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25th International Symposium on Trends in Functional programming

作者： Huijben, Reg Aaldering, Jordy Achten, Peter Scholz, Sven-Bodo Radboud Univ Nijmegen Nijmegen Netherlands

ISBN: (纸本)9783031745577;9783031745584

Flattening is known to be a performance-boosting technique to orchestrate parallel computations on arbitrarily deeply nested arrays. In this paper, we propose a flattening transformation that deals with nested data structures that are composed of combinations of arrays and records. We choose the functional array programming language SaC as basis for this work, as it already supports flattening of homogeneously nested arrays, i.e. arrays in which all elements have the same shape. We propose an extension of SaC's syntax for records that allows records and arrays to be used in homogeneously nested form, and provide an implementation of this record transformation in the SaC compiler. Based on that extension, we show how any legal program that operates with such data structures can be transformed into an equivalent one that does not require any records at runtime.

关键词： nested data structures records array programming program transformation

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High-level object oriented programming with array technology 00

High-level object oriented programming with array technology

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Proceedings of the international conference on APL-Berlin-2000 conference

作者： Philippe Mougin TechMetrix Research Paris - France

ISBN: (纸本)9781581131826

Although classical object-oriented programming languages provide high-level modeling capacities (abstract data type, inheritance etc.), they remain low-level relative to data manipulation. Addressing this problem with object oriented programming languages is an important mission of today's research. Considerable work has already been done, leading to the development of tools such as object query languages, with mixed results. In this paper, we present the key points of a new approach to this problem. We propose an enhancement of object oriented programming at the core level, by integrating array programming, a high-level model for computing. Our solution is based on an extension to object oriented programming. This integration of object technology and array programming allows for high-level object-oriented programming. At the same time, it opens array programming to the powerful world of objects.

关键词： F-script array programming high order messaging object query language object-oriented programming smalltalk APL

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Multiarray: a C++ library for generic programming with arrays

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SOFTWARE-PRACTICE & EXPERIENCE 2005年第2期35卷 159-188页

作者： Garcia, R Lumsdaine, A Indiana Univ Open Syst Lab Bloomington IN 47405 USA

In C++, multi-dimensional arrays are often used but the language provides limited native support for them. The language, in its Standard Library, supplies sophisticated interfaces for manipulating sequential data. but relies on its bare-bones C heritage for arrays. The Multiarray library. a part of the Boost library collection, enhances a C++ programmer's tool set with versatile multi-dimensional array abstractions. It includes a general array class template and native array adaptors that support idiomatic array operations and interoperate with C++ Standard Library containers and algorithms. The arrays share a common interface, expressed as a generic programming concept, in terms of which generic array algorithms can be implemented. We present the library design, introduce a generic interface for array programming, demonstrate how the arrays integrate with the C++ Standard Library, and discuss the essential aspects of their implementation. Copyright (C) 2004 John Wiley Sons, Ltd.

关键词： C plus array programming generic programming Standard Template Library Boost

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Improving the game theoretic analysis of electricity auctions applied in medium markets

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JOURNAL OF COMPUTATIONAL SCIENCE 2016年第Part1期17卷 83-96页

作者： Zarei, Mohammad Salami, Abolfazl Arak Univ Technol Dept Elect Engn Arak Iran

Payment cost minimization (PCM) is an appropriate method for bid selection. Solving auctions by PCM is complex and time consuming, particularly under game theoretic analysis of electricity auctions, because it requires many computational iterations. The present study proposes a new algorithm to solve electricity auctions in a game theoretic analysis framework with a multi-player matrix game. The proposed algorithm provides two innovations for solving the auction and finding the Nash equilibria in a fast and accurate manner. This method facilitates analysis of the market behavior for changes in strategy by suppliers. Numerical studies demonstrate the effectiveness of the proposed algorithm. (C) 2016 Elsevier B.V. All rights reserved.

