Fixed Points of Type Constructors and Primitive Recursion
Artikel i vetenskaplig tidskrift, 2004

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 non-strictly positive type constructors of arbitrary finite kinds, where fixed-point 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.

Författare

Andreas Abel

Chalmers, Institutionen för datavetenskap

Ralph Matthes

Lecture Notes in Computer Science

0302-9743 (ISSN)

Vol. 3210 190-204

Ämneskategorier

Data- och informationsvetenskap

DOI

10.1007/978-3-540-30124-0_17