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<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>Numeric.Interval.Internal</title><link href="ocean.css" rel="stylesheet" type="text/css" title="Ocean" /><script src="haddock-util.js" type="text/javascript"></script><script type="text/javascript">//<![CDATA[
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</script></head><body><div id="package-header"><ul class="links" id="page-menu"><li><a href="src/Numeric-Interval-Internal.html">Source</a></li><li><a href="index.html">Contents</a></li><li><a href="doc-index.html">Index</a></li></ul><p class="caption">intervals-0.7: Interval Arithmetic</p></div><div id="content"><div id="module-header"><table class="info"><tr><th>Portability</th><td>DeriveDataTypeable</td></tr><tr><th>Stability</th><td>experimental</td></tr><tr><th>Maintainer</th><td>ekmett@gmail.com</td></tr><tr><th>Safe Haskell</th><td>Safe-Inferred</td></tr></table><p class="caption">Numeric.Interval.Internal</p></div><div id="description"><p class="caption">Description</p><div class="doc"><p>Interval arithmetic
</p></div></div><div id="synopsis"><p id="control.syn" class="caption expander" onclick="toggleSection('syn')">Synopsis</p><ul id="section.syn" class="hide" onclick="toggleSection('syn')"><li class="src short"><span class="keyword">data</span>  <a href="#t:Interval">Interval</a> a<ul class="subs"><li>= <a href="#v:I">I</a> !a !a  </li><li>| <a href="#v:Empty">Empty</a>  </li></ul></li><li class="src short"><a href="#v:...">(...)</a> :: <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Ord.html#t:Ord">Ord</a> a =&gt; a -&gt; a -&gt; <a href="Numeric-Interval-Internal.html#t:Interval">Interval</a> a</li><li class="src short"><a href="#v:interval">interval</a> :: <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Ord.html#t:Ord">Ord</a> a =&gt; a -&gt; a -&gt; <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Maybe.html#t:Maybe">Maybe</a> (<a href="Numeric-Interval-Internal.html#t:Interval">Interval</a> a)</li><li class="src short"><a href="#v:whole">whole</a> :: <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Prelude.html#t:Fractional">Fractional</a> a =&gt; <a href="Numeric-Interval-Internal.html#t:Interval">Interval</a> a</li><li class="src short"><a href="#v:empty">empty</a> :: <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Ord.html#t:Ord">Ord</a> a =&gt; <a href="Numeric-Interval-Internal.html#t:Interval">Interval</a> a</li><li class="src short"><a href="#v:null">null</a> ::  <a href="Numeric-Interval-Internal.html#t:Interval">Interval</a> a -&gt; <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Bool.html#t:Bool">Bool</a></li><li class="src short"><a href="#v:singleton">singleton</a> ::  a -&gt; <a href="Numeric-Interval-Internal.html#t:Interval">Interval</a> a</li><li class="src short"><a href="#v:elem">elem</a> :: <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Ord.html#t:Ord">Ord</a> a =&gt; a -&gt; <a href="Numeric-Interval-Internal.html#t:Interval">Interval</a> a -&gt; <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Bool.html#t:Bool">Bool</a></li><li class="src short"><a href="#v:notElem">notElem</a> :: <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Ord.html#t:Ord">Ord</a> a =&gt; a -&gt; <a href="Numeric-Interval-Internal.html#t:Interval">Interval</a> a -&gt; <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Bool.html#t:Bool">Bool</a></li><li class="src short"><a href="#v:inf">inf</a> ::  <a href="Numeric-Interval-Internal.html#t:Interval">Interval</a> a -&gt; a</li><li class="src short"><a href="#v:sup">sup</a> ::  <a href="Numeric-Interval-Internal.html#t:Interval">Interval</a> a -&gt; a</li><li class="src short"><a href="#v:singular">singular</a> :: <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Ord.html#t:Ord">Ord</a> a =&gt; <a href="Numeric-Interval-Internal.html#t:Interval">Interval</a> a -&gt; <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Bool.html#t:Bool">Bool</a></li><li class="src short"><a href="#v:width">width</a> :: <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Prelude.html#t:Num">Num</a> a =&gt; <a href="Numeric-Interval-Internal.html#t:Interval">Interval</a> a -&gt; a</li><li class="src short"><a href="#v:midpoint">midpoint</a> :: <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Prelude.html#t:Fractional">Fractional</a> a =&gt; <a href="Numeric-Interval-Internal.html#t:Interval">Interval</a> a -&gt; a</li><li class="src short"><a href="#v:intersection">intersection</a> :: (<a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Prelude.html#t:Fractional">Fractional</a> a, <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Ord.html#t:Ord">Ord</a> a) =&gt; <a href="Numeric-Interval-Internal.html#t:Interval">Interval</a> a -&gt; <a href="Numeric-Interval-Internal.html#t:Interval">Interval</a> a -&gt; <a href="Numeric-Interval-Internal.html#t:Interval">Interval</a> a</li><li class="src short"><a href="#v:hull">hull</a> :: <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Ord.html#t:Ord">Ord</a> a =&gt; <a href="Numeric-Interval-Internal.html#t:Interval">Interval</a> a -&gt; <a href="Numeric-Interval-Internal.html#t:Interval">Interval</a> a -&gt; <a href="Numeric-Interval-Internal.html#t:Interval">Interval</a> a</li><li class="src short"><a href="#v:bisect">bisect</a> :: <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Prelude.html#t:Fractional">Fractional</a> a =&gt; <a href="Numeric-Interval-Internal.html#t:Interval">Interval</a> a -&gt; (<a href="Numeric-Interval-Internal.html#t:Interval">Interval</a> a, <a href="Numeric-Interval-Internal.html#t:Interval">Interval</a> a)</li><li class="src short"><a href="#v:bisectIntegral">bisectIntegral</a> :: <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Prelude.html#t:Integral">Integral</a> a =&gt; <a href="Numeric-Interval-Internal.html#t:Interval">Interval</a> a -&gt; (<a href="Numeric-Interval-Internal.html#t:Interval">Interval</a> a, <a href="Numeric-Interval-Internal.html#t:Interval">Interval</a> a)</li><li class="src short"><a href="#v:magnitude">magnitude</a> :: (<a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Prelude.html#t:Num">Num</a> a, <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Ord.html#t:Ord">Ord</a> a) =&gt; <a href="Numeric-Interval-Internal.html#t:Interval">Interval</a> a -&gt; a</li><li class="src short"><a href="#v:mignitude">mignitude</a> :: (<a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Prelude.html#t:Num">Num</a> a, <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Ord.html#t:Ord">Ord</a> a) =&gt; <a href="Numeric-Interval-Internal.html#t:Interval">Interval</a> a -&gt; a</li><li class="src short"><a href="#v:distance">distance</a> :: (<a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Prelude.html#t:Num">Num</a> a, <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Ord.html#t:Ord">Ord</a> a) =&gt; <a href="Numeric-Interval-Internal.html#t:Interval">Interval</a> a -&gt; <a href="Numeric-Interval-Internal.html#t:Interval">Interval</a> a -&gt; a</li><li class="src short"><a href="#v:contains">contains</a> :: <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Ord.html#t:Ord">Ord</a> a =&gt; <a href="Numeric-Interval-Internal.html#t:Interval">Interval</a> a -&gt; <a href="Numeric-Interval-Internal.html#t:Interval">Interval</a> a -&gt; <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Bool.html#t:Bool">Bool</a></li><li class="src short"><a href="#v:isSubsetOf">isSubsetOf</a> :: <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Ord.html#t:Ord">Ord</a> a =&gt; <a href="Numeric-Interval-Internal.html#t:Interval">Interval</a> a -&gt; <a href="Numeric-Interval-Internal.html#t:Interval">Interval</a> a -&gt; <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Bool.html#t:Bool">Bool</a></li><li class="src short"><a href="#v:certainly">certainly</a> :: <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Ord.html#t:Ord">Ord</a> a =&gt; (<span class="keyword">forall</span> b. <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Ord.html#t:Ord">Ord</a> b =&gt; b -&gt; b -&gt; <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Bool.html#t:Bool">Bool</a>) -&gt; <a href="Numeric-Interval-Internal.html#t:Interval">Interval</a> a -&gt; <a href="Numeric-Interval-Internal.html#t:Interval">Interval</a> a -&gt; <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Bool.html#t:Bool">Bool</a></li><li class="src short"><a href="#v:-60--33-">(&lt;!)</a> :: <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Ord.html#t:Ord">Ord</a> a =&gt; <a href="Numeric-Interval-Internal.html#t:Interval">Interval</a> a -&gt; <a href="Numeric-Interval-Internal.html#t:Interval">Interval</a> a -&gt; <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Bool.html#t:Bool">Bool</a></li><li class="src short"><a href="#v:-60--61--33-">(&lt;=!)</a> :: <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Ord.html#t:Ord">Ord</a> a =&gt; <a href="Numeric-Interval-Internal.html#t:Interval">Interval</a> a -&gt; <a href="Numeric-Interval-Internal.html#t:Interval">Interval</a> a -&gt; <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Bool.html#t:Bool">Bool</a></li><li class="src short"><a href="#v:-61--61--33-">(==!)</a> :: <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Eq.html#t:Eq">Eq</a> a =&gt; <a href="Numeric-Interval-Internal.html#t:Interval">Interval</a> a -&gt; <a href="Numeric-Interval-Internal.html#t:Interval">Interval</a> a -&gt; <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Bool.html#t:Bool">Bool</a></li><li class="src short"><a href="#v:-62--61--33-">(&gt;=!)</a> :: <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Ord.html#t:Ord">Ord</a> a =&gt; <a href="Numeric-Interval-Internal.html#t:Interval">Interval</a> a -&gt; <a href="Numeric-Interval-Internal.html#t:Interval">Interval</a> a -&gt; <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Bool.html#t:Bool">Bool</a></li><li class="src short"><a href="#v:-62--33-">(&gt;!)</a> :: <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Ord.html#t:Ord">Ord</a> a =&gt; <a href="Numeric-Interval-Internal.html#t:Interval">Interval</a> a -&gt; <a href="Numeric-Interval-Internal.html#t:Interval">Interval</a> a -&gt; <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Bool.html#t:Bool">Bool</a></li><li class="src short"><a href="#v:possibly">possibly</a> :: <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Ord.html#t:Ord">Ord</a> a =&gt; (<span class="keyword">forall</span> b. <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Ord.html#t:Ord">Ord</a> b =&gt; b -&gt; b -&gt; <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Bool.html#t:Bool">Bool</a>) -&gt; <a href="Numeric-Interval-Internal.html#t:Interval">Interval</a> a -&gt; <a href="Numeric-Interval-Internal.html#t:Interval">Interval</a> a -&gt; <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Bool.html#t:Bool">Bool</a></li><li class="src short"><a href="#v:-60--63-">(&lt;?)</a> :: <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Ord.html#t:Ord">Ord</a> a =&gt; <a href="Numeric-Interval-Internal.html#t:Interval">Interval</a> a -&gt; <a href="Numeric-Interval-Internal.html#t:Interval">Interval</a> a -&gt; <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Bool.html#t:Bool">Bool</a></li><li class="src short"><a href="#v:-60--61--63-">(&lt;=?)</a> :: <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Ord.html#t:Ord">Ord</a> a =&gt; <a href="Numeric-Interval-Internal.html#t:Interval">Interval</a> a -&gt; <a href="Numeric-Interval-Internal.html#t:Interval">Interval</a> a -&gt; <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Bool.html#t:Bool">Bool</a></li><li class="src short"><a href="#v:-61--61--63-">(==?)