Published in Volume XXX, Issue 2, 2020, pages 167–203, doi: 10.7561/SACS.2020.2.167

Authors: J.A. Bergstra


Sumterms are introduced as syntactic entities, and sumtuples are introduced as semantic entities. Equipped with these concepts a new description is obtained of the notion of a sum as (the name for) a role which can be played by a number. Sumterm splitting operators are introduced and it is argued that without further precautions the presence of these operators gives rise to an instance of the so-called sum splitting paradox. A survey of solutions to the sum splitting paradox is given.

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  title={Sumterms, Summands, Sumtuples, and Sums and the Meta-Arithmetic of Summation},
  author={J.A. Bergstra},
  journal={Scientific Annals of Computer Science},
  organization={Alexandru Ioan Cuza University, Ia\c si, Rom\^ania},
  publisher={Alexandru Ioan Cuza University Press, Ia\c si},