Open AccessAn Adequate Left-Associated Binary Numeral System in the lambda-Calculus (Revised Version)
Author(s) -
Mayer Goldberg
Publication year - 1996
Publication title -
brics report series
Language(s) - English
Resource type - Journals
eISSN - 1601-5355
pISSN - 0909-0878
DOI - 10.7146/brics.v3i6.19969
Subject(s) - numeral system , mathematics , lambda calculus , sequence (biology) , church encoding , successor cardinal , lambda , binary number , discrete mathematics , arithmetic , function (biology) , algorithm , combinatorics , calculus (dental) , typed lambda calculus , simply typed lambda calculus , mathematical analysis , genetics , dentistry , evolutionary biology , optics , biology , medicine , physics
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.