From e70a1a24ef7a7b596a92e1853fd44e96f36ad245 Mon Sep 17 00:00:00 2001
From: Gilles Dubochet <gilles.dubochet@epfl.ch>
Date: Fri, 16 Dec 2005 18:19:29 +0000
Subject: Removed scala latex documentation from the scal...

Removed scala latex documentation from the scala core module.
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-% $Id$
-
-\documentclass[a4paper,12pt,twoside,titlepage]{book}
-
-\usepackage{scaladoc}
-\usepackage{fleqn}
-\usepackage{modefs}
-\usepackage{math}
-\usepackage{scaladefs}
-\renewcommand{\todo}[1]{}
-
-
-
-\ifpdf
-    \pdfinfo {
-        /Author   (Martin Odersky)
-        /Title    (Scala by Example)
-        /Keywords (Scala)
-        /Subject  ()
-        /Creator  (TeX)
-        /Producer (PDFLaTeX)
-    }
-\fi
-
-\renewcommand{\doctitle}{Scala By Example\\[33mm]\ }
-\renewcommand{\docauthor}{Martin Odersky\\[53mm]\ }
-
-\begin{document}
-
-\frontmatter
-\makedoctitle
-\clearemptydoublepage
-\tableofcontents
-\mainmatter
-\sloppy
-
-\chapter{\label{chap:intro}Introduction}
-
-Scala smoothly integrates object-oriented and functional
-programming. It is designed to express common programming patterns in
-a consise, elegant, and type-safe way.  Scala introduces several
-innovative language constructs. For instance:
-\begin{itemize}
-\item
-Abstract types and mixin composition unify concepts from object and
-  module systems.
-\item
-Pattern matching over class hierarchies unifies functional and
-  object-oriented data access. It greatly simplifies the processing of
-  XML trees.
-\item
-A flexible syntax and type system enables the construction of advanced
-  libraries and new domain specific languages.
-\end{itemize}
-At the same time, Scala is compatible with Java.  Java libraries and
-frameworks can be used without glue code or additional declarations.
-
-This document introduces Scala in an informal way, through a sequence
-of examples.
-
-Chapters~\ref{chap:example-one} and \ref{chap:example-auction}
-highlight some of the features that make Scala interesting. The
-following chapters introduce the language constructs of Scala in a
-more thorough way, starting with simple expressions and functions, and
-working up through objects and classes, lists and streams, mutable
-state, pattern matching to more complete examples that show
-interesting programming techniques. The present informal exposition is
-meant to be complemented by the Scala Language Reference Manual which
-specifies Scala in a more detailed and precise way.
-
-\paragraph{Acknowledgment}
-We owe a great debt to Abelson's and Sussman's wonderful book
-``Structure and Interpretation of Computer
-Programs''\cite{abelson-sussman:structure}. Many of their examples and
-exercises are also present here. Of course, the working language has
-in each case been changed from Scheme to Scala. Furthermore, the
-examples make use of Scala's object-oriented constructs where
-appropriate.
-
-\input{ExamplesPart}
-\bibliographystyle{alpha}
-\bibliography{Scala}
-
-\end{document}
-
-
-
-\chapter{Implementing Abstract Types: Search Trees}
-
-This chapter presents unbalanced binary search trees, implemented in
-three different styles: algebraic, object-oriented, and imperative.
-In each case, a search tree package is seen as an implementation
-of a class {\em MapStruct}.
-\begin{lstlisting}
-  trait MapStruct[kt, vt] {
-    trait Map with Function1[kt, vt] {
-      def extend(key: kt, value: vt): Map;
-      def remove(key: kt): Map;
-      def domain: Stream[kt];
-      def range: Stream[vt];
-    }
-    type map <: Map;
-    val empty: map;
-  }
-\end{lstlisting}
-The \code{MapStruct} class is parameterized with a type of keys
-\code{kt} and a type of values \code{vt}. It
-specifies an abstract type \code{Map} and an abstract value
-\code{empty}, which represents empty maps.  Every implementation
-\code{Map} needs to conform to that abstract type, which
-extends the function type \code{kt => vt}
-with four new
-methods. The method \code{domain} yields a stream that enumerates the
-map's domain, i.e. the set of keys that are mapped to non-null values.
