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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 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... (Update)
Context of citations to this paper: More
.... [10,11,20,27] Typed lambda calculi featuring heterogeneous and higher kind inductive and coinductive constructors are the topic of [23,1,2]. A very accessible extended presentation of aspects of Fiore, Plotkin and Turi s work [15] appears in [14] Hofmann [21] has given a...
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Fixed Points of Type Constructors and Primitive Recursion - Abel, Matthes (Correct)
Substitution in Non-wellfounded Syntax with Variable Binding - Matthes, Uustalu (2003) (Correct)
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0.6: Generalized Iteration and Coiteration for Higher-Order.. - Abel, Matthes, Uustalu (2003) (Correct)
0.5: Monotone Inductive and Coinductive Constructors of Rank 2 - Matthes (2001) (Correct)
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2: Monotone inductive and coinductive constructors of rank - Matthes
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BibTeX entry: (Update)
Abel, A., R. Matthes and T. Uustalu, Generalized iteration and coiteration for higher-order nested datatypes, to appear in: A. Gordon, ed., Proc. of 6th Int. Conf. on Foundations of Software Science and Computation Structures, FoSSaCS'03 (Warsaw, Apr. 2003), Lect. Notes in Comput. Sci., Springer-Verlag. http://citeseer.ist.psu.edu/article/abel03generalized.html More
@misc{ abel03generalized,
author = "A. Abel and R. Matthes and T. Uustalu",
title = "Generalized iteration and coiteration for higher-order nested datatypes",
text = "Abel, A., R. Matthes and T. Uustalu, Generalized iteration and coiteration
for higher-order nested datatypes, to appear in: A. Gordon, ed., Proc. of
6th Int. Conf. on Foundations of Software Science and Computation Structures,
FoSSaCS'03 (Warsaw, Apr. 2003), Lect. Notes in Comput. Sci., Springer-Verlag.",
year = "2003",
url = "citeseer.ist.psu.edu/article/abel03generalized.html" }
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1 Haskell examples for iteration and coiteration on higher-ord.. - Abel - 2003
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A Predicative Strong Normalisation Proof for a.. - Abel, Altenkirch (2000) (Correct)
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A Third-Order Representation of the λμ-Calculus - Abel (2001) (Correct)
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