Abstract

In this paper we prove coinduction theorems for nal coalgebras of endofunctors on categories of partial orders and (generalized) metric spaces. These results characterize the order, respectively the metric, on a nal coalgebra as maximum amongst all simulations. As suggested in [15], and motivated by the idea that partial orders and metric spaces are types of enriched category, the notion of simulation is based on the enriched categorical counterpart of relations, called bimodules. In fact, the results above arise as instances of a coinduction theorem, parametric in a quantale applying to nal coalgebras of endofunctors on the category of all (small) all) 50147 and 18636-3 Also, we give a condition under which the operational notion of simulation coincides with the denotational notion of nal semantics. 1 Introduction Coinduction is a principle for reasoning about potentially innite or circular elements of recursive data types, like streams, processes or exact reals [14,5,7]. Typ...

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