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Semi-continuous Sized Types and Termination Andreas Abel

Summary: Semi-continuous Sized Types and Termination
Andreas Abel
Institut für Informatik
Ludwig-Maximilians-Universität München
Oettingenstr. 67, D-80538 München, GERMANY
Abstract. A type-based approach to termination uses sized types: an ordinal
bound for the size of a data structure is stored in its type. A recursive function
over a sized type is accepted if it is visible in the type system that recursive calls
occur just at a smaller size. This approach is only sound if the type of the recur-
sive function is admissible, i.e., depends on the size index in a certain way. To
explore the space of admissible functions in the presence of higher-kinded data
types and impredicative polymorphism, a semantics is developed where sized
types are interpreted as functions from ordinals into sets of strongly normalizing
terms. It is shown that upper semi-continuity of such functions is a sufficient se-
mantical criterion for admissibility. To provide a syntactical criterion, a calculus
for semi-continuous function is developed.
1 Introduction
Termination of computer programs has received continuous interest in the history of
computer science, and classical applications are total correctness and termination of


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


Collections: Computer Technologies and Information Sciences