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</script></head><body><div id="package-header"><ul class="links" id="page-menu"><li><a href="src/Data-Dependent-Map.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">dependent-map-0.2.3.0: Dependent finite maps (partial dependent products)</p></div><div id="content"><div id="module-header"><table class="info"><tr><th>Safe Haskell</th><td>Trustworthy</td></tr><tr><th>Language</th><td>Haskell98</td></tr></table><p class="caption">Data.Dependent.Map</p></div><div id="table-of-contents"><p class="caption">Contents</p><ul><li><a href="#g:1">Operators</a></li><li><a href="#g:2">Query</a></li><li><a href="#g:3">Construction</a><ul><li><a href="#g:4">Insertion</a></li><li><a href="#g:5">Delete/Update</a></li></ul></li><li><a href="#g:6">Combine</a><ul><li><a href="#g:7">Union</a></li><li><a href="#g:8">Difference</a></li><li><a href="#g:9">Intersection</a></li></ul></li><li><a href="#g:10">Traversal</a><ul><li><a href="#g:11">Map</a></li><li><a href="#g:12">Fold</a></li></ul></li><li><a href="#g:13">Conversion</a><ul><li><a href="#g:14">Lists</a></li><li><a href="#g:15">Ordered lists</a></li></ul></li><li><a href="#g:16">Filter </a></li><li><a href="#g:17">Submap</a></li><li><a href="#g:18">Indexed </a></li><li><a href="#g:19">Min/Max</a></li><li><a href="#g:20">Debugging</a></li><li><a href="#section.orphans">Orphan instances</a></li></ul></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:DMap">DMap</a> k f</li><li class="src short"><span class="keyword">data</span> <a href="#t:DSum">DSum</a> k tag f :: <span class="keyword">forall</span> k. (k -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Kind.html#t:-42-">*</a>) -> (k -> <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> <span class="keyword">where</span><ul class="subs"><li><a href="#v::-61--62-">(:=>)</a> :: <a href="Data-Dependent-Map.html#t:DSum">DSum</a> k tag f</li></ul></li><li class="src short"><span class="keyword">data</span> <a href="#t:Some">Some</a> k tag :: <span class="keyword">forall</span> k. (k -> <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> <span class="keyword">where</span><ul class="subs"><li><a href="#v:This">This</a> :: <a href="Data-Dependent-Map.html#t:Some">Some</a> k tag</li></ul></li><li class="src short"><span class="keyword">class</span> <a href="file:///usr/share/doc/libghc-dependent-sum-doc/html/Data-GADT-Compare.html#t:GEq">GEq</a> k f => <a href="#t:GCompare">GCompare</a> k f <span class="keyword">where</span><ul class="subs"><li><a href="#v:gcompare">gcompare</a> :: f a -> f b -> <a href="Data-Dependent-Map.html#t:GOrdering">GOrdering</a> k a b</li></ul></li><li class="src short"><span class="keyword">data</span> <a href="#t:GOrdering">GOrdering</a> k a b :: <span class="keyword">forall</span> k. k -> k -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Kind.html#t:-42-">*</a> <span class="keyword">where</span><ul class="subs"><li><a href="#v:GLT">GLT</a> :: <a href="Data-Dependent-Map.html#t:GOrdering">GOrdering</a> k a b</li><li><a href="#v:GEQ">GEQ</a> :: <a href="Data-Dependent-Map.html#t:GOrdering">GOrdering</a> k a a</li><li><a href="#v:GGT">GGT</a> :: <a href="Data-Dependent-Map.html#t:GOrdering">GOrdering</a> k a b</li></ul></li><li class="src short"><a href="#v:-33-">(!)</a> :: <a href="Data-Dependent-Map.html#t:GCompare">GCompare</a> k => <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> k v -> f v</li><li class="src short"><a href="#v:-92--92-">(\\)</a> :: <a href="Data-Dependent-Map.html#t:GCompare">GCompare</a> k => <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f</li><li class="src short"><a href="#v:null">null</a> :: <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> <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:size">size</a> :: <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Int.html#t:Int">Int</a></li><li class="src short"><a href="#v:member">member</a> :: <a href="Data-Dependent-Map.html#t:GCompare">GCompare</a> k => k a -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> <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:notMember">notMember</a> :: <a href="Data-Dependent-Map.html#t:GCompare">GCompare</a> k => k v -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> <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:lookup">lookup</a> :: <span class="keyword">forall</span> k f v. <a href="Data-Dependent-Map.html#t:GCompare">GCompare</a> k => k v -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Maybe.html#t:Maybe">Maybe</a> (f v)</li><li class="src short"><a href="#v:findWithDefault">findWithDefault</a> :: <a href="Data-Dependent-Map.html#t:GCompare">GCompare</a> k => f v -> k v -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> f v</li><li class="src short"><a href="#v:empty">empty</a> :: <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f</li><li class="src short"><a href="#v:singleton">singleton</a> :: k v -> f v -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f</li><li class="src short"><a href="#v:insert">insert</a> :: <span class="keyword">forall</span> k f v. <a href="Data-Dependent-Map.html#t:GCompare">GCompare</a> k => k v -> f v -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f</li><li class="src short"><a href="#v:insertWith">insertWith</a> :: <a href="Data-Dependent-Map.html#t:GCompare">GCompare</a> k => (f v -> f v -> f v) -> k v -> f v -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f</li><li class="src short"><a href="#v:insertWith-39-">insertWith'</a> :: <a href="Data-Dependent-Map.html#t:GCompare">GCompare</a> k => (f v -> f v -> f v) -> k v -> f v -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f</li><li class="src short"><a href="#v:insertWithKey">insertWithKey</a> :: <span class="keyword">forall</span> k f v. <a href="Data-Dependent-Map.html#t:GCompare">GCompare</a> k => (k v -> f v -> f v -> f v) -> k v -> f v -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f</li><li class="src short"><a href="#v:insertWithKey-39-">insertWithKey'</a> :: <span class="keyword">forall</span> k f v. <a href="Data-Dependent-Map.html#t:GCompare">GCompare</a> k => (k v -> f v -> f v -> f v) -> k v -> f v -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f</li><li class="src short"><a href="#v:insertLookupWithKey">insertLookupWithKey</a> :: <span class="keyword">forall</span> k f v. <a href="Data-Dependent-Map.html#t:GCompare">GCompare</a> k => (k v -> f v -> f v -> f v) -> k v -> f v -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Maybe.html#t:Maybe">Maybe</a> (f v), <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f)</li><li class="src short"><a href="#v:insertLookupWithKey-39-">insertLookupWithKey'</a> :: <span class="keyword">forall</span> k f v. <a href="Data-Dependent-Map.html#t:GCompare">GCompare</a> k => (k v -> f v -> f v -> f v) -> k v -> f v -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Maybe.html#t:Maybe">Maybe</a> (f v), <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f)</li><li class="src short"><a href="#v:delete">delete</a> :: <span class="keyword">forall</span> k f v. <a href="Data-Dependent-Map.html#t:GCompare">GCompare</a> k => k v -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f</li><li class="src short"><a href="#v:adjust">adjust</a> :: <a href="Data-Dependent-Map.html#t:GCompare">GCompare</a> k => (f v -> f v) -> k v -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f</li><li class="src short"><a href="#v:adjustWithKey">adjustWithKey</a> :: <a href="Data-Dependent-Map.html#t:GCompare">GCompare</a> k => (k v -> f v -> f v) -> k v -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f</li><li class="src short"><a href="#v:adjustWithKey-39-">adjustWithKey'</a> :: <a href="Data-Dependent-Map.html#t:GCompare">GCompare</a> k => (k v -> f v -> f v) -> k v -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f</li><li class="src short"><a href="#v:update">update</a> :: <a href="Data-Dependent-Map.html#t:GCompare">GCompare</a> k => (f v -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Maybe.html#t:Maybe">Maybe</a> (f v)) -> k v -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f</li><li class="src short"><a href="#v:updateWithKey">updateWithKey</a> :: <span class="keyword">forall</span> k f v. <a href="Data-Dependent-Map.html#t:GCompare">GCompare</a> k => (k v -> f v -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Maybe.html#t:Maybe">Maybe</a> (f v)) -> k v -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f</li><li class="src short"><a href="#v:updateLookupWithKey">updateLookupWithKey</a> :: <span class="keyword">forall</span> k f v. <a href="Data-Dependent-Map.html#t:GCompare">GCompare</a> k => (k v -> f v -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Maybe.html#t:Maybe">Maybe</a> (f v)) -> k v -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Maybe.html#t:Maybe">Maybe</a> (f v), <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f)</li><li class="src short"><a href="#v:alter">alter</a> :: <span class="keyword">forall</span> k f v. <a href="Data-Dependent-Map.html#t:GCompare">GCompare</a> k => (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Maybe.html#t:Maybe">Maybe</a> (f v) -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Maybe.html#t:Maybe">Maybe</a> (f v)) -> k v -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f</li><li class="src short"><a href="#v:union">union</a> :: <a href="Data-Dependent-Map.html#t:GCompare">GCompare</a> k => <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f</li><li class="src short"><a href="#v:unionWithKey">unionWithKey</a> :: <a href="Data-Dependent-Map.html#t:GCompare">GCompare</a> k => (<span class="keyword">forall</span> v. k v -> f v -> f v -> f v) -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f</li><li class="src short"><a href="#v:unions">unions</a> :: <a href="Data-Dependent-Map.html#t:GCompare">GCompare</a> k => [<a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f] -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f</li><li class="src short"><a href="#v:unionsWithKey">unionsWithKey</a> :: <a href="Data-Dependent-Map.html#t:GCompare">GCompare</a> k => (<span class="keyword">forall</span> v. k v -> f v -> f v -> f v) -> [<a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f] -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f</li><li class="src short"><a href="#v:difference">difference</a> :: <a href="Data-Dependent-Map.html#t:GCompare">GCompare</a> k => <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k g -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f</li><li class="src short"><a href="#v:differenceWithKey">differenceWithKey</a> :: <a href="Data-Dependent-Map.html#t:GCompare">GCompare</a> k => (<span class="keyword">forall</span> v. k v -> f v -> g v -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Maybe.html#t:Maybe">Maybe</a> (f v)) -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k g -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f</li><li class="src short"><a href="#v:intersection">intersection</a> :: <a href="Data-Dependent-Map.html#t:GCompare">GCompare</a> k => <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f</li><li class="src short"><a href="#v:intersectionWithKey">intersectionWithKey</a> :: <a href="Data-Dependent-Map.html#t:GCompare">GCompare</a> k => (<span class="keyword">forall</span> v. k v -> f v -> g v -> h v) -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k g -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k h</li><li class="src short"><a href="#v:map">map</a> :: (<span class="keyword">forall</span> v. f v -> g v) -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k g</li><li class="src short"><a href="#v:mapWithKey">mapWithKey</a> :: (<span class="keyword">forall</span> v. k v -> f v -> g v) -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k g</li><li class="src short"><a href="#v:traverseWithKey">traverseWithKey</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Control-Applicative.html#t:Applicative">Applicative</a> t => (<span class="keyword">forall</span> v. k v -> f v -> t (g v)) -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> t (<a href="Data-Dependent-Map.html#t:DMap">DMap</a> k g)</li><li class="src short"><a href="#v:mapAccumLWithKey">mapAccumLWithKey</a> :: (<span class="keyword">forall</span> v. a -> k v -> f v -> (a, g v)) -> a -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> (a, <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k g)</li><li class="src short"><a href="#v:mapAccumRWithKey">mapAccumRWithKey</a> :: (<span class="keyword">forall</span> v. a -> k v -> f v -> (a, g v)) -> a -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> (a, <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k g)</li><li class="src short"><a href="#v:mapKeysWith">mapKeysWith</a> :: <a href="Data-Dependent-Map.html#t:GCompare">GCompare</a> k2 => (<span class="keyword">forall</span> v. k2 v -> f v -> f v -> f v) -> (<span class="keyword">forall</span> v. k1 v -> k2 v) -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k1 f -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k2 f</li><li class="src short"><a href="#v:mapKeysMonotonic">mapKeysMonotonic</a> :: (<span class="keyword">forall</span> v. k1 v -> k2 v) -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k1 f -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k2 f</li><li class="src short"><a href="#v:foldWithKey">foldWithKey</a> :: (<span class="keyword">forall</span> v. k v -> f v -> b -> b) -> b -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> b</li><li class="src short"><a href="#v:foldrWithKey">foldrWithKey</a> :: (<span class="keyword">forall</span> v. k v -> f v -> b -> b) -> b -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> b</li><li class="src short"><a href="#v:foldlWithKey">foldlWithKey</a> :: (<span class="keyword">forall</span> v. b -> k v -> f v -> b) -> b -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> b</li><li class="src short"><a href="#v:keys">keys</a> :: <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> [<a href="Data-Dependent-Map.html#t:Some">Some</a> k]</li><li class="src short"><a href="#v:assocs">assocs</a> :: <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> [<a href="Data-Dependent-Map.html#t:DSum">DSum</a> k f]</li><li class="src short"><a href="#v:toList">toList</a> :: <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> [<a href="Data-Dependent-Map.html#t:DSum">DSum</a> k f]</li><li class="src short"><a href="#v:fromList">fromList</a> :: <a href="Data-Dependent-Map.html#t:GCompare">GCompare</a> k => [<a href="Data-Dependent-Map.html#t:DSum">DSum</a> k f] -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f</li><li class="src short"><a href="#v:fromListWithKey">fromListWithKey</a> :: <a href="Data-Dependent-Map.html#t:GCompare">GCompare</a> k => (<span class="keyword">forall</span> v. k v -> f v -> f v -> f v) -> [<a href="Data-Dependent-Map.html#t:DSum">DSum</a> k f] -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f</li><li class="src short"><a href="#v:toAscList">toAscList</a> :: <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> [<a href="Data-Dependent-Map.html#t:DSum">DSum</a> k f]</li><li class="src short"><a href="#v:toDescList">toDescList</a> :: <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> [<a href="Data-Dependent-Map.html#t:DSum">DSum</a> k f]</li><li class="src short"><a href="#v:fromAscList">fromAscList</a> :: <a href="file:///usr/share/doc/libghc-dependent-sum-doc/html/Data-GADT-Compare.html#t:GEq">GEq</a> k => [<a href="Data-Dependent-Map.html#t:DSum">DSum</a> k f] -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f</li><li class="src short"><a href="#v:fromAscListWithKey">fromAscListWithKey</a> :: <a href="file:///usr/share/doc/libghc-dependent-sum-doc/html/Data-GADT-Compare.html#t:GEq">GEq</a> k => (<span class="keyword">forall</span> v. k v -> f v -> f v -> f v) -> [<a href="Data-Dependent-Map.html#t:DSum">DSum</a> k f] -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f</li><li class="src short"><a href="#v:fromDistinctAscList">fromDistinctAscList</a> :: [<a href="Data-Dependent-Map.html#t:DSum">DSum</a> k f] -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f</li><li class="src short"><a href="#v:filter">filter</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] -> [a]</li><li class="src short"><a href="#v:filterWithKey">filterWithKey</a> :: <a href="Data-Dependent-Map.html#t:GCompare">GCompare</a> k => (<span class="keyword">forall</span> v. k v -> f v -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Bool.html#t:Bool">Bool</a>) -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f</li><li class="src short"><a href="#v:partitionWithKey">partitionWithKey</a> :: <a href="Data-Dependent-Map.html#t:GCompare">GCompare</a> k => (<span class="keyword">forall</span> v. k v -> f v -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Bool.html#t:Bool">Bool</a>) -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> (<a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f, <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f)</li><li class="src short"><a href="#v:mapMaybeWithKey">mapMaybeWithKey</a> :: <a href="Data-Dependent-Map.html#t:GCompare">GCompare</a> k => (<span class="keyword">forall</span> v. k v -> f v -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Maybe.html#t:Maybe">Maybe</a> (g v)) -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k g</li><li class="src short"><a href="#v:mapEitherWithKey">mapEitherWithKey</a> :: <a href="Data-Dependent-Map.html#t:GCompare">GCompare</a> k => (<span class="keyword">forall</span> v. k v -> f v -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Either.html#t:Either">Either</a> (g v) (h v)) -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> (<a href="Data-Dependent-Map.html#t:DMap">DMap</a> k g, <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k h)</li><li class="src short"><a href="#v:split">split</a> :: <span class="keyword">forall</span> k f v. <a href="Data-Dependent-Map.html#t:GCompare">GCompare</a> k => k v -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> (<a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f, <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f)</li><li class="src short"><a href="#v:splitLookup">splitLookup</a> :: <span class="keyword">forall</span> k f v. <a href="Data-Dependent-Map.html#t:GCompare">GCompare</a> k => k v -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> (<a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Maybe.html#t:Maybe">Maybe</a> (f v), <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f)</li><li class="src short"><a href="#v:isSubmapOf">isSubmapOf</a> :: (<a href="Data-Dependent-Map.html#t:GCompare">GCompare</a> k, <a href="file:///usr/share/doc/libghc-dependent-sum-doc/html/Data-Dependent-Sum.html#t:EqTag">EqTag</a> k f) => <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> <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:isSubmapOfBy">isSubmapOfBy</a> :: <a href="Data-Dependent-Map.html#t:GCompare">GCompare</a> k => (<span class="keyword">forall</span> v. k v -> k v -> f v -> g v -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Bool.html#t:Bool">Bool</a>) -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k g -> <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:isProperSubmapOf">isProperSubmapOf</a> :: (<a href="Data-Dependent-Map.html#t:GCompare">GCompare</a> k, <a href="file:///usr/share/doc/libghc-dependent-sum-doc/html/Data-Dependent-Sum.html#t:EqTag">EqTag</a> k f) => <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> <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:isProperSubmapOfBy">isProperSubmapOfBy</a> :: <a href="Data-Dependent-Map.html#t:GCompare">GCompare</a> k => (<span class="keyword">forall</span> v. k v -> k v -> f v -> g v -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Bool.html#t:Bool">Bool</a>) -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k g -> <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:lookupIndex">lookupIndex</a> :: <span class="keyword">forall</span> k f v. <a href="Data-Dependent-Map.html#t:GCompare">GCompare</a> k => k v -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Maybe.html#t:Maybe">Maybe</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Int.html#t:Int">Int</a></li><li class="src short"><a href="#v:findIndex">findIndex</a> :: <a href="Data-Dependent-Map.html#t:GCompare">GCompare</a> k => k v -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Int.html#t:Int">Int</a></li><li class="src short"><a href="#v:elemAt">elemAt</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="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> <a href="Data-Dependent-Map.html#t:DSum">DSum</a> k f</li><li class="src short"><a href="#v:updateAt">updateAt</a> :: (<span class="keyword">forall</span> v. k v -> f v -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Maybe.html#t:Maybe">Maybe</a> (f v)) -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Int.html#t:Int">Int</a> -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f</li><li class="src short"><a href="#v:deleteAt">deleteAt</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="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f</li><li class="src short"><a href="#v:findMin">findMin</a> :: <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> <a href="Data-Dependent-Map.html#t:DSum">DSum</a> k f</li><li class="src short"><a href="#v:findMax">findMax</a> :: <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> <a href="Data-Dependent-Map.html#t:DSum">DSum</a> k f</li><li class="src short"><a href="#v:lookupMin">lookupMin</a> :: <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Maybe.html#t:Maybe">Maybe</a> (<a href="Data-Dependent-Map.html#t:DSum">DSum</a> k f)</li><li class="src short"><a href="#v:lookupMax">lookupMax</a> :: <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Maybe.html#t:Maybe">Maybe</a> (<a href="Data-Dependent-Map.html#t:DSum">DSum</a> k f)</li><li class="src short"><a href="#v:deleteMin">deleteMin</a> :: <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f</li><li class="src short"><a href="#v:deleteMax">deleteMax</a> :: <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f</li><li class="src short"><a href="#v:deleteFindMin">deleteFindMin</a> :: <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> (<a href="Data-Dependent-Map.html#t:DSum">DSum</a> k f, <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f)</li><li class="src short"><a href="#v:deleteFindMax">deleteFindMax</a> :: <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> (<a href="Data-Dependent-Map.html#t:DSum">DSum</a> k f, <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f)</li><li class="src short"><a href="#v:updateMinWithKey">updateMinWithKey</a> :: (<span class="keyword">forall</span> v. k v -> f v -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Maybe.html#t:Maybe">Maybe</a> (f v)) -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f</li><li class="src short"><a href="#v:updateMaxWithKey">updateMaxWithKey</a> :: (<span class="keyword">forall</span> v. k v -> f v -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Maybe.html#t:Maybe">Maybe</a> (f v)) -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f</li><li class="src short"><a href="#v:minViewWithKey">minViewWithKey</a> :: <span class="keyword">forall</span> k f. <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Maybe.html#t:Maybe">Maybe</a> (<a href="Data-Dependent-Map.html#t:DSum">DSum</a> k f, <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f)</li><li class="src short"><a href="#v:maxViewWithKey">maxViewWithKey</a> :: <span class="keyword">forall</span> k f. <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Maybe.html#t:Maybe">Maybe</a> (<a href="Data-Dependent-Map.html#t:DSum">DSum</a> k f, <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f)</li><li class="src short"><a href="#v:showTree">showTree</a> :: <a href="file:///usr/share/doc/libghc-dependent-sum-doc/html/Data-Dependent-Sum.html#t:ShowTag">ShowTag</a> k f => <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-String.html#t:String">String</a></li><li class="src short"><a href="#v:showTreeWith">showTreeWith</a> :: (<span class="keyword">forall</span> v. k v -> f v -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-String.html#t:String">String</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="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Bool.html#t:Bool">Bool</a> -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-String.html#t:String">String</a></li><li class="src short"><a href="#v:valid">valid</a> :: <a href="Data-Dependent-Map.html#t:GCompare">GCompare</a> k => <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Bool.html#t:Bool">Bool</a></li></ul></div><div id="interface"><h1>Documentation</h1><div class="top"><p class="src"><span class="keyword">data</span> <a id="t:DMap" class="def">DMap</a> k f <a href="src/Data-Dependent-Map-Internal.html#DMap" class="link">Source</a> <a href="#t:DMap" class="selflink">#</a></p><div class="doc"><p>Dependent maps: <code>k</code> is a GADT-like thing with a facility for
rediscovering its type parameter, elements of which function as identifiers
tagged with the type of the thing they identify. Real GADTs are one
useful instantiation of <code>k</code>, as are <code>Tag</code>s from <a href="Data-Unique-Tag.html">Data.Unique.Tag</a> in the
'prim-uniq' package.</p><p>Semantically, <code><code><a href="Data-Dependent-Map.html#t:DMap">DMap</a></code> k f</code> is equivalent to a set of <code><code><a href="Data-Dependent-Map.html#t:DSum">DSum</a></code> k f</code> where no two
elements have the same tag.</p><p>More informally, <code><a href="Data-Dependent-Map.html#t:DMap">DMap</a></code> is to dependent products as <code><a href="M.html#v:Map">Map</a></code> is to <code>(->)</code>.
Thus it could also be thought of as a partial (in the sense of "partial
function") dependent product.</p></div></div><div class="top"><p class="src"><span class="keyword">data</span> <a id="t:DSum" class="def">DSum</a> k tag f :: <span class="keyword">forall</span> k. (k -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Kind.html#t:-42-">*</a>) -> (k -> <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> <span class="keyword">where</span> <a href="#t:DSum" class="selflink">#</a></p><div class="doc"><p>A basic dependent sum type; the first component is a tag that specifies
the type of the second; for example, think of a GADT such as:</p><pre>data Tag a where
AString :: Tag String
AnInt :: Tag Int</pre><p>Then, we have the following valid expressions of type <code>DSum Tag</code>:</p><pre>AString :=> "hello!"
AnInt :=> 42</pre><p>And we can write functions that consume <code>DSum Tag</code> values by matching,
such as:</p><pre>toString :: DSum Tag -> String
toString (AString :=> str) = str
toString (AnInt :=> int) = show int</pre><p>By analogy to the (key => value) construction for dictionary entries in
many dynamic languages, we use (key :=> value) as the constructor for
dependent sums. The :=> operator has very low precedence and binds to
the right, so if the <code>Tag</code> GADT is extended with an additional constructor
<code>Rec :: Tag (DSum Tag)</code>, then <code>Rec :=> AnInt :=> 3 + 4</code> is parsed as
would be expected (<code>Rec :=> (AnInt :=> (3 + 4))</code>) and has type <code>DSum Tag</code>.
