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2h3.5a.75.75 0 0 1 0 1.5h-3.5a.25.25 0 0 0-.25.25v8.5c0 .138.112.25.25.25h8.5a.25.25 0 0 0 .25-.25v-3.5a.75.75 0 0 1 1.5 0v3.5A1.75 1.75 0 0 1 12.25 14h-8.5A1.75 1.75 0 0 1 2 12.25v-8.5C2 2.784 2.784 2 3.75 2Zm6.854-1h4.146a.25.25 0 0 1 .25.25v4.146a.25.25 0 0 1-.427.177L13.03 4.03 9.28 7.78a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042l3.75-3.75-1.543-1.543A.25.25 0 0 1 10.604 1Z"></path> </svg> </a></li> </ul> </div> </div> </div> </li> <li class="HeaderMenu-item position-relative flex-wrap flex-justify-between flex-items-center d-block d-lg-flex flex-lg-nowrap flex-lg-items-center js-details-container js-header-menu-item"> <button type="button" class="HeaderMenu-link border-0 width-full width-lg-auto px-0 px-lg-2 py-lg-2 no-wrap d-flex flex-items-center flex-justify-between js-details-target" aria-expanded="false"> Solutions <svg opacity="0.5" aria-hidden="true" height="16" viewBox="0 0 16 16" version="1.1" width="16" data-view-component="true" class="octicon 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0 1 1.06 0Z"></path> </svg> </button> <div class="HeaderMenu-dropdown dropdown-menu rounded m-0 p-0 pt-2 pt-lg-4 position-relative position-lg-absolute left-0 left-lg-n3 pb-2 pb-lg-4 px-lg-4"> <div class="HeaderMenu-column"> <div class="border-bottom pb-3 pb-lg-0 pb-lg-3 mb-3 mb-lg-0 mb-lg-3"> <ul class="list-style-none f5" > <li> <a class="HeaderMenu-dropdown-link d-block no-underline position-relative py-2 Link--secondary d-flex flex-items-center Link--has-description" data-analytics-event="{"location":"navbar","action":"github_sponsors","context":"open_source","tag":"link","label":"github_sponsors_link_open_source_navbar"}" href="/sponsors"> <div> <div class="color-fg-default h4">GitHub Sponsors</div> Fund open source developers </div> </a></li> </ul> </div> <div class="border-bottom pb-3 pb-lg-0 pb-lg-3 mb-3 mb-lg-0 mb-lg-3"> <ul class="list-style-none f5" > <li> <a class="HeaderMenu-dropdown-link d-block no-underline position-relative py-2 Link--secondary d-flex flex-items-center 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1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cul dir=\"auto\"\u003e\n\u003cli\u003e\u003ca href=\"#background\"\u003eBackground\u003c/a\u003e\u003c/li\u003e\n\u003cli\u003e\u003ca href=\"#installation\"\u003eInstallation\u003c/a\u003e\u003c/li\u003e\n\u003cli\u003e\u003ca href=\"#examples\"\u003eExamples\u003c/a\u003e\u003c/li\u003e\n\u003cli\u003e\u003ca href=\"#semigroups\"\u003eSemigroups\u003c/a\u003e\u003c/li\u003e\n\u003cli\u003e\u003ca href=\"#monoids\"\u003eMonoids\u003c/a\u003e\u003c/li\u003e\n\u003cli\u003e\u003ca href=\"#functors\"\u003eFunctors\u003c/a\u003e\n\u003cul dir=\"auto\"\u003e\n\u003cli\u003e\u003ca href=\"#bifunctors\"\u003eBifunctors\u003c/a\u003e\u003c/li\u003e\n\u003cli\u003e\u003ca href=\"#profunctors\"\u003eProfunctors\u003c/a\u003e\u003c/li\u003e\n\u003cli\u003e\u003ca href=\"#applicatives\"\u003eApplicatives\u003c/a\u003e\u003c/li\u003e\n\u003cli\u003e\u003ca href=\"#monads\"\u003eMonads\u003c/a\u003e\u003c/li\u003e\n\u003cli\u003e\u003ca href=\"#traversables\"\u003eTraversables\u003c/a\u003e\u003c/li\u003e\n\u003c/ul\u003e\n\u003c/li\u003e\n\u003cli\u003e\u003ca href=\"#adts\"\u003eADTs\u003c/a\u003e\n\u003cul dir=\"auto\"\u003e\n\u003cli\u003e\u003ca href=\"#maybe\"\u003eMaybe\u003c/a\u003e\u003c/li\u003e\n\u003cli\u003e\u003ca href=\"#hlist\"\u003eHList\u003c/a\u003e\n\u003cul dir=\"auto\"\u003e\n\u003cli\u003e\u003ca href=\"#tuples\"\u003eTuples\u003c/a\u003e\u003c/li\u003e\n\u003c/ul\u003e\n\u003c/li\u003e\n\u003cli\u003e\u003ca href=\"#hmaps\"\u003eHMaps\u003c/a\u003e\u003c/li\u003e\n\u003cli\u003e\u003ca href=\"#coproducts\"\u003eCoProducts\u003c/a\u003e\n\u003cul dir=\"auto\"\u003e\n\u003cli\u003e\u003ca href=\"#either\"\u003eEither\u003c/a\u003e\u003c/li\u003e\n\u003c/ul\u003e\n\u003c/li\u003e\n\u003c/ul\u003e\n\u003c/li\u003e\n\u003cli\u003e\u003ca href=\"#lenses\"\u003eLenses\u003c/a\u003e\u003c/li\u003e\n\u003cli\u003e\u003ca href=\"#notes\"\u003eNotes\u003c/a\u003e\u003c/li\u003e\n\u003cli\u003e\u003ca href=\"#ecosystem\"\u003eEcosystem\u003c/a\u003e\u003c/li\u003e\n\u003cli\u003e\u003ca href=\"#license\"\u003eLicense\u003c/a\u003e\u003c/li\u003e\n\u003c/ul\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch2 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003e\u003ca name=\"user-content-background\"\u003eBackground\u003c/a\u003e\u003c/h2\u003e\u003ca id=\"user-content-background\" class=\"anchor\" aria-label=\"Permalink: Background\" href=\"#background\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eLambda was born out of a desire to use some of the same canonical functions (e.g. \u003ccode\u003eunfoldr\u003c/code\u003e, \u003ccode\u003etakeWhile\u003c/code\u003e, \u003ccode\u003ezipWith\u003c/code\u003e) and functional patterns (e.g. \u003ccode\u003eFunctor\u003c/code\u003e and friends) that are idiomatic in other languages and make them available for Java.\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eSome things a user of lambda most likely values:\u003c/p\u003e\n\u003cul dir=\"auto\"\u003e\n\u003cli\u003eLazy evaluation\u003c/li\u003e\n\u003cli\u003eImmutability by design\u003c/li\u003e\n\u003cli\u003eComposition\u003c/li\u003e\n\u003cli\u003eHigher-level abstractions\u003c/li\u003e\n\u003cli\u003eParametric polymorphism\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp dir=\"auto\"\u003eGenerally, everything that lambda produces is lazily-evaluated (except for terminal operations like \u003ccode\u003ereduce\u003c/code\u003e), immutable (except for \u003ccode\u003eIterator\u003c/code\u003es, since it's effectively impossible), composable (even between different arities, where possible), foundational (maximally contravariant), and parametrically type-checked (even where this adds unnecessary constraints due to a lack of higher-kinded types).\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eAlthough the library is currently (very) small, these values should always be the driving forces behind future growth.\u003c/p\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch2 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003e\u003ca name=\"user-content-installation\"\u003eInstallation\u003c/a\u003e\u003c/h2\u003e\u003ca id=\"user-content-installation\" class=\"anchor\" aria-label=\"Permalink: Installation\" href=\"#installation\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eAdd the following dependency to your:\u003c/p\u003e\n\u003cp dir=\"auto\"\u003e\u003ccode\u003epom.xml\u003c/code\u003e (\u003ca href=\"https://maven.apache.org/guides/introduction/introduction-to-dependency-mechanism.html\" rel=\"nofollow\"\u003eMaven\u003c/a\u003e):\u003c/p\u003e\n\u003cdiv class=\"highlight highlight-text-xml notranslate position-relative overflow-auto\" dir=\"auto\" data-snippet-clipboard-copy-content=\"\u0026lt;dependency\u0026gt;\n \u0026lt;groupId\u0026gt;com.jnape.palatable\u0026lt;/groupId\u0026gt;\n \u0026lt;artifactId\u0026gt;lambda\u0026lt;/artifactId\u0026gt;\n \u0026lt;version\u0026gt;5.4.0\u0026lt;/version\u0026gt;\n\u0026lt;/dependency\u0026gt;\"\u003e\u003cpre\u003e\u0026lt;\u003cspan class=\"pl-ent\"\u003edependency\u003c/span\u003e\u0026gt;\n \u0026lt;\u003cspan class=\"pl-ent\"\u003egroupId\u003c/span\u003e\u0026gt;com.jnape.palatable\u0026lt;/\u003cspan class=\"pl-ent\"\u003egroupId\u003c/span\u003e\u0026gt;\n \u0026lt;\u003cspan class=\"pl-ent\"\u003eartifactId\u003c/span\u003e\u0026gt;lambda\u0026lt;/\u003cspan class=\"pl-ent\"\u003eartifactId\u003c/span\u003e\u0026gt;\n \u0026lt;\u003cspan class=\"pl-ent\"\u003eversion\u003c/span\u003e\u0026gt;5.4.0\u0026lt;/\u003cspan class=\"pl-ent\"\u003eversion\u003c/span\u003e\u0026gt;\n\u0026lt;/\u003cspan class=\"pl-ent\"\u003edependency\u003c/span\u003e\u0026gt;\u003c/pre\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003e\u003ccode\u003ebuild.gradle\u003c/code\u003e (\u003ca href=\"https://docs.gradle.org/current/userguide/dependency_management.html\" rel=\"nofollow\"\u003eGradle\u003c/a\u003e):\u003c/p\u003e\n\u003cdiv class=\"highlight highlight-source-groovy-gradle notranslate position-relative overflow-auto\" dir=\"auto\" data-snippet-clipboard-copy-content=\"compile group: 'com.jnape.palatable', name: 'lambda', version: '5.4.0'\"\u003e\u003cpre\u003ecompile \u003cspan class=\"pl-c1\"\u003egroup\u003c/span\u003e: \u003cspan class=\"pl-s\"\u003e\u003cspan class=\"pl-pds\"\u003e'\u003c/span\u003ecom.jnape.palatable\u003cspan class=\"pl-pds\"\u003e'\u003c/span\u003e\u003c/span\u003e, \u003cspan class=\"pl-c1\"\u003ename\u003c/span\u003e: \u003cspan class=\"pl-s\"\u003e\u003cspan class=\"pl-pds\"\u003e'\u003c/span\u003elambda\u003cspan class=\"pl-pds\"\u003e'\u003c/span\u003e\u003c/span\u003e, \u003cspan class=\"pl-c1\"\u003eversion\u003c/span\u003e: \u003cspan class=\"pl-s\"\u003e\u003cspan class=\"pl-pds\"\u003e'\u003c/span\u003e5.4.0\u003cspan class=\"pl-pds\"\u003e'\u003c/span\u003e\u003c/span\u003e\u003c/pre\u003e\u003c/div\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch2 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003e\u003ca name=\"user-content-examples\"\u003eExamples\u003c/a\u003e\u003c/h2\u003e\u003ca id=\"user-content-examples\" class=\"anchor\" aria-label=\"Permalink: Examples\" href=\"#examples\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eFirst, the obligatory \u003ccode\u003emap\u003c/code\u003e/\u003ccode\u003efilter\u003c/code\u003e/\u003ccode\u003ereduce\u003c/code\u003e example:\u003c/p\u003e\n\u003cdiv class=\"highlight highlight-source-java notranslate position-relative overflow-auto\" dir=\"auto\" data-snippet-clipboard-copy-content=\"Maybe\u0026lt;Integer\u0026gt; sumOfEvenIncrements =\n reduceLeft((x, y) -\u0026gt; x + y,\n filter(x -\u0026gt; x % 2 == 0,\n map(x -\u0026gt; x + 1, asList(1, 2, 3, 4, 5))));\n//-\u0026gt; Just 12\"\u003e\u003cpre\u003e\u003cspan class=\"pl-smi\"\u003eMaybe\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e\u0026gt; \u003cspan class=\"pl-s1\"\u003esumOfEvenIncrements\u003c/span\u003e =\n \u003cspan class=\"pl-en\"\u003ereduceLeft\u003c/span\u003e((\u003cspan class=\"pl-s1\"\u003ex\u003c/span\u003e, \u003cspan class=\"pl-s1\"\u003ey\u003c/span\u003e) -\u0026gt; \u003cspan class=\"pl-s1\"\u003ex\u003c/span\u003e + \u003cspan class=\"pl-s1\"\u003ey\u003c/span\u003e,\n \u003cspan class=\"pl-en\"\u003efilter\u003c/span\u003e(\u003cspan class=\"pl-s1\"\u003ex\u003c/span\u003e -\u0026gt; \u003cspan class=\"pl-s1\"\u003ex\u003c/span\u003e % \u003cspan class=\"pl-c1\"\u003e2\u003c/span\u003e == \u003cspan class=\"pl-c1\"\u003e0\u003c/span\u003e,\n \u003cspan class=\"pl-en\"\u003emap\u003c/span\u003e(\u003cspan class=\"pl-s1\"\u003ex\u003c/span\u003e -\u0026gt; \u003cspan class=\"pl-s1\"\u003ex\u003c/span\u003e + \u003cspan class=\"pl-c1\"\u003e1\u003c/span\u003e, \u003cspan class=\"pl-en\"\u003easList\u003c/span\u003e(\u003cspan class=\"pl-c1\"\u003e1\u003c/span\u003e, \u003cspan class=\"pl-c1\"\u003e2\u003c/span\u003e, \u003cspan class=\"pl-c1\"\u003e3\u003c/span\u003e, \u003cspan class=\"pl-c1\"\u003e4\u003c/span\u003e, \u003cspan class=\"pl-c1\"\u003e5\u003c/span\u003e))));\n\u003cspan class=\"pl-c\"\u003e//-\u0026gt; Just 12\u003c/span\u003e\u003c/pre\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eEvery function in lambda is \u003ca href=\"https://www.wikiwand.com/en/Currying\" rel=\"nofollow\"\u003ecurried\u003c/a\u003e, so we could have also done this:\u003c/p\u003e\n\u003cdiv class=\"highlight highlight-source-java notranslate position-relative overflow-auto\" dir=\"auto\" data-snippet-clipboard-copy-content=\"Fn1\u0026lt;Iterable\u0026lt;Integer\u0026gt;, Maybe\u0026lt;Integer\u0026gt;\u0026gt; sumOfEvenIncrementsFn =\n map((Integer x) -\u0026gt; x + 1)\n .fmap(filter(x -\u0026gt; x % 2 == 0))\n .fmap(reduceLeft((x, y) -\u0026gt; x + y));\n\nMaybe\u0026lt;Integer\u0026gt; sumOfEvenIncrements = sumOfEvenIncrementsFn.apply(asList(1, 2, 3, 4, 5));\n//-\u0026gt; Just 12\"\u003e\u003cpre\u003e\u003cspan class=\"pl-smi\"\u003eFn1\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eIterable\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e\u0026gt;, \u003cspan class=\"pl-smi\"\u003eMaybe\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e\u0026gt;\u0026gt; \u003cspan class=\"pl-s1\"\u003esumOfEvenIncrementsFn\u003c/span\u003e =\n \u003cspan class=\"pl-en\"\u003emap\u003c/span\u003e((\u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e \u003cspan class=\"pl-s1\"\u003ex\u003c/span\u003e) -\u0026gt; \u003cspan class=\"pl-s1\"\u003ex\u003c/span\u003e + \u003cspan class=\"pl-c1\"\u003e1\u003c/span\u003e)\n .\u003cspan class=\"pl-en\"\u003efmap\u003c/span\u003e(\u003cspan class=\"pl-en\"\u003efilter\u003c/span\u003e(\u003cspan class=\"pl-s1\"\u003ex\u003c/span\u003e -\u0026gt; \u003cspan class=\"pl-s1\"\u003ex\u003c/span\u003e % \u003cspan class=\"pl-c1\"\u003e2\u003c/span\u003e == \u003cspan class=\"pl-c1\"\u003e0\u003c/span\u003e))\n .\u003cspan class=\"pl-en\"\u003efmap\u003c/span\u003e(\u003cspan class=\"pl-en\"\u003ereduceLeft\u003c/span\u003e((\u003cspan class=\"pl-s1\"\u003ex\u003c/span\u003e, \u003cspan class=\"pl-s1\"\u003ey\u003c/span\u003e) -\u0026gt; \u003cspan class=\"pl-s1\"\u003ex\u003c/span\u003e + \u003cspan class=\"pl-s1\"\u003ey\u003c/span\u003e));\n\n\u003cspan class=\"pl-smi\"\u003eMaybe\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e\u0026gt; \u003cspan class=\"pl-s1\"\u003esumOfEvenIncrements\u003c/span\u003e = \u003cspan class=\"pl-s1\"\u003esumOfEvenIncrementsFn\u003c/span\u003e.\u003cspan class=\"pl-en\"\u003eapply\u003c/span\u003e(\u003cspan class=\"pl-en\"\u003easList\u003c/span\u003e(\u003cspan class=\"pl-c1\"\u003e1\u003c/span\u003e, \u003cspan class=\"pl-c1\"\u003e2\u003c/span\u003e, \u003cspan class=\"pl-c1\"\u003e3\u003c/span\u003e, \u003cspan class=\"pl-c1\"\u003e4\u003c/span\u003e, \u003cspan class=\"pl-c1\"\u003e5\u003c/span\u003e));\n\u003cspan class=\"pl-c\"\u003e//-\u0026gt; Just 12\u003c/span\u003e\u003c/pre\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eHow about the positive squares below 100:\u003c/p\u003e\n\u003cdiv class=\"highlight highlight-source-java notranslate position-relative overflow-auto\" dir=\"auto\" data-snippet-clipboard-copy-content=\"Iterable\u0026lt;Integer\u0026gt; positiveSquaresBelow100 =\n takeWhile(x -\u0026gt; x \u0026lt; 100, map(x -\u0026gt; x * x, iterate(x -\u0026gt; x + 1, 1)));\n//-\u0026gt; [1, 4, 9, 16, 25, 36, 49, 64, 81]\"\u003e\u003cpre\u003e\u003cspan class=\"pl-smi\"\u003eIterable\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e\u0026gt; \u003cspan class=\"pl-s1\"\u003epositiveSquaresBelow100\u003c/span\u003e =\n \u003cspan class=\"pl-en\"\u003etakeWhile\u003c/span\u003e(\u003cspan class=\"pl-s1\"\u003ex\u003c/span\u003e -\u0026gt; \u003cspan class=\"pl-s1\"\u003ex\u003c/span\u003e \u0026lt; \u003cspan class=\"pl-c1\"\u003e100\u003c/span\u003e, \u003cspan class=\"pl-en\"\u003emap\u003c/span\u003e(\u003cspan class=\"pl-s1\"\u003ex\u003c/span\u003e -\u0026gt; \u003cspan class=\"pl-s1\"\u003ex\u003c/span\u003e * \u003cspan class=\"pl-s1\"\u003ex\u003c/span\u003e, \u003cspan class=\"pl-en\"\u003eiterate\u003c/span\u003e(\u003cspan class=\"pl-s1\"\u003ex\u003c/span\u003e -\u0026gt; \u003cspan class=\"pl-s1\"\u003ex\u003c/span\u003e + \u003cspan class=\"pl-c1\"\u003e1\u003c/span\u003e, \u003cspan class=\"pl-c1\"\u003e1\u003c/span\u003e)));\n\u003cspan class=\"pl-c\"\u003e//-\u0026gt; [1, 4, 9, 16, 25, 36, 49, 64, 81]\u003c/span\u003e\u003c/pre\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eWe could have also used \u003ccode\u003eunfoldr\u003c/code\u003e:\u003c/p\u003e\n\u003cdiv class=\"highlight highlight-source-java notranslate position-relative overflow-auto\" dir=\"auto\" data-snippet-clipboard-copy-content=\"Iterable\u0026lt;Integer\u0026gt; positiveSquaresBelow100 = unfoldr(x -\u0026gt; {\n int square = x * x;\n return square \u0026lt; 100 ? Maybe.just(tuple(square, x + 1)) : Maybe.nothing();\n }, 1);\n//-\u0026gt; [1, 4, 9, 16, 25, 36, 49, 64, 81]\"\u003e\u003cpre\u003e\u003cspan class=\"pl-smi\"\u003eIterable\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e\u0026gt; \u003cspan class=\"pl-s1\"\u003epositiveSquaresBelow100\u003c/span\u003e = \u003cspan class=\"pl-en\"\u003eunfoldr\u003c/span\u003e(\u003cspan class=\"pl-s1\"\u003ex\u003c/span\u003e -\u0026gt; {\n \u003cspan class=\"pl-smi\"\u003eint\u003c/span\u003e \u003cspan class=\"pl-s1\"\u003esquare\u003c/span\u003e = \u003cspan class=\"pl-s1\"\u003ex\u003c/span\u003e * \u003cspan class=\"pl-s1\"\u003ex\u003c/span\u003e;\n \u003cspan class=\"pl-k\"\u003ereturn\u003c/span\u003e \u003cspan class=\"pl-s1\"\u003esquare\u003c/span\u003e \u0026lt; \u003cspan class=\"pl-c1\"\u003e100\u003c/span\u003e ? \u003cspan class=\"pl-smi\"\u003eMaybe\u003c/span\u003e.\u003cspan class=\"pl-en\"\u003ejust\u003c/span\u003e(\u003cspan class=\"pl-en\"\u003etuple\u003c/span\u003e(\u003cspan class=\"pl-s1\"\u003esquare\u003c/span\u003e, \u003cspan class=\"pl-s1\"\u003ex\u003c/span\u003e + \u003cspan class=\"pl-c1\"\u003e1\u003c/span\u003e)) : \u003cspan class=\"pl-smi\"\u003eMaybe\u003c/span\u003e.\u003cspan class=\"pl-en\"\u003enothing\u003c/span\u003e();\n }, \u003cspan class=\"pl-c1\"\u003e1\u003c/span\u003e);\n\u003cspan class=\"pl-c\"\u003e//-\u0026gt; [1, 4, 9, 16, 25, 36, 49, 64, 81]\u003c/span\u003e\u003c/pre\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eWhat if we want the cross product of a domain and codomain:\u003c/p\u003e\n\u003cdiv class=\"highlight highlight-source-java notranslate position-relative overflow-auto\" dir=\"auto\" data-snippet-clipboard-copy-content=\"Iterable\u0026lt;Tuple2\u0026lt;Integer, String\u0026gt;\u0026gt; crossProduct =\n take(10, cartesianProduct(asList(1, 2, 3), asList(\u0026quot;a\u0026quot;, \u0026quot;b\u0026quot;, \u0026quot;c\u0026quot;)));\n//-\u0026gt; [(1,\u0026quot;a\u0026quot;), (1,\u0026quot;b\u0026quot;), (1,\u0026quot;c\u0026quot;), (2,\u0026quot;a\u0026quot;), (2,\u0026quot;b\u0026quot;), (2,\u0026quot;c\u0026quot;), (3,\u0026quot;a\u0026quot;), (3,\u0026quot;b\u0026quot;), (3,\u0026quot;c\u0026quot;)]\"\u003e\u003cpre\u003e\u003cspan class=\"pl-smi\"\u003eIterable\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eTuple2\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003eString\u003c/span\u003e\u0026gt;\u0026gt; \u003cspan class=\"pl-s1\"\u003ecrossProduct\u003c/span\u003e =\n \u003cspan class=\"pl-en\"\u003etake\u003c/span\u003e(\u003cspan class=\"pl-c1\"\u003e10\u003c/span\u003e, \u003cspan class=\"pl-en\"\u003ecartesianProduct\u003c/span\u003e(\u003cspan class=\"pl-en\"\u003easList\u003c/span\u003e(\u003cspan class=\"pl-c1\"\u003e1\u003c/span\u003e, \u003cspan class=\"pl-c1\"\u003e2\u003c/span\u003e, \u003cspan class=\"pl-c1\"\u003e3\u003c/span\u003e), \u003cspan class=\"pl-en\"\u003easList\u003c/span\u003e(\u003cspan class=\"pl-s\"\u003e\"a\"\u003c/span\u003e, \u003cspan class=\"pl-s\"\u003e\"b\"\u003c/span\u003e, \u003cspan class=\"pl-s\"\u003e\"c\"\u003c/span\u003e)));\n\u003cspan class=\"pl-c\"\u003e//-\u0026gt; [(1,\"a\"), (1,\"b\"), (1,\"c\"), (2,\"a\"), (2,\"b\"), (2,\"c\"), (3,\"a\"), (3,\"b\"), (3,\"c\")]\u003c/span\u003e\u003c/pre\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eLet's compose two functions:\u003c/p\u003e\n\u003cdiv class=\"highlight highlight-source-java notranslate position-relative overflow-auto\" dir=\"auto\" data-snippet-clipboard-copy-content=\"Fn1\u0026lt;Integer, Integer\u0026gt; add = x -\u0026gt; x + 1;\nFn1\u0026lt;Integer, Integer\u0026gt; subtract = x -\u0026gt; x -1;\n\nFn1\u0026lt;Integer, Integer\u0026gt; noOp = add.fmap(subtract);\n// same as\nFn1\u0026lt;Integer, Integer\u0026gt; alsoNoOp = subtract.contraMap(add);\"\u003e\u003cpre\u003e\u003cspan class=\"pl-smi\"\u003eFn1\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e\u0026gt; \u003cspan class=\"pl-s1\"\u003eadd\u003c/span\u003e = \u003cspan class=\"pl-s1\"\u003ex\u003c/span\u003e -\u0026gt; \u003cspan class=\"pl-s1\"\u003ex\u003c/span\u003e + \u003cspan class=\"pl-c1\"\u003e1\u003c/span\u003e;\n\u003cspan class=\"pl-smi\"\u003eFn1\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e\u0026gt; \u003cspan class=\"pl-s1\"\u003esubtract\u003c/span\u003e = \u003cspan class=\"pl-s1\"\u003ex\u003c/span\u003e -\u0026gt; \u003cspan class=\"pl-s1\"\u003ex\u003c/span\u003e -\u003cspan class=\"pl-c1\"\u003e1\u003c/span\u003e;\n\n\u003cspan class=\"pl-smi\"\u003eFn1\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e\u0026gt; \u003cspan class=\"pl-s1\"\u003enoOp\u003c/span\u003e = \u003cspan class=\"pl-s1\"\u003eadd\u003c/span\u003e.\u003cspan class=\"pl-en\"\u003efmap\u003c/span\u003e(\u003cspan class=\"pl-s1\"\u003esubtract\u003c/span\u003e);\n\u003cspan class=\"pl-c\"\u003e// same as\u003c/span\u003e\n\u003cspan class=\"pl-smi\"\u003eFn1\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e\u0026gt; \u003cspan class=\"pl-s1\"\u003ealsoNoOp\u003c/span\u003e = \u003cspan class=\"pl-s1\"\u003esubtract\u003c/span\u003e.\u003cspan class=\"pl-en\"\u003econtraMap\u003c/span\u003e(\u003cspan class=\"pl-s1\"\u003eadd\u003c/span\u003e);\u003c/pre\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eAnd partially apply some:\u003c/p\u003e\n\u003cdiv class=\"highlight highlight-source-java notranslate position-relative overflow-auto\" dir=\"auto\" data-snippet-clipboard-copy-content=\"Fn2\u0026lt;Integer, Integer, Integer\u0026gt; add = (x, y) -\u0026gt; x + y;\n\nFn1\u0026lt;Integer, Integer\u0026gt; add1 = add.apply(1);\nadd1.apply(2);\n//-\u0026gt; 3\"\u003e\u003cpre\u003e\u003cspan class=\"pl-smi\"\u003eFn2\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e\u0026gt; \u003cspan class=\"pl-s1\"\u003eadd\u003c/span\u003e = (\u003cspan class=\"pl-s1\"\u003ex\u003c/span\u003e, \u003cspan class=\"pl-s1\"\u003ey\u003c/span\u003e) -\u0026gt; \u003cspan class=\"pl-s1\"\u003ex\u003c/span\u003e + \u003cspan class=\"pl-s1\"\u003ey\u003c/span\u003e;\n\n\u003cspan class=\"pl-smi\"\u003eFn1\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e\u0026gt; \u003cspan class=\"pl-s1\"\u003eadd1\u003c/span\u003e = \u003cspan class=\"pl-s1\"\u003eadd\u003c/span\u003e.\u003cspan class=\"pl-en\"\u003eapply\u003c/span\u003e(\u003cspan class=\"pl-c1\"\u003e1\u003c/span\u003e);\n\u003cspan class=\"pl-s1\"\u003eadd1\u003c/span\u003e.\u003cspan class=\"pl-en\"\u003eapply\u003c/span\u003e(\u003cspan class=\"pl-c1\"\u003e2\u003c/span\u003e);\n\u003cspan class=\"pl-c\"\u003e//-\u0026gt; 3\u003c/span\u003e\u003c/pre\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eAnd have fun with 3s:\u003c/p\u003e\n\u003cdiv class=\"highlight highlight-source-java notranslate position-relative overflow-auto\" dir=\"auto\" data-snippet-clipboard-copy-content=\"Iterable\u0026lt;Iterable\u0026lt;Integer\u0026gt;\u0026gt; multiplesOf3InGroupsOf3 =\n take(3, inGroupsOf(3, unfoldr(x -\u0026gt; Maybe.just(tuple(x * 3, x + 1)), 1)));\n//-\u0026gt; [[3, 6, 9], [12, 15, 18], [21, 24, 27]]\"\u003e\u003cpre\u003e\u003cspan class=\"pl-smi\"\u003eIterable\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eIterable\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e\u0026gt;\u0026gt; \u003cspan class=\"pl-s1\"\u003emultiplesOf3InGroupsOf3\u003c/span\u003e =\n \u003cspan class=\"pl-en\"\u003etake\u003c/span\u003e(\u003cspan class=\"pl-c1\"\u003e3\u003c/span\u003e, \u003cspan class=\"pl-en\"\u003einGroupsOf\u003c/span\u003e(\u003cspan class=\"pl-c1\"\u003e3\u003c/span\u003e, \u003cspan class=\"pl-en\"\u003eunfoldr\u003c/span\u003e(\u003cspan class=\"pl-s1\"\u003ex\u003c/span\u003e -\u0026gt; \u003cspan class=\"pl-smi\"\u003eMaybe\u003c/span\u003e.\u003cspan class=\"pl-en\"\u003ejust\u003c/span\u003e(\u003cspan class=\"pl-en\"\u003etuple\u003c/span\u003e(\u003cspan class=\"pl-s1\"\u003ex\u003c/span\u003e * \u003cspan class=\"pl-c1\"\u003e3\u003c/span\u003e, \u003cspan class=\"pl-s1\"\u003ex\u003c/span\u003e + \u003cspan class=\"pl-c1\"\u003e1\u003c/span\u003e)), \u003cspan class=\"pl-c1\"\u003e1\u003c/span\u003e)));\n\u003cspan class=\"pl-c\"\u003e//-\u0026gt; [[3, 6, 9], [12, 15, 18], [21, 24, 27]]\u003c/span\u003e\u003c/pre\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eCheck out the \u003ca href=\"https://github.com/palatable/lambda/tree/master/src/test/java/com/jnape/palatable/lambda/functions/builtin\"\u003etests\u003c/a\u003e or \u003ca href=\"http://palatable.github.io/lambda/javadoc/\" rel=\"nofollow\"\u003ejavadoc\u003c/a\u003e for more examples.\u003c/p\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch2 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003e\u003ca name=\"user-content-semigroups\"\u003eSemigroups\u003c/a\u003e\u003c/h2\u003e\u003ca id=\"user-content-semigroups\" class=\"anchor\" aria-label=\"Permalink: Semigroups\" href=\"#semigroups\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003e\u003ca href=\"https://en.wikipedia.org/wiki/Semigroup\" rel=\"nofollow\"\u003eSemigroups\u003c/a\u003e are supported via \u003ccode\u003eSemigroup\u0026lt;A\u0026gt;\u003c/code\u003e, a subtype of \u003ccode\u003eFn2\u0026lt;A,A,A\u0026gt;\u003c/code\u003e, and add left and right folds over an \u003ccode\u003eIterable\u0026lt;A\u0026gt;\u003c/code\u003e.\u003c/p\u003e\n\u003cdiv class=\"highlight highlight-source-java notranslate position-relative overflow-auto\" dir=\"auto\" data-snippet-clipboard-copy-content=\"Semigroup\u0026lt;Integer\u0026gt; add = (augend, addend) -\u0026gt; augend + addend;\nadd.apply(1, 2); //-\u0026gt; 3\nadd.foldLeft(0, asList(1, 2, 3)); //-\u0026gt; 6\"\u003e\u003cpre\u003e\u003cspan class=\"pl-smi\"\u003eSemigroup\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e\u0026gt; \u003cspan class=\"pl-s1\"\u003eadd\u003c/span\u003e = (\u003cspan class=\"pl-s1\"\u003eaugend\u003c/span\u003e, \u003cspan class=\"pl-s1\"\u003eaddend\u003c/span\u003e) -\u0026gt; \u003cspan class=\"pl-s1\"\u003eaugend\u003c/span\u003e + \u003cspan class=\"pl-s1\"\u003eaddend\u003c/span\u003e;\n\u003cspan class=\"pl-s1\"\u003eadd\u003c/span\u003e.