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Higher-Order Positive Set Constraints

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Book cover Computer Science Logic (CSL 2002)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2471))

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Abstract

We introduce a natural notion of positive set constraints on simply-typed λ-terms. We show that satisfiability of these so-called positive higher-order set constraints is decidable in 2-NEXPTIME. We explore a number of subcases solvable in 2-DEXPTIME, among which higher-order definite set constraints, a.k.a., emptiness of higher-order pushdown processes. This uses a first-order clause format on so-called shallow higher-order patterns, and automated deduction techniques based on ordered resolution with splitting. This technique is then applied to the task of approximating success sets for a restricted subset of λ-Prolog, à la Frühwirth et al.

Partially supported by the ACI VERNAM, the RNTL project EVA and the ACI jeunes chercheurs “Sécurité informatique, protocoles cryptographiques et détection d’intrusions”.

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Author information

Authors and Affiliations

  1. LSV/CNRS UMR, 8643, ENS Cachan 61, av. du président-Wilson, 94235, Cachan, Cedex, France

    Jean Goubault-Larrecq

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  1. Jean Goubault-Larrecq
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Editor information

Editors and Affiliations

  1. Laboratory for Foundations of Computer Science Division of Informatics, University of Edinburgh, King’s Buildings, Mayfield Road, Edinburgh, EH9 3JZ, UK

    Julian Bradfield

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Goubault-Larrecq, J. (2002). Higher-Order Positive Set Constraints. In: Bradfield, J. (eds) Computer Science Logic. CSL 2002. Lecture Notes in Computer Science, vol 2471. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45793-3_32

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  • DOI: https://doi.org/10.1007/3-540-45793-3_32

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-44240-0

  • Online ISBN: 978-3-540-45793-0

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