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

We show that a non-duplicating CPS transformation has no effect on control-flow analysis and that it has a positive effect on binding-time analysis: a monovariant control-flow analysis yields equivalent results on a direct-style program and on its CPS counterpart, and a monovariant binding-time analysis yields more precise results on a CPS program than on its direct-style counterpart. Our proof technique amounts to constructing the continuation-passing style (CPS) counterpart of flow information and of binding times. Our results confirm a folklore theorem about binding-time analysis, namely that CPS has a positive effect on binding times. What may be more surprising is that this benefit holds even if contexts or continuations are not duplicated. 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.

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

BRICS Report Series ◽

10.7146/brics.v8i54.21715 ◽

2001 ◽

Vol 8 (54) ◽

Cited By ~ 2

Author(s):

Daniel Damian ◽

Olivier Danvy

Keyword(s):

Program Analysis ◽

Partial Evaluation ◽

Flow Analysis ◽

Control Flow ◽

Time Analysis ◽

Binding Time ◽

The Impact ◽

Positive Effect ◽

Binding Time Analysis ◽

Control Flow Analysis

We show that a non-duplicating transformation into continuation-passing style (CPS) has no effect on control-flow analysis, a positive effect on binding-time 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 binding-time 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.

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A Simple CPS Transformation of Control-Flow Information

BRICS Report Series ◽

10.7146/brics.v8i55.21716 ◽

2001 ◽

Vol 8 (55) ◽

Cited By ~ 2

Author(s):

Daniel Damian ◽

Olivier Danvy

Keyword(s):

Program Transformation ◽

Flow Analysis ◽

Control Flow ◽

Intermediate Result ◽

Time Analysis ◽

First Order ◽

Flow Information ◽

Binding Time ◽

Binding Time Analysis ◽

Control Flow Analysis

We build on Danvy and Nielsen's first-order program transformation into continuation-passing style (CPS) to design a new CPS transformation of flow information that is simpler and more efficient than what has been presented in previous work. The key to simplicity and efficiency is that our CPS transformation constructs the flow information in one go, instead of first computing an intermediate result and then exploiting it to construct the flow information. More precisely, we show how to compute control-flow information for CPS-transformed programs from control-flow information for direct-style programs and vice-versa. As a corollary, we confirm that CPS transformation has no effect on the control-flow information obtained by constraint-based control-flow analysis. The transformation has immediate applications in assessing the effect of the CPS transformation over other analyses such as, for instance, binding-time analysis.

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CPS Transformation of Flow Information, Part II: Administrative Reductions

BRICS Report Series ◽

10.7146/brics.v9i36.21751 ◽

2002 ◽

Vol 9 (36) ◽

Author(s):

Daniel Damian ◽

Olivier Danvy

Keyword(s):

Present Article ◽

Linear Time ◽

Flow Analysis ◽

Control Flow ◽

Flow Information ◽

Least Solution ◽

The Impact ◽

Control Flow Analysis ◽

Flow Constraints

We characterize the impact of a linear beta-reduction on the result of a control-flow analysis. (By "a linear beta-reduction'' we mean the beta-reduction of a linear lambda-abstraction, i.e., of a lambda-abstraction whose parameter occurs exactly once in its body.) As a corollary, we consider the administrative reductions of a Plotkin-style transformation into continuation-passing style (CPS), and how they affect the result of a constraint-based control-flow analysis and, in particular, the least element in the space of solutions. We show that administrative reductions preserve the least solution. Preservation of least solutions solves a problem that was left open in Palsberg and Wand's article "CPS Transformation of Flow Information.'' Together, Palsberg and Wand's article and the present article show how to map in linear time the least solution of the flow constraints of a program into the least solution of the flow constraints of the CPS counterpart of this program, after administrative reductions. Furthermore, we show how to CPS transform control-flow information in one pass. Supersedes BRICS-RS-01-40.

