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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 Munchen, 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 de nitions which are accepted
by the type-based termination calculus of Barthe, Frade, Gimenez, 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 nite-depth (inductive) structures (like natural numbers,
lists, in nitely branching trees) and in nite-depth (coinductive) structures (like
streams, processes, trees with in nite 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 e ort has been put on the development
of means to de ne total functions in the type theories of the abovementioned


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


Collections: Computer Technologies and Information Sciences