Algorithmic Composition: A Guide to Composing Music with Nyquist

Chapter 12. Iteration

148 Chapter 12 Iteration Iteration in programming means repeated evaluation. In SAL, iteration is accomplished through loops. Loops evaluate a set of expressions over and over again. A loop should terminate after a specified number of repetitions or when a condition is met. SAL has several iterative forms, including a loop command with many variations. This chapter will show how to solve many of the same problems presented in Chapter 11, only using iteration instead of recursion, so the reader can easily compare recursive and iterative forms. 12.1 The loop Command with a for-below Clause The most general iterative form in SAL is the loop command, which like a begin-end block organizes a set of commands, but unlike begin-end, the commands are repeated. Loop commands can include clauses that create, initialize, and update local variables for each repetition. Loop commands can also include clauses that stop the repetition when certain conditions are met. For now, we will start with a simple form of loop, using a for clause to control the number of iterations. The template for this simple form of loop is loop for counter below count-expression commands end This loop is evaluated as follows: First, counter (a variable) is initialized to zero, and count-expression is evaluated to obtain a number we will call limit. If counter is less than limit, commands (any number of commands) are evaluated. Then counter is incremented by 1, and the loop repeats by again comparing counter to limit and evaluating commands again. When counter reaches or exceeds limit, the loop ends. In Example 12.1.1, we use a loop to increment the counter count. As we enter the loop, the variable count starts counting at 0. We enter the body of the loop and print the value of count. count is then incremented (to 1). Because the new value of count is less than the count expression (4), the body of the loop is executed again. The iterative process stops when count equals 4. The number of iterations 12.1 The loop Command with a for-below Clause 149 is given by the limit (4), and the values of the count range from 0 to limit - 1. Example 12.1.1: A simple loop SAL> loop for count below 4 display “loop”, count end loop : COUNT = 0 loop : COUNT = 1 loop : COUNT = 2 loop : COUNT = 3 In Example 12.1.2, we define a function make-a-chromatic-lick using iteration rather than recursion. The purpose of the function is to create a list that generates a specified number of half steps from a starting key number. The begin statement first initializes the variable the-list (to nil). The notes we generate will be collected into the-list. The body of the begin contains a loop. The loop counter is index, and the count-expression is the number-of-notes we need to create. When the list ends, we return the-list of notes. In the body of the loop, we use set with @= to cons the sum of starting-note and the index onto the-list. The list cons’ing process continues until the variable index is equal to the number-of-notes. The list is returned. To help understand the iterative process, a display statement has been inserted into the loop body. Example 12.1.2: make-a-chromatic-lick.sal define function make-a-chromatic-lick( starting-note, number-of-notes) begin with the-list loop for index below number-of-notes set the-list @= starting-note + index display "make-a-lick", index, the-list end return the-list end When we call the function, we get the following results: 150 Chapter 12 ⋅ Iteration Example 12.1.3: output from make-a-chromatic-lick SAL> print make-a-chromatic-lick(60, 6) make-a-lick : INDEX = 0 THE-LIST = (60) make-a-lick : INDEX = 1 THE-LIST = (61 60) make-a-lick : INDEX = 2 THE-LIST = (62 61 60) make-a-lick : INDEX = 3 THE-LIST = (63 62 61 60) make-a-lick : INDEX = 4 THE-LIST = (64 63 62 61 60) make-a-lick : INDEX = 5 the-list = (65 64 63 62 61 60) {65 64 63 62 61 60} Why does the list go from largest to smallest? Because we cons’ed the newly created element onto the front of the list (using @=). If we want a list in...