关键词： Bid cost minimization (BCM) Payment cost minimization (PCM) Nash equilibrium Matrix game array programming

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Merging compositions of array skeletons in SAC

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PARALLEL COMPUTING 2006年第7-8期32卷 507-522页

作者： Grelck, Clemens Scholz, Sven-Bodo Med Univ Lubeck Inst Software Technol & Programming Languages D-23538 Lubeck Germany Univ Hertfordshire Dept Comp Sci Hatfield AL10 9AB Herts England

The design of skeletons for expressing concurrent computations usually faces a conflict between software engineering demands and performance issues. Whereas the former favour versatile fine-grain skeletons that can be successively combined into larger programs, coarse-grain skeletons are more desirable from a performance perspective. We describe a way out of this dilemma for array skeletons. In the functional array language SAC We internally represent individual array skeletons by one or more meta skeletons, called WITH-loops. The design Of WITH-loops is carefully chosen to be versatile enough to cope with a large variety of skeletons, yet to be simple enough to allow for compilation into efficiently executable (parallel) code. Furthermore, WITH-loops are closed with respect to three tailor-made optimisation techniques, that systematically transform compositions of simple, computationally light-weight skeletons into few complex and computationally heavier-weight skeletons. (c) 2006 Elsevier B.V. All rights reserved.

关键词： Single Assignment C Algorithmic skeletons array programming Program optimisation

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Dependently typed array programs don't go wrong

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JOURNAL OF LOGIC AND ALGEBRAIC programming 2009年第7期78卷 643-664页

作者： Trojahner, Kai Grelck, Clemens Med Univ Lubeck Inst Software Technol & Programming Languages Lubeck Germany

The array programming paradigm adopts multidimensional arrays as the fundamental data structures of computation. array operations process entire arrays instead of just single elements. This makes array programs highly expressive and introduces data parallelism in a natural way. array programming imposes non-trivial structural constraints on ranks, shapes, and element values of arrays. A prominent example where such constraints are violated are out-of-bound array accesses. Usually, such constraints are enforced by means of run time checks. Both the run time overhead inflicted by dynamic constraint checking and the uncertainty of proper program evaluation are undesirable. We propose a novel type system for array programs based on dependent types. Our type system makes dynamic constraint checks obsolete and guarantees orderly evaluation of well-typed programs. We employ integer vectors of statically unknown length to index array types. We also show how constraints on these vectors are resolved using a suitable reduction to integer scalars. Our presentation is based on a functional array calculus that captures the essence of the paradigm without the legacy and obfuscation of a fully-fledged array programming language. (C) 2009 Elsevier Inc. All rights reserved.

关键词： array programming Dependent types Program verification

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Verified Tensor-Program Optimization Via High-Level Scheduling Rewrites

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PROCEEDINGS OF THE ACM ON programming LANGUAGES-PACMPL 2022年第POPL期6卷 1–28页

作者： Liu, Amanda Bernstein, Gilbert Louis Chlipala, Adam Ragan-Kelley, Jonathan MIT CSAIL 77 Massachusetts Ave Cambridge MA 02139 USA Univ Calif Berkeley Berkeley CA 94720 USA

We present a lightweight Coq framework for optimizing tensor kernels written in a pure, functional array language. Optimizations rely on user scheduling using series of verified, semantics-preserving rewrites. Unusually for compilation targeting imperative code with arrays and nested loops, all rewrites are source-to-source within a purely functional language. Our language comprises a set of core constructs for expressing high-level computation detail and a set of what we call reshape operators, which can be derived from core constructs but trigger low-level decisions about storage patterns and ordering. We demonstrate that not only is this system capable of deriving the optimizations of existing state-of-the-art languages like Halide and generating comparably performant code, it is also able to schedule a family of useful program transformations beyond what is reachable in Halide.

关键词： formal verification proof assistants array programming optimization

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APL Since 1978

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PROCEEDINGS OF THE ACM ON programming LANGUAGES-PACMPL 2020年第HOPL期4卷 1–108页

作者： Hui, Roger K. W. Kromberg, Morten J. Dyalog Ltd Toronto ON Canada Dyalog Ltd Bramley RG26 5BH Hants England