</a> :: <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Ord.html#t:Ord">Ord</a> a =&gt; <a href="Numeric-Interval-Internal.html#t:Interval">Interval</a> a -&gt; <a href="Numeric-Interval-Internal.html#t:Interval">Interval</a> a -&gt; <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Bool.html#t:Bool">Bool</a></li><li class="src short"><a href="#v:-62--61--63-">(&gt;=?)</a> :: <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Ord.html#t:Ord">Ord</a> a =&gt; <a href="Numeric-Interval-Internal.html#t:Interval">Interval</a> a -&gt; <a href="Numeric-Interval-Internal.html#t:Interval">Interval</a> a -&gt; <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Bool.html#t:Bool">Bool</a></li><li class="src short"><a href="#v:-62--63-">(&gt;?)</a> :: <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Ord.html#t:Ord">Ord</a> a =&gt; <a href="Numeric-Interval-Internal.html#t:Interval">Interval</a> a -&gt; <a href="Numeric-Interval-Internal.html#t:Interval">Interval</a> a -&gt; <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Bool.html#t:Bool">Bool</a></li><li class="src short"><a href="#v:idouble">idouble</a> :: <a href="Numeric-Interval-Internal.html#t:Interval">Interval</a> <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Prelude.html#t:Double">Double</a> -&gt; <a href="Numeric-Interval-Internal.html#t:Interval">Interval</a> <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Prelude.html#t:Double">Double</a></li><li class="src short"><a href="#v:ifloat">ifloat</a> :: <a href="Numeric-Interval-Internal.html#t:Interval">Interval</a> <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Prelude.html#t:Float">Float</a> -&gt; <a href="Numeric-Interval-Internal.html#t:Interval">Interval</a> <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Prelude.html#t:Float">Float</a></li></ul></div><div id="interface"><h1>Documentation</h1><div class="top"><p class="src"><span class="keyword">data</span>  <a name="t:Interval" class="def">Interval</a> a <a href="src/Numeric-Interval-Internal.html#Interval" class="link">Source</a></p><div class="subs constructors"><p class="caption">Constructors</p><table><tr><td class="src"><a name="v:I" class="def">I</a> !a !a</td><td class="doc empty">&nbsp;</td></tr><tr><td class="src"><a name="v:Empty" class="def">Empty</a></td><td class="doc empty">&nbsp;</td></tr></table></div><div class="subs instances"><p id="control.i:Interval" class="caption collapser" onclick="toggleSection('i:Interval')">Instances</p><div id="section.i:Interval" class="show"><table><tr><td class="src"><a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Typeable-Internal.html#t:Typeable1">Typeable1</a> <a href="Numeric-Interval-Internal.html#t:Interval">Interval</a></td><td class="doc empty">&nbsp;</td></tr><tr><td class="src"><a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Foldable.html#t:Foldable">Foldable</a> <a href="Numeric-Interval-Internal.html#t:Interval">Interval</a></td><td class="doc empty">&nbsp;</td></tr><tr><td class="src"><a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Eq.html#t:Eq">Eq</a> a =&gt; <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Eq.html#t:Eq">Eq</a> (<a href="Numeric-Interval-Internal.html#t:Interval">Interval</a> a)</td><td class="doc empty">&nbsp;</td></tr><tr><td class="src">(<a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Prelude.html#t:RealFloat">RealFloat</a> a, <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Ord.html#t:Ord">Ord</a> a) =&gt; <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Prelude.html#t:Floating">Floating</a> (<a href="Numeric-Interval-Internal.html#t:Interval">Interval</a> a)</td><td class="doc empty">&nbsp;</td></tr><tr><td class="src">(<a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Prelude.html#t:Fractional">Fractional</a> a, <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Ord.html#t:Ord">Ord</a> a) =&gt; <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Prelude.html#t:Fractional">Fractional</a> (<a href="Numeric-Interval-Internal.html#t:Interval">Interval</a> a)</td><td class="doc empty">&nbsp;</td></tr><tr><td class="src"><a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Data.html#t:Data">Data</a> a =&gt; <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Data.html#t:Data">Data</a> (<a href="Numeric-Interval-Internal.html#t:Interval">Interval</a> a)</td><td class="doc empty">&nbsp;</td></tr><tr><td class="src">(<a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Prelude.html#t:Num">Num</a> a, <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Ord.html#t:Ord">Ord</a> a) =&gt; <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Prelude.html#t:Num">Num</a> (<a href="Numeric-Interval-Internal.html#t:Interval">Interval</a> a)</td><td class="doc empty">&nbsp;</td></tr><tr><td class="src"><a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Ord.html#t:Ord">Ord</a> a =&gt; <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Ord.html#t:Ord">Ord</a> (<a href="Numeric-Interval-Internal.html#t:Interval">Interval</a> a)</td><td class="doc empty">&nbsp;</td></tr><tr><td class="src"><a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Prelude.html#t:Real">Real</a> a =&gt; <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Prelude.html#t:Real">Real</a> (<a href="Numeric-Interval-Internal.html#t:Interval">Interval</a> a)</td><td class="doc"><p><code><a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Prelude.html#v:realToFrac">realToFrac</a></code> will use the midpoint
</p></td></tr><tr><td class="src"><a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Prelude.html#t:RealFloat">RealFloat</a> a =&gt; <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Prelude.html#t:RealFloat">RealFloat</a> (<a href="Numeric-Interval-Internal.html#t:Interval">Interval</a> a)</td><td class="doc"><p>We have to play some semantic games to make these methods make sense.
 Most compute with the midpoint of the interval.
