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</script></head><body><div id="package-header"><ul class="links" id="page-menu"><li><a href="src/Numeric-Interval.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-0.7.2: Interval Arithmetic</p></div><div id="content"><div id="module-header"><table class="info"><tr><th>Copyright</th><td>(c) Edward Kmett 2010-2014</td></tr><tr><th>License</th><td>BSD3</td></tr><tr><th>Maintainer</th><td>ekmett@gmail.com</td></tr><tr><th>Stability</th><td>experimental</td></tr><tr><th>Portability</th><td>DeriveDataTypeable</td></tr><tr><th>Safe Haskell</th><td>Safe</td></tr><tr><th>Language</th><td>Haskell98</td></tr></table><p class="caption">Numeric.Interval</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</li><li class="src short"><a href="#v:...">(...)</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Ord.html#t:Ord">Ord</a> a => a -> a -> <a href="Numeric-Interval.html#t:Interval">Interval</a> a</li><li class="src short"><a href="#v:-43--47--45-">(+/-)</a> :: (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Num">Num</a> a, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Ord.html#t:Ord">Ord</a> a) => a -> a -> <a href="Numeric-Interval.html#t:Interval">Interval</a> a</li><li class="src short"><a href="#v:interval">interval</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Ord.html#t:Ord">Ord</a> a => a -> a -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Maybe.html#t:Maybe">Maybe</a> (<a href="Numeric-Interval.html#t:Interval">Interval</a> a)</li><li class="src short"><a href="#v:whole">whole</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Fractional">Fractional</a> a => <a href="Numeric-Interval.html#t:Interval">Interval</a> a</li><li class="src short"><a href="#v:empty">empty</a> :: <a href="Numeric-Interval.html#t:Interval">Interval</a> a</li><li class="src short"><a href="#v:null">null</a> :: <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Bool.html#t:Bool">Bool</a></li><li class="src short"><a href="#v:singleton">singleton</a> :: a -> <a href="Numeric-Interval.html#t:Interval">Interval</a> a</li><li class="src short"><a href="#v:elem">elem</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Ord.html#t:Ord">Ord</a> a => a -> <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Bool.html#t:Bool">Bool</a></li><li class="src short"><a href="#v:notElem">notElem</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Ord.html#t:Ord">Ord</a> a => a -> <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Bool.html#t:Bool">Bool</a></li><li class="src short"><a href="#v:inf">inf</a> :: <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> a</li><li class="src short"><a href="#v:sup">sup</a> :: <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> a</li><li class="src short"><a href="#v:singular">singular</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Ord.html#t:Ord">Ord</a> a => <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Bool.html#t:Bool">Bool</a></li><li class="src short"><a href="#v:width">width</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Num">Num</a> a => <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> a</li><li class="src short"><a href="#v:midpoint">midpoint</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Fractional">Fractional</a> a => <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> a</li><li class="src short"><a href="#v:intersection">intersection</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Ord.html#t:Ord">Ord</a> a => <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="Numeric-Interval.html#t:Interval">Interval</a> a</li><li class="src short"><a href="#v:hull">hull</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Ord.html#t:Ord">Ord</a> a => <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="Numeric-Interval.html#t:Interval">Interval</a> a</li><li class="src short"><a href="#v:bisect">bisect</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Fractional">Fractional</a> a => <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> (<a href="Numeric-Interval.html#t:Interval">Interval</a> a, <a href="Numeric-Interval.html#t:Interval">Interval</a> a)</li><li class="src short"><a href="#v:bisectIntegral">bisectIntegral</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Integral">Integral</a> a => <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> (<a href="Numeric-Interval.html#t:Interval">Interval</a> a, <a href="Numeric-Interval.html#t:Interval">Interval</a> a)</li><li class="src short"><a href="#v:magnitude">magnitude</a> :: (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Num">Num</a> a, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Ord.html#t:Ord">Ord</a> a) => <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> a</li><li class="src short"><a href="#v:mignitude">mignitude</a> :: (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Num">Num</a> a, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Ord.html#t:Ord">Ord</a> a) => <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> a</li><li class="src short"><a href="#v:distance">distance</a> :: (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Num">Num</a> a, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Ord.html#t:Ord">Ord</a> a) => <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> a</li><li class="src short"><a href="#v:inflate">inflate</a> :: (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Num">Num</a> a, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Ord.html#t:Ord">Ord</a> a) => a -> <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="Numeric-Interval.html#t:Interval">Interval</a> a</li><li class="src short"><a href="#v:deflate">deflate</a> :: (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Fractional">Fractional</a> a, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Ord.html#t:Ord">Ord</a> a) => a -> <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="Numeric-Interval.html#t:Interval">Interval</a> a</li><li class="src short"><a href="#v:scale">scale</a> :: (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Fractional">Fractional</a> a, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Ord.html#t:Ord">Ord</a> a) => a -> <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="Numeric-Interval.html#t:Interval">Interval</a> a</li><li class="src short"><a href="#v:symmetric">symmetric</a> :: (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Num">Num</a> a, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Ord.html#t:Ord">Ord</a> a) => a -> <a href="Numeric-Interval.html#t:Interval">Interval</a> a</li><li class="src short"><a href="#v:contains">contains</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Ord.html#t:Ord">Ord</a> a => <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Bool.html#t:Bool">Bool</a></li><li class="src short"><a href="#v:isSubsetOf">isSubsetOf</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Ord.html#t:Ord">Ord</a> a => <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Bool.html#t:Bool">Bool</a></li><li class="src short"><a href="#v:certainly">certainly</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Ord.html#t:Ord">Ord</a> a => (<span class="keyword">forall</span> b. <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Ord.html#t:Ord">Ord</a> b => b -> b -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Bool.html#t:Bool">Bool</a>) -> <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Bool.html#t:Bool">Bool</a></li><li class="src short"><a href="#v:-60--33-">(<!)</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Ord.html#t:Ord">Ord</a> a => <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Bool.html#t:Bool">Bool</a></li><li class="src short"><a href="#v:-60--61--33-">(<=!)</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Ord.html#t:Ord">Ord</a> a => <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Bool.html#t:Bool">Bool</a></li><li class="src short"><a href="#v:-61--61--33-">(==!)</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Eq.html#t:Eq">Eq</a> a => <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Bool.html#t:Bool">Bool</a></li><li class="src short"><a href="#v:-62--61--33-">(>=!)</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Ord.html#t:Ord">Ord</a> a => <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Bool.html#t:Bool">Bool</a></li><li class="src short"><a href="#v:-62--33-">(>!)</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Ord.html#t:Ord">Ord</a> a => <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Bool.html#t:Bool">Bool</a></li><li class="src short"><a href="#v:possibly">possibly</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Ord.html#t:Ord">Ord</a> a => (<span class="keyword">forall</span> b. <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Ord.html#t:Ord">Ord</a> b => b -> b -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Bool.html#t:Bool">Bool</a>) -> <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Bool.html#t:Bool">Bool</a></li><li class="src short"><a href="#v:-60--63-">(<?)</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Ord.html#t:Ord">Ord</a> a => <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Bool.html#t:Bool">Bool</a></li><li class="src short"><a href="#v:-60--61--63-">(<=?)</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Ord.html#t:Ord">Ord</a> a => <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Bool.html#t:Bool">Bool</a></li><li class="src short"><a href="#v:-61--61--63-">(==?)</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Ord.html#t:Ord">Ord</a> a => <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Bool.html#t:Bool">Bool</a></li><li class="src short"><a href="#v:-62--61--63-">(>=?)</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Ord.html#t:Ord">Ord</a> a => <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Bool.html#t:Bool">Bool</a></li><li class="src short"><a href="#v:-62--63-">(>?)