An Analytical Approach to Programs as Data Objects

This essay accompanies a selection of 32 articles (referred to in bold face in the text and marginally marked in the bibliographic references) submitted to Aarhus University towards a Doctor Scientiarum degree in Computer Science.The author's previous academic degree, beyond a doctoral degree in June 1986, is an "Habilitation à diriger les recherches" from the Université Pierre et Marie Curie (Paris VI) in France; the corresponding material was submitted in September 1992 and the degree was obtained in January 1993.The present 32 articles have all been written since 1993 and while at DAIMI.Except for one other PhD student, all co-authors are or have been the author's students here in Aarhus

An Operational Foundation for Delimited Continuations in<br><br> the<br><br><br> CPS<br><br> Hierarchy

We present an abstract machine and a reduction semantics for the lambda-calculus extended with control operators that give access to delimited continuations in the CPS hierarchy. The abstract machine is derived from an evaluator in continuation-passing style (CPS); the reduction semantics (i.e., a small-step operational semantics with an explicit representation of evaluation contexts) is constructed from the abstract machine; and the control operators are the shift and reset family. We also present new applications of delimited continuations in the CPS hierarchy: finding list prefixes and normalization by evaluation for a hierarchical language of units and products.Comment: 39 page

A Rational Deconstruction of Landin's SECD Machine with the J Operator

Landin's SECD machine was the first abstract machine for applicative expressions, i.e., functional programs. Landin's J operator was the first control operator for functional languages, and was specified by an extension of the SECD machine. We present a family of evaluation functions corresponding to this extension of the SECD machine, using a series of elementary transformations (transformation into continu-ation-passing style (CPS) and defunctionalization, chiefly) and their left inverses (transformation into direct style and refunctionalization). To this end, we modernize the SECD machine into a bisimilar one that operates in lockstep with the original one but that (1) does not use a data stack and (2) uses the caller-save rather than the callee-save convention for environments. We also identify that the dump component of the SECD machine is managed in a callee-save way. The caller-save counterpart of the modernized SECD machine precisely corresponds to Thielecke's double-barrelled continuations and to Felleisen's encoding of J in terms of call/cc. We then variously characterize the J operator in terms of CPS and in terms of delimited-control operators in the CPS hierarchy. As a byproduct, we also present several reduction semantics for applicative expressions with the J operator, based on Curien's original calculus of explicit substitutions. These reduction semantics mechanically correspond to the modernized versions of the SECD machine and to the best of our knowledge, they provide the first syntactic theories of applicative expressions with the J operator

The Weak Call-By-Value {\lambda}-Calculus is Reasonable for Both Time and Space

We study the weak call-by-value $\lambda$-calculus as a model for computational complexity theory and establish the natural measures for time and space -- the number of beta-reductions and the size of the largest term in a computation -- as reasonable measures with respect to the invariance thesis of Slot and van Emde Boas [STOC~84]. More precisely, we show that, using those measures, Turing machines and the weak call-by-value $\lambda$-calculus can simulate each other within a polynomial overhead in time and a constant factor overhead in space for all computations that terminate in (encodings) of 'true' or 'false'. We consider this result as a solution to the long-standing open problem, explicitly posed by Accattoli [ENTCS~18], of whether the natural measures for time and space of the $\lambda$-calculus are reasonable, at least in case of weak call-by-value evaluation. Our proof relies on a hybrid of two simulation strategies of reductions in the weak call-by-value $\lambda$-calculus by Turing machines, both of which are insufficient if taken alone. The first strategy is the most naive one in the sense that a reduction sequence is simulated precisely as given by the reduction rules; in particular, all substitutions are executed immediately. This simulation runs within a constant overhead in space, but the overhead in time might be exponential. The second strategy is heap-based and relies on structure sharing, similar to existing compilers of eager functional languages. This strategy only has a polynomial overhead in time, but the space consumption might require an additional factor of $\log n$, which is essentially due to the size of the pointers required for this strategy. Our main contribution is the construction and verification of a space-aware interleaving of the two strategies, which is shown to yield both a constant overhead in space and a polynomial overhead in time

