Semi-continuous Sized Types and Termination

Details Semi-continuous Sized Types and Termination Semi-continuous Sized Types and Termination

2008-04-05

arxiv.org/abs/0804.0876v2

LMCS 4 (2:3) 2008

Computer Science

Programming Languages

33 pages, extended version of CSL'06

Scientific paper

10.2168/LMCS-4(2:3)2008

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.

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