</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Ord.html#t:Ord">Ord</a> a => <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Bool.html#t:Bool">Bool</a></li><li class="src short"><a href="#v:idouble">idouble</a> :: <a href="Numeric-Interval.html#t:Interval">Interval</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Double">Double</a> -> <a href="Numeric-Interval.html#t:Interval">Interval</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Double">Double</a></li><li class="src short"><a href="#v:ifloat">ifloat</a> :: <a href="Numeric-Interval.html#t:Interval">Interval</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Float">Float</a> -> <a href="Numeric-Interval.html#t:Interval">Interval</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/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 id="t:Interval" class="def">Interval</a> a <a href="src/Numeric-Interval-Internal.html#Interval" class="link">Source</a> <a href="#t:Interval" class="selflink">#</a></p><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 clearfix"><span class="inst-left"><span id="control.i:id:Interval:Foldable:1" class="instance expander" onclick="toggleSection('i:id:Interval:Foldable:1')"></span> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Foldable.html#t:Foldable">Foldable</a> <a href="Numeric-Interval.html#t:Interval">Interval</a></span> <a href="src/Numeric-Interval-Internal.html#line-81" class="link">Source</a> <a href="#t:Interval" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:id:Interval:Foldable:1" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:fold">fold</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Monoid.html#t:Monoid">Monoid</a> m => <a href="Numeric-Interval.html#t:Interval">Interval</a> m -> m <a href="#v:fold" class="selflink">#</a></p><p class="src"><a href="#v:foldMap">foldMap</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Monoid.html#t:Monoid">Monoid</a> m => (a -> m) -> <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> m <a href="#v:foldMap" class="selflink">#</a></p><p class="src"><a href="#v:foldr">foldr</a> :: (a -> b -> b) -> b -> <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> b <a href="#v:foldr" class="selflink">#</a></p><p class="src"><a href="#v:foldr-39-">foldr'</a> :: (a -> b -> b) -> b -> <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> b <a href="#v:foldr-39-" class="selflink">#</a></p><p class="src"><a href="#v:foldl">foldl</a> :: (b -> a -> b) -> b -> <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> b <a href="#v:foldl" class="selflink">#</a></p><p class="src"><a href="#v:foldl-39-">foldl'</a> :: (b -> a -> b) -> b -> <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> b <a href="#v:foldl-39-" class="selflink">#</a></p><p class="src"><a href="#v:foldr1">foldr1</a> :: (a -> a -> a) -> <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> a <a href="#v:foldr1" class="selflink">#</a></p><p class="src"><a href="#v:foldl1">foldl1</a> :: (a -> a -> a) -> <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> a <a href="#v:foldl1" class="selflink">#</a></p><p class="src"><a href="#v:toList">toList</a> :: <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> [a] <a href="#v:toList" class="selflink">#</a></p><p class="src"><a href="#v:null">null</a> :: <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Bool.html#t:Bool">Bool</a> <a href="#v:null" class="selflink">#</a></p><p class="src"><a href="#v:length">length</a> :: <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Int.html#t:Int">Int</a> <a href="#v:length" class="selflink">#</a></p><p class="src"><a href="#v:elem">elem</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Eq.html#t:Eq">Eq</a> a => a -> <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Bool.html#t:Bool">Bool</a> <a href="#v:elem" class="selflink">#</a></p><p class="src"><a href="#v:maximum">maximum</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Ord.html#t:Ord">Ord</a> a => <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> a <a href="#v:maximum" class="selflink">#</a></p><p class="src"><a href="#v:minimum">minimum</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Ord.html#t:Ord">Ord</a> a => <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> a <a href="#v:minimum" class="selflink">#</a></p><p class="src"><a href="#v:sum">sum</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Num">Num</a> a => <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> a <a href="#v:sum" class="selflink">#</a></p><p class="src"><a href="#v:product">product</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Num">Num</a> a => <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> a <a href="#v:product" class="selflink">#</a></p></div></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:id:Interval:Generic1:2" class="instance expander" onclick="toggleSection('i:id:Interval:Generic1:2')"></span> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/GHC-Generics.html#t:Generic1">Generic1</a> <a href="Numeric-Interval.html#t:Interval">Interval</a></span> <a href="src/Numeric-Interval-Internal.html#line-76" class="link">Source</a> <a href="#t:Interval" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:id:Interval:Generic1:2" class="inst-details hide"><div class="subs associated-types"><p class="caption">Associated Types</p><p class="src"><span class="keyword">type</span> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/GHC-Generics.html#t:Rep1">Rep1</a> (<a href="Numeric-Interval.html#t:Interval">Interval</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Kind.html#t:-42-">*</a> -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Kind.html#t:-42-">*</a>) :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Kind.html#t:-42-">*</a> -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Kind.html#t:-42-">*</a> <a href="#t:Rep1" class="selflink">#</a></p></div> <div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:from1">from1</a> :: <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/GHC-Generics.html#t:Rep1">Rep1</a> <a href="Numeric-Interval.html#t:Interval">Interval</a> a <a href="#v:from1" class="selflink">#</a></p><p class="src"><a href="#v:to1">to1</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/GHC-Generics.html#t:Rep1">Rep1</a> <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="Numeric-Interval.html#t:Interval">Interval</a> a <a href="#v:to1" class="selflink">#</a></p></div></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:id:Interval:Eq:3" class="instance expander" onclick="toggleSection('i:id:Interval:Eq:3')"></span> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Eq.html#t:Eq">Eq</a> a => <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Eq.html#t:Eq">Eq</a> (<a href="Numeric-Interval.html#t:Interval">Interval</a> a)</span> <a href="src/Numeric-Interval-Internal.html#line-194" class="link">Source</a> <a href="#t:Interval" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:id:Interval:Eq:3" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:-61--61-">(==)</a> :: <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Bool.html#t:Bool">Bool</a> <a href="#v:-61--61-" class="selflink">#</a></p><p class="src"><a href="#v:-47--61-">(/=)</a> :: <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Bool.html#t:Bool">Bool</a> <a href="#v:-47--61-" class="selflink">#</a></p></div></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:id:Interval:Floating:4" class="instance expander" onclick="toggleSection('i:id:Interval:Floating:4')"></span> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:RealFloat">RealFloat</a> a, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Ord.html#t:Ord">Ord</a> a) => <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Numeric.html#t:Floating">Floating</a> (<a href="Numeric-Interval.html#t:Interval">Interval</a> a)</span> <a href="src/Numeric-Interval-Internal.html#line-537" class="link">Source</a> <a href="#t:Interval" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:id:Interval:Floating:4" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:pi">pi</a> :: <a href="Numeric-Interval.html#t:Interval">Interval</a> a <a href="#v:pi" class="selflink">#</a></p><p class="src"><a href="#v:exp">exp</a> :: <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="Numeric-Interval.html#t:Interval">Interval</a> a <a href="#v:exp" class="selflink">#</a></p><p class="src"><a href="#v:log">log</a> :: <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="Numeric-Interval.html#t:Interval">Interval</a> a <a href="#v:log" class="selflink">#</a></p><p class="src"><a href="#v:sqrt">sqrt</a> :: <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="Numeric-Interval.html#t:Interval">Interval</a> a <a href="#v:sqrt" class="selflink">#</a></p><p class="src"><a href="#v:-42--42-">(**)</a> :: <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="Numeric-Interval.html#t:Interval">Interval</a> a <a href="#v:-42--42-" class="selflink">#</a></p><p class="src"><a href="#v:logBase">logBase</a> :: <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="Numeric-Interval.html#t:Interval">Interval</a> a <a href="#v:logBase" class="selflink">#</a></p><p class="src"><a href="#v:sin">sin</a> :: <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="Numeric-Interval.html#t:Interval">Interval</a> a <a href="#v:sin" class="selflink">#</a></p><p class="src"><a href="#v:cos">cos</a> :: <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="Numeric-Interval.html#t:Interval">Interval</a> a <a href="#v:cos" class="selflink">#</a></p><p class="src"><a href="#v:tan">tan</a> :: <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="Numeric-Interval.html#t:Interval">Interval</a> a <a href="#v:tan" class="selflink">#</a></p><p class="src"><a