Reading 26: Little Languages
Software in 6.005
Safe from bugs | Easy to understand | Ready for change |
---|---|---|
Correct today and correct in the unknown future. | Communicating clearly with future programmers, including future you. | Designed to accommodate change without rewriting. |
Objectives
In this reading we will begin to explore the design of a little language for constructing and manipulating music. Here’s the bottom line: when you need to solve a problem, instead of writing a program to solve just that one problem, build a language that can solve a range of related problems.
The goal for this reading is to introduce the idea of representing code as data and familiarize you with an initial version of the music language.
Representing code as data
Recall the Formula
datatype from Recursive Data Types:
Formula = Variable(name:String)
+ Not(formula:Formula)
+ And(left:Formula, right:Formula)
+ Or(left:Formula, right:Formula)
We used instances of Formula
to take propositional logic formulas, e.g. (p ∨ q) ∧ (¬p ∨ r), and represent them in a data structure, e.g.:
And(Or(Variable("p"), Variable("q")),
Or(Not(Variable("p")), Variable("r")))
In the parlance of grammars and parsers, formulas are a language, and Formula
is an abstract syntax tree.
But why did we define a Formula
type?
Java already has a way to represent expressions of Boolean variables with logical and, or, and not.
For example, given boolean
variables p
, q
, and r
:
(p || q) && ((!p) || r)
Done!
The answer is that the Java code expression (p || q) && ((!p) || r)
is evaluated as soon as we encounter it in our running program.
The Formula
value And(Or(...), Or(...))
is a first-class value that can be stored, passed and returned from one method to another, manipulated, and evaluated now or later (or more than once) as needed.
The Formula
type is an example of representing code as data, and we’ve seen many more.
Consider this functional object:
class VariableNameComparator implements Comparator<Variable> {
public int compare(Variable v1, Variable v2) {
return v1.name().compareTo(v2.name());
}
}
An instance of VariableNameComparator
is a value that can be passed around, returned, and stored.
But at any time, the function that it represents can be invoked by calling its compare
method with a couple of Variable
arguments:
Variable v1, v2;
Comparator<Variable> c = new VariableNameComparator();
...
int a = c.compare(v1, v2);
int b = c.compare(v2, v1);
SortedSet<Variable> vars = new TreeSet<>(c); // vars is sorted by name
Lambda expressions allow us to create functional objects with a compact syntax:
Comparator<Variable> c = (v1, v2) -> v1.name().compareTo(v2.name());
Building languages to solve problems
When we define an abstract data type, we’re extending the universe of built-in types provided by Java to include a new type, with new operations, appropriate to our problem domain. This new type is like a new language: a new set of nouns (values) and verbs (operations) we can manipulate. Of course, those nouns and verbs are abstractions built on top the existing nouns and verbs which were themselves already abstractions.
A language has greater flexibility than a mere program, because we can use a language to solve a large class of related problems, instead of just a single problem.
That’s the difference between writing
(p || q) && ((!p) || r)
and devising aFormula
type to represent the semantically-equivalent Boolean formula.And it’s the difference between writing a matrix multiplication function and devising a
MatrixExpression
type to represent matrix multiplications — and store them, manipulate them, optimize them, evaluate them, and so on.
First-class functions and functional objects enable us to create particularly powerful languages because we can capture patterns of computation as reusable abstractions.
Music language
In class, we will design and implement a language for generating and playing music.
To prepare, let’s first understand the Java APIs for playing music with the MIDI synthesizer.
We’ll see how to write a program to play MIDI music.
Then we’ll begin to develop our music language by writing a recursive abstract data type for simple musical tunes.
We’ll choose a notation for writing music in strings, and we’ll implement a parser to create instances of our Music
type.
The full source code for the basic music language is on GitHub.
Clone the sp16-ex26-music-starting repo so you can run the code and follow the discussion below.
Playing MIDI music
music.midi.MidiSequencePlayer
uses the Java MIDI APIs to play sequences of notes.
It’s quite a bit of code, and you don’t need to understand how it works.
MidiSequencePlayer
implements the music.SequencePlayer
interface, allowing clients to use it without depending on the particular MIDI implementation.
We do need to understand this interface and the types it depends on:
addNote : SequencePlayer × Instrument × Pitch × double × double → void
(SequencePlayer.java:15) is the workhorse of our music player.