Its precedence is just above that of <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Function.html#v:-36-">$</a></code>, so <code>foo bar $ AString :=> "eep"</code>
is equivalent to <code>foo bar (AString :=> "eep")</code>.</p></div><div class="subs constructors"><p class="caption">Constructors</p><table><tr><td class="src"><a id="v::-61--62-" class="def">(:=>)</a> :: <a href="Data-Dependent-Map.html#t:DSum">DSum</a> k tag f <span class="fixity">infixr 1</span><span class="rightedge"></span></td><td class="doc empty"> </td></tr></table></div><div class="subs instances"><p id="control.i:DSum" class="caption collapser" onclick="toggleSection('i:DSum')">Instances</p><div id="section.i:DSum" class="show"><table><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:id:DSum:Eq:1" class="instance expander" onclick="toggleSection('i:id:DSum:Eq:1')"></span> <a href="file:///usr/share/doc/libghc-dependent-sum-doc/html/Data-Dependent-Sum.html#t:EqTag">EqTag</a> k tag f => <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Eq.html#t:Eq">Eq</a> (<a href="Data-Dependent-Map.html#t:DSum">DSum</a> k tag f)</span></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:id:DSum:Eq:1" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:-61--61-">(==)</a> :: <a href="Data-Dependent-Map.html#t:DSum">DSum</a> k tag f -> <a href="Data-Dependent-Map.html#t:DSum">DSum</a> k tag f -> <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="Data-Dependent-Map.html#t:DSum">DSum</a> k tag f -> <a href="Data-Dependent-Map.html#t:DSum">DSum</a> k tag f -> <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:DSum:Ord:2" class="instance expander" onclick="toggleSection('i:id:DSum:Ord:2')"></span> <a href="file:///usr/share/doc/libghc-dependent-sum-doc/html/Data-Dependent-Sum.html#t:OrdTag">OrdTag</a> k tag f => <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Ord.html#t:Ord">Ord</a> (<a href="Data-Dependent-Map.html#t:DSum">DSum</a> k tag f)</span></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:id:DSum:Ord:2" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:compare">compare</a> :: <a href="Data-Dependent-Map.html#t:DSum">DSum</a> k tag f -> <a href="Data-Dependent-Map.html#t:DSum">DSum</a> k tag f -> <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="Data-Dependent-Map.html#t:DSum">DSum</a> k tag f -> <a href="Data-Dependent-Map.html#t:DSum">DSum</a> k tag f -> <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="Data-Dependent-Map.html#t:DSum">DSum</a> k tag f -> <a href="Data-Dependent-Map.html#t:DSum">DSum</a> k tag f -> <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="Data-Dependent-Map.html#t:DSum">DSum</a> k tag f -> <a href="Data-Dependent-Map.html#t:DSum">DSum</a> k tag f -> <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="Data-Dependent-Map.html#t:DSum">DSum</a> k tag f -> <a href="Data-Dependent-Map.html#t:DSum">DSum</a> k tag f -> <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="Data-Dependent-Map.html#t:DSum">DSum</a> k tag f -> <a href="Data-Dependent-Map.html#t:DSum">DSum</a> k tag f -> <a href="Data-Dependent-Map.html#t:DSum">DSum</a> k tag f <a href="#v:max" class="selflink">#</a></p><p class="src"><a href="#v:min">min</a> :: <a href="Data-Dependent-Map.html#t:DSum">DSum</a> k tag f -> <a href="Data-Dependent-Map.html#t:DSum">DSum</a> k tag f -> <a href="Data-Dependent-Map.html#t:DSum">DSum</a> k tag f <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:DSum:Read:3" class="instance expander" onclick="toggleSection('i:id:DSum:Read:3')"></span> <a href="file:///usr/share/doc/libghc-dependent-sum-doc/html/Data-Dependent-Sum.html#t:ReadTag">ReadTag</a> k tag f => <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Text-Read.html#t:Read">Read</a> (<a href="Data-Dependent-Map.html#t:DSum">DSum</a> k tag f)</span></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:id:DSum:Read:3" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:readsPrec">readsPrec</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/Text-ParserCombinators-ReadP.html#t:ReadS">ReadS</a> (<a href="Data-Dependent-Map.html#t:DSum">DSum</a> k tag f) <a href="#v:readsPrec" class="selflink">#</a></p><p class="src"><a href="#v:readList">readList</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Text-ParserCombinators-ReadP.html#t:ReadS">ReadS</a> [<a href="Data-Dependent-Map.html#t:DSum">DSum</a> k tag f] <a href="#v:readList" class="selflink">#</a></p><p class="src"><a href="#v:readPrec">readPrec</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Text-ParserCombinators-ReadPrec.html#t:ReadPrec">ReadPrec</a> (<a href="Data-Dependent-Map.html#t:DSum">DSum</a> k tag f) <a href="#v:readPrec" class="selflink">#</a></p><p class="src"><a href="#v:readListPrec">readListPrec</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Text-ParserCombinators-ReadPrec.html#t:ReadPrec">ReadPrec</a> [<a href="Data-Dependent-Map.html#t:DSum">DSum</a> k tag f] <a href="#v:readListPrec" class="selflink">#</a></p></div></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:id:DSum:Show:4" class="instance expander" onclick="toggleSection('i:id:DSum:Show:4')"></span> <a href="file:///usr/share/doc/libghc-dependent-sum-doc/html/Data-Dependent-Sum.html#t:ShowTag">ShowTag</a> k tag f => <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Text-Show.html#t:Show">Show</a> (<a href="Data-Dependent-Map.html#t:DSum">DSum</a> k tag f)</span></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:id:DSum:Show:4" 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="Data-Dependent-Map.html#t:DSum">DSum</a> k tag f -> <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="Data-Dependent-Map.html#t:DSum">DSum</a> k tag f -> <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="Data-Dependent-Map.html#t:DSum">DSum</a> k tag f] -> <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></table></div></div></div><div class="top"><p class="src"><span class="keyword">data</span> <a id="t:Some" class="def">Some</a> k tag :: <span class="keyword">forall</span> k. (k -> <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> <span class="keyword">where</span> <a href="#t:Some" class="selflink">#</a></p><div class="subs constructors"><p class="caption">Constructors</p><table><tr><td class="src"><a id="v:This" class="def">This</a> :: <a href="Data-Dependent-Map.html#t:Some">Some</a> k tag</td><td class="doc empty"> </td></tr></table></div><div class="subs instances"><p id="control.i:Some" class="caption collapser" onclick="toggleSection('i:Some')">Instances</p><div id="section.i:Some" class="show"><table><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:id:Some:Eq:1" class="instance expander" onclick="toggleSection('i:id:Some:Eq:1')"></span> <a href="file:///usr/share/doc/libghc-dependent-sum-doc/html/Data-GADT-Compare.html#t:GEq">GEq</a> k tag => <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Eq.html#t:Eq">Eq</a> (<a href="Data-Dependent-Map.html#t:Some">Some</a> k tag)</span></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:id:Some:Eq:1" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:-61--61-">(==)</a> :: <a href="Data-Dependent-Map.html#t:Some">Some</a> k tag -> <a href="Data-Dependent-Map.html#t:Some">Some</a> k tag -> <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="Data-Dependent-Map.html#t:Some">Some</a> k tag -> <a href="Data-Dependent-Map.html#t:Some">Some</a> k tag -> <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:Some:Ord:2" class="instance expander" onclick="toggleSection('i:id:Some:Ord:2')"></span> <a href="Data-Dependent-Map.html#t:GCompare">GCompare</a> k tag => <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Ord.html#t:Ord">Ord</a> (<a href="Data-Dependent-Map.html#t:Some">Some</a> k tag)</span></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:id:Some:Ord:2" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:compare">compare</a> :: <a href="Data-Dependent-Map.html#t:Some">Some</a> k tag -> <a href="Data-Dependent-Map.html#t:Some">Some</a> k tag -> <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="Data-Dependent-Map.html#t:Some">Some</a> k tag -> <a href="Data-Dependent-Map.html#t:Some">Some</a> k tag -> <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="Data-Dependent-Map.html#t:Some">Some</a> k tag -> <a href="Data-Dependent-Map.html#t:Some">Some</a> k tag -> <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="Data-Dependent-Map.html#t:Some">Some</a> k tag -> <a href="Data-Dependent-Map.html#t:Some">Some</a> k tag -> <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="Data-Dependent-Map.html#t:Some">Some</a> k tag -> <a href="Data-Dependent-Map.html#t:Some">Some</a> k tag -> <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="Data-Dependent-Map.html#t:Some">Some</a> k tag -> <a href="Data-Dependent-Map.html#t:Some">Some</a> k tag -> <a href="Data-Dependent-Map.html#t:Some">Some</a> k tag <a href="#v:max" class="selflink">#</a></p><p class="src"><a href="#v:min">min</a> :: <a href="Data-Dependent-Map.html#t:Some">Some</a> k tag -> <a href="Data-Dependent-Map.html#t:Some">Some</a> k tag -> <a href="Data-Dependent-Map.html#t:Some">Some</a> k tag <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:Some:Read:3" class="instance expander" onclick="toggleSection('i:id:Some:Read:3')"></span> <a href="file:///usr/share/doc/libghc-dependent-sum-doc/html/Data-GADT-Show.html#t:GRead">GRead</a> k f => <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Text-Read.html#t:Read">Read</a> (<a href="Data-Dependent-Map.html#t:Some">Some</a> k f)</span></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:id:Some:Read:3" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:readsPrec">readsPrec</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/Text-ParserCombinators-ReadP.html#t:ReadS">ReadS</a> (<a href="Data-Dependent-Map.html#t:Some">Some</a> k f) <a href="#v:readsPrec" class="selflink">#</a></p><p class="src"><a href="#v:readList">readList</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Text-ParserCombinators-ReadP.html#t:ReadS">ReadS</a> [<a href="Data-Dependent-Map.html#t:Some">Some</a> k f] <a href="#v:readList" class="selflink">#</a></p><p class="src"><a href="#v:readPrec">readPrec</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Text-ParserCombinators-ReadPrec.html#t:ReadPrec">ReadPrec</a> (<a href="Data-Dependent-Map.html#t:Some">Some</a> k f) <a href="#v:readPrec" class="selflink">#</a></p><p class="src"><a href="#v:readListPrec">readListPrec</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Text-ParserCombinators-ReadPrec.html#t:ReadPrec">ReadPrec</a> [<a href="Data-Dependent-Map.html#t:Some">Some</a> k f] <a href="#v:readListPrec" class="selflink">#</a></p></div></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:id:Some:Show:4" class="instance expander" onclick="toggleSection('i:id:Some:Show:4')"></span> <a href="file:///usr/share/doc/libghc-dependent-sum-doc/html/Data-GADT-Show.html#t:GShow">GShow</a> k tag => <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Text-Show.html#t:Show">Show</a> (<a href="Data-Dependent-Map.html#t:Some">Some</a> k tag)</span></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:id:Some:Show:4" 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="Data-Dependent-Map.html#t:Some">Some</a> k tag -> <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="Data-Dependent-Map.html#t:Some">Some</a> k tag -> <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="Data-Dependent-Map.html#t:Some">Some</a> k tag] -> <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></table></div></div></div><div class="top"><p class="src"><span class="keyword">class</span> <a href="file:///usr/share/doc/libghc-dependent-sum-doc/html/Data-GADT-Compare.html#t:GEq">GEq</a> k f => <a id="t:GCompare" class="def">GCompare</a> k f <span class="keyword">where</span> <a href="#t:GCompare" class="selflink">#</a></p><div class="doc"><p>Type class for comparable GADT-like structures. When 2 things are equal,
must return a witness that their parameter types are equal as well (<code><a href="Data-Dependent-Map.html#v:GEQ">GEQ</a></code>).</p></div><div class="subs instances"><p id="control.i:GCompare" class="caption collapser" onclick="toggleSection('i:GCompare')">Instances</p><div id="section.i:GCompare" class="show"><table><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:ic:GCompare:GCompare:1" class="instance expander" onclick="toggleSection('i:ic:GCompare:GCompare:1')"></span> <a href="Data-Dependent-Map.html#t:GCompare">GCompare</a> k (<a href="file:///usr/share/doc/libghc-dependent-sum-doc/html/Data-GADT-Compare.html#t::-61-">(:=)</a> k a)</span></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:ic:GCompare:GCompare:1" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:gcompare">gcompare</a> :: f a -> f b -> <a href="Data-Dependent-Map.html#t:GOrdering">GOrdering</a> (k <a href="file:///usr/share/doc/libghc-dependent-sum-doc/html/Data-GADT-Compare.html#t::-61-">:=</a> a) a b <a href="#v:gcompare" class="selflink">#</a></p></div></div></td></tr></table></div></div></div><div class="top"><p class="src"><span class="keyword">data</span> <a id="t:GOrdering" class="def">GOrdering</a> k a b :: <span class="keyword">forall</span> k. k -> k -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Kind.html#t:-42-">*</a> <span class="keyword">where</span> <a href="#t:GOrdering" class="selflink">#</a></p><div class="doc"><p>A type for the result of comparing GADT constructors; the type parameters
of the GADT values being compared are included so that in the case where
