Download e-book for kindle: Algebra and Coalgebra in Computer Science: Third by Gordon Plotkin (auth.), Alexander Kurz, Marina Lenisa,

By Gordon Plotkin (auth.), Alexander Kurz, Marina Lenisa, Andrzej Tarlecki (eds.)

ISBN-10: 3642037410

ISBN-13: 9783642037412

This booklet constitutes the lawsuits of the 3rd overseas convention on Algebra and Coalgebra in laptop 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 was once divided into the next classes: algebraic results and recursive equations, conception of coalgebra, coinduction, bisimulation, stone duality, video game concept, graph transformation, and software program improvement techniques.

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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

1) Let Σ be a signature of operation symbols with prescribed arity. The associated signature functor is the polynomial endofunctor given by HΣ X = n n∈N Σn × X ; the elements of HΣ X are written suggestively as flat terms σ(x1 , . . , xn ). Clearly HΣ is analytic (take An,G = Σn for the trivial subgroup G = {id} ≤ Sn and An,G = 0 else). (2) The functor H assigning to a set X the set of finite multisets over X is analytic, since it arises from putting HX = n∈N X n /Sn . (3) The functor H assigning to a set X the set of trees (always taken to be rooted and ordered) with nodes labelled in X is analytic.

Vn )) = i → σ(v1 (i), . . , vn (i)) for σ ∈ Σn and v1 , . . , vn : E → X and i ∈ E. More generally, there exists a canonical distributive law of every endofunctor H over M as follows: observe that X E ∼ = X E E i∈E X with projections πi : X → X for each i ∈ E. Define λX : H(X ) → (HX)E as the unique morphism such that πiHX · λX = HπiX for every i ∈ E. It is easy to prove that λ is a distributive law of H over M . 9 the identity transformation λ = id : M ⇒ M (which, in fact, is a distributive law for any monad).

11(2). The unique solution of e : X → HΣ X +PFΣ Y assigns to a variable x the set of all possible tree unfoldings (taking into account that e(x ) ⊆ FΣ Y for some variables x ) of the recursive definition of x if all these unfoldings are finite and ∅ else. For example, for the signature with one binary operation symbol ∗ the system ∗ ∗ x ≈ x1 ∗ x2 x ≈ x ∗ x2 x1 ≈ { , y3 } x2 ≈ { } y1 y2 y3 y4 has the unique solution with e† (x) given by the set of trees with elements ∗ ∗ ∗ ∗ and y3 ∗ y1 y2 y3 y4 y3 y4 and with e (x ) = ∅.

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Algebra and Coalgebra in Computer Science: Third International Conference, CALCO 2009, Udine, Italy, September 7-10, 2009. Proceedings by Gordon Plotkin (auth.), Alexander Kurz, Marina Lenisa, Andrzej Tarlecki (eds.)


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