Abstract

The linear lambda calculus is very weak in terms of expressive power: in particular, all functions terminate in linear time. In this paper we consider a simple extension with Booleans, natural numbers and a linear iterator. We show properties of this linear version of Godel’s System $\mathcal{T}$ and study the class of functions that can be represented. Surprisingly, this linear calculus is extremely expressive: it is as powerful as System $\mathcal{T}$

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