1IFIP WG1.3, Udine, September 12, 2009 - Ugo Montanari, Coalgebras for Named Sets

Ugo MontanariDipartimento di Informatica

Università di Pisa

Coalgebras for Named Sets

Work in collaboration withVincenzo Ciancia

Universidad Complutense Madrid

IFIP WG1.3, Udine, September 12, 2009

2IFIP WG1.3, Udine, September 12, 2009 - Ugo Montanari, Coalgebras for Named Sets

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

3IFIP WG1.3, Udine, September 12, 2009 - Ugo Montanari, Coalgebras for Named Sets

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

9IFIP WG1.3, Udine, September 12, 2009 - Ugo Montanari, Coalgebras for Named Sets

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

: states with name symmetries

13IFIP WG1.3, Udine, September 12, 2009 - Ugo Montanari, Coalgebras for Named Sets

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

Axioms: (’(x)= o ’(x) id(x)=x

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

21IFIP WG1.3, Udine, September 12, 2009 - Ugo Montanari, Coalgebras for Named Sets

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

25IFIP WG1.3, Udine, September 12, 2009 - Ugo Montanari, Coalgebras for Named Sets

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

Generating fresh names

Exactly corresponds to

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

Garbage collecting unused names

Product in named sets

Inputting names

43IFIP WG1.3, Udine, September 12, 2009 - Ugo Montanari, Coalgebras for Named Sets

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

46IFIP WG1.3, Udine, September 12, 2009 - Ugo Montanari, Coalgebras for Named Sets

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