\u003cspan class=\"pl-en\"\u003eapply\u003c/span\u003e(\u003cspan class=\"pl-c1\"\u003e1\u003c/span\u003e, \u003cspan class=\"pl-c1\"\u003e2\u003c/span\u003e); \u003cspan class=\"pl-c\"\u003e//-\u0026gt; 3\u003c/span\u003e\n\u003cspan class=\"pl-s1\"\u003eadd\u003c/span\u003e.\u003cspan class=\"pl-en\"\u003efoldLeft\u003c/span\u003e(\u003cspan class=\"pl-c1\"\u003e0\u003c/span\u003e, \u003cspan class=\"pl-en\"\u003easList\u003c/span\u003e(\u003cspan class=\"pl-c1\"\u003e1\u003c/span\u003e, \u003cspan class=\"pl-c1\"\u003e2\u003c/span\u003e, \u003cspan class=\"pl-c1\"\u003e3\u003c/span\u003e)); \u003cspan class=\"pl-c\"\u003e//-\u0026gt; 6\u003c/span\u003e\u003c/pre\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eLambda ships some default logical semigroups for lambda types and core JDK types. Common examples are:\u003c/p\u003e\n\u003cul dir=\"auto\"\u003e\n\u003cli\u003e\u003ccode\u003eAddAll\u003c/code\u003e for concatenating two \u003ccode\u003eCollection\u003c/code\u003es\u003c/li\u003e\n\u003cli\u003e\u003ccode\u003eCollapse\u003c/code\u003e for collapsing two \u003ccode\u003eTuple2\u003c/code\u003es together\u003c/li\u003e\n\u003cli\u003e\u003ccode\u003eMerge\u003c/code\u003e for merging two \u003ccode\u003eEither\u003c/code\u003es using left-biasing semantics\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp dir=\"auto\"\u003eCheck out the \u003ca href=\"https://palatable.github.io/lambda/javadoc/com/jnape/palatable/lambda/semigroup/builtin/package-summary.html\" rel=\"nofollow\"\u003esemigroup\u003c/a\u003e package for more examples.\u003c/p\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch2 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003e\u003ca name=\"user-content-monoids\"\u003eMonoids\u003c/a\u003e\u003c/h2\u003e\u003ca id=\"user-content-monoids\" class=\"anchor\" aria-label=\"Permalink: Monoids\" href=\"#monoids\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003e\u003ca href=\"https://en.wikipedia.org/wiki/Monoid\" rel=\"nofollow\"\u003eMonoids\u003c/a\u003e are supported via \u003ccode\u003eMonoid\u0026lt;A\u0026gt;\u003c/code\u003e, a subtype of \u003ccode\u003eSemigroup\u0026lt;A\u0026gt;\u003c/code\u003e with an \u003ccode\u003eA #identity()\u003c/code\u003e method, and add left and right reduces over an \u003ccode\u003eIterable\u0026lt;A\u0026gt;\u003c/code\u003e, as well as \u003ccode\u003efoldMap\u003c/code\u003e.\u003c/p\u003e\n\u003cdiv class=\"highlight highlight-source-java notranslate position-relative overflow-auto\" dir=\"auto\" data-snippet-clipboard-copy-content=\"Monoid\u0026lt;Integer\u0026gt; multiply = monoid((x, y) -\u0026gt; x * y, 1);\nmultiply.reduceLeft(emptyList()); //-\u0026gt; 1\nmultiply.reduceLeft(asList(1, 2, 3)); //-\u0026gt; 6\nmultiply.foldMap(Integer::parseInt, asList(\u0026quot;1\u0026quot;, \u0026quot;2\u0026quot;, \u0026quot;3\u0026quot;)); //-\u0026gt; also 6\"\u003e\u003cpre\u003e\u003cspan class=\"pl-smi\"\u003eMonoid\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e\u0026gt; \u003cspan class=\"pl-s1\"\u003emultiply\u003c/span\u003e = \u003cspan class=\"pl-en\"\u003emonoid\u003c/span\u003e((\u003cspan class=\"pl-s1\"\u003ex\u003c/span\u003e, \u003cspan class=\"pl-s1\"\u003ey\u003c/span\u003e) -\u0026gt; \u003cspan class=\"pl-s1\"\u003ex\u003c/span\u003e * \u003cspan class=\"pl-s1\"\u003ey\u003c/span\u003e, \u003cspan class=\"pl-c1\"\u003e1\u003c/span\u003e);\n\u003cspan class=\"pl-s1\"\u003emultiply\u003c/span\u003e.\u003cspan class=\"pl-en\"\u003ereduceLeft\u003c/span\u003e(\u003cspan class=\"pl-en\"\u003eemptyList\u003c/span\u003e()); \u003cspan class=\"pl-c\"\u003e//-\u0026gt; 1\u003c/span\u003e\n\u003cspan class=\"pl-s1\"\u003emultiply\u003c/span\u003e.\u003cspan class=\"pl-en\"\u003ereduceLeft\u003c/span\u003e(\u003cspan class=\"pl-en\"\u003easList\u003c/span\u003e(\u003cspan class=\"pl-c1\"\u003e1\u003c/span\u003e, \u003cspan class=\"pl-c1\"\u003e2\u003c/span\u003e, \u003cspan class=\"pl-c1\"\u003e3\u003c/span\u003e)); \u003cspan class=\"pl-c\"\u003e//-\u0026gt; 6\u003c/span\u003e\n\u003cspan class=\"pl-s1\"\u003emultiply\u003c/span\u003e.\u003cspan class=\"pl-en\"\u003efoldMap\u003c/span\u003e(\u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e::\u003cspan class=\"pl-s1\"\u003eparseInt\u003c/span\u003e, \u003cspan class=\"pl-en\"\u003easList\u003c/span\u003e(\u003cspan class=\"pl-s\"\u003e\"1\"\u003c/span\u003e, \u003cspan class=\"pl-s\"\u003e\"2\"\u003c/span\u003e, \u003cspan class=\"pl-s\"\u003e\"3\"\u003c/span\u003e)); \u003cspan class=\"pl-c\"\u003e//-\u0026gt; also 6\u003c/span\u003e\u003c/pre\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eSome commonly used lambda monoid implementations include:\u003c/p\u003e\n\u003cul dir=\"auto\"\u003e\n\u003cli\u003e\u003ccode\u003ePresent\u003c/code\u003e for merging together two \u003ccode\u003eOptional\u003c/code\u003es\u003c/li\u003e\n\u003cli\u003e\u003ccode\u003eJoin\u003c/code\u003e for joining two \u003ccode\u003eString\u003c/code\u003es\u003c/li\u003e\n\u003cli\u003e\u003ccode\u003eAnd\u003c/code\u003e for logical conjunction of two \u003ccode\u003eBoolean\u003c/code\u003es\u003c/li\u003e\n\u003cli\u003e\u003ccode\u003eOr\u003c/code\u003e for logical disjunction of two \u003ccode\u003eBoolean\u003c/code\u003es\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp dir=\"auto\"\u003eAdditionally, instances of \u003ccode\u003eMonoid\u0026lt;A\u0026gt;\u003c/code\u003e can be trivially synthesized from instances of \u003ccode\u003eSemigroup\u0026lt;A\u0026gt;\u003c/code\u003e via the \u003ccode\u003eMonoid#monoid\u003c/code\u003e static factory method, taking the \u003ccode\u003eSemigroup\u003c/code\u003e and the identity element \u003ccode\u003eA\u003c/code\u003e or a supplier of the identity element \u003ccode\u003eSupplier\u0026lt;A\u0026gt;\u003c/code\u003e.\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eCheck out the \u003ca href=\"https://palatable.github.io/lambda/javadoc/com/jnape/palatable/lambda/monoid/builtin/package-summary.html\" rel=\"nofollow\"\u003emonoid\u003c/a\u003e package for more examples.\u003c/p\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch2 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003e\u003ca name=\"user-content-functors\"\u003eFunctors\u003c/a\u003e\u003c/h2\u003e\u003ca id=\"user-content-functors\" class=\"anchor\" aria-label=\"Permalink: Functors\" href=\"#functors\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eFunctors are implemented via the \u003ccode\u003eFunctor\u003c/code\u003e interface, and are sub-typed by every function type that lambda exports, as well as many of the \u003ca href=\"#adts\"\u003eADTs\u003c/a\u003e.\u003c/p\u003e\n\u003cdiv class=\"highlight highlight-source-java notranslate position-relative overflow-auto\" dir=\"auto\" data-snippet-clipboard-copy-content=\"public final class Slot\u0026lt;A\u0026gt; implements Functor\u0026lt;A, Slot\u0026gt; {\n private final A a;\n\n public Slot(A a) {\n this.a = a;\n }\n\n public A getA() {\n return a;\n }\n\n @Override\n public \u0026lt;B\u0026gt; Slot\u0026lt;B\u0026gt; fmap(Function\u0026lt;? super A, ? extends B\u0026gt; fn) {\n return new Slot\u0026lt;\u0026gt;(fn.apply(a));\n }\n}\n\nSlot\u0026lt;Integer\u0026gt; intSlot = new Slot\u0026lt;\u0026gt;(1);\nSlot\u0026lt;String\u0026gt; stringSlot = intSlot.fmap(x -\u0026gt; \u0026quot;number: \u0026quot; + x);\nstringSlot.getA(); //-\u0026gt; \u0026quot;number: 1\u0026quot;\"\u003e\u003cpre\u003e\u003cspan class=\"pl-k\"\u003epublic\u003c/span\u003e \u003cspan class=\"pl-k\"\u003efinal\u003c/span\u003e \u003cspan class=\"pl-k\"\u003eclass\u003c/span\u003e \u003cspan class=\"pl-smi\"\u003eSlot\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eA\u003c/span\u003e\u0026gt; \u003cspan class=\"pl-k\"\u003eimplements\u003c/span\u003e \u003cspan class=\"pl-smi\"\u003eFunctor\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eA\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003eSlot\u003c/span\u003e\u0026gt; {\n \u003cspan class=\"pl-k\"\u003eprivate\u003c/span\u003e \u003cspan class=\"pl-k\"\u003efinal\u003c/span\u003e \u003cspan class=\"pl-smi\"\u003eA\u003c/span\u003e \u003cspan class=\"pl-s1\"\u003ea\u003c/span\u003e;\n\n \u003cspan class=\"pl-k\"\u003epublic\u003c/span\u003e \u003cspan class=\"pl-smi\"\u003eSlot\u003c/span\u003e(\u003cspan class=\"pl-smi\"\u003eA\u003c/span\u003e \u003cspan class=\"pl-s1\"\u003ea\u003c/span\u003e) {\n \u003cspan class=\"pl-smi\"\u003ethis\u003c/span\u003e.\u003cspan class=\"pl-s1\"\u003ea\u003c/span\u003e = \u003cspan class=\"pl-s1\"\u003ea\u003c/span\u003e;\n }\n\n \u003cspan class=\"pl-k\"\u003epublic\u003c/span\u003e \u003cspan class=\"pl-smi\"\u003eA\u003c/span\u003e \u003cspan class=\"pl-en\"\u003egetA\u003c/span\u003e() {\n \u003cspan class=\"pl-k\"\u003ereturn\u003c/span\u003e \u003cspan class=\"pl-s1\"\u003ea\u003c/span\u003e;\n }\n\n \u003cspan class=\"pl-c1\"\u003e@\u003c/span\u003e\u003cspan class=\"pl-c1\"\u003eOverride\u003c/span\u003e\n \u003cspan class=\"pl-k\"\u003epublic\u003c/span\u003e \u0026lt;\u003cspan class=\"pl-smi\"\u003eB\u003c/span\u003e\u0026gt; \u003cspan class=\"pl-smi\"\u003eSlot\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eB\u003c/span\u003e\u0026gt; \u003cspan class=\"pl-en\"\u003efmap\u003c/span\u003e(\u003cspan class=\"pl-smi\"\u003eFunction\u003c/span\u003e\u0026lt;? \u003cspan class=\"pl-en\"\u003esuper\u003c/span\u003e \u003cspan class=\"pl-smi\"\u003eA\u003c/span\u003e, ? \u003cspan class=\"pl-k\"\u003eextends\u003c/span\u003e \u003cspan class=\"pl-smi\"\u003eB\u003c/span\u003e\u0026gt; \u003cspan class=\"pl-s1\"\u003efn\u003c/span\u003e) {\n \u003cspan class=\"pl-k\"\u003ereturn\u003c/span\u003e \u003cspan class=\"pl-k\"\u003enew\u003c/span\u003e \u003cspan class=\"pl-smi\"\u003eSlot\u003c/span\u003e\u0026lt;\u0026gt;(\u003cspan class=\"pl-s1\"\u003efn\u003c/span\u003e.\u003cspan class=\"pl-en\"\u003eapply\u003c/span\u003e(\u003cspan class=\"pl-s1\"\u003ea\u003c/span\u003e));\n }\n}\n\n\u003cspan class=\"pl-smi\"\u003eSlot\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e\u0026gt; \u003cspan class=\"pl-s1\"\u003eintSlot\u003c/span\u003e = \u003cspan class=\"pl-k\"\u003enew\u003c/span\u003e \u003cspan class=\"pl-smi\"\u003eSlot\u003c/span\u003e\u0026lt;\u0026gt;(\u003cspan class=\"pl-c1\"\u003e1\u003c/span\u003e);\n\u003cspan class=\"pl-smi\"\u003eSlot\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eString\u003c/span\u003e\u0026gt; \u003cspan class=\"pl-s1\"\u003estringSlot\u003c/span\u003e = \u003cspan class=\"pl-s1\"\u003eintSlot\u003c/span\u003e.\u003cspan class=\"pl-en\"\u003efmap\u003c/span\u003e(\u003cspan class=\"pl-s1\"\u003ex\u003c/span\u003e -\u0026gt; \u003cspan class=\"pl-s\"\u003e\"number: \"\u003c/span\u003e + \u003cspan class=\"pl-s1\"\u003ex\u003c/span\u003e);\n\u003cspan class=\"pl-s1\"\u003estringSlot\u003c/span\u003e.\u003cspan class=\"pl-en\"\u003egetA\u003c/span\u003e(); \u003cspan class=\"pl-c\"\u003e//-\u0026gt; \"number: 1\"\u003c/span\u003e\u003c/pre\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eExamples of functors include:\u003c/p\u003e\n\u003cul dir=\"auto\"\u003e\n\u003cli\u003e\u003ccode\u003eFn*\u003c/code\u003e, \u003ccode\u003eSemigroup\u003c/code\u003e, and \u003ccode\u003eMonoid\u003c/code\u003e\u003c/li\u003e\n\u003cli\u003e\u003ccode\u003eSingletonHList\u003c/code\u003e and \u003ccode\u003eTuple*\u003c/code\u003e\u003c/li\u003e\n\u003cli\u003e\u003ccode\u003eChoice*\u003c/code\u003e\u003c/li\u003e\n\u003cli\u003e\u003ccode\u003eEither\u003c/code\u003e\u003c/li\u003e\n\u003cli\u003e\u003ccode\u003eConst\u003c/code\u003e, \u003ccode\u003eIdentity\u003c/code\u003e, and \u003ccode\u003eCompose\u003c/code\u003e\u003c/li\u003e\n\u003cli\u003e\u003ccode\u003eLens\u003c/code\u003e\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp dir=\"auto\"\u003eImplementing \u003ccode\u003eFunctor\u003c/code\u003e is as simple as providing a definition for the covariant mapping function \u003ccode\u003e#fmap\u003c/code\u003e (ideally satisfying the \u003ca href=\"https://hackage.haskell.org/package/base-4.9.1.0/docs/Data-Functor.html\" rel=\"nofollow\"\u003etwo laws\u003c/a\u003e).\u003c/p\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch3 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003e\u003ca name=\"user-content-bifunctors\"\u003eBifunctors\u003c/a\u003e\u003c/h3\u003e\u003ca id=\"user-content-bifunctors\" class=\"anchor\" aria-label=\"Permalink: Bifunctors\" href=\"#bifunctors\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eBifunctors -- functors that support two parameters that can be covariantly mapped over -- are implemented via the \u003ccode\u003eBifunctor\u003c/code\u003e interface.\u003c/p\u003e\n\u003cdiv class=\"highlight highlight-source-java notranslate position-relative overflow-auto\" dir=\"auto\" data-snippet-clipboard-copy-content=\"public final class Pair\u0026lt;A, B\u0026gt; implements Bifunctor\u0026lt;A, B, Pair\u0026gt; {\n private final A a;\n private final B b;\n\n public Pair(A a, B b) {\n this.a = a;\n this.b = b;\n }\n\n public A getA() {\n return a;\n }\n\n public B getB() {\n return b;\n }\n\n @Override\n public \u0026lt;C, D\u0026gt; Pair\u0026lt;C, D\u0026gt; biMap(Function\u0026lt;? super A, ? extends C\u0026gt; lFn,\n Function\u0026lt;? super B, ? extends D\u0026gt; rFn) {\n return new Pair\u0026lt;\u0026gt;(lFn.apply(a), rFn.apply(b));\n }\n}\n\nPair\u0026lt;String,Integer\u0026gt; stringIntPair = new Pair\u0026lt;\u0026gt;(\u0026quot;str\u0026quot;, 1);\nPair\u0026lt;Integer, Boolean\u0026gt; intBooleanPair = stringIntPair.biMap(String::length, x -\u0026gt; x % 2 == 0);\nintBooleanPair.getA(); //-\u0026gt; 3\nintBooleanPair.getB(); //-\u0026gt; false\"\u003e\u003cpre\u003e\u003cspan class=\"pl-k\"\u003epublic\u003c/span\u003e \u003cspan class=\"pl-k\"\u003efinal\u003c/span\u003e \u003cspan class=\"pl-k\"\u003eclass\u003c/span\u003e \u003cspan class=\"pl-smi\"\u003ePair\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eA\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003eB\u003c/span\u003e\u0026gt; \u003cspan class=\"pl-k\"\u003eimplements\u003c/span\u003e \u003cspan class=\"pl-smi\"\u003eBifunctor\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eA\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003eB\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003ePair\u003c/span\u003e\u0026gt; {\n \u003cspan class=\"pl-k\"\u003eprivate\u003c/span\u003e \u003cspan class=\"pl-k\"\u003efinal\u003c/span\u003e \u003cspan class=\"pl-smi\"\u003eA\u003c/span\u003e \u003cspan class=\"pl-s1\"\u003ea\u003c/span\u003e;\n \u003cspan class=\"pl-k\"\u003eprivate\u003c/span\u003e \u003cspan class=\"pl-k\"\u003efinal\u003c/span\u003e \u003cspan class=\"pl-smi\"\u003eB\u003c/span\u003e \u003cspan class=\"pl-s1\"\u003eb\u003c/span\u003e;\n\n \u003cspan class=\"pl-k\"\u003epublic\u003c/span\u003e \u003cspan class=\"pl-smi\"\u003ePair\u003c/span\u003e(\u003cspan class=\"pl-smi\"\u003eA\u003c/span\u003e \u003cspan class=\"pl-s1\"\u003ea\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003eB\u003c/span\u003e \u003cspan class=\"pl-s1\"\u003eb\u003c/span\u003e) {\n \u003cspan class=\"pl-smi\"\u003ethis\u003c/span\u003e.\u003cspan class=\"pl-s1\"\u003ea\u003c/span\u003e = \u003cspan class=\"pl-s1\"\u003ea\u003c/span\u003e;\n \u003cspan class=\"pl-smi\"\u003ethis\u003c/span\u003e.\u003cspan class=\"pl-s1\"\u003eb\u003c/span\u003e = \u003cspan class=\"pl-s1\"\u003eb\u003c/span\u003e;\n }\n\n \u003cspan class=\"pl-k\"\u003epublic\u003c/span\u003e \u003cspan class=\"pl-smi\"\u003eA\u003c/span\u003e \u003cspan class=\"pl-en\"\u003egetA\u003c/span\u003e() {\n \u003cspan class=\"pl-k\"\u003ereturn\u003c/span\u003e \u003cspan class=\"pl-s1\"\u003ea\u003c/span\u003e;\n }\n\n \u003cspan class=\"pl-k\"\u003epublic\u003c/span\u003e \u003cspan class=\"pl-smi\"\u003eB\u003c/span\u003e \u003cspan class=\"pl-en\"\u003egetB\u003c/span\u003e() {\n \u003cspan class=\"pl-k\"\u003ereturn\u003c/span\u003e \u003cspan class=\"pl-s1\"\u003eb\u003c/span\u003e;\n }\n\n \u003cspan class=\"pl-c1\"\u003e@\u003c/span\u003e\u003cspan class=\"pl-c1\"\u003eOverride\u003c/span\u003e\n \u003cspan class=\"pl-k\"\u003epublic\u003c/span\u003e \u0026lt;\u003cspan class=\"pl-smi\"\u003eC\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003eD\u003c/span\u003e\u0026gt; \u003cspan class=\"pl-smi\"\u003ePair\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eC\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003eD\u003c/span\u003e\u0026gt; \u003cspan class=\"pl-en\"\u003ebiMap\u003c/span\u003e(\u003cspan class=\"pl-smi\"\u003eFunction\u003c/span\u003e\u0026lt;? \u003cspan class=\"pl-en\"\u003esuper\u003c/span\u003e \u003cspan class=\"pl-smi\"\u003eA\u003c/span\u003e, ? \u003cspan class=\"pl-k\"\u003eextends\u003c/span\u003e \u003cspan class=\"pl-smi\"\u003eC\u003c/span\u003e\u0026gt; \u003cspan class=\"pl-s1\"\u003elFn\u003c/span\u003e,\n \u003cspan class=\"pl-smi\"\u003eFunction\u003c/span\u003e\u0026lt;? \u003cspan class=\"pl-en\"\u003esuper\u003c/span\u003e \u003cspan class=\"pl-smi\"\u003eB\u003c/span\u003e, ? \u003cspan class=\"pl-k\"\u003eextends\u003c/span\u003e \u003cspan class=\"pl-smi\"\u003eD\u003c/span\u003e\u0026gt; \u003cspan class=\"pl-s1\"\u003erFn\u003c/span\u003e) {\n \u003cspan class=\"pl-k\"\u003ereturn\u003c/span\u003e \u003cspan class=\"pl-k\"\u003enew\u003c/span\u003e \u003cspan class=\"pl-smi\"\u003ePair\u003c/span\u003e\u0026lt;\u0026gt;(\u003cspan class=\"pl-s1\"\u003elFn\u003c/span\u003e.\u003cspan class=\"pl-en\"\u003eapply\u003c/span\u003e(\u003cspan class=\"pl-s1\"\u003ea\u003c/span\u003e), \u003cspan class=\"pl-s1\"\u003erFn\u003c/span\u003e.\u003cspan class=\"pl-en\"\u003eapply\u003c/span\u003e(\u003cspan class=\"pl-s1\"\u003eb\u003c/span\u003e));\n }\n}\n\n\u003cspan class=\"pl-smi\"\u003ePair\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eString\u003c/span\u003e,\u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e\u0026gt; \u003cspan class=\"pl-s1\"\u003estringIntPair\u003c/span\u003e = \u003cspan class=\"pl-k\"\u003enew\u003c/span\u003e \u003cspan class=\"pl-smi\"\u003ePair\u003c/span\u003e\u0026lt;\u0026gt;(\u003cspan class=\"pl-s\"\u003e\"str\"\u003c/span\u003e, \u003cspan class=\"pl-c1\"\u003e1\u003c/span\u003e);\n\u003cspan class=\"pl-smi\"\u003ePair\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003eBoolean\u003c/span\u003e\u0026gt; \u003cspan class=\"pl-s1\"\u003eintBooleanPair\u003c/span\u003e = \u003cspan class=\"pl-s1\"\u003estringIntPair\u003c/span\u003e.\u003cspan class=\"pl-en\"\u003ebiMap\u003c/span\u003e(\u003cspan class=\"pl-smi\"\u003eString\u003c/span\u003e::\u003cspan class=\"pl-s1\"\u003elength\u003c/span\u003e, \u003cspan class=\"pl-s1\"\u003ex\u003c/span\u003e -\u0026gt; \u003cspan class=\"pl-s1\"\u003ex\u003c/span\u003e % \u003cspan class=\"pl-c1\"\u003e2\u003c/span\u003e == \u003cspan class=\"pl-c1\"\u003e0\u003c/span\u003e);\n\u003cspan class=\"pl-s1\"\u003eintBooleanPair\u003c/span\u003e.\u003cspan class=\"pl-en\"\u003egetA\u003c/span\u003e(); \u003cspan class=\"pl-c\"\u003e//-\u0026gt; 3\u003c/span\u003e\n\u003cspan class=\"pl-s1\"\u003eintBooleanPair\u003c/span\u003e.\u003cspan class=\"pl-en\"\u003egetB\u003c/span\u003e(); \u003cspan class=\"pl-c\"\u003e//-\u0026gt; false\u003c/span\u003e\u003c/pre\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eExamples of bifunctors include:\u003c/p\u003e\n\u003cul dir=\"auto\"\u003e\n\u003cli\u003e\u003ccode\u003eTuple*\u003c/code\u003e\u003c/li\u003e\n\u003cli\u003e\u003ccode\u003eChoice*\u003c/code\u003e\u003c/li\u003e\n\u003cli\u003e\u003ccode\u003eEither\u003c/code\u003e\u003c/li\u003e\n\u003cli\u003e\u003ccode\u003eConst\u003c/code\u003e\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp dir=\"auto\"\u003eImplementing \u003ccode\u003eBifunctor\u003c/code\u003e requires implementing \u003cem\u003eeither\u003c/em\u003e \u003ccode\u003ebiMapL\u003c/code\u003e and \u003ccode\u003ebiMapR\u003c/code\u003e \u003cem\u003eor\u003c/em\u003e \u003ccode\u003ebiMap\u003c/code\u003e. As with \u003ccode\u003eFunctor\u003c/code\u003e, there are a \u003ca href=\"https://hackage.haskell.org/package/base-4.9.1.0/docs/Data-Bifunctor.html\" rel=\"nofollow\"\u003efew laws\u003c/a\u003e that well-behaved instances of \u003ccode\u003eBifunctor\u003c/code\u003e should adhere to.\u003c/p\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch3 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003e\u003ca name=\"user-content-profunctors\"\u003eProfunctors\u003c/a\u003e\u003c/h3\u003e\u003ca id=\"user-content-profunctors\" class=\"anchor\" aria-label=\"Permalink: Profunctors\" href=\"#profunctors\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eProfunctors -- functors that support one parameter that can be mapped over contravariantly, and a second parameter that can be mapped over covariantly -- are implemented via the \u003ccode\u003eProfunctor\u003c/code\u003e interface.\u003c/p\u003e\n\u003cdiv class=\"highlight highlight-source-java notranslate position-relative overflow-auto\" dir=\"auto\" data-snippet-clipboard-copy-content=\"Fn1\u0026lt;Integer, Integer\u0026gt; add2 = (x) -\u0026gt; x + 2;\nadd2.\u0026lt;String, String\u0026gt;diMap(Integer::parseInt, Object::toString).apply(\u0026quot;1\u0026quot;); //-\u0026gt; \u0026quot;3\u0026quot;\"\u003e\u003cpre\u003e\u003cspan class=\"pl-smi\"\u003eFn1\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e\u0026gt; \u003cspan class=\"pl-s1\"\u003eadd2\u003c/span\u003e = (\u003cspan class=\"pl-s1\"\u003ex\u003c/span\u003e) -\u0026gt; \u003cspan class=\"pl-s1\"\u003ex\u003c/span\u003e + \u003cspan class=\"pl-c1\"\u003e2\u003c/span\u003e;\n\u003cspan class=\"pl-s1\"\u003eadd2\u003c/span\u003e.\u0026lt;\u003cspan class=\"pl-smi\"\u003eString\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003eString\u003c/span\u003e\u0026gt;\u003cspan class=\"pl-en\"\u003ediMap\u003c/span\u003e(\u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e::\u003cspan class=\"pl-s1\"\u003eparseInt\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003eObject\u003c/span\u003e::\u003cspan class=\"pl-s1\"\u003etoString\u003c/span\u003e).\u003cspan class=\"pl-en\"\u003eapply\u003c/span\u003e(\u003cspan class=\"pl-s\"\u003e\"1\"\u003c/span\u003e); \u003cspan class=\"pl-c\"\u003e//-\u0026gt; \"3\"\u003c/span\u003e\u003c/pre\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eExamples of profunctors include:\u003c/p\u003e\n\u003cul dir=\"auto\"\u003e\n\u003cli\u003e\u003ccode\u003eFn*\u003c/code\u003e\u003c/li\u003e\n\u003cli\u003e\u003ccode\u003eLens\u003c/code\u003e\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp dir=\"auto\"\u003eImplementing \u003ccode\u003eProfunctor\u003c/code\u003e requires implementing \u003cem\u003eeither\u003c/em\u003e \u003ccode\u003ediMapL\u003c/code\u003e and \u003ccode\u003ediMapR\u003c/code\u003e \u003cem\u003eor\u003c/em\u003e \u003ccode\u003ediMap\u003c/code\u003e. As with \u003ccode\u003eFunctor\u003c/code\u003e and \u003ccode\u003eBifunctor\u003c/code\u003e, there are \u003ca href=\"https://hackage.haskell.org/package/profunctors-5.2/docs/Data-Profunctor.html\" rel=\"nofollow\"\u003esome laws\u003c/a\u003e that well behaved instances of \u003ccode\u003eProfunctor\u003c/code\u003e should adhere to.\u003c/p\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch3 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003e\u003ca name=\"user-content-applicatives\"\u003eApplicatives\u003c/a\u003e\u003c/h3\u003e\u003ca id=\"user-content-applicatives\" class=\"anchor\" aria-label=\"Permalink: Applicatives\" href=\"#applicatives\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eApplicative functors -- functors that can be applied together with a 2-arity or higher function -- are implemented via the \u003ccode\u003eApplicative\u003c/code\u003e interface.\u003c/p\u003e\n\u003cdiv class=\"highlight highlight-source-java notranslate position-relative overflow-auto\" dir=\"auto\" data-snippet-clipboard-copy-content=\"public final class Slot\u0026lt;A\u0026gt; implements Applicative\u0026lt;A, Slot\u0026gt; {\n private final A a;\n\n public Slot(A a) {\n this.a = a;\n }\n\n public A getA() {\n return a;\n }\n\n @Override\n public \u0026lt;B\u0026gt; Slot\u0026lt;B\u0026gt; fmap(Function\u0026lt;? super A, ? extends B\u0026gt; fn) {\n return pure(fn.apply(a));\n }\n\n @Override\n public \u0026lt;B\u0026gt; Slot\u0026lt;B\u0026gt; pure(B b) {\n return new Slot\u0026lt;\u0026gt;(b);\n }\n\n @Override\n public \u0026lt;B\u0026gt; Slot\u0026lt;B\u0026gt; zip(Applicative\u0026lt;Function\u0026lt;? super A, ? extends B\u0026gt;, Slot\u0026gt; appFn) {\n return pure(appFn.\u0026lt;Slot\u0026lt;Function\u0026lt;? super A, ? extends B\u0026gt;\u0026gt;\u0026gt;coerce().getA().apply(getA()));\n }\n}\n\nFn2\u0026lt;Integer, Integer, Integer\u0026gt; add = (x, y) -\u0026gt; x + y;\nSlot\u0026lt;Integer\u0026gt; x = new Slot\u0026lt;\u0026gt;(1);\nSlot\u0026lt;Integer\u0026gt; y = new Slot\u0026lt;\u0026gt;(2);\nSlot\u0026lt;Integer\u0026gt; z = y.zip(x.fmap(add)); //-\u0026gt; Slot{a=3}\"\u003e\u003cpre\u003e\u003cspan class=\"pl-k\"\u003epublic\u003c/span\u003e \u003cspan class=\"pl-k\"\u003efinal\u003c/span\u003e \u003cspan class=\"pl-k\"\u003eclass\u003c/span\u003e \u003cspan class=\"pl-smi\"\u003eSlot\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eA\u003c/span\u003e\u0026gt; \u003cspan class=\"pl-k\"\u003eimplements\u003c/span\u003e \u003cspan class=\"pl-smi\"\u003eApplicative\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eA\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003eSlot\u003c/span\u003e\u0026gt; {\n \u003cspan class=\"pl-k\"\u003eprivate\u003c/span\u003e \u003cspan class=\"pl-k\"\u003efinal\u003c/span\u003e \u003cspan class=\"pl-smi\"\u003eA\u003c/span\u003e \u003cspan class=\"pl-s1\"\u003ea\u003c/span\u003e;\n\n \u003cspan class=\"pl-k\"\u003epublic\u003c/span\u003e \u003cspan class=\"pl-smi\"\u003eSlot\u003c/span\u003e(\u003cspan class=\"pl-smi\"\u003eA\u003c/span\u003e \u003cspan class=\"pl-s1\"\u003ea\u003c/span\u003e) {\n \u003cspan class=\"pl-smi\"\u003ethis\u003c/span\u003e.