-The method \code{range} yields a stream that enumerates the function's
-range, i.e.\ the values obtained by applying the function to arguments
-in its domain.  The method
-\code{extend} extends the map with a given key/value binding, whereas
-\code{remove} removes a given key from the map's domain. Both
-methods yield a new map value as result, which has the same
-representation as the receiver object.
-
-\begin{figure}[t]
-\begin{lstlisting}
-class AlgBinTree[kt extends Ord, vt] extends MapStruct[kt, vt] {
-  private case
-    Empty extends Map,
-    Node(key: kt, value: vt, l: Map, r: Map) extends Map
-
-  final class Map extends kt => vt {
-    def apply(key: kt): vt = this match {
-      case Empty => null
-      case Node(k, v, l, r) =>
-        if (key < k) l.apply(key)
-        else if (key > k) r.apply(key)
-        else v
-    }
-
-    def extend(key: kt, value: vt): Map = this match {
-      case Empty => Node(k, v, Empty, Empty)
-      case Node(k, v, l, r) =>
-        if (key < k) Node(k, v, l.extend(key, value), r)
-        else if (key > k) Node(k, v, l, r.extend(key, value))
-        else Node(k, value, l, r)
-    }
-
-    def remove(key: kt): Map = this match {
-      case Empty => Empty
-      case Node(k, v, l, r) =>
-        if (key < k) Node(k, v, l.remove(key), r)
-        else if (key > k) Node(k, v, l, r.remove(key))
-        else if (l == Empty) r
-        else if (r == Empty) l
-        else {
-          val midKey = r.domain.head
-          Node(midKey, r.apply(midKey), l, r.remove(midKey))
-        }
-    }
-
-    def domain: Stream[kt] = this match {
-      case Empty => []
-      case Node(k, v, l, r) => Stream.concat([l.domain, [k], r.domain])
-    }
-    def range: Stream[vt] = this match {
-      case Empty => []
-      case Node(k, v, l, r) => Stream.concat([l.range, [v], r.range])
-    }
-  }
-  def empty: Map = Empty
-}
-\end{lstlisting}
-\caption{\label{fig:algbintree}Algebraic implementation of binary
-search trees}
-\end{figure}
-We now present three implementations of \code{Map}, which are all
-based on binary search trees. The \code{apply} method of a map is
-implemented in each case by the usual search function over binary
-trees, which compares a given key with the key stored in the topmost
-tree node, and depending on the result of the comparison, searches the
-left or the right hand sub-tree. The type of keys must implement the
-\code{Ord} class, which contains comparison methods
-(see Chapter~\ref{chap:classes} for a definition of class \code{Ord}).
-
-The first implementation, \code{AlgBinTree}, is given in
-Figure~\ref{fig:algbintree}. It represents a map with a
-data type \code{Map} with two cases, \code{Empty} and \code{Node}.
-
-Every method of \code{AlgBinTree[kt, vt].Map} performs a pattern
-match on the value of
-\code{this} using the \code{match} method which is defined as postfix
-function application in class \code{Object} (\sref{sec:class-object}).
-
-The functions \code{domain} and \code{range} return their results as
-lazily constructed lists. The \code{Stream} class is an alias of
-\code{List} which should be used to indicate the fact that its values
-are constructed lazily.
