Abel, Andreas - Semi-continuous Sized Types and Termination

lmcs:1236 - Logical Methods in Computer Science, April 10, 2008, Volume 4, Issue 2
Semi-continuous Sized Types and Termination

Authors: Abel, Andreas

Some type-based approaches to termination use 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 recursive 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 semantic criterion for admissibility. To provide a syntactical criterion, a calculus for semi-continuous functions is developed.


Source : oai:arXiv.org:0804.0876
DOI : 10.2168/LMCS-4(2:3)2008
Volume: Volume 4, Issue 2
Published on: April 10, 2008
Submitted on: January 4, 2007
Keywords: Computer Science - Programming Languages,Computer Science - Logic in Computer Science,D.1.1,F.3.2,F.4.1


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