Multi-stage Programming with Functors and Monads: Eliminating Abstraction Overhead from Generic Code

With Gaussian Elimination as a representative family of numerical and symbolic algorithms, we use multi-stage programming, monads and Ocaml’s advanced module system to demonstrate the complete elimination of the abstraction overhead while avoiding any inspection of the generated code. We parameterize our Gaussian Elimination code to a great extent (over domain, matrix representations, determinant tracking, pivoting policies, result types, etc) …