@MISC{Bartels02generalizedcoinduction, author = {Falk Bartels}, title = {Generalized Coinduction}, year = {2002} }

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Abstract

this paper express that the above principles work under dierent additional assumptions which are needed to show that the large system can actually be constructed inside the category. The basic Theorem requires the existence of countable coproducts. Later we also present a variant where the functor T comes a as a monad, the functor F is taken from a copointed functor, and the distributive law is assumed to interact nicely with this additional structure (i.e. should be a distributive law of the monad over the copointed functor, see again (Lenisa et al., 2000)). As a trivial instance of the new framework one recovers the basic coiteration schema and the standard coinduction proof principle. More interesting settings for T and yield the known schemata of primitive corecursion and the dual of course-of-value iteration mentioned above. In some more detail we explain another instance of the framework which deals with certain sets of auxiliary operators, like e.g. parallel and sequential composition for labelled transition systems. More precisely, it can handle such operators which are denable by a format introduced by Turi and Plotkin (Turi and Plotkin, 1997) as a categorical generalization of the known GSOS rule format (Bloom et al., 1995). On the one hand one obtains denition principles guaranteeing unique solutions for (guarded) recursive equations involving these operators, one the other hand this leads to a proof principle up-to-context for contexts built from them. 1.1. Related Work A rst proposal for a parameterised description covering several extended coinduction principles on a categorical level has been made by Lenisa in the course of her comparison of set-theoretic and coalgebraic (categorical) formulations of coinduction (Lenisa, 1999). Recently but ind...