Stefan Karpinski

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.

Novel algebras for advanced analytics in Julia

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.

Julia: dynamism and performance reconciled by design

Julia is a programming language for the scientific community that combines features of productivity languages, such as Python or MATLAB, with characteristics of performance-oriented languages, such as C++ or Fortran. Julias productivity features include: dynamic typing, automatic memory management, rich type annotations, and multiple dispatch. At the same time, Julia allows programmers to control memory layout and leverages a specializing just-in-time compiler to eliminate much of the overhead of those features. This paper details the design choices made by the creators of Julia and reflects on the implications of those choices for performance and usability.