href="#v:asin">asin</a> :: <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="Numeric-Interval.html#t:Interval">Interval</a> a <a href="#v:asin" class="selflink">#</a></p><p class="src"><a href="#v:acos">acos</a> :: <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="Numeric-Interval.html#t:Interval">Interval</a> a <a href="#v:acos" class="selflink">#</a></p><p class="src"><a href="#v:atan">atan</a> :: <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="Numeric-Interval.html#t:Interval">Interval</a> a <a href="#v:atan" class="selflink">#</a></p><p class="src"><a href="#v:sinh">sinh</a> :: <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="Numeric-Interval.html#t:Interval">Interval</a> a <a href="#v:sinh" class="selflink">#</a></p><p class="src"><a href="#v:cosh">cosh</a> :: <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="Numeric-Interval.html#t:Interval">Interval</a> a <a href="#v:cosh" class="selflink">#</a></p><p class="src"><a href="#v:tanh">tanh</a> :: <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="Numeric-Interval.html#t:Interval">Interval</a> a <a href="#v:tanh" class="selflink">#</a></p><p class="src"><a href="#v:asinh">asinh</a> :: <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="Numeric-Interval.html#t:Interval">Interval</a> a <a href="#v:asinh" class="selflink">#</a></p><p class="src"><a href="#v:acosh">acosh</a> :: <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="Numeric-Interval.html#t:Interval">Interval</a> a <a href="#v:acosh" class="selflink">#</a></p><p class="src"><a href="#v:atanh">atanh</a> :: <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="Numeric-Interval.html#t:Interval">Interval</a> a <a href="#v:atanh" class="selflink">#</a></p><p class="src"><a href="#v:log1p">log1p</a> :: <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="Numeric-Interval.html#t:Interval">Interval</a> a <a href="#v:log1p" class="selflink">#</a></p><p class="src"><a href="#v:expm1">expm1</a> :: <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="Numeric-Interval.html#t:Interval">Interval</a> a <a href="#v:expm1" class="selflink">#</a></p><p class="src"><a href="#v:log1pexp">log1pexp</a> :: <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="Numeric-Interval.html#t:Interval">Interval</a> a <a href="#v:log1pexp" class="selflink">#</a></p><p class="src"><a href="#v:log1mexp">log1mexp</a> :: <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="Numeric-Interval.html#t:Interval">Interval</a> a <a href="#v:log1mexp" class="selflink">#</a></p></div></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:id:Interval:Fractional:5" class="instance expander" onclick="toggleSection('i:id:Interval:Fractional:5')"></span> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Fractional">Fractional</a> a, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Ord.html#t:Ord">Ord</a> a) => <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Fractional">Fractional</a> (<a href="Numeric-Interval.html#t:Interval">Interval</a> a)</span> <a href="src/Numeric-Interval-Internal.html#line-505" class="link">Source</a> <a href="#t:Interval" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:id:Interval:Fractional:5" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:-47-">(/)</a> :: <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="Numeric-Interval.html#t:Interval">Interval</a> a <a href="#v:-47-" class="selflink">#</a></p><p class="src"><a href="#v:recip">recip</a> :: <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="Numeric-Interval.html#t:Interval">Interval</a> a <a href="#v:recip" class="selflink">#</a></p><p class="src"><a href="#v:fromRational">fromRational</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Rational">Rational</a> -> <a href="Numeric-Interval.html#t:Interval">Interval</a> a <a href="#v:fromRational" class="selflink">#</a></p></div></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:id:Interval:Data:6" class="instance expander" onclick="toggleSection('i:id:Interval:Data:6')"></span> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Data.html#t:Data">Data</a> a => <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Data.html#t:Data">Data</a> (<a href="Numeric-Interval.html#t:Interval">Interval</a> a)</span> <a href="src/Numeric-Interval-Internal.html#line-71" class="link">Source</a> <a href="#t:Interval" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:id:Interval:Data:6" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:gfoldl">gfoldl</a> :: (<span class="keyword">forall</span> d b. <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Data.html#t:Data">Data</a> d => c (d -> b) -> d -> c b) -> (<span class="keyword">forall</span> g. g -> c g) -> <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> c (<a href="Numeric-Interval.html#t:Interval">Interval</a> a) <a href="#v:gfoldl" class="selflink">#</a></p><p class="src"><a href="#v:gunfold">gunfold</a> :: (<span class="keyword">forall</span> b r. <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Data.html#t:Data">Data</a> b => c (b -> r) -> c r) -> (<span class="keyword">forall</span> r. r -> c r) -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Data.html#t:Constr">Constr</a> -> c (<a href="Numeric-Interval.html#t:Interval">Interval</a> a) <a href="#v:gunfold" class="selflink">#</a></p><p class="src"><a href="#v:toConstr">toConstr</a> :: <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Data.html#t:Constr">Constr</a> <a href="#v:toConstr" class="selflink">#</a></p><p class="src"><a href="#v:dataTypeOf">dataTypeOf</a> :: <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Data.html#t:DataType">DataType</a> <a href="#v:dataTypeOf" class="selflink">#</a></p><p class="src"><a href="#v:dataCast1">dataCast1</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Typeable-Internal.html#t:Typeable">Typeable</a> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Kind.html#t:-42-">*</a> -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Kind.html#t:-42-">*</a>) t => (<span class="keyword">forall</span> d. <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Data.html#t:Data">Data</a> d => c (t d)) -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Maybe.html#t:Maybe">Maybe</a> (c (<a href="Numeric-Interval.html#t:Interval">Interval</a> a)) <a href="#v:dataCast1" class="selflink">#</a></p><p class="src"><a href="#v:dataCast2">dataCast2</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Typeable-Internal.html#t:Typeable">Typeable</a> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Kind.html#t:-42-">*</a> -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Kind.html#t:-42-">*</a> -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Kind.html#t:-42-">*</a>) t => (<span class="keyword">forall</span> d e. (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Data.html#t:Data">Data</a> d, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Data.html#t:Data">Data</a> e) => c (t d e)) -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Maybe.html#t:Maybe">Maybe</a> (c (<a href="Numeric-Interval.html#t:Interval">Interval</a> a)) <a href="#v:dataCast2" class="selflink">#</a></p><p class="src"><a href="#v:gmapT">gmapT</a> :: (<span class="keyword">forall</span> b. <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Data.html#t:Data">Data</a> b => b -> b) -> <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="Numeric-Interval.html#t:Interval">Interval</a> a <a href="#v:gmapT" class="selflink">#</a></p><p class="src"><a href="#v:gmapQl">gmapQl</a> :: (r -> r' -> r) -> r -> (<span class="keyword">forall</span> d. <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Data.html#t:Data">Data</a> d => d -> r') -> <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> r <a href="#v:gmapQl" class="selflink">#</a></p><p class="src"><a href="#v:gmapQr">gmapQr</a> :: (r' -> r -> r) -> r -> (<span class="keyword">forall</span> d. <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Data.html#t:Data">Data</a> d => d -> r') -> <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> r <a href="#v:gmapQr" class="selflink">#</a></p><p class="src"><a href="#v:gmapQ">gmapQ</a> :: (<span class="keyword">forall</span> d. <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Data.html#t:Data">Data</a> d => d -> u) -> <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> [u] <a href="#v:gmapQ" class="selflink">#</a></p><p class="src"><a href="#v:gmapQi">gmapQi</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Int.html#t:Int">Int</a> -> (<span class="keyword">forall</span> d. <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Data.html#t:Data">Data</a> d => d -> u) -> <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> u <a href="#v:gmapQi" class="selflink">#</a></p><p class="src"><a href="#v:gmapM">gmapM</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Control-Monad.html#t:Monad">Monad</a> m => (<span class="keyword">forall</span> d. <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Data.html#t:Data">Data</a> d => d -> m d) -> <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> m (<a href="Numeric-Interval.html#t:Interval">Interval</a> a) <a href="#v:gmapM" class="selflink">#</a></p><p class="src"><a href="#v:gmapMp">gmapMp</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Control-Monad.html#t:MonadPlus">MonadPlus</a> m => (<span class="keyword">forall</span> d. <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Data.html#t:Data">Data</a> d => d -> m d) -> <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> m (<a href="Numeric-Interval.html#t:Interval">Interval</a> a) <a href="#v:gmapMp" class="selflink">#</a></p><p class="src"><a href="#v:gmapMo">gmapMo</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Control-Monad.html#t:MonadPlus">MonadPlus</a> m => (<span class="keyword">forall</span> d. <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Data.html#t:Data">Data</a> d => d -> m d) -> <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> m (<a href="Numeric-Interval.html#t:Interval">Interval</a> a) <a href="#v:gmapMo" class="selflink">#</a></p></div></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:id:Interval:Num:7" class="instance expander" onclick="toggleSection('i:id:Interval:Num:7')"></span> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Num">Num</a> a, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Ord.html#t:Ord">Ord</a> a) => <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Num">Num</a> (<a href="Numeric-Interval.html#t:Interval">Interval</a> a)</span> <a href="src/Numeric-Interval-Internal.html#line-338" class="link">Source</a> <a href="#t:Interval" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:id:Interval:Num:7" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:-43-">(+)</a> :: <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="Numeric-Interval.html#t:Interval">Interval</a> a <a href="#v:-43-" class="selflink">#</a></p><p class="src"><a href="#v:-45-">(-)</a> :: <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="Numeric-Interval.html#t:Interval">Interval</a> a <a href="#v:-45-" class="selflink">#</a></p><p class="src"><a href="#v:-42-">(*)</a> :: <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="Numeric-Interval.html#t:Interval">Interval</a> a <a href="#v:-42-" class="selflink">#</a></p><p class="src"><a href="#v:negate">negate</a> :: <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="Numeric-Interval.html#t:Interval">Interval</a> a <a href="#v:negate" class="selflink">#</a></p><p class="src"><a href="#v:abs">abs</a> :: <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="Numeric-Interval.html#t:Interval">Interval</a> a <a href="#v:abs" class="selflink">#</a></p><p class="src"><a href="#v:signum">signum</a> :: <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="Numeric-Interval.html#t:Interval">Interval</a> a <a href="#v:signum" class="selflink">#</a></p><p class="src"><a href="#v:fromInteger">fromInteger</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Integer">Integer</a> -> <a href="Numeric-Interval.html#t:Interval">Interval</a> a <a href="#v:fromInteger" class="selflink">#</a></p></div></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:id:Interval:Ord:8" class="instance expander" onclick="toggleSection('i:id:Interval:Ord:8')"></span> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Ord.html#t:Ord">Ord</a> a => <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Ord.html#t:Ord">Ord</a> (<a href="Numeric-Interval.html#t:Interval">Interval</a> a)</span> <a href="src/Numeric-Interval-Internal.html#line-447" class="link">Source</a> <a href="#t:Interval" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:id:Interval:Ord:8" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:compare">compare</a> :: <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Ord.html#t:Ordering">Ordering</a> <a href="#v:compare" class="selflink">#</a></p><p class="src"><a href="#v:-60-">(<)</a> :: <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Bool.html#t:Bool">Bool</a> <a href="#v:-60-" class="selflink">#</a></p><p class="src"><a href="#v:-60--61-">(<=)</a> :: <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Bool.html#t:Bool">Bool</a> <a href="#v:-60--61-" class="selflink">#</a></p><p class="src"><a href="#v:-62-">(>)</a> :: <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Bool.html#t:Bool">Bool</a> <a href="#v:-62-" class="selflink">#</a></p><p class="src"><a href="#v:-62--61-">(>=)</a> :: <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Bool.html#t:Bool">Bool</a> <a href="#v:-62--61-" class="selflink">#</a></p><p class="src"><a href="#v:max">max</a> :: <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="Numeric-Interval.html#t:Interval">Interval</a> a <a href="#v:max" class="selflink">#</a></p><p class="src"><a href="#v:min">min</a> :: <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="Numeric-Interval.html#t:Interval">Interval</a> a <a href="#v:min" class="selflink">#</a></p></div></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:id:Interval:Real:9" class="instance expander" onclick="toggleSection('i:id:Interval:Real:9')"></span> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Real">Real</a> a => <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Real">Real</a> (<a href="Numeric-Interval.html#t:Interval">Interval</a> a)</span> <a href="src/Numeric-Interval-Internal.html#line-440" class="link">Source</a> <a href="#t:Interval" class="selflink">#</a></td><td class="doc"><p><code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#v:realToFrac">realToFrac</a></code> will use the midpoint</p></td></tr><tr><td colspan="2"><div id="section.i:id:Interval:Real:9" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:toRational">toRational</a> :: <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Rational">Rational</a> <a href="#v:toRational" class="selflink">#</a></p></div></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:id:Interval:RealFloat:10" class="instance expander" onclick="toggleSection('i:id:Interval:RealFloat:10')"></span> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:RealFloat">RealFloat</a> a => <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:RealFloat">RealFloat</a> (<a href="Numeric-Interval.html#t:Interval">Interval</a> a)</span> <a href="src/Numeric-Interval-Internal.html#line-629" class="link">Source</a> <a href="#t:Interval" class="selflink">#</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 colspan="2"><div id="section.i:id:Interval:RealFloat:10" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:floatRadix">floatRadix</a> :: <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Integer">Integer</a> <a href="#v:floatRadix" class="selflink">#</a></p><p class="src"><a href="#v:floatDigits">floatDigits</a> :: <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Int.html#t:Int">Int</a> <a href="#v:floatDigits" class="selflink">#</a></p><p class="src"><a href="#v:floatRange">floatRange</a> :: <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Int.html#t:Int">Int</a>, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Int.html#t:Int">Int</a>) <a href="#v:floatRange" class="selflink">#</a></p><p class="src"><a href="#v:decodeFloat">decodeFloat</a> :: <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Integer">Integer</a>, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Int.html#t:Int">Int</a>) <a href="#v:decodeFloat" class="selflink">#</a></p><p class="src"><a href="#v:encodeFloat">encodeFloat</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Integer">Integer</a> -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Int.html#t:Int">Int</a> -> <a href="Numeric-Interval.html#t:Interval">Interval</a> a <a href="#v:encodeFloat" class="selflink">#</a></p><p class="src"><a href="#v:exponent">exponent</a> :: <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Int.html#t:Int">Int</a> <a href="#v:exponent" class="selflink">#</a></p><p class="src"><a href="#v:significand">significand</a> :: <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="Numeric-Interval.html#t:Interval">Interval</a> a <a href="#v:significand" class="selflink">#</a></p><p class="src"><a href="#v:scaleFloat">scaleFloat</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Int.html#t:Int">Int</a> -> <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="Numeric-Interval.html#t:Interval">Interval</a> a <a href="#v:scaleFloat" class="selflink">#</a></p><p class="src"><a href="#v:isNaN">isNaN</a> :: <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Bool.html#t:Bool">Bool</a> <a href="#v:isNaN" class="selflink">#</a></p><p class="src"><a href="#v:isInfinite">isInfinite</a> :: <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Bool.html#t:Bool">Bool</a> <a href="#v:isInfinite" class="selflink">#</a></p><p class="src"><a href="#v:isDenormalized">isDenormalized</a> :: <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Bool.html#t:Bool">Bool</a> <a href="#v:isDenormalized" class="selflink">#</a></p><p class="src"><a href="#v:isNegativeZero">isNegativeZero</a> :: <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Bool.html#t:Bool">Bool</a> <a href="#v:isNegativeZero" class="selflink">#</a></p><p class="src"><a href="#v:isIEEE">isIEEE</a> :: <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Bool.html#t:Bool">Bool</a> <a href="#v:isIEEE" class="selflink">#</a></p><p class="src"><a href="#v:atan2">atan2</a> :: <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="Numeric-Interval.html#t:Interval">Interval</a> a <a href="#v:atan2" class="selflink">#</a></p></div></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:id:Interval:RealFrac:11" class="instance expander" onclick="toggleSection('i:id:Interval:RealFrac:11')"></span> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:RealFrac">RealFrac</a> a => <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:RealFrac">RealFrac</a> (<a href="Numeric-Interval.html#t:Interval">Interval</a> a)</span> <a href="src/Numeric-Interval-Internal.html#line-523" class="link">Source</a> <a href="#t:Interval" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:id:Interval:RealFrac:11" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:properFraction">properFraction</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Integral">Integral</a> b => <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> (b, <a href="Numeric-Interval.html#t:Interval">Interval</a> a) <a href="#v:properFraction" class="selflink">#</a></p><p class="src"><a href="#v:truncate">truncate</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Integral">Integral</a> b => <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> b <a href="#v:truncate" class="selflink">#</a></p><p class="src"><a href="#v:round">round</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Integral">Integral</a> b => <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> b <a href="#v:round" class="selflink">#</a></p><p class="src"><a href="#v:ceiling">ceiling</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Integral">Integral</a> b => <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> b <a href="#v:ceiling" class="selflink">#</a></p><p class="src"><a href="#v:floor">floor</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Integral">Integral</a> b => <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> b <a href="#v:floor" class="selflink">#</a></p></div></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:id:Interval:Show:12" class="instance expander" onclick="toggleSection('i:id:Interval:Show:12')"></span> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Text-Show.html#t:Show">Show</a> a => <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Text-Show.html#t:Show">Show</a> (<a href="Numeric-Interval.html#t:Interval">Interval</a> a)</span> <a href="src/Numeric-Interval-Internal.html#line-198" class="link">Source</a> <a href="#t:Interval" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:id:Interval:Show:12" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:showsPrec">showsPrec</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Int.html#t:Int">Int</a> -> <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Text-Show.html#t:ShowS">ShowS</a> <a href="#v:showsPrec" class="selflink">#</a></p><p class="src"><a href="#v:show">show</a> :: <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-String.html#t:String">String</a> <a href="#v:show" class="selflink">#</a></p><p class="src"><a href="#v:showList">showList</a> :: [<a href="Numeric-Interval.html#t:Interval">Interval</a> a] -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Text-Show.html#t:ShowS">ShowS</a> <a href="#v:showList" class="selflink">#</a></p></div></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:id:Interval:Generic:13" class="instance expander" onclick="toggleSection('i:id:Interval:Generic:13')"></span> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/GHC-Generics.html#t:Generic">Generic</a> (<a href="Numeric-Interval.html#t:Interval">Interval</a> a)</span> <a href="src/Numeric-Interval-Internal.html#line-74" class="link">Source</a> <a href="#t:Interval" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:id:Interval:Generic:13" class="inst-details hide"><div class="subs associated-types"><p class="caption">Associated Types</p><p class="src"><span class="keyword">type</span> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/GHC-Generics.html#t:Rep">Rep</a> (<a href="Numeric-Interval.html#t:Interval">Interval</a> a) :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Kind.html#t:-42-">*</a> -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Kind.html#t:-42-">*</a> <a href="#t:Rep" class="selflink">#</a></p></div> <div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:from">from</a> :: <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/GHC-Generics.html#t:Rep">Rep</a> (<a href="Numeric-Interval.html#t:Interval">Interval</a> a) x <a href="#v:from" class="selflink">#</a></p><p class="src"><a href="#v:to">to</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/GHC-Generics.html#t:Rep">Rep</a> (<a href="Numeric-Interval.html#t:Interval">Interval</a> a) x -> <a href="Numeric-Interval.html#t:Interval">Interval</a> a <a href="#v:to" class="selflink">#</a></p></div></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:id:Interval:Rep1:14" class="instance expander" onclick="toggleSection('i:id:Interval:Rep1:14')"></span> <span class="keyword">type</span> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/GHC-Generics.html#t:Rep1">Rep1</a> <a href="Numeric-Interval.html#t:Interval">Interval</a></span> <a href="src/Numeric-Interval-Internal.html#line-70" class="link">Source</a> <a href="#t:Interval" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:id:Interval:Rep1:14" class="inst-details hide"><div class="src"><span class="keyword">type</span> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/GHC-Generics.html#t:Rep1">Rep1</a> <a href="Numeric-Interval.html#t:Interval">Interval</a> = <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/GHC-Generics.html#t:D1">D1</a> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/GHC-Generics.html#v:MetaData">MetaData</a> "Interval" "Numeric.Interval.Internal" "intervals-0.7.2-312AZefP9Cn5wGdNaWhuud" <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Bool.html#v:False">False</a>) (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/GHC-Generics.html#t::-43-:">(:+:)</a> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/GHC-Generics.html#t:C1">C1</a> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/GHC-Generics.html#v:MetaCons">MetaCons</a> "I" <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/GHC-Generics.html#v:PrefixI">PrefixI</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Bool.html#v:False">False</a>) (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/GHC-Generics.html#t::-42-:">(:*:)</a> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/GHC-Generics.html#t:S1">S1</a> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/GHC-Generics.html#v:MetaSel">MetaSel</a> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Maybe.html#v:Nothing">Nothing</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/GHC-TypeLits.html#t:Symbol">Symbol</a>) <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/GHC-Generics.html#v:NoSourceUnpackedness">NoSourceUnpackedness</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/GHC-Generics.html#v:SourceStrict">SourceStrict</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/GHC-Generics.html#v:DecidedStrict">DecidedStrict</a>) <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/GHC-Generics.html#t:Par1">Par1</a>) (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/GHC-Generics.html#t:S1">S1</a> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/GHC-Generics.html#v:MetaSel">MetaSel</a> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Maybe.html#v:Nothing">Nothing</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/GHC-TypeLits.html#t:Symbol">Symbol</a>) <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/GHC-Generics.html#v:NoSourceUnpackedness">NoSourceUnpackedness</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/GHC-Generics.html#v:SourceStrict">SourceStrict</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/GHC-Generics.html#v:DecidedStrict">DecidedStrict</a>) <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/GHC-Generics.html#t:Par1">Par1</a>))) (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/GHC-Generics.html#t:C1">C1</a> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/GHC-Generics.html#v:MetaCons">MetaCons</a> "Empty" <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/GHC-Generics.html#v:PrefixI">PrefixI</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Bool.html#v:False">False</a>) <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/GHC-Generics.html#t:U1">U1</a>))</div></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:id:Interval:Rep:15" class="instance expander" onclick="toggleSection('i:id:Interval:Rep:15')"></span> <span class="keyword">type</span> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/GHC-Generics.html#t:Rep">Rep</a> (<a href="Numeric-Interval.html#t:Interval">Interval</a> a)</span> <a href="src/Numeric-Interval-Internal.html#line-70" class="link">Source</a> <a href="#t:Interval" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:id:Interval:Rep:15" class="inst-details hide"><div class="src"><span class="keyword">type</span> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/GHC-Generics.html#t:Rep">Rep</a> (<a href="Numeric-Interval.html#t:Interval">Interval</a> a) = <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/GHC-Generics.html#t:D1">D1</a> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/GHC-Generics.html#v:MetaData">MetaData</a> "Interval" "Numeric.Interval.Internal" "intervals-0.7.2-312AZefP9Cn5wGdNaWhuud" <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Bool.html#v:False">False</a>) (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/GHC-Generics.html#t::-43-:">(:+:)</a> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/GHC-Generics.html#t:C1">C1</a> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/GHC-Generics.html#v:MetaCons">MetaCons</a> "I" <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/GHC-Generics.html#v:PrefixI">PrefixI</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Bool.html#v:False">False</a>) (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/GHC-Generics.html#t::-42-:">(:*:)</a> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/GHC-Generics.html#t:S1">S1</a> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/GHC-Generics.html#v:MetaSel">MetaSel</a> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Maybe.html#v:Nothing">Nothing</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/GHC-TypeLits.html#t:Symbol">Symbol</a>) <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/GHC-Generics.html#v:NoSourceUnpackedness">NoSourceUnpackedness</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/GHC-Generics.html#v:SourceStrict">SourceStrict</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/GHC-Generics.html#v:DecidedStrict">DecidedStrict</a>) (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/GHC-Generics.html#t:Rec0">Rec0</a> a)) (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/GHC-Generics.html#t:S1">S1</a> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/GHC-Generics.html#v:MetaSel">MetaSel</a> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Maybe.html#v:Nothing">Nothing</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/GHC-TypeLits.html#t:Symbol">Symbol</a>) <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/GHC-Generics.html#v:NoSourceUnpackedness">NoSourceUnpackedness</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/GHC-Generics.html#v:SourceStrict">SourceStrict</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/GHC-Generics.html#v:DecidedStrict">DecidedStrict</a>) (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/GHC-Generics.html#t:Rec0">Rec0</a> a)))) (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/GHC-Generics.html#t:C1">C1</a> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/GHC-Generics.html#v:MetaCons">MetaCons</a> "Empty" <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/GHC-Generics.html#v:PrefixI">PrefixI</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Bool.html#v:False">False</a>) <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/GHC-Generics.html#t:U1">U1</a>))</div></div></td></tr></table></div></div></div><div class="top"><p class="src"><a id="v:..." class="def">(...)