they are equal their parameter types can be unified.</p></div><div class="subs constructors"><p class="caption">Constructors</p><table><tr><td class="src"><a id="v:GLT" class="def">GLT</a> :: <a href="Data-Dependent-Map.html#t:GOrdering">GOrdering</a> k a b</td><td class="doc empty"> </td></tr><tr><td class="src"><a id="v:GEQ" class="def">GEQ</a> :: <a href="Data-Dependent-Map.html#t:GOrdering">GOrdering</a> k a a</td><td class="doc empty"> </td></tr><tr><td class="src"><a id="v:GGT" class="def">GGT</a> :: <a href="Data-Dependent-Map.html#t:GOrdering">GOrdering</a> k a b</td><td class="doc empty"> </td></tr></table></div><div class="subs instances"><p id="control.i:GOrdering" class="caption collapser" onclick="toggleSection('i:GOrdering')">Instances</p><div id="section.i:GOrdering" class="show"><table><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:id:GOrdering:GShow:1" class="instance expander" onclick="toggleSection('i:id:GOrdering:GShow:1')"></span> <a href="file:///usr/share/doc/libghc-dependent-sum-doc/html/Data-GADT-Show.html#t:GShow">GShow</a> k (<a href="Data-Dependent-Map.html#t:GOrdering">GOrdering</a> k a)</span></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:id:GOrdering:GShow:1" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:gshowsPrec">gshowsPrec</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Int.html#t:Int">Int</a> -> t 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:gshowsPrec" class="selflink">#</a></p></div></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:id:GOrdering:GRead:2" class="instance expander" onclick="toggleSection('i:id:GOrdering:GRead:2')"></span> <a href="file:///usr/share/doc/libghc-dependent-sum-doc/html/Data-GADT-Show.html#t:GRead">GRead</a> k (<a href="Data-Dependent-Map.html#t:GOrdering">GOrdering</a> k a)</span></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:id:GOrdering:GRead:2" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:greadsPrec">greadsPrec</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/libghc-dependent-sum-doc/html/Data-GADT-Show.html#t:GReadS">GReadS</a> (<a href="Data-Dependent-Map.html#t:GOrdering">GOrdering</a> k a) t <a href="#v:greadsPrec" class="selflink">#</a></p></div></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:id:GOrdering:ShowTag:3" class="instance expander" onclick="toggleSection('i:id:GOrdering:ShowTag:3')"></span> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Text-Show.html#t:Show">Show</a> (f a) => <a href="file:///usr/share/doc/libghc-dependent-sum-doc/html/Data-Dependent-Sum.html#t:ShowTag">ShowTag</a> k (<a href="Data-Dependent-Map.html#t:GOrdering">GOrdering</a> k a) f</span></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:id:GOrdering:ShowTag:3" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:showTaggedPrec">showTaggedPrec</a> :: f a -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Int.html#t:Int">Int</a> -> f 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:showTaggedPrec" class="selflink">#</a></p></div></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:id:GOrdering:Eq:4" class="instance expander" onclick="toggleSection('i:id:GOrdering:Eq:4')"></span> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Eq.html#t:Eq">Eq</a> (<a href="Data-Dependent-Map.html#t:GOrdering">GOrdering</a> k a b)</span></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:id:GOrdering:Eq:4" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:-61--61-">(==)</a> :: <a href="Data-Dependent-Map.html#t:GOrdering">GOrdering</a> k a b -> <a href="Data-Dependent-Map.html#t:GOrdering">GOrdering</a> k a 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="#v:-61--61-" class="selflink">#</a></p><p class="src"><a href="#v:-47--61-">(/=)</a> :: <a href="Data-Dependent-Map.html#t:GOrdering">GOrdering</a> k a b -> <a href="Data-Dependent-Map.html#t:GOrdering">GOrdering</a> k a 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="#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:GOrdering:Ord:5" class="instance expander" onclick="toggleSection('i:id:GOrdering:Ord:5')"></span> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Ord.html#t:Ord">Ord</a> (<a href="Data-Dependent-Map.html#t:GOrdering">GOrdering</a> k a b)</span></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:id:GOrdering:Ord:5" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:compare">compare</a> :: <a href="Data-Dependent-Map.html#t:GOrdering">GOrdering</a> k a b -> <a href="Data-Dependent-Map.html#t:GOrdering">GOrdering</a> k a b -> <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="Data-Dependent-Map.html#t:GOrdering">GOrdering</a> k a b -> <a href="Data-Dependent-Map.html#t:GOrdering">GOrdering</a> k a 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="#v:-60-" class="selflink">#</a></p><p class="src"><a href="#v:-60--61-">(<=)</a> :: <a href="Data-Dependent-Map.html#t:GOrdering">GOrdering</a> k a b -> <a href="Data-Dependent-Map.html#t:GOrdering">GOrdering</a> k a 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="#v:-60--61-" class="selflink">#</a></p><p class="src"><a href="#v:-62-">(>)</a> :: <a href="Data-Dependent-Map.html#t:GOrdering">GOrdering</a> k a b -> <a href="Data-Dependent-Map.html#t:GOrdering">GOrdering</a> k a 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="#v:-62-" class="selflink">#</a></p><p class="src"><a href="#v:-62--61-">(>=)</a> :: <a href="Data-Dependent-Map.html#t:GOrdering">GOrdering</a> k a b -> <a href="Data-Dependent-Map.html#t:GOrdering">GOrdering</a> k a 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="#v:-62--61-" class="selflink">#</a></p><p class="src"><a href="#v:max">max</a> :: <a href="Data-Dependent-Map.html#t:GOrdering">GOrdering</a> k a b -> <a href="Data-Dependent-Map.html#t:GOrdering">GOrdering</a> k a b -> <a href="Data-Dependent-Map.html#t:GOrdering">GOrdering</a> k a b <a href="#v:max" class="selflink">#</a></p><p class="src"><a href="#v:min">min</a> :: <a href="Data-Dependent-Map.html#t:GOrdering">GOrdering</a> k a b -> <a href="Data-Dependent-Map.html#t:GOrdering">GOrdering</a> k a b -> <a href="Data-Dependent-Map.html#t:GOrdering">GOrdering</a> k a b <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:GOrdering:Show:6" class="instance expander" onclick="toggleSection('i:id:GOrdering:Show:6')"></span> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Text-Show.html#t:Show">Show</a> (<a href="Data-Dependent-Map.html#t:GOrdering">GOrdering</a> k a b)</span></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:id:GOrdering:Show:6" 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="Data-Dependent-Map.html#t:GOrdering">GOrdering</a> k a b -> <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="Data-Dependent-Map.html#t:GOrdering">GOrdering</a> k a b -> <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="Data-Dependent-Map.html#t:GOrdering">GOrdering</a> k a b] -> <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></table></div></div></div><h1 id="g:1">Operators</h1><div class="top"><p class="src"><a id="v:-33-" class="def">(!)</a> :: <a href="Data-Dependent-Map.html#t:GCompare">GCompare</a> k => <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> k v -> f v <span class="fixity">infixl 9</span><span class="rightedge"></span> <a href="src/Data-Dependent-Map.html#%21" class="link">Source</a> <a href="#v:-33-" class="selflink">#</a></p><div class="doc"><p><em>O(log n)</em>. Find the value at a key.
Calls <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#v:error">error</a></code> when the element can not be found.</p><pre>fromList [(5,'a'), (3,'b')] ! 1 Error: element not in the map
fromList [(5,'a'), (3,'b')] ! 5 == 'a'</pre></div></div><div class="top"><p class="src"><a id="v:-92--92-" class="def">(\\)</a> :: <a href="Data-Dependent-Map.html#t:GCompare">GCompare</a> k => <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f <span class="fixity">infixl 9</span><span class="rightedge"></span> <a href="src/Data-Dependent-Map.html#%5C%5C" class="link">Source</a> <a href="#v:-92--92-" class="selflink">#</a></p><div class="doc"><p>Same as <code><a href="Data-Dependent-Map.html#v:difference">difference</a></code>.</p></div></div><h1 id="g:2">Query</h1><div class="top"><p class="src"><a id="v:null" class="def">null</a> :: <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> <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/Data-Dependent-Map-Internal.html#null" class="link">Source</a> <a href="#v:null" class="selflink">#</a></p><div class="doc"><p><em>O(1)</em>. Is the map empty?</p></div></div><div class="top"><p class="src"><a id="v:size" class="def">size</a> :: <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Int.html#t:Int">Int</a> <a href="src/Data-Dependent-Map-Internal.html#size" class="link">Source</a> <a href="#v:size" class="selflink">#</a></p><div class="doc"><p><em>O(1)</em>. The number of elements in the map.</p></div></div><div class="top"><p class="src"><a id="v:member" class="def">member</a> :: <a href="Data-Dependent-Map.html#t:GCompare">GCompare</a> k => k a -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> <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/Data-Dependent-Map.html#member" class="link">Source</a> <a href="#v:member" class="selflink">#</a></p><div class="doc"><p><em>O(log n)</em>. Is the key a member of the map? See also <code><a href="Data-Dependent-Map.html#v:notMember">notMember</a></code>.</p></div></div><div class="top"><p class="src"><a id="v:notMember" class="def">notMember</a> :: <a href="Data-Dependent-Map.html#t:GCompare">GCompare</a> k => k v -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> <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/Data-Dependent-Map.html#notMember" class="link">Source</a> <a href="#v:notMember" class="selflink">#</a></p><div class="doc"><p><em>O(log n)</em>. Is the key not a member of the map? See also <code><a href="Data-Dependent-Map.html#v:member">member</a></code>.</p></div></div><div class="top"><p class="src"><a id="v:lookup" class="def">lookup</a> :: <span class="keyword">forall</span> k f v. <a href="Data-Dependent-Map.html#t:GCompare">GCompare</a> k => k v -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Maybe.html#t:Maybe">Maybe</a> (f v) <a href="src/Data-Dependent-Map-Internal.html#lookup" class="link">Source</a> <a href="#v:lookup" class="selflink">#</a></p><div class="doc"><p><em>O(log n)</em>. Lookup the value at a key in the map.</p><p>The function will return the corresponding value as <code>(<code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Maybe.html#v:Just">Just</a></code> value)</code>,
or <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Maybe.html#v:Nothing">Nothing</a></code> if the key isn't in the map.</p></div></div><div class="top"><p class="src"><a id="v:findWithDefault" class="def">findWithDefault</a> :: <a href="Data-Dependent-Map.html#t:GCompare">GCompare</a> k => f v -> k v -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> f v <a href="src/Data-Dependent-Map.html#findWithDefault" class="link">Source</a> <a href="#v:findWithDefault" class="selflink">#</a></p><div class="doc"><p><em>O(log n)</em>. The expression <code>(<code><a href="Data-Dependent-Map.html#v:findWithDefault">findWithDefault</a></code> def k map)</code> returns
the value at key <code>k</code> or returns default value <code>def</code>
when the key is not in the map.</p></div></div><h1 id="g:3">Construction</h1><div class="top"><p class="src"><a id="v:empty" class="def">empty</a> :: <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f <a href="src/Data-Dependent-Map-Internal.html#empty" class="link">Source</a> <a href="#v:empty" class="selflink">#</a></p><div class="doc"><p><em>O(1)</em>. The empty map.</p><pre>empty == fromList []
size empty == 0</pre></div></div><div class="top"><p class="src"><a id="v:singleton" class="def">singleton</a> :: k v -> f v -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f <a href="src/Data-Dependent-Map-Internal.html#singleton" class="link">Source</a> <a href="#v:singleton" class="selflink">#</a></p><div class="doc"><p><em>O(1)</em>. A map with a single element.</p><pre>singleton 1 'a' == fromList [(1, 'a')]
size (singleton 1 'a') == 1</pre></div></div><h2 id="g:4">Insertion</h2><div class="top"><p class="src"><a id="v:insert" class="def">insert</a> :: <span class="keyword">forall</span> k f v. <a href="Data-Dependent-Map.html#t:GCompare">GCompare</a> k => k v -> f v -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f <a href="src/Data-Dependent-Map.html#insert" class="link">Source</a> <a href="#v:insert" class="selflink">#</a></p><div class="doc"><p><em>O(log n)</em>. Insert a new key and value in the map.
If the key is already present in the map, the associated value is
replaced with the supplied value. <code><a href="Data-Dependent-Map.html#v:insert">insert</a></code> is equivalent to
<code><code><a href="Data-Dependent-Map.html#v:insertWith">insertWith</a></code> <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Function.html#v:const">const</a></code></code>.</p></div></div><div class="top"><p class="src"><a id="v:insertWith" class="def">insertWith</a> :: <a href="Data-Dependent-Map.html#t:GCompare">GCompare</a> k => (f v -> f v -> f v) -> k v -> f v -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f <a href="src/Data-Dependent-Map.html#insertWith" class="link">Source</a> <a href="#v:insertWith" class="selflink">#</a></p><div class="doc"><p><em>O(log n)</em>. Insert with a function, combining new value and old value.
<code><code><a href="Data-Dependent-Map.html#v:insertWith">insertWith</a></code> f key value mp</code>
will insert the entry <code>key :=> value</code> into <code>mp</code> if key does
not exist in the map. If the key does exist, the function will
insert the entry <code>key :=> f new_value old_value</code>.</p></div></div><div class="top"><p class="src"><a id="v:insertWith-39-" class="def">insertWith'</a> :: <a href="Data-Dependent-Map.html#t:GCompare">GCompare</a> k => (f v -> f v -> f v) -> k v -> f v -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f <a href="src/Data-Dependent-Map.html#insertWith%27" class="link">Source</a> <a href="#v:insertWith-39-" class="selflink">#</a></p><div class="doc"><p>Same as <code><a href="Data-Dependent-Map.html#v:insertWith">insertWith</a></code>, but the combining function is applied strictly.
This is often the most desirable behavior.</p></div></div><div class="top"><p class="src"><a id="v:insertWithKey" class="def">insertWithKey</a> :: <span class="keyword">forall</span> k f v. <a href="Data-Dependent-Map.html#t:GCompare">GCompare</a> k => (k v -> f v -> f v -> f v) -> k v -> f v -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f <a href="src/Data-Dependent-Map.html#insertWithKey" class="link">Source</a> <a href="#v:insertWithKey" class="selflink">#</a></p><div class="doc"><p><em>O(log n)</em>. Insert with a function, combining key, new value and old value.
<code><code><a href="Data-Dependent-Map.html#v:insertWithKey">insertWithKey</a></code> f key value mp</code>
will insert the entry <code>key :=> value</code> into <code>mp</code> if key does
not exist in the map. If the key does exist, the function will
insert the entry <code>key :=> f key new_value old_value</code>.