Calling this method schedules a musical pitch to be played at some time during the piece of music.
play : SequencePlayer → void
(SequencePlayer.java:20) actually plays the music.
Until we call this method, we’re just scheduling music that will, eventually, be played.
The addNote
operation depends on two more types:
Instrument
is an enumeration of all the available MIDI instruments.
Pitch
is an abstract data type for musical pitches (think keys on the piano keyboard).
Read and understand the Pitch
documentation and the specifications for its public constructor and all its public methods.
Our music data type will rely on Pitch
in its rep, so be sure to understand the Pitch
spec as well as its rep and abstraction function.
Using the MIDI sequence player and Pitch
, we’re ready to write code for our first bit of music!
Read and understand the music.examples.ScaleSequence
code.
Run the main method in ScaleSequence
.
You should hear a one-octave scale!
reading exercises
Which observers could MidiSequencePlayer
use to determine what frequency an arbitrary Pitch
represents?
(missing explanation)
Pitch.transpose(int)
is a:
(missing explanation)
SequencePlayer.addNote(..)
is a:
(missing explanation)
Music data type
The Pitch
datatype is useful, but if we want to represent a whole piece of music using Pitch
objects, we should create an abstract data type to encapsulate that representation.
To start, we’ll define the Music
type with a few operations:
notes : String × Instrument → Music
(MusicLanguage.java:51) makes a new Music from a string of simplified abc notation, described below.
duration : Music → double
(Music.java:11) returns the duration, in beats, of the piece of music.
play : Music × SequencePlayer × double → void
(Music.java:18) plays the piece of music using the given sequence player.
We’ll implement duration
and play
as instance methods of Music
, so we declare them in the Music
interface.
notes
will be a static factory method; rather than put it in Music
(which we could do), we’ll put it in a separate class: MusicLanguage
will be our place for all the static methods we write to operate on Music
.
Now that we’ve chosen some operations in the spec of Music
, let’s choose a representation.
Looking at
ScaleSequence
, the first concrete variant that might jump out at us is one to capture the information in each call toaddNote
: a particular pitch on a particular instrument played for some amount of time. We’ll call this aNote
.The other basic element of music is the silence between notes:
Rest
.Finally, we need a way to glue these basic elements together into larger pieces of music. We’ll choose a tree-like structure:
Concat(m1,m2:Music)
representsm1
followed bym2
, wherem1
andm2
are any music.This tree structure turns out to be an elegant decision as we further develop our
Music
type later on. In a real design process, we might iterate on the recursive structure ofMusic
before we find the best implementation.
Here’s the datatype definition:
Music = Note(duration:double, pitch:Pitch, instrument:Instrument)
+ Rest(duration:double)
+ Concat(m1:Music, m2:Music)
Composite
Music
is an example of the composite pattern, in which we treat both single objects (primitives, e.g. Note
and Rest
) and groups of objects (composites, e.g. Concat
) the same way.
Formula
is also an example of the composite pattern.The GUI view tree relies heavily on the composite pattern: there are primitive views like
JLabel
andJTextField
that don’t have children, and composite views likeJPanel
andJScollPage
that do contain other views as children. Both implement the commonJComponent
interface.
The composite pattern gives rise to a tree data structure, with primitives at the leaves and composites at the internal nodes.
Emptiness
One last design consideration: how do we represent the empty music?
It’s always good to have a representation for nothing, and we’re certainly not going to use null
.
We could introduce an Empty
variant, but instead we’ll use a Rest
of duration 0
to represent emptiness.
Implementing basic operations
First we need to create the Note
, Rest
, and Concat
variants.
All three are straightforward to implement, starting with constructors, checkRep
, some observers, toString
, and the equality methods.
Since the
duration
operation is an instance method, each variant implementsduration
appropriately.The
play
operation is also an instance method; we’ll discuss it below under implementing the player.
And we’ll discuss the notes
operation in implementing the parser.
To avoid representation exposure, let’s add some additional static factory methods to the Music
interface:
note : double × Pitch × Instrument → Music
(MusicLanguage.java:92)
rest : double → Music
(MusicLanguage.java:100)
concat : Music × Music → Music
(MusicLanguage.java:113) is our first producer operation.
All three of them are easy to implement by constructing the appropriate variant.
reading exercises
Assume we have
import music.*;
import static music.Instrument.*;
import static music.MusicLanguage.*;
Which of the following represent a middle C followed by A above middle C?
