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<title>Using Poly/ML - Chapter 4: Vectors and Arrays</title>
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<h1><font SIZE="6"><a name="VectorsArrays4">Chapter 4: Vectors and Arrays</a></font></h1>
<p><font SIZE="3">This chapter describes Poly/ML's implementation of vectors and arrays
(vectors are non-updatable arrays). The structures </font><b><font FACE="Courier" SIZE="3">Vector</font></b><font SIZE="3"> and </font><b><font FACE="Courier" SIZE="3">Array</font></b><font SIZE="3"> are
not part of the Standard ML Initial Basis and may not be supported by all implementations
of Standard ML, but we don't know of any serious implementation that doesn't support them.</font></p>
<h2><font SIZE="4"><b><a name="Vectors4.1">4.1 Vectors</a></b></font></h2>
<p><font SIZE="3">The structure </font><b><font FACE="Courier" SIZE="3">Vector</font></b><font SIZE="3"> contains the following items:</font></p>
<p><font FACE="Courier" SIZE="3"><b>eqtype 'a vector<br>
val vector : 'a list -> 'a vector</b></font></p>
<p><font FACE="Courier" SIZE="3"><b>val length : 'a vector int</b></font></p>
<p><font FACE="Courier" SIZE="3"><b>exception Subscript<br>
val sub : 'a vector * int -> 'a</b></font></p>
<p><font FACE="Courier" SIZE="3"><b>exception Size<br>
val tabulate : int * (int -> 'a) -> 'a vector</b></font></p>
<p><font SIZE="3">The purpose of these is as follows:</font></p>
<p><b><font FACE="Courier" SIZE="3">Vector.vector l</font></b><font SIZE="3"> produces a
vector whose elements<b> </b>are the members of the list </font><font FACE="Courier" SIZE="3"><b>l</b></font><font SIZE="3">.</font> </p>
<p><b><font FACE="Courier" SIZE="3">Vector.length v</font></b><font SIZE="3"> returns the
number of elements in the vector </font><font FACE="Courier" SIZE="3"><b>v</b></font><font SIZE="3">.</font></p>
<p><font FACE="Courier" SIZE="3"><b>Vector.sub (v,n) </b></font><font SIZE="3">returns the
n'th element of the vector </font><font FACE="Courier" SIZE="3"><b>v</b></font><font SIZE="3">. It raises the exception </font><b><font FACE="Courier" SIZE="3">Vector.Subscript</font></b><font SIZE="3"> if </font><b><font FACE="Courier" SIZE="3">n</font></b><font SIZE="3"> is
outside the range 0 <u><</u> n < </font><font FACE="Courier" SIZE="3"><b>Vector.length
v</b></font><font SIZE="3">.</font></p>
<p><b><font FACE="Courier" SIZE="3">Vector.tabulate (n,f)</font></b><font SIZE="3"> is an
alternative way to create a vector. It raises the exception </font><b><font FACE="Courier" SIZE="3">Vector.Size</font></b><font SIZE="3"> if </font><b><font FACE="Courier" SIZE="3">n
</font></b><font SIZE="3">is negative; otherwise it creates a vector of length </font><b><font FACE="Courier" SIZE="3">n</font></b><font SIZE="3"> whose i'th element is </font><font FACE="Courier" SIZE="3"><b>(f i)</b></font><font SIZE="3">.</font></p>
<p><b><font SIZE="3">Note: </font><font FACE="Courier" SIZE="3">vector</font></b><font SIZE="3"> is an equality type. Two vectors are equal if they consist of the same elements
in the same order.</font></p>
<h2><font SIZE="4"><a name="Arrays4.2">4.2 <b>Arrays</b></a></font></h2>
<p><font SIZE="3">The structure </font><b><font FACE="Courier" SIZE="3">Array</font></b><font SIZE="3"> contains the following items:</font></p>
<p><font FACE="Courier" SIZE="3"><b>eqtype 'a array<br>
val arrayoflist : '_a list -> '_a array</b></font></p>
<p><font FACE="Courier" SIZE="3"><b>val length : 'a array -> int</b></font></p>
<p><font FACE="Courier" SIZE="3"><b>exception Subscript<br>
val sub : 'a array * int -> 'a<br>
val update : 'a array * int 'a -> unit</b></font></p>
<p><font FACE="Courier" SIZE="3"><b>exception Size<br>
val tabulate : int * (int -> '_a) -> '_a array<br>
val array : int * '_a -> '_a array</b></font></p>
<p><font SIZE="3">The purpose of these is as follows:</font></p>
<p><b><font FACE="Courier" SIZE="3">Array.arrayoflist l</font></b><font SIZE="3"> produces
