Fixed points of type constructors and primitive recursion

Fixed points of type constructors and primitive recursion (2004)

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by Andreas Abel , Ralph Matthes

Venue:	Computer Science Logic, 18th International Workshop, CSL 2004, 13th Annual Conference of the EACSL, Karpacz, Poland, September 20-24, 2004, Proceedings, volume 3210 of Lecture Notes in Computer Science
Citations:	6 - 3 self

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@INPROCEEDINGS{Abel04fixedpoints,
    author = {Andreas Abel and Ralph Matthes},
    title = {Fixed points of type constructors and primitive recursion},
    booktitle = {Computer Science Logic, 18th International Workshop, CSL 2004, 13th Annual Conference of the EACSL, Karpacz, Poland, September 20-24, 2004, Proceedings, volume 3210 of Lecture Notes in Computer Science},
    year = {2004},
    pages = {190--204},
    publisher = {SpringerVerlag}
}

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Abstract

Abstract. For nested or heterogeneous datatypes, terminating recursion schemes considered so far have been instances of iteration, excluding efficient definitions of fixed-point unfolding. Two solutions of this problem are proposed: The first one is a system with equi-recursive nonstrictly positive type constructors of arbitrary finite kinds, where fixedpoint unfolding is computationally invisible due to its treatment on the level of type equality. Positivity is ensured by a polarized kinding system, and strong normalization is proven by a model construction based on saturated sets. The second solution is a formulation of primitive recursion for arbitrary type constructors of any rank. Although without positivity restriction, the second system embeds—even operationally—into the first one. 1

Citations

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