Parallel Programming With Big Operators

In the sciences, it is common to use the so-called "big operator" notation to express the iteration of a binary operator (the reducer) over a collection of values. Such a notation typically assumes that the reducer is associative and abstracts the iteration process. Consequently, from a programming point-of-view, we can organize the reducer operations to minimize the depth of the overall reduction, allowing a potentially parallel evaluation of a big operator expression. We believe that the big operator notation is indeed an effective construct to express parallel computations in the Generate/Map/Reduce programming model, and our goal is to introduce it in programming languages to support parallel programming. The effective definition of such a big operator expression requires a simple way to generate elements, and a simple way to declare algebraic properties of the reducer (such as its identity, or its commutativity). In this poster, we want to present an extension of Scala with support for big operator expressions. We show how big operator expressions are defined and how the API is organized to support the simple definition of reducers with their algebraic properties.