</p></td></tr><tr><td class="src"><a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Prelude.html#t:RealFrac">RealFrac</a> a =&gt; <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Prelude.html#t:RealFrac">RealFrac</a> (<a href="Numeric-Interval-Internal.html#t:Interval">Interval</a> a)</td><td class="doc empty">&nbsp;</td></tr><tr><td class="src"><a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Text-Show.html#t:Show">Show</a> a =&gt; <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Text-Show.html#t:Show">Show</a> (<a href="Numeric-Interval-Internal.html#t:Interval">Interval</a> a)</td><td class="doc empty">&nbsp;</td></tr></table></div></div></div><div class="top"><p class="src"><a name="v:..." class="def">(...)</a> :: <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Ord.html#t:Ord">Ord</a> a =&gt; a -&gt; a -&gt; <a href="Numeric-Interval-Internal.html#t:Interval">Interval</a> a<a href="src/Numeric-Interval-Internal.html#..." class="link">Source</a></p></div><div class="top"><p class="src"><a name="v:interval" class="def">interval</a> :: <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Ord.html#t:Ord">Ord</a> a =&gt; a -&gt; a -&gt; <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Maybe.html#t:Maybe">Maybe</a> (<a href="Numeric-Interval-Internal.html#t:Interval">Interval</a> a)<a href="src/Numeric-Interval-Internal.html#interval" class="link">Source</a></p></div><div class="top"><p class="src"><a name="v:whole" class="def">whole</a> :: <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Prelude.html#t:Fractional">Fractional</a> a =&gt; <a href="Numeric-Interval-Internal.html#t:Interval">Interval</a> a<a href="src/Numeric-Interval-Internal.html#whole" class="link">Source</a></p><div class="doc"><p>The whole real number line
</p><pre class="screen"><code class="prompt">&gt;&gt;&gt; </code><strong class="userinput"><code>whole
</code></strong>-Infinity ... Infinity
</pre></div></div><div class="top"><p class="src"><a name="v:empty" class="def">empty</a> :: <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Ord.html#t:Ord">Ord</a> a =&gt; <a href="Numeric-Interval-Internal.html#t:Interval">Interval</a> a<a href="src/Numeric-Interval-Internal.html#empty" class="link">Source</a></p><div class="doc"><p>An empty interval
</p><pre class="screen"><code class="prompt">&gt;&gt;&gt; </code><strong class="userinput"><code>empty
</code></strong>Empty
</pre></div></div><div class="top"><p class="src"><a name="v:null" class="def">null</a> ::  <a href="Numeric-Interval-Internal.html#t:Interval">Interval</a> a -&gt; <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Bool.html#t:Bool">Bool</a><a href="src/Numeric-Interval-Internal.html#null" class="link">Source</a></p><div class="doc"><p>Check if an interval is empty
</p><pre class="screen"><code class="prompt">&gt;&gt;&gt; </code><strong class="userinput"><code>null (1 ... 5)
</code></strong>False
</pre><pre class="screen"><code class="prompt">&gt;&gt;&gt; </code><strong class="userinput"><code>null (1 ... 1)
</code></strong>False
</pre><pre class="screen"><code class="prompt">&gt;&gt;&gt; </code><strong class="userinput"><code>null empty
</code></strong>True
</pre></div></div><div class="top"><p class="src"><a name="v:singleton" class="def">singleton</a> ::  a -&gt; <a href="Numeric-Interval-Internal.html#t:Interval">Interval</a> a<a href="src/Numeric-Interval-Internal.html#singleton" class="link">Source</a></p><div class="doc"><p>A singleton point
</p><pre class="screen"><code class="prompt">&gt;&gt;&gt; </code><strong class="userinput"><code>singleton 1
</code></strong>1 ... 1
</pre></div></div><div class="top"><p class="src"><a name="v:elem" class="def">elem</a> :: <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Ord.html#t:Ord">Ord</a> a =&gt; a -&gt; <a href="Numeric-Interval-Internal.html#t:Interval">Interval</a> a -&gt; <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Bool.html#t:Bool">Bool</a><a href="src/Numeric-Interval-Internal.html#elem" class="link">Source</a></p><div class="doc"><p>Determine if a point is in the interval.
</p><pre class="screen"><code class="prompt">&gt;&gt;&gt; </code><strong class="userinput"><code>elem 3.2 (1.0 ... 5.0)
</code></strong>True
</pre><pre class="screen"><code class="prompt">&gt;&gt;&gt; </code><strong class="userinput"><code>elem 5 (1.0 ... 5.0)
</code></strong>True
</pre><pre class="screen"><code class="prompt">&gt;&gt;&gt; </code><strong class="userinput"><code>elem 1 (1.0 ... 5.0)
</code></strong>True
</pre><pre class="screen"><code class="prompt">&gt;&gt;&gt; </code><strong class="userinput"><code>elem 8 (1.0 ... 5.0)
</code></strong>False
</pre><pre class="screen"><code class="prompt">&gt;&gt;&gt; </code><strong class="userinput"><code>elem 5 empty
</code></strong>False
</pre></div></div><div class="top"><p class="src"><a name="v:notElem" class="def">notElem</a> :: <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Ord.html#t:Ord">Ord</a> a =&gt; a -&gt; <a href="Numeric-Interval-Internal.html#t:Interval">Interval</a> a -&gt; <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Bool.html#t:Bool">Bool</a><a href="src/Numeric-Interval-Internal.html#notElem" class="link">Source</a></p><div class="doc"><p>Determine if a point is not included in the interval
</p><pre class="screen"><code class="prompt">&gt;&gt;&gt; </code><strong class="userinput"><code>notElem 8 (1.0 ... 5.0)
</code></strong>True
</pre><pre class="screen"><code class="prompt">&gt;&gt;&gt; </code><strong class="userinput"><code>notElem 1.4 (1.0 ... 5.0)
</code></strong>False
</pre><p>And of course, nothing is a member of the empty interval.
</p><pre class="screen"><code class="prompt">&gt;&gt;&gt; </code><strong class="userinput"><code>notElem 5 empty
</code></strong>True
</pre></div></div><div class="top"><p class="src"><a name="v:inf" class="def">inf</a> ::  <a href="Numeric-Interval-Internal.html#t:Interval">Interval</a> a -&gt; a<a href="src/Numeric-Interval-Internal.html#inf" class="link">Source</a></p><div class="doc"><p>The infimum (lower bound) of an interval
</p><pre class="screen"><code class="prompt">&gt;&gt;&gt; </code><strong class="userinput"><code>inf (1.0 ... 20.0)
</code></strong>1.0
</pre><pre class="screen"><code class="prompt">&gt;&gt;&gt; </code><strong class="userinput"><code>inf empty
</code></strong>*** Exception: empty interval
</pre></div></div><div class="top"><p class="src"><a name="v:sup" class="def">sup</a> ::  <a href="Numeric-Interval-Internal.html#t:Interval">Interval</a> a -&gt; a<a href="src/Numeric-Interval-Internal.html#sup" class="link">Source</a></p><div class="doc"><p>The supremum (upper bound) of an interval
</p><pre class="screen"><code class="prompt">&gt;&gt;&gt; </code><strong class="userinput"><code>sup (1.0 ... 20.0)
</code></strong>20.0
</pre><pre class="screen"><code class="prompt">&gt;&gt;&gt; </code><strong class="userinput"><code>sup empty
</code></strong>*** Exception: empty interval
</pre></div></div><div class="top"><p class="src"><a name="v:singular" class="def">singular</a> :: <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Ord.html#t:Ord">Ord</a> a =&gt; <a href="Numeric-Interval-Internal.html#t:Interval">Interval</a> a -&gt; <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Bool.html#t:Bool">Bool</a><a href="src/Numeric-Interval-Internal.html#singular" class="link">Source</a></p><div class="doc"><p>Is the interval a singleton point?
