diff -r 739039774cee -r 94b84d880c2b handouts/scala-ho.tex --- a/handouts/scala-ho.tex Mon Jan 24 00:14:02 2022 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,1016 +0,0 @@ -\documentclass{article} -\usepackage{../style} -\usepackage{../langs} -\usepackage{marvosym} - -%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} - -%%% Local Variables: -%%% mode: latex -%%% TeX-master: t -%%% End: