Harry Potter and the Prisoner of Azkaban (Piano Solos) by John Williams

By John Williams

This astonishing keepsake folio comes loaded with full-color and black and white images from the blockbuster Harry Potter movie. Titles: * Aunt Marge's Waltz * Buckbeak's Flight * Double difficulty * Hagrid the Professor * Hedwig's topic * The Snowball struggle * A Window to the earlier * A Winter's Spell.

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Example text

So you can see that naming—using either top-level equations or equations within a let expression—is an example of the abstraction principle in action. Details: An equation such as c = 42 is called a binding. A simple rule to remember when programming in Haskell is never to give more than one binding for the same name in a context where the names can be confused, whether at the top level of your program or nestled within a let expression. 2 Functional Abstraction The design of functions such as simple can be viewed as the abstraction principle in action.

Even a whole number, say the number 42, will print as 42 % 1 if it is a Rational number. To create a Rational number in a program, however, once it is given the proper type, we can use the normal division operator, as in the following definition of a quarter note: qn :: Dur qn = 1/4 -- quarter note So far so good. But what about PitchClass? We might try to use integers to represent pitch classes as well, but this is not very elegant—ideally we would like to write something that looks more like the conventional pitch class names C, C , D , D, etc.

As a simple example of this problem, consider the distributive law, expressed here as a calculation in Haskell, and used earlier in this chapter in calculations involving the function simple: CHAPTER 1. COMPUTER MUSIC, EUTERPEA, AND HASKELL 26 a ∗ (b + c) ⇒ a ∗ b + a ∗ c For most floating-point numbers, this law is perfectly valid. 99115. But funny things can happen when the magnitude of b + c differs significantly from the magnitude of either b or c. 00679e − 6 Although the discrepancy here is small, its very existence is worrisome, and in certain situations it could be disastrous.

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