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International Symposium on Practical Aspects of Declarative Languages

PADL 2016: Practical Aspects of Declarative Languages pp 99–116Cite as

A Size-Proportionate Bijective Encoding of Lambda Terms as Catalan Objects Endowed with Arithmetic Operations

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Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 9585))

Abstract

We describe a size-proportionate bijection between lambda terms in a compressed de Bruijn notation and the Catalan family of combinatorial objects implemented as a Haskell type class, that has as instances binary trees and multiway-trees with empty leaves, as well as standard bitstring-represented natural numbers.

By building on previous work that defines arithmetic operations on instances of this family, we extend lambda calculus with efficient arithmetic operations.

At the same time, operations like normalization of lambda terms are made available to members of the Catalan family of combinatorial objects.

As a practical application to software testing we derive a mechanism for generating large random lambda terms from Rémy’s algorithm for efficient generation of random binary trees.

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Acknowledgement

This research has been supported by NSF grant 1423324. We thanks the reviewers of PADL’16 for their constructive suggestions and comments.

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Authors and Affiliations

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

    Paul Tarau

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  1. Paul Tarau
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Correspondence to Paul Tarau .

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Editors and Affiliations

  1. Dipartimento di Ingegneria,, Università di Ferrara, Ferrara, Italy

    Marco Gavanelli

  2. University of Chicago, Chicago, USA

    John Reppy

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Tarau, P. (2016). A Size-Proportionate Bijective Encoding of Lambda Terms as Catalan Objects Endowed with Arithmetic Operations. In: Gavanelli, M., Reppy, J. (eds) Practical Aspects of Declarative Languages. PADL 2016. Lecture Notes in Computer Science(), vol 9585. Springer, Cham. https://doi.org/10.1007/978-3-319-28228-2_7

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  • DOI: https://doi.org/10.1007/978-3-319-28228-2_7

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-28227-5

  • Online ISBN: 978-3-319-28228-2

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