 N.B. This is fairly fragile and likely will not hold after
 even a few operations that only involve singletons
</p><pre class="screen"><code class="prompt">&gt;&gt;&gt; </code><strong class="userinput"><code>singular (singleton 1)
</code></strong>True
</pre><pre class="screen"><code class="prompt">&gt;&gt;&gt; </code><strong class="userinput"><code>singular (1.0 ... 20.0)
</code></strong>False
</pre></div></div><div class="top"><p class="src"><a name="v:width" class="def">width</a> :: <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Prelude.html#t:Num">Num</a> a =&gt; <a href="Numeric-Interval-Internal.html#t:Interval">Interval</a> a -&gt; a<a href="src/Numeric-Interval-Internal.html#width" class="link">Source</a></p><div class="doc"><p>Calculate the width of an interval.
</p><pre class="screen"><code class="prompt">&gt;&gt;&gt; </code><strong class="userinput"><code>width (1 ... 20)
</code></strong>19
</pre><pre class="screen"><code class="prompt">&gt;&gt;&gt; </code><strong class="userinput"><code>width (singleton 1)
</code></strong>0
</pre><pre class="screen"><code class="prompt">&gt;&gt;&gt; </code><strong class="userinput"><code>width empty
</code></strong>0
</pre></div></div><div class="top"><p class="src"><a name="v:midpoint" class="def">midpoint</a> :: <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Prelude.html#t:Fractional">Fractional</a> a =&gt; <a href="Numeric-Interval-Internal.html#t:Interval">Interval</a> a -&gt; a<a href="src/Numeric-Interval-Internal.html#midpoint" class="link">Source</a></p><div class="doc"><p>Nearest point to the midpoint of the interval.
</p><pre class="screen"><code class="prompt">&gt;&gt;&gt; </code><strong class="userinput"><code>midpoint (10.0 ... 20.0)
</code></strong>15.0
</pre><pre class="screen"><code class="prompt">&gt;&gt;&gt; </code><strong class="userinput"><code>midpoint (singleton 5.0)
</code></strong>5.0
</pre><pre class="screen"><code class="prompt">&gt;&gt;&gt; </code><strong class="userinput"><code>midpoint empty
</code></strong>*** Exception: empty interval
</pre></div></div><div class="top"><p class="src"><a name="v:intersection" class="def">intersection</a> :: (<a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Prelude.html#t:Fractional">Fractional</a> a, <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Ord.html#t:Ord">Ord</a> a) =&gt; <a href="Numeric-Interval-Internal.html#t:Interval">Interval</a> a -&gt; <a href="Numeric-Interval-Internal.html#t:Interval">Interval</a> a -&gt; <a href="Numeric-Interval-Internal.html#t:Interval">Interval</a> a<a href="src/Numeric-Interval-Internal.html#intersection" class="link">Source</a></p><div class="doc"><p>Calculate the intersection of two intervals.
</p><pre class="screen"><code class="prompt">&gt;&gt;&gt; </code><strong class="userinput"><code>intersection (1 ... 10 :: Interval Double) (5 ... 15 :: Interval Double)
</code></strong>5.0 ... 10.0
</pre></div></div><div class="top"><p class="src"><a name="v:hull" class="def">hull</a> :: <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Ord.html#t:Ord">Ord</a> a =&gt; <a href="Numeric-Interval-Internal.html#t:Interval">Interval</a> a -&gt; <a href="Numeric-Interval-Internal.html#t:Interval">Interval</a> a -&gt; <a href="Numeric-Interval-Internal.html#t:Interval">Interval</a> a<a href="src/Numeric-Interval-Internal.html#hull" class="link">Source</a></p><div class="doc"><p>Calculate the convex hull of two intervals
</p><pre class="screen"><code class="prompt">&gt;&gt;&gt; </code><strong class="userinput"><code>hull (0 ... 10 :: Interval Double) (5 ... 15 :: Interval Double)
</code></strong>0.0 ... 15.0
</pre><pre class="screen"><code class="prompt">&gt;&gt;&gt; </code><strong class="userinput"><code>hull (15 ... 85 :: Interval Double) (0 ... 10 :: Interval Double)
</code></strong>0.0 ... 85.0
</pre></div></div><div class="top"><p class="src"><a name="v:bisect" class="def">bisect</a> :: <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Prelude.html#t:Fractional">Fractional</a> a =&gt; <a href="Numeric-Interval-Internal.html#t:Interval">Interval</a> a -&gt; (<a href="Numeric-Interval-Internal.html#t:Interval">Interval</a> a, <a href="Numeric-Interval-Internal.html#t:Interval">Interval</a> a)<a href="src/Numeric-Interval-Internal.html#bisect" class="link">Source</a></p><div class="doc"><p>Bisect an interval at its midpoint.
</p><pre class="screen"><code class="prompt">&gt;&gt;&gt; </code><strong class="userinput"><code>bisect (10.0 ... 20.0)
</code></strong>(10.0 ... 15.0,15.0 ... 20.0)
</pre><pre class="screen"><code class="prompt">&gt;&gt;&gt; </code><strong class="userinput"><code>bisect (singleton 5.0)
</code></strong>(5.0 ... 5.0,5.0 ... 5.0)
</pre><pre class="screen"><code class="prompt">&gt;&gt;&gt; </code><strong class="userinput"><code>bisect Empty
</code></strong>(Empty,Empty)
</pre></div></div><div class="top"><p class="src"><a name="v:bisectIntegral" class="def">bisectIntegral</a> :: <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Prelude.html#t:Integral">Integral</a> a =&gt; <a href="Numeric-Interval-Internal.html#t:Interval">Interval</a> a -&gt; (<a href="Numeric-Interval-Internal.html#t:Interval">Interval</a> a, <a href="Numeric-Interval-Internal.html#t:Interval">Interval</a> a)<a href="src/Numeric-Interval-Internal.html#bisectIntegral" class="link">Source</a></p></div><div class="top"><p class="src"><a name="v:magnitude" class="def">magnitude</a> :: (<a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Prelude.html#t:Num">Num</a> a, <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Ord.html#t:Ord">Ord</a> a) =&gt; <a href="Numeric-Interval-Internal.html#t:Interval">Interval</a> a -&gt; a<a href="src/Numeric-Interval-Internal.html#magnitude" class="link">Source</a></p><div class="doc"><p>Magnitude
</p><pre class="screen"><code class="prompt">&gt;&gt;&gt; </code><strong class="userinput"><code>magnitude (1 ... 20)
</code></strong>20
</pre><pre class="screen"><code class="prompt">&gt;&gt;&gt; </code><strong class="userinput"><code>magnitude (-20 ... 10)
</code></strong>20
</pre><pre class="screen"><code class="prompt">&gt;&gt;&gt; </code><strong class="userinput"><code>magnitude (singleton 5)
</code></strong>5
</pre><p>throws <code><a href="Numeric-Interval-Exception.html#t:EmptyInterval">EmptyInterval</a></code> if the interval is empty.