The Evolution of APL, the HOPL I paper by Falkoff and Iverson on APL, recounted the fundamental design principles which shaped the implementation of the APL language in 1966, and the early uses and other influences which shaped its first decade of *** the 40 years that have elapsed since HOPL I, several dozen APL implementations have come and gone. In the first decade or two, interpreters were typically born and buried along with the hardware or operating system that they were created for. More recently, the use of C as an implementation language provided APL interpreters with greater longevity and *** started its life on IBM mainframes which were time-shared by multiple users. As the demand for computing resources grew and costs dropped, APL first moved in-house to mainframes, then to mini- and micro-computers. Today, APL runs on PCs and tablets, Apples and Raspberry Pis, smartphones and *** operating systems, and the software application platforms that APL runs on, have evolved beyond recognition. Tools like database systems have taken over many of the tasks that were initially implemented in APL or provided by the APL system, and new capabilities like parallel hardware have also changed the focus of design and implementation efforts through the *** first wave of significant language enhancements occurred shortly after HOPL I, resulting in so-called second-generation APL systems. The most important feature of the second generation is the addition of general arrays—in which any item of an array can be another array—and a number of new functions and operators aligned with, if not always motivated by, the new data *** majority of implementations followed IBM’s path with APL2 “floating” arrays; others aligned themselves with SHARP APL and “grounded” arrays. While the APL2 style of APL interpreters came to dominate the mainstream of the APL community, two new cousins of APL descended from the SHARP APL family tree: J (cr

关键词： APL array programming executable mathematical notation functional programming higher-order functions programming languages

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AUTOMAP: Inferring Rank-Polymorphic Function Applications with Integer Linear programming

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PROCEEDINGS OF THE ACM ON programming LANGUAGES-PACMPL 2024年第OOPSLA2期8卷 1787-1813页

作者： Schenck, Robert Hinnerskov, Nikolaj Hey Henriksen, Troels Madsen, Magnus Elsman, Martin Univ Copenhagen Copenhagen Denmark Aarhus Univ Aarhus Denmark

Dynamically typed array languages such as Python, APL, and Matlab lift scalar operations to arrays and replicate scalars to fit applications. We present a mechanism for automatically inferring map and replicate operations in a statically-typed language in a way that resembles the programming experience of a dynamically-typed language while preserving the static typing guarantees. Our type system-which supports parametric polymorphism, higher-order functions, and top-level let-generalization-makes use of integer linear programming in order to find the minimum number of operations needed to elaborate to a well-typed program. We argue that the inference system provides useful and unsurprising guarantees to the programmer. We demonstrate important theoretical properties of the mechanism and report on the implementation of the mechanism in the statically-typed array programming language Futhark.

关键词： data parallelism constraint-based type systems array programming

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A Verified Compiler for a Functional Tensor Language

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PROCEEDINGS OF THE ACM ON programming LANGUAGES-PACMPL 2024年第PLDI期8卷 320-342页

作者： Liu, Amanda Bernstein, Gilbert Chlipala, Adam Ragan-Kelley, Jonathan MIT 77 Massachusetts Ave Cambridge MA 02139 USA Univ Washington Seattle WA 98195 USA

Producing efficient array code is crucial in high-performance domains like image processing and machine learning. It requires the ability to control factors like compute intensity and locality by reordering computations into different stages and granularities with respect to where they are stored. However, traditional pure, functional tensor languages struggle to do so. In a previous publication, we introduced ATL as a pure, functional tensor language capable of systematically decoupling compute and storage order via a set of high-level combinators known as reshape operators. Reshape operators are a unique functional-programming construct since they manipulate storage location in the generated code by modifying the indices that appear on the left-hand sides of storage expressions. We present a formal correctness proof for an implementation of the compilation algorithm, marking the first verification of a lowering algorithm targeting imperative loop nests from a source functional language that enables separate control of compute and storage ordering. One of the core difficulties of this proof required properly formulating the complex invariants to ensure that these storage-index remappings were well-formed. Notably, this exercise revealed a soundness bug in the original published compilation algorithm regarding the truncation reshape operators. Our fix is a new type system that captures safety conditions that were previously implicit and enables us to prove compiler correctness for well-typed source programs. We evaluate this type system and compiler implementation on a range of common programs and optimizations, including but not limited to those previously studied to demonstrate performance comparable to established compilers like Halide.

关键词： functional programming array programming formal verification type systems tensors

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