</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Ord.html#t:Ord">Ord</a> a => a -> a -> <a href="Numeric-Interval.html#t:Interval">Interval</a> a <span class="fixity">infix 3</span><span class="rightedge"></span> <a href="src/Numeric-Interval-Internal.html#..." class="link">Source</a> <a href="#v:..." class="selflink">#</a></p></div><div class="top"><p class="src"><a id="v:-43--47--45-" class="def">(+/-)</a> :: (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Num">Num</a> a, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Ord.html#t:Ord">Ord</a> a) => a -> a -> <a href="Numeric-Interval.html#t:Interval">Interval</a> a <span class="fixity">infixl 6</span><span class="rightedge"></span> <a href="src/Numeric-Interval-Internal.html#%2B%2F-" class="link">Source</a> <a href="#v:-43--47--45-" class="selflink">#</a></p></div><div class="top"><p class="src"><a id="v:interval" class="def">interval</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Ord.html#t:Ord">Ord</a> a => a -> a -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Maybe.html#t:Maybe">Maybe</a> (<a href="Numeric-Interval.html#t:Interval">Interval</a> a) <a href="src/Numeric-Interval-Internal.html#interval" class="link">Source</a> <a href="#v:interval" class="selflink">#</a></p></div><div class="top"><p class="src"><a id="v:whole" class="def">whole</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Fractional">Fractional</a> a => <a href="Numeric-Interval.html#t:Interval">Interval</a> a <a href="src/Numeric-Interval-Internal.html#whole" class="link">Source</a> <a href="#v:whole" class="selflink">#</a></p><div class="doc"><p>The whole real number line</p><pre class="screen"><code class="prompt">>>> </code><strong class="userinput"><code>whole
</code></strong>-Infinity ... Infinity
</pre></div></div><div class="top"><p class="src"><a id="v:empty" class="def">empty</a> :: <a href="Numeric-Interval.html#t:Interval">Interval</a> a <a href="src/Numeric-Interval-Internal.html#empty" class="link">Source</a> <a href="#v:empty" class="selflink">#</a></p><div class="doc"><p>An empty interval</p><pre class="screen"><code class="prompt">>>> </code><strong class="userinput"><code>empty
</code></strong>Empty
</pre></div></div><div class="top"><p class="src"><a id="v:null" class="def">null</a> :: <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Bool.html#t:Bool">Bool</a> <a href="src/Numeric-Interval-Internal.html#null" class="link">Source</a> <a href="#v:null" class="selflink">#</a></p><div class="doc"><p>Check if an interval is empty</p><pre class="screen"><code class="prompt">>>> </code><strong class="userinput"><code>null (1 ... 5)
</code></strong>False
</pre><pre class="screen"><code class="prompt">>>> </code><strong class="userinput"><code>null (1 ... 1)
</code></strong>False
</pre><pre class="screen"><code class="prompt">>>> </code><strong class="userinput"><code>null empty
</code></strong>True
</pre></div></div><div class="top"><p class="src"><a id="v:singleton" class="def">singleton</a> :: a -> <a href="Numeric-Interval.html#t:Interval">Interval</a> a <a href="src/Numeric-Interval-Internal.html#singleton" class="link">Source</a> <a href="#v:singleton" class="selflink">#</a></p><div class="doc"><p>A singleton point</p><pre class="screen"><code class="prompt">>>> </code><strong class="userinput"><code>singleton 1
</code></strong>1 ... 1
</pre></div></div><div class="top"><p class="src"><a id="v:elem" class="def">elem</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Ord.html#t:Ord">Ord</a> a => a -> <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Bool.html#t:Bool">Bool</a> <a href="src/Numeric-Interval-Internal.html#elem" class="link">Source</a> <a href="#v:elem" class="selflink">#</a></p><div class="doc"><p>Determine if a point is in the interval.</p><pre class="screen"><code class="prompt">>>> </code><strong class="userinput"><code>elem 3.2 (1.0 ... 5.0)
</code></strong>True
</pre><pre class="screen"><code class="prompt">>>> </code><strong class="userinput"><code>elem 5 (1.0 ... 5.0)
</code></strong>True
</pre><pre class="screen"><code class="prompt">>>> </code><strong class="userinput"><code>elem 1 (1.0 ... 5.0)
</code></strong>True
</pre><pre class="screen"><code class="prompt">>>> </code><strong class="userinput"><code>elem 8 (1.0 ... 5.0)
</code></strong>False
</pre><pre class="screen"><code class="prompt">>>> </code><strong class="userinput"><code>elem 5 empty
</code></strong>False
</pre></div></div><div class="top"><p class="src"><a id="v:notElem" class="def">notElem</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Ord.html#t:Ord">Ord</a> a => a -> <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Bool.html#t:Bool">Bool</a> <a href="src/Numeric-Interval-Internal.html#notElem" class="link">Source</a> <a href="#v:notElem" class="selflink">#</a></p><div class="doc"><p>Determine if a point is not included in the interval</p><pre class="screen"><code class="prompt">>>> </code><strong class="userinput"><code>notElem 8 (1.0 ... 5.0)
</code></strong>True
</pre><pre class="screen"><code class="prompt">>>> </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">>>> </code><strong class="userinput"><code>notElem 5 empty
</code></strong>True
</pre></div></div><div class="top"><p class="src"><a id="v:inf" class="def">inf</a> :: <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> a <a href="src/Numeric-Interval-Internal.html#inf" class="link">Source</a> <a href="#v:inf" class="selflink">#</a></p><div class="doc"><p>The infimum (lower bound) of an interval</p><pre class="screen"><code class="prompt">>>> </code><strong class="userinput"><code>inf (1.0 ... 20.0)
</code></strong>1.0
</pre><pre class="screen"><code class="prompt">>>> </code><strong class="userinput"><code>inf empty
</code></strong>*** Exception: empty interval
</pre></div></div><div class="top"><p class="src"><a id="v:sup" class="def">sup</a> :: <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> a <a href="src/Numeric-Interval-Internal.html#sup" class="link">Source</a> <a href="#v:sup" class="selflink">#</a></p><div class="doc"><p>The supremum (upper bound) of an interval</p><pre class="screen"><code class="prompt">>>> </code><strong class="userinput"><code>sup (1.0 ... 20.0)
</code></strong>20.0
</pre><pre class="screen"><code class="prompt">>>> </code><strong class="userinput"><code>sup empty
</code></strong>*** Exception: empty interval
</pre></div></div><div class="top"><p class="src"><a id="v:singular" class="def">singular</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Ord.html#t:Ord">Ord</a> a => <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Bool.html#t:Bool">Bool</a> <a href="src/Numeric-Interval-Internal.html#singular" class="link">Source</a> <a href="#v:singular" class="selflink">#</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">>>> </code><strong class="userinput"><code>singular (singleton 1)
</code></strong>True
</pre><pre class="screen"><code class="prompt">>>> </code><strong class="userinput"><code>singular (1.0 ... 20.0)
</code></strong>False
</pre></div></div><div class="top"><p class="src"><a id="v:width" class="def">width</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Num">Num</a> a => <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> a <a href="src/Numeric-Interval-Internal.html#width" class="link">Source</a> <a href="#v:width" class="selflink">#</a></p><div class="doc"><p>Calculate the width of an interval.</p><pre class="screen"><code class="prompt">>>> </code><strong class="userinput"><code>width (1 ... 20)
</code></strong>19
</pre><pre class="screen"><code class="prompt">>>> </code><strong class="userinput"><code>width (singleton 1)
</code></strong>0
</pre><pre class="screen"><code class="prompt">>>> </code><strong class="userinput"><code>width empty
</code></strong>0
</pre></div></div><div class="top"><p class="src"><a id="v:midpoint" class="def">midpoint</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Fractional">Fractional</a> a => <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> a <a href="src/Numeric-Interval-Internal.html#midpoint" class="link">Source</a> <a href="#v:midpoint" class="selflink">#</a></p><div class="doc"><p>Nearest point to the midpoint of the interval.</p><pre class="screen"><code class="prompt">>>> </code><strong class="userinput"><code>midpoint (10.0 ... 20.0)
</code></strong>15.0
</pre><pre class="screen"><code class="prompt">>>> </code><strong class="userinput"><code>midpoint (singleton 5.0)
</code></strong>5.0
</pre><pre class="screen"><code class="prompt">>>> </code><strong class="userinput"><code>midpoint empty
</code></strong>*** Exception: empty interval
