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General recursion via coinductive types
 Logical Methods in Computer Science
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From coalgebraic specifications to implementation: The Mihda toolkit
 In Second International Symposium on Formal Methods for Components and Objects, Lecture Notes in Computer Science
, 2003
"... Abstract. This paper describes the architecture of a toolkit, called Mihda, providing facilities to minimise labelled transition systems for name passing calculi. The structure of the toolkit is derived from the coalgebraic formulation of the partitionrefinement minimisation algorithm for HDautom ..."
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Cited by 11 (9 self)
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Abstract. This paper describes the architecture of a toolkit, called Mihda, providing facilities to minimise labelled transition systems for name passing calculi. The structure of the toolkit is derived from the coalgebraic formulation of the partitionrefinement minimisation algorithm for HDautomata. HDautomata have been specifically designed to allocate and garbage collect names and they provide faithful finite state representations of the behaviours of πcalculus processes. The direct correspondence between the coalgebraic specification and the implementation structure facilitates the proof of correctness of the implementation. We evaluate the usefulness of Mihda in practise by performing finite state verification of πcalculus specifications. 1
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.
www.lmcsonline.org GENERAL RECURSION VIA COINDUCTIVE TYPES
, 2004
"... Abstract. A fertile field of research in theoretical computer science investigates the representation of general recursive functions in intensional type theories. Among the most successful approaches are: the use of wellfounded relations, implementation of operational semantics, formalization of dom ..."
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Abstract. A fertile field of research in theoretical computer science investigates the representation of general recursive functions in intensional type theories. Among the most successful approaches are: the use of wellfounded relations, implementation of operational semantics, formalization of domain theory, and inductive definition of domain predicates. Here, a different solution is proposed: exploiting coinductive types to model infinite computations. To every type A we associate a type of partial elements A ν, coinductively generated by two constructors: the first, �a � just returns an element a: A; the second, ⊲ x, adds a computation step to a recursive element x: A ν. We show how this simple device is sufficient to formalize all recursive functions between two given types. It allows the definition of fixed points of finitary, that is, continuous, operators. We will compare this approach to different ones from the literature. Finally, we mention that the formalization, with appropriate structural maps, defines a strong monad. 1.
found at the ENTCS Macro Home Page. Inductive and Coinductive Components of Corecursive Functions in Coq
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