Generalized Iteration and Coiteration for Higher-Order Nested Datatypes

Generalized Iteration and Coiteration for Higher-Order Nested Datatypes (2003)

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by Andreas Abel , Ralph Matthes , Tarmo Uustalu

Venue:	PROC. OF FOSSACS 2003
Citations:	8 - 5 self

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Datum	Value	Source
TITLE	Generalized Iteration and Coiteration for Higher-Order Nested Datatypes	user correction - Legacy Corrections
AUTHOR NAME	Andreas Abel	user correction
AUTHOR AFFIL	1 Department of Computer Science, University of Munich	user correction
AUTHOR NAME	Ralph Matthes	user correction
AUTHOR AFFIL	1 Department of Computer Science, University of Munich	user correction
AUTHOR NAME	Tarmo Uustalu	user correction
AUTHOR AFFIL	Department of Computer Science, University of Munich	user correction
ABSTRACT	We solve the problem of extending Bird and Paterson's generalized folds for nested datatypes and its dual to inductive and coinductive 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 notions like positivity or monotonicity of a constructor and facilitate programming in a natural and elegant 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 its dual are achieved; for rank 1, the schemes instantiate to Mendler's original (re)formulation of iteration and coiteration. Several examples demonstrate the power of the approach. Strong normalization of our proposed extension of system F of higherorder parametric polymorphism is proven by a reduction-preserving embedding into pure F .	user correction
YEAR	2003	INFERENCE
VENUE	PROC. OF FOSSACS 2003	user correction
VENUE TYPE	CONFERENCE	INFERENCE
PAGES	54--69	INFERENCE
VOLUME	2620	INFERENCE
CITATIONS	10 found	ParsCit 1.0