\documentclass{article}
\usepackage{../style}
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%cheat sheet
%http://worldline.github.io/scala-cheatsheet/

\begin{document}

\section*{A Crash-Course on Scala}

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 years or so. 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.\footnote{There are also experimental backends for
Android and JavaScript; and also work is under way to have a
native compiler, see \url{https://github.com/scala-native/scala-native}.} Unlike Java, however, Scala often
allows programmers to write very concise and elegant code.
Some therefore say: Scala is the much better Java. A number of
companies, The Guardian, Twitter, Coursera, FourSquare,
LinkedIn to name a few, either use Scala exclusively in
production code, or at least to some substantial degree. It
also seems to be useful in job-interviews (in Data Science)
according to this annectotical report

\begin{quote}
\url{https://techcrunch.com/2016/06/14/scala-is-the-new-golden-child/}
\end{quote}

\noindent
If you want to try out Scala yourself, the official Scala compiler can be
downloaded from

\begin{quote}
\url{http://www.scala-lang.org}
\end{quote}

\noindent
A ready-made bundle with the Eclipse IDE is at

\begin{quote}
\url{http://scala-ide.org/download/sdk.html}
\end{quote}

Why do I use Scala in the AFL module? Actually, you can do
\emph{any} part of the coursework in \emph{any} programming
language you like. I use Scala for showing you code during the
lectures because its functional programming-style allows me to
implement the functions we will discuss with very small
code-snippets. If I had to do this in Java, I would first have
to go through heaps of boilerplate code and the code-snippets
would not look pretty. Since the Scala compiler is free, you
can download the code-snippets and run every example I give.
But if you prefer, you can also easily translate them into any
other functional language, for example Haskell, Swift,
Standard ML, F$^\#$, Ocaml and so on.

Developing programs in Scala can be done with the Eclipse IDE
and also with the IntelliJ IDE, but for the small programs I will
develop the good old Emacs-editor is adequate for me and I
will run the programs on the command line. 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 the compiler. This helps a lot with interactively
developing 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 version 2.11.8 (Java HotSpot(TM) 64-Bit Server VM).
Type in expressions for evaluation. Or try :help.

scala>
\end{lstlisting}

\noindent Of course the precise response may vary due to 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 indicating that the result of the addition is of
type \code{Int} and the actual result is 5. 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{resXX} 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.

If you want to write a stand-alone app in Scala, you can
implement an object that is an instance of \code{App}, say

\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 and runtime environment:

\begin{lstlisting}[language={},numbers=none,basicstyle=\ttfamily\small]
$ scalac hello-world.scala
$ scala Hello
hello world
\end{lstlisting}

As mentioned above, 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*{Inductive Datatypes}

The elegance and conciseness of Scala programs are often a
result of inductive datatypes that can be easily defined in
Scala. For example in ``every-day mathematics'' we define
regular expressions simply by giving the grammar

\begin{center}
\begin{tabular}{r@{\hspace{2mm}}r@{\hspace{2mm}}l@{\hspace{13mm}}l}
  $r$ & $::=$ &   $\ZERO$            & null\\
        & $\mid$ & $\ONE$            & empty string\\
        & $\mid$ & $c$               & single character\\
        & $\mid$ & $r_1 \cdot r_2$   & sequence\\
        & $\mid$ & $r_1 + r_2$       & alternative / choice\\
        & $\mid$ & $r^\star$             & star (zero or more)\\
  \end{tabular}
\end{center}

\noindent This grammar specifies what regular expressions are
(essentially a kind of tree-structure with three kinds of
inner nodes---sequence, alternative and star---and three kinds
of leave nodes---null, empty and character). If you are
familiar with Java, it might be an instructive exercise to
define this kind of inductive datatypes in Java\footnote{Happy
programming! \Smiley} and then compare it with how it can be
implemented in Scala.

Implementing the regular expressions from above in Scala is
actually very simple: It first requires an \emph{abstract
class}, say, \code{Rexp}. This will act as the type for
regular expressions. Second, it requires a case for each
clause in the grammar. The cases for $\ZERO$ and $\ONE$ do not
have any arguments, while in all the other cases we do have
arguments. For example the character regular expression needs
to take as an argument the character it is supposed to
recognise. In Scala, the cases without arguments are called
\emph{case objects}, whereas the ones with arguments are
\emph{case classes}. The corresponding Scala code is as
follows:

\begin{lstlisting}[numbers=none]
abstract class Rexp 
case object ZERO extends Rexp
case object ONE extends Rexp
case class CHAR (c: Char) extends Rexp
case class SEQ (r1: Rexp, r2: Rexp) extends Rexp 
case class ALT (r1: Rexp, r2: Rexp) extends Rexp 
case class STAR (r: Rexp) extends Rexp 
\end{lstlisting}

\noindent In order to be an instance of \code{Rexp}, each case
object and case class needs to extend \code{Rexp}. Given the
grammar above, I hope you can see the underlying pattern. If
you want to play further with such definitions of inductive
datatypes, feel free to define for example binary trees.