-
-\begin{figure}[thb]
-\begin{lstlisting}
-class OOBinTree[kt extends Ord, vt] extends MapStruct[kt, vt] {
-  abstract class Map extends kt => vt {
-    def apply(key: kt): v
-    def extend(key: kt, value: vt): Map
-    def remove(key: kt): Map
-    def domain: Stream[kt]
-    def range: Stream[vt]
-  }
-  module empty extends Map {
-    def apply(key: kt) = null
-    def extend(key: kt, value: vt) = Node(key, value, empty, empty)
-    def remove(key: kt) = empty
-    def domain = []
-    def range = []
-  }
-  private class Node(k: kt, v: vt, l: Map, r: Map) extends Map {
-    def apply(key: kt): vt =
-      if (key < k) l.apply(key)
-      else if (key > k) r.apply(key)
-      else v
-    def extend(key: kt, value: vt): Map =
-      if (key < k) Node(k, v, l.extend(key, value), r)
-      else if (key > k) Node(k, v, l, r.extend(key, value))
-      else Node(k, value, l, r)
-    def remove(key: kt): Map =
-      if (key < k) Node(k, v, l.remove(key), r)
-      else if (key > k) Node(k, v, l, r.remove(key))
-      else if (l == empty) r
-      else if (r == empty) l
-      else {
-        val midKey = r.domain.head
-        Node(midKey, r(midKey), l, r.remove(midKey))
-      }
-    def domain: Stream[kt] = Stream.concat([l.domain, [k], r.domain])
-    def range: Stream[vt] = Stream.concat([l.range, [v], r.range])
-  }
-}
-\end{lstlisting}
-\caption{\label{fig:oobintree}Object-oriented implementation of binary
-search trees}
-\end{figure}
-
-The second implementation of maps is given in
-Figure~\ref{fig:oobintree}.  Class \code{OOBinTree} implements the
-type \code{Map} with a module \code{empty} and a class
-\code{Node}, which define the behavior of empty and non-empty trees,
-respectively.
-
-Note the different nesting structure of \code{AlgBinTree} and
-\code{OOBinTree}. In the former, all methods form part of the base
-class \code{Map}. The different behavior of empty and non-empty trees
-is expressed using a pattern match on the tree itself. In the
-latter, each subclass of \code{Map} defines its own set of
-methods, which override the methods in the base class. The pattern
-matches of the algebraic implementation have been replaced by the
-dynamic binding that comes with method overriding.
-
-Which of the two schemes is preferable depends to a large degree on
-which extensions of the type are anticipated. If the type is later
-extended with a new alternative, it is best to keep methods in each
-alternative, the way it was done in \code{OOBinTree}.  On the other
-hand, if the type is extended with additional methods, then it is
-preferable to keep only one implementation of methods and to rely on
-pattern matching, since this way existing subclasses need not be
-modified.
-
-\begin{figure}
-\begin{lstlisting}
-class MutBinTree[kt extends Ord, vt] extends MapStruct[kt, vt] {
-  class Map(key: kt, value: vt) extends kt => vt {
-    val k = key
-    var v = value
-    var l = empty, r = empty
-
-    def apply(key: kt): vt =
-      if (this eq empty) null
-      else if (key < k) l.apply(key)
-      else if (key > k) r.apply(key)
-      else v
-
-    def extend(key: kt, value: vt): Map =
-      if (this eq empty) Map(key, value)
-      else {
-        if (key < k) l = l.extend(key, value)
-        else if (key > k) r = r.extend(key, value)
-        else v = value
-        this
-      }
-
-    def remove(key: kt): Map =
-      if (this eq empty) this
-      else if (key < k) { l = l.remove(key) ; this }
-      else if (key > k) { r = r.remove(key) ; this }
-      else if (l eq empty) r
-      else if (r eq empty) l
-      else {
-        var mid = r
-        while (!(mid.l eq empty)) { mid = mid.l }
-        mid.r = r.remove(mid.k)
-        mid.l = l
-        mid
-      }
-
-    def domain: Stream[kt] = Stream.concat([l.domain, [k], r.domain])
-    def range: Stream[vt] = Stream.concat([l.range, [v], r.range])
-  }
-  let empty = new Map(null, null)
-}
-\end{lstlisting}
-\caption{\label{fig:impbintree}Side-effecting implementation of binary
-search trees}
-\end{figure}
-
-The two versions of binary trees presented so far are {\em
-persistent}, in the sense that maps are values that cannot be changed
-by side effects. By contrast, in the next implementation of binary
-trees, the implementations of \code{extend} and
-\code{remove} do have an effect on the state of their receiver
-object. This corresponds to the way binary trees are usually
-implemented in imperative languages. The new implementation can lead
-to some savings in computing time and memory allocation, but care is
-required not to use the original tree after it has been modified by a
-side-effecting operation.
