@MISC{Gardner94discoveringneeded, author = {Philippa Gardner}, title = {Discovering Needed Reductions Using Type Theory}, year = {1994} }

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Abstract

The identification 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 satisfies L'evy's notion of optimal reduction.