<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd"> <!--Rendered using the Haskell Html Library v0.2--> <HTML ><HEAD ><META HTTP-EQUIV="Content-Type" CONTENT="text/html; charset=UTF-8" ><TITLE >Data.Ix</TITLE ><LINK HREF="haddock.css" REL="stylesheet" TYPE="text/css" ><SCRIPT SRC="haddock-util.js" TYPE="text/javascript" ></SCRIPT ><SCRIPT TYPE="text/javascript" >window.onload = function () {setSynopsis("mini_Data-Ix.html")};</SCRIPT ></HEAD ><BODY ><TABLE CLASS="vanilla" CELLSPACING="0" CELLPADDING="0" ><TR ><TD CLASS="topbar" ><TABLE CLASS="vanilla" CELLSPACING="0" CELLPADDING="0" ><TR ><TD ><IMG SRC="haskell_icon.gif" WIDTH="16" HEIGHT="16" ALT=" " ></TD ><TD CLASS="title" >base-4.2.0.2: Basic libraries</TD ><TD CLASS="topbut" ><A HREF="index.html" >Contents</A ></TD ><TD CLASS="topbut" ><A HREF="doc-index.html" >Index</A ></TD ></TR ></TABLE ></TD ></TR ><TR ><TD CLASS="modulebar" ><TABLE CLASS="vanilla" CELLSPACING="0" CELLPADDING="0" ><TR ><TD ><FONT SIZE="6" >Data.Ix</FONT ></TD ><TD ALIGN="right" ><TABLE CLASS="narrow" CELLSPACING="0" CELLPADDING="0" ><TR ><TD CLASS="infohead" >Portability</TD ><TD CLASS="infoval" >portable</TD ></TR ><TR ><TD CLASS="infohead" >Stability</TD ><TD CLASS="infoval" >stable</TD ></TR ><TR ><TD CLASS="infohead" >Maintainer</TD ><TD CLASS="infoval" >libraries@haskell.org</TD ></TR ></TABLE ></TD ></TR ></TABLE ></TD ></TR ><TR ><TD CLASS="s15" ></TD ></TR ><TR ><TD ><TABLE CLASS="vanilla" CELLSPACING="0" CELLPADDING="0" ><TR ><TD CLASS="section4" ><B >Contents</B ></TD ></TR ><TR ><TD ><DL ><DT ><A HREF="#1" >The <TT ><A HREF="Data-Ix.html#t%3AIx" >Ix</A ></TT > class </A ></DT ><DT ><A HREF="#2" >Deriving Instances of <TT ><A HREF="Data-Ix.html#t%3AIx" >Ix</A ></TT > </A ></DT ></DL ></TD ></TR ></TABLE ></TD ></TR ><TR ><TD CLASS="s15" ></TD ></TR ><TR ><TD CLASS="section1" >Description</TD ></TR ><TR ><TD CLASS="doc" >The <TT ><A HREF="Data-Ix.html#t%3AIx" >Ix</A ></TT > class is used to map a contiguous subrange of values in type onto integers. It is used primarily for array indexing (see the array package). </TD ></TR ><TR ><TD CLASS="s15" ></TD ></TR ><TR ><TD CLASS="section1" >Synopsis</TD ></TR ><TR ><TD CLASS="s15" ></TD ></TR ><TR ><TD CLASS="body" ><TABLE CLASS="vanilla" CELLSPACING="0" CELLPADDING="0" ><TR ><TD CLASS="decl" ><SPAN CLASS="keyword" >class</SPAN > <A HREF="Data-Ord.html#t%3AOrd" >Ord</A > a => <A HREF="#t%3AIx" >Ix</A > a <SPAN CLASS="keyword" >where</SPAN ></TD ></TR ><TR ><TD CLASS="body" ><TABLE CLASS="vanilla" CELLSPACING="0" CELLPADDING="0" ><TR ><TD CLASS="decl" ><A HREF="#v%3Arange" >range</A > :: (a, a) -> [a]</TD ></TR ><TR ><TD CLASS="decl" ><A HREF="#v%3Aindex" >index</A > :: (a, a) -> a -> <A HREF="Data-Int.html#t%3AInt" >Int</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="#v%3AinRange" >inRange</A > :: (a, a) -> a -> <A