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