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\documentclass{article}
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\usepackage{../langs}
\usepackage{tikz}
\usepackage{pgf}
\usepackage{marvosym}
\usepackage{boxedminipage}
%cheat sheet
%http://worldline.github.io/scala-cheatsheet/
% case class, apply, unapply
% see https://medium.com/@thejasbabu/scala-pattern-matching-9c9e73ba9a8a
% the art of programming
% https://www.youtube.com/watch?v=QdVFvsCWXrA
% functional programming in Scala
%https://www.amazon.com/gp/product/1449311032/ref=as_li_ss_tl?ie=UTF8&tag=aleottshompag-20&linkCode=as2&camp=1789&creative=390957&creativeASIN=1449311032
% functional programming in C
%https://www.amazon.com/gp/product/0201419505/ref=as_li_ss_tl?ie=UTF8&camp=1789&creative=390957&creativeASIN=0201419505&linkCode=as2&tag=aleottshompag-20
%speeding through haskell
%https://openlibra.com/en/book/download/speeding-through-haskell
% fp books --- ocaml
% http://courses.cms.caltech.edu/cs134/cs134b/book.pdf
% http://alexott.net/en/fp/books/
%John Hughes’ simple words:
%A combinator is a function which builds program fragments
%from program fragments.
%explain graph coloring program (examples from)
%https://www.metalevel.at/prolog/optimization
% nice example for map and reduce using Harry potter characters
% https://www.matthewgerstman.com/map-filter-reduce/
\begin{document}
\fnote{\copyright{} Christian Urban, King's College London, 2017, 2018, 2019}
\section*{A Crash-Course in Scala}
\mbox{}\hfill\textit{``Scala --- \underline{S}lowly \underline{c}ompiled
\underline{a}cademic \underline{la}nguage''}\smallskip\\
\mbox{}\hfill\textit{ --- a joke(?) found on Twitter}\bigskip
\subsection*{Introduction}
\noindent
Scala is a programming language that combines functional and
object-oriented programming-styles. It has received quite a bit of
attention in the last five or so years. One reason for this attention is
that, like the Java programming language, Scala compiles to the Java
Virtual Machine (JVM) and therefore Scala programs can run under MacOSX,
Linux and Windows. Because of this it has also access to
the myriads of Java libraries. Unlike Java, however, Scala often allows
programmers to write very concise and elegant code. Some therefore say
``Scala is the better Java''.\footnote{from
\url{https://www.slideshare.net/maximnovak/joy-of-scala}}
A number of companies---the Guardian, Twitter, Coursera, FourSquare,
Netflix, LinkedIn, ITV to name a few---either use Scala exclusively in
production code, or at least to some substantial degree. Scala seems
also useful in job-interviews (especially in data science) according to
this anecdotal report
\begin{quote}
\url{http://techcrunch.com/2016/06/14/scala-is-the-new-golden-child}
\end{quote}
\noindent
The official Scala compiler can be downloaded from
\begin{quote}
\url{http://www.scala-lang.org}\medskip
\end{quote}
\noindent
If you are interested, there are also experimental backends of Scala
for producing code under Android (\url{http://scala-android.org}); for
generating JavaScript code (\url{https://www.scala-js.org}); and there
is work under way to have a native Scala compiler generating X86-code
(\url{http://www.scala-native.org}). Though be warned these backends
are still rather beta or even alpha.
\subsection*{VS Code and Scala}
I found a convenient IDE for writing Scala programs is Microsoft's
\textit{Visual Studio Code} (VS Code) which runs under MacOSX, Linux and
obviously Windows.\footnote{\ldots{}unlike \emph{Microsoft Visual Studio}---note
the minuscule difference in the name---which is a heavy-duty,
Windows-only IDE\ldots{}jeez, with all their money could they not have come
up with a completely different name for a complete different project?
For the pedantic, Microsoft Visual Studio is an IDE, whereas Visual
Studio Code is considered to be a \emph{source code editor}. Anybody knows what the
difference is?} It can be downloaded for free from
\begin{quote}
\url{https://code.visualstudio.com}
\end{quote}
\noindent
and should already come pre-installed in the Department (together with
the Scala compiler). Being a project that just started in 2015, VS Code is
relatively new and thus far from perfect. However it includes a
\textit{Marketplace} from which a multitude of extensions can be
downloaded that make editing and running Scala code a little easier (see
Figure~\ref{vscode} for my setup).
\begin{figure}[t]
\begin{boxedminipage}{\textwidth}
\begin{center}
\includegraphics[scale=0.15]{../pics/vscode.png}\\[-10mm]\mbox{}
\end{center}
\caption{My installation of VS Code includes the following
packages from Marketplace: \textbf{Scala Syntax (official)} 0.3.4,
\textbf{Code Runner} 0.9.12, \textbf{Code Spell Checker} 1.7.17,
\textbf{Rewrap} 1.9.1 and \textbf{Subtle Match
Brackets} 3.0.0. I have also bound the keys \keys{Ctrl} \keys{Ret} to the
action ``Run-Selected-Text-In-Active-Terminal'' in order to quickly
evaluate small code snippets in the Scala REPL. I use the internal
terminal to run Scala.\label{vscode}}
\end{boxedminipage}
\end{figure}
What I like most about VS Code is that it provides easy access to the
Scala REPL. But if you prefer another editor for coding, it is also
painless to work with Scala completely on the command line (as you might
have done with \texttt{g++} in the earlier part of PEP). For the
lazybones among us, there are even online editors and environments for
developing and running Scala programs: \textit{ScalaFiddle}
and \textit{Scastie} are two of them. They require zero setup
(assuming you have a browser handy). You can access them at
\begin{quote}
\url{https://scalafiddle.io}\\
\url{https://scastie.scala-lang.org}\medskip
\end{quote}
\noindent
But you should be careful if you use them for your coursework: they
are meant to play around, not really for serious work.
As one might expect, Scala can be used with the heavy-duty IDEs Eclipse and IntelliJ.
