Associations—Wolfram Language Documentation

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They associate keys with values, allowing highly efficient lookup and updating, even with millions of elements. Associations provide generalizations of symbolically indexed lists, associative arrays, dictionaries, hashmaps, structs, and a variety of other powerful data structures. 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value="q" id="search-button"><input id="query" name="query" type="text" value="" placeholder="Search"><button class="clearfield"></button> </form> <a class="language-home" href="http://www.wolfram.com/language">Wolfram Language Home Page »</a> </div> </div> </header>  <div class="inner main-content"> <nav class="topContentWrap"><span class="badge">GUIDE</span><ul class="dropdown"> <li> <a href="#" class="menu see-also">Functions</a> <ul class="sub_menu"> <li> <a class="sub-ref" href="/language/ref/AssociateTo.html"><span class="dropdownPad">AssociateTo</span></a> </li> <li> <a class="sub-ref" href="/language/ref/Association.html"><span class="dropdownPad">Association</span></a> </li> <li> <a class="sub-ref" href="/language/ref/AssociationMap.html"><span class="dropdownPad">AssociationMap</span></a> </li> <li> <a class="sub-ref" href="/language/ref/AssociationQ.html"><span class="dropdownPad">AssociationQ</span></a> </li> <li> <a class="sub-ref" 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<a class="sub-ref" href="/language/ref/KeyComplement.html"><span class="dropdownPad">KeyComplement</span></a> </li> <li> <a class="sub-ref" href="/language/ref/KeyDrop.html"><span class="dropdownPad">KeyDrop</span></a> </li> <li> <a class="sub-ref" href="/language/ref/KeyDropFrom.html"><span class="dropdownPad">KeyDropFrom</span></a> </li> <li> <a class="sub-ref" href="/language/ref/KeyExistsQ.html"><span class="dropdownPad">KeyExistsQ</span></a> </li> <li> <a class="sub-ref" href="/language/ref/KeyFreeQ.html"><span class="dropdownPad">KeyFreeQ</span></a> </li> <li> <a class="sub-ref" href="/language/ref/KeyIntersection.html"><span class="dropdownPad">KeyIntersection</span></a> </li> <li> <a class="sub-ref" href="/language/ref/KeyMap.html"><span class="dropdownPad">KeyMap</span></a> </li> <li> <a class="sub-ref" href="/language/ref/KeyMemberQ.html"><span class="dropdownPad">KeyMemberQ</span></a> </li> <li> <a class="sub-ref" href="/language/ref/Keys.html"><span class="dropdownPad">Keys</span></a> </li> <li> <a class="sub-ref" href="/language/ref/KeySelect.html"><span class="dropdownPad">KeySelect</span></a> </li> <li> <a class="sub-ref" href="/language/ref/KeySort.html"><span class="dropdownPad">KeySort</span></a> </li> <li> <a class="sub-ref" href="/language/ref/KeySortBy.html"><span class="dropdownPad">KeySortBy</span></a> </li> <li> <a class="sub-ref" href="/language/ref/KeyTake.html"><span class="dropdownPad">KeyTake</span></a> </li> <li> <a class="sub-ref" href="/language/ref/KeyUnion.html"><span class="dropdownPad">KeyUnion</span></a> </li> <li> <a class="sub-ref" href="/language/ref/KeyValueMap.html"><span class="dropdownPad">KeyValueMap</span></a> </li> <li> <a class="sub-ref" href="/language/ref/KeyValuePattern.html"><span class="dropdownPad">KeyValuePattern</span></a> </li> <li> <a class="sub-ref" href="/language/ref/ListPlot.html"><span class="dropdownPad">ListPlot</span></a> </li> <li> <a class="sub-ref" href="/language/ref/Lookup.html"><span class="dropdownPad">Lookup</span></a> </li> <li> <a class="sub-ref" href="/language/ref/Map.html"><span class="dropdownPad">Map</span></a> </li> <li> <a class="sub-ref" href="/language/ref/Merge.html"><span class="dropdownPad">Merge</span></a> </li> <li> <a class="sub-ref" href="/language/ref/Missing.html"><span class="dropdownPad">Missing</span></a> </li> <li> <a class="sub-ref" href="/language/ref/Slot.html"><span class="dropdownPad">name</span></a> </li> <li> <a class="sub-ref" href="/language/ref/Normal.html"><span class="dropdownPad">Normal</span></a> </li> <li> <a class="sub-ref" href="/language/ref/Plus.html"><span