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Termination and Productivity Checking with Continuous Types

Summary: Termination and Productivity Checking with
Continuous Types
Andreas Abel
Department of Computer Science, University of Munich
Oettingenstr. 67, 80538 M¨unchen, Germany
Abstract. We analyze the interpretation of inductive and coinductive
types as sets of strongly normalizing terms and isolate classes of types
with certain continuity properties. Our result enables us to relax some
side conditions on the shape of recursive definitions which are accepted
by the type-based termination calculus of Barthe, Frade, Gim´enez, Pinto
and Uustalu, thus enlarging its expressivity.
1 Introduction and Related Work
Interactive theorem provers like Coq [13], LEGO [20] and Twelf [18] support
proofs by induction on finite-depth (inductive) structures (like natural numbers,
lists, infinitely branching trees) and infinite-depth (coinductive) structures (like
streams, processes, trees with infinite paths) in the form of recursive programs.
However, these programs constitute valid proofs only if they denote total func-
tions. In the last decade, considerable effort has been put on the development
of means to define total functions in the type theories of the abovementioned


Source: Abel, Andreas - Theoretische Informatik, Ludwig-Maximilians-Universität München


Collections: Computer Technologies and Information Sciences