Daniele Turi and J.J.M.M. Rutten, "On the foundations of final semantics: nonstandard sets, metric spaces, partial orders." Mathematical Structures in Computer Science, vol. 8, no. 5 (1998), 481--540. 22  Home/Search   Document Details and Download   Summary   Related Articles

....examples. Section 5 shows how a good part of the development of Vicious Circles [3] for example, can be unified and simplified by using the much more general work that we do in this paper. One particular focus of our study is the notion of a uniform functor on sets, introduced by Turi and Rutten [11] and Turi [9] We generalize their notion slightly, prove the main result about such functors (that their greatest fixed points are final coalgebras) and we also use our earlier work to check that many functors of interest are uniform. Taken together, the work of this paper shows that much of the ....

....a solution satisfying an appropriate recursion principle. There is no evident way to do this without extra maps. We use j to get a related map e 0 : a a. Having this, we can use Theorem 2.17. 17 Our definition of uniformity is a modification of the one found in Turi [9] and Turi and Rutten [11]. The difference is that the original did not use L = LP but rather the well founded version of this functor, taking a set a to the smallest set a such that a = P(a a ) So our definition above is satisfied by more functors than the original definition. Functors which use ....

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Daniele Turi and J.J.M.M. Rutten, "On the foundations of final semantics: nonstandard sets, metric spaces, partial orders." Mathematical Structures in Computer Science, vol. 8, no. 5 (1998), 481--540. 22

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