(missing explanation)
Music notation
We will write pieces of music using a simplified version of abc notation, a text-based music format.
We’ve already been representing pitches using their familiar letters. Our simplified abc notation represents sequences of notes and rests with syntax for indicating their duration, accidental (sharp or flat), and octave.
For example:
C D E F G A B C' B A G F E D C
represents the one-octave ascending and descending C major scale we played in ScaleSequence
.
C
is middle C, and C'
is C one octave above middle C.
Each note is a quarter note.
C/2 D/2 _E/2 F/2 G/2 _A/2 _B/2 C'
is the ascending scale in C minor, played twice as fast.
The E, A, and B are flat.
Each note is an eighth note.
Read and understand the specification of notes
in MusicLanguage
.
You don’t need to understand the parser implementation yet, but you should understand the simplified abc notation enough to make sense of the examples.
If you’re not familiar with music theory — why is an octave 8 notes but only 12 semitones? — don’t worry. You might not be able to look at the abc strings and guess what they sound like, but you can understand the point of choosing a convenient textual syntax.
reading exercises
Which of these notes are twice as long as E/4
?
(missing explanation)
Implementing the parser
The notes
method parses strings of simplified abc notation into Music
.
notes : String × Instrument → Music
(MusicLanguage.java:51) splits the input into individual symbols (e.g. A,,/2
, .1/2
).
We start with the empty Music
, rest(0)
, symbols are parsed individually, and we build up the Music
using concat
.
parseSymbol : String × Instrument → Music
(MusicLanguage.java:62) returns a Rest
or a Note
for a single abc symbol (symbol
in the grammar).
It only parses the type (rest or note) and duration; it relies on parsePitch
to handle pitch letters, accidentals, and octaves.
parsePitch : String → Pitch
(MusicLanguage.java:77) returns a Pitch
by parsing a pitch
grammar production.
You should be able to understand the recursion — what’s the base case? What are the recursive cases?
reading exercises
Which of these inputs is handled by the base case of parsePitch
?
(missing explanation)
Implementing the player
Recall our operation for playing music:
play : Music × SequencePlayer × double → void
(Music.java:18) plays the piece of music using the given sequence player after the given number of beats delay.
Why does this operation take atBeat
?
Why not simply play the music now?
If we define play
in that way, we won’t be able to play sequences of notes over time unless we actually pause during the play
operation, for example with Thread.sleep
.
Our sequence player’s addNote
operation is already designed to schedule notes in the future — it handles the delay.
With that design decision, it’s straightforward to implement play
in every variant of Music
.
Read and understand the Note.play
, Rest.play
, and Concat.play
methods.
You should be able to follow their recursive implementations.
Just one more piece of utility code before we’re ready to jam: music.midi.MusicPlayer
plays a Music
using the MidiSequencePlayer
.
Music
doesn’t know about the concrete type of the sequence player, so we need a bit of code to bring them together.
Bringing this all together, let’s use the Music
ADT:
Read and understand the music.examples.ScaleMusic
code.
Run the main method in ScaleMusic
.
You should hear the same one-octave scale again.
That’s not very exciting, so read music.examples.RowYourBoatInitial
and run the main method.
You should hear Row, row, row your boat!
Can you follow the flow of the code from calling notes(..)
to having an instance of Music
to the recursive play(..)
call to individual addNote(..)
calls?
reading exercises
There are 27 notes in Row, row, row your boat.
Given the actual implementation, how many Music
objects will be created by the notes
call in RowYourBoatInitial
?
(missing explanation)
What should be the result of rowYourBoat.duration()
?
(missing explanation)
Assume we have
import music.*;
import static music.Instrument.*;
import static music.MusicLanguage.*;
And
Music r = rest(1);
Pitch p = new Pitch('A').transpose(6);
Music n = note(1, p, GLOCKENSPIEL);
List<Music> s = Arrays.asList(r, n);
Which of the following is a valid Music
?
(missing explanation)
To be continued
Playing Row, row, row your boat is pretty exciting, but so far the most powerful thing we’ve done is not so much the music language as it is the very basic music parser.
Writing music using the simplified abc notation is clearly much more easy to understand, safe from bugs, and ready for change than writing page after page of addNote
addNote
addNote
…
In class, we’ll expand our music language and turn it into a powerful tool for constructing and manipulating complex musical structures.