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Iteration and Coiteration Schemes for Higher-Order and Nested Datatypes

Summary: Iteration and Coiteration Schemes for
Higher-Order and Nested Datatypes
Andreas Abel a; , Ralph Matthes b , Tarmo Uustalu c
a Department of Computer Science, Chalmers University of Technology
Rannvagen 6, SWE-41296 Goteborg, Sweden
b Institut fur Informatik der Ludwig-Maximilians-Universitat Munchen
Oettingenstrae 67, D-80538 Munchen, Germany
c Institute of Cybernetics, Tallinn Technical University
Akadeemia tee 21, EE-12618 Tallinn, Estonia
This article studies the implementation of inductive and coinductive construc-
tors of higher kinds (higher-order nested datatypes) in typed term rewriting, with
emphasis on the choice of the iteration and coiteration constructions to support
as primitive. We propose and compare several well-behaved extensions of Sys-
tem F ! with some form of iteration and coiteration uniform in all kinds. In what
we call Mendler-style systems, the iterator and coiterator have a computational
behavior similar to the general recursor, but their types guarantee termination. In
conventional-style systems, monotonicity witnesses are used for a notion of mono-
tonicity de ned uniformly for all kinds. Our most expressive systems GMIt ! and GIt !
of generalized Mendler resp. conventional (co)iteration encompass Martin, Gibbons


Source: Abel, Andreas - Theoretische Informatik, Ludwig-Maximilians-Universit√§t M√ľnchen


Collections: Computer Technologies and Information Sciences