An Adequate Left-Associated Binary Numeral System in the lambda-Calculus (Revised Version)

Mayer Goldberg

Abstract


This paper introduces a sequence of lambda-expressions modelling the binary expansion of integers. We derive expressions computing the test for zero, the successor function, and the predecessor function, thereby showing the sequence to be an adequate numeral system. These functions can be computed efficiently. Their complexity is independent of the order of evaluation.


Keywords: Programming calculi, lambda-calculus, functional programming.


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DOI: http://dx.doi.org/10.7146/brics.v3i6.19969
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ISSN: 0909-0878 

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