Download Algebra and Coalgebra in Computer Science: Third by Alexander Kurz, Marina Lenisa PDF

By Alexander Kurz, Marina Lenisa

This publication constitutes the lawsuits of the 3rd foreign convention on Algebra and Coalgebra in machine technological know-how, CALCO 2009, shaped in 2005 through becoming a member of CMCS and WADT. This yr the convention was once held in Udine, Italy, September 7-10, 2009. The 23 complete papers have been rigorously reviewed and chosen from forty two submissions. they're provided including 4 invited talks and workshop papers from the CALCO-tools Workshop. The convention used to be divided into the next periods: algebraic results and recursive equations, concept of coalgebra, coinduction, bisimulation, stone duality, video game idea, graph transformation, and software program improvement concepts.

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Extra resources for Algebra and Coalgebra in Computer Science: Third International Conference, CALCO 2009, Udine, Italy, September 7-10, 2009, Proceedings

Example text

Next we recall the notion of an analytic functor on Set and a characterisation that we shall subsequently use. 5. (A. Joyal [5, 6]) An endofunctor H on Set is called analytic provided that it is the left Kan extension of a functor from the category B of natural numbers and bijections to Set along the inclusion. 6. (1) In fact, Joyal defined analytic functors by explicitly stating what these Kan extensions are. Let Sn be the symmetric group of all permutations of n. For every subgroup G of Sn the symmetrised representable functor sends each set X to the set X n /G of orbits under the action of G on X n by coordinate interchange, i.

An ] = α(a1 ) · · · · · α(an ) · [1] where · denotes concatenation of lists. , so that we have ai = 1 for all i = 1, . . , n. But then the two sides of the above equation are lists of different length, a contradiction. So there is no solution of e in A, and A is no Kleisli-cia.

On the other hand, we identify a natural restriction on programs which brings the continuous case back into the realm of tractability. Theorem 12. e. Proof. We prove this theorem in much the same manner as Theorem 11. e. complete. This encoding is inspired by [10]. Again, let Σ = {a, b, c}, and { p1 , q1 , . . , pn , qn } be an instance of PCP in the alphabet Σ \ {c}. Besides the term s from Theorem 11, Kleene Monads: Handling Iteration in a Framework of Generic Effects 29 which presents all pairs of strings generated by the PCP instance, we need a term t presenting pairs of distinct strings.

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