</pre></div></div><div class="top"><p class="src"><a id="v:intersection" class="def">intersection</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Ord.html#t:Ord">Ord</a> a => <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="Numeric-Interval.html#t:Interval">Interval</a> a <a href="src/Numeric-Interval-Internal.html#intersection" class="link">Source</a> <a href="#v:intersection" class="selflink">#</a></p><div class="doc"><p>Calculate the intersection of two intervals.</p><pre class="screen"><code class="prompt">>>> </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 id="v:hull" class="def">hull</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Ord.html#t:Ord">Ord</a> a => <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="Numeric-Interval.html#t:Interval">Interval</a> a <a href="src/Numeric-Interval-Internal.html#hull" class="link">Source</a> <a href="#v:hull" class="selflink">#</a></p><div class="doc"><p>Calculate the convex hull of two intervals</p><pre class="screen"><code class="prompt">>>> </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">>>> </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 id="v:bisect" class="def">bisect</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Fractional">Fractional</a> a => <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> (<a href="Numeric-Interval.html#t:Interval">Interval</a> a, <a href="Numeric-Interval.html#t:Interval">Interval</a> a) <a href="src/Numeric-Interval-Internal.html#bisect" class="link">Source</a> <a href="#v:bisect" class="selflink">#</a></p><div class="doc"><p>Bisect an interval at its midpoint.</p><pre class="screen"><code class="prompt">>>> </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">>>> </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">>>> </code><strong class="userinput"><code>bisect Empty
</code></strong>(Empty,Empty)
</pre></div></div><div class="top"><p class="src"><a id="v:bisectIntegral" class="def">bisectIntegral</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Integral">Integral</a> a => <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> (<a href="Numeric-Interval.html#t:Interval">Interval</a> a, <a href="Numeric-Interval.html#t:Interval">Interval</a> a) <a href="src/Numeric-Interval-Internal.html#bisectIntegral" class="link">Source</a> <a href="#v:bisectIntegral" class="selflink">#</a></p></div><div class="top"><p class="src"><a id="v:magnitude" class="def">magnitude</a> :: (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Num">Num</a> a, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Ord.html#t:Ord">Ord</a> a) => <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> a <a href="src/Numeric-Interval-Internal.html#magnitude" class="link">Source</a> <a href="#v:magnitude" class="selflink">#</a></p><div class="doc"><p>Magnitude</p><pre class="screen"><code class="prompt">>>> </code><strong class="userinput"><code>magnitude (1 ... 20)
</code></strong>20
</pre><pre class="screen"><code class="prompt">>>> </code><strong class="userinput"><code>magnitude (-20 ... 10)
</code></strong>20
</pre><pre class="screen"><code class="prompt">>>> </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">>>> </code><strong class="userinput"><code>magnitude empty
</code></strong>*** Exception: empty interval
</pre></div></div><div class="top"><p class="src"><a id="v:mignitude" class="def">mignitude</a> :: (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Num">Num</a> a, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Ord.html#t:Ord">Ord</a> a) => <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> a <a href="src/Numeric-Interval-Internal.html#mignitude" class="link">Source</a> <a href="#v:mignitude" class="selflink">#</a></p><div class="doc"><p>"mignitude"</p><pre class="screen"><code class="prompt">>>> </code><strong class="userinput"><code>mignitude (1 ... 20)
</code></strong>1
</pre><pre class="screen"><code class="prompt">>>> </code><strong class="userinput"><code>mignitude (-20 ... 10)
</code></strong>0
</pre><pre class="screen"><code class="prompt">>>> </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">>>> </code><strong class="userinput"><code>mignitude empty
</code></strong>*** Exception: empty interval
</pre></div></div><div class="top"><p class="src"><a id="v:distance" class="def">distance</a> :: (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Num">Num</a> a, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Ord.html#t:Ord">Ord</a> a) => <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> a <a href="src/Numeric-Interval-Internal.html#distance" class="link">Source</a> <a href="#v:distance" class="selflink">#</a></p><div class="doc"><p>Hausdorff distance between intervals.</p><pre class="screen"><code class="prompt">>>> </code><strong class="userinput"><code>distance (1 ... 7) (6 ... 10)
</code></strong>0
</pre><pre class="screen"><code class="prompt">>>> </code><strong class="userinput"><code>distance (1 ... 7) (15 ... 24)
</code></strong>8
</pre><pre class="screen"><code class="prompt">>>> </code><strong class="userinput"><code>distance (1 ... 7) (-10 ... -2)
</code></strong>3
</pre><pre class="screen"><code class="prompt">>>> </code><strong class="userinput"><code>distance Empty (1 ... 1)
</code></strong>*** Exception: empty interval
</pre></div></div><div class="top"><p class="src"><a id="v:inflate" class="def">inflate</a> :: (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Num">Num</a> a, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Ord.html#t:Ord">Ord</a> a) => a -> <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="Numeric-Interval.html#t:Interval">Interval</a> a <a href="src/Numeric-Interval-Internal.html#inflate" class="link">Source</a> <a href="#v:inflate" class="selflink">#</a></p><div class="doc"><p>Inflate an interval by enlarging it at both ends.</p><pre class="screen"><code class="prompt">>>> </code><strong class="userinput"><code>inflate 3 (-1 ... 7)
</code></strong>-4 ... 10
</pre><pre class="screen"><code class="prompt">>>> </code><strong class="userinput"><code>inflate (-2) (0 ... 4)
</code></strong>-2 ... 6
</pre><pre class="screen"><code class="prompt">>>> </code><strong class="userinput"><code>inflate 1 empty
</code></strong>Empty
</pre></div></div><div class="top"><p class="src"><a id="v:deflate" class="def">deflate</a> :: (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Fractional">Fractional</a> a, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Ord.html#t:Ord">Ord</a> a) => a -> <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="Numeric-Interval.html#t:Interval">Interval</a> a <a href="src/Numeric-Interval-Internal.html#deflate" class="link">Source</a> <a href="#v:deflate" class="selflink">#</a></p><div class="doc"><p>Deflate an interval by shrinking it from both ends.</p><pre class="screen"><code class="prompt">>>> </code><strong class="userinput"><code>deflate 3.0 (-4.0 ... 10.0)
</code></strong>-1.0 ... 7.0
</pre><pre class="screen"><code class="prompt">>>> </code><strong class="userinput"><code>deflate 2.0 (-1.0 ... 1.0)
</code></strong>Empty
</pre><pre class="screen"><code class="prompt">>>> </code><strong class="userinput"><code>deflate 1.0 empty
</code></strong>Empty
</pre></div></div><div class="top"><p class="src"><a id="v:scale" class="def">scale</a> :: (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Fractional">Fractional</a> a, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Ord.html#t:Ord">Ord</a> a) => a -> <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="Numeric-Interval.html#t:Interval">Interval</a> a <a href="src/Numeric-Interval-Internal.html#scale" class="link">Source</a> <a href="#v:scale" class="selflink">#</a></p><div class="doc"><p>Scale an interval about its midpoint.</p><pre class="screen"><code class="prompt">>>> </code><strong class="userinput"><code>scale 1.1 (-6.0 ... 4.0)
</code></strong>-6.5 ... 4.5
</pre><pre class="screen"><code class="prompt">>>> </code><strong class="userinput"><code>scale (-2.0) (-1.0 ... 1.0)
</code></strong>Empty
</pre><pre class="screen"><code class="prompt">>>> </code><strong class="userinput"><code>scale 3.0 empty
</code></strong>Empty
</pre></div></div><div class="top"><p class="src"><a id="v:symmetric" class="def">symmetric</a> :: (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Num">Num</a> a, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Ord.html#t:Ord">Ord</a> a) => a -> <a href="Numeric-Interval.html#t:Interval">Interval</a> a <a href="src/Numeric-Interval-Internal.html#symmetric" class="link">Source</a> <a href="#v:symmetric" class="selflink">#</a></p><div class="doc"><p>Construct a symmetric interval.</p><pre class="screen"><code class="prompt">>>> </code><strong class="userinput"><code>symmetric 3
</code></strong>-3 ... 3
</pre><pre class="screen"><code class="prompt">>>> </code><strong class="userinput"><code>symmetric (-2)
</code></strong>-2 ... 2
</pre></div></div><div class="top"><p class="src"><a id="v:contains" class="def">contains</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Ord.html#t:Ord">Ord</a> a => <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Bool.html#t:Bool">Bool</a> <a href="src/Numeric-Interval-Internal.html#contains" class="link">Source</a> <a href="#v:contains" class="selflink">#</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">>>> </code><strong class="userinput"><code>(20 ... 40 :: Interval Double) `contains` (25 ... 35 :: Interval Double)
</code></strong>True
</pre><pre class="screen"><code class="prompt">>>> </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 id="v:isSubsetOf" class="def">isSubsetOf</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Ord.html#t:Ord">Ord</a> a => <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Bool.html#t:Bool">Bool</a> <a href="src/Numeric-Interval-Internal.html#isSubsetOf" class="link">Source</a> <a href="#v:isSubsetOf" class="selflink">#</a></p><div class="doc"><p>Flipped version of <code><a href="Numeric-Interval.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">>>> </code><strong class="userinput"><code>(25 ... 35 :: Interval Double) `isSubsetOf` (20 ... 40 :: Interval Double)