\u003cspan class=\"pl-s1\"\u003ea\u003c/span\u003e = \u003cspan class=\"pl-s1\"\u003ea\u003c/span\u003e;\n }\n\n \u003cspan class=\"pl-k\"\u003epublic\u003c/span\u003e \u003cspan class=\"pl-smi\"\u003eA\u003c/span\u003e \u003cspan class=\"pl-en\"\u003egetA\u003c/span\u003e() {\n \u003cspan class=\"pl-k\"\u003ereturn\u003c/span\u003e \u003cspan class=\"pl-s1\"\u003ea\u003c/span\u003e;\n }\n\n \u003cspan class=\"pl-c1\"\u003e@\u003c/span\u003e\u003cspan class=\"pl-c1\"\u003eOverride\u003c/span\u003e\n \u003cspan class=\"pl-k\"\u003epublic\u003c/span\u003e \u0026lt;\u003cspan class=\"pl-smi\"\u003eB\u003c/span\u003e\u0026gt; \u003cspan class=\"pl-smi\"\u003eSlot\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eB\u003c/span\u003e\u0026gt; \u003cspan class=\"pl-en\"\u003efmap\u003c/span\u003e(\u003cspan class=\"pl-smi\"\u003eFunction\u003c/span\u003e\u0026lt;? \u003cspan class=\"pl-en\"\u003esuper\u003c/span\u003e \u003cspan class=\"pl-smi\"\u003eA\u003c/span\u003e, ? \u003cspan class=\"pl-k\"\u003eextends\u003c/span\u003e \u003cspan class=\"pl-smi\"\u003eB\u003c/span\u003e\u0026gt; \u003cspan class=\"pl-s1\"\u003efn\u003c/span\u003e) {\n \u003cspan class=\"pl-k\"\u003ereturn\u003c/span\u003e \u003cspan class=\"pl-en\"\u003epure\u003c/span\u003e(\u003cspan class=\"pl-s1\"\u003efn\u003c/span\u003e.\u003cspan class=\"pl-en\"\u003eapply\u003c/span\u003e(\u003cspan class=\"pl-s1\"\u003ea\u003c/span\u003e));\n }\n\n \u003cspan class=\"pl-c1\"\u003e@\u003c/span\u003e\u003cspan class=\"pl-c1\"\u003eOverride\u003c/span\u003e\n \u003cspan class=\"pl-k\"\u003epublic\u003c/span\u003e \u0026lt;\u003cspan class=\"pl-smi\"\u003eB\u003c/span\u003e\u0026gt; \u003cspan class=\"pl-smi\"\u003eSlot\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eB\u003c/span\u003e\u0026gt; \u003cspan class=\"pl-en\"\u003epure\u003c/span\u003e(\u003cspan class=\"pl-smi\"\u003eB\u003c/span\u003e \u003cspan class=\"pl-s1\"\u003eb\u003c/span\u003e) {\n \u003cspan class=\"pl-k\"\u003ereturn\u003c/span\u003e \u003cspan class=\"pl-k\"\u003enew\u003c/span\u003e \u003cspan class=\"pl-smi\"\u003eSlot\u003c/span\u003e\u0026lt;\u0026gt;(\u003cspan class=\"pl-s1\"\u003eb\u003c/span\u003e);\n }\n\n \u003cspan class=\"pl-c1\"\u003e@\u003c/span\u003e\u003cspan class=\"pl-c1\"\u003eOverride\u003c/span\u003e\n \u003cspan class=\"pl-k\"\u003epublic\u003c/span\u003e \u0026lt;\u003cspan class=\"pl-smi\"\u003eB\u003c/span\u003e\u0026gt; \u003cspan class=\"pl-smi\"\u003eSlot\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eB\u003c/span\u003e\u0026gt; \u003cspan class=\"pl-en\"\u003ezip\u003c/span\u003e(\u003cspan class=\"pl-smi\"\u003eApplicative\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eFunction\u003c/span\u003e\u0026lt;? \u003cspan class=\"pl-en\"\u003esuper\u003c/span\u003e \u003cspan class=\"pl-smi\"\u003eA\u003c/span\u003e, ? \u003cspan class=\"pl-k\"\u003eextends\u003c/span\u003e \u003cspan class=\"pl-smi\"\u003eB\u003c/span\u003e\u0026gt;, \u003cspan class=\"pl-smi\"\u003eSlot\u003c/span\u003e\u0026gt; \u003cspan class=\"pl-s1\"\u003eappFn\u003c/span\u003e) {\n \u003cspan class=\"pl-k\"\u003ereturn\u003c/span\u003e \u003cspan class=\"pl-en\"\u003epure\u003c/span\u003e(\u003cspan class=\"pl-s1\"\u003eappFn\u003c/span\u003e.\u0026lt;\u003cspan class=\"pl-smi\"\u003eSlot\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eFunction\u003c/span\u003e\u0026lt;? \u003cspan class=\"pl-en\"\u003esuper\u003c/span\u003e \u003cspan class=\"pl-smi\"\u003eA\u003c/span\u003e, ? \u003cspan class=\"pl-k\"\u003eextends\u003c/span\u003e \u003cspan class=\"pl-smi\"\u003eB\u003c/span\u003e\u0026gt;\u0026gt;\u0026gt;\u003cspan class=\"pl-en\"\u003ecoerce\u003c/span\u003e().\u003cspan class=\"pl-en\"\u003egetA\u003c/span\u003e().\u003cspan class=\"pl-en\"\u003eapply\u003c/span\u003e(\u003cspan class=\"pl-en\"\u003egetA\u003c/span\u003e()));\n }\n}\n\n\u003cspan class=\"pl-smi\"\u003eFn2\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e\u0026gt; \u003cspan class=\"pl-s1\"\u003eadd\u003c/span\u003e = (\u003cspan class=\"pl-s1\"\u003ex\u003c/span\u003e, \u003cspan class=\"pl-s1\"\u003ey\u003c/span\u003e) -\u0026gt; \u003cspan class=\"pl-s1\"\u003ex\u003c/span\u003e + \u003cspan class=\"pl-s1\"\u003ey\u003c/span\u003e;\n\u003cspan class=\"pl-smi\"\u003eSlot\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e\u0026gt; \u003cspan class=\"pl-s1\"\u003ex\u003c/span\u003e = \u003cspan class=\"pl-k\"\u003enew\u003c/span\u003e \u003cspan class=\"pl-smi\"\u003eSlot\u003c/span\u003e\u0026lt;\u0026gt;(\u003cspan class=\"pl-c1\"\u003e1\u003c/span\u003e);\n\u003cspan class=\"pl-smi\"\u003eSlot\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e\u0026gt; \u003cspan class=\"pl-s1\"\u003ey\u003c/span\u003e = \u003cspan class=\"pl-k\"\u003enew\u003c/span\u003e \u003cspan class=\"pl-smi\"\u003eSlot\u003c/span\u003e\u0026lt;\u0026gt;(\u003cspan class=\"pl-c1\"\u003e2\u003c/span\u003e);\n\u003cspan class=\"pl-smi\"\u003eSlot\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e\u0026gt; \u003cspan class=\"pl-s1\"\u003ez\u003c/span\u003e = \u003cspan class=\"pl-s1\"\u003ey\u003c/span\u003e.\u003cspan class=\"pl-en\"\u003ezip\u003c/span\u003e(\u003cspan class=\"pl-s1\"\u003ex\u003c/span\u003e.\u003cspan class=\"pl-en\"\u003efmap\u003c/span\u003e(\u003cspan class=\"pl-s1\"\u003eadd\u003c/span\u003e)); \u003cspan class=\"pl-c\"\u003e//-\u0026gt; Slot{a=3}\u003c/span\u003e\u003c/pre\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eExamples of applicative functors include:\u003c/p\u003e\n\u003cul dir=\"auto\"\u003e\n\u003cli\u003e\u003ccode\u003eFn*\u003c/code\u003e, \u003ccode\u003eSemigroup\u003c/code\u003e, and \u003ccode\u003eMonoid\u003c/code\u003e\u003c/li\u003e\n\u003cli\u003e\u003ccode\u003eSingletonHList\u003c/code\u003e and \u003ccode\u003eTuple*\u003c/code\u003e\u003c/li\u003e\n\u003cli\u003e\u003ccode\u003eChoice*\u003c/code\u003e\u003c/li\u003e\n\u003cli\u003e\u003ccode\u003eEither\u003c/code\u003e\u003c/li\u003e\n\u003cli\u003e\u003ccode\u003eConst\u003c/code\u003e, \u003ccode\u003eIdentity\u003c/code\u003e, and \u003ccode\u003eCompose\u003c/code\u003e\u003c/li\u003e\n\u003cli\u003e\u003ccode\u003eLens\u003c/code\u003e\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp dir=\"auto\"\u003eIn addition to implementing \u003ccode\u003efmap\u003c/code\u003e from \u003ccode\u003eFunctor\u003c/code\u003e, implementing an applicative functor involves providing two methods: \u003ccode\u003epure\u003c/code\u003e, a method that lifts a value into the functor; and \u003ccode\u003ezip\u003c/code\u003e, a method that applies a lifted function to a lifted value, returning a new lifted value. As usual, there are \u003ca href=\"https://hackage.haskell.org/package/base-4.9.1.0/docs/Control-Applicative.html\" rel=\"nofollow\"\u003esome laws\u003c/a\u003e that should be adhered to.\u003c/p\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch3 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003e\u003ca name=\"user-content-monads\"\u003eMonads\u003c/a\u003e\u003c/h3\u003e\u003ca id=\"user-content-monads\" class=\"anchor\" aria-label=\"Permalink: Monads\" href=\"#monads\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eMonads are applicative functors that additionally support a chaining operation, \u003ccode\u003eflatMap :: (a -\u0026gt; f b) -\u0026gt; f a -\u0026gt; f b\u003c/code\u003e: a function from the functor's parameter to a new instance of the same functor over a potentially different parameter. Because the function passed to \u003ccode\u003eflatMap\u003c/code\u003e can return a different instance of the same functor, functors can take advantage of multiple constructions that yield different functorial operations, like short-circuiting, as in the following example using \u003ccode\u003eEither\u003c/code\u003e:\u003c/p\u003e\n\u003cdiv class=\"highlight highlight-source-java notranslate position-relative overflow-auto\" dir=\"auto\" data-snippet-clipboard-copy-content=\"class Person {\n Optional\u0026lt;Occupation\u0026gt; occupation() {\n return Optional.empty();\n } \n}\n\nclass Occupation {\n}\n\npublic static void main(String[] args) {\n Fn1\u0026lt;String, Either\u0026lt;String, Integer\u0026gt;\u0026gt; parseId = str -\u0026gt; Either.trying(() -\u0026gt; Integer.parseInt(str), __ -\u0026gt; str + \u0026quot; is not a valid id\u0026quot;); \n\n Map\u0026lt;Integer, Person\u0026gt; database = new HashMap\u0026lt;\u0026gt;();\n Fn1\u0026lt;Integer, Either\u0026lt;String, Person\u0026gt;\u0026gt; lookupById = id -\u0026gt; Either.fromOptional(Optional.ofNullable(database.get(id)),\n () -\u0026gt; \u0026quot;No person found for id \u0026quot; + id);\n Fn1\u0026lt;Person, Either\u0026lt;String, Occupation\u0026gt;\u0026gt; getOccupation = p -\u0026gt; Either.fromOptional(p.occupation(), () -\u0026gt; \u0026quot;Person was unemployed\u0026quot;);\n\n Either\u0026lt;String, Occupation\u0026gt; occupationOrError = \n parseId.apply(\u0026quot;12\u0026quot;) // Either\u0026lt;String, Integer\u0026gt;\n .flatMap(lookupById) // Either\u0026lt;String, Person\u0026gt;\n .flatMap(getOccupation); // Either\u0026lt;String, Occupation\u0026gt;\n}\"\u003e\u003cpre\u003e\u003cspan class=\"pl-k\"\u003eclass\u003c/span\u003e \u003cspan class=\"pl-smi\"\u003ePerson\u003c/span\u003e {\n \u003cspan class=\"pl-smi\"\u003eOptional\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eOccupation\u003c/span\u003e\u0026gt; \u003cspan class=\"pl-en\"\u003eoccupation\u003c/span\u003e() {\n \u003cspan class=\"pl-k\"\u003ereturn\u003c/span\u003e \u003cspan class=\"pl-smi\"\u003eOptional\u003c/span\u003e.\u003cspan class=\"pl-en\"\u003eempty\u003c/span\u003e();\n } \n}\n\n\u003cspan class=\"pl-k\"\u003eclass\u003c/span\u003e \u003cspan class=\"pl-smi\"\u003eOccupation\u003c/span\u003e {\n}\n\n\u003cspan class=\"pl-k\"\u003epublic\u003c/span\u003e \u003cspan class=\"pl-k\"\u003estatic\u003c/span\u003e \u003cspan class=\"pl-smi\"\u003evoid\u003c/span\u003e \u003cspan class=\"pl-en\"\u003emain\u003c/span\u003e(\u003cspan class=\"pl-smi\"\u003eString\u003c/span\u003e[] \u003cspan class=\"pl-s1\"\u003eargs\u003c/span\u003e) {\n \u003cspan class=\"pl-smi\"\u003eFn1\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eString\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003eEither\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eString\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e\u0026gt;\u0026gt; \u003cspan class=\"pl-s1\"\u003eparseId\u003c/span\u003e = \u003cspan class=\"pl-s1\"\u003estr\u003c/span\u003e -\u0026gt; \u003cspan class=\"pl-smi\"\u003eEither\u003c/span\u003e.\u003cspan class=\"pl-en\"\u003etrying\u003c/span\u003e(() -\u0026gt; \u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e.\u003cspan class=\"pl-en\"\u003eparseInt\u003c/span\u003e(\u003cspan class=\"pl-s1\"\u003estr\u003c/span\u003e), \u003cspan class=\"pl-s1\"\u003e__\u003c/span\u003e -\u0026gt; \u003cspan class=\"pl-s1\"\u003estr\u003c/span\u003e + \u003cspan class=\"pl-s\"\u003e\" is not a valid id\"\u003c/span\u003e); \n\n \u003cspan class=\"pl-smi\"\u003eMap\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003ePerson\u003c/span\u003e\u0026gt; \u003cspan class=\"pl-s1\"\u003edatabase\u003c/span\u003e = \u003cspan class=\"pl-k\"\u003enew\u003c/span\u003e \u003cspan class=\"pl-smi\"\u003eHashMap\u003c/span\u003e\u0026lt;\u0026gt;();\n \u003cspan class=\"pl-smi\"\u003eFn1\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003eEither\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eString\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003ePerson\u003c/span\u003e\u0026gt;\u0026gt; \u003cspan class=\"pl-s1\"\u003elookupById\u003c/span\u003e = \u003cspan class=\"pl-s1\"\u003eid\u003c/span\u003e -\u0026gt; \u003cspan class=\"pl-smi\"\u003eEither\u003c/span\u003e.\u003cspan class=\"pl-en\"\u003efromOptional\u003c/span\u003e(\u003cspan class=\"pl-smi\"\u003eOptional\u003c/span\u003e.\u003cspan class=\"pl-en\"\u003eofNullable\u003c/span\u003e(\u003cspan class=\"pl-s1\"\u003edatabase\u003c/span\u003e.\u003cspan class=\"pl-en\"\u003eget\u003c/span\u003e(\u003cspan class=\"pl-s1\"\u003eid\u003c/span\u003e)),\n () -\u0026gt; \u003cspan class=\"pl-s\"\u003e\"No person found for id \"\u003c/span\u003e + \u003cspan class=\"pl-s1\"\u003eid\u003c/span\u003e);\n \u003cspan class=\"pl-smi\"\u003eFn1\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003ePerson\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003eEither\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eString\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003eOccupation\u003c/span\u003e\u0026gt;\u0026gt; \u003cspan class=\"pl-s1\"\u003egetOccupation\u003c/span\u003e = \u003cspan class=\"pl-s1\"\u003ep\u003c/span\u003e -\u0026gt; \u003cspan class=\"pl-smi\"\u003eEither\u003c/span\u003e.\u003cspan class=\"pl-en\"\u003efromOptional\u003c/span\u003e(\u003cspan class=\"pl-s1\"\u003ep\u003c/span\u003e.\u003cspan class=\"pl-en\"\u003eoccupation\u003c/span\u003e(), () -\u0026gt; \u003cspan class=\"pl-s\"\u003e\"Person was unemployed\"\u003c/span\u003e);\n\n \u003cspan class=\"pl-smi\"\u003eEither\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eString\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003eOccupation\u003c/span\u003e\u0026gt; \u003cspan class=\"pl-s1\"\u003eoccupationOrError\u003c/span\u003e = \n \u003cspan class=\"pl-s1\"\u003eparseId\u003c/span\u003e.\u003cspan class=\"pl-en\"\u003eapply\u003c/span\u003e(\u003cspan class=\"pl-s\"\u003e\"12\"\u003c/span\u003e) \u003cspan class=\"pl-c\"\u003e// Either\u0026lt;String, Integer\u0026gt;\u003c/span\u003e\n .\u003cspan class=\"pl-en\"\u003eflatMap\u003c/span\u003e(\u003cspan class=\"pl-s1\"\u003elookupById\u003c/span\u003e) \u003cspan class=\"pl-c\"\u003e// Either\u0026lt;String, Person\u0026gt;\u003c/span\u003e\n .\u003cspan class=\"pl-en\"\u003eflatMap\u003c/span\u003e(\u003cspan class=\"pl-s1\"\u003egetOccupation\u003c/span\u003e); \u003cspan class=\"pl-c\"\u003e// Either\u0026lt;String, Occupation\u0026gt;\u003c/span\u003e\n}\u003c/pre\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eIn the previous example, if any of \u003ccode\u003eparseId\u003c/code\u003e, \u003ccode\u003elookupById\u003c/code\u003e, or \u003ccode\u003egetOccupation\u003c/code\u003e fail, no further \u003ccode\u003eflatMap\u003c/code\u003e computations can succeed, so the result short-circuits to the first \u003ccode\u003eleft\u003c/code\u003e value that is returned. This is completely predictable from the type signature of \u003ccode\u003eMonad\u003c/code\u003e and \u003ccode\u003eEither\u003c/code\u003e: \u003ccode\u003eEither\u0026lt;L, R\u0026gt;\u003c/code\u003e is a \u003ccode\u003eMonad\u0026lt;R\u0026gt;\u003c/code\u003e, so the single arity \u003ccode\u003eflatMap\u003c/code\u003e can have nothing to map in the case where there is no \u003ccode\u003eR\u003c/code\u003e value. With experience, it generally becomes quickly clear what the logical behavior of \u003ccode\u003eflatMap\u003c/code\u003e \u003cem\u003emust\u003c/em\u003e be given the type signatures.\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eThat's it. Monads are neither \u003ca href=\"http://james-iry.blogspot.com/2007/09/monads-are-elephants-part-1.html\" rel=\"nofollow\"\u003eelephants\u003c/a\u003e nor are they \u003ca href=\"https://blog.plover.com/prog/burritos.html\" rel=\"nofollow\"\u003eburritos\u003c/a\u003e; they're simply types that support a) the ability to lift a value into them, and b) a chaining function \u003ccode\u003eflatMap :: (a -\u0026gt; f b) -\u0026gt; f a -\u0026gt; f b\u003c/code\u003e that can potentially return different instances of the same monad. If a type can do those two things (and obeys \u003ca href=\"https://wiki.haskell.org/Monad_laws\" rel=\"nofollow\"\u003ethe laws\u003c/a\u003e), it is a monad.\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eFurther, if a type is a monad, it is necessarily an \u003ccode\u003eApplicative\u003c/code\u003e, which makes it necessarily a \u003ccode\u003eFunctor\u003c/code\u003e, so \u003cem\u003elambda\u003c/em\u003e enforces this tautology via a hierarchical constraint.\u003c/p\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch3 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003e\u003ca name=\"user-content-traversables\"\u003eTraversables\u003c/a\u003e\u003c/h3\u003e\u003ca id=\"user-content-traversables\" class=\"anchor\" aria-label=\"Permalink: Traversables\" href=\"#traversables\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eTraversable functors -- functors that can be \"traversed from left to right\" -- are implemented via the \u003ccode\u003eTraversable\u003c/code\u003e interface.\u003c/p\u003e\n\u003cdiv class=\"highlight highlight-source-java notranslate position-relative overflow-auto\" dir=\"auto\" data-snippet-clipboard-copy-content=\"public abstract class Maybe\u0026lt;A\u0026gt; implements Traversable\u0026lt;A, Maybe\u0026gt; {\n private Maybe() {\n }\n\n @Override\n public abstract \u0026lt;B, App extends Applicative\u0026gt; Applicative\u0026lt;Maybe\u0026lt;B\u0026gt;, App\u0026gt; traverse(\n Function\u0026lt;? super A, ? extends Applicative\u0026lt;B, App\u0026gt;\u0026gt; fn,\n Function\u0026lt;? super Traversable\u0026lt;B, Maybe\u0026gt;, ? extends Applicative\u0026lt;? extends Traversable\u0026lt;B, Maybe\u0026gt;, App\u0026gt;\u0026gt; pure);\n\n @Override\n public abstract \u0026lt;B\u0026gt; Maybe\u0026lt;B\u0026gt; fmap(Function\u0026lt;? super A, ? extends B\u0026gt; fn);\n\n private static final class Just\u0026lt;A\u0026gt; extends Maybe\u0026lt;A\u0026gt; {\n private final A a;\n\n private Just(A a) {\n this.a = a;\n }\n\n @Override\n public \u0026lt;B, App extends Applicative\u0026gt; Applicative\u0026lt;Maybe\u0026lt;B\u0026gt;, App\u0026gt; traverse(\n Function\u0026lt;? super A, ? extends Applicative\u0026lt;B, App\u0026gt;\u0026gt; fn,\n Function\u0026lt;? super Traversable\u0026lt;B, Maybe\u0026gt;, ? extends Applicative\u0026lt;? extends Traversable\u0026lt;B, Maybe\u0026gt;, App\u0026gt;\u0026gt; pure) {\n return fn.apply(a).fmap(Just::new);\n }\n\n @Override\n public \u0026lt;B\u0026gt; Maybe\u0026lt;B\u0026gt; fmap(Function\u0026lt;? super A, ? extends B\u0026gt; fn) {\n return new Just\u0026lt;\u0026gt;(fn.apply(a));\n }\n }\n\n private static final class Nothing\u0026lt;A\u0026gt; extends Maybe\u0026lt;A\u0026gt; {\n @Override\n @SuppressWarnings(\u0026quot;unchecked\u0026quot;)\n public \u0026lt;B, App extends Applicative\u0026gt; Applicative\u0026lt;Maybe\u0026lt;B\u0026gt;, App\u0026gt; traverse(\n Function\u0026lt;? super A, ? extends Applicative\u0026lt;B, App\u0026gt;\u0026gt; fn,\n Function\u0026lt;? super Traversable\u0026lt;B, Maybe\u0026gt;, ? extends Applicative\u0026lt;? extends Traversable\u0026lt;B, Maybe\u0026gt;, App\u0026gt;\u0026gt; pure) {\n return pure.apply((Maybe\u0026lt;B\u0026gt;) this).fmap(x -\u0026gt; (Maybe\u0026lt;B\u0026gt;) x);\n }\n\n @Override\n @SuppressWarnings(\u0026quot;unchecked\u0026quot;)\n public \u0026lt;B\u0026gt; Maybe\u0026lt;B\u0026gt; fmap(Function\u0026lt;? super A, ? extends B\u0026gt; fn) {\n return (Maybe\u0026lt;B\u0026gt;) this;\n }\n }\n}\n\nMaybe\u0026lt;Integer\u0026gt; just1 = Maybe.just(1);\nMaybe\u0026lt;Integer\u0026gt; nothing = Maybe.nothing();\n\nEither\u0026lt;String, Maybe\u0026lt;Integer\u0026gt;\u0026gt; traversedJust = just1.traverse(x -\u0026gt; right(x + 1), empty -\u0026gt; left(\u0026quot;empty\u0026quot;))\n .fmap(x -\u0026gt; (Maybe\u0026lt;Integer\u0026gt;) x)\n .coerce(); //-\u0026gt; Right(Just(2))\n\nEither\u0026lt;String, Maybe\u0026lt;Integer\u0026gt;\u0026gt; traversedNothing = nothing.traverse(x -\u0026gt; right(x + 1), empty -\u0026gt; left(\u0026quot;empty\u0026quot;))\n .fmap(x -\u0026gt; (Maybe\u0026lt;Integer\u0026gt;) x)\n .coerce(); //-\u0026gt; Left(\u0026quot;empty\u0026quot;)\"\u003e\u003cpre\u003e\u003cspan class=\"pl-k\"\u003epublic\u003c/span\u003e \u003cspan class=\"pl-k\"\u003eabstract\u003c/span\u003e \u003cspan class=\"pl-k\"\u003eclass\u003c/span\u003e \u003cspan class=\"pl-smi\"\u003eMaybe\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eA\u003c/span\u003e\u0026gt; \u003cspan class=\"pl-k\"\u003eimplements\u003c/span\u003e \u003cspan class=\"pl-smi\"\u003eTraversable\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eA\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003eMaybe\u003c/span\u003e\u0026gt; {\n \u003cspan class=\"pl-k\"\u003eprivate\u003c/span\u003e \u003cspan class=\"pl-smi\"\u003eMaybe\u003c/span\u003e() {\n }\n\n \u003cspan class=\"pl-c1\"\u003e@\u003c/span\u003e\u003cspan class=\"pl-c1\"\u003eOverride\u003c/span\u003e\n \u003cspan class=\"pl-k\"\u003epublic\u003c/span\u003e \u003cspan class=\"pl-k\"\u003eabstract\u003c/span\u003e \u0026lt;\u003cspan class=\"pl-smi\"\u003eB\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003eApp\u003c/span\u003e \u003cspan class=\"pl-k\"\u003eextends\u003c/span\u003e \u003cspan class=\"pl-smi\"\u003eApplicative\u003c/span\u003e\u0026gt; \u003cspan class=\"pl-smi\"\u003eApplicative\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eMaybe\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eB\u003c/span\u003e\u0026gt;, \u003cspan class=\"pl-smi\"\u003eApp\u003c/span\u003e\u0026gt; \u003cspan class=\"pl-en\"\u003etraverse\u003c/span\u003e(\n \u003cspan class=\"pl-smi\"\u003eFunction\u003c/span\u003e\u0026lt;? \u003cspan class=\"pl-en\"\u003esuper\u003c/span\u003e \u003cspan class=\"pl-smi\"\u003eA\u003c/span\u003e, ? \u003cspan class=\"pl-k\"\u003eextends\u003c/span\u003e \u003cspan class=\"pl-smi\"\u003eApplicative\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eB\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003eApp\u003c/span\u003e\u0026gt;\u0026gt; \u003cspan class=\"pl-s1\"\u003efn\u003c/span\u003e,\n \u003cspan class=\"pl-smi\"\u003eFunction\u003c/span\u003e\u0026lt;? \u003cspan class=\"pl-en\"\u003esuper\u003c/span\u003e \u003cspan class=\"pl-smi\"\u003eTraversable\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eB\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003eMaybe\u003c/span\u003e\u0026gt;, ? \u003cspan class=\"pl-k\"\u003eextends\u003c/span\u003e \u003cspan class=\"pl-smi\"\u003eApplicative\u003c/span\u003e\u0026lt;? \u003cspan class=\"pl-k\"\u003eextends\u003c/span\u003e \u003cspan class=\"pl-smi\"\u003eTraversable\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eB\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003eMaybe\u003c/span\u003e\u0026gt;, \u003cspan class=\"pl-smi\"\u003eApp\u003c/span\u003e\u0026gt;\u0026gt; \u003cspan class=\"pl-s1\"\u003epure\u003c/span\u003e);\n\n \u003cspan class=\"pl-c1\"\u003e@\u003c/span\u003e\u003cspan class=\"pl-c1\"\u003eOverride\u003c/span\u003e\n \u003cspan class=\"pl-k\"\u003epublic\u003c/span\u003e \u003cspan class=\"pl-k\"\u003eabstract\u003c/span\u003e \u0026lt;\u003cspan class=\"pl-smi\"\u003eB\u003c/span\u003e\u0026gt; \u003cspan class=\"pl-smi\"\u003eMaybe\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eB\u003c/span\u003e\u0026gt; \u003cspan class=\"pl-en\"\u003efmap\u003c/span\u003e(\u003cspan class=\"pl-smi\"\u003eFunction\u003c/span\u003e\u0026lt;? \u003cspan class=\"pl-en\"\u003esuper\u003c/span\u003e \u003cspan class=\"pl-smi\"\u003eA\u003c/span\u003e, ? \u003cspan class=\"pl-k\"\u003eextends\u003c/span\u003e \u003cspan class=\"pl-smi\"\u003eB\u003c/span\u003e\u0026gt; \u003cspan class=\"pl-s1\"\u003efn\u003c/span\u003e);\n\n \u003cspan class=\"pl-k\"\u003eprivate\u003c/span\u003e \u003cspan class=\"pl-k\"\u003estatic\u003c/span\u003e \u003cspan class=\"pl-k\"\u003efinal\u003c/span\u003e \u003cspan class=\"pl-k\"\u003eclass\u003c/span\u003e \u003cspan class=\"pl-smi\"\u003eJust\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eA\u003c/span\u003e\u0026gt; \u003cspan class=\"pl-k\"\u003eextends\u003c/span\u003e \u003cspan class=\"pl-smi\"\u003eMaybe\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eA\u003c/span\u003e\u0026gt; {\n \u003cspan class=\"pl-k\"\u003eprivate\u003c/span\u003e \u003cspan class=\"pl-k\"\u003efinal\u003c/span\u003e \u003cspan class=\"pl-smi\"\u003eA\u003c/span\u003e \u003cspan class=\"pl-s1\"\u003ea\u003c/span\u003e;\n\n \u003cspan class=\"pl-k\"\u003eprivate\u003c/span\u003e \u003cspan class=\"pl-smi\"\u003eJust\u003c/span\u003e(\u003cspan class=\"pl-smi\"\u003eA\u003c/span\u003e \u003cspan class=\"pl-s1\"\u003ea\u003c/span\u003e) {\n \u003cspan class=\"pl-smi\"\u003ethis\u003c/span\u003e.