With this machinery, we can give a common structure to programs based on different notions of computation. The generality of arrows tends to force one into a point-free style, which is useful for proving general properties. However it is not to everyone's taste, and can be awkward for programming specific instances. The solution is a point-wise notation for arrows, which is automatically translated to the functional language Haskell. Each notion of computation thus defines a special sublanguage of Haskell. 1 Notions of computation We shall explore what we mean by a notion of computation using four varied examples. As a point of comparison, we shall consider how the following operator on functions may be generalized to the various types of `function-like ' components.

Abstract. In this paper, we present an implementation of a modular synthesizer in Haskell using Yampa. A synthesizer, be it a hardware instrument or a pure software implementation, as here, is said to be modular if it provides sound-generating and sound-shaping components that can be interconnected in arbitrary ways. Yampa, a Haskell-embedded implementation of Functional Reactive Programming, supports flexible, purely declarative construction of hybrid systems. Since music is a hybrid continuous-time and discrete-time phenomenon, Yampa is a good fit for such applications, offering some unique possibilities compared to most languages targeting music or audio applications. Through the presentation of our synthesizer application, we demonstrate this point and provide insight into the Yampa approach to programming reactive, hybrid systems. We develop the synthesizer gradually, starting with fundamental synthesizer components and ending with an application that is capable of rendering a standard MIDI file as audio with respectable performance.

This chapter gives an introduction to all the main programming paradigms, their underlying concepts, and the relationships between them. We give a broad view to help programmers choose the right concepts they need to solve the problems at hand. We give a taxonomy of almost 30 useful programming paradigms and how they are related. Most of them differ only in one or a few concepts, but this can make a world of difference in programming. We explain briefly how programming paradigms influence language design, and we show two sweet spots: dual-paradigm languages and a definitive language. We introduce the main concepts of programming languages: records, closures, independence (concurrency), and named state. We explain the main principles of data abstraction and how it lets us organize large programs. Finally, we conclude by focusing on concurrency, which is widely considered the hardest concept to program with. We present four little-known but important paradigms that greatly simplify concurrent programming with respect to mainstream languages: declarative concurrency (both eager and lazy), functional reactive programming, discrete synchronous programming, and constraint programming. These paradigms have no race conditions and can be used in cases where no other paradigm works. We explain why for multi-core processors and we give several examples from computer music, which often uses these paradigms. More is not better (or worse) than less, just different. – The paradigm paradox. 1