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Generalised Coinduction
, 2001
"... We introduce the lambdacoiteration schema for a distributive law lambda of a functor T over a functor F. Under certain conditions it can be shown to uniquely characterise functions into the carrier of a final Fcoalgebra, generalising the basic coiteration schema as given by finality. The duals of ..."
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Cited by 16 (3 self)
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We introduce the lambdacoiteration schema for a distributive law lambda of a functor T over a functor F. Under certain conditions it can be shown to uniquely characterise functions into the carrier of a final Fcoalgebra, generalising the basic coiteration schema as given by finality. The duals of primitive recursion and courseofvalue iteration, which are known extensions of coiteration, arise as instances of our framework. One can furthermore obtain schemata justifying recursive specifications that involve operators such as addition of power series, regular operators on languages, or parallel and sequential composition of processes. Next...
Generalized Coinduction
, 2003
"... this paper express that the above principles work under di#erent 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 ..."
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this paper express that the above principles work under di#erent 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))
Substitution in nonwellfounded . . .
 ELECTRONIC NOTES IN THEORETICAL COMPUTER SCIENCE 82 NO. 1 (2003)
, 2003
"... Inspired from the recent developments in theories of nonwellfounded syntax (coinductively defined languages) and of syntax with binding operators, the structure of algebras of wellfounded and nonwellfounded terms is studied for a very general notion of signature permitting both simple variable bin ..."
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Inspired from the recent developments in theories of nonwellfounded syntax (coinductively defined languages) and of syntax with binding operators, the structure of algebras of wellfounded and nonwellfounded terms is studied for a very general notion of signature permitting both simple variable binding operators as well as operators of explicit substitution. This is done in an extensional mathematical setting of initial algebras and final coalgebras of endofunctors on a functor category. In the nonwellfounded case, the fundamental operation of substitution is more beneficially defined in terms of primitive corecursion than coiteration.