Note that the key passed to f is the same key passed to <code><a href="Data-Dependent-Map.html#v:insertWithKey">insertWithKey</a></code>.</p></div></div><div class="top"><p class="src"><a id="v:insertWithKey-39-" class="def">insertWithKey'</a> :: <span class="keyword">forall</span> k f v. <a href="Data-Dependent-Map.html#t:GCompare">GCompare</a> k => (k v -> f v -> f v -> f v) -> k v -> f v -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f <a href="src/Data-Dependent-Map.html#insertWithKey%27" class="link">Source</a> <a href="#v:insertWithKey-39-" class="selflink">#</a></p><div class="doc"><p>Same as <code><a href="Data-Dependent-Map.html#v:insertWithKey">insertWithKey</a></code>, but the combining function is applied strictly.</p></div></div><div class="top"><p class="src"><a id="v:insertLookupWithKey" class="def">insertLookupWithKey</a> :: <span class="keyword">forall</span> k f v. <a href="Data-Dependent-Map.html#t:GCompare">GCompare</a> k => (k v -> f v -> f v -> f v) -> k v -> f v -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Maybe.html#t:Maybe">Maybe</a> (f v), <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f) <a href="src/Data-Dependent-Map.html#insertLookupWithKey" class="link">Source</a> <a href="#v:insertLookupWithKey" class="selflink">#</a></p><div class="doc"><p><em>O(log n)</em>. Combines insert operation with old value retrieval.
The expression (<code><code><a href="Data-Dependent-Map.html#v:insertLookupWithKey">insertLookupWithKey</a></code> f k x map</code>)
is a pair where the first element is equal to (<code><code><a href="Data-Dependent-Map.html#v:lookup">lookup</a></code> k map</code>)
and the second element equal to (<code><code><a href="Data-Dependent-Map.html#v:insertWithKey">insertWithKey</a></code> f k x map</code>).</p></div></div><div class="top"><p class="src"><a id="v:insertLookupWithKey-39-" class="def">insertLookupWithKey'</a> :: <span class="keyword">forall</span> k f v. <a href="Data-Dependent-Map.html#t:GCompare">GCompare</a> k => (k v -> f v -> f v -> f v) -> k v -> f v -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Maybe.html#t:Maybe">Maybe</a> (f v), <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f) <a href="src/Data-Dependent-Map.html#insertLookupWithKey%27" class="link">Source</a> <a href="#v:insertLookupWithKey-39-" class="selflink">#</a></p><div class="doc"><p><em>O(log n)</em>. A strict version of <code><a href="Data-Dependent-Map.html#v:insertLookupWithKey">insertLookupWithKey</a></code>.</p></div></div><h2 id="g:5">Delete/Update</h2><div class="top"><p class="src"><a id="v:delete" class="def">delete</a> :: <span class="keyword">forall</span> k f v. <a href="Data-Dependent-Map.html#t:GCompare">GCompare</a> k => k v -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f <a href="src/Data-Dependent-Map.html#delete" class="link">Source</a> <a href="#v:delete" class="selflink">#</a></p><div class="doc"><p><em>O(log n)</em>. Delete a key and its value from the map. When the key is not
a member of the map, the original map is returned.</p></div></div><div class="top"><p class="src"><a id="v:adjust" class="def">adjust</a> :: <a href="Data-Dependent-Map.html#t:GCompare">GCompare</a> k => (f v -> f v) -> k v -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f <a href="src/Data-Dependent-Map.html#adjust" class="link">Source</a> <a href="#v:adjust" class="selflink">#</a></p><div class="doc"><p><em>O(log n)</em>. Update a value at a specific key with the result of the provided function.
When the key is not
a member of the map, the original map is returned.</p></div></div><div class="top"><p class="src"><a id="v:adjustWithKey" class="def">adjustWithKey</a> :: <a href="Data-Dependent-Map.html#t:GCompare">GCompare</a> k => (k v -> f v -> f v) -> k v -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f <a href="src/Data-Dependent-Map.html#adjustWithKey" class="link">Source</a> <a href="#v:adjustWithKey" class="selflink">#</a></p><div class="doc"><p><em>O(log n)</em>. Adjust a value at a specific key. When the key is not
a member of the map, the original map is returned.</p></div></div><div class="top"><p class="src"><a id="v:adjustWithKey-39-" class="def">adjustWithKey'</a> :: <a href="Data-Dependent-Map.html#t:GCompare">GCompare</a> k => (k v -> f v -> f v) -> k v -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f <a href="src/Data-Dependent-Map.html#adjustWithKey%27" class="link">Source</a> <a href="#v:adjustWithKey-39-" class="selflink">#</a></p><div class="doc"><p><em>O(log n)</em>. A strict version of <code><a href="Data-Dependent-Map.html#v:adjustWithKey">adjustWithKey</a></code>.</p></div></div><div class="top"><p class="src"><a id="v:update" class="def">update</a> :: <a href="Data-Dependent-Map.html#t:GCompare">GCompare</a> k => (f v -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Maybe.html#t:Maybe">Maybe</a> (f v)) -> k v -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f <a href="src/Data-Dependent-Map.html#update" class="link">Source</a> <a href="#v:update" class="selflink">#</a></p><div class="doc"><p><em>O(log n)</em>. The expression (<code><code><a href="Data-Dependent-Map.html#v:update">update</a></code> f k map</code>) updates the value <code>x</code>
at <code>k</code> (if it is in the map). If (<code>f x</code>) is <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Maybe.html#v:Nothing">Nothing</a></code>, the element is
deleted. If it is (<code><code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Maybe.html#v:Just">Just</a></code> y</code>), the key <code>k</code> is bound to the new value <code>y</code>.</p></div></div><div class="top"><p class="src"><a id="v:updateWithKey" class="def">updateWithKey</a> :: <span class="keyword">forall</span> k f v. <a href="Data-Dependent-Map.html#t:GCompare">GCompare</a> k => (k v -> f v -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Maybe.html#t:Maybe">Maybe</a> (f v)) -> k v -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f <a href="src/Data-Dependent-Map.html#updateWithKey" class="link">Source</a> <a href="#v:updateWithKey" class="selflink">#</a></p><div class="doc"><p><em>O(log n)</em>. The expression (<code><code><a href="Data-Dependent-Map.html#v:updateWithKey">updateWithKey</a></code> f k map</code>) updates the
value <code>x</code> at <code>k</code> (if it is in the map). If (<code>f k x</code>) is <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Maybe.html#v:Nothing">Nothing</a></code>,
the element is deleted. If it is (<code><code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Maybe.html#v:Just">Just</a></code> y</code>), the key <code>k</code> is bound
to the new value <code>y</code>.</p></div></div><div class="top"><p class="src"><a id="v:updateLookupWithKey" class="def">updateLookupWithKey</a> :: <span class="keyword">forall</span> k f v. <a href="Data-Dependent-Map.html#t:GCompare">GCompare</a> k => (k v -> f v -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Maybe.html#t:Maybe">Maybe</a> (f v)) -> k v -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Maybe.html#t:Maybe">Maybe</a> (f v), <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f) <a href="src/Data-Dependent-Map.html#updateLookupWithKey" class="link">Source</a> <a href="#v:updateLookupWithKey" class="selflink">#</a></p><div class="doc"><p><em>O(log n)</em>. Lookup and update. See also <code><a href="Data-Dependent-Map.html#v:updateWithKey">updateWithKey</a></code>.
The function returns changed value, if it is updated.
Returns the original key value if the map entry is deleted. </p></div></div><div class="top"><p class="src"><a id="v:alter" class="def">alter</a> :: <span class="keyword">forall</span> k f v. <a href="Data-Dependent-Map.html#t:GCompare">GCompare</a> k => (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Maybe.html#t:Maybe">Maybe</a> (f v) -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Maybe.html#t:Maybe">Maybe</a> (f v)) -> k v -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f <a href="src/Data-Dependent-Map.html#alter" class="link">Source</a> <a href="#v:alter" class="selflink">#</a></p><div class="doc"><p><em>O(log n)</em>. The expression (<code><code><a href="Data-Dependent-Map.html#v:alter">alter</a></code> f k map</code>) alters the value <code>x</code> at <code>k</code>, or absence thereof.
<code><a href="Data-Dependent-Map.html#v:alter">alter</a></code> can be used to insert, delete, or update a value in a <code>Map</code>.
In short : <code><code><a href="Data-Dependent-Map.html#v:lookup">lookup</a></code> k (<code><a href="Data-Dependent-Map.html#v:alter">alter</a></code> f k m) = f (<code><a href="Data-Dependent-Map.html#v:lookup">lookup</a></code> k m)</code>.</p></div></div><h1 id="g:6">Combine</h1><h2 id="g:7">Union</h2><div class="top"><p class="src"><a id="v:union" class="def">union</a> :: <a href="Data-Dependent-Map.html#t:GCompare">GCompare</a> k => <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f <a href="src/Data-Dependent-Map.html#union" class="link">Source</a> <a href="#v:union" class="selflink">#</a></p><div class="doc"><p><em>O(m*log(n/m + 1)), m <= n</em>.
The expression (<code><code><a href="Data-Dependent-Map.html#v:union">union</a></code> t1 t2</code>) takes the left-biased union of <code>t1</code> and <code>t2</code>.
It prefers <code>t1</code> when duplicate keys are encountered,
i.e. (<code><code><a href="Data-Dependent-Map.html#v:union">union</a></code> == <code>unionWith</code> <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Function.html#v:const">const</a></code></code>).</p></div></div><div class="top"><p class="src"><a id="v:unionWithKey" class="def">unionWithKey</a> :: <a href="Data-Dependent-Map.html#t:GCompare">GCompare</a> k => (<span class="keyword">forall</span> v. k v -> f v -> f v -> f v) -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f <a href="src/Data-Dependent-Map.html#unionWithKey" class="link">Source</a> <a href="#v:unionWithKey" class="selflink">#</a></p><div class="doc"><p><em>O(n+m)</em>.
Union with a combining function.</p></div></div><div class="top"><p class="src"><a id="v:unions" class="def">unions</a> :: <a href="Data-Dependent-Map.html#t:GCompare">GCompare</a> k => [<a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f] -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f <a href="src/Data-Dependent-Map.html#unions" class="link">Source</a> <a href="#v:unions" class="selflink">#</a></p><div class="doc"><p>The union of a list of maps:
(<code><code><a href="Data-Dependent-Map.html#v:unions">unions</a></code> == <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Foldable.html#v:foldl">foldl</a></code> <code><a href="Data-Dependent-Map.html#v:union">union</a></code> <code><a href="Data-Dependent-Map.html#v:empty">empty</a></code></code>).</p></div></div><div class="top"><p class="src"><a id="v:unionsWithKey" class="def">unionsWithKey</a> :: <a href="Data-Dependent-Map.html#t:GCompare">GCompare</a> k => (<span class="keyword">forall</span> v. k v -> f v -> f v -> f v) -> [<a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f] -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f <a href="src/Data-Dependent-Map.html#unionsWithKey" class="link">Source</a> <a href="#v:unionsWithKey" class="selflink">#</a></p><div class="doc"><p>The union of a list of maps, with a combining operation:
(<code><code><a href="Data-Dependent-Map.html#v:unionsWithKey">unionsWithKey</a></code> f == <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Foldable.html#v:foldl">foldl</a></code> (<code><a href="Data-Dependent-Map.html#v:unionWithKey">unionWithKey</a></code> f) <code><a href="Data-Dependent-Map.html#v:empty">empty</a></code></code>).</p></div></div><h2 id="g:8">Difference</h2><div class="top"><p class="src"><a id="v:difference" class="def">difference</a> :: <a href="Data-Dependent-Map.html#t:GCompare">GCompare</a> k => <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k g -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f <a href="src/Data-Dependent-Map.html#difference" class="link">Source</a> <a href="#v:difference" class="selflink">#</a></p><div class="doc"><p><em>O(m * log (n/m + 1)), m <= n</em>. Difference of two maps.
Return elements of the first map not existing in the second map.</p></div></div><div class="top"><p class="src"><a id="v:differenceWithKey" class="def">differenceWithKey</a> :: <a href="Data-Dependent-Map.html#t:GCompare">GCompare</a> k => (<span class="keyword">forall</span> v. k v -> f v -> g v -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Maybe.html#t:Maybe">Maybe</a> (f v)) -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k g -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f <a href="src/Data-Dependent-Map.html#differenceWithKey" class="link">Source</a> <a href="#v:differenceWithKey" class="selflink">#</a></p><div class="doc"><p><em>O(n+m)</em>. Difference with a combining function. When two equal keys are
encountered, the combining function is applied to the key and both values.
If it returns <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Maybe.html#v:Nothing">Nothing</a></code>, the element is discarded (proper set difference). If
it returns (<code><code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Maybe.html#v:Just">Just</a></code> y</code>), the element is updated with a new value <code>y</code>. </p></div></div><h2 id="g:9">Intersection</h2><div class="top"><p class="src"><a id="v:intersection" class="def">intersection</a> :: <a href="Data-Dependent-Map.html#t:GCompare">GCompare</a> k => <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f <a href="src/Data-Dependent-Map.html#intersection" class="link">Source</a> <a href="#v:intersection" class="selflink">#</a></p><div class="doc"><p><em>O(m * log (n/m + 1), m <= n</em>. Intersection of two maps.
Return data in the first map for the keys existing in both maps.
