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Generalized Iteration and Coiteration for Higher-Order Nested Datatypes

Summary: Generalized Iteration and Coiteration for
Higher-Order Nested Datatypes
Andreas Abel 1? , Ralph Matthes 2 and Tarmo Uustalu 3??
1 Department of Computer Science, University of Munich
2 Preuves, Programmes et Systemes,
CNRS, Universite Paris VII (on leave from University of Munich)
3 Inst. of Cybernetics, Tallinn Technical University
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-
tions like positivity or monotonicity of a constructor and facilitate pro-
gramming in a natural and elegant style close to programming with the
customary letrec construct, where the typings of the schemes, how-
ever, guarantee termination. For rank 2, a smoothened version of Bird
and Paterson's generalized folds and its dual are achieved; for rank 1, the


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


Collections: Computer Technologies and Information Sciences