an array whose initial values are the members of the list </font><font FACE="Courier" SIZE="3"><b>1</b></font><font SIZE="3">.</font></p>
<p><b><font FACE="Courier" SIZE="3">Array.length a</font></b><font SIZE="3"> returns the
number of elements in the array</font><font FACE="Courier" SIZE="3"> <b>a.</b></font></p>
<p><b><font FACE="Courier" SIZE="3">Array.sub (a,n)</font></b><font SIZE="3"> returns the
n'th element of the array </font><b><font FACE="Courier" SIZE="3">a</font></b><font SIZE="3">. It raises the exception </font><b><font FACE="Courier" SIZE="3">Array.Subscript</font></b><font SIZE="3"> if </font><b><font FACE="Courier New" SIZE="3">n</font></b><font SIZE="3"> is
outside the range 0 <u><</u> n < </font><b><font FACE="Courier" SIZE="3">Array.length
a</font></b><font SIZE="3">.</font></p>
<p><b><font FACE="Courier" SIZE="3">Array.update (a,n,x)</font></b><font SIZE="3"> updates
the n'th element of the array <b>a </b>to be </font><b><font FACE="Courier" SIZE="3">x</font></b><font SIZE="3">. It raises the exception </font><b><font FACE="Courier" SIZE="3">Array.Subscript</font></b><font SIZE="3"> if </font><b><font FACE="Courier" SIZE="3">n</font></b><font SIZE="3"> is
outside the range 0 <u><</u> n<b> <</b> </font><b><font FACE="Courier" SIZE="3">Array.length
a</font></b><font SIZE="3">.</font></p>
<p><b><font FACE="Courier" SIZE="3">Array.tabulate (n,f)</font></b><font SIZE="3"> is an
alternative way to create an array. It raises the exception </font><b><font FACE="Courier" SIZE="3">Array.Size</font></b><font SIZE="3"> if </font><b><font FACE="Courier" SIZE="3">n</font></b><font SIZE="3"> is negative; otherwise it creates an array of length </font><b><font FACE="Courier" SIZE="3">n</font></b><font SIZE="3"> whose i'th element is </font><font FACE="Courier" SIZE="3"><b>(f i)</b></font><font SIZE="3">.</font></p>
<p><b><font FACE="Courier" SIZE="3">Array.array (n,x)</font></b><font SIZE="3"> creates an
array of length</font><font FACE="Courier" SIZE="3"> <b>n</b></font><font SIZE="3"> where
every element of the array has the initial value </font><b><font FACE="Courier" SIZE="3">x</font></b><font SIZE="3">. It raises the exception </font><b><font FACE="Courier" SIZE="3">Array.Size</font></b><font SIZE="3"> if </font><font FACE="Courier" SIZE="3"><b>n</b></font><font SIZE="3"> is
negative.</font></p>
<p><b><font SIZE="3">Note 1: </font><font FACE="Courier" SIZE="3">array</font></b><font SIZE="3"> is an equality type that behaves rather like </font><font FACE="Courier" SIZE="3"><b>ref</b></font><font SIZE="3">; two arrays are distinct if it is possible to
update one without updating the other. This means that they are equal if they were created
by the same function call or if they are both of length zero.</font></p>
<p><font SIZE="3"><b>Note 2: </b>arrays are like refs in that they can be updated; this is
why imperative type variables ('</font><b><font FACE="Courier" SIZE="3">_a</font></b><font SIZE="3">) must appear in the types of the array-creation functions.</font></p>
<p><font SIZE="3"><b>Note 3: </b>The two </font><b><font FACE="Courier" SIZE="3">Subscript</font></b><font SIZE="3"> exceptions (</font><b><font FACE="Courier" SIZE="3">Vector.Subscript</font></b><font SIZE="3"> and </font><font FACE="Courier" SIZE="3"><b>Array.Subscript</b></font><font SIZE="3">) are identical, as are the two </font><b><font FACE="Courier" SIZE="3">Size</font></b><font SIZE="3"> exceptions (</font><b><font FACE="Courier" SIZE="3">Vector.Size</font></b><font SIZE="3"> and </font><font FACE="Courier" SIZE="3"><b>Array.Size</b></font><font SIZE="3">).
This means that a handler for </font><b><font FACE="Courier" SIZE="3">Vector.Subscript</font></b><font SIZE="3"> will also catch </font><b><font FACE="Courier" SIZE="3">Array.Subscript</font></b><font SIZE="3"> and vice versa.</font></p>
<p><font size="2"><b>Copyright (c) 2000 CUTS and contributers. </b></font></p>
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