The (In)Efficiency of interaction

Evaluating higher-order functional programs through abstract machines inspired by the geometry of the interaction is known to induce space efficiencies, the price being time performances often poorer than those obtainable with traditional, environment-based, abstract machines. Although families of lambda-terms for which the former is exponentially less efficient than the latter do exist, it is currently unknown how general this phenomenon is, and how far the inefficiencies can go, in the worst case. We answer these questions formulating four different well-known abstract machines inside a common definitional framework, this way being able to give sharp results about the relative time efficiencies. We also prove that non-idempotent intersection type theories are able to precisely reflect the time performances of the interactive abstract machine, this way showing that its time-inefficiency ultimately descends from the presence of higher-order types

Improving the Performance of SQL Join Operation in the Distributed Enterprise Information System by Caching

The enterprise information system (EIS) contains databases and other data sources in multiple data centers. Users query the EIS via clients. The client has a working space in the cloud. Caching data in client space will reduce the total execution time of the query. However, the client space has limited resources to store data. There are two options for caching data at the client space: caching the final results of query operations, or caching the source data tables. The problem is that some query operations such as “joining multiple big tables” will simply produce a result too big to store in cache in some cases. By contrast, caching source data tables may be a better choice in those situations. This paper presents an algorithm that combines active caching and passive caching to improve the cache hit, thus improving performance of the SQL join query in the cloud computing environment

Language Support for Programming High-Performance Code

Nowadays, the computing landscape is becoming increasingly heterogeneous and this trend is currently showing no signs of turning around. In particular, hardware becomes more and more specialized and exhibits different forms of parallelism. For performance-critical codes it is indispensable to address hardware-specific peculiarities. Because of the halting problem, however, it is unrealistic to assume that a program implemented in a general-purpose programming language can be fully automatically compiled to such specialized hardware while still delivering peak performance. One form of parallelism is single instruction, multiple data (SIMD). Part I of this thesis presents Sierra: an extension for C ++ that facilitates portable and effective SIMD programming. Part II discusses AnyDSL. This framework allows to embed a so-called domain-specific language (DSL) into a host language. On the one hand, a DSL offers the application developer a convenient interface; on the other hand, a DSL can perform domain-specific optimizations and effectively map DSL constructs to various architectures. In order to implement a DSL, one usually has to write or modify a compiler. With AnyDSL though, the DSL constructs are directly implemented in the host language while a partial evaluator removes any abstractions that are required in the implementation of the DSL.Die Rechnerlandschaft wird heutzutage immer heterogener und derzeit ist keine Trendwende in Sicht. Insbesondere wird die Hardware immer spezialisierter und weist verschiedene Formen der Parallelität auf. Für performante Programme ist es unabdingbar, hardwarespezifische Eigenheiten zu adressieren. Wegen des Halteproblems ist es allerdings unrealistisch anzunehmen, dass ein Programm, das in einer universell einsetzbaren Programmiersprache implementiert ist, vollautomatisch auf solche spezialisierte Hardware übersetzt werden kann und dabei noch Spitzenleistung erzielt. Eine Form der Parallelität ist „single instruction, multiple data (SIMD)“. Teil I dieser Arbeit stellt Sierra vor: eine Erweiterung für C++, die portable und effektive SIMD-Programmierung unterstützt. Teil II behandelt AnyDSL. Dieses Rahmenwerk ermöglicht es, eine sogenannte domänenspezifische Sprache (DSL) in eine Gastsprache einzubetten. Auf der einen Seite bietet eine DSL dem Anwendungsentwickler eine komfortable Schnittstelle; auf der anderen Seiten kann eine DSL domänenspezifische Optimierungen durchführen und DSL-Konstrukte effektiv auf verschiedene Architekturen abbilden. Um eine DSL zu implementieren, muss man gewöhnlich einen Compiler schreiben oder modifizieren. In AnyDSL werden die DSL-Konstrukte jedoch direkt in der Gastsprache implementiert und ein partieller Auswerter entfernt jegliche Abstraktionen, die in der Implementierung der DSL benötigt werden

Bisimulations for Delimited-Control Operators

We present a comprehensive study of the behavioral theory of an untyped $\lambda$-calculus extended with the delimited-control operators shift and reset. To that end, we define a contextual equivalence for this calculus, that we then aim to characterize with coinductively defined relations, called bisimilarities. We consider different styles of bisimilarities (namely applicative, normal-form, and environmental) within a unifying framework, and we give several examples to illustrate their respective strengths and weaknesses. We also discuss how to extend this work to other delimited-control operators