A ready-made Scala bundle for Eclipse is available from
\begin{quote}
\url{http://scala-ide.org/download/sdk.html}
\end{quote}
\noindent
Also IntelliJ includes plugins for Scala. \underline{\textbf{BUT}},
I do \textbf{not} recommend the usage of either Eclipse or IntelliJ for PEP: these IDEs
seem to make your life harder, rather than easier, for the small
programs that we will write in this module. They are really meant to be used
when you have a million-lines codebase than with our small
``toy-programs''\ldots{}for example why on earth am I required to create a
completely new project with several subdirectories when I just want to
try out 20-lines of Scala code? Your mileage may vary though.~\texttt{;o)}
\subsection*{Why Functional Programming?}
Before we go on, let me explain a bit more why we want to inflict upon
you another programming language. You hopefully have mastered Java and
C++\ldots{}the world should be your oyster, no? Well, this is not as
simple as one might wish. We do require Scala in PEP, but actually we
do not religiously care whether you learn Scala---after all it is just
a programming language (albeit a nifty one IMHO). What we do care
about is that you learn about \textit{functional programming}. Scala
is just the vehicle for that. Still, you need to learn Scala well
enough to get good marks in PEP, but functional programming could
equally be taught with Haskell, F\#, SML, Ocaml, Kotlin, Clojure,
Scheme, Elm and many other functional programming languages.
%Your
%friendly lecturer just happens to like Scala
%and the Department agreed that it is a good idea to inflict Scala upon
%you.
Very likely writing programs in a functional programming language is
quite different from what you are used to in your study so far. It
might even be totally alien to you. The reason is that functional
programming seems to go against the core principles of
\textit{imperative programming} (which is what you do in Java and C/C++
for example). The main idea of imperative programming is that you have
some form of \emph{state} in your program and you continuously change this
state by issuing some commands---for example for updating a field in an
array or for adding one to a variable and so on. The classic
example for this style of programming is \texttt{for}-loops in C/C++. Consider
the snippet:
\begin{lstlisting}[language=C,numbers=none]
for (int i = 10; i < 20; i++) {
//...do something with i...
}
\end{lstlisting}
\noindent Here the integer variable \texttt{i} embodies the state, which
is first set to \texttt{10} and then increased by one in each
loop-iteration until it reaches \texttt{20} at which point the loop
exits. When this code is compiled and actually runs, there will be some
dedicated space reserved for \texttt{i} in memory. This space of
typically 32 bits contains \texttt{i}'s current value\ldots\texttt{10}
at the beginning, and then the content will be overwritten with
new content in every iteration. The main point here is that this kind of
updating, or manipulating, memory is 25.806\ldots or \textbf{THE ROOT OF
ALL EVIL}!!
\begin{center}
\includegraphics[scale=0.25]{../pics/root-of-all-evil.png}
\end{center}
\noindent
\ldots{}Well, it is perfectly benign if you have a sequential program
that gets run instruction by instruction...nicely one after another.
This kind of running code uses a single core of your CPU and goes as
fast as your CPU frequency, also called clock-speed, allows. The problem
is that this clock-speed has not much increased over the past decade and
no dramatic increases are predicted for any time soon. So you are a bit
stuck, unlike previous generations of developers who could rely upon the
fact that every 2 years or so their code would run twice as fast (in
ideal circumstances) because the clock-speed of their CPUs got twice as
fast. This unfortunately does not happen any more nowadays. To get you
out of this dreadful situation, CPU producers pile more and more
cores into CPUs in order to make them more powerful and potentially make
software faster. The task for you as developer is to take somehow
advantage of these cores by running as much of your code as possible in
parallel on as many cores you have available (typically 4 in modern
laptops and sometimes much more on high-end machines). In this
situation, \textit{mutable} variables like \texttt{i} above are evil, or
at least a major nuisance: Because if you want to distribute some of the
loop-iterations over the cores that are currently idle in your system,
you need to be extremely careful about who can read and overwrite
the variable \texttt{i}.\footnote{If you are of the mistaken belief that nothing
nasty can happen to \texttt{i} inside the \texttt{for}-loop, then you
need to go back over the C++ material.} Especially the writing operation
is critical because you do not want that conflicting writes mess about
with \texttt{i}. Take my word: an untold amount of misery has arisen
from this problem. The catch is that if you try to solve this problem in
C/C++ or Java, and be as defensive as possible about reads and writes to
\texttt{i}, then you need to synchronise access to it. The result is that
very often your program waits more than it runs, thereby
defeating the point of trying to run the program in parallel in the
first place. If you are less defensive, then usually all hell breaks
loose by seemingly obtaining random results. And forget the idea of
being able to debug such code.
The central idea of functional programming is to eliminate any state
from programs---or at least from the ``interesting bits'' of the
programs. Because then it is easy to parallelise the resulting
programs: if you do not have any state, then once created, all memory
content stays unchanged and reads to such memory are absolutely safe
without the need of any synchronisation. An example is given in
Figure~\ref{mand} where in the absence of the annoying state, Scala
makes it very easy to calculate the Mandelbrot set on as many cores of
your CPU as possible. Why is it so easy in this example? Because each
pixel in the Mandelbrot set can be calculated independently and the
calculation does not need to update any variable. It is so easy in
fact that going from the sequential version of the Mandelbrot program
to the parallel version can be achieved by adding just eight
characters---in two places you have to add \texttt{.par}. Try the same
in C/C++ or Java!
\begin{figure}[p]
\begin{boxedminipage}{\textwidth}
A Scala program for generating pretty pictures of the Mandelbrot set.\smallskip\\
(See \url{https://en.wikipedia.org/wiki/Mandelbrot_set} or\\
\phantom{(See }\url{https://www.youtube.com/watch?v=aSg2Db3jF_4}):
\begin{center}
\begin{tabular}{c}
\includegraphics[scale=0.11]{../pics/mand1.png}\\[-8mm]\mbox{}
\end{tabular}
\end{center}
\begin{center}
\begin{tabular}{@{}p{0.45\textwidth}|p{0.45\textwidth}@{}}
\bf sequential version: & \bf parallel version on 4 cores:\smallskip\\
{\hfill\includegraphics[scale=0.11]{../pics/mand4.png}\hfill} &
{\hfill\includegraphics[scale=0.11]{../pics/mand3.png}\hfill} \\
{\footnotesize\begin{lstlisting}[xleftmargin=-1mm]
for (y <- (0 until H)) {
for (x <- (0 until W)) {
val c = start +
(x * d_x + y * d_y * i)
val iters = iterations(c, max)
val colour =
if (iters == max) black
else colours(iters % 16)
pixel(x, y, colour)
}
viewer.updateUI()
}
\end{lstlisting}}
&
{\footnotesize\begin{lstlisting}[xleftmargin=0mm]
for (y <- (0 until H)/*@\keys{\texttt{.par}}@*/) {
for (x <- (0 until W)/*@\keys{\texttt{.par}}@*/) {
val c = start +
(x * d_x + y * d_y * i)
val iters = iterations(c, max)
val colour =
if (iters == max) black
else colours(iters % 16)
pixel(x, y, colour)
}
viewer.updateUI()
}
\end{lstlisting}}\\[-2mm]
\centering\includegraphics[scale=0.5]{../pics/cpu2.png} &
\centering\includegraphics[scale=0.5]{../pics/cpu1.png}
\end{tabular}
\end{center}
\caption{The code of the ``main'' loops in my version of the mandelbrot program.
