Specifying the correctness of binding-time analysis

1993 ◽  
Vol 3 (3) ◽  
pp. 365-387 ◽  
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.

scholarly journals Binding Time Analysis: Abstract Interpretation vs. Type Inference

1992 ◽  
Vol 21 (393) ◽  
Author(s):  
Jens Palsberg ◽  
Michael I. Schwartzbach
Keyword(s):  
Abstract Interpretation ◽  
Lambda Calculus ◽  
Type Inference ◽  
Time Analysis ◽  
Binding Time ◽  
Better Than ◽  
Binding Time Analysis

Binding time analysis is important in partial evaluators. Its task is to determine which parts of a program can be specialized if some of the expected input is known. Two approaches to do this are abstract interpretation and type inference. We compare two specific such analyses to see which one determines most program parts to be eliminable. The first is the abstract interpretation approach of Bondorf, and the second is the type inference approach o£ Gomard. Both apply to the untyped lambda calculus. We prove that Bondorf's analysis is better than Gomard's.

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

2001 ◽  
Vol 8 (54) ◽  
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.<br /> <br />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.<br /> <br />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.

scholarly journals Efficient analyses for realistic off-line partial evaluation

1993 ◽  
Vol 3 (3) ◽  
pp. 315-346 ◽  
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.

scholarly journals A Simple CPS Transformation of Control-Flow Information

2001 ◽  
Vol 8 (55) ◽  
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.<br /> <br />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.

A Temporal-Logic Approach to Binding-Time Analysis

1995 ◽  
Vol 2 (51) ◽  
Author(s):  
Rowan Davies
Keyword(s):  
Temporal Logic ◽  
Linear Time ◽  
Partial Evaluation ◽  
Lambda Calculus ◽  
Time Analysis ◽  
Typed Lambda Calculus ◽  
Binding Time ◽  
Logic Approach ◽  
Multi Level ◽  
Binding Time Analysis

<p>The Curry-Howard isomorphism identifies proofs with typed lambda-<br />calculus terms, and correspondingly identifies propositions with<br />types. We show how this isomorphism can be extended to relate<br />constructive temporal logic with binding-time analysis. In particular,<br />we show how to extend the Curry-Howard isomorphism<br />to include the   ("next") operator from linear-time temporal<br />logic. This yields the simply typed lambda-calculus which we prove<br />to be equivalent to a multi-level binding-time analysis like those<br />used in partial evaluation.</p><p><br />Keywords: Curry-Howard isomorphism, partial evaluation, binding-time analysis, temporal logic.</p>

scholarly journals Eta-Expansion Does The Trick

1995 ◽  
Vol 2 (41) ◽  
Author(s):  
Olivier Danvy ◽  
Karoline Malmkjær ◽  
Jens Palsberg
Keyword(s):  
Partial Evaluation ◽  
Lambda Calculus ◽  
Product Type ◽  
Proper Treatment ◽  
Time Analysis ◽  
Function Type ◽  
Dynamic Case ◽  
Unified View ◽  
Binding Time ◽  
Binding Time Analysis

Partial-evaluation folklore has it that massaging one's source programs can make them specialize better. In Jones, Gomard, and Sestoft's recent textbook, a whole chapter is dedicated to listing such "binding-time improvements'': non-standard use of continuation-passing style, eta-expansion, and a popular transformation called "The Trick''. We provide a unified view of these binding-time improvements, from a typing perspective.<br /> <br />Just as a proper treatment of product values in partial evaluation requires partially static values, a proper treatment of disjoint sums requires moving static contexts across dynamic case expressions. This requirement precisely accounts for the non-standard use of continuation-passing style encountered in partial evaluation. In this setting, eta-expansion acts as a uniform binding-time coercion between values and contexts, be they of function type, product type, or disjoint-sum type. For the latter case, it achieves "The Trick''.<br /> <br />In this paper, we extend Gomard and Jones's partial evaluator for the lambda-calculus, lambda-Mix, with products and disjoint sums; we point out how eta-expansion for disjoint sums does The Trick; we generalize our earlier work by identifying that eta-expansion can be obtained in the binding-time analysis simply by adding two coercion rules; and we specify and prove the correctness of our extension to lambda-Mix.<br /><br /> See revised version BRICS-RS-96-17.

scholarly journals Polyvariant Analysis of the Untyped Lambda Calculus

1992 ◽  
Vol 21 (386) ◽  
Author(s):  
Jens Palsberg ◽  
Michael I. Schwartzbach
Keyword(s):  
Fixed Point ◽  
Program Transformation ◽  
Lambda Calculus ◽  
Safety Analysis ◽  
Type Inference ◽  
Simple Type ◽  
Time Analysis ◽  
Fixed Point Computation ◽  
Binding Time ◽  
Binding Time Analysis

<p>We present a polyvariant closure, safety, and binding time analysis for the untyped lambda calculus. The innovation is to analyze each abstraction afresh at all syntactic application points. This is achieved by a semantics-preserving program transformation followed by a novel monovariant analysis, expressed using type constraints. The constraints are solved in cubic time by a single fixed-point computation.</p><p>Safety analysis is aimed at determining if a term will cause an error during evaluation. We have recently proved that the monovariant safety analysis accepts strictly more terms than simple type inference. This paper demonstrates that the polyvariant transformation makes even more terms acceptable, even some without higher-order polymorphic types. Furthermore, polyvariant binding time analysis can improve the partial evaluators that base a polyvariant specialization on only monovariant binding time analysis.</p>

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

2000 ◽  
Vol 7 (15) ◽  
Author(s):  
Daniel Damian ◽  
Olivier Danvy
Keyword(s):  
Program Analysis ◽  
Flow Analysis ◽  
Control Flow ◽  
Time Analysis ◽  
Flow Information ◽  
Binding Time ◽  
The Impact ◽  
Positive Effect ◽  
Binding Time Analysis ◽  
Control Flow Analysis

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<br />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.<br />Our results confirm a folklore theorem about binding-time analysis, namely<br />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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