Alexander Kurz, Marina Lenisa's 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 technology, CALCO 2009, shaped in 2005 through becoming a member of CMCS and WADT. This 12 months the convention used to be held in Udine, Italy, September 7-10, 2009. The 23 complete papers have been rigorously reviewed and chosen from forty two submissions. they're awarded 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, thought of coalgebra, coinduction, bisimulation, stone duality, online game thought, graph transformation, and software program improvement ideas.

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

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Comput. Sci. : Coalgebras and Monads in the Semantics of Java. Theoret. Comput. Sci. : Termination of a set of rules modulo a set of equations. E. ) CADE 1984. LNCS, vol. 170, pp. 175–193. : Backtracking, interleaving, and terminating monad transformers. In: Functional Programming, ICFP 2005, pp. 192–203. : 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.

A : A → 1 is the unique morphism into the terminal object, and , denotes pairing of morphisms. We say that an equation Γ ✄ t = s, where Γ ✄t : A and Γ ✄s : A, is satisfied by the interpretation over T, and shortly write T |= Γ ✄ t = s, if [[Γ ✄ t : A]] = [[Γ ✄ s : A]]. It is shown in [12] that equality in the metalanguage of effects is completely axiomatised by the standard rules of many-sorted equational logic plus the equations Kleene Monads: Handling Iteration in a Framework of Generic Effects 23 do x ← (do y ← p; q); r = do x ← p; y ← q; r do x ← ret a; p = p[a/x] do x ← p; ret x = p By results of [1], it is moreover immediate that the metalanguage of effects is decidable.

If we choose a = 10 in the above equation, the unique solution of x is {10, 20, 30, 40, 50, 60, 70, 80, 90, 100} ⊆ A. Observe that, in general, the notion of a Kleisli-cia automatically connects effectful operations of an algebra with effectful recursive equations. One might want to consider these two separately. To this end we propose λ-cias as a notion of algebras with effectful operations where effects in recursive equations are allowed in the parameters only. 9. For the monad M a (flat) M -equation morphism in an object A is a ¯ α : HA ◦ / A is a morphism e : X → HX + M A.

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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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