The parallel version differs only in \texttt{.par} being added to the
``ranges'' of the x and y coordinates. As can be seen from the CPU loads, in
the sequential version there is a lower peak for an extended period,
while in the parallel version there is a short sharp burst for
essentially the same workload\ldots{}meaning you get more work done
in a shorter amount of time. This easy \emph{parallelisation}
only works reliably with an immutable program.
\label{mand}}
\end{boxedminipage}
\end{figure}
But remember this easy parallelisation of code requires that we
have no state in our programs\ldots{}that is no counters like
\texttt{i} in \texttt{for}-loops. You might then ask, how do I write
loops without such counters? Well, teaching you that this is possible is
one of the main points of the Scala-part in PEP. I can assure you it is
possible, but you have to get your head around it. Once you have
mastered this, it will be fun to have no state in your programs (a side
product is that it much easier to debug state-less code and also more
often than not easier to understand). So have fun with
Scala!\footnote{If you are still not convinced about the function
programming ``thing'', there are a few more arguments: a lot of research
in programming languages happens to take place in functional programming
languages. This has resulted in ultra-useful features such as
pattern-matching, strong type-systems, laziness, implicits, algebraic
datatypes to name a few. Imperative languages seem to often lag behind
in adopting them: I know, for example, that Java will at some point in
the future support pattern-matching, which has been used for example
in SML for at
least 40(!) years. See
\url{http://cr.openjdk.java.net/~briangoetz/amber/pattern-match.html}.
Also Rust, a C-like programming language that has been developed since
2010 and is gaining quite some interest, borrows many ideas from
functional programming from yesteryear.}
\subsection*{The Very Basics}
One advantage of Scala over Java is that it includes an interpreter (a
REPL, or
\underline{R}ead-\underline{E}val-\underline{P}rint-\underline{L}oop)
with which you can run and test small code snippets without the need
of a compiler. This helps a lot with interactively developing
programs. It is my preferred way of writing small Scala
programs. Once you installed Scala, you can start the interpreter by
typing on the command line:
\begin{lstlisting}[language={},numbers=none,basicstyle=\ttfamily\small]
$ scala
Welcome to Scala 2.13.0 (Java HotSpot(TM) 64-Bit Server VM, Java 9).
Type in expressions for evaluation. Or try :help.
scala>
\end{lstlisting}%$
\noindent The precise response may vary depending
on the version and platform where you installed Scala. At the Scala
prompt you can type things like \code{2 + 3}\;\keys{Ret} and
the output will be
\begin{lstlisting}[numbers=none]
scala> 2 + 3
res0: Int = 5
\end{lstlisting}
\noindent The answer means that he result of the addition is of type
\code{Int} and the actual result is 5; \code{res0} is a name that
Scala gives automatically to the result. You can reuse this name later
on, for example
\begin{lstlisting}[numbers=none]
scala> res0 + 4
res1: Int = 9
\end{lstlisting}
\noindent
Another classic example you can try out is
\begin{lstlisting}[numbers=none]
scala> print("hello world")
hello world
\end{lstlisting}
\noindent Note that in this case there is no result. The
reason is that \code{print} does not actually produce a result
(there is no \code{resX} and no type), rather it is a
function that causes the \emph{side-effect} of printing out a
string. Once you are more familiar with the functional
programming-style, you will know what the difference is
between a function that returns a result, like addition, and a
function that causes a side-effect, like \code{print}. We
shall come back to this point later, but if you are curious
now, the latter kind of functions always has \code{Unit} as
return type. It is just not printed by Scala.
You can try more examples with the Scala REPL, but feel free to
first guess what the result is (not all answers by Scala are obvious):
\begin{lstlisting}[numbers=none]
scala> 2 + 2
scala> 1 / 2
scala> 1.0 / 2
scala> 1 / 2.0
scala> 1 / 0
scala> 1.0 / 0.0
scala> true == false
scala> true && false
scala> 1 > 1.0
scala> "12345".length
scala> List(1,2,1).size
scala> Set(1,2,1).size
scala> List(1) == List(1)
scala> Array(1) == Array(1)
scala> Array(1).sameElements(Array(1))
\end{lstlisting}\smallskip
\noindent
Please take the Scala REPL seriously: If you want to take advantage of my
reference implementation for the assignments, you will need to be
able to ``play around'' with it!
\subsection*{Standalone Scala Apps}
If you want to write a stand-alone app in Scala, you can
implement an object that is an instance of \code{App}. For example
write
\begin{lstlisting}[numbers=none]
object Hello extends App {
println("hello world")
}
\end{lstlisting}
\noindent save it in a file, say {\tt hello-world.scala}, and
then run the compiler (\texttt{scalac}) and start the runtime
environment (\texttt{scala}):
\begin{lstlisting}[language={},numbers=none,basicstyle=\ttfamily\small]
$ scalac hello-world.scala
$ scala Hello
hello world
\end{lstlisting}
\noindent
Like Java, Scala targets the JVM and consequently
Scala programs can also be executed by the bog-standard Java
Runtime. This only requires the inclusion of {\tt
scala-library.jar}, which on my computer can be done as
follows:
\begin{lstlisting}[language={},numbers=none,basicstyle=\ttfamily\small]
$ scalac hello-world.scala
$ java -cp /usr/local/src/scala/lib/scala-library.jar:. Hello
hello world
\end{lstlisting}
\noindent You might need to adapt the path to where you have
installed Scala.
\subsection*{Values}
In the lectures I will try to avoid as much as possible the term
\emph{variables} familiar from other programming languages. The reason
is that Scala has \emph{values}, which can be seen as abbreviations of
larger expressions. The keyword for defining values is \code{val}.
For example
\begin{lstlisting}[numbers=none]
scala> val x = 42
x: Int = 42
scala> val y = 3 + 4
y: Int = 7
scala> val z = x / y
z: Int = 6
\end{lstlisting}
\noindent
As can be seen, we first define \code{x} and {y} with admittedly some silly
expressions, and then reuse these values in the definition of \code{z}.
All easy, right? Why the kerfuffle about values? Well, values are
\emph{immutable}. You cannot change their value after you defined them.
