Download e-book for iPad: 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 court cases of the 3rd foreign convention on Algebra and Coalgebra in laptop technological know-how, CALCO 2009, shaped in 2005 through 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 provided including 4 invited talks and workshop papers from the CALCO-tools Workshop. The convention used to be divided into the subsequent periods: algebraic results and recursive equations, conception of coalgebra, coinduction, bisimulation, stone duality, online game thought, graph transformation, and software program improvement techniques.

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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

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.

Here n ranges over naturals (excluding 0), 1n denotes the n-fold product of the terminal type 1 with itself, n is a shortcut for the n-tuple , . . , for n > 1 and is just for n = 1. As usual, we have omitted contexts, which are easily reconstructed except possibly in the second and third rules on the left. Their uncut versions look as follows. Γ ✄ fst(p), n : A × 1n Γ ✄ n , snd(p) : 1n × A Γ ✄ p : A × 1n Γ ✄ p : 1n × A Consider the extra rewrite rules, capturing nondeterminism. p+∅ ∅+p p p do x ← p; (q + r) do x ← (p + q); r do x ← p; ∅ do x ← ∅; p ∅ ∅ do x ← p; q + do x ← p; r do x ← p; r + do x ← q; r (∗∗) Let λ stand for the reduction relation defined by rules in (∗), and ω for the reduction relation corresponding to the rules in (∗∗).

If we spell out the definition of a cia in SetM , we see that a flat equation morphism is a map e : X → M (HX + A), and a solution of e in the algebra α : HA → M A is a map e† : X → M A such that e M(λ·He† +ηA ) e† = (X −→ M (HX + A) −−−−−−−−−→ M (M HA + M A) μX+A ·M[Minl,Minr] μA ·[α,ηA ] −−−−−−−−−−−−−→ M (HA + A) −−−−−−→ M A) This means that the algebra (A, α) as well as the recursive equation e and its solution are “effectful”. For example, for M = P the effect is non-determinism. 2) gives rise to a flat equation morphism.

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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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