\u003cspan class=\"pl-s1\"\u003ea\u003c/span\u003e = \u003cspan class=\"pl-s1\"\u003ea\u003c/span\u003e;\n }\n\n \u003cspan class=\"pl-c1\"\u003e@\u003c/span\u003e\u003cspan class=\"pl-c1\"\u003eOverride\u003c/span\u003e\n \u003cspan class=\"pl-k\"\u003epublic\u003c/span\u003e \u0026lt;\u003cspan class=\"pl-smi\"\u003eB\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003eApp\u003c/span\u003e \u003cspan class=\"pl-k\"\u003eextends\u003c/span\u003e \u003cspan class=\"pl-smi\"\u003eApplicative\u003c/span\u003e\u0026gt; \u003cspan class=\"pl-smi\"\u003eApplicative\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eMaybe\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eB\u003c/span\u003e\u0026gt;, \u003cspan class=\"pl-smi\"\u003eApp\u003c/span\u003e\u0026gt; \u003cspan class=\"pl-en\"\u003etraverse\u003c/span\u003e(\n \u003cspan class=\"pl-smi\"\u003eFunction\u003c/span\u003e\u0026lt;? \u003cspan class=\"pl-en\"\u003esuper\u003c/span\u003e \u003cspan class=\"pl-smi\"\u003eA\u003c/span\u003e, ? \u003cspan class=\"pl-k\"\u003eextends\u003c/span\u003e \u003cspan class=\"pl-smi\"\u003eApplicative\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eB\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003eApp\u003c/span\u003e\u0026gt;\u0026gt; \u003cspan class=\"pl-s1\"\u003efn\u003c/span\u003e,\n \u003cspan class=\"pl-smi\"\u003eFunction\u003c/span\u003e\u0026lt;? \u003cspan class=\"pl-en\"\u003esuper\u003c/span\u003e \u003cspan class=\"pl-smi\"\u003eTraversable\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eB\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003eMaybe\u003c/span\u003e\u0026gt;, ? \u003cspan class=\"pl-k\"\u003eextends\u003c/span\u003e \u003cspan class=\"pl-smi\"\u003eApplicative\u003c/span\u003e\u0026lt;? \u003cspan class=\"pl-k\"\u003eextends\u003c/span\u003e \u003cspan class=\"pl-smi\"\u003eTraversable\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eB\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003eMaybe\u003c/span\u003e\u0026gt;, \u003cspan class=\"pl-smi\"\u003eApp\u003c/span\u003e\u0026gt;\u0026gt; \u003cspan class=\"pl-s1\"\u003epure\u003c/span\u003e) {\n \u003cspan class=\"pl-k\"\u003ereturn\u003c/span\u003e \u003cspan class=\"pl-s1\"\u003efn\u003c/span\u003e.\u003cspan class=\"pl-en\"\u003eapply\u003c/span\u003e(\u003cspan class=\"pl-s1\"\u003ea\u003c/span\u003e).\u003cspan class=\"pl-en\"\u003efmap\u003c/span\u003e(\u003cspan class=\"pl-smi\"\u003eJust\u003c/span\u003e::\u003cspan class=\"pl-k\"\u003enew\u003c/span\u003e);\n }\n\n \u003cspan class=\"pl-c1\"\u003e@\u003c/span\u003e\u003cspan class=\"pl-c1\"\u003eOverride\u003c/span\u003e\n \u003cspan class=\"pl-k\"\u003epublic\u003c/span\u003e \u0026lt;\u003cspan class=\"pl-smi\"\u003eB\u003c/span\u003e\u0026gt; \u003cspan class=\"pl-smi\"\u003eMaybe\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eB\u003c/span\u003e\u0026gt; \u003cspan class=\"pl-en\"\u003efmap\u003c/span\u003e(\u003cspan class=\"pl-smi\"\u003eFunction\u003c/span\u003e\u0026lt;? \u003cspan class=\"pl-en\"\u003esuper\u003c/span\u003e \u003cspan class=\"pl-smi\"\u003eA\u003c/span\u003e, ? \u003cspan class=\"pl-k\"\u003eextends\u003c/span\u003e \u003cspan class=\"pl-smi\"\u003eB\u003c/span\u003e\u0026gt; \u003cspan class=\"pl-s1\"\u003efn\u003c/span\u003e) {\n \u003cspan class=\"pl-k\"\u003ereturn\u003c/span\u003e \u003cspan class=\"pl-k\"\u003enew\u003c/span\u003e \u003cspan class=\"pl-smi\"\u003eJust\u003c/span\u003e\u0026lt;\u0026gt;(\u003cspan class=\"pl-s1\"\u003efn\u003c/span\u003e.\u003cspan class=\"pl-en\"\u003eapply\u003c/span\u003e(\u003cspan class=\"pl-s1\"\u003ea\u003c/span\u003e));\n }\n }\n\n \u003cspan class=\"pl-k\"\u003eprivate\u003c/span\u003e \u003cspan class=\"pl-k\"\u003estatic\u003c/span\u003e \u003cspan class=\"pl-k\"\u003efinal\u003c/span\u003e \u003cspan class=\"pl-k\"\u003eclass\u003c/span\u003e \u003cspan class=\"pl-smi\"\u003eNothing\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eA\u003c/span\u003e\u0026gt; \u003cspan class=\"pl-k\"\u003eextends\u003c/span\u003e \u003cspan class=\"pl-smi\"\u003eMaybe\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eA\u003c/span\u003e\u0026gt; {\n \u003cspan class=\"pl-c1\"\u003e@\u003c/span\u003e\u003cspan class=\"pl-c1\"\u003eOverride\u003c/span\u003e\n \u003cspan class=\"pl-c1\"\u003e@\u003c/span\u003e\u003cspan class=\"pl-c1\"\u003eSuppressWarnings\u003c/span\u003e(\u003cspan class=\"pl-s\"\u003e\"unchecked\"\u003c/span\u003e)\n \u003cspan class=\"pl-k\"\u003epublic\u003c/span\u003e \u0026lt;\u003cspan class=\"pl-smi\"\u003eB\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003eApp\u003c/span\u003e \u003cspan class=\"pl-k\"\u003eextends\u003c/span\u003e \u003cspan class=\"pl-smi\"\u003eApplicative\u003c/span\u003e\u0026gt; \u003cspan class=\"pl-smi\"\u003eApplicative\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eMaybe\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eB\u003c/span\u003e\u0026gt;, \u003cspan class=\"pl-smi\"\u003eApp\u003c/span\u003e\u0026gt; \u003cspan class=\"pl-en\"\u003etraverse\u003c/span\u003e(\n \u003cspan class=\"pl-smi\"\u003eFunction\u003c/span\u003e\u0026lt;? \u003cspan class=\"pl-en\"\u003esuper\u003c/span\u003e \u003cspan class=\"pl-smi\"\u003eA\u003c/span\u003e, ? \u003cspan class=\"pl-k\"\u003eextends\u003c/span\u003e \u003cspan class=\"pl-smi\"\u003eApplicative\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eB\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003eApp\u003c/span\u003e\u0026gt;\u0026gt; \u003cspan class=\"pl-s1\"\u003efn\u003c/span\u003e,\n \u003cspan class=\"pl-smi\"\u003eFunction\u003c/span\u003e\u0026lt;? \u003cspan class=\"pl-en\"\u003esuper\u003c/span\u003e \u003cspan class=\"pl-smi\"\u003eTraversable\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eB\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003eMaybe\u003c/span\u003e\u0026gt;, ? \u003cspan class=\"pl-k\"\u003eextends\u003c/span\u003e \u003cspan class=\"pl-smi\"\u003eApplicative\u003c/span\u003e\u0026lt;? \u003cspan class=\"pl-k\"\u003eextends\u003c/span\u003e \u003cspan class=\"pl-smi\"\u003eTraversable\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eB\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003eMaybe\u003c/span\u003e\u0026gt;, \u003cspan class=\"pl-smi\"\u003eApp\u003c/span\u003e\u0026gt;\u0026gt; \u003cspan class=\"pl-s1\"\u003epure\u003c/span\u003e) {\n \u003cspan class=\"pl-k\"\u003ereturn\u003c/span\u003e \u003cspan class=\"pl-s1\"\u003epure\u003c/span\u003e.\u003cspan class=\"pl-en\"\u003eapply\u003c/span\u003e((\u003cspan class=\"pl-smi\"\u003eMaybe\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eB\u003c/span\u003e\u0026gt;) \u003cspan class=\"pl-smi\"\u003ethis\u003c/span\u003e).\u003cspan class=\"pl-en\"\u003efmap\u003c/span\u003e(\u003cspan class=\"pl-s1\"\u003ex\u003c/span\u003e -\u0026gt; (\u003cspan class=\"pl-smi\"\u003eMaybe\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eB\u003c/span\u003e\u0026gt;) \u003cspan class=\"pl-s1\"\u003ex\u003c/span\u003e);\n }\n\n \u003cspan class=\"pl-c1\"\u003e@\u003c/span\u003e\u003cspan class=\"pl-c1\"\u003eOverride\u003c/span\u003e\n \u003cspan class=\"pl-c1\"\u003e@\u003c/span\u003e\u003cspan class=\"pl-c1\"\u003eSuppressWarnings\u003c/span\u003e(\u003cspan class=\"pl-s\"\u003e\"unchecked\"\u003c/span\u003e)\n \u003cspan class=\"pl-k\"\u003epublic\u003c/span\u003e \u0026lt;\u003cspan class=\"pl-smi\"\u003eB\u003c/span\u003e\u0026gt; \u003cspan class=\"pl-smi\"\u003eMaybe\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eB\u003c/span\u003e\u0026gt; \u003cspan class=\"pl-en\"\u003efmap\u003c/span\u003e(\u003cspan class=\"pl-smi\"\u003eFunction\u003c/span\u003e\u0026lt;? \u003cspan class=\"pl-en\"\u003esuper\u003c/span\u003e \u003cspan class=\"pl-smi\"\u003eA\u003c/span\u003e, ? \u003cspan class=\"pl-k\"\u003eextends\u003c/span\u003e \u003cspan class=\"pl-smi\"\u003eB\u003c/span\u003e\u0026gt; \u003cspan class=\"pl-s1\"\u003efn\u003c/span\u003e) {\n \u003cspan class=\"pl-k\"\u003ereturn\u003c/span\u003e (\u003cspan class=\"pl-smi\"\u003eMaybe\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eB\u003c/span\u003e\u0026gt;) \u003cspan class=\"pl-smi\"\u003ethis\u003c/span\u003e;\n }\n }\n}\n\n\u003cspan class=\"pl-smi\"\u003eMaybe\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e\u0026gt; \u003cspan class=\"pl-s1\"\u003ejust1\u003c/span\u003e = \u003cspan class=\"pl-smi\"\u003eMaybe\u003c/span\u003e.\u003cspan class=\"pl-en\"\u003ejust\u003c/span\u003e(\u003cspan class=\"pl-c1\"\u003e1\u003c/span\u003e);\n\u003cspan class=\"pl-smi\"\u003eMaybe\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e\u0026gt; \u003cspan class=\"pl-s1\"\u003enothing\u003c/span\u003e = \u003cspan class=\"pl-smi\"\u003eMaybe\u003c/span\u003e.\u003cspan class=\"pl-en\"\u003enothing\u003c/span\u003e();\n\n\u003cspan class=\"pl-smi\"\u003eEither\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eString\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003eMaybe\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e\u0026gt;\u0026gt; \u003cspan class=\"pl-s1\"\u003etraversedJust\u003c/span\u003e = \u003cspan class=\"pl-s1\"\u003ejust1\u003c/span\u003e.\u003cspan class=\"pl-en\"\u003etraverse\u003c/span\u003e(\u003cspan class=\"pl-s1\"\u003ex\u003c/span\u003e -\u0026gt; \u003cspan class=\"pl-en\"\u003eright\u003c/span\u003e(\u003cspan class=\"pl-s1\"\u003ex\u003c/span\u003e + \u003cspan class=\"pl-c1\"\u003e1\u003c/span\u003e), \u003cspan class=\"pl-s1\"\u003eempty\u003c/span\u003e -\u0026gt; \u003cspan class=\"pl-en\"\u003eleft\u003c/span\u003e(\u003cspan class=\"pl-s\"\u003e\"empty\"\u003c/span\u003e))\n .\u003cspan class=\"pl-en\"\u003efmap\u003c/span\u003e(\u003cspan class=\"pl-s1\"\u003ex\u003c/span\u003e -\u0026gt; (\u003cspan class=\"pl-smi\"\u003eMaybe\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e\u0026gt;) \u003cspan class=\"pl-s1\"\u003ex\u003c/span\u003e)\n .\u003cspan class=\"pl-en\"\u003ecoerce\u003c/span\u003e(); \u003cspan class=\"pl-c\"\u003e//-\u0026gt; Right(Just(2))\u003c/span\u003e\n\n\u003cspan class=\"pl-smi\"\u003eEither\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eString\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003eMaybe\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e\u0026gt;\u0026gt; \u003cspan class=\"pl-s1\"\u003etraversedNothing\u003c/span\u003e = \u003cspan class=\"pl-s1\"\u003enothing\u003c/span\u003e.\u003cspan class=\"pl-en\"\u003etraverse\u003c/span\u003e(\u003cspan class=\"pl-s1\"\u003ex\u003c/span\u003e -\u0026gt; \u003cspan class=\"pl-en\"\u003eright\u003c/span\u003e(\u003cspan class=\"pl-s1\"\u003ex\u003c/span\u003e + \u003cspan class=\"pl-c1\"\u003e1\u003c/span\u003e), \u003cspan class=\"pl-s1\"\u003eempty\u003c/span\u003e -\u0026gt; \u003cspan class=\"pl-en\"\u003eleft\u003c/span\u003e(\u003cspan class=\"pl-s\"\u003e\"empty\"\u003c/span\u003e))\n .\u003cspan class=\"pl-en\"\u003efmap\u003c/span\u003e(\u003cspan class=\"pl-s1\"\u003ex\u003c/span\u003e -\u0026gt; (\u003cspan class=\"pl-smi\"\u003eMaybe\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e\u0026gt;) \u003cspan class=\"pl-s1\"\u003ex\u003c/span\u003e)\n .\u003cspan class=\"pl-en\"\u003ecoerce\u003c/span\u003e(); \u003cspan class=\"pl-c\"\u003e//-\u0026gt; Left(\"empty\")\u003c/span\u003e\u003c/pre\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eExamples of traversable functors include:\u003c/p\u003e\n\u003cul dir=\"auto\"\u003e\n\u003cli\u003e\u003ccode\u003eSingletonHList\u003c/code\u003e and \u003ccode\u003eTuple*\u003c/code\u003e\u003c/li\u003e\n\u003cli\u003e\u003ccode\u003eChoice*\u003c/code\u003e\u003c/li\u003e\n\u003cli\u003e\u003ccode\u003eEither\u003c/code\u003e\u003c/li\u003e\n\u003cli\u003e\u003ccode\u003eConst\u003c/code\u003e and \u003ccode\u003eIdentity\u003c/code\u003e\u003c/li\u003e\n\u003cli\u003e\u003ccode\u003eLambdaIterable\u003c/code\u003e for wrapping \u003ccode\u003eIterable\u003c/code\u003e in an instance of \u003ccode\u003eTraversable\u003c/code\u003e\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp dir=\"auto\"\u003eIn addition to implementing \u003ccode\u003efmap\u003c/code\u003e from \u003ccode\u003eFunctor\u003c/code\u003e, implementing a traversable functor involves providing an implementation of \u003ccode\u003etraverse\u003c/code\u003e.\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eAs always, there are \u003ca href=\"https://hackage.haskell.org/package/base-4.9.1.0/docs/Data-Traversable.html\" rel=\"nofollow\"\u003esome laws\u003c/a\u003e that should be observed.\u003c/p\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch2 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003e\u003ca name=\"user-content-adts\"\u003eADTs\u003c/a\u003e\u003c/h2\u003e\u003ca id=\"user-content-adts\" class=\"anchor\" aria-label=\"Permalink: ADTs\" href=\"#adts\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eLambda also supports a few first-class \u003ca href=\"https://www.wikiwand.com/en/Algebraic_data_type\" rel=\"nofollow\"\u003ealgebraic data types\u003c/a\u003e.\u003c/p\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch3 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003e\u003ca name=\"user-content-maybe\"\u003eMaybe\u003c/a\u003e\u003c/h3\u003e\u003ca id=\"user-content-maybe\" class=\"anchor\" aria-label=\"Permalink: Maybe\" href=\"#maybe\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003e\u003ccode\u003eMaybe\u003c/code\u003e is the \u003cem\u003elambda\u003c/em\u003e analog to \u003ccode\u003ejava.util.Optional\u003c/code\u003e. It behaves in much of the same way as \u003ccode\u003ej.u.Optional\u003c/code\u003e, except that it quite intentionally does not support the inherently unsafe \u003ccode\u003ej.u.Optional#get\u003c/code\u003e.\u003c/p\u003e\n\u003cdiv class=\"highlight highlight-source-java notranslate position-relative overflow-auto\" dir=\"auto\" data-snippet-clipboard-copy-content=\"Maybe\u0026lt;Integer\u0026gt; maybeInt = Maybe.just(1); // Just 1\nMaybe\u0026lt;String\u0026gt; maybeString = Maybe.nothing(); // Nothing\"\u003e\u003cpre\u003e\u003cspan class=\"pl-smi\"\u003eMaybe\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e\u0026gt; \u003cspan class=\"pl-s1\"\u003emaybeInt\u003c/span\u003e = \u003cspan class=\"pl-smi\"\u003eMaybe\u003c/span\u003e.\u003cspan class=\"pl-en\"\u003ejust\u003c/span\u003e(\u003cspan class=\"pl-c1\"\u003e1\u003c/span\u003e); \u003cspan class=\"pl-c\"\u003e// Just 1\u003c/span\u003e\n\u003cspan class=\"pl-smi\"\u003eMaybe\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eString\u003c/span\u003e\u0026gt; \u003cspan class=\"pl-s1\"\u003emaybeString\u003c/span\u003e = \u003cspan class=\"pl-smi\"\u003eMaybe\u003c/span\u003e.\u003cspan class=\"pl-en\"\u003enothing\u003c/span\u003e(); \u003cspan class=\"pl-c\"\u003e// Nothing\u003c/span\u003e\u003c/pre\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eAlso, because it's a \u003cem\u003elambda\u003c/em\u003e type, it takes advantage of the full functor hierarchy, as well as some helpful conversion functions:\u003c/p\u003e\n\u003cdiv class=\"highlight highlight-source-java notranslate position-relative overflow-auto\" dir=\"auto\" data-snippet-clipboard-copy-content=\"Maybe\u0026lt;String\u0026gt; just = Maybe.maybe(\u0026quot;string\u0026quot;); // Just \u0026quot;string\u0026quot;\nMaybe\u0026lt;String\u0026gt; nothing = Maybe.maybe(null); // Nothing\n\nMaybe\u0026lt;Integer\u0026gt; maybeX = Maybe.just(1);\nMaybe\u0026lt;Integer\u0026gt; maybeY = Maybe.just(2);\n\nmaybeY.zip(maybeX.fmap(x -\u0026gt; y -\u0026gt; x + y)); // Just 3\nmaybeY.zip(nothing()); // Nothing\nMaybe.\u0026lt;Integer\u0026gt;nothing().zip(maybeX.fmap(x -\u0026gt; y -\u0026gt; x + y)); // Nothing\n\nEither\u0026lt;String, Integer\u0026gt; right = maybeX.toEither(() -\u0026gt; \u0026quot;was empty\u0026quot;); // Right 1\nEither\u0026lt;String, Integer\u0026gt; left = Maybe.\u0026lt;Integer\u0026gt;nothing().toEither(() -\u0026gt; \u0026quot;was empty\u0026quot;); // Left \u0026quot;was empty\u0026quot;\n\nMaybe.fromEither(right); // Just 1\nMaybe.fromEither(left); // Nothing\"\u003e\u003cpre\u003e\u003cspan class=\"pl-smi\"\u003eMaybe\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eString\u003c/span\u003e\u0026gt; \u003cspan class=\"pl-s1\"\u003ejust\u003c/span\u003e = \u003cspan class=\"pl-smi\"\u003eMaybe\u003c/span\u003e.\u003cspan class=\"pl-en\"\u003emaybe\u003c/span\u003e(\u003cspan class=\"pl-s\"\u003e\"string\"\u003c/span\u003e); \u003cspan class=\"pl-c\"\u003e// Just \"string\"\u003c/span\u003e\n\u003cspan class=\"pl-smi\"\u003eMaybe\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eString\u003c/span\u003e\u0026gt; \u003cspan class=\"pl-s1\"\u003enothing\u003c/span\u003e = \u003cspan class=\"pl-smi\"\u003eMaybe\u003c/span\u003e.\u003cspan class=\"pl-en\"\u003emaybe\u003c/span\u003e(\u003cspan class=\"pl-c1\"\u003enull\u003c/span\u003e); \u003cspan class=\"pl-c\"\u003e// Nothing\u003c/span\u003e\n\n\u003cspan class=\"pl-smi\"\u003eMaybe\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e\u0026gt; \u003cspan class=\"pl-s1\"\u003emaybeX\u003c/span\u003e = \u003cspan class=\"pl-smi\"\u003eMaybe\u003c/span\u003e.\u003cspan class=\"pl-en\"\u003ejust\u003c/span\u003e(\u003cspan class=\"pl-c1\"\u003e1\u003c/span\u003e);\n\u003cspan class=\"pl-smi\"\u003eMaybe\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e\u0026gt; \u003cspan class=\"pl-s1\"\u003emaybeY\u003c/span\u003e = \u003cspan class=\"pl-smi\"\u003eMaybe\u003c/span\u003e.\u003cspan class=\"pl-en\"\u003ejust\u003c/span\u003e(\u003cspan class=\"pl-c1\"\u003e2\u003c/span\u003e);\n\n\u003cspan class=\"pl-s1\"\u003emaybeY\u003c/span\u003e.\u003cspan class=\"pl-en\"\u003ezip\u003c/span\u003e(\u003cspan class=\"pl-s1\"\u003emaybeX\u003c/span\u003e.\u003cspan class=\"pl-en\"\u003efmap\u003c/span\u003e(\u003cspan class=\"pl-s1\"\u003ex\u003c/span\u003e -\u0026gt; \u003cspan class=\"pl-s1\"\u003ey\u003c/span\u003e -\u0026gt; \u003cspan class=\"pl-s1\"\u003ex\u003c/span\u003e + \u003cspan class=\"pl-s1\"\u003ey\u003c/span\u003e)); \u003cspan class=\"pl-c\"\u003e// Just 3\u003c/span\u003e\n\u003cspan class=\"pl-s1\"\u003emaybeY\u003c/span\u003e.\u003cspan class=\"pl-en\"\u003ezip\u003c/span\u003e(\u003cspan class=\"pl-en\"\u003enothing\u003c/span\u003e()); \u003cspan class=\"pl-c\"\u003e// Nothing\u003c/span\u003e\n\u003cspan class=\"pl-smi\"\u003eMaybe\u003c/span\u003e.\u0026lt;\u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e\u0026gt;\u003cspan class=\"pl-en\"\u003enothing\u003c/span\u003e().\u003cspan class=\"pl-en\"\u003ezip\u003c/span\u003e(\u003cspan class=\"pl-s1\"\u003emaybeX\u003c/span\u003e.\u003cspan class=\"pl-en\"\u003efmap\u003c/span\u003e(\u003cspan class=\"pl-s1\"\u003ex\u003c/span\u003e -\u0026gt; \u003cspan class=\"pl-s1\"\u003ey\u003c/span\u003e -\u0026gt; \u003cspan class=\"pl-s1\"\u003ex\u003c/span\u003e + \u003cspan class=\"pl-s1\"\u003ey\u003c/span\u003e)); \u003cspan class=\"pl-c\"\u003e// Nothing\u003c/span\u003e\n\n\u003cspan class=\"pl-smi\"\u003eEither\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eString\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e\u0026gt; \u003cspan class=\"pl-s1\"\u003eright\u003c/span\u003e = \u003cspan class=\"pl-s1\"\u003emaybeX\u003c/span\u003e.\u003cspan class=\"pl-en\"\u003etoEither\u003c/span\u003e(() -\u0026gt; \u003cspan class=\"pl-s\"\u003e\"was empty\"\u003c/span\u003e); \u003cspan class=\"pl-c\"\u003e// Right 1\u003c/span\u003e\n\u003cspan class=\"pl-smi\"\u003eEither\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eString\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e\u0026gt; \u003cspan class=\"pl-s1\"\u003eleft\u003c/span\u003e = \u003cspan class=\"pl-smi\"\u003eMaybe\u003c/span\u003e.\u0026lt;\u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e\u0026gt;\u003cspan class=\"pl-en\"\u003enothing\u003c/span\u003e().\u003cspan class=\"pl-en\"\u003etoEither\u003c/span\u003e(() -\u0026gt; \u003cspan class=\"pl-s\"\u003e\"was empty\"\u003c/span\u003e); \u003cspan class=\"pl-c\"\u003e// Left \"was empty\"\u003c/span\u003e\n\n\u003cspan class=\"pl-smi\"\u003eMaybe\u003c/span\u003e.\u003cspan class=\"pl-en\"\u003efromEither\u003c/span\u003e(\u003cspan class=\"pl-s1\"\u003eright\u003c/span\u003e); \u003cspan class=\"pl-c\"\u003e// Just 1\u003c/span\u003e\n\u003cspan class=\"pl-smi\"\u003eMaybe\u003c/span\u003e.\u003cspan class=\"pl-en\"\u003efromEither\u003c/span\u003e(\u003cspan class=\"pl-s1\"\u003eleft\u003c/span\u003e); \u003cspan class=\"pl-c\"\u003e// Nothing\u003c/span\u003e\u003c/pre\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eFinally, for compatibility purposes, \u003ccode\u003eMaybe\u003c/code\u003e and \u003ccode\u003ej.u.Optional\u003c/code\u003e can be trivially converted back and forth:\u003c/p\u003e\n\u003cdiv class=\"highlight highlight-source-java notranslate position-relative overflow-auto\" dir=\"auto\" data-snippet-clipboard-copy-content=\"Maybe\u0026lt;Integer\u0026gt; just1 = Maybe.just(1); // Just 1\nOptional\u0026lt;Integer\u0026gt; present1 = just1.toOptional(); // Optional.of(1)\n\nOptional\u0026lt;String\u0026gt; empty = Optional.empty(); // Optional.empty()\nMaybe\u0026lt;String\u0026gt; nothing = Maybe.fromOptional(empty); // Nothing\"\u003e\u003cpre\u003e\u003cspan class=\"pl-smi\"\u003eMaybe\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e\u0026gt; \u003cspan class=\"pl-s1\"\u003ejust1\u003c/span\u003e = \u003cspan class=\"pl-smi\"\u003eMaybe\u003c/span\u003e.\u003cspan class=\"pl-en\"\u003ejust\u003c/span\u003e(\u003cspan class=\"pl-c1\"\u003e1\u003c/span\u003e); \u003cspan class=\"pl-c\"\u003e// Just 1\u003c/span\u003e\n\u003cspan class=\"pl-smi\"\u003eOptional\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e\u0026gt; \u003cspan class=\"pl-s1\"\u003epresent1\u003c/span\u003e = \u003cspan class=\"pl-s1\"\u003ejust1\u003c/span\u003e.\u003cspan class=\"pl-en\"\u003etoOptional\u003c/span\u003e(); \u003cspan class=\"pl-c\"\u003e// Optional.of(1)\u003c/span\u003e\n\n\u003cspan class=\"pl-smi\"\u003eOptional\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eString\u003c/span\u003e\u0026gt; \u003cspan class=\"pl-s1\"\u003eempty\u003c/span\u003e = \u003cspan class=\"pl-smi\"\u003eOptional\u003c/span\u003e.\u003cspan class=\"pl-en\"\u003eempty\u003c/span\u003e(); \u003cspan class=\"pl-c\"\u003e// Optional.empty()\u003c/span\u003e\n\u003cspan class=\"pl-smi\"\u003eMaybe\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eString\u003c/span\u003e\u0026gt; \u003cspan class=\"pl-s1\"\u003enothing\u003c/span\u003e = \u003cspan class=\"pl-smi\"\u003eMaybe\u003c/span\u003e.\u003cspan class=\"pl-en\"\u003efromOptional\u003c/span\u003e(\u003cspan class=\"pl-s1\"\u003eempty\u003c/span\u003e); \u003cspan class=\"pl-c\"\u003e// Nothing\u003c/span\u003e\u003c/pre\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003e\u003cem\u003e\u003cstrong\u003eNote\u003c/strong\u003e\u003c/em\u003e: One compatibility difference between \u003ccode\u003ej.u.Optional\u003c/code\u003e and \u003ccode\u003eMaybe\u003c/code\u003e is how \u003ccode\u003emap\u003c/code\u003e/\u003ccode\u003efmap\u003c/code\u003e behave regarding functions that return \u003ccode\u003enull\u003c/code\u003e: \u003ccode\u003ej.u.Optional\u003c/code\u003e re-wraps \u003ccode\u003enull\u003c/code\u003e results from \u003ccode\u003emap\u003c/code\u003e operations in another \u003ccode\u003ej.u.Optional\u003c/code\u003e, whereas \u003ccode\u003eMaybe\u003c/code\u003e considers this to be an error, and throws an exception. The reason \u003ccode\u003eMaybe\u003c/code\u003e throws in this case is because \u003ccode\u003efmap\u003c/code\u003e is not an operation to be called speculatively, and so any function that returns \u003ccode\u003enull\u003c/code\u003e in the context of an \u003ccode\u003efmap\u003c/code\u003e operation is considered to be erroneous. Instead of calling \u003ccode\u003efmap\u003c/code\u003e with a function that might return \u003ccode\u003enull\u003c/code\u003e, the function result should be wrapped in a \u003ccode\u003eMaybe\u003c/code\u003e and \u003ccode\u003eflatMap\u003c/code\u003e should be used, as illustrated in the following example:\u003c/p\u003e\n\u003cdiv class=\"highlight highlight-source-java notranslate position-relative overflow-auto\" dir=\"auto\" data-snippet-clipboard-copy-content=\"Function\u0026lt;Integer, Object\u0026gt; nullResultFn = __ -\u0026gt; null;\n\nOptional.of(1).map(nullResultFn); // Optional.empty()\nMaybe.just(1).fmap(nullResultFn); // throws NullPointerException\n\nMaybe.just(1).flatMap(nullResultFn.andThen(Maybe::maybe)); // Nothing\"\u003e\u003cpre\u003e\u003cspan class=\"pl-smi\"\u003eFunction\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003eObject\u003c/span\u003e\u0026gt; \u003cspan class=\"pl-s1\"\u003enullResultFn\u003c/span\u003e = \u003cspan class=\"pl-s1\"\u003e__\u003c/span\u003e -\u0026gt; \u003cspan class=\"pl-c1\"\u003enull\u003c/span\u003e;\n\n\u003cspan class=\"pl-smi\"\u003eOptional\u003c/span\u003e.\u003cspan class=\"pl-en\"\u003eof\u003c/span\u003e(\u003cspan class=\"pl-c1\"\u003e1\u003c/span\u003e).\u003cspan class=\"pl-en\"\u003emap\u003c/span\u003e(\u003cspan class=\"pl-s1\"\u003enullResultFn\u003c/span\u003e); \u003cspan class=\"pl-c\"\u003e// Optional.empty()\u003c/span\u003e\n\u003cspan class=\"pl-smi\"\u003eMaybe\u003c/span\u003e.\u003cspan class=\"pl-en\"\u003ejust\u003c/span\u003e(\u003cspan class=\"pl-c1\"\u003e1\u003c/span\u003e).\u003cspan class=\"pl-en\"\u003efmap\u003c/span\u003e(\u003cspan class=\"pl-s1\"\u003enullResultFn\u003c/span\u003e); \u003cspan class=\"pl-c\"\u003e// throws NullPointerException\u003c/span\u003e\n\n\u003cspan class=\"pl-smi\"\u003eMaybe\u003c/span\u003e.\u003cspan class=\"pl-en\"\u003ejust\u003c/span\u003e(\u003cspan class=\"pl-c1\"\u003e1\u003c/span\u003e).\u003cspan class=\"pl-en\"\u003eflatMap\u003c/span\u003e(\u003cspan class=\"pl-s1\"\u003enullResultFn\u003c/span\u003e.\u003cspan class=\"pl-en\"\u003eandThen\u003c/span\u003e(\u003cspan class=\"pl-smi\"\u003eMaybe\u003c/span\u003e::\u003cspan class=\"pl-s1\"\u003emaybe\u003c/span\u003e)); \u003cspan class=\"pl-c\"\u003e// Nothing\u003c/span\u003e\u003c/pre\u003e\u003c/div\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch3 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003e\u003ca name=\"user-content-hlists\"\u003eHeterogeneous Lists (HLists)\u003c/a\u003e\u003c/h3\u003e\u003ca id=\"user-content-heterogeneous-lists-hlists\" class=\"anchor\" aria-label=\"Permalink: Heterogeneous Lists (HLists)\" href=\"#heterogeneous-lists-hlists\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eHLists are type-safe heterogeneous lists, meaning they can store elements of different types in the same list while facilitating certain type-safe interactions.