PERs from Projections for Binding-Time Analysis

First order projection based binding time analysis has proven genuinely useful in partial evaluation Lau a Lau c There have been three notable generalisations of projection based analysis to higher order The rst lacked a formal basis Mog the second used structures strictly more general that projections namely partial equivalence relations PERs HS the third involved a complex con struction that gave rise to impractically large abstract do mains Dav This paper presents a technique free of these shortcomings it is simple entirely projection based satis es a formal correctness condition and gives rise to reason ably small abstract domains Though the technique is cast in terms of projections there is also an interpretation in terms of PERs The principal limitation of the technique is the restriction to monomorphic typing Introduction and Background We take as given that binding time analysis is essential for good partial evaluation and we do not address the issue of annotating programs according to the results of analy sis Numerous binding time analysis techniques have been proposed and implemented we greatly narrow the eld of discussion by restricting attention to those for which there is a formally stated notion of correctness that the technique has been proven to satisfy Analysis techniques can usually be identi ed as being based on either a non standard denotational semantics or a non standard typing Examples in the latter category in clude those of Gomard Go Jensen Jen the Nielsons NN Schmidt Sch and Henglein and Mossin HM Our focus is on those techniques based on non standard in terpretation in particular those using projections or partial equivalence relations PERs as the basic abstract values A domain projection is a continuous idempotent func tion that approximates the identity Launchbury Lau hit upon the idea of using projections to encode degrees of staticness of data The basic idea is that a projection maps to that part of a data structure that is dynamic possibly not determined and acts as the identity on that part which is static de nitely determined Examples are the identity ID the greatest projection which speci es that values are entirely static the constant function BOT the least pro jection which speci es that values are entirely dynamic and projections FST and SND on product domains de ned by