If you try to reassign \code{z} above, Scala will yell at you:
\begin{lstlisting}[numbers=none]
scala> z = 9
error: reassignment to val
z = 9
^
\end{lstlisting}
\noindent
So it would be a bit absurd to call values as variables...you cannot
change them; they cannot vary. You might think you can reassign them like
\begin{lstlisting}[numbers=none]
scala> val x = 42
scala> val z = x / 7
scala> val x = 70
scala> println(z)
\end{lstlisting}
\noindent but try to guess what Scala will print out
for \code{z}? Will it be \code{6} or \code{10}? A final word about
values: Try to stick to the convention that names of values should be
lower case, like \code{x}, \code{y}, \code{foo41} and so on. Upper-case
names you should reserve for what is called \emph{constructors}. And
forgive me when I call values as variables\ldots{}it is just something that
has been in imprinted into my developer-DNA during my early days and
is difficult to get rid of.~\texttt{;o)}
\subsection*{Function Definitions}
We do functional programming! So defining functions will be our main occupation.
As an example, a function named \code{f} taking a single argument of type
\code{Int} can be defined in Scala as follows:
\begin{lstlisting}[numbers=none]
def f(x: Int) : String = ...EXPR...
\end{lstlisting}
\noindent
This function returns the value resulting from evaluating the expression
\code{EXPR} (whatever is substituted for this). Since we declared
\code{String}, the result of this function will be of type
\code{String}. It is a good habit to always include this information
about the return type, while it is only strictly necessary to give this
type in recursive functions. Simple examples of Scala functions are:
\begin{lstlisting}[numbers=none]
def incr(x: Int) : Int = x + 1
def double(x: Int) : Int = x + x
def square(x: Int) : Int = x * x
\end{lstlisting}
\noindent
The general scheme for a function is
\begin{lstlisting}[numbers=none]
def fname(arg1: ty1, arg2: ty2,..., argn: tyn): rty = {
...BODY...
}
\end{lstlisting}
\noindent
where each argument, \texttt{arg1}, \texttt{arg2} and so on, requires
its type and the result type of the
function, \code{rty}, should also be given. If the body of the function is
more complex, then it can be enclosed in braces, like above. If it it
is just a simple expression, like \code{x + 1}, you can omit the
braces. Very often functions are recursive (that is call themselves),
like the venerable factorial function:
\begin{lstlisting}[numbers=none]
def fact(n: Int) : Int =
if (n == 0) 1 else n * fact(n - 1)
\end{lstlisting}
\noindent
We could also have written this with braces as
\begin{lstlisting}[numbers=none]
def fact(n: Int) : Int = {
if (n == 0) 1
else n * fact(n - 1)
}
\end{lstlisting}
\noindent
but this seems a bit overkill for a small function like \code{fact}.
Note that Scala does not have a \code{then}-keyword in an \code{if}-statement.
Note also that there are a few other ways of how to define a function. We
will see some of them in the next sections.
Before we go on, let me explain one tricky point in function
definitions, especially in larger definitions. What does a Scala function
actually return? Scala has a \code{return} keyword, but it is
used for something different than in Java (and C/C++). Therefore please
make sure no \code{return} slips into your Scala code.
So in the absence of \code{return}, what value does a Scala function
actually produce? A rule-of-thumb is whatever is in the last line of the
function is the value that will be returned. Consider the following
example:\footnote{We could have written this function in just one line,
but for the sake of argument lets keep the two intermediate values.}
\begin{lstlisting}[numbers=none]
def iaverage(xs: List[Int]) : Int = {
val s = xs.sum
val n = xs.length
s / n
}
\end{lstlisting}
\noindent In this example the expression \code{s / n} is in the last
line of the function---so this will be the result the function
calculates. The two lines before just calculate intermediate values.
This principle of the `last-line' comes in handy when you need to print
out values, for example, for debugging purposes. Suppose you want
rewrite the function as
\begin{lstlisting}[numbers=none]
def iaverage(xs: List[Int]) : Int = {
val s = xs.sum
val n = xs.length
val h = xs.head
println(s"Input $xs with first element $h")
s / n
}
\end{lstlisting}
\noindent
Here the function still only returns the expression in the last line.
The \code{println} before just prints out some information about the
input of this function, but does not contribute to the result of the
function. Similarly, the value \code{h} is used in the \code{println}
but does not contribute to what integer is returned. However note that
the idea with the ``last line'' is only a rough rule-of-thumb. A better
rule is probably, the last expression that is evaluated in the function.
Consider the following version of \code{iaverage}:
\begin{lstlisting}[numbers=none]
def iaverage(xs: List[Int]) : Int = {
if (xs.length == 0) 0
else xs.sum / xs.length
}
\end{lstlisting}
\noindent
What does this function return? Well are two possibilities: either the
result of \code{xs.sum / xs.length} in the last line provided the list
\code{xs} is nonempty, \textbf{or} if the list is empty, then it will
return \code{0} from the \code{if}-branch (which is technically not the
last line, but the last expression evaluated by the function in the
empty-case).
Summing up, do not use \code{return} in your Scala code! A function
returns what is evaluated by the function as the last expression. There
is always only one such last expression. Previous expressions might
calculate intermediate values, but they are not returned.
\subsection*{Loops, or better the Absence thereof}
Coming from Java or C/C++, you might be surprised that Scala does
not really have loops. It has instead, what is in functional
programming called, \emph{maps}. To illustrate how they work,
let us assume you have a list of numbers from 1 to 8 and want to
build the list of squares. The list of numbers from 1 to 8
can be constructed in Scala as follows:
\begin{lstlisting}[numbers=none]
scala> (1 to 8).toList
res1: List[Int] = List(1, 2, 3, 4, 5, 6, 7, 8)
\end{lstlisting}
\noindent Generating from this list the list of corresponding
squares in a programming language such as Java, you would assume
the list is given as a kind of array. You would then iterate, or loop,
an index over this array and replace each entry in the array
by the square. Right? In Scala, and in other functional
programming languages, you use maps to achieve the same.
