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The Haskell School of Music

'The Haskell School of Music'
The Haskell School of Music — From Signals to Symphonies — Paul Hudak Yale University Department of Computer Science Version 2.6 (January 2014) i The Haskell School of Music — From Signals to Symphonies — Paul Hudak Yale University Department of Computer Science New Haven, CT, USA Version 2.6 (January 2014) Copyright c ? Paul Hudak January 2011, 2012, 2013, 2014 All rights reserved. No part of this publication may be reproduced or distributed in any form or by any means, or stored in a data base or retrieval system, without the prior written permission of the author. Cover image: Euterpe, the Greek Muse of Music (attribution unknown) Contents Prefacexv 1Computer Music, Euterpea, and Haskell1 1.1The Note vs. Signal Dichotomy . . . . . . . . . . . . . . . . .2 1.2Basic Principles of Programming . . . . . . . . . . . . . . . .3 1.3Computation by Calculation . . . . . . . . . . . . . . . . . . .4 1.4Expressions and Values. . . . . . . . . . . . . . . . . . . . .8 1.5Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .10 1.6Function Types and Type Signatures . . . . . . . . . . . . . .11 1.7Abstraction, Abstraction, Abstraction . . . . . . . . . . . . .13 1.7.1Naming . . . . . . . . . . . . . . . . . . . . . . . . . .13 1.7.2Functional Abstraction . . . . . . . . . . . . . . . . . .16 1.7.3Data Abstraction . . . . . . . . . . . . . . . . . . . . .19 1.8Haskell Equality vs. Euterpean Equality . . . . . . . . . . . .22 1.9Code Reuse and Modularity . . . . . . . . . . . . . . . . . . .23 1.10 [Advanced] Programming with Numbers . . . . . . . . . . . .24 2Simple Music28 2.1Preliminaries. . . . . . . . . . . . . . . . . . . . . . . . . . .28 2.2Notes, Music, and Polymorphism . . . . . . . . . . . . . . . .30 2.3Convenient Auxiliary Functions . . . . . . . . . . . . . . . . .34 2.3.1A Simple Example . . . . . . . . . . . . . . . . . . . .36 2.4Absolute Pitches . . . . . . . . . . . . . . . . . . . . . . . . .41 ii CONTENTSiii 3Polymorphic bottom: pr2). . . . . . . . .90 6.3Trills in Stars and Stripes Forever. . . . . . . . . . . . . . . 100 6.4General MIDI Percussion Names . . . . . . . . . . . . . . . . 102 7.1Common Type Classes and Their Instances . . . . . . . . . . 120 7.2Numeric Class Hierarchy . . . . . . . . . . . . . . . . . . . . . 123 7.3Standard Numeric Types. . . . . . . . . . . . . . . . . . . . 124 7.4Euterpea’ s Data Types with Deriving Clauses . . . . . . . . . 128 8.1An abstract perform function . . . . . . . . . . . . . . . . . . 137 8.2Block Diagram of Performance Concepts . . . . . . . . . . . . 139 8.3 A more effi cient perform function . . . . . . . . . . . . . . . . 141 xi LIST OF FIGURESxii 8.4Phrase Attributes . . . . . . . . . . . . . . . . . . . . . . . . . 143 8.5 Defi nition of default player defPlayer . . . . . . . . . . . . 145 8.6 Defi nition of Player fancyPlayer. . . . . . . . . . . . . . . . . 151 9.1An Example of Self-Similar Music. . . . . . . . . . . . . . . 153 10.1 Some Useful Properties of map and fol
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