GPUArrays.jl

ld is to specialize on the type of matrix you have. With Julia, you can set it up so that way the user passes what type of matrix they have (Tridiagonal, sparse, PETSc for multi-node parallelism, or a special matrix type with \ overloaded to do multigrid) and the optimization, differential equation, etc. routine will use the fast linear solver routine specific to the problem. This makes it easy to expose very large amounts of performance gains and specialization opportunities to the user in ways that are usually automatic (i.e. sometimes that user doesn't even have to know!). 3. Complex numbers. Large fields of scientific computing (physicists and engineers) use complex numbers. Many libraries have pitiful support for complex numbers. Generic typing helps a lot here. Those are 3 off the top of my head, and there are many more diffeq-specific examples that have come up as users have asked to have resizing control models with discrete variables mixed in with continuous variables, etc., and this can all be handled efficiently via the type system without having to restructure the core algorithms to handle these extra features. The key thing here is that users can add new features specific to their problem into your algorithm as they need to, without having to modify your code, just by smart uses of the type system.