Scientific computation and functional programming

Abstract

Modern functional programming languages and lazy functional techniques are useful for describing and implementing abstract mathematical objects in quantum mechanics. Scientists can use them both for pedagogical purposes and for real, not too computationally intensive, but conceptually and algorithmically difficult applications. This article shows how to perform simple abstract computations on state vectors and discusses the construction of lazy algorithms that enormously simplify manipulation of potentially infinite data structures or iterative processes. Lazy functional techniques can often replace the use of symbolic computer algebra packages, while also offering an interesting algorithmic complement to the manipulation of mathematical data. These techniques are more efficient than blindly used symbolic algebra and are easy to integrate with the numerical code.