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An adequate and efficient left-associated binary numeral system in the λ-calculus

Published online by Cambridge University Press:  01 March 2001

MAYER GOLDBERG
Affiliation:
Department of Computer Science, Ben Gurion University, Beer Sheva 84105, Israel (e-mail: gmayer@cs.bgu.ac.il)
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Abstract

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This paper introduces a sequence of λ-expressions modeling 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, i.e. one in which all recursive functions are lambda-definable. These functions can be computed efficiently; To this end, we introduce a notion of complexity that is independent of the order of evaluation.

Type
THEORETICAL PEARLS
Copyright
© 2000 Cambridge University Press
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