A map essentially takes a function that describes how each element is
transformed (in this example the function is $n \rightarrow n * n$) and
a list over which this function should work. Pictorially you can think
of the idea behind maps as follows:
\begin{center}
\begin{tikzpicture}
\node (A0) at (1.2,0) {\texttt{List(}};
\node (A1) at (2.0,0) {\texttt{1\makebox[0mm]{ ,}}};
\node (A2) at (2.9,0) {\texttt{2\makebox[0mm]{ ,}}};
\node (A3) at (3.8,0) {\texttt{3\makebox[0mm]{ ,}}};
\node (A4) at (4.7,0) {\texttt{4\makebox[0mm]{ ,}}};
\node (A5) at (5.6,0) {\texttt{5\makebox[0mm]{ ,}}};
\node (A6) at (6.5,0) {\texttt{6\makebox[0mm]{ ,}}};
\node (A7) at (7.4,0) {\texttt{7\makebox[0mm]{ ,}}};
\node (A8) at (8.3,0) {\texttt{8)}};
\node (B0) at (1.2,-3) {\texttt{List(}};
\node (B1) at (2.0,-3) {\texttt{1\makebox[0mm]{ ,}}};
\node (B2) at (3.0,-3) {\texttt{4\makebox[0mm]{ ,}}};
\node (B3) at (4.1,-3) {\texttt{9\makebox[0mm]{ ,}}};
\node (B4) at (5.2,-3) {\texttt{16\makebox[0mm]{ ,}}};
\node (B5) at (6.3,-3) {\texttt{25\makebox[0mm]{ ,}}};
\node (B6) at (7.4,-3) {\texttt{36\makebox[0mm]{ ,}}};
\node (B7) at (8.4,-3) {\texttt{49\makebox[0mm]{ ,}}};
\node (B8) at (9.4,-3) {\texttt{64\makebox[0mm]{ )}}};
\draw [->,line width=1mm] (A1.south) -- (B1.north);
\draw [->,line width=1mm] (A2.south) -- (B2.north);
\draw [->,line width=1mm] (A3.south) -- (B3.north);
\draw [->,line width=1mm] (A4.south) -- (B4.north);
\draw [->,line width=1mm] (A5.south) -- (B5.north);
\draw [->,line width=1mm] (A6.south) -- (B6.north);
\draw [->,line width=1mm] (A7.south) -- (B7.north);
\draw [->,line width=1mm] (A8.south) -- (B8.north);
\node [red] (Q0) at (-0.3,0) {\large\texttt{n}};
\node (Q1) at (-0.3,-0.1) {};
\node (Q2) at (-0.3,-2.8) {};
\node [red] (Q3) at (-0.3,-2.95) {\large\texttt{n\,*\,n}};
\draw [->,red,line width=1mm] (Q1.south) -- (Q2.north);
\node [red] at (-1.3,-1.5) {\huge{}\it\textbf{map}};
\end{tikzpicture}
\end{center}
\noindent
On top is the ``input'' list we want to transform; on the left is the
``map'' function for how to transform each element in the input list
(the square function in this case); at the bottom is the result list of
the map. This means that a map produces a \emph{new} list as a result,
unlike a for-loop in Java or C/C++ which would most likely update the list
exists in memory after the map.
Now there are two ways to express such maps in Scala. The first way is
called a \emph{for-comprehension}. The keywords are \code{for} and
\code{yield}. Squaring the numbers from 1 to 8 with a for-comprehension
would look as follows:
\begin{lstlisting}[numbers=none]
scala> for (n <- (1 to 8).toList) yield n * n
res2: List[Int] = List(1, 4, 9, 16, 25, 36, 49, 64)
\end{lstlisting}
\noindent This for-comprehension states that from the list of numbers
we draw elements that are given the name \code{n} (which can be
arbitrary, not just \code{n}) and compute the result of \code{n * n}.
This way of writing a map resembles a bit the for-loops from imperative
languages, even though the idea behind for-loops and for-comprehensions
is quite different. Also, this is a simple example---what comes after
\code{yield} can be a complex expression enclosed in \texttt{\{...\}}.
An example might be
\begin{lstlisting}[numbers=none]
scala> for (n <- (1 to 8).toList) yield {
val i = n + 1
val j = n - 1
i * j
}
res3: List[Int] = List(0, 3, 8, 15, 24, 35, 48, 63)
\end{lstlisting}
As you can see in for-comprehensions above, we specified the list where
each \code{n} comes from, namely \code{(1 to 8).toList}, and how each
element needs to be transformed. This can also be expressed in a second
way in Scala by using directly the function \code{map} as follows:
\begin{lstlisting}[numbers=none]
scala> (1 to 8).toList.map(n => n * n)
res3 = List(1, 4, 9, 16, 25, 36, 49, 64)
\end{lstlisting}
\noindent In this way, the expression \code{n => n * n} stands for the
function that calculates the square (this is how the \code{n}s are
transformed by the map). It might not be obvious, but
for-comprehensions above are just syntactic sugar: when compiling, Scala
translates for-comprehensions into equivalent maps. This even works when
for-comprehensions get more complicated (see below).
The very charming feature of Scala is that such maps or
for-comprehensions can be written for any kind of data collection, such
as lists, sets, vectors, options and so on. For example if we instead
compute the remainders modulo 3 of this list, we can write
\begin{lstlisting}[numbers=none]
scala> (1 to 8).toList.map(n => n % 3)
res4 = List(1, 2, 0, 1, 2, 0, 1, 2)
\end{lstlisting}
\noindent If we, however, transform the numbers 1 to 8 not
into a list, but into a set, and then compute the remainders
modulo 3 we obtain
\begin{lstlisting}[numbers=none]
scala> (1 to 8).toSet[Int].map(n => n % 3)
res5 = Set(2, 1, 0)
\end{lstlisting}
\noindent This is the correct result for sets, as there are
only three equivalence classes of integers modulo 3. Note that
in this example we need to ``help'' Scala to transform the
numbers into a set of integers by explicitly annotating the
type \code{Int}. Since maps and for-comprehensions are
just syntactic variants of each other, the latter can also be
written as
\begin{lstlisting}[numbers=none]
scala> for (n <- (1 to 8).toSet[Int]) yield n % 3
res5 = Set(2, 1, 0)
\end{lstlisting}
For-comprehensions can also be nested and the selection of
elements can be guarded. For example if we want to pair up
the numbers 1 to 4 with the letters a to c, we can write
\begin{lstlisting}[numbers=none]
scala> for (n <- (1 to 4).toList;
m <- ('a' to 'c').toList) yield (n, m)
res6 = List((1,a), (1,b), (1,c), (2,a), (2,b), (2,c),
(3,a), (3,b), (3,c), (4,a), (4,b), (4,c))
\end{lstlisting}
\noindent
In this example the for-comprehension ranges over two lists, and
produces a list of pairs as output. Or if we want to find all pairs of
numbers between 1 and 3 where the sum is an even number, we can write
\begin{lstlisting}[numbers=none]
scala> for (n <- (1 to 3).toList;
m <- (1 to 3).toList;
if (n + m) % 2 == 0) yield (n, m)
res7 = List((1,1), (1,3), (2,2), (3,1), (3,3))
\end{lstlisting}
\noindent The \code{if}-condition in this for-comprehension filters out
all pairs where the sum is not even (therefore \code{(1, 2)} is not in
the result because the sum is odd).
