Julia: A Fresh Approach to Numerical Computing

Bridging cultures that have often been distant, Julia combines expertise from the diverse fields of computer science and computational science to create a new approach to numerical computing. Julia is designed to be easy and fast. Julia questions notions generally held as "laws of nature" by practitioners of numerical computing: 1. High-level dynamic programs have to be slow. 2. One must prototype in one language and then rewrite in another language for speed or deployment, and 3. There are parts of a system for the programmer, and other parts best left untouched as they are built by the experts. We introduce the Julia programming language and its design --- a dance between specialization and abstraction. Specialization allows for custom treatment. Multiple dispatch, a technique from computer science, picks the right algorithm for the right circumstance. Abstraction, what good computation is really about, recognizes what remains the same after differences are stripped away. Abstractions in mathematics are captured as code through another technique from computer science, generic programming. Julia shows that one can have machine performance without sacrificing human convenience.Comment: 37 page

Array operators using multiple dispatch: a design methodology for array implementations in dynamic languages

Arrays are such a rich and fundamental data type that they tend to be built into a language, either in the compiler or in a large low-level library. Defining this functionality at the user level instead provides greater flexibility for application domains not envisioned by the language designer. Only a few languages, such as C++ and Haskell, provide the necessary power to define $n$-dimensional arrays, but these systems rely on compile-time abstraction, sacrificing some flexibility. In contrast, dynamic languages make it straightforward for the user to define any behavior they might want, but at the possible expense of performance. As part of the Julia language project, we have developed an approach that yields a novel trade-off between flexibility and compile-time analysis. The core abstraction we use is multiple dispatch. We have come to believe that while multiple dispatch has not been especially popular in most kinds of programming, technical computing is its killer application. By expressing key functions such as array indexing using multi-method signatures, a surprising range of behaviors can be obtained, in a way that is both relatively easy to write and amenable to compiler analysis. The compact factoring of concerns provided by these methods makes it easier for user-defined types to behave consistently with types in the standard library.Comment: 6 pages, 2 figures, workshop paper for the ARRAY '14 workshop, June 11, 2014, Edinburgh, United Kingdo

Julia Subtyping: A Rational Reconstruction

OOPSLA, Article 113International audienceProgramming languages that support multiple dispatch rely on an expressive notion of subtyping to specify method applicability. In these languages, type annotations on method declarations are used to select, out of a potentially large set of methods, the one that is most appropriate for a particular tuple of arguments. Julia is a language for scientific computing built around multiple dispatch and an expressive subtyping relation. This paper provides the first formal definition of Julia's subtype relation and motivates its design. We validate our specification empirically with an implementation of our definition that we compare against the existing Julia implementation on a collection of real-world programs. Our subtype implementation differs on 122 subtype tests out of 6,014,476. The first 120 differences are due to a bug in Julia that was fixed once reported; the remaining 2 are under discussion

Interflow: interprocedural flow-sensitive type inference and method duplication

Scala heavily relies on a number of object-oriented abstractions to support its feature-rich collections library. There are known techniques that optimize those abstractions away in just-in-time (JIT) compilers, but applying them in the ahead-of-time (AOT) setting is problematic. Profile-guided optimization (PGO) lets AOT compilers apply some of the same optimizations that JIT compilers employ, but it comes at a high complexity cost. In this paper, we introduce Interflow, an alternative approach towards ahead-of-time optimization of Scala programs which relies on interprocedural flow-sensitive type inference and method duplication. Our evaluation shows that an Interflow-based optimizing compiler built on top of the Scala Native toolchain outperforms existing PGO-based optimizing compilers for Scala. Moreover, we demonstrate that Interflow and PGO can be combined to achieve further improvements. On our benchmarks, with both Interflow and PGO enabled, the Scala Native toolchain approaches the performance of the HotSpot JVM

Novel Algebras for Advanced Analytics in Julia

Abstract—A linear algebraic approach to graph algorithms that exploits the sparse adjacency matrix representation of graphs can provide a variety of benefits. These benefits include syntactic simplicity, easier implementation, and higher performance. One way to employ linear algebra techniques for graph algorithms is to use a broader definition of matrix and vector multiplication. We demonstrate through the use of the Julia language system how easy it is to explore semirings using linear algebraic methodologies. A. Semiring algebra I

MATLAB doesn't love me: an essay

Programming is everywhere, and is becoming an increasingly essential component of knowledge work outside the realms of traditional software development. Examples include data journalism, scientific computing, machine control, machine learning, financial management, and others. A key aspect of this trend is that users have to use programming tools, but typically lack programming education, let alone a computer science background. In this short paper we revisit potential assumptions and preconceptions underlying traditional programming system design, from the perspective of practicing scientists using tools like MATLAB, R, Bash, Python, C++, and others. Specifically, we aim to peel off some ingrained assumptions that have informed programming language and system design for decades. Without giving a lot of answers, we hope some of our contrarian observations may turn out to be controversial, and stimulate a meaningful discussion towards a better programmer experience in the domain of science