(<code><code><a href="Data-Dependent-Map.html#v:intersection">intersection</a></code> m1 m2 == <code>intersectionWith</code> <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Function.html#v:const">const</a></code> m1 m2</code>).</p></div></div><div class="top"><p class="src"><a id="v:intersectionWithKey" class="def">intersectionWithKey</a> :: <a href="Data-Dependent-Map.html#t:GCompare">GCompare</a> k => (<span class="keyword">forall</span> v. k v -> f v -> g v -> h v) -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k g -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k h <a href="src/Data-Dependent-Map.html#intersectionWithKey" class="link">Source</a> <a href="#v:intersectionWithKey" class="selflink">#</a></p><div class="doc"><p><em>O(m * log (n/m + 1), m <= n</em>. Intersection with a combining function.</p></div></div><h1 id="g:10">Traversal</h1><h2 id="g:11">Map</h2><div class="top"><p class="src"><a id="v:map" class="def">map</a> :: (<span class="keyword">forall</span> v. f v -> g v) -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k g <a href="src/Data-Dependent-Map.html#map" class="link">Source</a> <a href="#v:map" class="selflink">#</a></p><div class="doc"><p><em>O(n)</em>. Map a function over all values in the map.</p></div></div><div class="top"><p class="src"><a id="v:mapWithKey" class="def">mapWithKey</a> :: (<span class="keyword">forall</span> v. k v -> f v -> g v) -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k g <a href="src/Data-Dependent-Map.html#mapWithKey" class="link">Source</a> <a href="#v:mapWithKey" class="selflink">#</a></p><div class="doc"><p><em>O(n)</em>. Map a function over all values in the map.</p></div></div><div class="top"><p class="src"><a id="v:traverseWithKey" class="def">traverseWithKey</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Control-Applicative.html#t:Applicative">Applicative</a> t => (<span class="keyword">forall</span> v. k v -> f v -> t (g v)) -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> t (<a href="Data-Dependent-Map.html#t:DMap">DMap</a> k g) <a href="src/Data-Dependent-Map.html#traverseWithKey" class="link">Source</a> <a href="#v:traverseWithKey" class="selflink">#</a></p><div class="doc"><p><em>O(n)</em>.
<code><code><a href="Data-Dependent-Map.html#v:traverseWithKey">traverseWithKey</a></code> f m == <code><a href="Data-Dependent-Map.html#v:fromList">fromList</a></code> <a href="$">$</a> <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Traversable.html#v:traverse">traverse</a></code> ((k, v) -> (,) k <a href="$">$</a> f k v) (<code><a href="Data-Dependent-Map.html#v:toList">toList</a></code> m)</code>
That is, behaves exactly like a regular <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Traversable.html#v:traverse">traverse</a></code> except that the traversing
function also has access to the key associated with a value.</p></div></div><div class="top"><p class="src"><a id="v:mapAccumLWithKey" class="def">mapAccumLWithKey</a> :: (<span class="keyword">forall</span> v. a -> k v -> f v -> (a, g v)) -> a -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> (a, <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k g) <a href="src/Data-Dependent-Map.html#mapAccumLWithKey" class="link">Source</a> <a href="#v:mapAccumLWithKey" class="selflink">#</a></p><div class="doc"><p><em>O(n)</em>. The function <code><a href="Data-Dependent-Map.html#v:mapAccumLWithKey">mapAccumLWithKey</a></code> threads an accumulating
argument throught the map in ascending order of keys.</p></div></div><div class="top"><p class="src"><a id="v:mapAccumRWithKey" class="def">mapAccumRWithKey</a> :: (<span class="keyword">forall</span> v. a -> k v -> f v -> (a, g v)) -> a -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> (a, <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k g) <a href="src/Data-Dependent-Map.html#mapAccumRWithKey" class="link">Source</a> <a href="#v:mapAccumRWithKey" class="selflink">#</a></p><div class="doc"><p><em>O(n)</em>. The function <code><a href="Data-Dependent-Map.html#v:mapAccumRWithKey">mapAccumRWithKey</a></code> threads an accumulating
argument through the map in descending order of keys.</p></div></div><div class="top"><p class="src"><a id="v:mapKeysWith" class="def">mapKeysWith</a> :: <a href="Data-Dependent-Map.html#t:GCompare">GCompare</a> k2 => (<span class="keyword">forall</span> v. k2 v -> f v -> f v -> f v) -> (<span class="keyword">forall</span> v. k1 v -> k2 v) -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k1 f -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k2 f <a href="src/Data-Dependent-Map.html#mapKeysWith" class="link">Source</a> <a href="#v:mapKeysWith" class="selflink">#</a></p><div class="doc"><p><em>O(n*log n)</em>.
<code><code><a href="Data-Dependent-Map.html#v:mapKeysWith">mapKeysWith</a></code> c f s</code> is the map obtained by applying <code>f</code> to each key of <code>s</code>.</p><p>The size of the result may be smaller if <code>f</code> maps two or more distinct
keys to the same new key. In this case the associated values will be
combined using <code>c</code>.</p></div></div><div class="top"><p class="src"><a id="v:mapKeysMonotonic" class="def">mapKeysMonotonic</a> :: (<span class="keyword">forall</span> v. k1 v -> k2 v) -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k1 f -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k2 f <a href="src/Data-Dependent-Map.html#mapKeysMonotonic" class="link">Source</a> <a href="#v:mapKeysMonotonic" class="selflink">#</a></p><div class="doc"><p><em>O(n)</em>.
<code><code><a href="Data-Dependent-Map.html#v:mapKeysMonotonic">mapKeysMonotonic</a></code> f s == <code>mapKeys</code> f s</code>, but works only when <code>f</code>
is strictly monotonic.
That is, for any values <code>x</code> and <code>y</code>, if <code>x</code> < <code>y</code> then <code>f x</code> < <code>f y</code>.
<em>The precondition is not checked.</em>
Semi-formally, we have:</p><pre>and [x < y ==> f x < f y | x <- ls, y <- ls]
==> mapKeysMonotonic f s == mapKeys f s
where ls = keys s</pre><p>This means that <code>f</code> maps distinct original keys to distinct resulting keys.
This function has better performance than <code>mapKeys</code>.</p></div></div><h2 id="g:12">Fold</h2><div class="top"><p class="src"><a id="v:foldWithKey" class="def">foldWithKey</a> :: (<span class="keyword">forall</span> v. k v -> f v -> b -> b) -> b -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> b <a href="src/Data-Dependent-Map.html#foldWithKey" class="link">Source</a> <a href="#v:foldWithKey" class="selflink">#</a></p><div class="doc"><div class="warning"><p>Deprecated: Use foldrWithKey instead</p></div><p><em>O(n)</em>. Fold the keys and values in the map, such that
<code><code><a href="Data-Dependent-Map.html#v:foldWithKey">foldWithKey</a></code> f z == <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Foldable.html#v:foldr">foldr</a></code> (<code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Tuple.html#v:uncurry">uncurry</a></code> f) z . <code><a href="Data-Dependent-Map.html#v:toAscList">toAscList</a></code></code>.</p><p>This is identical to <code><a href="Data-Dependent-Map.html#v:foldrWithKey">foldrWithKey</a></code>, and you should use that one instead of
this one. This name is kept for backward compatibility.</p></div></div><div class="top"><p class="src"><a id="v:foldrWithKey" class="def">foldrWithKey</a> :: (<span class="keyword">forall</span> v. k v -> f v -> b -> b) -> b -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> b <a href="src/Data-Dependent-Map.html#foldrWithKey" class="link">Source</a> <a href="#v:foldrWithKey" class="selflink">#</a></p><div class="doc"><p><em>O(n)</em>. Post-order fold. The function will be applied from the lowest
value to the highest.</p></div></div><div class="top"><p class="src"><a id="v:foldlWithKey" class="def">foldlWithKey</a> :: (<span class="keyword">forall</span> v. b -> k v -> f v -> b) -> b -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> b <a href="src/Data-Dependent-Map.html#foldlWithKey" class="link">Source</a> <a href="#v:foldlWithKey" class="selflink">#</a></p><div class="doc"><p><em>O(n)</em>. Pre-order fold. The function will be applied from the highest
value to the lowest.</p></div></div><h1 id="g:13">Conversion</h1><div class="top"><p class="src"><a id="v:keys" class="def">keys</a> :: <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> [<a href="Data-Dependent-Map.html#t:Some">Some</a> k] <a href="src/Data-Dependent-Map.html#keys" class="link">Source</a> <a href="#v:keys" class="selflink">#</a></p><div class="doc"><p><em>O(n)</em>. Return all keys of the map in ascending order.</p><pre>keys (fromList [(5,"a"), (3,"b")]) == [3,5]
keys empty == []</pre></div></div><div class="top"><p class="src"><a id="v:assocs" class="def">assocs</a> :: <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> [<a href="Data-Dependent-Map.html#t:DSum">DSum</a> k f] <a href="src/Data-Dependent-Map.html#assocs" class="link">Source</a> <a href="#v:assocs" class="selflink">#</a></p><div class="doc"><p><em>O(n)</em>. Return all key/value pairs in the map in ascending key order.</p></div></div><h2 id="g:14">Lists</h2><div class="top"><p class="src"><a id="v:toList" class="def">toList</a> :: <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> [<a href="Data-Dependent-Map.html#t:DSum">DSum</a> k f] <a href="src/Data-Dependent-Map.html#toList" class="link">Source</a> <a href="#v:toList" class="selflink">#</a></p><div class="doc"><p><em>O(n)</em>. Convert to a list of key/value pairs.</p></div></div><div class="top"><p class="src"><a id="v:fromList" class="def">fromList</a> :: <a href="Data-Dependent-Map.html#t:GCompare">GCompare</a> k => [<a href="Data-Dependent-Map.html#t:DSum">DSum</a> k f] -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f <a href="src/Data-Dependent-Map.html#fromList" class="link">Source</a> <a href="#v:fromList" class="selflink">#</a></p><div class="doc"><p><em>O(n*log n)</em>. Build a map from a list of key/value pairs. See also <code><a href="Data-Dependent-Map.html#v:fromAscList">fromAscList</a></code>.
If the list contains more than one value for the same key, the last value
for the key is retained.</p></div></div><div class="top"><p class="src"><a id="v:fromListWithKey" class="def">fromListWithKey</a> :: <a href="Data-Dependent-Map.html#t:GCompare">GCompare</a> k => (<span class="keyword">forall</span> v. k v -> f v -> f v -> f v) -> [<a href="Data-Dependent-Map.html#t:DSum">DSum</a> k f] -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f <a href="src/Data-Dependent-Map.html#fromListWithKey" class="link">Source</a> <a href="#v:fromListWithKey" class="selflink">#</a></p><div class="doc"><p><em>O(n*log n)</em>. Build a map from a list of key/value pairs with a combining function. See also <code><a href="Data-Dependent-Map.html#v:fromAscListWithKey">fromAscListWithKey</a></code>.</p></div></div><h2 id="g:15">Ordered lists</h2><div class="top"><p class="src"><a id="v:toAscList" class="def">toAscList</a> :: <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> [<a href="Data-Dependent-Map.html#t:DSum">DSum</a> k f] <a href="src/Data-Dependent-Map.html#toAscList" class="link">Source</a> <a href="#v:toAscList" class="selflink">#</a></p><div class="doc"><p><em>O(n)</em>. Convert to an ascending list.</p></div></div><div class="top"><p class="src"><a id="v:toDescList" class="def">toDescList</a> :: <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> [<a href="Data-Dependent-Map.html#t:DSum">DSum</a> k f] <a href="src/Data-Dependent-Map.html#toDescList" class="link">Source</a> <a href="#v:toDescList" class="selflink">#</a></p><div class="doc"><p><em>O(n)</em>. Convert to a descending list.</p></div></div><div class="top"><p class="src"><a id="v:fromAscList" class="def">fromAscList</a> :: <a href="file:///usr/share/doc/libghc-dependent-sum-doc/html/Data-GADT-Compare.html#t:GEq">GEq</a> k => [<a href="Data-Dependent-Map.html#t:DSum">DSum</a> k f] -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f <a href="src/Data-Dependent-Map.html#fromAscList" class="link">Source</a> <a href="#v:fromAscList" class="selflink">#</a></p><div class="doc"><p><em>O(n)</em>. Build a map from an ascending list in linear time.
<em>The precondition (input list is ascending) is not checked.</em></p></div></div><div class="top"><p class="src"><a id="v:fromAscListWithKey" class="def">fromAscListWithKey</a> :: <a href="file:///usr/share/doc/libghc-dependent-sum-doc/html/Data-GADT-Compare.html#t:GEq">GEq</a> k => (<span class="keyword">forall</span> v. k v -> f v -> f v -> f v) -> [<a href="Data-Dependent-Map.html#t:DSum">DSum</a> k f] -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f <a href="src/Data-Dependent-Map.html#fromAscListWithKey" class="link">Source</a> <a href="#v:fromAscListWithKey" class="selflink">#</a></p><div class="doc"><p><em>O(n)</em>. Build a map from an ascending list in linear time with a
combining function for equal keys.
<em>The precondition (input list is ascending) is not checked.</em></p></div></div><div class="top"><p class="src"><a id="v:fromDistinctAscList" class="def">fromDistinctAscList</a> :: [<a href="Data-Dependent-Map.html#t:DSum">DSum</a> k f] -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f <a href="src/Data-Dependent-Map.html#fromDistinctAscList" class="link">Source</a> <a href="#v:fromDistinctAscList" class="selflink">#</a></p><div class="doc"><p><em>O(n)</em>. Build a map from an ascending list of distinct elements in linear time.