\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eThe following illustrates how the linear expansion of the recursive type signature for \u003ccode\u003eHList\u003c/code\u003e prevents ill-typed expressions:\u003c/p\u003e\n\u003cdiv class=\"highlight highlight-source-java notranslate position-relative overflow-auto\" dir=\"auto\" data-snippet-clipboard-copy-content=\"HCons\u0026lt;Integer, HCons\u0026lt;String, HNil\u0026gt;\u0026gt; hList = HList.cons(1, HList.cons(\u0026quot;foo\u0026quot;, HList.nil()));\n\nSystem.out.println(hList.head()); // prints 1\nSystem.out.println(hList.tail().head()); // prints \u0026quot;foo\u0026quot;\n\nHNil nil = hList.tail().tail();\n//nil.head() won't type-check\"\u003e\u003cpre\u003e\u003cspan class=\"pl-smi\"\u003eHCons\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003eHCons\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eString\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003eHNil\u003c/span\u003e\u0026gt;\u0026gt; \u003cspan class=\"pl-s1\"\u003ehList\u003c/span\u003e = \u003cspan class=\"pl-smi\"\u003eHList\u003c/span\u003e.\u003cspan class=\"pl-en\"\u003econs\u003c/span\u003e(\u003cspan class=\"pl-c1\"\u003e1\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003eHList\u003c/span\u003e.\u003cspan class=\"pl-en\"\u003econs\u003c/span\u003e(\u003cspan class=\"pl-s\"\u003e\"foo\"\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003eHList\u003c/span\u003e.\u003cspan class=\"pl-en\"\u003enil\u003c/span\u003e()));\n\n\u003cspan class=\"pl-smi\"\u003eSystem\u003c/span\u003e.\u003cspan class=\"pl-s1\"\u003eout\u003c/span\u003e.\u003cspan class=\"pl-en\"\u003eprintln\u003c/span\u003e(\u003cspan class=\"pl-s1\"\u003ehList\u003c/span\u003e.\u003cspan class=\"pl-en\"\u003ehead\u003c/span\u003e()); \u003cspan class=\"pl-c\"\u003e// prints 1\u003c/span\u003e\n\u003cspan class=\"pl-smi\"\u003eSystem\u003c/span\u003e.\u003cspan class=\"pl-s1\"\u003eout\u003c/span\u003e.\u003cspan class=\"pl-en\"\u003eprintln\u003c/span\u003e(\u003cspan class=\"pl-s1\"\u003ehList\u003c/span\u003e.\u003cspan class=\"pl-en\"\u003etail\u003c/span\u003e().\u003cspan class=\"pl-en\"\u003ehead\u003c/span\u003e()); \u003cspan class=\"pl-c\"\u003e// prints \"foo\"\u003c/span\u003e\n\n\u003cspan class=\"pl-smi\"\u003eHNil\u003c/span\u003e \u003cspan class=\"pl-s1\"\u003enil\u003c/span\u003e = \u003cspan class=\"pl-s1\"\u003ehList\u003c/span\u003e.\u003cspan class=\"pl-en\"\u003etail\u003c/span\u003e().\u003cspan class=\"pl-en\"\u003etail\u003c/span\u003e();\n\u003cspan class=\"pl-c\"\u003e//nil.head() won't type-check\u003c/span\u003e\u003c/pre\u003e\u003c/div\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch4 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003e\u003ca name=\"user-content-tuples\"\u003eTuples\u003c/a\u003e\u003c/h4\u003e\u003ca id=\"user-content-tuples\" class=\"anchor\" aria-label=\"Permalink: Tuples\" href=\"#tuples\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eOne of the primary downsides to using \u003ccode\u003eHList\u003c/code\u003es in Java is how quickly the type signature grows.\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eTo address this, tuples in lambda are specializations of \u003ccode\u003eHList\u003c/code\u003es up to 8 elements deep, with added support for index-based accessor methods.\u003c/p\u003e\n\u003cdiv class=\"highlight highlight-source-java notranslate position-relative overflow-auto\" dir=\"auto\" data-snippet-clipboard-copy-content=\"HNil nil = HList.nil();\nSingletonHList\u0026lt;Integer\u0026gt; singleton = nil.cons(8);\nTuple2\u0026lt;Integer, Integer\u0026gt; tuple2 = singleton.cons(7);\nTuple3\u0026lt;Integer, Integer, Integer\u0026gt; tuple3 = tuple2.cons(6);\nTuple4\u0026lt;Integer, Integer, Integer, Integer\u0026gt; tuple4 = tuple3.cons(5);\nTuple5\u0026lt;Integer, Integer, Integer, Integer, Integer\u0026gt; tuple5 = tuple4.cons(4);\nTuple6\u0026lt;Integer, Integer, Integer, Integer, Integer, Integer\u0026gt; tuple6 = tuple5.cons(3);\nTuple7\u0026lt;Integer, Integer, Integer, Integer, Integer, Integer, Integer\u0026gt; tuple7 = tuple6.cons(2);\nTuple8\u0026lt;Integer, Integer, Integer, Integer, Integer, Integer, Integer, Integer\u0026gt; tuple8 = tuple7.cons(1);\n\nSystem.out.println(tuple2._1()); // prints 7\nSystem.out.println(tuple8._8()); // prints 8\"\u003e\u003cpre\u003e\u003cspan class=\"pl-smi\"\u003eHNil\u003c/span\u003e \u003cspan class=\"pl-s1\"\u003enil\u003c/span\u003e = \u003cspan class=\"pl-smi\"\u003eHList\u003c/span\u003e.\u003cspan class=\"pl-en\"\u003enil\u003c/span\u003e();\n\u003cspan class=\"pl-smi\"\u003eSingletonHList\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e\u0026gt; \u003cspan class=\"pl-s1\"\u003esingleton\u003c/span\u003e = \u003cspan class=\"pl-s1\"\u003enil\u003c/span\u003e.\u003cspan class=\"pl-en\"\u003econs\u003c/span\u003e(\u003cspan class=\"pl-c1\"\u003e8\u003c/span\u003e);\n\u003cspan class=\"pl-smi\"\u003eTuple2\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e\u0026gt; \u003cspan class=\"pl-s1\"\u003etuple2\u003c/span\u003e = \u003cspan class=\"pl-s1\"\u003esingleton\u003c/span\u003e.\u003cspan class=\"pl-en\"\u003econs\u003c/span\u003e(\u003cspan class=\"pl-c1\"\u003e7\u003c/span\u003e);\n\u003cspan class=\"pl-smi\"\u003eTuple3\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e\u0026gt; \u003cspan class=\"pl-s1\"\u003etuple3\u003c/span\u003e = \u003cspan class=\"pl-s1\"\u003etuple2\u003c/span\u003e.\u003cspan class=\"pl-en\"\u003econs\u003c/span\u003e(\u003cspan class=\"pl-c1\"\u003e6\u003c/span\u003e);\n\u003cspan class=\"pl-smi\"\u003eTuple4\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e\u0026gt; \u003cspan class=\"pl-s1\"\u003etuple4\u003c/span\u003e = \u003cspan class=\"pl-s1\"\u003etuple3\u003c/span\u003e.\u003cspan class=\"pl-en\"\u003econs\u003c/span\u003e(\u003cspan class=\"pl-c1\"\u003e5\u003c/span\u003e);\n\u003cspan class=\"pl-smi\"\u003eTuple5\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e\u0026gt; \u003cspan class=\"pl-s1\"\u003etuple5\u003c/span\u003e = \u003cspan class=\"pl-s1\"\u003etuple4\u003c/span\u003e.\u003cspan class=\"pl-en\"\u003econs\u003c/span\u003e(\u003cspan class=\"pl-c1\"\u003e4\u003c/span\u003e);\n\u003cspan class=\"pl-smi\"\u003eTuple6\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e\u0026gt; \u003cspan class=\"pl-s1\"\u003etuple6\u003c/span\u003e = \u003cspan class=\"pl-s1\"\u003etuple5\u003c/span\u003e.\u003cspan class=\"pl-en\"\u003econs\u003c/span\u003e(\u003cspan class=\"pl-c1\"\u003e3\u003c/span\u003e);\n\u003cspan class=\"pl-smi\"\u003eTuple7\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e\u0026gt; \u003cspan class=\"pl-s1\"\u003etuple7\u003c/span\u003e = \u003cspan class=\"pl-s1\"\u003etuple6\u003c/span\u003e.\u003cspan class=\"pl-en\"\u003econs\u003c/span\u003e(\u003cspan class=\"pl-c1\"\u003e2\u003c/span\u003e);\n\u003cspan class=\"pl-smi\"\u003eTuple8\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e\u0026gt; \u003cspan class=\"pl-s1\"\u003etuple8\u003c/span\u003e = \u003cspan class=\"pl-s1\"\u003etuple7\u003c/span\u003e.\u003cspan class=\"pl-en\"\u003econs\u003c/span\u003e(\u003cspan class=\"pl-c1\"\u003e1\u003c/span\u003e);\n\n\u003cspan class=\"pl-smi\"\u003eSystem\u003c/span\u003e.\u003cspan class=\"pl-s1\"\u003eout\u003c/span\u003e.\u003cspan class=\"pl-en\"\u003eprintln\u003c/span\u003e(\u003cspan class=\"pl-s1\"\u003etuple2\u003c/span\u003e.\u003cspan class=\"pl-en\"\u003e_1\u003c/span\u003e()); \u003cspan class=\"pl-c\"\u003e// prints 7\u003c/span\u003e\n\u003cspan class=\"pl-smi\"\u003eSystem\u003c/span\u003e.\u003cspan class=\"pl-s1\"\u003eout\u003c/span\u003e.\u003cspan class=\"pl-en\"\u003eprintln\u003c/span\u003e(\u003cspan class=\"pl-s1\"\u003etuple8\u003c/span\u003e.\u003cspan class=\"pl-en\"\u003e_8\u003c/span\u003e()); \u003cspan class=\"pl-c\"\u003e// prints 8\u003c/span\u003e\u003c/pre\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eAdditionally, \u003ccode\u003eHList\u003c/code\u003e provides convenience static factory methods for directly constructing lists of up to 8 elements:\u003c/p\u003e\n\u003cdiv class=\"highlight highlight-source-java notranslate position-relative overflow-auto\" dir=\"auto\" data-snippet-clipboard-copy-content=\"SingletonHList\u0026lt;Integer\u0026gt; singleton = HList.singletonHList(1);\nTuple2\u0026lt;Integer, Integer\u0026gt; tuple2 = HList.tuple(1, 2);\nTuple3\u0026lt;Integer, Integer, Integer\u0026gt; tuple3 = HList.tuple(1, 2, 3);\nTuple4\u0026lt;Integer, Integer, Integer, Integer\u0026gt; tuple4 = HList.tuple(1, 2, 3, 4);\nTuple5\u0026lt;Integer, Integer, Integer, Integer, Integer\u0026gt; tuple5 = HList.tuple(1, 2, 3, 4, 5);\nTuple6\u0026lt;Integer, Integer, Integer, Integer, Integer, Integer\u0026gt; tuple6 = HList.tuple(1, 2, 3, 4, 5, 6);\nTuple7\u0026lt;Integer, Integer, Integer, Integer, Integer, Integer, Integer\u0026gt; tuple7 = HList.tuple(1, 2, 3, 4, 5, 6, 7);\nTuple8\u0026lt;Integer, Integer, Integer, Integer, Integer, Integer, Integer, Integer\u0026gt; tuple8 = HList.tuple(1, 2, 3, 4, 5, 6, 7, 8);\"\u003e\u003cpre\u003e\u003cspan class=\"pl-smi\"\u003eSingletonHList\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e\u0026gt; \u003cspan class=\"pl-s1\"\u003esingleton\u003c/span\u003e = \u003cspan class=\"pl-smi\"\u003eHList\u003c/span\u003e.\u003cspan class=\"pl-en\"\u003esingletonHList\u003c/span\u003e(\u003cspan class=\"pl-c1\"\u003e1\u003c/span\u003e);\n\u003cspan class=\"pl-smi\"\u003eTuple2\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e\u0026gt; \u003cspan class=\"pl-s1\"\u003etuple2\u003c/span\u003e = \u003cspan class=\"pl-smi\"\u003eHList\u003c/span\u003e.\u003cspan class=\"pl-en\"\u003etuple\u003c/span\u003e(\u003cspan class=\"pl-c1\"\u003e1\u003c/span\u003e, \u003cspan class=\"pl-c1\"\u003e2\u003c/span\u003e);\n\u003cspan class=\"pl-smi\"\u003eTuple3\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e\u0026gt; \u003cspan class=\"pl-s1\"\u003etuple3\u003c/span\u003e = \u003cspan class=\"pl-smi\"\u003eHList\u003c/span\u003e.\u003cspan class=\"pl-en\"\u003etuple\u003c/span\u003e(\u003cspan class=\"pl-c1\"\u003e1\u003c/span\u003e, \u003cspan class=\"pl-c1\"\u003e2\u003c/span\u003e, \u003cspan class=\"pl-c1\"\u003e3\u003c/span\u003e);\n\u003cspan class=\"pl-smi\"\u003eTuple4\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e\u0026gt; \u003cspan class=\"pl-s1\"\u003etuple4\u003c/span\u003e = \u003cspan class=\"pl-smi\"\u003eHList\u003c/span\u003e.\u003cspan class=\"pl-en\"\u003etuple\u003c/span\u003e(\u003cspan class=\"pl-c1\"\u003e1\u003c/span\u003e, \u003cspan class=\"pl-c1\"\u003e2\u003c/span\u003e, \u003cspan class=\"pl-c1\"\u003e3\u003c/span\u003e, \u003cspan class=\"pl-c1\"\u003e4\u003c/span\u003e);\n\u003cspan class=\"pl-smi\"\u003eTuple5\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e\u0026gt; \u003cspan class=\"pl-s1\"\u003etuple5\u003c/span\u003e = \u003cspan class=\"pl-smi\"\u003eHList\u003c/span\u003e.\u003cspan class=\"pl-en\"\u003etuple\u003c/span\u003e(\u003cspan class=\"pl-c1\"\u003e1\u003c/span\u003e, \u003cspan class=\"pl-c1\"\u003e2\u003c/span\u003e, \u003cspan class=\"pl-c1\"\u003e3\u003c/span\u003e, \u003cspan class=\"pl-c1\"\u003e4\u003c/span\u003e, \u003cspan class=\"pl-c1\"\u003e5\u003c/span\u003e);\n\u003cspan class=\"pl-smi\"\u003eTuple6\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e\u0026gt; \u003cspan class=\"pl-s1\"\u003etuple6\u003c/span\u003e = \u003cspan class=\"pl-smi\"\u003eHList\u003c/span\u003e.\u003cspan class=\"pl-en\"\u003etuple\u003c/span\u003e(\u003cspan class=\"pl-c1\"\u003e1\u003c/span\u003e, \u003cspan class=\"pl-c1\"\u003e2\u003c/span\u003e, \u003cspan class=\"pl-c1\"\u003e3\u003c/span\u003e, \u003cspan class=\"pl-c1\"\u003e4\u003c/span\u003e, \u003cspan class=\"pl-c1\"\u003e5\u003c/span\u003e, \u003cspan class=\"pl-c1\"\u003e6\u003c/span\u003e);\n\u003cspan class=\"pl-smi\"\u003eTuple7\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e\u0026gt; \u003cspan class=\"pl-s1\"\u003etuple7\u003c/span\u003e = \u003cspan class=\"pl-smi\"\u003eHList\u003c/span\u003e.\u003cspan class=\"pl-en\"\u003etuple\u003c/span\u003e(\u003cspan class=\"pl-c1\"\u003e1\u003c/span\u003e, \u003cspan class=\"pl-c1\"\u003e2\u003c/span\u003e, \u003cspan class=\"pl-c1\"\u003e3\u003c/span\u003e, \u003cspan class=\"pl-c1\"\u003e4\u003c/span\u003e, \u003cspan class=\"pl-c1\"\u003e5\u003c/span\u003e, \u003cspan class=\"pl-c1\"\u003e6\u003c/span\u003e, \u003cspan class=\"pl-c1\"\u003e7\u003c/span\u003e);\n\u003cspan class=\"pl-smi\"\u003eTuple8\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e\u0026gt; \u003cspan class=\"pl-s1\"\u003etuple8\u003c/span\u003e = \u003cspan class=\"pl-smi\"\u003eHList\u003c/span\u003e.\u003cspan class=\"pl-en\"\u003etuple\u003c/span\u003e(\u003cspan class=\"pl-c1\"\u003e1\u003c/span\u003e, \u003cspan class=\"pl-c1\"\u003e2\u003c/span\u003e, \u003cspan class=\"pl-c1\"\u003e3\u003c/span\u003e, \u003cspan class=\"pl-c1\"\u003e4\u003c/span\u003e, \u003cspan class=\"pl-c1\"\u003e5\u003c/span\u003e, \u003cspan class=\"pl-c1\"\u003e6\u003c/span\u003e, \u003cspan class=\"pl-c1\"\u003e7\u003c/span\u003e, \u003cspan class=\"pl-c1\"\u003e8\u003c/span\u003e);\u003c/pre\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003e\u003ccode\u003eIndex\u003c/code\u003e can be used for type-safe retrieval and updating of elements at specific indexes:\u003c/p\u003e\n\u003cdiv class=\"highlight highlight-source-java notranslate position-relative overflow-auto\" dir=\"auto\" data-snippet-clipboard-copy-content=\"HCons\u0026lt;Integer, HCons\u0026lt;String, HCons\u0026lt;Character, HNil\u0026gt;\u0026gt;\u0026gt; hList = cons(1, cons(\u0026quot;2\u0026quot;, cons('3', nil())));\nHCons\u0026lt;Integer, Tuple2\u0026lt;String, Character\u0026gt;\u0026gt; tuple = tuple(1, \u0026quot;2\u0026quot;, '3');\nTuple5\u0026lt;Integer, String, Character, Double, Boolean\u0026gt; longerHList = tuple(1, \u0026quot;2\u0026quot;, '3', 4.0d, false);\n\nIndex\u0026lt;Character, HCons\u0026lt;Integer, ? extends HCons\u0026lt;String, ? extends HCons\u0026lt;Character, ?\u0026gt;\u0026gt;\u0026gt;\u0026gt; characterIndex =\n Index.\u0026lt;Character\u0026gt;index().\u0026lt;String\u0026gt;after().after();\n\ncharacterIndex.get(hList); // '3'\ncharacterIndex.get(tuple); // '3'\ncharacterIndex.get(longerHList); // '3'\n\ncharacterIndex.set('4', hList); // HList{ 1 :: \u0026quot;2\u0026quot; :: '4' }\"\u003e\u003cpre\u003e\u003cspan class=\"pl-smi\"\u003eHCons\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003eHCons\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eString\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003eHCons\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eCharacter\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003eHNil\u003c/span\u003e\u0026gt;\u0026gt;\u0026gt; \u003cspan class=\"pl-s1\"\u003ehList\u003c/span\u003e = \u003cspan class=\"pl-en\"\u003econs\u003c/span\u003e(\u003cspan class=\"pl-c1\"\u003e1\u003c/span\u003e, \u003cspan class=\"pl-en\"\u003econs\u003c/span\u003e(\u003cspan class=\"pl-s\"\u003e\"2\"\u003c/span\u003e, \u003cspan class=\"pl-en\"\u003econs\u003c/span\u003e(\u003cspan class=\"pl-s\"\u003e'3'\u003c/span\u003e, \u003cspan class=\"pl-en\"\u003enil\u003c/span\u003e())));\n\u003cspan class=\"pl-smi\"\u003eHCons\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003eTuple2\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eString\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003eCharacter\u003c/span\u003e\u0026gt;\u0026gt; \u003cspan class=\"pl-s1\"\u003etuple\u003c/span\u003e = \u003cspan class=\"pl-en\"\u003etuple\u003c/span\u003e(\u003cspan class=\"pl-c1\"\u003e1\u003c/span\u003e, \u003cspan class=\"pl-s\"\u003e\"2\"\u003c/span\u003e, \u003cspan class=\"pl-s\"\u003e'3'\u003c/span\u003e);\n\u003cspan class=\"pl-smi\"\u003eTuple5\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003eString\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003eCharacter\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003eDouble\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003eBoolean\u003c/span\u003e\u0026gt; \u003cspan class=\"pl-s1\"\u003elongerHList\u003c/span\u003e = \u003cspan class=\"pl-en\"\u003etuple\u003c/span\u003e(\u003cspan class=\"pl-c1\"\u003e1\u003c/span\u003e, \u003cspan class=\"pl-s\"\u003e\"2\"\u003c/span\u003e, \u003cspan class=\"pl-s\"\u003e'3'\u003c/span\u003e, \u003cspan class=\"pl-c1\"\u003e4.0d\u003c/span\u003e, \u003cspan class=\"pl-c1\"\u003efalse\u003c/span\u003e);\n\n\u003cspan class=\"pl-smi\"\u003eIndex\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eCharacter\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003eHCons\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e, ? \u003cspan class=\"pl-k\"\u003eextends\u003c/span\u003e \u003cspan class=\"pl-smi\"\u003eHCons\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eString\u003c/span\u003e, ? \u003cspan class=\"pl-k\"\u003eextends\u003c/span\u003e \u003cspan class=\"pl-smi\"\u003eHCons\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eCharacter\u003c/span\u003e, ?\u0026gt;\u0026gt;\u0026gt;\u0026gt; \u003cspan class=\"pl-s1\"\u003echaracterIndex\u003c/span\u003e =\n \u003cspan class=\"pl-smi\"\u003eIndex\u003c/span\u003e.\u0026lt;\u003cspan class=\"pl-smi\"\u003eCharacter\u003c/span\u003e\u0026gt;\u003cspan class=\"pl-en\"\u003eindex\u003c/span\u003e().\u0026lt;\u003cspan class=\"pl-smi\"\u003eString\u003c/span\u003e\u0026gt;\u003cspan class=\"pl-en\"\u003eafter\u003c/span\u003e().\u003cspan class=\"pl-en\"\u003eafter\u003c/span\u003e();\n\n\u003cspan class=\"pl-s1\"\u003echaracterIndex\u003c/span\u003e.\u003cspan class=\"pl-en\"\u003eget\u003c/span\u003e(\u003cspan class=\"pl-s1\"\u003ehList\u003c/span\u003e); \u003cspan class=\"pl-c\"\u003e// '3'\u003c/span\u003e\n\u003cspan class=\"pl-s1\"\u003echaracterIndex\u003c/span\u003e.\u003cspan class=\"pl-en\"\u003eget\u003c/span\u003e(\u003cspan class=\"pl-s1\"\u003etuple\u003c/span\u003e); \u003cspan class=\"pl-c\"\u003e// '3'\u003c/span\u003e\n\u003cspan class=\"pl-s1\"\u003echaracterIndex\u003c/span\u003e.\u003cspan class=\"pl-en\"\u003eget\u003c/span\u003e(\u003cspan class=\"pl-s1\"\u003elongerHList\u003c/span\u003e); \u003cspan class=\"pl-c\"\u003e// '3'\u003c/span\u003e\n\n\u003cspan class=\"pl-s1\"\u003echaracterIndex\u003c/span\u003e.\u003cspan class=\"pl-en\"\u003eset\u003c/span\u003e(\u003cspan class=\"pl-s\"\u003e'4'\u003c/span\u003e, \u003cspan class=\"pl-s1\"\u003ehList\u003c/span\u003e); \u003cspan class=\"pl-c\"\u003e// HList{ 1 :: \"2\" :: '4' }\u003c/span\u003e\u003c/pre\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eFinally, all \u003ccode\u003eTuple*\u003c/code\u003e classes are instances of both \u003ccode\u003eFunctor\u003c/code\u003e and \u003ccode\u003eBifunctor\u003c/code\u003e:\u003c/p\u003e\n\u003cdiv class=\"highlight highlight-source-java notranslate position-relative overflow-auto\" dir=\"auto\" data-snippet-clipboard-copy-content=\"Tuple2\u0026lt;Integer, String\u0026gt; mappedTuple2 = tuple(1, 2).biMap(x -\u0026gt; x + 1, Object::toString);\n\nSystem.out.println(mappedTuple2._1()); // prints 2\nSystem.out.println(mappedTuple2._2()); // prints \u0026quot;2\u0026quot;\n\nTuple3\u0026lt;String, Boolean, Integer\u0026gt; mappedTuple3 = tuple(\u0026quot;foo\u0026quot;, true, 1).biMap(x -\u0026gt; !x, x -\u0026gt; x + 1);\n\nSystem.out.println(mappedTuple3._1()); // prints \u0026quot;foo\u0026quot;\nSystem.out.println(mappedTuple3._2()); // prints false\nSystem.out.println(mappedTuple3._3()); // prints 2\"\u003e\u003cpre\u003e\u003cspan class=\"pl-smi\"\u003eTuple2\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003eString\u003c/span\u003e\u0026gt; \u003cspan class=\"pl-s1\"\u003emappedTuple2\u003c/span\u003e = \u003cspan class=\"pl-en\"\u003etuple\u003c/span\u003e(\u003cspan class=\"pl-c1\"\u003e1\u003c/span\u003e, \u003cspan class=\"pl-c1\"\u003e2\u003c/span\u003e).\u003cspan class=\"pl-en\"\u003ebiMap\u003c/span\u003e(\u003cspan class=\"pl-s1\"\u003ex\u003c/span\u003e -\u0026gt; \u003cspan class=\"pl-s1\"\u003ex\u003c/span\u003e + \u003cspan class=\"pl-c1\"\u003e1\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003eObject\u003c/span\u003e::\u003cspan class=\"pl-s1\"\u003etoString\u003c/span\u003e);\n\n\u003cspan class=\"pl-smi\"\u003eSystem\u003c/span\u003e.\u003cspan class=\"pl-s1\"\u003eout\u003c/span\u003e.\u003cspan class=\"pl-en\"\u003eprintln\u003c/span\u003e(\u003cspan class=\"pl-s1\"\u003emappedTuple2\u003c/span\u003e.\u003cspan class=\"pl-en\"\u003e_1\u003c/span\u003e()); \u003cspan class=\"pl-c\"\u003e// prints 2\u003c/span\u003e\n\u003cspan class=\"pl-smi\"\u003eSystem\u003c/span\u003e.\u003cspan class=\"pl-s1\"\u003eout\u003c/span\u003e.\u003cspan class=\"pl-en\"\u003eprintln\u003c/span\u003e(\u003cspan class=\"pl-s1\"\u003emappedTuple2\u003c/span\u003e.\u003cspan class=\"pl-en\"\u003e_2\u003c/span\u003e()); \u003cspan class=\"pl-c\"\u003e// prints \"2\"\u003c/span\u003e\n\n\u003cspan class=\"pl-smi\"\u003eTuple3\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eString\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003eBoolean\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e\u0026gt; \u003cspan class=\"pl-s1\"\u003emappedTuple3\u003c/span\u003e = \u003cspan class=\"pl-en\"\u003etuple\u003c/span\u003e(\u003cspan class=\"pl-s\"\u003e\"foo\"\u003c/span\u003e, \u003cspan class=\"pl-c1\"\u003etrue\u003c/span\u003e, \u003cspan class=\"pl-c1\"\u003e1\u003c/span\u003e).\u003cspan class=\"pl-en\"\u003ebiMap\u003c/span\u003e(\u003cspan class=\"pl-s1\"\u003ex\u003c/span\u003e -\u0026gt; !\u003cspan class=\"pl-s1\"\u003ex\u003c/span\u003e, \u003cspan class=\"pl-s1\"\u003ex\u003c/span\u003e -\u0026gt; \u003cspan class=\"pl-s1\"\u003ex\u003c/span\u003e + \u003cspan class=\"pl-c1\"\u003e1\u003c/span\u003e);\n\n\u003cspan class=\"pl-smi\"\u003eSystem\u003c/span\u003e.\u003cspan class=\"pl-s1\"\u003eout\u003c/span\u003e.\u003cspan class=\"pl-en\"\u003eprintln\u003c/span\u003e(\u003cspan class=\"pl-s1\"\u003emappedTuple3\u003c/span\u003e.\u003cspan class=\"pl-en\"\u003e_1\u003c/span\u003e()); \u003cspan class=\"pl-c\"\u003e// prints \"foo\"\u003c/span\u003e\n\u003cspan class=\"pl-smi\"\u003eSystem\u003c/span\u003e.\u003cspan class=\"pl-s1\"\u003eout\u003c/span\u003e.\u003cspan class=\"pl-en\"\u003eprintln\u003c/span\u003e(\u003cspan class=\"pl-s1\"\u003emappedTuple3\u003c/span\u003e.\u003cspan class=\"pl-en\"\u003e_2\u003c/span\u003e()); \u003cspan class=\"pl-c\"\u003e// prints false\u003c/span\u003e\n\u003cspan class=\"pl-smi\"\u003eSystem\u003c/span\u003e.\u003cspan class=\"pl-s1\"\u003eout\u003c/span\u003e.\u003cspan class=\"pl-en\"\u003eprintln\u003c/span\u003e(\u003cspan class=\"pl-s1\"\u003emappedTuple3\u003c/span\u003e.\u003cspan class=\"pl-en\"\u003e_3\u003c/span\u003e()); \u003cspan class=\"pl-c\"\u003e// prints 2\u003c/span\u003e\u003c/pre\u003e\u003c/div\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch3 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003e\u003ca name=\"user-content-hmaps\"\u003eHeterogeneous Maps\u003c/a\u003e\u003c/h3\u003e\u003ca id=\"user-content-heterogeneous-maps\" class=\"anchor\" aria-label=\"Permalink: Heterogeneous Maps\" href=\"#heterogeneous-maps\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eHMaps are type-safe heterogeneous maps, meaning they can store mappings to different value types in the same map; however, whereas HLists encode value types in their type signatures, HMaps rely on the keys to encode the value type that they point to.\u003c/p\u003e\n\u003cdiv class=\"highlight highlight-source-java notranslate position-relative overflow-auto\" dir=\"auto\" data-snippet-clipboard-copy-content=\"TypeSafeKey\u0026lt;String\u0026gt; stringKey = TypeSafeKey.typeSafeKey();\nTypeSafeKey\u0026lt;Integer\u0026gt; intKey = TypeSafeKey.typeSafeKey();\nHMap hmap = HMap.hMap(stringKey, \u0026quot;string value\u0026quot;,\n intKey, 1);\n\nOptional\u0026lt;String\u0026gt; stringValue = hmap.get(stringKey); // Optional[\u0026quot;string value\u0026quot;]\nOptional\u0026lt;Integer\u0026gt; intValue = hmap.get(intKey); // Optional[1]\nOptional\u0026lt;Integer\u0026gt; anotherIntValue = hmap.get(anotherIntKey); // Optional.empty\"\u003e\u003cpre\u003e\u003cspan class=\"pl-smi\"\u003eTypeSafeKey\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eString\u003c/span\u003e\u0026gt; \u003cspan class=\"pl-s1\"\u003estringKey\u003c/span\u003e = \u003cspan class=\"pl-smi\"\u003eTypeSafeKey\u003c/span\u003e.\u003cspan class=\"pl-en\"\u003etypeSafeKey\u003c/span\u003e();\n\u003cspan class=\"pl-smi\"\u003eTypeSafeKey\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e\u0026gt; \u003cspan class=\"pl-s1\"\u003eintKey\u003c/span\u003e = \u003cspan class=\"pl-smi\"\u003eTypeSafeKey\u003c/span\u003e.\u003cspan class=\"pl-en\"\u003etypeSafeKey\u003c/span\u003e();\n\u003cspan class=\"pl-smi\"\u003eHMap\u003c/span\u003e \u003cspan class=\"pl-s1\"\u003ehmap\u003c/span\u003e = \u003cspan class=\"pl-smi\"\u003eHMap\u003c/span\u003e.\u003cspan class=\"pl-en\"\u003ehMap\u003c/span\u003e(\u003cspan class=\"pl-s1\"\u003estringKey\u003c/span\u003e, \u003cspan class=\"pl-s\"\u003e\"string value\"\u003c/span\u003e,\n \u003cspan class=\"pl-s1\"\u003eintKey\u003c/span\u003e, \u003cspan class=\"pl-c1\"\u003e1\u003c/span\u003e);\n\n\u003cspan class=\"pl-smi\"\u003eOptional\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eString\u003c/span\u003e\u0026gt; \u003cspan class=\"pl-s1\"\u003estringValue\u003c/span\u003e = \u003cspan class=\"pl-s1\"\u003ehmap\u003c/span\u003e.\u003cspan class=\"pl-en\"\u003eget\u003c/span\u003e(\u003cspan class=\"pl-s1\"\u003estringKey\u003c/span\u003e); \u003cspan class=\"pl-c\"\u003e// Optional[\"string value\"]\u003c/span\u003e\n\u003cspan class=\"pl-smi\"\u003eOptional\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e\u0026gt; \u003cspan class=\"pl-s1\"\u003eintValue\u003c/span\u003e = \u003cspan class=\"pl-s1\"\u003ehmap\u003c/span\u003e.