</code></strong>True
</pre><pre class="screen"><code class="prompt">>>> </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 id="v:certainly" class="def">certainly</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Ord.html#t:Ord">Ord</a> a => (<span class="keyword">forall</span> b. <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Ord.html#t:Ord">Ord</a> b => b -> b -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Bool.html#t:Bool">Bool</a>) -> <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Bool.html#t:Bool">Bool</a> <a href="src/Numeric-Interval-Internal.html#certainly" class="link">Source</a> <a href="#v:certainly" class="selflink">#</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 id="v:-60--33-" class="def">(<!)</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Ord.html#t:Ord">Ord</a> a => <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Bool.html#t:Bool">Bool</a> <a href="src/Numeric-Interval-Internal.html#%3C%21" class="link">Source</a> <a href="#v:-60--33-" class="selflink">#</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="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Ord.html#v:-60-"><</a></code> y</code></p><pre class="screen"><code class="prompt">>>> </code><strong class="userinput"><code>(5 ... 10 :: Interval Double) <! (20 ... 30 :: Interval Double)
</code></strong>True
</pre><pre class="screen"><code class="prompt">>>> </code><strong class="userinput"><code>(5 ... 10 :: Interval Double) <! (10 ... 30 :: Interval Double)
</code></strong>False
</pre><pre class="screen"><code class="prompt">>>> </code><strong class="userinput"><code>(20 ... 30 :: Interval Double) <! (5 ... 10 :: Interval Double)
</code></strong>False
</pre></div></div><div class="top"><p class="src"><a id="v:-60--61--33-" class="def">(<=!)</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Ord.html#t:Ord">Ord</a> a => <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Bool.html#t:Bool">Bool</a> <a href="src/Numeric-Interval-Internal.html#%3C%3D%21" class="link">Source</a> <a href="#v:-60--61--33-" class="selflink">#</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="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Ord.html#v:-60--61-"><=</a></code> y</code></p><pre class="screen"><code class="prompt">>>> </code><strong class="userinput"><code>(5 ... 10 :: Interval Double) <=! (20 ... 30 :: Interval Double)
</code></strong>True
</pre><pre class="screen"><code class="prompt">>>> </code><strong class="userinput"><code>(5 ... 10 :: Interval Double) <=! (10 ... 30 :: Interval Double)
</code></strong>True
</pre><pre class="screen"><code class="prompt">>>> </code><strong class="userinput"><code>(20 ... 30 :: Interval Double) <=! (5 ... 10 :: Interval Double)
</code></strong>False
</pre></div></div><div class="top"><p class="src"><a id="v:-61--61--33-" class="def">(==!)</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Eq.html#t:Eq">Eq</a> a => <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Bool.html#t:Bool">Bool</a> <a href="src/Numeric-Interval-Internal.html#%3D%3D%21" class="link">Source</a> <a href="#v:-61--61--33-" class="selflink">#</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="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/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">>>> </code><strong class="userinput"><code>(singleton 5 :: Interval Double) ==! (singleton 5 :: Interval Double)
</code></strong>True
</pre><pre class="screen"><code class="prompt">>>> </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 id="v:-62--61--33-" class="def">(>=!)</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Ord.html#t:Ord">Ord</a> a => <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Bool.html#t:Bool">Bool</a> <a href="src/Numeric-Interval-Internal.html#%3E%3D%21" class="link">Source</a> <a href="#v:-62--61--33-" class="selflink">#</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="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Ord.html#v:-62--61-">>=</a></code> y</code></p><pre class="screen"><code class="prompt">>>> </code><strong class="userinput"><code>(20 ... 40 :: Interval Double) >=! (10 ... 20 :: Interval Double)
</code></strong>True
</pre><pre class="screen"><code class="prompt">>>> </code><strong class="userinput"><code>(5 ... 20 :: Interval Double) >=! (15 ... 40 :: Interval Double)
</code></strong>False
</pre></div></div><div class="top"><p class="src"><a id="v:-62--33-" class="def">(>!)</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Ord.html#t:Ord">Ord</a> a => <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Bool.html#t:Bool">Bool</a> <a href="src/Numeric-Interval-Internal.html#%3E%21" class="link">Source</a> <a href="#v:-62--33-" class="selflink">#</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="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Ord.html#v:-62-">></a></code> y</code></p><pre class="screen"><code class="prompt">>>> </code><strong class="userinput"><code>(20 ... 40 :: Interval Double) >! (10 ... 19 :: Interval Double)
</code></strong>True
</pre><pre class="screen"><code class="prompt">>>> </code><strong class="userinput"><code>(5 ... 20 :: Interval Double) >! (15 ... 40 :: Interval Double)
</code></strong>False
</pre></div></div><div class="top"><p class="src"><a id="v:possibly" class="def">possibly</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Ord.html#t:Ord">Ord</a> a => (<span class="keyword">forall</span> b. <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Ord.html#t:Ord">Ord</a> b => b -> b -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Bool.html#t:Bool">Bool</a>) -> <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Bool.html#t:Bool">Bool</a> <a href="src/Numeric-Interval-Internal.html#possibly" class="link">Source</a> <a href="#v:possibly" class="selflink">#</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 id="v:-60--63-" class="def">(<?)</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Ord.html#t:Ord">Ord</a> a => <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Bool.html#t:Bool">Bool</a> <a href="src/Numeric-Interval-Internal.html#%3C%3F" class="link">Source</a> <a href="#v:-60--63-" class="selflink">#</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="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Ord.html#v:-60-"><</a></code> y</code>?</p></div></div><div class="top"><p class="src"><a id="v:-60--61--63-" class="def">(<=?)</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Ord.html#t:Ord">Ord</a> a => <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Bool.html#t:Bool">Bool</a> <a href="src/Numeric-Interval-Internal.html#%3C%3D%3F" class="link">Source</a> <a href="#v:-60--61--63-" class="selflink">#</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="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Ord.html#v:-60--61-"><=</a></code> y</code>?</p></div></div><div class="top"><p class="src"><a id="v:-61--61--63-" class="def">(==?)</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Ord.html#t:Ord">Ord</a> a => <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Bool.html#t:Bool">Bool</a> <a href="src/Numeric-Interval-Internal.html#%3D%3D%3F" class="link">Source</a> <a href="#v:-61--61--63-" class="selflink">#</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="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Eq.html#v:-61--61-">==</a></code> y</code>?</p></div></div><div class="top"><p class="src"><a id="v:-62--61--63-" class="def">(>=?)</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Ord.html#t:Ord">Ord</a> a => <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Bool.html#t:Bool">Bool</a> <a href="src/Numeric-Interval-Internal.html#%3E%3D%3F" class="link">Source</a> <a href="#v:-62--61--63-" class="selflink">#</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="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Ord.html#v:-62--61-">>=</a></code> y</code>?</p></div></div><div class="top"><p class="src"><a id="v:-62--63-" class="def">(>?)</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Ord.html#t:Ord">Ord</a> a => <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="Numeric-Interval.html#t:Interval">Interval</a> a -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Bool.html#t:Bool">Bool</a> <a href="src/Numeric-Interval-Internal.html#%3E%3F" class="link">Source</a> <a href="#v:-62--63-" class="selflink">#</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="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Ord.html#v:-62-">></a></code> y</code>?</p></div></div><div class="top"><p class="src"><a id="v:idouble" class="def">idouble</a> :: <a href="Numeric-Interval.html#t:Interval">Interval</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Double">Double</a> -> <a href="Numeric-Interval.html#t:Interval">Interval</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Double">Double</a> <a href="src/Numeric-Interval-Internal.html#idouble" class="link">Source</a> <a href="#v:idouble" class="selflink">#</a></p><div class="doc"><p>id function. Useful for type specification</p><pre class="screen"><code class="prompt">>>> </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 id="v:ifloat" class="def">ifloat</a> :: <a href="Numeric-Interval.html#t:Interval">Interval</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Float">Float</a> -> <a href="Numeric-Interval.html#t:Interval">Interval</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Float">Float</a> <a href="src/Numeric-Interval-Internal.html#ifloat" class="link">Source</a> <a href="#v:ifloat" class="selflink">#</a></p><div class="doc"><p>id function. Useful for type specification</p><pre class="screen"><code class="prompt">>>> </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 2.17.2</p></div></body></html>
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