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Fixed Points of Type Constructors and Primitive Recursion
 

Summary: Fixed Points of Type Constructors
and Primitive Recursion
Andreas Abel 1
and Ralph Matthes2
1
Department of Computer Science, Chalmers University of Technology
abel@cs.chalmers.se
2
Department of Computer Science, University of Munich
matthes@informatik.uni-muenchen.de
Abstract. For nested or heterogeneous datatypes, terminating recur-
sion schemes considered so far have been instances of iteration, exclud-
ing 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 sat-
urated sets. The second solution is a formulation of primitive recursion
for arbitrary type constructors of any rank. Although without positiv-

  

Source: Abel, Andreas - Theoretische Informatik, Ludwig-Maximilians-Universit√§t M√ľnchen

 

Collections: Computer Technologies and Information Sciences