902 research outputs found

    Edsger Wybe Dijkstra (1930 -- 2002): A Portrait of a Genius

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    We discuss the scientific contributions of Edsger Wybe Dijkstra, his opinions and his legacy.Comment: 10 pages. To appear in Formal Aspects of Computin

    Formalization of Universal Algebra in Agda

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    In this work we present a novel formalization of universal algebra in Agda. We show that heterogeneous signatures can be elegantly modelled in type-theory using sets indexed by arities to represent operations. We prove elementary results of heterogeneous algebras, including the proof that the term algebra is initial and the proofs of the three isomorphism theorems. We further formalize equational theory and prove soundness and completeness. At the end, we define (derived) signature morphisms, from which we get the contravariant functor between algebras; moreover, we also proved that, under some restrictions, the translation of a theory induces a contra-variant functor between models.Fil: Gunther, Emmanuel. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Gadea, Alejandro Emilio. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Pagano, Miguel Maria. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentin

    Modelling Garbage Collection Algorithms --- Extend abstract

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    We show how abstract requirements of garbage collection can be captured using temporal logic. The temporal logic specification can then be used as a basis for process algebra specifications which can involve varying amounts of parallelism. We present two simple CCS specifications as an example, followed by a more complex specification of the cyclic reference counting algorithm. The verification of such algorithms is then briefly discussed

    Edsger Dijkstra. The Man Who Carried Computer Science on His Shoulders

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    This a biographical essay about Edsger Wybe Dijkstra.Comment: 12 pages. Originally appeared in Inference, Volume 5, Issue 3, 2020, see https://inference-review.com/article/the-man-who-carried-computer-science-on-his-shoulder

    Computation calculus bridging a formalization gap

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    AbstractWe present an algebra that is intended to bridge the gap between programming formalisms that have a high level of abstraction and the operational interpretations these formalisms have been designed to capture. In order to prove a high-level formalism sound for its intended operational interpretation, one needs a mathematical handle on the latter. To this end we design the computation calculus. As an expression mechanism, it is sufficiently transparent to avoid begging the question. As an algebra, it is quite powerful and relatively simple

    Z-style notation for Probabilities

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    A notation for probabilities is proposed that differs from the traditional, conventional notation by making explicit the domains and bound variables involved. The notation borrows from the Z notation, and lends itself well to calculational manipulations, with a smooth transition back and forth to set and predicate notation
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