Get Algebra and Coalgebra in Computer Science: Third PDF

By Alexander Kurz, Marina Lenisa

ISBN-10: 3642037402

ISBN-13: 9783642037405

This e-book constitutes the lawsuits of the 3rd foreign convention on Algebra and Coalgebra in desktop 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 provided 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, thought of coalgebra, coinduction, bisimulation, stone duality, online game thought, graph transformation, and software program improvement concepts.

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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

6. (1) In fact, Joyal defined analytic functors by explicitly stating what these Kan extensions are. Let Sn be the symmetric group of all permutations of n. For every subgroup G of Sn the symmetrised representable functor sends each set X to the set X n /G of orbits under the action of G on X n by coordinate interchange, i. , X n /G is the quotient of X n modulo the equivalence ∼G with (x1 , . . , xn ) ∼G (y1 , . . , yn ) iff (xp(1) , . . , xp(n) ) = (y1 , . . , yn ) for some p ∈ G. It is straightforward to work out that an endofunctor on Set is analytic iff it is a coproduct of symmetrised representables.

It is well known that giving the structure of a commutative monad is equivalent to giving the structure of a symmetric monoidal monad, see [8, 9]. So every commutative monad (M, η, μ) on Set comes equipped with a double strength, i. , a family of maps mX,Y : M X × M Y → M (X × Y ) natural in X and Y such that the following axioms hold: mX,Y · (ηX × ηY ) = ηX×Y , μX×Y · M mX,Y · mMX,MY = mX,Y · (μX × μY ) and mX×Y,Z · (mX,Y × idMZ ) = mX,Y ×Z · (idMX × mY,Z ) . Moreover, the monad is symmetric monoidal, i.

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. Inf. Comput. : Monadic encapsulation of effects: A revised approach (extended version). J. Funct. Prog. : A generic complete dynamic logic for reasoning about purity and effects (Extended version to appear in Formal Aspects of Computing).

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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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