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Linear numeral systems

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posted on 2023-06-21, 06:02 authored by Ian MackieIan Mackie
We investigate numeral systems in the lambda calculus; specifically in the linear lambda calculus where terms cannot be copied or erased. Our interest is threefold: representing numbers in the linear calculus, finding constant time arithmetic operations when possible for successor, addition and predecessor, and finally, efficiently encoding subtraction—an operation that is problematic in many numeral systems. This paper defines systems that address these points, and in addition provides a characterisation of linear numeral systems.

History

Publication status

  • Published

File Version

  • Published version

Journal

Journal of Automated Reasoning

ISSN

0168-7433

Publisher

Springer Verlag

Issue

4

Volume

63

Page range

887-909

Department affiliated with

  • Informatics Publications

Full text available

  • Yes

Peer reviewed?

  • Yes

Legacy Posted Date

2018-02-19

First Open Access (FOA) Date

2018-02-19

First Compliant Deposit (FCD) Date

2018-02-17

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