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Summary: Generalized Iteration and Coiteration for
Higher-Order Nested Datatypes
Andreas Abel1
, Ralph Matthes2
and Tarmo Uustalu3
1
Department of Computer Science, University of Munich
abel@informatik.uni-muenchen.de
2
Preuves, Programmes et Syst`emes,
CNRS, Universit´e Paris VII (on leave from University of Munich)
matthes@informatik.uni-muenchen.de
3
Inst. of Cybernetics, Tallinn Technical University
tarmo@cs.ioc.ee
Abstract. We solve the problem of extending Bird and Paterson's gen-
eralized folds for nested datatypes and its dual to inductive and coinduc-
tive constructors of arbitrarily high ranks by appropriately generalizing
Mendler-style (co)iteration. Characteristically to Mendler-style schemes
of disciplined (co)recursion, the schemes we propose do not rest on no-
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