Syntactic Accidents in Program Analysis: On the Impact of the CPS Transformation

Abstract

We show that a non-duplicating transformation into continuation-passing style (CPS) has no effect on control-flow analysis, a positive effect on bindingtime analysis for traditional partial evaluation, and no effect on binding-time analysis for continuation-based partial evaluation: a monovariant control-flow analysis yields equivalent results on a direct-style program and on its CPS counterpart, a monovariant binding-time analysis yields less precise results on a direct-style program than on its CPS counterpart, and an enhanced monovariant binding-time analysis yields equivalent results on a direct-style program and on its CPS counterpart. Our proof technique amounts to constructing the CPS counterpart of flow information and of binding times.Our results formalize and confirm a folklore theorem about traditional bindingtime analysis, namely that CPS has a positive effect on binding times. What may be more surprising is that the benefit does not arise from a standard refinement of program analysis, as, for instance, duplicating continuations.The present study is symptomatic of an unsettling property of program analyses: their quality is unpredictably vulnerable to syntactic accidents in source programs, i.e., to the way these programs are written. More reliable program analyses require a better understanding of the effect of syntactic change. * Extended version of an article to appear in the Journal of Functional Programming. † Current affiliation:

Control-flow analysis of functional programs

“…They attributed increased precision to the duplication of continuations and decreased precision to the confusion of return points. It was later pointed out [43,122], however, that Sabry and Felleisen were comparing a flow-sensitive analysis to a flow-insensitive analysis.…”

“…Damian and Danvy [43] proved that a non-duplicating CPS transformation does not affect the precision of a flow-insensitive textbook 0-CFA. They also proved that CPS transformation can improve and does not degrade the precision of binding-time analysis.…”

ILP-Based Resource-Aware Compilation

“…Meyer and Wand [11] have shown that typability is preserved by CPS transformation, and Damian and Danvy [4] and Palsberg and Wand [25] have shown that a set-based flow analysis is preserved by CPS transformation. Examples of end-to-end type-preserving compilers with proofs include the TIL compiler of Tarditi et al [33] and the compiler from System F to typed assembly language of Morrisett, Walker, Crary, and Glew [13].…”

“…Example: Suppose the example program has four dependencies, namely, that v += u must begin executing no earlier than 1 cycle after u := c u and v := c v have begun executing, and that y += x must begin executing no earlier than 1 cycle after x := c x and y := c y have begun executing, i.e., Depn= { (3, 4, 1, 2, 1), (3, 4, 2, 3, 1), (6,7,4,5,1), (6,7,5,6, 1) }. With R = 2, the optimal solution to the ILP obtained from the above ILP formulation and the example program yields a target program with schedule length 3.…”

On One-Pass CPS Transformations

“…Transforming functional programs into continuation-passing style (CPS) is a classical topic, with a long publication history [2,4,8,9,11,15,17,18,20,23,24,25,26,29,30,31,32,33,35,38,41,42,43,44,45,46,47,48,49,50,52], 1 including chapters in programming-languages textbooks [1,21,40], and many applications. Yet no standard algorithm for CPS transformation has emerged, and this lack contributes to maintaining continuations, CPS, and CPS transformations as mystifying artefacts in the land of programming and programming languages.…”