\u003cspan class=\"pl-en\"\u003eget\u003c/span\u003e(\u003cspan class=\"pl-s1\"\u003eintKey\u003c/span\u003e); \u003cspan class=\"pl-c\"\u003e// Optional[1]\u003c/span\u003e\n\u003cspan class=\"pl-smi\"\u003eOptional\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e\u0026gt; \u003cspan class=\"pl-s1\"\u003eanotherIntValue\u003c/span\u003e = \u003cspan class=\"pl-s1\"\u003ehmap\u003c/span\u003e.\u003cspan class=\"pl-en\"\u003eget\u003c/span\u003e(\u003cspan class=\"pl-s1\"\u003eanotherIntKey\u003c/span\u003e); \u003cspan class=\"pl-c\"\u003e// Optional.empty\u003c/span\u003e\u003c/pre\u003e\u003c/div\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch3 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003e\u003ca name=\"user-content-coproducts\"\u003eCoProducts\u003c/a\u003e\u003c/h3\u003e\u003ca id=\"user-content-coproducts\" class=\"anchor\" aria-label=\"Permalink: CoProducts\" href=\"#coproducts\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003e\u003ccode\u003eCoProduct\u003c/code\u003es generalize unions of disparate types in a single consolidated type, and the \u003ccode\u003eChoiceN\u003c/code\u003e ADTs represent canonical implementations of these coproduct types.\u003c/p\u003e\n\u003cdiv class=\"highlight highlight-source-java notranslate position-relative overflow-auto\" dir=\"auto\" data-snippet-clipboard-copy-content=\"CoProduct3\u0026lt;String, Integer, Character, ?\u0026gt; string = Choice3.a(\u0026quot;string\u0026quot;);\nCoProduct3\u0026lt;String, Integer, Character, ?\u0026gt; integer = Choice3.b(1);\nCoProduct3\u0026lt;String, Integer, Character, ?\u0026gt; character = Choice3.c('a');\"\u003e\u003cpre\u003e\u003cspan class=\"pl-smi\"\u003eCoProduct3\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eString\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003eCharacter\u003c/span\u003e, ?\u0026gt; \u003cspan class=\"pl-s1\"\u003estring\u003c/span\u003e = \u003cspan class=\"pl-smi\"\u003eChoice3\u003c/span\u003e.\u003cspan class=\"pl-en\"\u003ea\u003c/span\u003e(\u003cspan class=\"pl-s\"\u003e\"string\"\u003c/span\u003e);\n\u003cspan class=\"pl-smi\"\u003eCoProduct3\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eString\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003eCharacter\u003c/span\u003e, ?\u0026gt; \u003cspan class=\"pl-s1\"\u003einteger\u003c/span\u003e = \u003cspan class=\"pl-smi\"\u003eChoice3\u003c/span\u003e.\u003cspan class=\"pl-en\"\u003eb\u003c/span\u003e(\u003cspan class=\"pl-c1\"\u003e1\u003c/span\u003e);\n\u003cspan class=\"pl-smi\"\u003eCoProduct3\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eString\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003eCharacter\u003c/span\u003e, ?\u0026gt; \u003cspan class=\"pl-s1\"\u003echaracter\u003c/span\u003e = \u003cspan class=\"pl-smi\"\u003eChoice3\u003c/span\u003e.\u003cspan class=\"pl-en\"\u003ec\u003c/span\u003e(\u003cspan class=\"pl-s\"\u003e'a'\u003c/span\u003e);\u003c/pre\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eRather than supporting explicit value unwrapping, which would necessarily jeopardize type safety, \u003ccode\u003eCoProduct\u003c/code\u003es support a \u003ccode\u003ematch\u003c/code\u003e method that takes one function per possible value type and maps it to a final common result type:\u003c/p\u003e\n\u003cdiv class=\"highlight highlight-source-java notranslate position-relative overflow-auto\" dir=\"auto\" data-snippet-clipboard-copy-content=\"CoProduct3\u0026lt;String, Integer, Character, ?\u0026gt; string = Choice3.a(\u0026quot;string\u0026quot;);\nCoProduct3\u0026lt;String, Integer, Character, ?\u0026gt; integer = Choice3.b(1);\nCoProduct3\u0026lt;String, Integer, Character, ?\u0026gt; character = Choice3.c('a');\n\nInteger result = string.\u0026lt;Integer\u0026gt;match(String::length, identity(), Character::charCount); // 6\"\u003e\u003cpre\u003e\u003cspan class=\"pl-smi\"\u003eCoProduct3\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eString\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003eCharacter\u003c/span\u003e, ?\u0026gt; \u003cspan class=\"pl-s1\"\u003estring\u003c/span\u003e = \u003cspan class=\"pl-smi\"\u003eChoice3\u003c/span\u003e.\u003cspan class=\"pl-en\"\u003ea\u003c/span\u003e(\u003cspan class=\"pl-s\"\u003e\"string\"\u003c/span\u003e);\n\u003cspan class=\"pl-smi\"\u003eCoProduct3\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eString\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003eCharacter\u003c/span\u003e, ?\u0026gt; \u003cspan class=\"pl-s1\"\u003einteger\u003c/span\u003e = \u003cspan class=\"pl-smi\"\u003eChoice3\u003c/span\u003e.\u003cspan class=\"pl-en\"\u003eb\u003c/span\u003e(\u003cspan class=\"pl-c1\"\u003e1\u003c/span\u003e);\n\u003cspan class=\"pl-smi\"\u003eCoProduct3\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eString\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003eCharacter\u003c/span\u003e, ?\u0026gt; \u003cspan class=\"pl-s1\"\u003echaracter\u003c/span\u003e = \u003cspan class=\"pl-smi\"\u003eChoice3\u003c/span\u003e.\u003cspan class=\"pl-en\"\u003ec\u003c/span\u003e(\u003cspan class=\"pl-s\"\u003e'a'\u003c/span\u003e);\n\n\u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e \u003cspan class=\"pl-s1\"\u003eresult\u003c/span\u003e = \u003cspan class=\"pl-s1\"\u003estring\u003c/span\u003e.\u0026lt;\u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e\u0026gt;\u003cspan class=\"pl-en\"\u003ematch\u003c/span\u003e(\u003cspan class=\"pl-smi\"\u003eString\u003c/span\u003e::\u003cspan class=\"pl-s1\"\u003elength\u003c/span\u003e, \u003cspan class=\"pl-en\"\u003eidentity\u003c/span\u003e(), \u003cspan class=\"pl-smi\"\u003eCharacter\u003c/span\u003e::\u003cspan class=\"pl-s1\"\u003echarCount\u003c/span\u003e); \u003cspan class=\"pl-c\"\u003e// 6\u003c/span\u003e\u003c/pre\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eAdditionally, because a \u003ccode\u003eCoProduct2\u0026lt;A, B, ?\u0026gt;\u003c/code\u003e guarantees a subset of a \u003ccode\u003eCoProduct3\u0026lt;A, B, C, ?\u0026gt;\u003c/code\u003e, the \u003ccode\u003ediverge\u003c/code\u003e method exists between \u003ccode\u003eCoProduct\u003c/code\u003e types of single magnitude differences to make it easy to use a more convergent \u003ccode\u003eCoProduct\u003c/code\u003e where a more divergent \u003ccode\u003eCoProduct\u003c/code\u003e is expected:\u003c/p\u003e\n\u003cdiv class=\"highlight highlight-source-java notranslate position-relative overflow-auto\" dir=\"auto\" data-snippet-clipboard-copy-content=\"CoProduct2\u0026lt;String, Integer, ?\u0026gt; coProduct2 = Choice2.a(\u0026quot;string\u0026quot;);\nCoProduct3\u0026lt;String, Integer, Character, ?\u0026gt; coProduct3 = coProduct2.diverge(); // still just the coProduct2 value, adapted to the coProduct3 shape\"\u003e\u003cpre\u003e\u003cspan class=\"pl-smi\"\u003eCoProduct2\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eString\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e, ?\u0026gt; \u003cspan class=\"pl-s1\"\u003ecoProduct2\u003c/span\u003e = \u003cspan class=\"pl-smi\"\u003eChoice2\u003c/span\u003e.\u003cspan class=\"pl-en\"\u003ea\u003c/span\u003e(\u003cspan class=\"pl-s\"\u003e\"string\"\u003c/span\u003e);\n\u003cspan class=\"pl-smi\"\u003eCoProduct3\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eString\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003eCharacter\u003c/span\u003e, ?\u0026gt; \u003cspan class=\"pl-s1\"\u003ecoProduct3\u003c/span\u003e = \u003cspan class=\"pl-s1\"\u003ecoProduct2\u003c/span\u003e.\u003cspan class=\"pl-en\"\u003ediverge\u003c/span\u003e(); \u003cspan class=\"pl-c\"\u003e// still just the coProduct2 value, adapted to the coProduct3 shape\u003c/span\u003e\u003c/pre\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eThere are \u003ccode\u003eCoProduct\u003c/code\u003e and \u003ccode\u003eChoice\u003c/code\u003e specializations for type unions of up to 8 different types: \u003ccode\u003eCoProduct2\u003c/code\u003e through \u003ccode\u003eCoProduct8\u003c/code\u003e, and \u003ccode\u003eChoice2\u003c/code\u003e through \u003ccode\u003eChoice8\u003c/code\u003e, respectively.\u003c/p\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch3 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003e\u003ca name=\"user-content-either\"\u003eEither\u003c/a\u003e\u003c/h3\u003e\u003ca id=\"user-content-either\" class=\"anchor\" aria-label=\"Permalink: Either\" href=\"#either\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003e\u003ccode\u003eEither\u0026lt;L, R\u0026gt;\u003c/code\u003e represents a specialized \u003ccode\u003eCoProduct2\u0026lt;L, R\u0026gt;\u003c/code\u003e, which resolve to one of two possible values: a left value wrapping an \u003ccode\u003eL\u003c/code\u003e, or a right value wrapping an \u003ccode\u003eR\u003c/code\u003e (typically an exceptional value or a successful value, respectively).\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eAs with \u003ccode\u003eCoProduct2\u003c/code\u003e, rather than supporting explicit value unwrapping, \u003ccode\u003eEither\u003c/code\u003e supports many useful comprehensions to help facilitate type-safe interactions:\u003c/p\u003e\n\u003cdiv class=\"highlight highlight-source-java notranslate position-relative overflow-auto\" dir=\"auto\" data-snippet-clipboard-copy-content=\"Either\u0026lt;String, Integer\u0026gt; right = Either.right(1);\nEither\u0026lt;String, Integer\u0026gt; left = Either.left(\u0026quot;Head fell off\u0026quot;);\n\nInteger result = right.orElse(-1);\n//-\u0026gt; 1\n\nList\u0026lt;Integer\u0026gt; values = left.match(l -\u0026gt; Collections.emptyList(), Collections::singletonList);\n//-\u0026gt; [] \"\u003e\u003cpre\u003e\u003cspan class=\"pl-smi\"\u003eEither\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eString\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e\u0026gt; \u003cspan class=\"pl-s1\"\u003eright\u003c/span\u003e = \u003cspan class=\"pl-smi\"\u003eEither\u003c/span\u003e.\u003cspan class=\"pl-en\"\u003eright\u003c/span\u003e(\u003cspan class=\"pl-c1\"\u003e1\u003c/span\u003e);\n\u003cspan class=\"pl-smi\"\u003eEither\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eString\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e\u0026gt; \u003cspan class=\"pl-s1\"\u003eleft\u003c/span\u003e = \u003cspan class=\"pl-smi\"\u003eEither\u003c/span\u003e.\u003cspan class=\"pl-en\"\u003eleft\u003c/span\u003e(\u003cspan class=\"pl-s\"\u003e\"Head fell off\"\u003c/span\u003e);\n\n\u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e \u003cspan class=\"pl-s1\"\u003eresult\u003c/span\u003e = \u003cspan class=\"pl-s1\"\u003eright\u003c/span\u003e.\u003cspan class=\"pl-en\"\u003eorElse\u003c/span\u003e(-\u003cspan class=\"pl-c1\"\u003e1\u003c/span\u003e);\n\u003cspan class=\"pl-c\"\u003e//-\u0026gt; 1\u003c/span\u003e\n\n\u003cspan class=\"pl-smi\"\u003eList\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e\u0026gt; \u003cspan class=\"pl-s1\"\u003evalues\u003c/span\u003e = \u003cspan class=\"pl-s1\"\u003eleft\u003c/span\u003e.\u003cspan class=\"pl-en\"\u003ematch\u003c/span\u003e(\u003cspan class=\"pl-s1\"\u003el\u003c/span\u003e -\u0026gt; \u003cspan class=\"pl-smi\"\u003eCollections\u003c/span\u003e.\u003cspan class=\"pl-en\"\u003eemptyList\u003c/span\u003e(), \u003cspan class=\"pl-smi\"\u003eCollections\u003c/span\u003e::\u003cspan class=\"pl-s1\"\u003esingletonList\u003c/span\u003e);\n\u003cspan class=\"pl-c\"\u003e//-\u0026gt; [] \u003c/span\u003e\u003c/pre\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eCheck out the tests for \u003ca href=\"https://github.com/palatable/lambda/blob/master/src/test/java/com/jnape/palatable/lambda/adt/EitherTest.java\"\u003emore examples\u003c/a\u003e of ways to interact with \u003ccode\u003eEither\u003c/code\u003e.\u003c/p\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch2 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003e\u003ca name=\"user-content-lenses\"\u003eLenses\u003c/a\u003e\u003c/h2\u003e\u003ca id=\"user-content-lenses\" class=\"anchor\" aria-label=\"Permalink: Lenses\" href=\"#lenses\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eLambda also ships with a first-class \u003ca href=\"https://www.youtube.com/watch?v=cefnmjtAolY\u0026amp;feature=youtu.be\u0026amp;hd=1\" rel=\"nofollow\"\u003elens\u003c/a\u003e type, as well as a small library of useful general lenses:\u003c/p\u003e\n\u003cdiv class=\"highlight highlight-source-java notranslate position-relative overflow-auto\" dir=\"auto\" data-snippet-clipboard-copy-content=\"Lens\u0026lt;List\u0026lt;String\u0026gt;, List\u0026lt;String\u0026gt;, Optional\u0026lt;String\u0026gt;, String\u0026gt; stringAt0 = ListLens.at(0);\n\nList\u0026lt;String\u0026gt; strings = asList(\u0026quot;foo\u0026quot;, \u0026quot;bar\u0026quot;, \u0026quot;baz\u0026quot;);\nview(stringAt0, strings); // Optional[foo]\nset(stringAt0, \u0026quot;quux\u0026quot;, strings); // [quux, bar, baz]\nover(stringAt0, s -\u0026gt; s.map(String::toUpperCase).orElse(\u0026quot;\u0026quot;), strings); // [FOO, bar, baz]\"\u003e\u003cpre\u003e\u003cspan class=\"pl-smi\"\u003eLens\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eList\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eString\u003c/span\u003e\u0026gt;, \u003cspan class=\"pl-smi\"\u003eList\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eString\u003c/span\u003e\u0026gt;, \u003cspan class=\"pl-smi\"\u003eOptional\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eString\u003c/span\u003e\u0026gt;, \u003cspan class=\"pl-smi\"\u003eString\u003c/span\u003e\u0026gt; \u003cspan class=\"pl-s1\"\u003estringAt0\u003c/span\u003e = \u003cspan class=\"pl-smi\"\u003eListLens\u003c/span\u003e.\u003cspan class=\"pl-en\"\u003eat\u003c/span\u003e(\u003cspan class=\"pl-c1\"\u003e0\u003c/span\u003e);\n\n\u003cspan class=\"pl-smi\"\u003eList\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eString\u003c/span\u003e\u0026gt; \u003cspan class=\"pl-s1\"\u003estrings\u003c/span\u003e = \u003cspan class=\"pl-en\"\u003easList\u003c/span\u003e(\u003cspan class=\"pl-s\"\u003e\"foo\"\u003c/span\u003e, \u003cspan class=\"pl-s\"\u003e\"bar\"\u003c/span\u003e, \u003cspan class=\"pl-s\"\u003e\"baz\"\u003c/span\u003e);\n\u003cspan class=\"pl-en\"\u003eview\u003c/span\u003e(\u003cspan class=\"pl-s1\"\u003estringAt0\u003c/span\u003e, \u003cspan class=\"pl-s1\"\u003estrings\u003c/span\u003e); \u003cspan class=\"pl-c\"\u003e// Optional[foo]\u003c/span\u003e\n\u003cspan class=\"pl-en\"\u003eset\u003c/span\u003e(\u003cspan class=\"pl-s1\"\u003estringAt0\u003c/span\u003e, \u003cspan class=\"pl-s\"\u003e\"quux\"\u003c/span\u003e, \u003cspan class=\"pl-s1\"\u003estrings\u003c/span\u003e); \u003cspan class=\"pl-c\"\u003e// [quux, bar, baz]\u003c/span\u003e\n\u003cspan class=\"pl-en\"\u003eover\u003c/span\u003e(\u003cspan class=\"pl-s1\"\u003estringAt0\u003c/span\u003e, \u003cspan class=\"pl-s1\"\u003es\u003c/span\u003e -\u0026gt; \u003cspan class=\"pl-s1\"\u003es\u003c/span\u003e.\u003cspan class=\"pl-en\"\u003emap\u003c/span\u003e(\u003cspan class=\"pl-smi\"\u003eString\u003c/span\u003e::\u003cspan class=\"pl-s1\"\u003etoUpperCase\u003c/span\u003e).\u003cspan class=\"pl-en\"\u003eorElse\u003c/span\u003e(\u003cspan class=\"pl-s\"\u003e\"\"\u003c/span\u003e), \u003cspan class=\"pl-s1\"\u003estrings\u003c/span\u003e); \u003cspan class=\"pl-c\"\u003e// [FOO, bar, baz]\u003c/span\u003e\u003c/pre\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eThere are three functions that lambda provides that interface directly with lenses: \u003ccode\u003eview\u003c/code\u003e, \u003ccode\u003eover\u003c/code\u003e, and \u003ccode\u003eset\u003c/code\u003e. As the name implies, \u003ccode\u003eview\u003c/code\u003e and \u003ccode\u003eset\u003c/code\u003e are used to retrieve values and store values, respectively, whereas \u003ccode\u003eover\u003c/code\u003e is used to apply a function to the value a lens is focused on, alter it, and store it (you can think of \u003ccode\u003eset\u003c/code\u003e as a specialization of \u003ccode\u003eover\u003c/code\u003e using \u003ccode\u003econstantly\u003c/code\u003e).\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eLenses can be easily created. Consider the following \u003ccode\u003ePerson\u003c/code\u003e class:\u003c/p\u003e\n\u003cdiv class=\"highlight highlight-source-java notranslate position-relative overflow-auto\" dir=\"auto\" data-snippet-clipboard-copy-content=\"public final class Person {\n private final int age;\n\n public Person(int age) {\n this.age = age;\n }\n\n public int getAge() {\n return age;\n }\n\n public Person setAge(int age) {\n return new Person(age);\n }\n\n public Person setAge(LocalDate dob) {\n return setAge((int) YEARS.between(dob, LocalDate.now()));\n }\n}\"\u003e\u003cpre\u003e\u003cspan class=\"pl-k\"\u003epublic\u003c/span\u003e \u003cspan class=\"pl-k\"\u003efinal\u003c/span\u003e \u003cspan class=\"pl-k\"\u003eclass\u003c/span\u003e \u003cspan class=\"pl-smi\"\u003ePerson\u003c/span\u003e {\n \u003cspan class=\"pl-k\"\u003eprivate\u003c/span\u003e \u003cspan class=\"pl-k\"\u003efinal\u003c/span\u003e \u003cspan class=\"pl-smi\"\u003eint\u003c/span\u003e \u003cspan class=\"pl-s1\"\u003eage\u003c/span\u003e;\n\n \u003cspan class=\"pl-k\"\u003epublic\u003c/span\u003e \u003cspan class=\"pl-smi\"\u003ePerson\u003c/span\u003e(\u003cspan class=\"pl-smi\"\u003eint\u003c/span\u003e \u003cspan class=\"pl-s1\"\u003eage\u003c/span\u003e) {\n \u003cspan class=\"pl-smi\"\u003ethis\u003c/span\u003e.\u003cspan class=\"pl-s1\"\u003eage\u003c/span\u003e = \u003cspan class=\"pl-s1\"\u003eage\u003c/span\u003e;\n }\n\n \u003cspan class=\"pl-k\"\u003epublic\u003c/span\u003e \u003cspan class=\"pl-smi\"\u003eint\u003c/span\u003e \u003cspan class=\"pl-en\"\u003egetAge\u003c/span\u003e() {\n \u003cspan class=\"pl-k\"\u003ereturn\u003c/span\u003e \u003cspan class=\"pl-s1\"\u003eage\u003c/span\u003e;\n }\n\n \u003cspan class=\"pl-k\"\u003epublic\u003c/span\u003e \u003cspan class=\"pl-smi\"\u003ePerson\u003c/span\u003e \u003cspan class=\"pl-en\"\u003esetAge\u003c/span\u003e(\u003cspan class=\"pl-smi\"\u003eint\u003c/span\u003e \u003cspan class=\"pl-s1\"\u003eage\u003c/span\u003e) {\n \u003cspan class=\"pl-k\"\u003ereturn\u003c/span\u003e \u003cspan class=\"pl-k\"\u003enew\u003c/span\u003e \u003cspan class=\"pl-smi\"\u003ePerson\u003c/span\u003e(\u003cspan class=\"pl-s1\"\u003eage\u003c/span\u003e);\n }\n\n \u003cspan class=\"pl-k\"\u003epublic\u003c/span\u003e \u003cspan class=\"pl-smi\"\u003ePerson\u003c/span\u003e \u003cspan class=\"pl-en\"\u003esetAge\u003c/span\u003e(\u003cspan class=\"pl-smi\"\u003eLocalDate\u003c/span\u003e \u003cspan class=\"pl-s1\"\u003edob\u003c/span\u003e) {\n \u003cspan class=\"pl-k\"\u003ereturn\u003c/span\u003e \u003cspan class=\"pl-en\"\u003esetAge\u003c/span\u003e((\u003cspan class=\"pl-smi\"\u003eint\u003c/span\u003e) \u003cspan class=\"pl-c1\"\u003eYEARS\u003c/span\u003e.\u003cspan class=\"pl-en\"\u003ebetween\u003c/span\u003e(\u003cspan class=\"pl-s1\"\u003edob\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003eLocalDate\u003c/span\u003e.\u003cspan class=\"pl-en\"\u003enow\u003c/span\u003e()));\n }\n}\u003c/pre\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003e...and a lens for getting and setting \u003ccode\u003eage\u003c/code\u003e as an \u003ccode\u003eint\u003c/code\u003e:\u003c/p\u003e\n\u003cdiv class=\"highlight highlight-source-java notranslate position-relative overflow-auto\" dir=\"auto\" data-snippet-clipboard-copy-content=\"Lens\u0026lt;Person, Person, Integer, Integer\u0026gt; ageLensWithInt = Lens.lens(Person::getAge, Person::setAge);\n\n//or, when each pair of type arguments match...\n\nLens.Simple\u0026lt;Person, Integer\u0026gt; alsoAgeLensWithInt = Lens.simpleLens(Person::getAge, Person::setAge);\"\u003e\u003cpre\u003e\u003cspan class=\"pl-smi\"\u003eLens\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003ePerson\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003ePerson\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e\u0026gt; \u003cspan class=\"pl-s1\"\u003eageLensWithInt\u003c/span\u003e = \u003cspan class=\"pl-smi\"\u003eLens\u003c/span\u003e.\u003cspan class=\"pl-en\"\u003elens\u003c/span\u003e(\u003cspan class=\"pl-smi\"\u003ePerson\u003c/span\u003e::\u003cspan class=\"pl-s1\"\u003egetAge\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003ePerson\u003c/span\u003e::\u003cspan class=\"pl-s1\"\u003esetAge\u003c/span\u003e);\n\n\u003cspan class=\"pl-c\"\u003e//or, when each pair of type arguments match...\u003c/span\u003e\n\n\u003cspan class=\"pl-smi\"\u003eLens\u003c/span\u003e.\u003cspan class=\"pl-smi\"\u003eSimple\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003ePerson\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e\u0026gt; \u003cspan class=\"pl-s1\"\u003ealsoAgeLensWithInt\u003c/span\u003e = \u003cspan class=\"pl-smi\"\u003eLens\u003c/span\u003e.\u003cspan class=\"pl-en\"\u003esimpleLens\u003c/span\u003e(\u003cspan class=\"pl-smi\"\u003ePerson\u003c/span\u003e::\u003cspan class=\"pl-s1\"\u003egetAge\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003ePerson\u003c/span\u003e::\u003cspan class=\"pl-s1\"\u003esetAge\u003c/span\u003e);\u003c/pre\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eIf we wanted a lens for the \u003ccode\u003eLocalDate\u003c/code\u003e version of \u003ccode\u003esetAge\u003c/code\u003e, we could use the same method references and only alter the type signature:\u003c/p\u003e\n\u003cdiv class=\"highlight highlight-source-java notranslate position-relative overflow-auto\" dir=\"auto\" data-snippet-clipboard-copy-content=\"Lens\u0026lt;Person, Person, Integer, LocalDate\u0026gt; ageLensWithLocalDate = Lens.lens(Person::getAge, Person::setAge);\"\u003e\u003cpre\u003e\u003cspan class=\"pl-smi\"\u003eLens\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003ePerson\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003ePerson\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003eLocalDate\u003c/span\u003e\u0026gt; \u003cspan class=\"pl-s1\"\u003eageLensWithLocalDate\u003c/span\u003e = \u003cspan class=\"pl-smi\"\u003eLens\u003c/span\u003e.\u003cspan class=\"pl-en\"\u003elens\u003c/span\u003e(\u003cspan class=\"pl-smi\"\u003ePerson\u003c/span\u003e::\u003cspan class=\"pl-s1\"\u003egetAge\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003ePerson\u003c/span\u003e::\u003cspan class=\"pl-s1\"\u003esetAge\u003c/span\u003e);\u003c/pre\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eCompatible lenses can be trivially composed:\u003c/p\u003e\n\u003cdiv class=\"highlight highlight-source-java notranslate position-relative overflow-auto\" dir=\"auto\" data-snippet-clipboard-copy-content=\"Lens\u0026lt;List\u0026lt;Integer\u0026gt;, List\u0026lt;Integer\u0026gt;, Optional\u0026lt;Integer\u0026gt;, Integer\u0026gt; at0 = ListLens.at(0);\nLens\u0026lt;Map\u0026lt;String, List\u0026lt;Integer\u0026gt;\u0026gt;, Map\u0026lt;String, List\u0026lt;Integer\u0026gt;\u0026gt;, List\u0026lt;Integer\u0026gt;, List\u0026lt;Integer\u0026gt;\u0026gt; atFoo = MapLens.atKey(\u0026quot;foo\u0026quot;, emptyList());\n\nview(atFoo.andThen(at0), singletonMap(\u0026quot;foo\u0026quot;, asList(1, 2, 3))); // Optional[1]\"\u003e\u003cpre\u003e\u003cspan class=\"pl-smi\"\u003eLens\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eList\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e\u0026gt;, \u003cspan class=\"pl-smi\"\u003eList\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e\u0026gt;, \u003cspan class=\"pl-smi\"\u003eOptional\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e\u0026gt;, \u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e\u0026gt; \u003cspan class=\"pl-s1\"\u003eat0\u003c/span\u003e = \u003cspan class=\"pl-smi\"\u003eListLens\u003c/span\u003e.\u003cspan class=\"pl-en\"\u003eat\u003c/span\u003e(\u003cspan class=\"pl-c1\"\u003e0\u003c/span\u003e);\n\u003cspan class=\"pl-smi\"\u003eLens\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eMap\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eString\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003eList\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e\u0026gt;\u0026gt;, \u003cspan class=\"pl-smi\"\u003eMap\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eString\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003eList\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e\u0026gt;\u0026gt;, \u003cspan class=\"pl-smi\"\u003eList\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e\u0026gt;, \u003cspan class=\"pl-smi\"\u003eList\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e\u0026gt;\u0026gt; \u003cspan class=\"pl-s1\"\u003eatFoo\u003c/span\u003e = \u003cspan class=\"pl-smi\"\u003eMapLens\u003c/span\u003e.\u003cspan class=\"pl-en\"\u003eatKey\u003c/span\u003e(\u003cspan class=\"pl-s\"\u003e\"foo\"\u003c/span\u003e, \u003cspan class=\"pl-en\"\u003eemptyList\u003c/span\u003e());\n\n\u003cspan class=\"pl-en\"\u003eview\u003c/span\u003e(\u003cspan class=\"pl-s1\"\u003eatFoo\u003c/span\u003e.