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From urelements to Computation

Abstract : Around 1922-1938, a new permutation model of set theory was defined. The permutation model served as a counterexample in the first proof of independence of the Axiom of Choice from the other axioms of Zermelo-Fraenkel set theory. Almost a century later, a model introduced as part of a proof in abstract mathematics fostered a plethora of research results, ranging from the area of syntax and semantics of programming languages to minimization algorithms and automated verification of systems. Among these results, we find Lawvere-style algebraic syntax with binders, final-coalgebra semantics with resource allocation, and minimization algorithms for mobile systems. These results are also obtained in various different ways, by describing, in terms of category theory, a number of models equivalent to the permutation model.We aim at providing both a brief history of some of these developments, and a mild introduction to the recent research line of “nominal computation theory”, where the essential notion of name is declined in several different ways.
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https://hal.inria.fr/hal-01615302
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Vincenzo Ciancia. From urelements to Computation. 3rd International Conference on History and Philosophy of Computing (HaPoC), Oct 2015, Pisa, Italy. pp.141-155, ⟨10.1007/978-3-319-47286-7_10⟩. ⟨hal-01615302⟩

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