Machine Based on Linear Logic and Explicit Substitutions

We present xLIN, a novel linear abstract machine that introduces no penalty in computing with non-linear resources, while computing with linear resources might, in principle, be as fast as a series of destructive updates. Garbage collection would not be required for linear objects, while still present for non-linear objects. We propose a weak calculus of explicit substitutions as its foundations, and show how it may be easily \derived" from it. A proof of correctness, then, comes for free. We illustrate in which way this machine may be seen as a re nement of Krivine's abstract machine, and hint at how non-linear computation could be optimized to serve as framework for the implementation of functional languages. Besides, not to sound so optimistic at this rather preliminary stage of development, we comment on the inherent incompatibilities that exist between the techniques suggested by the high-level description of the machine.