We present a framework for representing quantum entities in Haskell.

A method is presented for computing all higher-order partial derivatives of a multivariate function R n → R. This method works by evaluating the function under a nonstandard interpretation, lifting reals to multivariate power series. Multivariate power series, with potentially an infinite number of terms with nonzero coefficients, are represented using a lazy data structure constructed out of linear terms. A complete implementation of this method in SCHEME is presented, along with a straightforward exposition, based on Taylor expansions, of the method’s correctness.

Data streams make preeminent instruments for playing certain classical themes from analysis. Complex networks of processes, e#ortlessly orchestrated by lazy evaluation, can enumerate terms of formal power series ad infinitum. Expressed in a language like Haskell, working programs for power-series operations are tiny gems, because the natural programming style for data streams fits the mathematics so well---often better than time-honored summation notation. The cleverest copyist is the one whose music is performed with the most ease without the performer guessing why. --- Jean Jacques Rousseau, Dictionary of Music 1 Overture Like persistent folk tunes, the themes I intend to play here have been arranged for various ensembles over many years. Some performances have been angular, and some melodic, but all share the staying power of good music. The themes stick in mind, to be enjoyed again and again as each performance exposes new surfaces and depths. My subject is "power-stream compositio...

Abstract. We present an application of functional programming in the domain of sound generation and processing. We use the lazy language Clean to define purely functional stream generators, filters and other processors, such as reverberators. Audio signals are represented (before the final output to arrays processed by the system primitives) as co-recursive lazy streams, and the processing algorithms have a strong dataflow taste. This formalism seems particularly appropriate to implement the ‘waveguide’, or ‘physically-oriented ’ sound models. Lazy programming allocates the dynamical memory quite heavily, so we do not propose a real-time, industrial strength package, but rather a pedagogical library, offering natural, easy to understand coding tools. We believe that, thanks to their simplicity and clearness, such functional tools can be also taught to students interested in audio processing, but with a limited competence in programming.

CWI is a founding member of ERCIM, the European Research Consortium for Informatics and Mathematics. CWI's research has a theme-oriented structure and is grouped into four clusters. Listed below are the names of the clusters and in parentheses their acronyms.

solutions for a family of discretely