</p><pre class="screen"><code class="prompt">&gt;&gt;&gt; </code><strong class="userinput"><code>magnitude empty
</code></strong>*** Exception: empty interval
</pre></div></div><div class="top"><p class="src"><a name="v:mignitude" class="def">mignitude</a> :: (<a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Prelude.html#t:Num">Num</a> a, <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Ord.html#t:Ord">Ord</a> a) =&gt; <a href="Numeric-Interval-Internal.html#t:Interval">Interval</a> a -&gt; a<a href="src/Numeric-Interval-Internal.html#mignitude" class="link">Source</a></p><div class="doc"><p>&quot;mignitude&quot;
</p><pre class="screen"><code class="prompt">&gt;&gt;&gt; </code><strong class="userinput"><code>mignitude (1 ... 20)
</code></strong>1
</pre><pre class="screen"><code class="prompt">&gt;&gt;&gt; </code><strong class="userinput"><code>mignitude (-20 ... 10)
</code></strong>0
</pre><pre class="screen"><code class="prompt">&gt;&gt;&gt; </code><strong class="userinput"><code>mignitude (singleton 5)
</code></strong>5
</pre><p>throws <code><a href="Numeric-Interval-Exception.html#t:EmptyInterval">EmptyInterval</a></code> if the interval is empty.
</p><pre class="screen"><code class="prompt">&gt;&gt;&gt; </code><strong class="userinput"><code>mignitude empty
</code></strong>*** Exception: empty interval
</pre></div></div><div class="top"><p class="src"><a name="v:distance" class="def">distance</a> :: (<a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Prelude.html#t:Num">Num</a> a, <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Ord.html#t:Ord">Ord</a> a) =&gt; <a href="Numeric-Interval-Internal.html#t:Interval">Interval</a> a -&gt; <a href="Numeric-Interval-Internal.html#t:Interval">Interval</a> a -&gt; a<a href="src/Numeric-Interval-Internal.html#distance" class="link">Source</a></p><div class="doc"><p>Hausdorff distance between intervals.
</p><pre class="screen"><code class="prompt">&gt;&gt;&gt; </code><strong class="userinput"><code>distance (1 ... 7) (6 ... 10)
</code></strong>0
</pre><pre class="screen"><code class="prompt">&gt;&gt;&gt; </code><strong class="userinput"><code>distance (1 ... 7) (15 ... 24)
</code></strong>8
</pre><pre class="screen"><code class="prompt">&gt;&gt;&gt; </code><strong class="userinput"><code>distance (1 ... 7) (-10 ... -2)
</code></strong>3
</pre><pre class="screen"><code class="prompt">&gt;&gt;&gt; </code><strong class="userinput"><code>distance Empty (1 ... 1)
</code></strong>*** Exception: empty interval
</pre></div></div><div class="top"><p class="src"><a name="v:contains" class="def">contains</a> :: <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Ord.html#t:Ord">Ord</a> a =&gt; <a href="Numeric-Interval-Internal.html#t:Interval">Interval</a> a -&gt; <a href="Numeric-Interval-Internal.html#t:Interval">Interval</a> a -&gt; <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Bool.html#t:Bool">Bool</a><a href="src/Numeric-Interval-Internal.html#contains" class="link">Source</a></p><div class="doc"><p>Check if interval <code>X</code> totally contains interval <code>Y</code>
</p><pre class="screen"><code class="prompt">&gt;&gt;&gt; </code><strong class="userinput"><code>(20 ... 40 :: Interval Double) `contains` (25 ... 35 :: Interval Double)
</code></strong>True
</pre><pre class="screen"><code class="prompt">&gt;&gt;&gt; </code><strong class="userinput"><code>(20 ... 40 :: Interval Double) `contains` (15 ... 35 :: Interval Double)
</code></strong>False
</pre></div></div><div class="top"><p class="src"><a name="v:isSubsetOf" class="def">isSubsetOf</a> :: <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Ord.html#t:Ord">Ord</a> a =&gt; <a href="Numeric-Interval-Internal.html#t:Interval">Interval</a> a -&gt; <a href="Numeric-Interval-Internal.html#t:Interval">Interval</a> a -&gt; <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Bool.html#t:Bool">Bool</a><a href="src/Numeric-Interval-Internal.html#isSubsetOf" class="link">Source</a></p><div class="doc"><p>Flipped version of <code><a href="Numeric-Interval-Internal.html#v:contains">contains</a></code>. Check if interval <code>X</code> a subset of interval <code>Y</code>
</p><pre class="screen"><code class="prompt">&gt;&gt;&gt; </code><strong class="userinput"><code>(25 ... 35 :: Interval Double) `isSubsetOf` (20 ... 40 :: Interval Double)
</code></strong>True
</pre><pre class="screen"><code class="prompt">&gt;&gt;&gt; </code><strong class="userinput"><code>(20 ... 40 :: Interval Double) `isSubsetOf` (15 ... 35 :: Interval Double)
</code></strong>False
</pre></div></div><div class="top"><p class="src"><a name="v:certainly" class="def">certainly</a> :: <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Ord.html#t:Ord">Ord</a> a =&gt; (<span class="keyword">forall</span> b. <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Ord.html#t:Ord">Ord</a> b =&gt; b -&gt; b -&gt; <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Bool.html#t:Bool">Bool</a>) -&gt; <a href="Numeric-Interval-Internal.html#t:Interval">Interval</a> a -&gt; <a href="Numeric-Interval-Internal.html#t:Interval">Interval</a> a -&gt; <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Bool.html#t:Bool">Bool</a><a href="src/Numeric-Interval-Internal.html#certainly" class="link">Source</a></p><div class="doc"><p>For all <code>x</code> in <code>X</code>, <code>y</code> in <code>Y</code>. <code>x <code>op</code> y</code>
</p></div></div><div class="top"><p class="src"><a name="v:-60--33-" class="def">(&lt;!)</a> :: <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Ord.html#t:Ord">Ord</a> a =&gt; <a href="Numeric-Interval-Internal.html#t:Interval">Interval</a> a -&gt; <a href="Numeric-Interval-Internal.html#t:Interval">Interval</a> a -&gt; <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Bool.html#t:Bool">Bool</a><a href="src/Numeric-Interval-Internal.html#%3C%21" class="link">Source</a></p><div class="doc"><p>For all <code>x</code> in <code>X</code>, <code>y</code> in <code>Y</code>. <code>x <code><a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Ord.html#v:-60-">&lt;</a></code> y</code>
