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The linear lambda calculus, where variables are restricted to occur in terms exactly once, has a very weak expressive power: in particular, all functions terminate in linear time. In this paper we consider a simple extension with natural numbers and a restricted iterator: only closed linear functions can be iterated. We show properties of this linear version of Gödel's T using a closed reduction strategy, and study the class of functions that can be represented. Surprisingly, this lineardoi:10.1016/j.tcs.2009.11.014 fatcat:of7xz4qeezf45bkiosv3xisibq