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Coinduction for recursive data types: partial orders, metric spaces and Omegacategories
, 2000
"... 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 ..."
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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 186363 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...
Coinductive Interpreters for Process Calculi
 In Sixth International Symposium on Functional and Logic Programming, volume 2441 of LNCS
, 2002
"... This paper suggests functional programming languages with coinductive types as suitable devices for prototyping process calculi. The proposed approach is independent of any particular process calculus and makes explicit the dierent ingredients present in the design of any such calculi. In partic ..."
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This paper suggests functional programming languages with coinductive types as suitable devices for prototyping process calculi. The proposed approach is independent of any particular process calculus and makes explicit the dierent ingredients present in the design of any such calculi. In particular structural aspects of the underlying behaviour model become clearly separated from the interaction structure which de nes the synchronisation discipline. The approach is illustrated by the detailed development in Charity of an interpreter for a family of process languages.