\u003cspan class=\"pl-en\"\u003eandThen\u003c/span\u003e(\u003cspan class=\"pl-s1\"\u003eat0\u003c/span\u003e), \u003cspan class=\"pl-en\"\u003esingletonMap\u003c/span\u003e(\u003cspan class=\"pl-s\"\u003e\"foo\"\u003c/span\u003e, \u003cspan class=\"pl-en\"\u003easList\u003c/span\u003e(\u003cspan class=\"pl-c1\"\u003e1\u003c/span\u003e, \u003cspan class=\"pl-c1\"\u003e2\u003c/span\u003e, \u003cspan class=\"pl-c1\"\u003e3\u003c/span\u003e))); \u003cspan class=\"pl-c\"\u003e// Optional[1]\u003c/span\u003e\u003c/pre\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eLens provides independent \u003ccode\u003emap\u003c/code\u003e operations for each parameter, so incompatible lenses can also be composed:\u003c/p\u003e\n\u003cdiv class=\"highlight highlight-source-java notranslate position-relative overflow-auto\" dir=\"auto\" data-snippet-clipboard-copy-content=\"Lens\u0026lt;List\u0026lt;Integer\u0026gt;, List\u0026lt;Integer\u0026gt;, Optional\u0026lt;Integer\u0026gt;, Integer\u0026gt; at0 = ListLens.at(0);\nLens\u0026lt;Map\u0026lt;String, List\u0026lt;Integer\u0026gt;\u0026gt;, Map\u0026lt;String, List\u0026lt;Integer\u0026gt;\u0026gt;, Optional\u0026lt;List\u0026lt;Integer\u0026gt;\u0026gt;, List\u0026lt;Integer\u0026gt;\u0026gt; atFoo = MapLens.atKey(\u0026quot;foo\u0026quot;);\nLens\u0026lt;Map\u0026lt;String, List\u0026lt;Integer\u0026gt;\u0026gt;, Map\u0026lt;String, List\u0026lt;Integer\u0026gt;\u0026gt;, Optional\u0026lt;Integer\u0026gt;, Integer\u0026gt; composed =\n atFoo.mapA(optL -\u0026gt; optL.orElse(singletonList(-1)))\n .andThen(at0);\n\nview(composed, singletonMap(\u0026quot;foo\u0026quot;, emptyList())); // Optional.empty\"\u003e\u003cpre\u003e\u003cspan class=\"pl-smi\"\u003eLens\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eList\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e\u0026gt;, \u003cspan class=\"pl-smi\"\u003eList\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e\u0026gt;, \u003cspan class=\"pl-smi\"\u003eOptional\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e\u0026gt;, \u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e\u0026gt; \u003cspan class=\"pl-s1\"\u003eat0\u003c/span\u003e = \u003cspan class=\"pl-smi\"\u003eListLens\u003c/span\u003e.\u003cspan class=\"pl-en\"\u003eat\u003c/span\u003e(\u003cspan class=\"pl-c1\"\u003e0\u003c/span\u003e);\n\u003cspan class=\"pl-smi\"\u003eLens\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eMap\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eString\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003eList\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e\u0026gt;\u0026gt;, \u003cspan class=\"pl-smi\"\u003eMap\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eString\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003eList\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e\u0026gt;\u0026gt;, \u003cspan class=\"pl-smi\"\u003eOptional\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eList\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e\u0026gt;\u0026gt;, \u003cspan class=\"pl-smi\"\u003eList\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e\u0026gt;\u0026gt; \u003cspan class=\"pl-s1\"\u003eatFoo\u003c/span\u003e = \u003cspan class=\"pl-smi\"\u003eMapLens\u003c/span\u003e.\u003cspan class=\"pl-en\"\u003eatKey\u003c/span\u003e(\u003cspan class=\"pl-s\"\u003e\"foo\"\u003c/span\u003e);\n\u003cspan class=\"pl-smi\"\u003eLens\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eMap\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eString\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003eList\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e\u0026gt;\u0026gt;, \u003cspan class=\"pl-smi\"\u003eMap\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eString\u003c/span\u003e, \u003cspan class=\"pl-smi\"\u003eList\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e\u0026gt;\u0026gt;, \u003cspan class=\"pl-smi\"\u003eOptional\u003c/span\u003e\u0026lt;\u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e\u0026gt;, \u003cspan class=\"pl-smi\"\u003eInteger\u003c/span\u003e\u0026gt; \u003cspan class=\"pl-s1\"\u003ecomposed\u003c/span\u003e =\n \u003cspan class=\"pl-s1\"\u003eatFoo\u003c/span\u003e.\u003cspan class=\"pl-en\"\u003emapA\u003c/span\u003e(\u003cspan class=\"pl-s1\"\u003eoptL\u003c/span\u003e -\u0026gt; \u003cspan class=\"pl-s1\"\u003eoptL\u003c/span\u003e.\u003cspan class=\"pl-en\"\u003eorElse\u003c/span\u003e(\u003cspan class=\"pl-en\"\u003esingletonList\u003c/span\u003e(-\u003cspan class=\"pl-c1\"\u003e1\u003c/span\u003e)))\n .\u003cspan class=\"pl-en\"\u003eandThen\u003c/span\u003e(\u003cspan class=\"pl-s1\"\u003eat0\u003c/span\u003e);\n\n\u003cspan class=\"pl-en\"\u003eview\u003c/span\u003e(\u003cspan class=\"pl-s1\"\u003ecomposed\u003c/span\u003e, \u003cspan class=\"pl-en\"\u003esingletonMap\u003c/span\u003e(\u003cspan class=\"pl-s\"\u003e\"foo\"\u003c/span\u003e, \u003cspan class=\"pl-en\"\u003eemptyList\u003c/span\u003e())); \u003cspan class=\"pl-c\"\u003e// Optional.empty\u003c/span\u003e\u003c/pre\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eCheck out the tests or the \u003ca href=\"http://palatable.github.io/lambda/javadoc/\" rel=\"nofollow\"\u003ejavadoc\u003c/a\u003e for more info.\u003c/p\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch2 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003e\u003ca name=\"user-content-notes\"\u003eNotes\u003c/a\u003e\u003c/h2\u003e\u003ca id=\"user-content-notes\" class=\"anchor\" aria-label=\"Permalink: Notes\" href=\"#notes\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eWherever possible, \u003cem\u003elambda\u003c/em\u003e maintains interface compatibility with similar, familiar core Java types. Some examples of where this works well is with both \u003ccode\u003eFn1\u003c/code\u003e and \u003ccode\u003ePredicate\u003c/code\u003e, which extend \u003ccode\u003ej.u.f.Function\u003c/code\u003e and \u003ccode\u003ej.u.f.Predicate\u003c/code\u003e, respectively. In these examples, they also override any implemented methods to return their \u003cem\u003elambda\u003c/em\u003e-specific counterparts (\u003ccode\u003eFn1.compose\u003c/code\u003e returning \u003ccode\u003eFn1\u003c/code\u003e instead of \u003ccode\u003ej.u.f.Function\u003c/code\u003e as an example).\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eUnfortunately, due to Java's type hierarchy and inheritance inconsistencies, this is not always possible. One surprising example of this is how \u003ccode\u003eFn1\u003c/code\u003e extends \u003ccode\u003ej.u.f.Function\u003c/code\u003e, but \u003ccode\u003eFn2\u003c/code\u003e does not extend \u003ccode\u003ej.u.f.BiFunction\u003c/code\u003e. This is because \u003ccode\u003ej.u.f.BiFunction\u003c/code\u003e itself does not extend \u003ccode\u003ej.u.f.Function\u003c/code\u003e, but it does define methods that collide with \u003ccode\u003ej.u.f.Function\u003c/code\u003e. For this reason, both \u003ccode\u003eFn1\u003c/code\u003e and \u003ccode\u003eFn2\u003c/code\u003e cannot extend their Java counterparts without sacrificing their own inheritance hierarchy. These types of asymmetries are, unfortunately, not uncommon; however, wherever these situations arise, measures are taken to attempt to ease the transition in and out of core Java types (in the case of \u003ccode\u003eFn2\u003c/code\u003e, a supplemental \u003ccode\u003e#toBiFunction\u003c/code\u003e method is added). I do not take these inconveniences for granted, and I'm regularly looking for ways to minimize the negative impact of this as much as possible. Suggestions and use cases that highlight particular pain points here are particularly appreciated.\u003c/p\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch2 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003e\u003ca name=\"user-content-ecosystem\"\u003eEcosystem\u003c/a\u003e\u003c/h2\u003e\u003ca id=\"user-content-ecosystem\" class=\"anchor\" aria-label=\"Permalink: Ecosystem\" href=\"#ecosystem\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch3 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eOfficial extension libraries:\u003c/h3\u003e\u003ca id=\"user-content-official-extension-libraries\" class=\"anchor\" aria-label=\"Permalink: Official extension libraries:\" href=\"#official-extension-libraries\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eThese are officially supported libraries that extend lambda's core functionality and are developed under the same governance and processes as lambda.\u003c/p\u003e\n\u003cul dir=\"auto\"\u003e\n\u003cli\u003e\u003ca href=\"https://github.com/palatable/shoki\"\u003eShōki\u003c/a\u003e - Purely functional, persistent data structures for the JVM\u003c/li\u003e\n\u003c/ul\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch3 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eThird-party community libraries:\u003c/h3\u003e\u003ca id=\"user-content-third-party-community-libraries\" class=\"anchor\" aria-label=\"Permalink: Third-party community libraries:\" href=\"#third-party-community-libraries\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eThese are open-sourced community projects that rely on \u003cem\u003elambda\u003c/em\u003e for significant functionality, but are not necessarily affiliated with lambda and have their own separate maintainers. If you use \u003cem\u003elambda\u003c/em\u003e in your own open-sourced project, feel free to create an issue and I'll be happy to review the project and add it to this section!\u003c/p\u003e\n\u003cul dir=\"auto\"\u003e\n\u003cli\u003e\u003ca href=\"https://github.com/kschuetz/enhanced-iterables\"\u003eEnhanced Iterables\u003c/a\u003e - Kevin Schuetz \u003ca href=\"https://github.com/kschuetz\"\u003e@kschuetz\u003c/a\u003e\u003c/li\u003e\n\u003cli\u003e\u003ca href=\"https://github.com/kschuetz/collection-views\"\u003eCollection Views\u003c/a\u003e - Kevin Schuetz \u003ca href=\"https://github.com/kschuetz\"\u003e@kschuetz\u003c/a\u003e\u003c/li\u003e\n\u003cli\u003e\u003ca href=\"https://github.com/nomicflux/WuWei\"\u003eWuWei\u003c/a\u003e - Michael Anderson \u003ca href=\"https://github.com/nomicflux\"\u003e@nomicflux\u003c/a\u003e - \u003ccode\u003eST\u003c/code\u003e monad for safe mutability\u003c/li\u003e\n\u003cli\u003e\u003ca href=\"https://github.com/kschuetz/kraftwerk\"\u003eKraftwerk\u003c/a\u003e - Kevin Schuetz \u003ca href=\"https://github.com/kschuetz\"\u003e@kschuetz\u003c/a\u003e - random data generators and combinators\u003c/li\u003e\n\u003c/ul\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch2 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003e\u003ca name=\"user-content-license\"\u003eLicense\u003c/a\u003e\u003c/h2\u003e\u003ca id=\"user-content-license\" class=\"anchor\" aria-label=\"Permalink: License\" href=\"#license\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003e\u003cem\u003elambda\u003c/em\u003e is part of \u003ca href=\"http://www.github.com/palatable\"\u003epalatable\u003c/a\u003e, which is distributed under \u003ca href=\"http://choosealicense.com/licenses/mit/\" rel=\"nofollow\"\u003eThe MIT License\u003c/a\u003e.\u003c/p\u003e\n\u003c/article\u003e","loaded":true,"timedOut":false,"errorMessage":null,"headerInfo":{"toc":[{"level":1,"text":"λ","anchor":"λ","htmlText":"λ"},{"level":4,"text":"Table of Contents","anchor":"table-of-contents","htmlText":"Table of Contents"},{"level":2,"text":"Background","anchor":"background","htmlText":"Background"},{"level":2,"text":"Installation","anchor":"installation","htmlText":"Installation"},{"level":2,"text":"Examples","anchor":"examples","htmlText":"Examples"},{"level":2,"text":"Semigroups","anchor":"semigroups","htmlText":"Semigroups"},{"level":2,"text":"Monoids","anchor":"monoids","htmlText":"Monoids"},{"level":2,"text":"Functors","anchor":"functors","htmlText":"Functors"},{"level":3,"text":"Bifunctors","anchor":"bifunctors","htmlText":"Bifunctors"},{"level":3,"text":"Profunctors","anchor":"profunctors","htmlText":"Profunctors"},{"level":3,"text":"Applicatives","anchor":"applicatives","htmlText":"Applicatives"},{"level":3,"text":"Monads","anchor":"monads","htmlText":"Monads"},{"level":3,"text":"Traversables","anchor":"traversables","htmlText":"Traversables"},{"level":2,"text":"ADTs","anchor":"adts","htmlText":"ADTs"},{"level":3,"text":"Maybe","anchor":"maybe","htmlText":"Maybe"},{"level":3,"text":"Heterogeneous Lists (HLists)","anchor":"heterogeneous-lists-hlists","htmlText":"Heterogeneous Lists (HLists)"},{"level":4,"text":"Tuples","anchor":"tuples","htmlText":"Tuples"},{"level":3,"text":"Heterogeneous Maps","anchor":"heterogeneous-maps","htmlText":"Heterogeneous Maps"},{"level":3,"text":"CoProducts","anchor":"coproducts","htmlText":"CoProducts"},{"level":3,"text":"Either","anchor":"either","htmlText":"Either"},{"level":2,"text":"Lenses","anchor":"lenses","htmlText":"Lenses"},{"level":2,"text":"Notes","anchor":"notes","htmlText":"Notes"},{"level":2,"text":"Ecosystem","anchor":"ecosystem","htmlText":"Ecosystem"},{"level":3,"text":"Official extension libraries:","anchor":"official-extension-libraries","htmlText":"Official extension libraries:"},{"level":3,"text":"Third-party community libraries:","anchor":"third-party-community-libraries","htmlText":"Third-party community libraries:"},{"level":2,"text":"License","anchor":"license","htmlText":"License"}],"siteNavLoginPath":"/login?return_to=https%3A%2F%2Fgithub.com%2Fpalatable%2Flambda"}},{"displayName":"LICENSE","repoName":"lambda","refName":"master","path":"LICENSE","preferredFileType":"license","tabName":"MIT","richText":null,"loaded":false,"timedOut":false,"errorMessage":null,"headerInfo":{"toc":null,"siteNavLoginPath":"/login?return_to=https%3A%2F%2Fgithub.com%2Fpalatable%2Flambda"}}],"overviewFilesProcessingTime":0}},"appPayload":{"helpUrl":"https://docs.github.com","findFileWorkerPath":"/assets-cdn/worker/find-file-worker-7d7eb7c71814.js","findInFileWorkerPath":"/assets-cdn/worker/find-in-file-worker-708ec8ade250.js","githubDevUrl":null,"enabled_features":{"copilot_workspace":null,"code_nav_ui_events":false,"overview_shared_code_dropdown_button":true,"react_blob_overlay":false,"accessible_code_button":true,"github_models_repo_integration":false}}}}</script> <div 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style="vertical-align:text-bottom"><path d="M5.75 2.5h8.5a.75.75 0 0 1 0 1.5h-8.5a.75.75 0 0 1 0-1.5Zm0 5h8.5a.75.75 0 0 1 0 1.5h-8.5a.75.75 0 0 1 0-1.5Zm0 5h8.5a.75.75 0 0 1 0 1.5h-8.5a.75.75 0 0 1 0-1.5ZM2 14a1 1 0 1 1 0-2 1 1 0 0 1 0 2Zm1-6a1 1 0 1 1-2 0 1 1 0 0 1 2 0ZM2 4a1 1 0 1 1 0-2 1 1 0 0 1 0 2Z"></path></svg></button></div><div class="Box-sc-g0xbh4-0 QkQOb js-snippet-clipboard-copy-unpositioned undefined" data-hpc="true"><article class="markdown-body entry-content container-lg" itemprop="text"><div class="markdown-heading" dir="auto"><h1 tabindex="-1" class="heading-element" dir="auto">λ</h1><a id="user-content-λ" class="anchor" aria-label="Permalink: λ" href="#λ"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <p dir="auto"><a href="https://github.com/palatable/lambda/actions"><img src="https://github.com/palatable/lambda/workflows/Java%20CI/badge.svg" alt="Actions Status" style="max-width: 100%;"></a> <a href="http://search.maven.org/#search%7Cga%7C1%7Ccom.jnape.palatable.lambda" rel="nofollow"><img src="https://camo.githubusercontent.com/47b46a7618f39c441682dcfaeb95344e11be6122e3a21b2812a0be5c6ecd8c4a/68747470733a2f2f696d672e736869656c64732e696f2f6d6176656e2d63656e7472616c2f762f636f6d2e6a6e6170652e70616c617461626c652f6c616d6264612e737667" alt="Lambda" data-canonical-src="https://img.shields.io/maven-central/v/com.jnape.palatable/lambda.svg" style="max-width: 100%;"></a> <a href="https://discord.gg/wR7k8RAKM5" rel="nofollow"><img src="https://camo.githubusercontent.com/7c672351512e944d67bccc606f76be67aad71dadda25a09a9da3bc60ee50c1cf/68747470733a2f2f646362616467652e76657263656c2e6170702f6170692f7365727665722f7752376b3852414b4d35" height="20" alt="Join the chat on Discord" data-canonical-src="https://dcbadge.vercel.app/api/server/wR7k8RAKM5" style="max-width: 100%;"></a> <a href="https://floobits.com/jnape/lambda/redirect" rel="nofollow"><img src="https://camo.githubusercontent.com/b48fbcc0c0d6aba7e8c2d4155b819f96c59b28503dae1a08af037d42645f6ef6/68747470733a2f2f666c6f6f626974732e636f6d2f6a6e6170652f6c616d6264612e737667" alt="Floobits Status" data-canonical-src="https://floobits.com/jnape/lambda.svg" style="max-width: 100%;"></a></p> <p dir="auto">Functional patterns for Java</p> <div class="markdown-heading" dir="auto"><h4 tabindex="-1" class="heading-element" dir="auto">Table of Contents</h4><a id="user-content-table-of-contents" class="anchor" aria-label="Permalink: Table of Contents" href="#table-of-contents"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <ul dir="auto"> <li><a href="#background">Background</a></li> <li><a href="#installation">Installation</a></li> <li><a href="#examples">Examples</a></li> <li><a href="#semigroups">Semigroups</a></li> <li><a href="#monoids">Monoids</a></li> <li><a href="#functors">Functors</a> <ul dir="auto"> <li><a href="#bifunctors">Bifunctors</a></li> <li><a href="#profunctors">Profunctors</a></li> <li><a href="#applicatives">Applicatives</a></li> <li><a href="#monads">Monads</a></li> <li><a href="#traversables">Traversables</a></li> </ul> </li> <li><a href="#adts">ADTs</a> <ul dir="auto"> <li><a href="#maybe">Maybe</a></li> <li><a href="#hlist">HList</a> <ul dir="auto"> <li><a href="#tuples">Tuples</a></li> </ul> </li> <li><a href="#hmaps">HMaps</a></li> <li><a href="#coproducts">CoProducts</a> <ul dir="auto"> <li><a href="#either">Either</a></li> </ul> </li> </ul> </li> <li><a href="#lenses">Lenses</a></li> <li><a href="#notes">Notes</a></li> <li><a href="#ecosystem">Ecosystem</a></li> <li><a href="#license">License</a></li> </ul> <div class="markdown-heading" dir="auto"><h2 tabindex="-1" class="heading-element" dir="auto"><a name="user-content-background">Background</a></h2><a id="user-content-background" class="anchor" aria-label="Permalink: Background" href="#background"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <p dir="auto">Lambda was born out of a desire to use some of the same canonical functions (e.g. <code>unfoldr</code>, <code>takeWhile</code>, <code>zipWith</code>) and functional patterns (e.g. <code>Functor</code> and friends) that are idiomatic in other languages and make them available for Java.</p> <p dir="auto">Some things a user of lambda most likely values:</p> <ul dir="auto"> <li>Lazy evaluation</li> <li>Immutability by design</li> <li>Composition</li> <li>Higher-level abstractions</li> <li>Parametric polymorphism</li> </ul> <p dir="auto">Generally, everything that lambda produces is lazily-evaluated (except for terminal operations like <code>reduce</code>), immutable (except for <code>Iterator</code>s, since it's effectively impossible), composable (even between different arities, where possible), foundational (maximally contravariant), and parametrically type-checked (even where this adds unnecessary constraints due to a lack of higher-kinded types).</p> <p dir="auto">Although the library is currently (very) small, these values should always be the driving forces behind future growth.</p> <div class="markdown-heading" dir="auto"><h2 tabindex="-1" class="heading-element" dir="auto"><a name="user-content-installation">Installation</a></h2><a id="user-content-installation" class="anchor" aria-label="Permalink: Installation" href="#installation"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <p dir="auto">Add the following dependency to your:</p> <p dir="auto"><code>pom.xml</code> (<a href="https://maven.apache.org/guides/introduction/introduction-to-dependency-mechanism.html" rel="nofollow">Maven</a>):</p> <div class="highlight highlight-text-xml notranslate position-relative overflow-auto" dir="auto" data-snippet-clipboard-copy-content="<dependency> <groupId>com.jnape.palatable</groupId> <artifactId>lambda</artifactId> <version>5.4.0</version> </dependency>"><pre><<span class="pl-ent">dependency</span>> <<span class="pl-ent">groupId</span>>com.jnape.palatable</<span class="pl-ent">groupId</span>> <<span class="pl-ent">artifactId</span>>lambda</<span class="pl-ent">artifactId</span>> <<span class="pl-ent">version</span>>5.4.0</<span class="pl-ent">version</span>> </<span class="pl-ent">dependency</span>></pre></div> <p dir="auto"><code>build.gradle</code> (<a href="https://docs.gradle.org/current/userguide/dependency_management.html" rel="nofollow">Gradle</a>):</p> <div class="highlight highlight-source-groovy-gradle notranslate position-relative overflow-auto" dir="auto" data-snippet-clipboard-copy-content="compile group: 'com.jnape.palatable', name: 'lambda', version: '5.4.0'"><pre>compile <span class="pl-c1">group</span>: <span class="pl-s"><span class="pl-pds">'</span>com.jnape.palatable<span class="pl-pds">'</span></span>, <span class="pl-c1">name</span>: <span class="pl-s"><span class="pl-pds">'</span>lambda<span class="pl-pds">'</span></span>, <span class="pl-c1">version</span>: <span class="pl-s"><span class="pl-pds">'</span>5.4.0<span class="pl-pds">'</span></span></pre></div> <div class="markdown-heading" dir="auto"><h2 tabindex="-1" class="heading-element" dir="auto"><a name="user-content-examples">Examples</a></h2><a id="user-content-examples" class="anchor" aria-label="Permalink: Examples" href="#examples"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <p dir="auto">First, the obligatory <code>map</code>/<code>filter</code>/<code>reduce</code> example:</p> <div class="highlight highlight-source-java notranslate position-relative overflow-auto" dir="auto" data-snippet-clipboard-copy-content="Maybe<Integer> sumOfEvenIncrements = reduceLeft((x, y) -> x + y, filter(x -> x % 2 == 0, map(x -> x + 1, asList(1, 2, 3, 4, 5)))); //-> Just 12"><pre><span class="pl-smi">Maybe</span><<span class="pl-smi">Integer</span>> <span class="pl-s1">sumOfEvenIncrements</span> = <span class="pl-en">reduceLeft</span>((<span class="pl-s1">x</span>, <span class="pl-s1">y</span>) -> <span class="pl-s1">x</span> + <span class="pl-s1">y</span>, <span class="pl-en">filter</span>(<span class="pl-s1">x</span> -> <span class="pl-s1">x</span> % <span class="pl-c1">2</span> == <span class="pl-c1">0</span>, <span class="pl-en">map</span>(<span class="pl-s1">x</span> -> <span class="pl-s1">x</span> + <span class="pl-c1">1</span>, <span class="pl-en">asList</span>(<span class="pl-c1">1</span>, <span class="pl-c1">2</span>, <span class="pl-c1">3</span>, <span class="pl-c1">4</span>, <span class="pl-c1">5</span>)))); <span class="pl-c">//-> Just 12</span></pre></div> <p dir="auto">Every function in lambda is <a href="https://www.wikiwand.com/en/Currying" rel="nofollow">curried</a>, so we could have also done this:</p> <div class="highlight highlight-source-java notranslate position-relative overflow-auto" dir="auto" data-snippet-clipboard-copy-content="Fn1<Iterable<Integer>, Maybe<Integer>> sumOfEvenIncrementsFn = map((Integer x) -> x + 1) .fmap(filter(x -> x % 2 == 0)) .fmap(reduceLeft((x, y) -> x + y)); Maybe<Integer> sumOfEvenIncrements = sumOfEvenIncrementsFn.apply(asList(1, 2, 3, 4, 5)); //-> Just 12"><pre><span class="pl-smi">Fn1</span><<span class="pl-smi">Iterable</span><<span class="pl-smi">Integer</span>>, <span class="pl-smi">Maybe</span><<span class="pl-smi">Integer</span>>> <span class="pl-s1">sumOfEvenIncrementsFn</span> = <span class="pl-en">map</span>((<span class="pl-smi">Integer</span> <span class="pl-s1">x</span>) -> <span class="pl-s1">x</span> + <span class="pl-c1">1</span>) .<span class="pl-en">fmap</span>(<span class="pl-en">filter</span>(<span class="pl-s1">x</span> -> <span class="pl-s1">x</span> % <span class="pl-c1">2</span> == <span class="pl-c1">0</span>)) .<span class="pl-en">fmap</span>(<span class="pl-en">reduceLeft</span>((<span class="pl-s1">x</span>, <span class="pl-s1">y</span>) -> <span class="pl-s1">x</span> + <span class="pl-s1">y</span>)); <span class="pl-smi">Maybe</span><<span class="pl-smi">Integer</span>> <span class="pl-s1">sumOfEvenIncrements</span> = <span class="pl-s1">sumOfEvenIncrementsFn</span>.<span class="pl-en">apply</span>(<span class="pl-en">asList</span>(<span class="pl-c1">1</span>, <span class="pl-c1">2</span>, <span class="pl-c1">3</span>, <span class="pl-c1">4</span>, <span class="pl-c1">5</span>)); <span class="pl-c">//-> Just 12</span></pre></div> <p dir="auto">How about the positive squares below 100:</p> <div class="highlight highlight-source-java notranslate position-relative overflow-auto" dir="auto" data-snippet-clipboard-copy-content="Iterable<Integer> positiveSquaresBelow100 = takeWhile(x -> x < 100, map(x -> x * x, iterate(x -> x + 1, 1))); //-> [1, 4, 9, 16, 25, 36, 49, 64, 81]"><pre><span class="pl-smi">Iterable</span><<span class="pl-smi">Integer</span>> <span class="pl-s1">positiveSquaresBelow100</span> = <span class="pl-en">takeWhile</span>(<span class="pl-s1">x</span> -> <span class="pl-s1">x</span> < <span class="pl-c1">100</span>, <span class="pl-en">map</span>(<span class="pl-s1">x</span> -> <span class="pl-s1">x</span> * <span class="pl-s1">x</span>, <span class="pl-en">iterate</span>(<span class="pl-s1">x</span> -> <span class="pl-s1">x</span> + <span class="pl-c1">1</span>, <span class="pl-c1">1</span>))); <span class="pl-c">//-> [1, 4, 9, 16, 25, 36, 49, 64, 81]</span></pre></div> <p dir="auto">We could have also used <code>unfoldr</code>:</p> <div class="highlight highlight-source-java notranslate position-relative overflow-auto" dir="auto" data-snippet-clipboard-copy-content="Iterable<Integer> positiveSquaresBelow100 = unfoldr(x -> { int square = x * x; return square < 100 ? Maybe.just(tuple(square, x + 1)) : Maybe.nothing(); }, 1); //-> [1, 4, 9, 16, 25, 36, 49, 64, 81]"><pre><span class="pl-smi">Iterable</span><<span class="pl-smi">Integer</span>> <span class="pl-s1">positiveSquaresBelow100</span> = <span class="pl-en">unfoldr</span>(<span class="pl-s1">x</span> -> { <span class="pl-smi">int</span> <span class="pl-s1">square</span> = <span class="pl-s1">x</span> * <span class="pl-s1">x</span>; <span class="pl-k">return</span> <span class="pl-s1">square</span> < <span class="pl-c1">100</span> ? <span class="pl-smi">Maybe</span>.<span class="pl-en">just</span>(<span class="pl-en">tuple</span>(<span class="pl-s1">square</span>, <span class="pl-s1">x</span> + <span class="pl-c1">1</span>)) : <span class="pl-smi">Maybe</span>.