Semi-continuous Sized Types and Termination

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Semi-continuous Sized Types and Termination
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 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 semicontinuous functions is developed.
Andreas Abel
Added 24 Jan 2011
Updated 24 Jan 2011
Type Journal
Year 2008
Where CORR
Authors Andreas Abel
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