Iteration and Coiteration Schemes for Higher-Order and Nested Datatypes

Iteration and Coiteration Schemes for Higher-Order and Nested Datatypes (2004)

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by Andreas Abel , Ralph Matthes , Tarmo Uustalu

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Datum	Value	Source
TITLE	Iteration and Coiteration Schemes for Higher-Order and Nested Datatypes	user correction - Legacy Corrections
AUTHOR NAME	Andreas Abel	user correction - Legacy Corrections
AUTHOR AFFIL	a;	user correction - Legacy Corrections
AUTHOR NAME	Ralph Matthes	user correction - Legacy Corrections
AUTHOR AFFIL	b	user correction - Legacy Corrections
AUTHOR NAME	Tarmo Uustalu	user correction - Legacy Corrections
ABSTRACT	This article studies the implementation of inductive and coinductive constructors 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 System 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 monotonicity de ned uniformly for all kinds. Our most expressive systems GMIt of generalized Mendler resp. conventional (co)iteration encompass Martin, Gibbons and Bailey's ecient folds for rank-2 inductive types. Strong normalization of all systems considered is proved by providing an embedding of the basic Mendler-style system MIt into System F .	user correction - Legacy Corrections
YEAR	2004	user correction - Legacy Corrections
CITATIONS	6 found	ParsCit 1.0