To sum up, maps (or for-comprehensions) transform one collection into
another. For example a list of \code{Int}s into a list of squares, or a
list of \code{Int}s into a set of \code{Int}s and so on. There is no need
for for-loops in Scala. But please do not be tempted to write anything like
\begin{lstlisting}[numbers=none]
scala> val cs = ('a' to 'h').toList
scala> for (n <- (0 until cs.length).toList)
yield cs(n).capitalize
res8: List[Char] = List(A, B, C, D, E, F, G, H)
\end{lstlisting}
\noindent
This is accepted Scala-code, but utterly bad style. It can be written
much clearer as:
\begin{lstlisting}[numbers=none]
scala> val cs = ('a' to 'h').toList
scala> for (c <- cs) yield c.capitalize
res9: List[Char] = List(A, B, C, D, E, F, G, H)
\end{lstlisting}
\subsection*{Results and Side-Effects}
While hopefully this all about maps looks reasonable, there is one
complication: In the examples above we always wanted to
transform one list into another list (e.g.~list of squares),
or one set into another set (set of numbers into set of
remainders modulo 3). What happens if we just want to print out
a list of integers? Then actually the for-comprehension
needs to be modified. The reason is that \code{print}, you
guessed it, does not produce any result, but only produces
what is in the functional-programming-lingo called a
\emph{side-effect}. Printing out the list of numbers from 1 to 5
would look as follows
\begin{lstlisting}[numbers=none]
scala> for (n <- (1 to 5).toList) print(n)
12345
\end{lstlisting}
\noindent
where you need to omit the keyword \code{yield}. You can
also do more elaborate calculations such as
\begin{lstlisting}[numbers=none]
scala> for (n <- (1 to 5).toList) {
val square = n * n
println(s"$n * $n = $square")
}
1 * 1 = 1
2 * 2 = 4
3 * 3 = 9
4 * 4 = 16
5 * 5 = 25
\end{lstlisting}%$
\noindent In this code I use a variable assignment (\code{val
square = ...} ) and also what is called in Scala a
\emph{string interpolation}, written \code{s"..."}. The latter
is for printing out an equation. It allows me to refer to the
integer values \code{n} and \code{square} inside a string.
This is very convenient for printing out ``things''.
The corresponding map construction for functions with
side-effects is in Scala called \code{foreach}. So you
could also write
\begin{lstlisting}[numbers=none]
scala> (1 to 5).toList.foreach(n => print(n))
12345
\end{lstlisting}
\noindent or even just
\begin{lstlisting}[numbers=none]
scala> (1 to 5).toList.foreach(print)
12345
\end{lstlisting}
\noindent Again I hope this reminds you a bit of your
lambda-calculus lessons, where an explanation is given why
both forms produce the same result.
If you want to find out more about maps and functions with
side-effects, you can ponder about the response Scala gives if
you replace \code{foreach} by \code{map} in the expression
above. Scala will still allow \code{map} with side-effect
functions, but then reacts with a slightly interesting result.
\subsection*{Higher-Order Functions}
\subsection*{Types}
In most functional programming languages, types play an
important role. Scala is such a language. You have already
seen built-in types, like \code{Int}, \code{Boolean},
\code{String} and \code{BigInt}, but also user-defined ones,
like \code{Rexp} (see coursework). Unfortunately, types can be a thorny
subject, especially in Scala. For example, why do we need to
give the type to \code{toSet[Int]}, but not to \code{toList}?
The reason is the power of Scala, which sometimes means it
cannot infer all necessary typing information. At the
beginning, while getting familiar with Scala, I recommend a
``play-it-by-ear-approach'' to types. Fully understanding
type-systems, especially complicated ones like in Scala, can
take a module on their own.\footnote{Still, such a study can
be a rewarding training: If you are in the business of
designing new programming languages, you will not be able to
turn a blind eye to types. They essentially help programmers
to avoid common programming errors and help with maintaining
code.}
In Scala, types are needed whenever you define an inductive
datatype and also whenever you define functions (their
arguments and their results need a type). Base types are types
that do not take any (type)arguments, for example \code{Int}
and \code{String}. Compound types take one or more arguments,
which as seen earlier need to be given in angle-brackets, for
example \code{List[Int]} or \code{Set[List[String]]} or
\code{Map[Int, Int]}.
There are a few special type-constructors that fall outside
this pattern. One is for tuples, where the type is written
with parentheses. For example
\begin{lstlisting}[ numbers=none]
(Int, Int, String)
\end{lstlisting}
\noindent is for a triple (a tuple with three components---two
integers and a string). Tuples are helpful if you want to
define functions with multiple results, say the function
returning the quotient and remainder of two numbers. For this
you might define:
\begin{lstlisting}[ numbers=none]
def quo_rem(m: Int, n: Int) : (Int, Int) = (m / n, m % n)
\end{lstlisting}
\noindent Since this function returns a pair of integers, its
return type needs to be of type \code{(Int, Int)}.
Incidentally, this is also the input type of this function.
Notice this function takes \emph{two} arguments, namely
\code{m} and \code{n}, both of which are integers. They are
``packaged'' in a pair. Consequently the complete type of
\code{quo_rem} is
\begin{lstlisting}[ numbers=none]
(Int, Int) => (Int, Int)
\end{lstlisting}
Another special type-constructor is for functions, written as
the arrow \code{=>}. For example, the type \code{Int =>
String} is for a function that takes an integer as input
argument and produces a string as result. A function of this
type is for instance
\begin{lstlisting}[numbers=none]
def mk_string(n: Int) : String = n match {
case 0 => "zero"
case 1 => "one"
case 2 => "two"
case _ => "many"
}
\end{lstlisting}
\noindent It takes an integer as input argument and returns a
string. Unlike other functional programming languages, there
is in Scala no easy way to find out the types of existing
functions, except by looking into the documentation
\begin{quote}
\url{http://www.scala-lang.org/api/current/}
\end{quote}
The function arrow can also be iterated, as in
\code{Int => String => Boolean}. This is the type for a function
taking an integer as first argument and a string as second,
and the result of the function is a boolean. Though silly, a
function of this type would be
\begin{lstlisting}[numbers=none]
def chk_string(n: Int)(s: String) : Boolean =
mk_string(n) == s
\end{lstlisting}
\noindent which checks whether the integer \code{n}
corresponds to the name \code{s} given by the function
\code{mk\_string}. Notice the unusual way of specifying the
arguments of this function: the arguments are given one after
the other, instead of being in a pair (what would be the type
of this function then?). This way of specifying the arguments
can be useful, for example in situations like this
\begin{lstlisting}[numbers=none]
scala> List("one", "two", "three", "many").map(chk_string(2))
res4 = List(false, true, false, false)
scala> List("one", "two", "three", "many").map(chk_string(3))
res5 = List(false, false, false, true)
\end{lstlisting}
\noindent In each case we can give to \code{map} a specialised
version of \code{chk_string}---once specialised to 2 and once
to 3. This kind of ``specialising'' a function is called
\emph{partial application}---we have not yet given to this
function all arguments it needs, but only some of them.
