Minimality in a Linear Calculus with Iteration

System L is a linear version of Gödel's System T, where the λ-calculus is replaced with a linear calculus; or alternatively a linear λ-calculus enriched with some constructs including an iterator. There is thus at the same time in this system a lot of freedom in reduction and a lot of information about resources, which makes it an ideal framework to start a fresh attempt at studying reduction strategies in λ-calculi. In particular, we show that call-by-need, the standard strategy of functional languages, can be defined directly and effectively in System L, and can be shown minimal among weak strategies.