 IFIP WG1.3, Udine, September 12, Ugo Montanari, Coalgebras for Named Sets Roadmap l Models for nominal process description languages l The basic idea of named sets l Permutation algebras l Named sets l Operations on named sets –Generating fresh names and garbage collecting unused ones –Product in named sets –Inputting names l Generalizing MIHDA l Conclusion

3 IFIP WG1.3, Udine, September 12, Ugo Montanari, Coalgebras for Named Sets Roadmap l Models for nominal process description languages l The basic idea of named sets l Permutation algebras l Named sets l Operations on named sets –Generating fresh names and garbage collecting unused ones –Product in named sets –Inputting names l Generalizing MIHDA l Conclusion

9 IFIP WG1.3, Udine, September 12, Ugo Montanari, Coalgebras for Named Sets Roadmap l Models for nominal process description languages l The basic idea of named sets l Permutation algebras l Named sets l Operations on named sets –Generating fresh names and garbage collecting unused ones –Product in named sets –Inputting names l Generalizing MIHDA l Conclusion

: states with name symmetries

13 IFIP WG1.3, Udine, September 12, Ugo Montanari, Coalgebras for Named Sets Roadmap l Models for nominal process description languages l The basic idea of named sets l Permutation algebras l Named sets l Operations on named sets –Generating fresh names and garbage collecting unused ones –Product in named sets –Inputting names l Generalizing MIHDA l Conclusion

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

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

21 IFIP WG1.3, Udine, September 12, Ugo Montanari, Coalgebras for Named Sets Roadmap l Models for nominal process description languages l The basic idea of named sets l Permutation algebras l Named sets l Operations on named sets –Generating fresh names and garbage collecting unused ones –Product in named sets –Inputting names l Generalizing MIHDA l Conclusion

25 IFIP WG1.3, Udine, September 12, Ugo Montanari, Coalgebras for Named Sets Roadmap l Models for nominal process description languages l The basic idea of named sets l Permutation algebras l Named sets l Operations on named sets –Generating fresh names and garbage collecting unused ones –Product in named sets –Inputting names l Generalizing MIHDA l Conclusion

Generating fresh names

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

Garbage collecting unused names

Product in named sets

Inputting names

43 IFIP WG1.3, Udine, September 12, Ugo Montanari, Coalgebras for Named Sets Roadmap l Models for nominal process description languages l The basic idea of named sets l Permutation algebras l Named sets l Operations on named sets –Generating fresh names and garbage collecting unused ones –Product in named sets –Inputting names l Generalizing MIHDA l Conclusion

46 IFIP WG1.3, Udine, September 12, Ugo Montanari, Coalgebras for Named Sets Roadmap l Models for nominal process description languages l The basic idea of named sets l Permutation algebras l Named sets l Operations on named sets –Generating fresh names and garbage collecting unused ones –Product in named sets –Inputting names l Generalizing MIHDA l Conclusion