</p><pre class="screen"><code class="prompt">&gt;&gt;&gt; </code><strong class="userinput"><code>(5 ... 10 :: Interval Double) &lt;! (20 ... 30 :: Interval Double)
</code></strong>True
</pre><pre class="screen"><code class="prompt">&gt;&gt;&gt; </code><strong class="userinput"><code>(5 ... 10 :: Interval Double) &lt;! (10 ... 30 :: Interval Double)
</code></strong>False
</pre><pre class="screen"><code class="prompt">&gt;&gt;&gt; </code><strong class="userinput"><code>(20 ... 30 :: Interval Double) &lt;! (5 ... 10 :: Interval Double)
</code></strong>False
</pre></div></div><div class="top"><p class="src"><a name="v:-60--61--33-" class="def">(&lt;=!)</a> :: <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Ord.html#t:Ord">Ord</a> a =&gt; <a href="Numeric-Interval-Internal.html#t:Interval">Interval</a> a -&gt; <a href="Numeric-Interval-Internal.html#t:Interval">Interval</a> a -&gt; <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Bool.html#t:Bool">Bool</a><a href="src/Numeric-Interval-Internal.html#%3C%3D%21" class="link">Source</a></p><div class="doc"><p>For all <code>x</code> in <code>X</code>, <code>y</code> in <code>Y</code>. <code>x <code><a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Ord.html#v:-60--61-">&lt;=</a></code> y</code>
</p><pre class="screen"><code class="prompt">&gt;&gt;&gt; </code><strong class="userinput"><code>(5 ... 10 :: Interval Double) &lt;=! (20 ... 30 :: Interval Double)
</code></strong>True
</pre><pre class="screen"><code class="prompt">&gt;&gt;&gt; </code><strong class="userinput"><code>(5 ... 10 :: Interval Double) &lt;=! (10 ... 30 :: Interval Double)
</code></strong>True
</pre><pre class="screen"><code class="prompt">&gt;&gt;&gt; </code><strong class="userinput"><code>(20 ... 30 :: Interval Double) &lt;=! (5 ... 10 :: Interval Double)
</code></strong>False
</pre></div></div><div class="top"><p class="src"><a name="v:-61--61--33-" class="def">(==!)</a> :: <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Eq.html#t:Eq">Eq</a> a =&gt; <a href="Numeric-Interval-Internal.html#t:Interval">Interval</a> a -&gt; <a href="Numeric-Interval-Internal.html#t:Interval">Interval</a> a -&gt; <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Bool.html#t:Bool">Bool</a><a href="src/Numeric-Interval-Internal.html#%3D%3D%21" class="link">Source</a></p><div class="doc"><p>For all <code>x</code> in <code>X</code>, <code>y</code> in <code>Y</code>. <code>x <code><a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Eq.html#v:-61--61-">==</a></code> y</code>
</p><p>Only singleton intervals or empty intervals can return true
</p><pre class="screen"><code class="prompt">&gt;&gt;&gt; </code><strong class="userinput"><code>(singleton 5 :: Interval Double) ==! (singleton 5 :: Interval Double)
</code></strong>True
</pre><pre class="screen"><code class="prompt">&gt;&gt;&gt; </code><strong class="userinput"><code>(5 ... 10 :: Interval Double) ==! (5 ... 10 :: Interval Double)
</code></strong>False
</pre></div></div><div class="top"><p class="src"><a name="v:-62--61--33-" class="def">(&gt;=!)</a> :: <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Ord.html#t:Ord">Ord</a> a =&gt; <a href="Numeric-Interval-Internal.html#t:Interval">Interval</a> a -&gt; <a href="Numeric-Interval-Internal.html#t:Interval">Interval</a> a -&gt; <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Bool.html#t:Bool">Bool</a><a href="src/Numeric-Interval-Internal.html#%3E%3D%21" class="link">Source</a></p><div class="doc"><p>For all <code>x</code> in <code>X</code>, <code>y</code> in <code>Y</code>. <code>x <code><a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Ord.html#v:-62--61-">&gt;=</a></code> y</code>
</p><pre class="screen"><code class="prompt">&gt;&gt;&gt; </code><strong class="userinput"><code>(20 ... 40 :: Interval Double) &gt;=! (10 ... 20 :: Interval Double)
</code></strong>True
</pre><pre class="screen"><code class="prompt">&gt;&gt;&gt; </code><strong class="userinput"><code>(5 ... 20 :: Interval Double) &gt;=! (15 ... 40 :: Interval Double)
</code></strong>False
</pre></div></div><div class="top"><p class="src"><a name="v:-62--33-" class="def">(&gt;!)</a> :: <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Ord.html#t:Ord">Ord</a> a =&gt; <a href="Numeric-Interval-Internal.html#t:Interval">Interval</a> a -&gt; <a href="Numeric-Interval-Internal.html#t:Interval">Interval</a> a -&gt; <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Bool.html#t:Bool">Bool</a><a href="src/Numeric-Interval-Internal.html#%3E%21" class="link">Source</a></p><div class="doc"><p>For all <code>x</code> in <code>X</code>, <code>y</code> in <code>Y</code>. <code>x <code><a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Ord.html#v:-62-">&gt;</a></code> y</code>
</p><pre class="screen"><code class="prompt">&gt;&gt;&gt; </code><strong class="userinput"><code>(20 ... 40 :: Interval Double) &gt;! (10 ... 19 :: Interval Double)
</code></strong>True
</pre><pre class="screen"><code class="prompt">&gt;&gt;&gt; </code><strong class="userinput"><code>(5 ... 20 :: Interval Double) &gt;! (15 ... 40 :: Interval Double)
</code></strong>False
</pre></div></div><div class="top"><p class="src"><a name="v:possibly" class="def">possibly</a> :: <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Ord.html#t:Ord">Ord</a> a =&gt; (<span class="keyword">forall</span> b. <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Ord.html#t:Ord">Ord</a> b =&gt; b -&gt; b -&gt; <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Bool.html#t:Bool">Bool</a>) -&gt; <a href="Numeric-Interval-Internal.html#t:Interval">Interval</a> a -&gt; <a href="Numeric-Interval-Internal.html#t:Interval">Interval</a> a -&gt; <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Bool.html#t:Bool">Bool</a><a href="src/Numeric-Interval-Internal.html#possibly" class="link">Source</a></p><div class="doc"><p>Does there exist an <code>x</code> in <code>X</code>, <code>y</code> in <code>Y</code> such that <code>x <code>op</code> y</code>?
