May 3-6, 2015 Asilomar, California

None, One, Many --- What's the Difference, Anyhow?

Friedrich Steimann

We observe that compared to natural and modelling languages, the differences in expression required to deal with no, one, or many objects in programming languages are particularly pronounced. We identify some problems inherent in type-based unifications of different numbers, and advocate a solution that builds on the introduction of multiplicity as a new grammatical category of programming languages.