HREF="Data-Bool.html#t%3ABool" >Bool</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="#v%3ArangeSize" >rangeSize</A > :: (a, a) -> <A HREF="Data-Int.html#t%3AInt" >Int</A ></TD ></TR ></TABLE ></TD ></TR ></TABLE ></TD ></TR ><TR ><TD CLASS="s15" ></TD ></TR ><TR ><TD CLASS="s15" ></TD ></TR ><TR ><TD CLASS="section1" ><A NAME="1" ><A NAME="1" >The <TT ><A HREF="Data-Ix.html#t%3AIx" >Ix</A ></TT > class </A ></A ></TD ></TR ><TR ><TD CLASS="s15" ></TD ></TR ><TR ><TD CLASS="decl" ><SPAN CLASS="keyword" >class</SPAN > <A HREF="Data-Ord.html#t%3AOrd" >Ord</A > a => <A NAME="t:Ix" ><A NAME="t%3AIx" ></A ></A ><B >Ix</B > a <SPAN CLASS="keyword" >where</SPAN ></TD ></TR ><TR ><TD CLASS="body" ><TABLE CLASS="vanilla" CELLSPACING="0" CELLPADDING="0" ><TR ><TD CLASS="ndoc" ><P >The <TT ><A HREF="Data-Ix.html#t%3AIx" >Ix</A ></TT > class is used to map a contiguous subrange of values in a type onto integers. It is used primarily for array indexing (see the array package). </P ><P >The first argument <TT >(l,u)</TT > of each of these operations is a pair specifying the lower and upper bounds of a contiguous subrange of values. </P ><P >An implementation is entitled to assume the following laws about these operations: </P ><UL ><LI ><PRE ><TT ><A HREF="Data-Ix.html#v%3AinRange" >inRange</A ></TT > (l,u) i == <TT ><A HREF="Data-List.html#v%3Aelem" >elem</A ></TT > i (<TT ><A HREF="Data-Ix.html#v%3Arange" >range</A ></TT > (l,u))</PRE ></LI ><LI > <TT ><TT ><A HREF="Data-Ix.html#v%3Arange" >range</A ></TT > (l,u) <TT ><A HREF="Data-List.html#v%3A%21%21" >!!</A ></TT > <TT ><A HREF="Data-Ix.html#v%3Aindex" >index</A ></TT > (l,u) i == i</TT >, when <TT ><TT ><A HREF="Data-Ix.html#v%3AinRange" >inRange</A ></TT > (l,u) i</TT > </LI ><LI ><PRE ><TT ><A HREF="Data-List.html#v%3Amap" >map</A ></TT > (<TT ><A HREF="Data-Ix.html#v%3Aindex" >index</A ></TT > (l,u)) (<TT ><A HREF="Data-Ix.html#v%3Arange" >range</A ></TT > (l,u))) == [0..<TT ><A HREF="Data-Ix.html#v%3ArangeSize" >rangeSize</A ></TT > (l,u)-1]</PRE ></LI ><LI ><PRE ><TT ><A HREF="Data-Ix.html#v%3ArangeSize" >rangeSize</A ></TT > (l,u) == <TT ><A HREF="Data-List.html#v%3Alength" >length</A ></TT > (<TT ><A HREF="Data-Ix.html#v%3Arange" >range</A ></TT > (l,u))</PRE ></LI ></UL ><P >Minimal complete instance: <TT ><A HREF="Data-Ix.html#v%3Arange" >range</A ></TT >, <TT ><A HREF="Data-Ix.html#v%3Aindex" >index</A ></TT > and <TT ><A HREF="Data-Ix.html#v%3AinRange" >inRange</A ></TT >. </P ></TD ></TR ><TR ><TD CLASS="s8" ></TD ></TR ><TR ><TD CLASS="section4" >Methods</TD ></TR ><TR ><TD CLASS="body" ><TABLE CLASS="vanilla" CELLSPACING="0" CELLPADDING="0" ><TR ><TD CLASS="decl" ><A NAME="v:range" ><A NAME="v%3Arange" ></A ></A ><B >range</B > :: (a, a) -> [a]</TD ></TR ><TR ><TD CLASS="doc" >The list of values in the subrange defined by a bounding pair. </TD ></TR ><TR ><TD CLASS="s8" ></TD ></TR ><TR ><TD CLASS="decl" ><A NAME="v:index" ><A NAME="v%3Aindex" ></A ></A ><B >index</B > :: (a, a) -> a -> <A HREF="Data-Int.html#t%3AInt" >Int</A ></TD ></TR ><TR ><TD CLASS="doc" >The position of a subscript in the subrange. </TD ></TR ><TR ><TD CLASS="s8" ></TD ></TR ><TR ><TD CLASS="decl" ><A NAME="v:inRange" ><A NAME="v%3AinRange" ></A ></A ><B >inRange</B > :: (a, a) -> a -> <A HREF="Data-Bool.html#t%3ABool" >Bool</A ></TD ></TR ><TR ><TD CLASS="doc" >Returns <TT ><A HREF="Data-Bool.html#v%3ATrue" >True</A ></TT > the given subscript lies in the range defined the bounding pair. </TD ></TR ><TR ><TD CLASS="s8" ></TD ></TR ><TR ><TD CLASS="decl" ><A NAME="v:rangeSize" ><A NAME="v%3ArangeSize" ></A ></A ><B >rangeSize</B > :: (a, a) -> <A HREF="Data-Int.html#t%3AInt" >Int</A ></TD ></TR ><TR ><TD CLASS="doc" >The size of the subrange defined by a bounding pair. </TD ></TR ></TABLE ></TD ></TR ><TR ><TD CLASS="s8" ></TD ></TR ><TR ><TD CLASS="section4" ><IMG SRC="minus.gif" CLASS="coll" ONCLICK="toggle(this,'i:Ix')" ALT="show/hide" > Instances</TD ></TR ><TR ><TD CLASS="body" ><DIV ID="i:Ix" STYLE="display:block;" ><TABLE CLASS="vanilla" CELLSPACING="1" CELLPADDING="0" ><TR ><TD CLASS="decl" ><A HREF="Data-Ix.html#t%3AIx" >Ix</A > <A HREF="Data-Bool.html#t%3ABool" >Bool</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-Ix.html#t%3AIx" >Ix</A > <A HREF="Data-Char.html#t%3AChar" >Char</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-Ix.html#t%3AIx" >Ix</A > <A HREF="Data-Int.html#t%3AInt" >Int</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-Ix.html#t%3AIx" >Ix</A > <A HREF="Data-Int.html#t%3AInt8" >Int8</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-Ix.html#t%3AIx" >Ix</A > <A HREF="Data-Int.html#t%3AInt16" >Int16</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-Ix.html#t%3AIx" >Ix</A > <A HREF="Data-Int.html#t%3AInt32" >Int32</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-Ix.html#t%3AIx" >Ix</A > <A HREF="Data-Int.html#t%3AInt64" >Int64</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-Ix.html#t%3AIx" >Ix</A > <A HREF="Prelude.html#t%3AInteger" >Integer</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-Ix.html#t%3AIx" >Ix</A > <A HREF="Data-Ord.html#t%3AOrdering" >Ordering</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-Ix.html#t%3AIx" >Ix</A > <A HREF="Data-Word.html#t%3AWord" >Word</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-Ix.html#t%3AIx" >Ix</A > <A HREF="Data-Word.html#t%3AWord8" >Word8</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-Ix.html#t%3AIx" >Ix</A > <A HREF="Data-Word.html#t%3AWord16" >Word16</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-Ix.html#t%3AIx" >Ix</A > <A HREF="Data-Word.html#t%3AWord32" >Word32</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-Ix.html#t%3AIx" >Ix</A > <A HREF="Data-Word.html#t%3AWord64" >Word64</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-Ix.html#t%3AIx" >Ix</A > ()</TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-Ix.html#t%3AIx" >Ix</A > <A HREF="System-IO.html#t%3AIOMode" >IOMode</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-Ix.html#t%3AIx" >Ix</A > <A HREF="GHC-IO-Device.html#t%3ASeekMode" >SeekMode</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-Ix.html#t%3AIx" >Ix</A > <A HREF="Data-Char.html#t%3AGeneralCategory" >GeneralCategory</A ></TD ></TR ><TR ><TD CLASS="decl" >(<A HREF="Data-Ix.html#t%3AIx" >Ix</A > a, <A HREF="Data-Ix.html#t%3AIx" >Ix</A > b) => <A HREF="Data-Ix.html#t%3AIx" >Ix</A > (a, b)</TD ></TR ><TR ><TD CLASS="decl" >(<A HREF="Data-Ix.html#t%3AIx" >Ix</A > a1, <A HREF="Data-Ix.html#t%3AIx" >Ix</A > a2, <A HREF="Data-Ix.html#t%3AIx" >Ix</A > a3) => <A HREF="Data-Ix.html#t%3AIx" >Ix</A > (a1, a2, a3)</TD ></TR ><TR ><TD CLASS="decl" >(<A HREF="Data-Ix.html#t%3AIx" >Ix</A > a1, <A HREF="Data-Ix.html#t%3AIx" >Ix</A > a2, <A HREF="Data-Ix.html#t%3AIx" >Ix</A > a3, <A HREF="Data-Ix.html#t%3AIx" >Ix</A > a4) => <A HREF="Data-Ix.html#t%3AIx" >Ix</A > (a1, a2, a3, a4)</TD ></TR ><TR ><TD CLASS="decl" >(<A HREF="Data-Ix.html#t%3AIx" >Ix</A > a1, <A HREF="Data-Ix.html#t%3AIx" >Ix</A > a2, <A HREF="Data-Ix.html#t%3AIx" >Ix</A > a3, <A HREF="Data-Ix.html#t%3AIx" >Ix</A > a4, <A HREF="Data-Ix.html#t%3AIx" >Ix</A > a5) => <A HREF="Data-Ix.html#t%3AIx" >Ix</A > (a1, a2, a3, a4, a5)</TD ></TR ></TABLE ></DIV ></TD ></TR ></TABLE ></TD ></TR ><TR ><TD CLASS="s15" ></TD ></TR ><TR ><TD CLASS="section1" ><A NAME="2" ><A NAME="2" >Deriving Instances of <TT ><A HREF="Data-Ix.html#t%3AIx" >Ix</A ></TT > </A ></A ></TD ></TR ><TR ><TD CLASS="s15" ></TD ></TR ><TR ><TD CLASS="doc" ><P >Derived instance declarations for the class <TT ><A HREF="Data-Ix.html#t%3AIx" >Ix</A ></TT > are only possible for enumerations (i.e. datatypes having only nullary constructors) and single-constructor datatypes, including arbitrarily large tuples, whose constituent types are instances of <TT ><A HREF="Data-Ix.html#t%3AIx" >Ix</A ></TT >. </P ><UL ><LI > For an enumeration, the nullary constructors are assumed to be numbered left-to-right with the indices being 0 to n-1 inclusive. This is the same numbering defined by the Enum class. For example, given the datatype: </LI ></UL ><PRE > data Colour = Red | Orange | Yellow | Green | Blue | Indigo | Violet </PRE ><P >we would have: </P ><PRE > range (Yellow,Blue) == [Yellow,Green,Blue] index (Yellow,Blue) Green == 1 inRange (Yellow,Blue) Red == False </PRE ><UL ><LI > For single-constructor datatypes, the derived instance declarations are as shown for tuples in Figure 1 <A HREF="http://www.haskell.org/onlinelibrary/ix.html#prelude-index" >http://www.haskell.org/onlinelibrary/ix.html#prelude-index</A >. </LI ></UL ></TD ></TR ><TR ><TD CLASS="s15" ></TD ></TR ><TR ><TD CLASS="botbar" >Produced by <A HREF="http://www.haskell.org/haddock/" >Haddock</A > version 2.6.1</TD ></TR ></TABLE ></BODY ></HTML >