By Alexander Kurz, Marina Lenisa

ISBN-10: 3642037402

ISBN-13: 9783642037405

This booklet constitutes the court cases of the 3rd foreign convention on Algebra and Coalgebra in machine 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 conscientiously 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 periods: algebraic results and recursive equations, idea of coalgebra, coinduction, bisimulation, stone duality, online game idea, graph transformation, and software program improvement thoughts.

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

**Example text**

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.

Var) (pair) x:A∈Γ Γ ✄x:A (app) f :A→B ∈Σ Γ ✄t:A Γ ✄ f (t) : B (1) Γ✄ :1 Γ ✄t:A Γ ✄u:B Γ ✄t: A×B Γ ✄t: A×B (fst) (snd) Γ ✄ t, u : A × B Γ ✄ fst(t) : A Γ ✄ snd(t) : A Γ ✄t :A Γ ✄ p : T A Γ, x : A ✄ q : T B (ret) (do) Γ ✄ do x ← p; q : T B Γ ✄ ret t : T A Fig. 1. Term formation in the metalanguage of effects Given an interpretation of atomic types W as objects [[W ]] in a Cartesian category C equipped with a strong monad as above, we obtain obvious interpretations [[A]], [[Γ ]] of types A and contexts Γ as objects in C.

Do z ← t; ret πn+1 z. Decidability follows from the algorithmic character of the reduction steps (1) – (3) and the fact that Kleene algebra is decidable. The definition of regularity might seem overly restrictive. It is easy to find examples of programs that do not satisfy regularity directly, but are still equivalent to a regular program. A typical example of this kind is init x ← p in(do x ← q; ret a)∗ , which is equivalent to p + do x ← (init x ← q in q[a/x]∗ ); ret a. But in fact, it is not even semi-decidable to check whether a program admits a regular implementation.

### 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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