By Alexander Kurz, Marina Lenisa

ISBN-10: 3642037402

ISBN-13: 9783642037405

This publication constitutes the court cases 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 12 months 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 offered including 4 invited talks and workshop papers from the CALCO-tools Workshop. The convention used to be divided into the next classes: algebraic results and recursive equations, concept of coalgebra, coinduction, bisimulation, stone duality, online game thought, graph transformation, and software program improvement thoughts.

**Read or Download Algebra and Coalgebra in Computer Science: Third International Conference, CALCO 2009, Udine, Italy, September 7-10, 2009, Proceedings PDF**

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

**Example text**

In this paper we study complete iterativity for algebras with computational effects (described by a monad). First, we prove that for every analytic endofunctor on Set there exists a canonical distributive law over any commutative monad M , hence a lifting of that endofunctor to the Kleisli category of M . Then, for an arbitrary distributive law λ of an endofunctor H on Set over a monad M we introduce λ-cias. The cias for the corresponding lifting of H (called Kleisli-cias) form a full subcategory of the category of λ-cias.

Hard), and hence fails to be finitely axiomatisable. On the positive side, we show that a natural regular fragment of the MCE is complete and decidable. This fragment contains both Kleene algebra and the metalanguage of effects, and hence may be regarded as a suitable abstract framework for combined reasoning about control and effects. The situation is partly summarised in the diagram below. , undecidable Regular metalanguage of decidable control and effects gg { g { gg {{ g {{ Kleene algebra Metalanguage (control) of effects ∗ : Over continuous Kleene monads We illustrate the calculus with an extended example, the proof of a property of a further, more natural implementation of list reverse.

The situation is partly summarised in the diagram below. , undecidable Regular metalanguage of decidable control and effects gg { g { gg {{ g {{ Kleene algebra Metalanguage (control) of effects ∗ : Over continuous Kleene monads We illustrate the calculus with an extended example, the proof of a property of a further, more natural implementation of list reverse. Kleene Monads: Handling Iteration in a Framework of Generic Effects 21 2 Preliminaries: Monads and Generic Imperative Programs Intuitively, a monad associates to each type A a type T A of computations with results in A; a function with side effects that takes inputs of type A and returns values of type B is, then, just a function of type A → T B.

### Algebra and Coalgebra in Computer Science: Third International Conference, CALCO 2009, Udine, Italy, September 7-10, 2009, Proceedings by Alexander Kurz, Marina Lenisa

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