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International Symposium on Practical Aspects of Declarative Languages

PADL 2015: Practical Aspects of Declarative Languages pp 115–131Cite as

On Logic Programming Representations of Lambda Terms: de Bruijn Indices, Compression, Type Inference, Combinatorial Generation, Normalization

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Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 9131))

Abstract

We introduce a compressed de Bruijn representation of lambda terms and define its bijections to standard representations. Compact combinatorial generation algorithms are given for several families of lambda terms, including open, closed, simply typed and linear terms as well as type inference and normal order reduction algorithms. We specify our algorithms as a literate Prolog program. In the process, we rely in creative ways on unification of logic variables, cyclic terms, backtracking and definite clause grammars.

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Author information

Authors and Affiliations

  1. Department of Computer Science and Engineering, University of North Texas, Denton, USA

    Paul Tarau

Authors
  1. Paul Tarau
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Correspondence to Paul Tarau .

Editor information

Editors and Affiliations

  1. New Mexico State University, Las Cruces, New Mexico, USA

    Enrico Pontelli

  2. Department of Computer Science, New Mexico State University, Las Cruces, New Mexico, USA

    Tran Cao Son

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Tarau, P. (2015). On Logic Programming Representations of Lambda Terms: de Bruijn Indices, Compression, Type Inference, Combinatorial Generation, Normalization. In: Pontelli, E., Son, T. (eds) Practical Aspects of Declarative Languages. PADL 2015. Lecture Notes in Computer Science(), vol 9131. Springer, Cham. https://doi.org/10.1007/978-3-319-19686-2_9

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  • DOI: https://doi.org/10.1007/978-3-319-19686-2_9

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-19685-5

  • Online ISBN: 978-3-319-19686-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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