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authorMartin Odersky <odersky@gmail.com>2003-05-09 12:32:49 +0000
committerMartin Odersky <odersky@gmail.com>2003-05-09 12:32:49 +0000
commitce9a82d6382486a0badc794b22807fc53de2f63e (patch)
tree4657a588ed92d1a362321899ed3007b002dbb8ba /doc
parent51b150938ec586267f04055df1872c4e07da6996 (diff)
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Diffstat (limited to 'doc')
-rw-r--r--doc/reference/examples.verb.tex55
1 files changed, 38 insertions, 17 deletions
diff --git a/doc/reference/examples.verb.tex b/doc/reference/examples.verb.tex
index 61afe0dab4..85b78b6af2 100644
--- a/doc/reference/examples.verb.tex
+++ b/doc/reference/examples.verb.tex
@@ -2196,7 +2196,7 @@ result types is very tedious. It should also be unneccessary because
all such classes have exactly the same structure. In Scala, the
repetition can be avoided by defining a {\em generic class}:
\begin{verbatim}
-case class Pair[a, b](first: a, second: b);
+case class Pair[+a, +b](first: a, second: b);
def divmod(x: int, y: int): Pair[int, int] = new Pair[Int, Int](x / y, x % y)
\end{verbatim}
@@ -2220,12 +2220,27 @@ divmod(x, y) match {
case Pair(n, d) => System.out.println("quotient: " + n + ", rest: " + d);
}
\end{verbatim}
+The type parameters in class \verb@Pair@ are each prefixed by a
+\verb@+@ sign. This indicates that \verb@Pair@s are {\em
+covariant}. That is, if types \verb@T$_1$@ and \verb@T$_2$@ are
+subtypes of types \verb@S$_1$@ and \verb@S$_2$@, then
+\verb@Pair[T$_1$, T$_2$]@ is a subtype of
+\verb@Pair[S$_1$, S$_2$]@. For instance, \verb@Pair[String, int]@ is a
+subtype of \verb@Pair[Object, long]@. If the \verb@+@-annotation was
+missing, the type constructor would be treated as being
+non-variant. That is, pairs with different element types would never
+be in a subtype relation.
+Besides, \verb@+@, there is also a prefix
+\verb@-@ for contra-variant type constructors.
+The precise rules that
+for variance annotations are given in Chapter~\ref{sec:variance}.
+
The idea of pairs is generalized in Scala to tuples of greater arity.
There is a predefined case class \verb@Tuple$_n$@ for every \verb@n@
from \verb@2@ to \verb@9@ in Scala's standard library. The
definitions all follow the template
\begin{verbatim}
-case class Tuple$_n$[a$_1$, ..., a$_n$](_1: a$_1$, ..., _n: a$_n$);
+case class Tuple$_n$[+a$_1$, ..., +a$_n$](_1: a$_1$, ..., _n: a$_n$);
\end{verbatim}
Class \verb@Pair@ (as well as class \verb@Triple@) are also
predefined, but not as classes of their own. Instead
@@ -2325,11 +2340,11 @@ def isort(xs: List[int]): List[int] =
\exercise Provide an implementation of the missing function
\verb@insert@.
-\paragraph{List patterns.} In fact, both \verb@Nil@ and \verb@::@ are
-defined as case classes in Scala's standard library. Hence, it is
-possible to decompose lists by pattern matching, using patterns
-composed from the \verb@Nil@ and \verb@::@ constructors. For instance, \verb@isort@ can
-be written alternatively as follows.
+\paragraph{List patterns.} In fact, \verb@::@ is
+defined defined as a case class in Scala's standard library. Hence, it
+is possible to decompose lists by pattern matching, using patterns
+composed from the \verb@Nil@ and \verb@::@ constructors. For instance,
+\verb@isort@ can be written alternatively as follows.
\begin{verbatim}
def isort(xs: List[int]): List[int] = xs match {
case List() => List()
@@ -2408,13 +2423,16 @@ Lists are not built in in Scala; they are defined by an abstract class
In the following we present a tour through class \verb@List@.
\begin{verbatim}
package scala;
-abstract class List[a] {
+abstract class List[+a] {
\end{verbatim}
\verb@List@ is an abstract class, so one cannot define elements by
-calling the empty \verb@List@ constructor (e.g. by \verb@new List).
-The class is situated in the package \verb@scala@. This is a package
-containing the most important standard classes of Scala. \verb@List@
-defines a number of methods, which are explained in the following.
+calling the empty \verb@List@ constructor (e.g. by
+\verb@new List). The class has a type parameter \verb@a@. It is
+co-variant in this parameter, which means \verb@T <: S@ implies that
+\verb@List[T] <: List[S]@. The class is situated in the package
+\verb@scala@. This is a package containing the most important standard
+classes of Scala. \verb@List@ defines a number of methods, which are
+explained in the following.
First, there are the three basic functions \verb@isEmpty@,
\verb@head@, \verb@tail@. Their implementation in terms of pattern
@@ -2536,10 +2554,10 @@ left-associative. E.g.,
\begin{verbatim}
x :: y :: z = x :: (y :: z) \=$\mbox{\rm whereas}$ x + y + z = (x + y) + z
\end{verbatim}
-With these conventions, the definition of \verb@::@ as a method in
-class \verb@List@ is straightforward:
+The definition of \verb@::@ as a method in
+class \verb@List@ is as follows:
\begin{verbatim}
-def ::(x: a): List[a] = new scala.::(x, this);
+def ::[b >: a](x: a): List[a] = new scala.::(x, this);
\end{verbatim}
An operation similar to \verb@::@ is list concatenation, written
`\verb@:::@'. The result of \verb@(xs ::: ys)@ is a list consisting of
@@ -2644,6 +2662,9 @@ val intSort = msort(iless)
val reverseSort = msort(x: int, y: int => x > y)
\end{verbatim}
+\section*{Higher-Order Methods}
+
+
\bibliography{examples}
\end{document}
@@ -3486,8 +3507,8 @@ l = Branch(Leaf(1), Leaf(2)), r = Branch(Leaf(3), Leaf(4)).
\end{verbatim}
As another example, consider the following class
\begin{verbatim}
-abstract final class Option[a];
-case class None[a] extends Option[a];
+abstract final class Option[+a];
+case object None extends Option[All];
case class Some[a](item: a) extends Option[a];
\end{verbatim}
...