Once you make a definition like the one above in Scala, you
can represent the regular expression for $a + b$, for example,
as \code{ALT(CHAR('a'), CHAR('b'))}. Expressions such as
\code{'a'} stand for ASCII characters, though in the output
syntax, as you can see below, the quotes are omitted. In a
later section we will see how we can support the more
mathematical infix notation for regular expression operators
in Scala. If you want to assign this regular expression to a
variable, you can use the keyword \code{val} and type

\begin{lstlisting}[numbers=none]
scala> val r = ALT(CHAR('a'), CHAR('b'))
r: ALT = ALT(CHAR(a),CHAR(b))
\end{lstlisting}

\noindent As you can see, in order to make such assignments,
no \code{new} or constructor is required in the class (as in
Java). However, if there is the need for some non-standard
initialisation, you can of course define such a constructor in
Scala too. But we omit such ``tricks'' here. 

Note that Scala in its response says the variable \code{r} is
of type \code{ALT}, not \code{Rexp}. This might be a bit
unexpected, but can be explained as follows: Scala always
tries to find the most general type that is needed for a
variable or expression, but does not ``over-generalise''. In
our definition the type \code{Rexp} is more general than
\code{ALT}, since it is the abstract class for all regular
expressions. But in this particular case there is no need to
give \code{r} the more general type of \code{Rexp}. This is
different if you want to form a list of regular expressions,
for example

\begin{lstlisting}[numbers=none]
scala> val ls = List(ALT(CHAR('a'), CHAR('b')), ZERO)
ls: List[Rexp] = List(ALT(CHAR(a),CHAR(b)), ZERO)
\end{lstlisting}

\noindent In this case, Scala needs to assign a common type to
the regular expressions so that it is compatible with the
fact that lists can only contain elements of a single type. In
this case the first common type is \code{Rexp}.\footnote{If you
type in this example, you will notice that the type contains
some further information, but let us ignore this for the
moment.} 

For compound types like \code{List[...]}, the general rule is
that when a type takes another type as argument, then this
argument type is written in angle-brackets. This can also
contain nested types as in \code{List[Set[Rexp]]}, which is a
list of sets each of which contains regular expressions.

\subsection*{Functions and Pattern-Matching}

I mentioned above that Scala is a very elegant programming
language for the code we will write in this module. This
elegance mainly stems from the fact that in addition to
inductive datatypes, also functions can be implemented very
easily in Scala. To show you this, let us first consider a
problem from number theory, called the \emph{Collatz-series},
which corresponds to a famous unsolved problem in
mathematics.\footnote{See for example
\url{http://mathworld.wolfram.com/CollatzProblem.html}.}
Mathematicians define this series as:

\[
collatz_{n + 1} \dn 
\begin{cases}
\frac{1}{2} * collatz_n & \text{if $collatz_n$ is even}\\
3 * collatz_n + 1 & \text{if $collatz_n$ is odd}
\end{cases}
\]

\noindent The famous unsolved question is whether this
series started with any $n > 0$ as $collatz_0$ will always
return to $1$. This is obvious when started with $1$, and also
with $2$, but already needs a bit of head-scratching for the
case of $3$.

If we want to avoid the head-scratching, we could implement
this as the following function in Scala:

\lstinputlisting[numbers=none]{../progs/collatz.scala}

\noindent The keyword for function definitions is \code{def}
followed by the name of the function. After that you have a
list of arguments (enclosed in parentheses and separated by
commas). Each argument in this list needs its type to be
annotated. In this case we only have one argument, which is of
type \code{BigInt}. This type stands in Scala for arbitrary
precision integers (in case you want to try out the function
on really big numbers). After the arguments comes the type of
what the function returns---a Boolean in this case for
indicating that the function has reached 1. Finally, after the
\code{=} comes the \emph{body} of the function implementing
what the function is supposed to do. What the \code{collatz}
function does should be pretty self-explanatory: the function
first tests whether \code{n} is equal to 1 in which case it
returns \code{true} and so on.

