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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
abel@informatik.uni-muenchen.de
2 Preuves, Programmes et Systemes,
CNRS, Universite 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 de ning generalized iteration (gen-
eralized in the direction of generalized folds by Bird and Paterson) and
its dual for inductive and coinductive constructors (nested datatypes) of
arbitrary rank by appropriately generalizing Mendler-style (co)iteration.
Characteristically to Mendler-style schemes of disciplined (co)recursion,
the schemes we propose do not rest on notions like positivity or mono-
tonicity of a constructor and facilitate programming in a natural and el-
egant style close to programming with the customary letrec construct,
where the typings of the schemes, however, guarantee termination. For
rank 2, a smoothened version of Bird and Paterson's generalized folds and

  

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

 

Collections: Computer Technologies and Information Sciences