Coming back to the type \code{Int => String => Boolean}. The
rule about such function types is that the right-most type
specifies what the function returns (a boolean in this case).
The types before that specify how many arguments the function
expects and what their type is (in this case two arguments,
one of type \code{Int} and another of type \code{String}).
Given this rule, what kind of function has type
\mbox{\code{(Int => String) => Boolean}}? Well, it returns a
boolean. More interestingly, though, it only takes a single
argument (because of the parentheses). The single argument
happens to be another function (taking an integer as input and
returning a string). Remember that \code{mk_string} is just
such a function. So how can we use it? For this define
the somewhat silly function \code{apply_3}:
\begin{lstlisting}[numbers=none]
def apply_3(f: Int => String): Bool = f(3) == "many"
scala> apply_3(mk_string)
res6 = true
\end{lstlisting}
You might ask: Apart from silly functions like above, what is
the point of having functions as input arguments to other
functions? In Java there is indeed no need of this kind of
feature: at least in the past it did not allow such
constructions. I think, the point of Java 8 and successors was to lift this
restriction. But in all functional programming languages,
including Scala, it is really essential to allow functions as
input argument. Above you already seen \code{map} and
\code{foreach} which need this. Consider the functions
\code{print} and \code{println}, which both print out strings,
but the latter adds a line break. You can call \code{foreach}
with either of them and thus changing how, for example, five
numbers are printed.
\begin{lstlisting}[numbers=none]
scala> (1 to 5).toList.foreach(print)
12345
scala> (1 to 5).toList.foreach(println)
1
2
3
4
5
\end{lstlisting}
\noindent This is actually one of the main design principles
in functional programming. You have generic functions like
\code{map} and \code{foreach} that can traverse data containers,
like lists or sets. They then take a function to specify what
should be done with each element during the traversal. This
requires that the generic traversal functions can cope with
any kind of function (not just functions that, for example,
take as input an integer and produce a string like above).
This means we cannot fix the type of the generic traversal
functions, but have to keep them
\emph{polymorphic}.\footnote{Another interesting topic about
types, but we omit it here for the sake of brevity.}
There is one more type constructor that is rather special. It
is called \code{Unit}. Recall that \code{Boolean} has two
values, namely \code{true} and \code{false}. This can be used,
for example, to test something and decide whether the test
succeeds or not. In contrast the type \code{Unit} has only a
single value, written \code{()}. This seems like a completely
useless type and return value for a function, but is actually
quite useful. It indicates when the function does not return
any result. The purpose of these functions is to cause
something being written on the screen or written into a file,
for example. This is what is called they cause some effect on
the side, namely a new content displayed on the screen or some
new data in a file. Scala uses the \code{Unit} type to indicate
that a function does not have a result, but potentially causes
some side-effect. Typical examples are the printing functions,
like \code{print}.
\subsection*{User-Defined Types}
% \subsection*{Cool Stuff}
% The first wow-moment I had with Scala was when I came across
% the following code-snippet for reading a web-page.
% \begin{lstlisting}[ numbers=none]
% import io.Source
% val url = """http://www.inf.kcl.ac.uk/staff/urbanc/"""
% Source.fromURL(url)("ISO-8859-1").take(10000).mkString
% \end{lstlisting}
% \noindent These three lines return a string containing the
% HTML-code of my webpage. It actually already does something
% more sophisticated, namely only returns the first 10000
% characters of a webpage in case it is too large. Why is that
% code-snippet of any interest? Well, try implementing
% reading-from-a-webpage in Java. I also like the possibility of
% triple-quoting strings, which I have only seen in Scala so
% far. The idea behind this is that in such a string all
% characters are interpreted literally---there are no escaped
% characters, like \verb|\n| for newlines.
% My second wow-moment I had with a feature of Scala that other
% functional programming languages do not have. This feature is
% about implicit type conversions. If you have regular
% expressions and want to use them for language processing you
% often want to recognise keywords in a language, for example
% \code{for},{} \code{if},{} \code{yield} and so on. But the
% basic regular expression \code{CHAR} can only recognise a
% single character. In order to recognise a whole string, like
% \code{for}, you have to put many of those together using
% \code{SEQ}:
% \begin{lstlisting}[numbers=none]
% SEQ(CHAR('f'), SEQ(CHAR('o'), CHAR('r')))
% \end{lstlisting}
% \noindent This gets quickly unreadable when the strings and
% regular expressions get more complicated. In other functional
% programming languages, you can explicitly write a conversion
% function that takes a string, say \dq{\pcode{for}}, and
% generates the regular expression above. But then your code is
% littered with such conversion functions.
% In Scala you can do better by ``hiding'' the conversion
% functions. The keyword for doing this is \code{implicit} and
% it needs a built-in library called
% \begin{lstlisting}[numbers=none]
% scala.language.implicitConversions
% \end{lstlisting}
% \noindent
% Consider the code
% \begin{lstlisting}[language=Scala]
% import scala.language.implicitConversions
% def charlist2rexp(s: List[Char]) : Rexp = s match {
% case Nil => EMPTY
% case c::Nil => CHAR(c)
% case c::s => SEQ(CHAR(c), charlist2rexp(s))
% }
% implicit def string2rexp(s: String) : Rexp =
% charlist2rexp(s.toList)
% \end{lstlisting}
% \noindent where the first seven lines implement a function
% that given a list of characters generates the corresponding
% regular expression. In Lines 9 and 10, this function is used
% for transforming a string into a regular expression. Since the
% \code{string2rexp}-function is declared as \code{implicit},
% the effect will be that whenever Scala expects a regular
% expression, but I only give it a string, it will automatically
% insert a call to the \code{string2rexp}-function. I can now
% write for example
% \begin{lstlisting}[numbers=none]
% scala> ALT("ab", "ac")
% res9 = ALT(SEQ(CHAR(a),CHAR(b)),SEQ(CHAR(a),CHAR(c)))
% \end{lstlisting}
% \noindent Recall that \code{ALT} expects two regular
% expressions as arguments, but I only supply two strings. The
% implicit conversion function will transform the string into a
% regular expression.
