Making Lambda Calculus Smaller, Faster

Some optimizations are speculative: they improve execution speed most but not all of the time, or they trade o faster execution for an increase in code size. Other optimizations, such as dead-variable elimination and algebraic simpli cation, are guaranteed to both reduce code size and speed execution. It makes sense to group all of these \contracting" optimizations together in a single phase of a compiler. This paper describes an e cient implementation of these optimizations for a language based on the lambda calculus, where a particularly interesting optimization of this sort is inlining for those functions called only once. And we prove that our contracting rewrites are con uent.