NumLin: Linear types for linear algebra

Abstract

We present NumLin, a functional programming language whose type system is designed to enforce the safe usage of the APIs of low-level linear algebra libraries (such as BLAS/LAPACK). We do so through a brief description of its key features and several illustrative examples. We show that NumLin’s type system is sound and that its implementation improves upon naïve implementations of linear algebra programs, almost towards C-levels of performance. By doing so, we demonstrate (a) that linear types are well-suited to expressing the APIs of low-level linear algebra libraries accurately and concisely and (b) that, despite the complexity of prior work on it, fractional permissions can actually be implemented using simple, well-known techniques and be used practically in real programs.