By Alexander Kurz, Marina Lenisa

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

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The second part of this condition can be put more vividly as follows: the graph with node set A \ {a0 } and with an edge from α(a) = a0 to a for all a is well-founded. Since any well-founded graph induces a well-founded (strict) order on its node set, we have yet another formulation: there is a well-founded order on A \ {a0 } for which α is strictly increasing in the sense that α(a) = a0 implies a < α(a) for all a ∈ A. (6) Classical algebras are seldom cias. For example, a group or a semilattice is a cia (for HX = X × X) iff they contain one element only (consider the unique solution of x ≈ x · 1 or x ≈ x ∨ x, respectively).

CADE 1984. LNCS, vol. 170, pp. 175–193. : Backtracking, interleaving, and terminating monad transformers. In: Functional Programming, ICFP 2005, pp. 192–203. : A completeness theorem for Kleene algebras and the algebra of regular events. Inf. Comput. : Kleene algebra with tests and commutativity conditions. , Steffen, B. ) TACAS 1996. LNCS, vol. 1055, pp. 14–33. : Nonlocal flow of control and Kleene algebra with tests. In: Logic in Computer Science, LICS 2008, pp. 105–117. : Notions of computation and monads.

Lenisa, and A. ): CALCO 2009, LNCS 5728, pp. 34–48, 2009. c Springer-Verlag Berlin Heidelberg 2009 Complete Iterativity for Algebras with Effects 35 The notion of iterative algebra was extended and generalised in [1]; there, iterative algebras are studied for finitary endofunctors on Set (or, more generally, on a locally finitely presentable category). 1) may be infinite. It is the aim of this paper to investigate iterativity of algebras in which the operations have side-effects (e. g. partial operations, non-deterministic ones or composite algebras).