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ContextSensitive Rewriting Strategies
, 1997
"... Contextsensitive rewriting is a simple restriction of rewriting which is formalized by imposing fixed restrictions on replacements. Such a restriction is given on a purely syntactic basis: it is (explicitly or automatically) specified on the arguments of symbols of the signature and inductively ..."
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Cited by 45 (32 self)
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Contextsensitive rewriting is a simple restriction of rewriting which is formalized by imposing fixed restrictions on replacements. Such a restriction is given on a purely syntactic basis: it is (explicitly or automatically) specified on the arguments of symbols of the signature and inductively extended to arbitrary positions of terms built from those symbols. Termination is not only preserved but usually improved and several methods have been developed to formally prove it. In this paper, we investigate the definition, properties, and use of contextsensitive rewriting strategies, i.e., particular, fixed sequences of contextsensitive rewriting steps. We study how to define them in order to obtain efficient computations and to ensure that contextsensitive computations terminate whenever possible. We give conditions enabling the use of these strategies for rootnormalization, normalization, and infinitary normalization. We show that this theory is suitable for formalizing ...
A policy iteration algorithm for computing fixed points in static analysis of programs
 IN CAV
, 2005
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SpaceEfficient Scheduling of Parallelism with Synchronization Variables
"... Recent work on scheduling algorithms has resulted in provable bounds on the space taken by parallel computations in relation to the space taken by sequential computations. The results for online versions of these algorithms, however, have been limited to computations in which threads can only synchr ..."
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Cited by 34 (10 self)
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Recent work on scheduling algorithms has resulted in provable bounds on the space taken by parallel computations in relation to the space taken by sequential computations. The results for online versions of these algorithms, however, have been limited to computations in which threads can only synchronize with ancestor or sibling threads. Such computations do not include languages with futures or userspecified synchronization constraints. Here we extend the results to languages with synchronization variables. Such languages include languages with futures, such as Multilisp and Cool, as well as other languages such asid. The main result is an online scheduling algorithm which, given a computation with w work (total operations), synchronizations, d depth (critical path) and s1 sequential space, will run in O(w=p + log(pd)=p + d log(pd)) time and s1 + O(pd log(pd)) space, on a pprocessor crcw pram with a fetchandadd primitive. This includes all time and space costs for both the computation and the scheduler. The scheduler is nonpreemptive in the sense that it will only move a thread if the thread suspends on a synchronization, forks a new thread, or exceeds a threshold when allocating space. For the special case where the computation is a planar graph with lefttoright synchronization edges, the scheduling algorithm can be implemented in O(w=p+d log p) time and s1 + O(pd log p) space. These are the first nontrivial space bounds described for such languages.
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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Cited by 27 (0 self)
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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...
Deriving algorithms from type inference systems: Application to strictness analysis
, 1994
"... The role of nonstandard type inference in static program analysis has been much studied recently. Early work emphasised the efficiency of type inference algorithms and paid little attention to the correctness of the inference system. Recently more powerful inference systems have been investigated b ..."
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Cited by 26 (8 self)
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The role of nonstandard type inference in static program analysis has been much studied recently. Early work emphasised the efficiency of type inference algorithms and paid little attention to the correctness of the inference system. Recently more powerful inference systems have been investigated but the connection with efficient inference algorithms has been obscured. The contribution of this paper is twofold: first we show how to transform a program logic into an algorithm and, second, we introduce the notion of lazy types and show how to derive an efficient algorithm for strictness analysis. 1 Introduction Two major formal frameworks have been proposed for static analysis of functional languages: abstract interpretation and type inference. A lot of work has been done to characterise formally the correctness and the power of abstract interpretation. However the development of algorithms has not kept pace with the theoretical developments. This is now a major barrier that is preven...
Separation Constraint Partitioning  A New Algorithm for Partitioning Nonstrict Programs into Sequential Threads
 In Conference Record of the 22nd ACM SIGPLANSIGACT Symposium on Principles of Programming Languages
, 1995
"... In this paper we present substantially improved thread partitioning algorithms for modern implicitly parallel languages. We present a new block partitioning algorithm, separation constraint partitioning, which is both more powerful and more flexible than previous algorithms. Our algorithm is guarant ..."
