A Terminating and Confluent Linear Lambda Calculus

We present a rewriting system for the linear lambda calculus corresponding to the {!, $\multimap$}-fragment of intuitionistic linear logic. This rewriting system is shown to be strongly normalizing, and Church-Rosser modulo the trivial commuting conversion. Thus it provides a simple decision method for the equational theory of the linear lambda calculus. As an application we prove the strong normalization of the simply typed computational lambda calculus by giving a reduction-preserving translation into the linear lambda calculus.

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