<em>The precondition is not checked.</em></p></div></div><h1 id="g:16">Filter </h1><div class="top"><p class="src"><a id="v:filter" class="def">filter</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] -> [a] <a href="#v:filter" class="selflink">#</a></p><div class="doc"><p><code><a href="Data-Dependent-Map.html#v:filter">filter</a></code>, applied to a predicate and a list, returns the list of
those elements that satisfy the predicate; i.e.,</p><pre>filter p xs = [ x | x <- xs, p x]</pre></div></div><div class="top"><p class="src"><a id="v:filterWithKey" class="def">filterWithKey</a> :: <a href="Data-Dependent-Map.html#t:GCompare">GCompare</a> k => (<span class="keyword">forall</span> v. k v -> f v -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Bool.html#t:Bool">Bool</a>) -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f <a href="src/Data-Dependent-Map.html#filterWithKey" class="link">Source</a> <a href="#v:filterWithKey" class="selflink">#</a></p><div class="doc"><p><em>O(n)</em>. Filter all keys/values that satisfy the predicate.</p></div></div><div class="top"><p class="src"><a id="v:partitionWithKey" class="def">partitionWithKey</a> :: <a href="Data-Dependent-Map.html#t:GCompare">GCompare</a> k => (<span class="keyword">forall</span> v. k v -> f v -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Bool.html#t:Bool">Bool</a>) -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> (<a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f, <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f) <a href="src/Data-Dependent-Map.html#partitionWithKey" class="link">Source</a> <a href="#v:partitionWithKey" class="selflink">#</a></p><div class="doc"><p><em>O(n)</em>. Partition the map according to a predicate. The first
map contains all elements that satisfy the predicate, the second all
elements that fail the predicate. See also <code><a href="Data-Dependent-Map.html#v:split">split</a></code>.</p></div></div><div class="top"><p class="src"><a id="v:mapMaybeWithKey" class="def">mapMaybeWithKey</a> :: <a href="Data-Dependent-Map.html#t:GCompare">GCompare</a> k => (<span class="keyword">forall</span> v. k v -> f v -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Maybe.html#t:Maybe">Maybe</a> (g v)) -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k g <a href="src/Data-Dependent-Map.html#mapMaybeWithKey" class="link">Source</a> <a href="#v:mapMaybeWithKey" class="selflink">#</a></p><div class="doc"><p><em>O(n)</em>. Map keys/values and collect the <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Maybe.html#v:Just">Just</a></code> results.</p></div></div><div class="top"><p class="src"><a id="v:mapEitherWithKey" class="def">mapEitherWithKey</a> :: <a href="Data-Dependent-Map.html#t:GCompare">GCompare</a> k => (<span class="keyword">forall</span> v. k v -> f v -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Either.html#t:Either">Either</a> (g v) (h v)) -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> (<a href="Data-Dependent-Map.html#t:DMap">DMap</a> k g, <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k h) <a href="src/Data-Dependent-Map.html#mapEitherWithKey" class="link">Source</a> <a href="#v:mapEitherWithKey" class="selflink">#</a></p><div class="doc"><p><em>O(n)</em>. Map keys/values and separate the <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Either.html#v:Left">Left</a></code> and <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Either.html#v:Right">Right</a></code> results.</p></div></div><div class="top"><p class="src"><a id="v:split" class="def">split</a> :: <span class="keyword">forall</span> k f v. <a href="Data-Dependent-Map.html#t:GCompare">GCompare</a> k => k v -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> (<a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f, <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f) <a href="src/Data-Dependent-Map.html#split" class="link">Source</a> <a href="#v:split" class="selflink">#</a></p><div class="doc"><p><em>O(log n)</em>. The expression (<code><code><a href="Data-Dependent-Map.html#v:split">split</a></code> k map</code>) is a pair <code>(map1,map2)</code> where
the keys in <code>map1</code> are smaller than <code>k</code> and the keys in <code>map2</code> larger than <code>k</code>.
Any key equal to <code>k</code> is found in neither <code>map1</code> nor <code>map2</code>.</p></div></div><div class="top"><p class="src"><a id="v:splitLookup" class="def">splitLookup</a> :: <span class="keyword">forall</span> k f v. <a href="Data-Dependent-Map.html#t:GCompare">GCompare</a> k => k v -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> (<a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Maybe.html#t:Maybe">Maybe</a> (f v), <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f) <a href="src/Data-Dependent-Map.html#splitLookup" class="link">Source</a> <a href="#v:splitLookup" class="selflink">#</a></p><div class="doc"><p><em>O(log n)</em>. The expression (<code><code><a href="Data-Dependent-Map.html#v:splitLookup">splitLookup</a></code> k map</code>) splits a map just
like <code><a href="Data-Dependent-Map.html#v:split">split</a></code> but also returns <code><code><a href="Data-Dependent-Map.html#v:lookup">lookup</a></code> k map</code>.</p></div></div><h1 id="g:17">Submap</h1><div class="top"><p class="src"><a id="v:isSubmapOf" class="def">isSubmapOf</a> :: (<a href="Data-Dependent-Map.html#t:GCompare">GCompare</a> k, <a href="file:///usr/share/doc/libghc-dependent-sum-doc/html/Data-Dependent-Sum.html#t:EqTag">EqTag</a> k f) => <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> <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/Data-Dependent-Map.html#isSubmapOf" class="link">Source</a> <a href="#v:isSubmapOf" class="selflink">#</a></p><div class="doc"><p><em>O(n+m)</em>.
This function is defined as (<code><code><a href="Data-Dependent-Map.html#v:isSubmapOf">isSubmapOf</a></code> = <code><a href="Data-Dependent-Map.html#v:isSubmapOfBy">isSubmapOfBy</a></code> <code><a href="file:///usr/share/doc/libghc-dependent-sum-doc/html/Data-Dependent-Sum.html#v:eqTagged">eqTagged</a></code>)</code>).</p></div></div><div class="top"><p class="src"><a id="v:isSubmapOfBy" class="def">isSubmapOfBy</a> :: <a href="Data-Dependent-Map.html#t:GCompare">GCompare</a> k => (<span class="keyword">forall</span> v. k v -> k v -> f v -> g v -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Bool.html#t:Bool">Bool</a>) -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k g -> <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/Data-Dependent-Map.html#isSubmapOfBy" class="link">Source</a> <a href="#v:isSubmapOfBy" class="selflink">#</a></p><div class="doc"><p><em>O(n+m)</em>.
The expression (<code><code><a href="Data-Dependent-Map.html#v:isSubmapOfBy">isSubmapOfBy</a></code> f t1 t2</code>) returns <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Bool.html#v:True">True</a></code> if
all keys in <code>t1</code> are in tree <code>t2</code>, and when <code>f</code> returns <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Bool.html#v:True">True</a></code> when
applied to their respective keys and values.</p></div></div><div class="top"><p class="src"><a id="v:isProperSubmapOf" class="def">isProperSubmapOf</a> :: (<a href="Data-Dependent-Map.html#t:GCompare">GCompare</a> k, <a href="file:///usr/share/doc/libghc-dependent-sum-doc/html/Data-Dependent-Sum.html#t:EqTag">EqTag</a> k f) => <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> <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/Data-Dependent-Map.html#isProperSubmapOf" class="link">Source</a> <a href="#v:isProperSubmapOf" class="selflink">#</a></p><div class="doc"><p><em>O(n+m)</em>. Is this a proper submap? (ie. a submap but not equal).
Defined as (<code><code><a href="Data-Dependent-Map.html#v:isProperSubmapOf">isProperSubmapOf</a></code> = <code><a href="Data-Dependent-Map.html#v:isProperSubmapOfBy">isProperSubmapOfBy</a></code> <code><a href="file:///usr/share/doc/libghc-dependent-sum-doc/html/Data-Dependent-Sum.html#v:eqTagged">eqTagged</a></code></code>).</p></div></div><div class="top"><p class="src"><a id="v:isProperSubmapOfBy" class="def">isProperSubmapOfBy</a> :: <a href="Data-Dependent-Map.html#t:GCompare">GCompare</a> k => (<span class="keyword">forall</span> v. k v -> k v -> f v -> g v -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Bool.html#t:Bool">Bool</a>) -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k g -> <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/Data-Dependent-Map.html#isProperSubmapOfBy" class="link">Source</a> <a href="#v:isProperSubmapOfBy" class="selflink">#</a></p><div class="doc"><p><em>O(n+m)</em>. Is this a proper submap? (ie. a submap but not equal).
The expression (<code><code><a href="Data-Dependent-Map.html#v:isProperSubmapOfBy">isProperSubmapOfBy</a></code> f m1 m2</code>) returns <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Bool.html#v:True">True</a></code> when
<code>m1</code> and <code>m2</code> are not equal,
all keys in <code>m1</code> are in <code>m2</code>, and when <code>f</code> returns <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Bool.html#v:True">True</a></code> when
applied to their respective keys and values. </p></div></div><h1 id="g:18">Indexed </h1><div class="top"><p class="src"><a id="v:lookupIndex" class="def">lookupIndex</a> :: <span class="keyword">forall</span> k f v. <a href="Data-Dependent-Map.html#t:GCompare">GCompare</a> k => k v -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Maybe.html#t:Maybe">Maybe</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="src/Data-Dependent-Map.html#lookupIndex" class="link">Source</a> <a href="#v:lookupIndex" class="selflink">#</a></p><div class="doc"><p><em>O(log n)</em>. Lookup the <em>index</em> of a key. The index is a number from
<em>0</em> up to, but not including, the <code><a href="Data-Dependent-Map.html#v:size">size</a></code> of the map.</p></div></div><div class="top"><p class="src"><a id="v:findIndex" class="def">findIndex</a> :: <a href="Data-Dependent-Map.html#t:GCompare">GCompare</a> k => k v -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Int.html#t:Int">Int</a> <a href="src/Data-Dependent-Map.html#findIndex" class="link">Source</a> <a href="#v:findIndex" class="selflink">#</a></p><div class="doc"><p><em>O(log n)</em>. Return the <em>index</em> of a key. The index is a number from
<em>0</em> up to, but not including, the <code><a href="Data-Dependent-Map.html#v:size">size</a></code> of the map. Calls <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#v:error">error</a></code> when
the key is not a <code><a href="Data-Dependent-Map.html#v:member">member</a></code> of the map.</p></div></div><div class="top"><p class="src"><a id="v:elemAt" class="def">elemAt</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="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> <a href="Data-Dependent-Map.html#t:DSum">DSum</a> k f <a href="src/Data-Dependent-Map.html#elemAt" class="link">Source</a> <a href="#v:elemAt" class="selflink">#</a></p><div class="doc"><p><em>O(log n)</em>. Retrieve an element by <em>index</em>. Calls <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#v:error">error</a></code> when an
invalid index is used.</p></div></div><div class="top"><p class="src"><a id="v:updateAt" class="def">updateAt</a> :: (<span class="keyword">forall</span> v. k v -> f v -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Maybe.html#t:Maybe">Maybe</a> (f v)) -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Int.html#t:Int">Int</a> -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f <a href="src/Data-Dependent-Map.html#updateAt" class="link">Source</a> <a href="#v:updateAt" class="selflink">#</a></p><div class="doc"><p><em>O(log n)</em>. Update the element at <em>index</em>. Does nothing when an
invalid index is used.</p></div></div><div class="top"><p class="src"><a id="v:deleteAt" class="def">deleteAt</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="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f <a href="src/Data-Dependent-Map.html#deleteAt" class="link">Source</a> <a href="#v:deleteAt" class="selflink">#</a></p><div class="doc"><p><em>O(log n)</em>. Delete the element at <em>index</em>.
