Shrinking lambda Expressions in Linear Time

Functional language compilers often perform optimizations based on beta and delta re duction To avoid speculative optimizations that can blow up the code size we might wish to use only shrinking reduction rules guaranteed to make the program smaller these include dead variable elimination constant folding and a restricted beta rule that inlines only functions that are called just once The restricted beta rule leads to a shrinking rewrite system that has not previously been studied We show some e cient normalization algorithms that are immediately useful in optimizing compilers and we give a con uence proof for our system showing that the choice of normalization algorithm does not a ect nal code quality