</p></div></div><div class="top"><p class="src"><a name="v:-60--63-" class="def">(&lt;?)</a> :: <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Ord.html#t:Ord">Ord</a> a =&gt; <a href="Numeric-Interval-Internal.html#t:Interval">Interval</a> a -&gt; <a href="Numeric-Interval-Internal.html#t:Interval">Interval</a> a -&gt; <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Bool.html#t:Bool">Bool</a><a href="src/Numeric-Interval-Internal.html#%3C%3F" class="link">Source</a></p><div class="doc"><p>Does there exist an <code>x</code> in <code>X</code>, <code>y</code> in <code>Y</code> such that <code>x <code><a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Ord.html#v:-60-">&lt;</a></code> y</code>?
</p></div></div><div class="top"><p class="src"><a name="v:-60--61--63-" class="def">(&lt;=?)</a> :: <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Ord.html#t:Ord">Ord</a> a =&gt; <a href="Numeric-Interval-Internal.html#t:Interval">Interval</a> a -&gt; <a href="Numeric-Interval-Internal.html#t:Interval">Interval</a> a -&gt; <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Bool.html#t:Bool">Bool</a><a href="src/Numeric-Interval-Internal.html#%3C%3D%3F" class="link">Source</a></p><div class="doc"><p>Does there exist an <code>x</code> in <code>X</code>, <code>y</code> in <code>Y</code> such that <code>x <code><a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Ord.html#v:-60--61-">&lt;=</a></code> y</code>?
</p></div></div><div class="top"><p class="src"><a name="v:-61--61--63-" class="def">(==?)</a> :: <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Ord.html#t:Ord">Ord</a> a =&gt; <a href="Numeric-Interval-Internal.html#t:Interval">Interval</a> a -&gt; <a href="Numeric-Interval-Internal.html#t:Interval">Interval</a> a -&gt; <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Bool.html#t:Bool">Bool</a><a href="src/Numeric-Interval-Internal.html#%3D%3D%3F" class="link">Source</a></p><div class="doc"><p>Does there exist an <code>x</code> in <code>X</code>, <code>y</code> in <code>Y</code> such that <code>x <code><a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Eq.html#v:-61--61-">==</a></code> y</code>?
</p></div></div><div class="top"><p class="src"><a name="v:-62--61--63-" class="def">(&gt;=?)</a> :: <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Ord.html#t:Ord">Ord</a> a =&gt; <a href="Numeric-Interval-Internal.html#t:Interval">Interval</a> a -&gt; <a href="Numeric-Interval-Internal.html#t:Interval">Interval</a> a -&gt; <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Bool.html#t:Bool">Bool</a><a href="src/Numeric-Interval-Internal.html#%3E%3D%3F" class="link">Source</a></p><div class="doc"><p>Does there exist an <code>x</code> in <code>X</code>, <code>y</code> in <code>Y</code> such that <code>x <code><a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Ord.html#v:-62--61-">&gt;=</a></code> y</code>?
</p></div></div><div class="top"><p class="src"><a name="v:-62--63-" class="def">(&gt;?)</a> :: <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Ord.html#t:Ord">Ord</a> a =&gt; <a href="Numeric-Interval-Internal.html#t:Interval">Interval</a> a -&gt; <a href="Numeric-Interval-Internal.html#t:Interval">Interval</a> a -&gt; <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Bool.html#t:Bool">Bool</a><a href="src/Numeric-Interval-Internal.html#%3E%3F" class="link">Source</a></p><div class="doc"><p>Does there exist an <code>x</code> in <code>X</code>, <code>y</code> in <code>Y</code> such that <code>x <code><a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Ord.html#v:-62-">&gt;</a></code> y</code>?
</p></div></div><div class="top"><p class="src"><a name="v:idouble" class="def">idouble</a> :: <a href="Numeric-Interval-Internal.html#t:Interval">Interval</a> <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Prelude.html#t:Double">Double</a> -&gt; <a href="Numeric-Interval-Internal.html#t:Interval">Interval</a> <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Prelude.html#t:Double">Double</a><a href="src/Numeric-Interval-Internal.html#idouble" class="link">Source</a></p><div class="doc"><p>id function. Useful for type specification
</p><pre class="screen"><code class="prompt">&gt;&gt;&gt; </code><strong class="userinput"><code>:t idouble (1 ... 3)
</code></strong>idouble (1 ... 3) :: Interval Double
</pre></div></div><div class="top"><p class="src"><a name="v:ifloat" class="def">ifloat</a> :: <a href="Numeric-Interval-Internal.html#t:Interval">Interval</a> <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Prelude.html#t:Float">Float</a> -&gt; <a href="Numeric-Interval-Internal.html#t:Interval">Interval</a> <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Prelude.html#t:Float">Float</a><a href="src/Numeric-Interval-Internal.html#ifloat" class="link">Source</a></p><div class="doc"><p>id function. Useful for type specification
</p><pre class="screen"><code class="prompt">&gt;&gt;&gt; </code><strong class="userinput"><code>:t ifloat (1 ... 3)
</code></strong>ifloat (1 ... 3) :: Interval Float
</pre></div></div></div></div><div id="footer"><p>Produced by <a href="http://www.haskell.org/haddock/">Haddock</a> version 2.13.2</p></div></body></html>