class="dropdownPad">Plus</span></a> </li> <li> <a class="sub-ref" href="/language/ref/PositionIndex.html"><span class="dropdownPad">PositionIndex</span></a> </li> <li> <a class="sub-ref" href="/language/ref/Select.html"><span class="dropdownPad">Select</span></a> </li> <li> <a class="sub-ref" href="/language/ref/Sort.html"><span class="dropdownPad">Sort</span></a> </li> <li> <a class="sub-ref" href="/language/ref/Values.html"><span class="dropdownPad">Values</span></a> </li> </ul> </li> <li> <a href="#" class="menu related-guides">Related Guides</a> <ul class="sub_menu"> <li> <a href="/language/guide/ListManipulation.html"><span class="dropdownPad">Lists & List Manipulation</span></a> </li> <li> <a href="/language/guide/ComputationWithStructuredDatasets.html"><span class="dropdownPad">Structured Datasets</span></a> </li> </ul> </li> </ul></nav><div class="main-heading"><h1 class="main-title">Associations</h1><div class="iconography" data-src="f= s= d= m= c= u= l= n= e="></div></div><p class="intro"><a name="2001916300"></a>Along with lists, associations are fundamental constructs in the Wolfram Language. They associate keys with values, allowing highly efficient lookup and updating, even with millions of elements. Associations provide generalizations of symbolically indexed lists, associative arrays, dictionaries, hashmaps, structs, and a variety of other powerful data structures. </p><div class="GuideDelimiterSubsection"></div><p class="singleFunction"><a name="203374175"></a><span class="IFSans"><a href="/language/ref/Association.html">Association</a></span> ( <span class="IFSans"><a href="/language/ref/Association.html"><|<span class="special-character Ellipsis">…</span>|></a></span> ) <span class="special-character LongDash">—</span> an association between keys and values </p><p class="singleFunction"><a name="1476693797"></a><span class="IFSans"><a href="/language/ref/Association.html"><|<span class="special-character Ellipsis">…</span>|>[<span class="TI2">key</span>]</a></span> <span class="dash">—</span> extract the value associated with any given key</p><h3><a name="2031900244"></a>Associations and Parts</h3><p class="singleFunction"><a name="530124000"></a><span class="IFSans"><a href="/language/ref/Part.html"><|<span class="special-character Ellipsis">…</span>|>[["<span class="TI2">str</span>"]]</a></span> <span class="dash">—</span> extract a value corresponding to a key that is a string</p><p class="singleFunction"><a name="1286284386"></a><span class="IFSans"><a href="/language/ref/Key.html">Key</a></span> <span class="dash">—</span> indicate a key within a part specification</p><p class="singleFunction"><a name="1450047538"></a><span class="IFSans"><a href="/language/ref/Missing.html">Missing</a></span> <span class="dash">—</span> default value if a key is not found</p><p class="singleFunction"><a name="76238973"></a><span class="InlineGuideFunction"><a href="/language/ref/Slot.html">#<span class="TI2">name</span></a></span> <span class="dash">—</span> a slot in a pure function that picks out value with key <span class="IF"><span class="TI">"name"</span></span> in an association </p><p class="singleFunction"><a name="1745212685"></a><span class="IFSans"><a href="/language/ref/AssociationQ.html">AssociationQ</a></span> <span class="dash">—</span> test if an expression is a valid association</p><div class="GuideDelimiterSubsection"></div><h3><a name="1768065795"></a>Elements of Associations</h3><p class="singleFunction"><a name="1971326609"></a><span class="IFSans"><a href="/language/ref/Keys.html">Keys</a></span> <span class="dash">—</span> list of keys</p><p class="singleFunction"><a name="708611547"></a><span class="IFSans"><a href="/language/ref/Values.html">Values</a></span> <span class="dash">—</span> list of values</p><p class="singleFunction"><a name="1837447814"></a><span class="IFSans"><a href="/language/ref/Normal.html">Normal</a></span> <span class="dash">—</span> convert to a list of rules</p><p class="singleFunction"><a name="1618793255"></a><span