Defined as (<code><code><a href="Data-Dependent-Map.html#v:deleteAt">deleteAt</a></code> i map = <code><a href="Data-Dependent-Map.html#v:updateAt">updateAt</a></code> (k x -> <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Maybe.html#v:Nothing">Nothing</a></code>) i map</code>).</p></div></div><h1 id="g:19">Min/Max</h1><div class="top"><p class="src"><a id="v:findMin" class="def">findMin</a> :: <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> <a href="Data-Dependent-Map.html#t:DSum">DSum</a> k f <a href="src/Data-Dependent-Map.html#findMin" class="link">Source</a> <a href="#v:findMin" class="selflink">#</a></p><div class="doc"><p><em>O(log n)</em>. The minimal key of the map. Calls <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#v:error">error</a></code> is the map is empty.</p></div></div><div class="top"><p class="src"><a id="v:findMax" class="def">findMax</a> :: <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> <a href="Data-Dependent-Map.html#t:DSum">DSum</a> k f <a href="src/Data-Dependent-Map.html#findMax" class="link">Source</a> <a href="#v:findMax" class="selflink">#</a></p><div class="doc"><p><em>O(log n)</em>. The maximal key of the map. Calls <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#v:error">error</a></code> is the map is empty.</p></div></div><div class="top"><p class="src"><a id="v:lookupMin" class="def">lookupMin</a> :: <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Maybe.html#t:Maybe">Maybe</a> (<a href="Data-Dependent-Map.html#t:DSum">DSum</a> k f) <a href="src/Data-Dependent-Map.html#lookupMin" class="link">Source</a> <a href="#v:lookupMin" class="selflink">#</a></p></div><div class="top"><p class="src"><a id="v:lookupMax" class="def">lookupMax</a> :: <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Maybe.html#t:Maybe">Maybe</a> (<a href="Data-Dependent-Map.html#t:DSum">DSum</a> k f) <a href="src/Data-Dependent-Map.html#lookupMax" class="link">Source</a> <a href="#v:lookupMax" class="selflink">#</a></p></div><div class="top"><p class="src"><a id="v:deleteMin" class="def">deleteMin</a> :: <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f <a href="src/Data-Dependent-Map.html#deleteMin" class="link">Source</a> <a href="#v:deleteMin" class="selflink">#</a></p><div class="doc"><p><em>O(log n)</em>. Delete the minimal key. Returns an empty map if the map is empty.</p></div></div><div class="top"><p class="src"><a id="v:deleteMax" class="def">deleteMax</a> :: <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f <a href="src/Data-Dependent-Map.html#deleteMax" class="link">Source</a> <a href="#v:deleteMax" class="selflink">#</a></p><div class="doc"><p><em>O(log n)</em>. Delete the maximal key. Returns an empty map if the map is empty.</p></div></div><div class="top"><p class="src"><a id="v:deleteFindMin" class="def">deleteFindMin</a> :: <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> (<a href="Data-Dependent-Map.html#t:DSum">DSum</a> k f, <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f) <a href="src/Data-Dependent-Map-Internal.html#deleteFindMin" class="link">Source</a> <a href="#v:deleteFindMin" class="selflink">#</a></p><div class="doc"><p><em>O(log n)</em>. Delete and find the minimal element.</p><pre>deleteFindMin (fromList [(5,"a"), (3,"b"), (10,"c")]) == ((3,"b"), fromList[(5,"a"), (10,"c")])
deleteFindMin Error: can not return the minimal element of an empty map</pre></div></div><div class="top"><p class="src"><a id="v:deleteFindMax" class="def">deleteFindMax</a> :: <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> (<a href="Data-Dependent-Map.html#t:DSum">DSum</a> k f, <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f) <a href="src/Data-Dependent-Map-Internal.html#deleteFindMax" class="link">Source</a> <a href="#v:deleteFindMax" class="selflink">#</a></p><div class="doc"><p><em>O(log n)</em>. Delete and find the maximal element.</p><pre>deleteFindMax (fromList [(5,"a"), (3,"b"), (10,"c")]) == ((10,"c"), fromList [(3,"b"), (5,"a")])
deleteFindMax empty Error: can not return the maximal element of an empty map</pre></div></div><div class="top"><p class="src"><a id="v:updateMinWithKey" class="def">updateMinWithKey</a> :: (<span class="keyword">forall</span> v. k v -> f v -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Maybe.html#t:Maybe">Maybe</a> (f v)) -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f <a href="src/Data-Dependent-Map.html#updateMinWithKey" class="link">Source</a> <a href="#v:updateMinWithKey" class="selflink">#</a></p><div class="doc"><p><em>O(log n)</em>. Update the value at the minimal key.</p></div></div><div class="top"><p class="src"><a id="v:updateMaxWithKey" class="def">updateMaxWithKey</a> :: (<span class="keyword">forall</span> v. k v -> f v -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Maybe.html#t:Maybe">Maybe</a> (f v)) -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f <a href="src/Data-Dependent-Map.html#updateMaxWithKey" class="link">Source</a> <a href="#v:updateMaxWithKey" class="selflink">#</a></p><div class="doc"><p><em>O(log n)</em>. Update the value at the maximal key.</p></div></div><div class="top"><p class="src"><a id="v:minViewWithKey" class="def">minViewWithKey</a> :: <span class="keyword">forall</span> k f. <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Maybe.html#t:Maybe">Maybe</a> (<a href="Data-Dependent-Map.html#t:DSum">DSum</a> k f, <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f) <a href="src/Data-Dependent-Map-Internal.html#minViewWithKey" class="link">Source</a> <a href="#v:minViewWithKey" class="selflink">#</a></p><div class="doc"><p><em>O(log n)</em>. Retrieves the minimal (key :=> value) entry of the map, and
the map stripped of that element, or <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Maybe.html#v:Nothing">Nothing</a></code> if passed an empty map.</p></div></div><div class="top"><p class="src"><a id="v:maxViewWithKey" class="def">maxViewWithKey</a> :: <span class="keyword">forall</span> k f. <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Maybe.html#t:Maybe">Maybe</a> (<a href="Data-Dependent-Map.html#t:DSum">DSum</a> k f, <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f) <a href="src/Data-Dependent-Map-Internal.html#maxViewWithKey" class="link">Source</a> <a href="#v:maxViewWithKey" class="selflink">#</a></p><div class="doc"><p><em>O(log n)</em>. Retrieves the maximal (key :=> value) entry of the map, and
the map stripped of that element, or <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Maybe.html#v:Nothing">Nothing</a></code> if passed an empty map.</p></div></div><h1 id="g:20">Debugging</h1><div class="top"><p class="src"><a id="v:showTree" class="def">showTree</a> :: <a href="file:///usr/share/doc/libghc-dependent-sum-doc/html/Data-Dependent-Sum.html#t:ShowTag">ShowTag</a> k f => <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-String.html#t:String">String</a> <a href="src/Data-Dependent-Map.html#showTree" class="link">Source</a> <a href="#v:showTree" class="selflink">#</a></p><div class="doc"><p><em>O(n)</em>. Show the tree that implements the map. The tree is shown
in a compressed, hanging format. See <code><a href="Data-Dependent-Map.html#v:showTreeWith">showTreeWith</a></code>.</p></div></div><div class="top"><p class="src"><a id="v:showTreeWith" class="def">showTreeWith</a> :: (<span class="keyword">forall</span> v. k v -> f v -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-String.html#t:String">String</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="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Bool.html#t:Bool">Bool</a> -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-String.html#t:String">String</a> <a href="src/Data-Dependent-Map.html#showTreeWith" class="link">Source</a> <a href="#v:showTreeWith" class="selflink">#</a></p><div class="doc"><p><em>O(n)</em>. The expression (<code><code><a href="Data-Dependent-Map.html#v:showTreeWith">showTreeWith</a></code> showelem hang wide map</code>) shows
the tree that implements the map. Elements are shown using the <code>showElem</code> function. If <code>hang</code> is
<code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Bool.html#v:True">True</a></code>, a <em>hanging</em> tree is shown otherwise a rotated tree is shown. If
<code>wide</code> is <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Bool.html#v:True">True</a></code>, an extra wide version is shown.</p></div></div><div class="top"><p class="src"><a id="v:valid" class="def">valid</a> :: <a href="Data-Dependent-Map.html#t:GCompare">GCompare</a> k => <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k f -> <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/Data-Dependent-Map.html#valid" class="link">Source</a> <a href="#v:valid" class="selflink">#</a></p><div class="doc"><p><em>O(n)</em>. Test if the internal map structure is valid.</p></div></div><h1>Orphan instances</h1><div id="section.orphans" class="show"><table><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:o:ic:Eq:Eq:1" class="instance expander" onclick="toggleSection('i:o:ic:Eq:Eq:1')"></span> <a href="file:///usr/share/doc/libghc-dependent-sum-doc/html/Data-Dependent-Sum.html#t:EqTag">EqTag</a> k k1 f => <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Eq.html#t:Eq">Eq</a> (<a href="Data-Dependent-Map.html#t:DMap">DMap</a> k k1 f)</span> <a href="src/Data-Dependent-Map.html#line-1090" class="link">Source</a> <a href="#v:-36-fEqDMap" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:o:ic:Eq:Eq:1" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:-61--61-">(==)</a> :: <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k k1 f -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k k1 f -> <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="Data-Dependent-Map.html#t:DMap">DMap</a> k k1 f -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k k1 f -> <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:o:ic:Ord:Ord:2" class="instance expander" onclick="toggleSection('i:o:ic:Ord:Ord:2')"></span> <a href="file:///usr/share/doc/libghc-dependent-sum-doc/html/Data-Dependent-Sum.html#t:OrdTag">OrdTag</a> k k1 f => <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Ord.html#t:Ord">Ord</a> (<a href="Data-Dependent-Map.html#t:DMap">DMap</a> k k1 f)</span> <a href="src/Data-Dependent-Map.html#line-1097" class="link">Source</a> <a href="#v:-36-fOrdDMap" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:o:ic:Ord:Ord:2" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:compare">compare</a> :: <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k k1 f -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k k1 f -> <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="Data-Dependent-Map.html#t:DMap">DMap</a> k k1 f -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k k1 f -> <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="Data-Dependent-Map.html#t:DMap">DMap</a> k k1 f -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k k1 f -> <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="Data-Dependent-Map.html#t:DMap">DMap</a> k k1 f -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k k1 f -> <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="Data-Dependent-Map.html#t:DMap">DMap</a> k k1 f -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k k1 f -> <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="Data-Dependent-Map.html#t:DMap">DMap</a> k k1 f -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k k1 f -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k k1 f <a href="#v:max" class="selflink">#</a></p><p class="src"><a href="#v:min">min</a> :: <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k k1 f -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k k1 f -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k k1 f <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:o:ic:Read:Read:3" class="instance expander" onclick="toggleSection('i:o:ic:Read:Read:3')"></span> (<a href="Data-Dependent-Map.html#t:GCompare">GCompare</a> k k1, <a href="file:///usr/share/doc/libghc-dependent-sum-doc/html/Data-Dependent-Sum.html#t:ReadTag">ReadTag</a> k k1 f) => <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Text-Read.html#t:Read">Read</a> (<a href="Data-Dependent-Map.html#t:DMap">DMap</a> k k1 f)</span> <a href="src/Data-Dependent-Map.html#line-1104" class="link">Source</a> <a href="#v:-36-fReadDMap" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:o:ic:Read:Read:3" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:readsPrec">readsPrec</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/Text-ParserCombinators-ReadP.html#t:ReadS">ReadS</a> (<a href="Data-Dependent-Map.html#t:DMap">DMap</a> k k1 f) <a href="#v:readsPrec" class="selflink">#</a></p><p class="src"><a href="#v:readList">readList</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Text-ParserCombinators-ReadP.html#t:ReadS">ReadS</a> [<a href="Data-Dependent-Map.html#t:DMap">DMap</a> k k1 f] <a href="#v:readList" class="selflink">#</a></p><p class="src"><a href="#v:readPrec">readPrec</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Text-ParserCombinators-ReadPrec.html#t:ReadPrec">ReadPrec</a> (<a href="Data-Dependent-Map.html#t:DMap">DMap</a> k k1 f) <a href="#v:readPrec" class="selflink">#</a></p><p class="src"><a href="#v:readListPrec">readListPrec</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Text-ParserCombinators-ReadPrec.html#t:ReadPrec">ReadPrec</a> [<a href="Data-Dependent-Map.html#t:DMap">DMap</a> k k1 f] <a href="#v:readListPrec" class="selflink">#</a></p></div></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:o:ic:Show:Show:4" class="instance expander" onclick="toggleSection('i:o:ic:Show:Show:4')"></span> <a href="file:///usr/share/doc/libghc-dependent-sum-doc/html/Data-Dependent-Sum.html#t:ShowTag">ShowTag</a> k k1 f => <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Text-Show.html#t:Show">Show</a> (<a href="Data-Dependent-Map.html#t:DMap">DMap</a> k k1 f)</span> <a href="src/Data-Dependent-Map.html#line-1115" class="link">Source</a> <a href="#v:-36-fShowDMap" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:o:ic:Show:Show:4" 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="Data-Dependent-Map.html#t:DMap">DMap</a> k k1 f -> <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="Data-Dependent-Map.html#t:DMap">DMap</a> k k1 f -> <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="Data-Dependent-Map.html#t:DMap">DMap</a> k k1 f] -> <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:o:ic:Monoid:Monoid:5" class="instance expander" onclick="toggleSection('i:o:ic:Monoid:Monoid:5')"></span> <a href="Data-Dependent-Map.html#t:GCompare">GCompare</a> k k1 => <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Monoid.html#t:Monoid">Monoid</a> (<a href="Data-Dependent-Map.html#t:DMap">DMap</a> k k1 f)</span> <a href="src/Data-Dependent-Map.html#line-161" class="link">Source</a> <a href="#v:-36-fMonoidDMap" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:o:ic:Monoid:Monoid:5" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:mempty">mempty</a> :: <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k k1 f <a href="#v:mempty" class="selflink">#</a></p><p class="src"><a href="#v:mappend">mappend</a> :: <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k k1 f -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k k1 f -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k k1 f <a href="#v:mappend" class="selflink">#</a></p><p class="src"><a href="#v:mconcat">mconcat</a> :: [<a href="Data-Dependent-Map.html#t:DMap">DMap</a> k k1 f] -> <a href="Data-Dependent-Map.html#t:DMap">DMap</a> k k1 f <a href="#v:mconcat" class="selflink">#</a></p></div></div></td></tr></table></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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