  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.
