Discovering Needed Reductions Using Type Theory

The identiication of the needed redexes in a term is an undecidable problem. We introduce a (partially decidable) type assignment system, which distinguishes certain redexes called the allowable redexes. For a well-typed term e, allowable redexes are needed redexes. In addition, with principal typing, all the needed redexes of a normalisable term are allowable. Using these results, we can identify all the needed reductions of a principally typed normalisable term. Possible applications of these results include strictness and sharing analysis for functional programming languages, and a reduction strategy for well-typed terms which satisses L evy's notion of optimal reduction.