(Co-)iteration for higher-order nested datatypes

(Co-)iteration for higher-order nested datatypes (2003)

by Andreas Abel , Ralph Matthes

Venue:	POST-CONF. PROC. OF IST WG TYPES 2ND ANN. MEETING, TYPES'02, LECT. NOTES IN COMPUT. SCI
Citations:	8 - 5 self

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Datum	Value	Source
TITLE	(Co-)iteration for higher-order nested datatypes	user correction
AUTHOR NAME	Andreas Abel	user correction
AUTHOR AFFIL	Department of Computer Science,; University of Munich	user correction
AUTHOR NAME	Ralph Matthes	user correction
AUTHOR AFFIL	CNRS, Université Paris VII (on leave from University of Munich)	user correction
ABSTRACT	The problem of defining iteration for higher-order nested datatypes of arbitrary (finite) rank is solved within the framework of System F ω of higher-order parametric polymorphism. The proposed solution heavily relies on a general notion of monotonicity as opposed to a syntactic criterion on the shape of the type constructors such as positivity 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 definition of the mapping operation (the functoriality) for those rank-1 type transformers (i. e., functions from types to types) arising as least fixed-points of monotone rank-2 type transformers. Strong normalization is shown by an embedding into F ω. The results dualize to greatest fixed-points, hence to coinductive constructors with coiteration.	user correction
YEAR	2003	INFERENCE
VENUE	POST-CONF. PROC. OF IST WG TYPES 2ND ANN. MEETING, TYPES'02, LECT. NOTES IN COMPUT. SCI	user correction
VENUE TYPE	CONFERENCE	INFERENCE
PAGES	1--20	INFERENCE
VOLUME	2646	INFERENCE
CITATIONS	21 found	ParsCit 1.0