A finite semantics for simply-typed lambda terms for infinite runs of automata. preprint (2006)
| Venue: | Procedings of the 20th international Workshop on Computer Science Logic (CSL ’06), volume 4207 of Lecture Notes in Computer Science |
| Citations: | 8 - 0 self |
BibTeX
@INPROCEEDINGS{Aehlig06afinite,
author = {Klaus Aehlig},
title = {A finite semantics for simply-typed lambda terms for infinite runs of automata. preprint},
booktitle = {Procedings of the 20th international Workshop on Computer Science Logic (CSL ’06), volume 4207 of Lecture Notes in Computer Science},
year = {2006},
pages = {104--118},
publisher = {Springer Verlag}
}
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Abstract
Abstract. Model checking properties are often described by means of finite automata. Any particular such automaton divides the set of infinite trees into finitely many classes, according to which state has an infinite run. Building the full type hierarchy upon this interpretation of the base type gives a finite semantics for simply-typed lambda-trees. A calculus based on this semantics is proven sound and complete. In particular, for regular infinite lambda-trees it is decidable whether a given automaton has a run or not. As regular lambda-trees are precisely recursion schemes, this decidability result holds for arbitrary recursion schemes of arbitrary level, without any syntactical restriction. This partially solves an open problem of Knapik, Niwinski and Urzyczyn. 1 Introduction and Related Work The lambda calculus has long been used as a model of computation. Restricting it to simple types allows for a particularly simple set-theoretic semantics. The drawback, however, is that only few functions can be defined in the simply-typed lambda calculus.
