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For a Better Support of Static Data Flow
 Functional Programming Languages and Computer Architecture
"... . This paper identifies and solves a class of problems that arise in binding time analysis and more generally in partial evaluation of programs: the approximation and loss of static information due to dynamic expressions with static subexpressions. Solving this class of problems yields substantial b ..."
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. This paper identifies and solves a class of problems that arise in binding time analysis and more generally in partial evaluation of programs: the approximation and loss of static information due to dynamic expressions with static subexpressions. Solving this class of problems yields substantial binding time improvements and thus dramatically better results not only in the case of partial evaluation but also for static analyses of programs  this last point actually is related to a theoretical result obtained by Nielson. Our work can also be interpreted as providing a solution to the problem of conditionally static data, the dual of partially static data. We point out which changes in the control flow of a source program may improve its static data flow. Unfortunately they require one to iterate earlier phases of partial evaluation. We show how these changes are subsumed by transforming the source program into continuationpassing style (CPS). The transformed programs get specializ...
Abstract Interpretation of Functional Languages: From Theory to Practice
, 1991
"... Abstract interpretation is the name applied to a number of techniques for reasoning about programs by evaluating them over nonstandard domains whose elements denote properties over the standard domains. This thesis is concerned with higherorder functional languages and abstract interpretations with ..."
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Abstract interpretation is the name applied to a number of techniques for reasoning about programs by evaluating them over nonstandard domains whose elements denote properties over the standard domains. This thesis is concerned with higherorder functional languages and abstract interpretations with a formal semantic basis. It is known how abstract interpretation for the simply typed lambda calculus can be formalised by using binary logical relations. This has the advantage of making correctness and other semantic concerns straightforward to reason about. Its main disadvantage is that it enforces the identification of properties as sets. This thesis shows how the known formalism can be generalised by the use of ternary logical relations, and in particular how this allows abstract values to deno...
Projections for Polymorphic FirstOrder Strictness Analysis
 Math. Struct. in Comp. Science
, 1991
"... this paper, that results from this kind of analysis are, in a sense, polymorphic. This confirms an earlier conjecture [19], and shows how the technique can be applied to firstorder polymorphic functions. The paper is organised as follows. In the next section, we review projectionbased strictness a ..."
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this paper, that results from this kind of analysis are, in a sense, polymorphic. This confirms an earlier conjecture [19], and shows how the technique can be applied to firstorder polymorphic functions. The paper is organised as follows. In the next section, we review projectionbased strictness analysis very briefly. In Section 3 we introduce the types we will be working with: they are the objects of a category. We show that parameterised types are functors, with certain cancellation properties. In Section 4 we define strong and weak polymorphism: polymorphic functions in programming languages are strongly polymorphic, but we will need to use projections with a slightly weaker property. We prove that, under certain conditions, weakly polymorphic functions are characterised by any nontrivial instance. We can therefore analyse one monomorphic instance of a polymorphic function using existing techniques, and apply the results to every instance. In Section 5 we choose a finite set of projections for each type, suitable for use in a practical compiler. We call these specially chosen projections contexts, and we show examples of factorising contexts for compound types in order to facilitate application of the results of Section 4. We give a number of examples of polymorphic strictness analysis. Finally, in Section 6 we discuss related work and draw some conclusions. 2. Projections for Strictness Analysis
Projectionbased Program Analysis
, 1994
"... Projectionbased program analysis techniques are remarkable for their ability togive highly detailed and useful information not obtainable by other methods. The rst proposed projectionbased analysis techniques were those of Wadler and Hughes for strictness analysis, and Launchbury for bindingtime ..."
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Projectionbased program analysis techniques are remarkable for their ability togive highly detailed and useful information not obtainable by other methods. The rst proposed projectionbased analysis techniques were those of Wadler and Hughes for strictness analysis, and Launchbury for bindingtime analysis � both techniques are restricted to analysis of rstorder monomorphic languages. Hughes and Launchbury generalised the strictness analysis technique, and Launchbury the bindingtime analysis technique, to handle polymorphic languages, again restricted to rst order. Other than a general approach to higherorder analysis suggested by Hughes, and an ad hoc implementation of higherorder bindingtime analysis by Mogensen, neither of which had any formal notion of correctness, there has been no successful generalisation to higherorder analysis. We present a complete redevelopment of monomorphic projectionbased program analysis from rst principles, starting by considering the analysis of functions (rather than programs) to establish bounds on the intrinsic power of projectionbased analysis, showing also that projectionbased analysis can capture interesting termination
A Note on the Choice of Domains for ProjectionBased Program Analysis
 In Functional Programming: Proceedings of the 1991 Glasgow Workshop
, 1992
"... Various nonstandard interpretations of functional programs have been proposed in which the basic nonstandard values are projections. We show that every stable function is completely determined by an appropriate abstract value in the backward analysis, and that every continuous function is complete ..."
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Various nonstandard interpretations of functional programs have been proposed in which the basic nonstandard values are projections. We show that every stable function is completely determined by an appropriate abstract value in the backward analysis, and that every continuous function is completely determined by an appropriate value in the forward analysis. 1 Introduction Strictness analysis by abstract (or nonstandard) interpretation is an important part of several compilers for lazy functional languages [1, 2], and a wide variety of strictness analysis techniques have been proposed. The term forward is used to describe abstract interpretations in which the goal is to discover information about an entire expression given information at its leaves, while backward describes interpretations in which information flows in the other direction: the goal is to determine information at the leaves of an expression, given information about the entire expression. The development of backward ...
Representing Demand by Partial Projections
 J. of Functional Programming
, 1993
"... The projectionbased strictness analysis of Wadler and Hughes is elegant and theoretically satisfying except in one respect: the need for lifting. The domains and functions over which the analysis is performed need to be transformed, leading to a less direct correspondence between analysis and progr ..."
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The projectionbased strictness analysis of Wadler and Hughes is elegant and theoretically satisfying except in one respect: the need for lifting. The domains and functions over which the analysis is performed need to be transformed, leading to a less direct correspondence between analysis and program than might be hoped for. In this paper we shall see that the projection analysis may be reformulated in terms of partial projections, so removing this infelicity. There are additional benefits of the formulation: the two forms of information captured by the projection are distinguished, and the operational significance of the range of the projection fits exactly with the theory of unboxed types. 1 Introduction The method of projectionbased backwards strictness analysis for firstorder, lazy functional languages was first presented by Wadler and Hughes (1987) in 1987, and has undergone significant development since then. The method is elegant and theoretically satisfying except in one r...
Introducing Parallelism in a Lazy Functional Language
, 1997
"... Interpretation  Combinator Systems . . . . . . . . 13 2.2.6 Backward Analysis . . . . . . . . . . . . . . . . . . . . . . . . 14 2.2.7 Evaluation transformers . . . . . . . . . . . . . . . . . . . . . 18 2.3 Granularity of Parallelism . . . . . . . . . . . . . . . . . . . . . . . . 20 2.3.1 Serial ..."
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Interpretation  Combinator Systems . . . . . . . . 13 2.2.6 Backward Analysis . . . . . . . . . . . . . . . . . . . . . . . . 14 2.2.7 Evaluation transformers . . . . . . . . . . . . . . . . . . . . . 18 2.3 Granularity of Parallelism . . . . . . . . . . . . . . . . . . . . . . . . 20 2.3.1 Serial Combinators . . . . . . . . . . . . . . . . . . . . . . . . 20 2.3.2 Complexity Analysis . . . . . . . . . . . . . . . . . . . . . . . 21 2.3.3 Strictness Analysis Applied to Time Analysis . . . . . . . . . 21 2.3.4 Using Type Information to Derive Time Information . . . . . 25 2.4 Parallel Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 2.4.1 HBCPP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 2.4.2 GranSim . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 2.5 Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . 30 2.5.1 Strictness Analysis . . . . . . . . . . . . . . . . . . . . . . . . 30 2.5.2 Granularity Analysis . . ...
Strictness Analysis  Another Method
, 1993
"... Strictness analysis is a compile time analysis applicable to lazy functional programming languages. Strictness analysis can be used to significantly improve uniprocessor implementation speed and to derive nonspeculative parallelism. Many methods for doing strictness analysis have been proposed. Mos ..."
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Strictness analysis is a compile time analysis applicable to lazy functional programming languages. Strictness analysis can be used to significantly improve uniprocessor implementation speed and to derive nonspeculative parallelism. Many methods for doing strictness analysis have been proposed. Most of these are based on abstract interpretation and require fixpoint iteration. In this thesis we survey existing methods and then go on to define a new method which does not require fixpoint iteration. The new method is significantly more efficient than methods based on abstract interpretation. The abstract domain used is not fixed and can be expanded to obtain better accuracy. Our method is also easy to prove correct. We discuss further work necessary for the new method to realise its potential as a framework for fast and practical analyses.