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CPS Transformation of Flow Information, Part II: Administrative Reductions

BRICS Report Series ◽

10.7146/brics.v8i40.21700 ◽

2001 ◽

Vol 8 (40) ◽

Author(s):

Daniel Damian ◽

Olivier Danvy

Keyword(s):

Present Article ◽

Linear Time ◽

Flow Analysis ◽

Control Flow ◽

Know How ◽

Flow Information ◽

Least Solution ◽

The Impact ◽

Control Flow Analysis ◽

Flow Constraints

We characterize the impact of a linear beta-reduction on the result of a control-flow analysis. (By ``a linear beta-reduction'' we mean the beta-reduction of a linear lambda-abstraction, i.e., of a lambda-abstraction whose parameter occurs exactly once in its body.) As a corollary, we consider the administrative reductions of a Plotkin-style transformation into continuation-passing style (CPS), and how they affect the result of a constraint-based control-flow analysis and in particular the least element in the space of solutions. We show that administrative reductions preserve the least solution. Since we know how to construct least solutions, preservation of least solutions solves a problem that was left open in Palsberg and Wand's paper ``CPS Transformation of Flow Information.'' Therefore, together, Palsberg and Wand's article ``CPS Transformation of Flow Information'' and the present article show how to map, in linear time, the least solution of the flow constraints of a program into the least solution of the flow constraints of the CPS counterpart of this program, after administrative reductions. Furthermore, we show how to CPS transform control-flow information in one pass. Superseded by BRICS-RS-02-36.

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Efficient analyses for realistic off-line partial evaluation

Journal of Functional Programming ◽

10.1017/s0956796800000769 ◽

1993 ◽

Vol 3 (3) ◽

pp. 315-346 ◽

Cited By ~ 44

Author(s):

Anders Bondorf ◽

Jesper Jørgensen

Keyword(s):

Linear Time ◽

Partial Evaluation ◽

Flow Analysis ◽

Higher Order ◽

Time Analysis ◽

Specific Order ◽

Binding Time ◽

And Function ◽

Constraint Sets ◽

Binding Time Analysis

AbstractBased on Henglein's efficient binding-time analysis for the lambda calculus (with constants and ‘fix’) (Henglein, 1991), we develop three efficient analyses for use in the preprocessing phase of Similix, a self-applicable partial evaluator for a higher-order subset of Scheme. The analyses developed in this paper are almost-linear in the size of the analysed program. (1) A flow analysis determines possible value flow between lambda-abstractions and function applications and between constructor applications and selector/predicate applications. The flow analysis is not particularly biased towards partial evaluation; the analysis corresponds to the closure analysis of Bondorf (1991b). (2) A (monovariant) binding-time analysis distinguishes static from dynamic values; the analysis treats both higher-order functions and partially static data structures. (3) A new is-used analysis, not present in Bondorf (1991b), finds a non-minimal binding-time annotation which is ‘safe’ in a certain way: a first-order value may only become static if its result is ‘needed’ during specialization; this ‘poor man's generalization’ (Holst, 1988) increases termination of specialization. The three analyses are performed sequentially in the above mentioned order since each depends on results from the previous analyses. The input to all three analyses are constraint sets generated from the program being analysed. The constraints are solved efficiently by a normalizing union/find-based algorithm in almost-linear time. Whenever possible, the constraint sets are partitioned into subsets which are solved in a specific order; this simplifies constraint normalization. The framework elegantly allows expressing both forwards and backwards components of analyses. In particular, the new is-used analysis is of backwards nature. The three constraint normalization algorithms are proved correct (soundness, completeness, termination, existence of a best solution). The analyses have been implemented and integrated in the Similix system. The new analyses are indeed much more efficient than those of Bondorf (1991b); the almost-linear complexity of the new analyses is confirmed by the implementation.

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Specifying the correctness of binding-time analysis

Journal of Functional Programming ◽

10.1017/s0956796800000782 ◽

1993 ◽

Vol 3 (3) ◽

pp. 365-387 ◽

Cited By ~ 19

Author(s):

Mitchell Wand

Keyword(s):

Flow Analysis ◽

Lambda Calculus ◽

Time Analysis ◽

Correctness Criterion ◽

Binding Time ◽

Binding Time Analysis

AbstractMogensen has exhibited a very compact partial evaluator for the pure lambda calculus, using binding-time analysis followed by specialization. We give a correctness criterion for this partial evaluator and prove its correctness relative to this specification. We show that the conventional properties of partial evaluators, such as the Futamura projections, are consequences of this specification. By considering both a flow analysis and the transformation it justifies together, this proof suggests a framework for incorporating flow analyses into verified compilers.

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