-
-In this implementation, \code{value}, \code{l} and \code{r} are
-variables that can be affected by method calls.  The
-class \code{MutBinTree[kt, vt].Map} takes two instance parameters
-which define the \code{key} value and the initial value of the
-\code{value} variable. Empty trees are represented by a
-value \code{empty}, which has \code{null} (signifying undefined) in
-both its key and value fields. Note that this value needs to be
-defined lazily using \code{let} since its definition involves the
-creation of a
-\code{Map} object,
-which accesses \code{empty} recursively as part of its initialization.
-All methods test first whether the current tree is empty using the
-reference equality operator \code{eq} (\sref{sec:class-object}).
-
-As a program using the \code{MapStruct} abstraction, consider a function
-which creates a map from strings to integers and then applies it to a
-key string:
-\begin{lstlisting}
-def mapTest(mapImpl: => MapStruct[String, int]): int = {
-  val map: mapImpl.Map = mapImpl.empty.extend("ab", 1).extend("bx", 3)
-  val x = map("ab")             // returns 1
-}
-\end{lstlisting}
-The function is parameterized with the particular implementation of
-\code{MapStruct}. It can be applied to any one of the three implementations
-described above. E.g.:
-\begin{lstlisting}
-mapTest(AlgBinTree[String, int])
-mapTest(OOBinTree[String, int])
-mapTest(MutBinTree[String, int])
-\end{lstlisting}
-}
- 
-
-
-
-
-\paragraph{Mixin Composition}
-We can now define a class of \code{Rational} numbers that
-support comparison operators.
-\begin{lstlisting}
-final class OrderedRational(n: int, d: int)
- extends Rational(n, d) with Ord {
-  override def ==(that: OrderedRational) =
-    numer == that.numer && denom == that.denom;
-  def <(that: OrderedRational): boolean =
-    numer * that.denom < that.numer * denom;
-}
-\end{lstlisting}
-Class \code{OrderedRational} redefines method \code{==}, which is
-defined as reference equality in class \code{Object}. It also
-implements the abstract method \code{<} from class \code{Ord}.  In
-addition, it inherits all members of class \code{Rational} and all
-non-abstract members of class \code{Ord}. The implementations of
-\code{==} and \code{<} replace the definition of \code{==} in class
-\code{Object} and the abstract declaration of \code{<} in class
-\code{Ord}. The other inherited comparison methods then refer to this
-implementation in their body.
-
-The clause ``\code{Rational(d, d) with Ord}'' is an instance of {\em
-mixin composition}. It describes a template for an object that is
-compatible with both \code{Rational} and \code{Ord} and that contains
-all members of either class. \code{Rational} is called the {\em
-superclass} of \code{OrderedRational} while \code{Ord} is called a
-{\em mixin class}. The type of this template is the {\em compound
-type} ``\code{Rational with Ord}''.
-
-On the surface, mixin composition looks much like multiple
-inheritance. The difference between the two becomes apparent if we
-look at superclasses of inherited classes. With multiple inheritance,
-both \code{Rational} and \code{Ord} would contribute a superclass
-\code{Object} to the template. We therefore have to answer some
-tricky questions, such as whether members of \code{Object} are present
-once or twice and whether the initializer of \code{Object} is called
-once or twice. Mixin composition avoids these complications.  In the
-mixin composition \code{Rational with Ord}, class
-\code{Rational} is treated as actual superclass of class \code{Ord}.