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Cited by 19 (1 self)
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In this paper we present substantially improved thread partitioning algorithms for modern implicitly parallel languages. We present a new block partitioning algorithm, separation constraint partitioning, which is both more powerful and more flexible than previous algorithms. Our algorithm is guaranteed to derive maximal threads. We present a theoretical framework for proving the correctness of our partitioning approach, and we show how separation constraint partitioning makes interprocedural partitioning viable. We have implemented the partitioning algorithms in an Id90 compiler for workstations and parallel machines. Using this experimental platform, we quantify the effectiveness of different partitioning schemes on whole applications. 1 Introduction Modern implicitly parallel languages, such as the functional language Id90, allow the elegant formulation of a broad class of problems while exposing substantial parallelism. However, their nonstrict semantics require finegrain dynami...
Compilation of Functional Languages Using Flow Graph Analysis
, 1994
"... syntax, and syntactic and semantic domains of a flow graph Figure 9. Semantic equations Def and Exp of a flow graph The first argument to the functions Def and Exp specifies a set of nodes that represent a flow graph, from which the element(s) of current interest are selected by pattern matching. ..."
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Cited by 19 (13 self)
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syntax, and syntactic and semantic domains of a flow graph Figure 9. Semantic equations Def and Exp of a flow graph The first argument to the functions Def and Exp specifies a set of nodes that represent a flow graph, from which the element(s) of current interest are selected by pattern matching.
Algebraic Query Optimisation for Database Programming Languages
 The VLDB Journal
, 1996
"... A major challenge still facing the designers and implementors of database programming languages (DBPLs) is that of query optimisation. We investigate algebraic query optimisation for DBPLs in the context of a purely declarative functional language that supports sets as firstclass objects. Since the ..."
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Cited by 12 (4 self)
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A major challenge still facing the designers and implementors of database programming languages (DBPLs) is that of query optimisation. We investigate algebraic query optimisation for DBPLs in the context of a purely declarative functional language that supports sets as firstclass objects. Since the language is computationally complete issues such as nontermination of expressions and construction of infinite data structures can be investigated, whilst its declarative nature allows the issue of side effects to be avoided and a rich set of equivalences to be developed. The language has a welldefined semantics which permits us to reason formally about the properties of expressions, such as their equivalence with other expressions and their termination. The support of a set bulk data type enables much prior work on the optimisation of relational languages to be utilised. In the paper we first give the syntax of an archetypal DBPL and briefly discuss its semantics. We then de...
The Evaluation Transformer Model of Reduction and Its Correctness
 in TAPSOFT 91
, 1991
"... Lazy evaluation of functional programs incurs time and memory overheads, and restricts parallelism compared with programs that are evaluated strictly. A number of analysis techniques, such as abstract interpretation and projection analysis, have been developed to find out information that can allevi ..."
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Cited by 11 (4 self)
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Lazy evaluation of functional programs incurs time and memory overheads, and restricts parallelism compared with programs that are evaluated strictly. A number of analysis techniques, such as abstract interpretation and projection analysis, have been developed to find out information that can alleviate these overheads. This paper formalises an evaluation model, the evaluation transformer model of reduction, which can use information from these analysis techniques, and proves that the resulting reduction strategies produce the same answers as those obtained using lazy evaluation.
On the Power and Limitations of Strictness Analysis
, 1997
"... this paper, we provide a precise and formal characterizationof the loss of information that leads to this incompleteness. Specifically, we establish the following characterization theorem for Mycroft's strictness analysis method and a natural generalization of his method to nonflat domains cal ..."
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Cited by 9 (0 self)
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this paper, we provide a precise and formal characterizationof the loss of information that leads to this incompleteness. Specifically, we establish the following characterization theorem for Mycroft's strictness analysis method and a natural generalization of his method to nonflat domains called eeanalysis: Mycroft's method will deduce a strictness property for program P iff the property is independent of any constant appearing in any evaluation of P . To prove this, we specify a small set of equations called Eaxioms, that capture the information loss in Mycroft's method and develop a new proof technique called Erewriting. Erewriting extends the standard notion of rewriting to permit the use of reductions using Eaxioms interspersed with standard reduction steps. Eaxioms are a syntactic characterization of information loss and Erewriting provides an algorithm independent proof technique for characterizing the power of analysis methods. It can be used to answer questions on completeness and incompleteness of Mycroft's method on certain natural classes of programs. Finally, the techniques developed in this paper provide a general principle for establishing similar results for other analysis methods such as those based on abstract interpretation. As a demonstration of the generality of our technique, we give a characterization theorem for another variation of Mycroft's method called ddanalysis. Categories and Subject Descriptors: D.3.1 [Programming Languages]: Formal Definitions and Theory; D.3.2 [Programming Languages]: Language Classificationsapplicative languages; D.3.4 [Programming Languages]: Processorscompilers ; optimization General Terms: Languages, Theory, Measurement Additional Key Words and Phrases: Program analysis, abstract interpretation, str...