Notice the quirk in Scala's syntax for \code{if}s: The condition
needs to be enclosed in parentheses and the then-case comes
right after the condition---there is no \code{then} keyword in
Scala.

The real power of Scala comes, however, from the ability to
define functions by \emph{pattern matching}. In the
\code{collatz} function above we need to test each case using a
sequence of \code{if}s. This can be very cumbersome and brittle
if there are many cases. If we wanted to define a function
over regular expressions in Java, for example, which does not
have pattern-matching, the resulting code would just be
awkward.

Mathematicians already use the power of pattern-matching when
they define the function that takes a regular expression and
produces another regular expression that can recognise the
reversed strings. They define this function as follows:

\begin{center}
\begin{tabular}{r@{\hspace{2mm}}c@{\hspace{2mm}}l}
$rev(\ZERO)$   & $\dn$ & $\ZERO$\\
$rev(\ONE)$      & $\dn$ & $\ONE$\\
$rev(c)$             & $\dn$ & $c$\\
$rev(r_1 + r_2)$     & $\dn$ & $rev(r_1) + rev(r_2)$\\
$rev(r_1 \cdot r_2)$ & $\dn$ & $rev(r_2) \cdot rev(r_1)$\\
$rev(r^*)$                   & $\dn$ & $rev(r)^*$\\
\end{tabular}
\end{center}

\noindent It is defined by recursion analysing each pattern of
what the regular expression might look like. The corresponding
Scala code looks very similar to this definition, thanks to
pattern-matching.

\lstinputlisting[language=Scala]{../progs/rev.scala}

\noindent The keyword for starting a pattern-match is
\code{match} followed by a list of \code{case}s. Before the
match keyword can be another pattern, but often, as in the
case above, it is just a variable you want to pattern-match
(the \code{r} after \code{=} in Line 1).

Each case in this definition follows the structure of how we
defined regular expressions as inductive datatype. For example
the case in Line 3 you can read as: if the regular expression
\code{r} is of the form \code{EMPTY} then do whatever follows
the \code{=>} (in this case just return \code{EMPTY}). Line 5
reads as: if the regular expression \code{r} is of the form
\code{ALT(r1, r2)}, where the left-branch of the alternative is
matched by the variable \code{r1} and the right-branch by
\code{r2} then do ``something''. The ``something'' can now use the
variables \code{r1} and \code{r2} from the match. 

If you want to play with this function, call it for example
with the regular expression $ab + ac$. This regular expression
can recognise the strings $ab$ and $ac$. The function 
\code{rev} produces $ba + ca$, which can recognise the reversed
strings $ba$ and $ca$.

In Scala each pattern-match can also be guarded as in

\begin{lstlisting}[ numbers=none]
case Pattern if Condition => Do_Something
\end{lstlisting}

\noindent This allows us, for example, to re-write the 
\code{collatz}-function from above as follows:
 
\lstinputlisting[language=Scala]{../progs/collatz2.scala}


\noindent Although in this particular case the pattern-match
does not improve the code in any way. In cases like
\code{rev}, however, it is really crucial. The underscore in
Line 4 indicates that we do not care what the pattern looks
like. Thus this case acts like a default case whenever the
cases above did not match. Cases are always tried out from top
to bottom.
 
\subsection*{Loops, or better the Absence thereof}

Coming from Java or 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 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 (for example squared) and a list over
which this function should work. There are two forms to
express such maps in Scala. The first way is called a
\emph{for-comprehension}. Squaring the numbers from 1 to 8
would look in this form 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 The important keywords are \code{for} and
\code{yield}. This for-comprehension roughly states that from
the list of numbers we draw \code{n}s and compute the result
of \code{n * n}. As you can see, 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
\code{map}s 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). This expression for functions
might remind you of your lessons about the lambda-calculus
where this would have been written as $\lambda n.\,n * n$. It
might not be obvious, but for-comprehensions 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 reminders 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 reminders
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 
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 the for-comprehension
filters out all pairs where the sum is not even.

While hopefully this all 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
reminders 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
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 * n
  println(s"$n * $n = $square_n") 
}
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_n = ...} ) 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\_n} 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*{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}. 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 reminder 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 is 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 interestic 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*{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.

\subsection*{More Info}

There is much more to Scala than I can possibly describe in
this document. 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}
\end{itemize}

\noindent There is also a 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. In the past two months
there have also been two forks of the Scala compiler.
It needs to be seen what the future brings for Scala.

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.



\end{document}

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