-A mixin composition \code{C with M} is well-formed as long as the
-first operand \code{C} conforms to the declared superclass of the
-second operand \code{M}. This holds in our example, because
-\code{Rational} conforms to \code{Object}. In a sense, mixin composition
-amounts to overriding the superclass of a class.
-
-\paragraph{Final Classes}
-Note that class \code{OrderedRational} was defined
-\code{final}. This means that no classes extending \code{OrderedRational}
-may be defined in other parts of the program.
-%Within final classes the
-%type \code{this} is an alias of the defined class itself. Therefore,
-%we could define our \code{<} method with an argument of type
-%\code{OrderedRational} as a well-formed implementation of the abstract class
-%\code{less(that: this)} in class \code{Ord}.
-
-\chapter{\label{sec:simple-examples}Pattern Matching}
-
-\todo{Complete}
-
-Consider binary trees whose leafs contain integer arguments. This can
-be described by a class for trees, with subclasses for leafs and
-branch nodes:
-\begin{lstlisting}
-abstract class Tree;
-case class Branch(left: Tree, right: Tree) extends Tree;
-case class Leaf(x: int) extends Tree;
-\end{lstlisting}
-Note that the class \code{Tree} is not followed by an extends
-clause or a body. This defines \code{Tree} to be an empty
-subclass of \code{Object}, as if we had written
-\begin{lstlisting}
-class Tree extends Object {}
-\end{lstlisting}
-Note also that the two subclasses of \code{Tree} have a \code{case}
-modifier.  That modifier has two effects. First, it lets us construct
-values of a case class by simply calling the constructor, without
-needing a preceding \code{new}. Example:
-\begin{lstlisting}
-val tree1 = Branch(Branch(Leaf(1), Leaf(2)), Branch(Leaf(3), Leaf(4)))
-\end{lstlisting}
-Second, it lets us use constructors for these classes in patterns, as
-is illustrated in the following example.
-\begin{lstlisting}
-def sumLeaves(t: Tree): int = t match {
-  case Branch(l, r) => sumLeaves(l) + sumLeaves(r)
-  case Leaf(x) => x
-}
-\end{lstlisting}
-The function \code{sumLeaves} sums up all the integer values in the
-leaves of a given tree \code{t}. It is is implemented by calling the
-\code{match} method of \code{t} with a {\em choice expression} as
-argument (\code{match} is a predefined method in class \code{Object}).
-The choice expression consists of two cases which botrelate a pattern with an expression. The pattern of the first case,
-\code{Branch(l, r)} matches all instances of class \code{Branch}
-and binds the {\em pattern variables} \code{l} and \code{r} to the
-constructor arguments, i.e.\ the left and right subtrees of the
-branch.  Pattern variables always start with a lower case letter; to
-avoid ambiguities, constructors in patterns should start with an upper
-case letter.
-
-The effect of the choice expression is to select the first alternative
-whose pattern matches the given select value, and to evaluate the body
-of this alternative in a context where pattern variables are bound to
-corresponding parts of the selector. For instance, the application
-\code{sumLeaves(tree1)} would select the first alternative with the
-\code{Branch(l,r)} pattern, and would evaluate the expression
-\code{sumLeaves(l) + sumLeaves(r)} with bindings
-\begin{lstlisting}
-l = Branch(Leaf(1), Leaf(2)), r = Branch(Leaf(3), Leaf(4)).
-\end{lstlisting}
-As another example, consider the following class
-\begin{lstlisting}
-abstract final class Option[+a];
-case object None extends Option[All];
-case class Some[a](item: a) extends Option[a];
-\end{lstlisting}
-...
-
-%\todo{Several simple and intermediate examples needed}.