% Using implicit definitions, Scala allows me to introduce
% some further syntactic sugar for regular expressions:
% \begin{lstlisting}[ numbers=none]
% implicit def RexpOps(r: Rexp) = new {
% def | (s: Rexp) = ALT(r, s)
% def ~ (s: Rexp) = SEQ(r, s)
% def % = STAR(r)
% }
% implicit def stringOps(s: String) = new {
% def | (r: Rexp) = ALT(s, r)
% def | (r: String) = ALT(s, r)
% def ~ (r: Rexp) = SEQ(s, r)
% def ~ (r: String) = SEQ(s, r)
% def % = STAR(s)
% }
% \end{lstlisting}
% \noindent This might seem a bit overly complicated, but its effect is
% that I can now write regular expressions such as $ab + ac$
% simply as
% \begin{lstlisting}[numbers=none]
% scala> "ab" | "ac"
% res10 = ALT(SEQ(CHAR(a),CHAR(b)),SEQ(CHAR(a),CHAR(c)))
% \end{lstlisting}
% \noindent I leave you to figure out what the other
% syntactic sugar in the code above stands for.
% One more useful feature of Scala is the ability to define
% functions with varying argument lists. This is a feature that
% is already present in old languages, like C, but seems to have
% been forgotten in the meantime---Java does not have it. In the
% context of regular expressions this feature comes in handy:
% Say you are fed up with writing many alternatives as
% \begin{lstlisting}[numbers=none]
% ALT(..., ALT(..., ALT(..., ...)))
% \end{lstlisting}
% \noindent To make it difficult, you do not know how deep such
% alternatives are nested. So you need something flexible that
% can take as many alternatives as needed. In Scala one can
% achieve this by adding a \code{*} to the type of an argument.
% Consider the code
% \begin{lstlisting}[language=Scala]
% def Alts(rs: List[Rexp]) : Rexp = rs match {
% case Nil => NULL
% case r::Nil => r
% case r::rs => ALT(r, Alts(rs))
% }
% def ALTS(rs: Rexp*) = Alts(rs.toList)
% \end{lstlisting}
% \noindent The function in Lines 1 to 5 takes a list of regular
% expressions and converts it into an appropriate alternative
% regular expression. In Line 7 there is a wrapper for this
% function which uses the feature of varying argument lists. The
% effect of this code is that I can write the regular
% expression for keywords as
% \begin{lstlisting}[numbers=none]
% ALTS("for", "def", "yield", "implicit", "if", "match", "case")
% \end{lstlisting}
% \noindent Again I leave it to you to find out how much this
% simplifies the regular expression in comparison with if I had
% to write this by hand using only the ``plain'' regular
% expressions from the inductive datatype.
%\bigskip\noindent
%\textit{More TBD.}
%\subsection*{Coursework}
\subsection*{More Info}
There is much more to Scala than I can possibly describe in
this document and teach in the lectures. Fortunately there are a
number of free books
about Scala and of course lots of help online. For example
\begin{itemize}
\item \url{http://www.scala-lang.org/docu/files/ScalaByExample.pdf}
\item \url{http://www.scala-lang.org/docu/files/ScalaTutorial.pdf}
\item \url{https://www.youtube.com/user/ShadowofCatron}
\item \url{http://docs.scala-lang.org/tutorials}
\item \url{https://www.scala-exercises.org}
\item \url{https://twitter.github.io/scala_school}
\end{itemize}
\noindent There is also an online course at Coursera on Functional
Programming Principles in Scala by Martin Odersky, the main
developer of the Scala language. And a document that explains
Scala for Java programmers
\begin{itemize}
\item \small\url{http://docs.scala-lang.org/tutorials/scala-for-java-programmers.html}
\end{itemize}
While I am quite enthusiastic about Scala, I am also happy to
admit that it has more than its fair share of faults. The
problem seen earlier of having to give an explicit type to
\code{toSet}, but not \code{toList} is one of them. There are
also many ``deep'' ideas about types in Scala, which even to
me as seasoned functional programmer are puzzling. Whilst
implicits are great, they can also be a source of great
headaches, for example consider the code:
\begin{lstlisting}[numbers=none]
scala> List (1, 2, 3) contains "your mom"
res1: Boolean = false
\end{lstlisting}
\noindent Rather than returning \code{false}, this code should
throw a typing-error. There are also many limitations Scala
inherited from the JVM that can be really annoying. For
example a fixed stack size. One can work around this
particular limitation, but why does one have to?
More such `puzzles' can be found at
\begin{center}
\url{http://scalapuzzlers.com} and
\url{http://latkin.org/blog/2017/05/02/when-the-scala-compiler-doesnt-help/}
\end{center}
Even if Scala has been a success in several high-profile companies,
there is also a company (Yammer) that first used Scala in their
production code, but then moved away from it. Allegedly they did not
like the steep learning curve of Scala and also that new versions of
Scala often introduced incompatibilities in old code. Also the Java
language is lately developing at lightening speed (in comparison to the past)
taking on many
features of Scala and other languages, and it seems even it introduces
new features on its own.
%So all in all, Scala might not be a great teaching language,
%but I hope this is mitigated by the fact that I never require
%you to write any Scala code. You only need to be able to read
%it. In the coursework you can use any programming language you
%like. If you want to use Scala for this, then be my guest; if
%you do not want, stick with the language you are most familiar
%with.
\subsection*{Conclusion}
I hope you liked the short journey through the Scala language---but remember we
like you to take on board the functional programming point of view,
rather than just learning another language. There is an interesting
blog article about Scala by a convert:
\begin{center}
\url{https://www.skedulo.com/tech-blog/technology-scala-programming/}
\end{center}
\noindent
He makes pretty much the same arguments about functional programming and
immutability (one section is teasingly called \textit{``Where Did all
the Bugs Go?''}). If you happen to moan about all the idiotic features
of Scala, well, I guess this is part of the package according to this
quote:\bigskip
%\begin{itemize}
%\item no exceptions....there two kinds, one ``global'' exceptions, like
%out of memory (not much can be done about this by the ``individual''
%programmer); and ``local one'' open a file that might not exists - in
%the latter you do not want to use exceptions, but Options
%\end{itemize}
\begin{flushright}\it
There are only two kinds of languages: the ones people complain
about\\ and the ones nobody uses.\smallskip\\
\mbox{}\hfill\small{}---Bjarne Stroustrup (the inventor of C++)
\end{flushright}
\end{document}
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