class="IFSans"><a href="/language/ref/Lookup.html">Lookup</a></span> <span class="dash">—</span> perform a lookup of a value by key, returning a specified default if it is not found</p><p class="singleFunction"><a name="1071458933"></a><span class="IFSans"><a href="/language/ref/KeyExistsQ.html">KeyExistsQ</a></span> <span class="dash">—</span> test whether a key exists in an association</p><div class="GuideDelimiterSubsection"></div><h3><a name="1307290438"></a><a href="/language/guide/HandlingArraysOfData.html">Functions That Apply to Values <span class="special-character RightGuillemet">»</span></a></h3><p class="inlineFunctionList"><a name="58033752"></a><span class="IFSans"><a href="/language/ref/Map.html">Map</a></span><span class="special-character NonBreakingSpace"> </span><span class="inlineBullet"> ▪ </span> <span class="IFSans"><a href="/language/ref/Select.html">Select</a></span><span class="special-character NonBreakingSpace"> </span><span class="inlineBullet"> ▪ </span> <span class="IFSans"><a href="/language/ref/Sort.html">Sort</a></span><span class="special-character NonBreakingSpace"> </span><span class="inlineBullet"> ▪ </span> <span class="IFSans"><a href="/language/ref/DeleteDuplicates.html">DeleteDuplicates</a></span><span class="special-character NonBreakingSpace"> </span><span class="inlineBullet"> ▪ </span> <span class="IFSans"><a href="/language/ref/ListPlot.html">ListPlot</a></span><span class="special-character NonBreakingSpace"> </span><span class="inlineBullet"> ▪ </span> <span class="IFSans"><a href="/language/ref/Plus.html">Plus</a></span><span class="special-character NonBreakingSpace"> </span><span class="inlineBullet"> ▪ </span> <span class="IFSans"><a href="/language/guide/HandlingArraysOfData.html">...</a></span></p><h3><a name="725199009"></a>Functions That Apply to Keys</h3><p class="singleFunction"><a name="605710499"></a><span class="IFSans"><a href="/language/ref/KeySort.html">KeySort</a></span>, <span class="IFSans"><a href="/language/ref/KeySortBy.html">KeySortBy</a></span> <span class="dash">—</span> sort an association by its keys</p><p class="singleFunction"><a name="1746386390"></a><span class="IFSans"><a href="/language/ref/KeyTake.html">KeyTake</a></span>, <span class="IFSans"><a href="/language/ref/KeyDrop.html">KeyDrop</a></span> <span class="dash">—</span> take, drop particular keys in an association</p><p class="singleFunction"><a name="2112971216"></a><span class="IFSans"><a href="/language/ref/KeySelect.html">KeySelect</a></span> <span class="dash">—</span> select elements based on a criterion on their keys</p><p class="singleFunction"><a name="215484229"></a><span class="IFSans"><a href="/language/ref/KeyMap.html">KeyMap</a></span> <span class="dash">—</span> map a function over the keys in an association</p><p class="singleFunction"><a name="486272556"></a><span class="IFSans"><a href="/language/ref/KeyValueMap.html">KeyValueMap</a></span> <span class="dash">—</span> map a function over keys and values in an association</p><p class="inlineFunctionList"><a name="789082147"></a><span class="IFSans"><a href="/language/ref/KeyMemberQ.html">KeyMemberQ</a></span><span class="special-character NonBreakingSpace"> </span><span class="inlineBullet"> ▪ </span> <span class="IFSans"><a href="/language/ref/KeyFreeQ.html">KeyFreeQ</a></span></p><h3><a name="541940104"></a>Modifying Associations</h3><p class="singleFunction"><a name="417058132"></a><span class="IF"><span class="specialcharacters"><<span class="verticalbar">|</span></span><span class="TR"><span class="special-character Ellipsis">…</span></span><span class="specialcharacters"><span class="verticalbar">|</span>></span><span class="openbracket">[</span><span class="TI">key</span><span class="closebracket">]</span>=<span class="TI">val</span></span> <span class="dash">—</span> change an element of an association</p><p class="singleFunction"><a name="345764851"></a><span class="IFSans"><a href="/language/ref/AssociateTo.html">AssociateTo</a></span> <span class="dash">—</span> add elements to