-
-\begin{lstlisting}
-def find[a,b](it: Iterator[(a, b)], x: a): Option[b] = {
-  var result: Option[b] = None;
-  while (it.hasNext && result == None) {
-    val (x1, y) = it.next;
-    if (x == x1) result = Some(y)
-  }
-  result
-}
-find(xs, x) match {
-  case Some(y) => System.out.println(y)
-  case None => System.out.println("no match")
-}
-\end{lstlisting}
-
-\comment{
-
-
-class MaxCounter {
-  var maxVal: Option[int] = None;
-  def set(x: int) = maxVal match {
-    case None => maxVal = Some(x)
-    case Some(y) => maxVal = Some(Math.max(x, y))
-  }
-}
-\end{lstlisting}
-}
-\comment{
-\begin{lstlisting}
-class Stream[a] = List[a]
-
-module Stream {
-  def concat(xss: Stream[Stream[a]]): Stream[a] = {
-    let result: Stream[a] = xss match {
-      case [] => []
-      case [] :: xss1 => concat(xss1)
-      case (x :: xs) :: xss1 => x :: concat(xs :: xss1)
-    }
-    result
-  }
-}
-\end{lstlisting}
-}
-\comment{
-}
-%\todo{We also need some XML examples.}
-
-\end{document}
-
-
-
-  case ([], _) => ys
-  case (_, []) => xs
-  case (x :: xs1, y :: ys1) =>
-    if (x < y) x :: merge(xs1, ys) else y :: merge(xs, ys1)
-}
-
-def split (xs: List[a]): (List[a], List[a]) = xs match {
-  case [] => ([], [])
-  case [x] => (x, [])
-  case y :: z :: xs1 => val (ys, zs) = split(xs1) ; (y :: ys, z :: zs)
-}
-
-def sort(xs: List[a]): List[a] = {
-  val (ys, zs) = split(xs)
-  merge(sort(ys), sort(zs))
-}
-
-
-def sort(a:Array[String]): Array[String] = {
-  val pivot = a(a.length / 2)
-  sort(a.filter(x => x < pivot)) ++
-       a.filter(x => x == pivot) ++
-  sort(a.filter(x => x > pivot))
-}
-
-def sort(a:Array[String]): Array[String] = {
-
-  def swap (i: int, j: int): unit = {
-    val t = a(i) ; a(i) = a(j) ; a(j) = t
-  }
-
-  def sort1(l: int, r: int): unit = {
-    val pivot = a((l + r) / 2)
-    var i = l, j = r
-    while (i <= r) {
-      while (i < r && a(i) < pivot) { i = i + 1 }
-      while (j > l && a(j) > pivot) { j = j - 1 }
-      if (i <= j) {
-        swap(i, j)
-        i = i + 1
-        j = j - 1
-      }
-    }
-    if (l < j) sort1(l, j)
-    if (j < r) sort1(i, r)
-  }
-
-  sort1(0, a.length - 1)
-}
-
-class Array[a] {
-
-  def copy(to: Array[a], src: int, dst: int, len: int): unit
-  val length: int
-  val apply(i: int): a
-  val update(i: int, x: a): unit
-
-  def filter (p: a => boolean): Array[a] = {
-    val temp = new Array[a](a.length)
-    var i = 0, j = 0
-    for (i < a.length, i = i + 1) {
-      val x = a(i)
-      if (p(x)) { temp(j) = x; j = j + 1 }
-    }
-    val res = new Array[a](j)
-    temp.copy(res, 0, 0, j)
-  }
-
-  def ++ (that: Array[a]): Array[a] = {
-    val a = new Array[a](this.length + that.length)
-    this.copy(a, 0, 0, this.length)
-    that.copy(a, 0, this.length, that.length)
-  }
-
-static
-
-  def concat [a] (as: List[Array[a]]) = {
-    val l = (as map (a => a.length)).sum
-    val dst = new Array[a](l)
-    var j = 0
-    as forall {a => { a.copy(dst, j, a.length) ; j = j + a.length }}
-    dst
-  }
-
-}
-
-module ABT extends AlgBinTree[kt, vt]
-ABT.Map
-- 
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