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(Co-)Iteration for Higher-Order Nested Datatypes

Summary: (Co-)Iteration for
Higher-Order Nested Datatypes
Andreas Abel 1? and Ralph Matthes 2??
1 Department of Computer Science,
University of Munich
2 PPS,
CNRS, Universite Paris VII (on leave from University of Munich)
Abstract. The problem of de ning iteration for higher-order nested
datatypes of arbitrary ( nite) rank is solved within the framework of
System F
! of higher-order parametric polymorphism. The proposed so-
lution heavily relies on a general notion of monotonicity as opposed to
a syntactic criterion on the shape of the type constructors such as posi-
tivity or even being polynomial. Its use is demonstrated for some rank-2
heterogeneous/nested datatypes such as powerlists and de Bruijn terms
with explicit substitutions. An important feature is the availability of an
iterative de nition of the mapping operation (the functoriality) for those
rank-1 type transformers (i. e., functions from types to types) arising as


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


Collections: Computer Technologies and Information Sciences