an association</p><p class="singleFunction"><a name="1382061756"></a><span class="IFSans"><a href="/language/ref/KeyDropFrom.html">KeyDropFrom</a></span> <span class="dash">—</span> drop elements from an association</p><h3><a name="1564889427"></a>Pattern Matching with Associations</h3><p class="singleFunction"><a name="864374780"></a><span class="IFSans"><a href="/language/ref/KeyValuePattern.html">KeyValuePattern</a></span> <span class="dash">—</span> elements that can appear anywhere in an association</p><div class="GuideDelimiterSubsection"></div><h3><a name="1170566038"></a>Functions That Create Associations</h3><p class="singleFunction"><a name="409575680"></a><span class="IFSans"><a href="/language/ref/Association.html">Association</a></span> <span class="dash">—</span> turn a list of rules into an association</p><p class="singleFunction"><a name="935902142"></a><span class="IFSans"><a href="/language/ref/AssociationMap.html">AssociationMap</a></span> <span class="dash">—</span> create an association by applying a function to a list of keys</p><p class="singleFunction"><a name="1617041028"></a><span class="IFSans"><a href="/language/ref/AssociationThread.html">AssociationThread</a></span> <span class="dash">—</span> create an association from a list of keys and a list of values</p><p class="singleFunction"><a name="123546173"></a><span class="IFSans"><a href="/language/ref/Counts.html">Counts</a></span>, <span class="IFSans"><a href="/language/ref/CountsBy.html">CountsBy</a></span> <span class="dash">—</span> associate values with the number of times they occur</p><p class="singleFunction"><a name="2011284800"></a><span class="IFSans"><a href="/language/ref/GroupBy.html">GroupBy</a></span> <span class="dash">—</span> group values by collecting those sharing a criterion ("map reduce")</p><p class="singleFunction"><a name="587912942"></a><span class="IFSans"><a href="/language/ref/PositionIndex.html">PositionIndex</a></span> <span class="dash">—</span> build an index of positions at which values occur</p><h3><a name="1730586421"></a>Functions Operating on Lists of Associations</h3><p class="inlineFunctionList"><a name="1387087218"></a><span class="IFSans"><a href="/language/ref/KeyUnion.html">KeyUnion</a></span><span class="special-character NonBreakingSpace"> </span><span class="inlineBullet"> ▪ </span> <span class="IFSans"><a href="/language/ref/KeyIntersection.html">KeyIntersection</a></span><span class="special-character NonBreakingSpace"> </span><span class="inlineBullet"> ▪ </span> <span class="IFSans"><a href="/language/ref/KeyComplement.html">KeyComplement</a></span></p><p class="singleFunction"><a name="1467792213"></a><span class="IFSans"><a href="/language/ref/Catenate.html">Catenate</a></span> <span class="dash">—</span> catenate elements from multiple associations</p><p class="singleFunction"><a name="937762382"></a><span class="IFSans"><a href="/language/ref/Merge.html">Merge</a></span> <span class="dash">—</span> merge associations using a function to combine elements with common keys</p><p class="singleFunction"><a name="447462779"></a><span class="IFSans"><a href="/language/ref/JoinAcross.html">JoinAcross</a></span> <span class="dash">—</span> do the analog of a database join on multiple associations</p><p class="singleFunction"><a name="19194859"></a><span class="IFSans"><a href="/language/ref/Dataset.html">Dataset</a></span> <span class="dash">—</span> representation supporting general structured data queries </p><section id="RelatedGuides" class="related-links"><div class="inner"> <h1>Related Guides</h1> <ul class="functionList"> <span class="special-character FilledVerySmallSquare">▪</span> <li> <a href="/language/guide/ListManipulation.html">Lists & List Manipulation</a> </li> <span class="special-character FilledVerySmallSquare">▪</span> <li> <a href="/language/guide/ComputationWithStructuredDatasets.html">Structured Datasets</a> </li> </ul> </div></section> </div> <section class="feedback-wrapper"> <div 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