<span class="pl-en">nothing</span>(); }, <span class="pl-c1">1</span>); <span class="pl-c">//-> [1, 4, 9, 16, 25, 36, 49, 64, 81]</span></pre></div> <p dir="auto">What if we want the cross product of a domain and codomain:</p> <div class="highlight highlight-source-java notranslate position-relative overflow-auto" dir="auto" data-snippet-clipboard-copy-content="Iterable<Tuple2<Integer, String>> crossProduct = take(10, cartesianProduct(asList(1, 2, 3), asList("a", "b", "c"))); //-> [(1,"a"), (1,"b"), (1,"c"), (2,"a"), (2,"b"), (2,"c"), (3,"a"), (3,"b"), (3,"c")]"><pre><span class="pl-smi">Iterable</span><<span class="pl-smi">Tuple2</span><<span class="pl-smi">Integer</span>, <span class="pl-smi">String</span>>> <span class="pl-s1">crossProduct</span> = <span class="pl-en">take</span>(<span class="pl-c1">10</span>, <span class="pl-en">cartesianProduct</span>(<span class="pl-en">asList</span>(<span class="pl-c1">1</span>, <span class="pl-c1">2</span>, <span class="pl-c1">3</span>), <span class="pl-en">asList</span>(<span class="pl-s">"a"</span>, <span class="pl-s">"b"</span>, <span class="pl-s">"c"</span>))); <span class="pl-c">//-> [(1,"a"), (1,"b"), (1,"c"), (2,"a"), (2,"b"), (2,"c"), (3,"a"), (3,"b"), (3,"c")]</span></pre></div> <p dir="auto">Let's compose two functions:</p> <div class="highlight highlight-source-java notranslate position-relative overflow-auto" dir="auto" data-snippet-clipboard-copy-content="Fn1<Integer, Integer> add = x -> x + 1; Fn1<Integer, Integer> subtract = x -> x -1; Fn1<Integer, Integer> noOp = add.fmap(subtract); // same as Fn1<Integer, Integer> alsoNoOp = subtract.contraMap(add);"><pre><span class="pl-smi">Fn1</span><<span class="pl-smi">Integer</span>, <span class="pl-smi">Integer</span>> <span class="pl-s1">add</span> = <span class="pl-s1">x</span> -> <span class="pl-s1">x</span> + <span class="pl-c1">1</span>; <span class="pl-smi">Fn1</span><<span class="pl-smi">Integer</span>, <span class="pl-smi">Integer</span>> <span class="pl-s1">subtract</span> = <span class="pl-s1">x</span> -> <span class="pl-s1">x</span> -<span class="pl-c1">1</span>; <span class="pl-smi">Fn1</span><<span class="pl-smi">Integer</span>, <span class="pl-smi">Integer</span>> <span class="pl-s1">noOp</span> = <span class="pl-s1">add</span>.<span class="pl-en">fmap</span>(<span class="pl-s1">subtract</span>); <span class="pl-c">// same as</span> <span class="pl-smi">Fn1</span><<span class="pl-smi">Integer</span>, <span class="pl-smi">Integer</span>> <span class="pl-s1">alsoNoOp</span> = <span class="pl-s1">subtract</span>.<span class="pl-en">contraMap</span>(<span class="pl-s1">add</span>);</pre></div> <p dir="auto">And partially apply some:</p> <div class="highlight highlight-source-java notranslate position-relative overflow-auto" dir="auto" data-snippet-clipboard-copy-content="Fn2<Integer, Integer, Integer> add = (x, y) -> x + y; Fn1<Integer, Integer> add1 = add.apply(1); add1.apply(2); //-> 3"><pre><span class="pl-smi">Fn2</span><<span class="pl-smi">Integer</span>, <span class="pl-smi">Integer</span>, <span class="pl-smi">Integer</span>> <span class="pl-s1">add</span> = (<span class="pl-s1">x</span>, <span class="pl-s1">y</span>) -> <span class="pl-s1">x</span> + <span class="pl-s1">y</span>; <span class="pl-smi">Fn1</span><<span class="pl-smi">Integer</span>, <span class="pl-smi">Integer</span>> <span class="pl-s1">add1</span> = <span class="pl-s1">add</span>.<span class="pl-en">apply</span>(<span class="pl-c1">1</span>); <span class="pl-s1">add1</span>.<span class="pl-en">apply</span>(<span class="pl-c1">2</span>); <span class="pl-c">//-> 3</span></pre></div> <p dir="auto">And have fun with 3s:</p> <div class="highlight highlight-source-java notranslate position-relative overflow-auto" dir="auto" data-snippet-clipboard-copy-content="Iterable<Iterable<Integer>> multiplesOf3InGroupsOf3 = take(3, inGroupsOf(3, unfoldr(x -> Maybe.just(tuple(x * 3, x + 1)), 1))); //-> [[3, 6, 9], [12, 15, 18], [21, 24, 27]]"><pre><span class="pl-smi">Iterable</span><<span class="pl-smi">Iterable</span><<span class="pl-smi">Integer</span>>> <span class="pl-s1">multiplesOf3InGroupsOf3</span> = <span class="pl-en">take</span>(<span class="pl-c1">3</span>, <span class="pl-en">inGroupsOf</span>(<span class="pl-c1">3</span>, <span class="pl-en">unfoldr</span>(<span class="pl-s1">x</span> -> <span class="pl-smi">Maybe</span>.<span class="pl-en">just</span>(<span class="pl-en">tuple</span>(<span class="pl-s1">x</span> * <span class="pl-c1">3</span>, <span class="pl-s1">x</span> + <span class="pl-c1">1</span>)), <span class="pl-c1">1</span>))); <span class="pl-c">//-> [[3, 6, 9], [12, 15, 18], [21, 24, 27]]</span></pre></div> <p dir="auto">Check out the <a href="https://github.com/palatable/lambda/tree/master/src/test/java/com/jnape/palatable/lambda/functions/builtin">tests</a> or <a href="http://palatable.github.io/lambda/javadoc/" rel="nofollow">javadoc</a> for more examples.</p> <div class="markdown-heading" dir="auto"><h2 tabindex="-1" class="heading-element" dir="auto"><a name="user-content-semigroups">Semigroups</a></h2><a id="user-content-semigroups" class="anchor" aria-label="Permalink: Semigroups" href="#semigroups"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <p dir="auto"><a href="https://en.wikipedia.org/wiki/Semigroup" rel="nofollow">Semigroups</a> are supported via <code>Semigroup<A></code>, a subtype of <code>Fn2<A,A,A></code>, and add left and right folds over an <code>Iterable<A></code>.</p> <div class="highlight highlight-source-java notranslate position-relative overflow-auto" dir="auto" data-snippet-clipboard-copy-content="Semigroup<Integer> add = (augend, addend) -> augend + addend; add.apply(1, 2); //-> 3 add.foldLeft(0, asList(1, 2, 3)); //-> 6"><pre><span class="pl-smi">Semigroup</span><<span class="pl-smi">Integer</span>> <span class="pl-s1">add</span> = (<span class="pl-s1">augend</span>, <span class="pl-s1">addend</span>) -> <span class="pl-s1">augend</span> + <span class="pl-s1">addend</span>; <span class="pl-s1">add</span>.<span class="pl-en">apply</span>(<span class="pl-c1">1</span>, <span class="pl-c1">2</span>); <span class="pl-c">//-> 3</span> <span class="pl-s1">add</span>.<span class="pl-en">foldLeft</span>(<span class="pl-c1">0</span>, <span class="pl-en">asList</span>(<span class="pl-c1">1</span>, <span class="pl-c1">2</span>, <span class="pl-c1">3</span>)); <span class="pl-c">//-> 6</span></pre></div> <p dir="auto">Lambda ships some default logical semigroups for lambda types and core JDK types. Common examples are:</p> <ul dir="auto"> <li><code>AddAll</code> for concatenating two <code>Collection</code>s</li> <li><code>Collapse</code> for collapsing two <code>Tuple2</code>s together</li> <li><code>Merge</code> for merging two <code>Either</code>s using left-biasing semantics</li> </ul> <p dir="auto">Check out the <a href="https://palatable.github.io/lambda/javadoc/com/jnape/palatable/lambda/semigroup/builtin/package-summary.html" rel="nofollow">semigroup</a> package for more examples.</p> <div class="markdown-heading" dir="auto"><h2 tabindex="-1" class="heading-element" dir="auto"><a name="user-content-monoids">Monoids</a></h2><a id="user-content-monoids" class="anchor" aria-label="Permalink: Monoids" href="#monoids"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <p dir="auto"><a href="https://en.wikipedia.org/wiki/Monoid" rel="nofollow">Monoids</a> are supported via <code>Monoid<A></code>, a subtype of <code>Semigroup<A></code> with an <code>A #identity()</code> method, and add left and right reduces over an <code>Iterable<A></code>, as well as <code>foldMap</code>.</p> <div class="highlight highlight-source-java notranslate position-relative overflow-auto" dir="auto" data-snippet-clipboard-copy-content="Monoid<Integer> multiply = monoid((x, y) -> x * y, 1); multiply.reduceLeft(emptyList()); //-> 1 multiply.reduceLeft(asList(1, 2, 3)); //-> 6 multiply.foldMap(Integer::parseInt, asList("1", "2", "3")); //-> also 6"><pre><span class="pl-smi">Monoid</span><<span class="pl-smi">Integer</span>> <span class="pl-s1">multiply</span> = <span class="pl-en">monoid</span>((<span class="pl-s1">x</span>, <span class="pl-s1">y</span>) -> <span class="pl-s1">x</span> * <span class="pl-s1">y</span>, <span class="pl-c1">1</span>); <span class="pl-s1">multiply</span>.<span class="pl-en">reduceLeft</span>(<span class="pl-en">emptyList</span>()); <span class="pl-c">//-> 1</span> <span class="pl-s1">multiply</span>.<span class="pl-en">reduceLeft</span>(<span class="pl-en">asList</span>(<span class="pl-c1">1</span>, <span class="pl-c1">2</span>, <span class="pl-c1">3</span>)); <span class="pl-c">//-> 6</span> <span class="pl-s1">multiply</span>.<span class="pl-en">foldMap</span>(<span class="pl-smi">Integer</span>::<span class="pl-s1">parseInt</span>, <span class="pl-en">asList</span>(<span class="pl-s">"1"</span>, <span class="pl-s">"2"</span>, <span class="pl-s">"3"</span>)); <span class="pl-c">//-> also 6</span></pre></div> <p dir="auto">Some commonly used lambda monoid implementations include:</p> <ul dir="auto"> <li><code>Present</code> for merging together two <code>Optional</code>s</li> <li><code>Join</code> for joining two <code>String</code>s</li> <li><code>And</code> for logical conjunction of two <code>Boolean</code>s</li> <li><code>Or</code> for logical disjunction of two <code>Boolean</code>s</li> </ul> <p dir="auto">Additionally, instances of <code>Monoid<A></code> can be trivially synthesized from instances of <code>Semigroup<A></code> via the <code>Monoid#monoid</code> static factory method, taking the <code>Semigroup</code> and the identity element <code>A</code> or a supplier of the identity element <code>Supplier<A></code>.</p> <p dir="auto">Check out the <a href="https://palatable.github.io/lambda/javadoc/com/jnape/palatable/lambda/monoid/builtin/package-summary.html" rel="nofollow">monoid</a> package for more examples.</p> <div class="markdown-heading" dir="auto"><h2 tabindex="-1" class="heading-element" dir="auto"><a name="user-content-functors">Functors</a></h2><a id="user-content-functors" class="anchor" aria-label="Permalink: Functors" href="#functors"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <p dir="auto">Functors are implemented via the <code>Functor</code> interface, and are sub-typed by every function type that lambda exports, as well as many of the <a href="#adts">ADTs</a>.</p> <div class="highlight highlight-source-java notranslate position-relative overflow-auto" dir="auto" data-snippet-clipboard-copy-content="public final class Slot<A> implements Functor<A, Slot> { private final A a; public Slot(A a) { this.a = a; } public A getA() { return a; } @Override public <B> Slot<B> fmap(Function<? super A, ? extends B> fn) { return new Slot<>(fn.apply(a)); } } Slot<Integer> intSlot = new Slot<>(1); Slot<String> stringSlot = intSlot.fmap(x -> "number: " + x); stringSlot.getA(); //-> "number: 1""><pre><span class="pl-k">public</span> <span class="pl-k">final</span> <span class="pl-k">class</span> <span class="pl-smi">Slot</span><<span class="pl-smi">A</span>> <span class="pl-k">implements</span> <span class="pl-smi">Functor</span><<span class="pl-smi">A</span>, <span class="pl-smi">Slot</span>> { <span class="pl-k">private</span> <span class="pl-k">final</span> <span class="pl-smi">A</span> <span class="pl-s1">a</span>; <span class="pl-k">public</span> <span class="pl-smi">Slot</span>(<span class="pl-smi">A</span> <span class="pl-s1">a</span>) { <span class="pl-smi">this</span>.<span class="pl-s1">a</span> = <span class="pl-s1">a</span>; } <span class="pl-k">public</span> <span class="pl-smi">A</span> <span class="pl-en">getA</span>() { <span class="pl-k">return</span> <span class="pl-s1">a</span>; } <span class="pl-c1">@</span><span class="pl-c1">Override</span> <span class="pl-k">public</span> <<span class="pl-smi">B</span>> <span class="pl-smi">Slot</span><<span class="pl-smi">B</span>> <span class="pl-en">fmap</span>(<span class="pl-smi">Function</span><? <span class="pl-en">super</span> <span class="pl-smi">A</span>, ? <span class="pl-k">extends</span> <span class="pl-smi">B</span>> <span class="pl-s1">fn</span>) { <span class="pl-k">return</span> <span class="pl-k">new</span> <span class="pl-smi">Slot</span><>(<span class="pl-s1">fn</span>.<span class="pl-en">apply</span>(<span class="pl-s1">a</span>)); } } <span class="pl-smi">Slot</span><<span class="pl-smi">Integer</span>> <span class="pl-s1">intSlot</span> = <span class="pl-k">new</span> <span class="pl-smi">Slot</span><>(<span class="pl-c1">1</span>); <span class="pl-smi">Slot</span><<span class="pl-smi">String</span>> <span class="pl-s1">stringSlot</span> = <span class="pl-s1">intSlot</span>.<span class="pl-en">fmap</span>(<span class="pl-s1">x</span> -> <span class="pl-s">"number: "</span> + <span class="pl-s1">x</span>); <span class="pl-s1">stringSlot</span>.<span class="pl-en">getA</span>(); <span class="pl-c">//-> "number: 1"</span></pre></div> <p dir="auto">Examples of functors include:</p> <ul dir="auto"> <li><code>Fn*</code>, <code>Semigroup</code>, and <code>Monoid</code></li> <li><code>SingletonHList</code> and <code>Tuple*</code></li> <li><code>Choice*</code></li> <li><code>Either</code></li> <li><code>Const</code>, <code>Identity</code>, and <code>Compose</code></li> <li><code>Lens</code></li> </ul> <p dir="auto">Implementing <code>Functor</code> is as simple as providing a definition for the covariant mapping function <code>#fmap</code> (ideally satisfying the <a href="https://hackage.haskell.org/package/base-4.9.1.0/docs/Data-Functor.html" rel="nofollow">two laws</a>).</p> <div class="markdown-heading" dir="auto"><h3 tabindex="-1" class="heading-element" dir="auto"><a name="user-content-bifunctors">Bifunctors</a></h3><a id="user-content-bifunctors" class="anchor" aria-label="Permalink: Bifunctors" href="#bifunctors"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <p dir="auto">Bifunctors -- functors that support two parameters that can be covariantly mapped over -- are implemented via the <code>Bifunctor</code> interface.</p> <div class="highlight highlight-source-java notranslate position-relative overflow-auto" dir="auto" data-snippet-clipboard-copy-content="public final class Pair<A, B> implements Bifunctor<A, B, Pair> { private final A a; private final B b; public Pair(A a, B b) { this.a = a; this.b = b; } public A getA() { return a; } public B getB() { return b; } @Override public <C, D> Pair<C, D> biMap(Function<? super A, ? extends C> lFn, Function<? super B, ? extends D> rFn) { return new Pair<>(lFn.apply(a), rFn.apply(b)); } } Pair<String,Integer> stringIntPair = new Pair<>("str", 1); Pair<Integer, Boolean> intBooleanPair = stringIntPair.biMap(String::length, x -> x % 2 == 0); intBooleanPair.getA(); //-> 3 intBooleanPair.getB(); //-> false"><pre><span class="pl-k">public</span> <span class="pl-k">final</span> <span class="pl-k">class</span> <span class="pl-smi">Pair</span><<span class="pl-smi">A</span>, <span class="pl-smi">B</span>> <span class="pl-k">implements</span> <span class="pl-smi">Bifunctor</span><<span class="pl-smi">A</span>, <span class="pl-smi">B</span>, <span class="pl-smi">Pair</span>> { <span class="pl-k">private</span> <span class="pl-k">final</span> <span class="pl-smi">A</span> <span class="pl-s1">a</span>; <span class="pl-k">private</span> <span class="pl-k">final</span> <span class="pl-smi">B</span> <span class="pl-s1">b</span>; <span class="pl-k">public</span> <span class="pl-smi">Pair</span>(<span class="pl-smi">A</span> <span class="pl-s1">a</span>, <span class="pl-smi">B</span> <span class="pl-s1">b</span>) { <span class="pl-smi">this</span>.<span class="pl-s1">a</span> = <span class="pl-s1">a</span>; <span class="pl-smi">this</span>.<span class="pl-s1">b</span> = <span class="pl-s1">b</span>; } <span class="pl-k">public</span> <span class="pl-smi">A</span> <span class="pl-en">getA</span>() { <span class="pl-k">return</span> <span class="pl-s1">a</span>; } <span class="pl-k">public</span> <span class="pl-smi">B</span> <span class="pl-en">getB</span>() { <span class="pl-k">return</span> <span class="pl-s1">b</span>; } <span class="pl-c1">@</span><span class="pl-c1">Override</span> <span class="pl-k">public</span> <<span class="pl-smi">C</span>, <span class="pl-smi">D</span>> <span class="pl-smi">Pair</span><<span class="pl-smi">C</span>, <span class="pl-smi">D</span>> <span class="pl-en">biMap</span>(<span class="pl-smi">Function</span><? <span class="pl-en">super</span> <span class="pl-smi">A</span>, ? <span class="pl-k">extends</span> <span class="pl-smi">C</span>> <span class="pl-s1">lFn</span>, <span class="pl-smi">Function</span><? <span class="pl-en">super</span> <span class="pl-smi">B</span>, ? <span class="pl-k">extends</span> <span class="pl-smi">D</span>> <span class="pl-s1">rFn</span>) { <span class="pl-k">return</span> <span class="pl-k">new</span> <span class="pl-smi">Pair</span><>(<span class="pl-s1">lFn</span>.<span class="pl-en">apply</span>(<span class="pl-s1">a</span>), <span class="pl-s1">rFn</span>.<span class="pl-en">apply</span>(<span class="pl-s1">b</span>)); } } <span class="pl-smi">Pair</span><<span class="pl-smi">String</span>,<span class="pl-smi">Integer</span>> <span class="pl-s1">stringIntPair</span> = <span class="pl-k">new</span> <span class="pl-smi">Pair</span><>(<span class="pl-s">"str"</span>, <span class="pl-c1">1</span>); <span class="pl-smi">Pair</span><<span class="pl-smi">Integer</span>, <span class="pl-smi">Boolean</span>> <span class="pl-s1">intBooleanPair</span> = <span class="pl-s1">stringIntPair</span>.<span class="pl-en">biMap</span>(<span class="pl-smi">String</span>::<span class="pl-s1">length</span>, <span class="pl-s1">x</span> -> <span class="pl-s1">x</span> % <span class="pl-c1">2</span> == <span class="pl-c1">0</span>); <span class="pl-s1">intBooleanPair</span>.<span class="pl-en">getA</span>(); <span class="pl-c">//-> 3</span> <span class="pl-s1">intBooleanPair</span>.<span class="pl-en">getB</span>(); <span class="pl-c">//-> false</span></pre></div> <p dir="auto">Examples of bifunctors include:</p> <ul dir="auto"> <li><code>Tuple*</code></li> <li><code>Choice*</code></li> <li><code>Either</code></li> <li><code>Const</code></li> </ul> <p dir="auto">Implementing <code>Bifunctor</code> requires implementing <em>either</em> <code>biMapL</code> and <code>biMapR</code> <em>or</em> <code>biMap</code>. As with <code>Functor</code>, there are a <a href="https://hackage.haskell.org/package/base-4.9.1.0/docs/Data-Bifunctor.html" rel="nofollow">few laws</a> that well-behaved instances of <code>Bifunctor</code> should adhere to.</p> <div class="markdown-heading" dir="auto"><h3 tabindex="-1" class="heading-element" dir="auto"><a name="user-content-profunctors">Profunctors</a></h3><a id="user-content-profunctors" class="anchor" aria-label="Permalink: Profunctors" href="#profunctors"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <p dir="auto">Profunctors -- functors that support one parameter that can be mapped over contravariantly, and a second parameter that can be mapped over covariantly -- are implemented via the <code>Profunctor</code> interface.</p> <div class="highlight highlight-source-java notranslate position-relative overflow-auto" dir="auto" data-snippet-clipboard-copy-content="Fn1<Integer, Integer> add2 = (x) -> x + 2; add2.<String, String>diMap(Integer::parseInt, Object::toString).apply("1"); //-> "3""><pre><span class="pl-smi">Fn1</span><<span class="pl-smi">Integer</span>, <span class="pl-smi">Integer</span>> <span class="pl-s1">add2</span> = (<span class="pl-s1">x</span>) -> <span class="pl-s1">x</span> + <span class="pl-c1">2</span>; <span class="pl-s1">add2</span>.<<span class="pl-smi">String</span>, <span class="pl-smi">String</span>><span class="pl-en">diMap</span>(<span class="pl-smi">Integer</span>::<span class="pl-s1">parseInt</span>, <span class="pl-smi">Object</span>::<span class="pl-s1">toString</span>).<span class="pl-en">apply</span>(<span class="pl-s">"1"</span>); <span class="pl-c">//-> "3"</span></pre></div> <p dir="auto">Examples of profunctors include:</p> <ul dir="auto"> <li><code>Fn*</code></li> <li><code>Lens</code></li> </ul> <p dir="auto">Implementing <code>Profunctor</code> requires implementing <em>either</em> <code>diMapL</code> and <code>diMapR</code> <em>or</em> <code>diMap</code>. As with <code>Functor</code> and <code>Bifunctor</code>, there are <a href="https://hackage.haskell.org/package/profunctors-5.2/docs/Data-Profunctor.html" rel="nofollow">some laws</a> that well behaved instances of <code>Profunctor</code> should adhere to.</p> <div class="markdown-heading" dir="auto"><h3 tabindex="-1" class="heading-element" dir="auto"><a name="user-content-applicatives">Applicatives</a></h3><a id="user-content-applicatives" class="anchor" aria-label="Permalink: Applicatives" href="#applicatives"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <p dir="auto">Applicative functors -- functors that can be applied together with a 2-arity or higher function -- are implemented via the <code>Applicative</code> interface.</p> <div class="highlight highlight-source-java notranslate position-relative overflow-auto" dir="auto" data-snippet-clipboard-copy-content="public final class Slot<A> implements Applicative<A, Slot> { private final A a; public Slot(A a) { this.a = a; } public A getA() { return a; } @Override public <B> Slot<B> fmap(Function<? super A, ? extends B> fn) { return pure(fn.apply(a)); } @Override public <B> Slot<B> pure(B b) { return new Slot<>(b); } @Override public <B> Slot<B> zip(Applicative<Function<? super A, ? extends B>, Slot> appFn) { return pure(appFn.<Slot<Function<? super A, ? extends B>>>coerce().getA().apply(getA())); } } Fn2<Integer, Integer, Integer> add = (x, y) -> x + y; Slot<Integer> x = new Slot<>(1); Slot<Integer> y = new Slot<>(2); Slot<Integer> z = y.zip(x.fmap(add)); //-> Slot{a=3}"><pre><span class="pl-k">public</span> <span class="pl-k">final</span> <span class="pl-k">class</span> <span class="pl-smi">Slot</span><<span class="pl-smi">A</span>> <span class="pl-k">implements</span> <span class="pl-smi">Applicative</span><<span class="pl-smi">A</span>, <span class="pl-smi">Slot</span>> { <span class="pl-k">private</span> <span class="pl-k">final</span> <span class="pl-smi">A</span> <span class="pl-s1">a</span>; <span class="pl-k">public</span> <span class="pl-smi">Slot</span>(<span class="pl-smi">A</span> <span class="pl-s1">a</span>) { <span class="pl-smi">this</span>.<span class="pl-s1">a</span> = <span class="pl-s1">a</span>; } <span class="pl-k">public</span> <span class="pl-smi">A</span> <span class="pl-en">getA</span>() { <span class="pl-k">return</span> <span class="pl-s1">a</span>; } <span class="pl-c1">@</span><span class="pl-c1">Override</span> <span class="pl-k">public</span> <<span class="pl-smi">B</span>> <span class="pl-smi">Slot</span><<span class="pl-smi">B</span>> <span class="pl-en">fmap</span>(<span class="pl-smi">Function</span><? <span class="pl-en">super</span> <span class="pl-smi">A</span>, ? <span class="pl-k">extends</span> <span class="pl-smi">B</span>> <span class="pl-s1">fn</span>) { <span class="pl-k">return</span> <span class="pl-en">pure</span>(<span class="pl-s1">fn</span>.<span class="pl-en">apply</span>(<span class="pl-s1">a</span>)); } <span class="pl-c1">@</span><span class="pl-c1">Override</span> <span class="pl-k">public</span> <<span class="pl-smi">B</span>> <span class="pl-smi">Slot</span><<span class="pl-smi">B</span>> <span class="pl-en">pure</span>(<span class="pl-smi">B</span> <span class="pl-s1">b</span>) { <span class="pl-k">return</span> <span class="pl-k">new</span> <span class="pl-smi">Slot</span><>(<span class="pl-s1">b</span>); } <span class="pl-c1">@</span><span class="pl-c1">Override</span> <span class="pl-k">public</span> <<span class="pl-smi">B</span>> <span class="pl-smi">Slot</span><<span class="pl-smi">B</span>> <span class="pl-en">zip</span>(<span class="pl-smi">Applicative</span><<span class="pl-smi">Function</span><? <span class="pl-en">super</span> <span class="pl-smi">A</span>, ? <span class="pl-k">extends</span> <span class="pl-smi">B</span>>, <span class="pl-smi">Slot</span>> <span class="pl-s1">appFn</span>) { <span class="pl-k">return</span> <span class="pl-en">pure</span>(<span class="pl-s1">appFn</span>.<<span class="pl-smi">Slot</span><<span class="pl-smi">Function</span><? <span class="pl-en">super</span> <span class="pl-smi">A</span>, ? <span class="pl-k">extends</span> <span class="pl-smi">B</span>>>><span class="pl-en">coerce</span>().<span class="pl-en">getA</span>().<span class="pl-en">apply</span>(<span class="pl-en">getA</span>())); } } <span class="pl-smi">Fn2</span><<span class="pl-smi">Integer</span>, <span class="pl-smi">Integer</span>, <span class="pl-smi">Integer</span>> <span class="pl-s1">add</span> = (<span class="pl-s1">x</span>, <span class="pl-s1">y</span>) -> <span class="pl-s1">x</span> + <span class="pl-s1">y</span>; <span class="pl-smi">Slot</span><<span class="pl-smi">Integer</span>> <span class="pl-s1">x</span> = <span class="pl-k">new</span> <span class="pl-smi">Slot</span><>(<span class="pl-c1">1</span>); <span class="pl-smi">Slot</span><<span class="pl-smi">Integer</span>> <span class="pl-s1">y</span> = <span class="pl-k">new</span> <span class="pl-smi">Slot</span><>(<span class="pl-c1">2</span>); <span class="pl-smi">Slot</span><<span class="pl-smi">Integer</span>> <span class="pl-s1">z</span> = <span class="pl-s1">y</span>.<span class="pl-en">zip</span>(<span class="pl-s1">x</span>.<span class="pl-en">fmap</span>(<span class="pl-s1">add</span>)); <span class="pl-c">//-> Slot{a=3}</span></pre></div> <p dir="auto">Examples of applicative functors include:</p> <ul dir="auto"> <li><code>Fn*</code>, <code>Semigroup</code>, and <code>Monoid</code></li> <li><code>SingletonHList</code> and <code>Tuple*</code></li> <li><code>Choice*</code></li> <li><code>Either</code></li> <li><code>Const</code>, <code>Identity</code>, and <code>Compose</code></li> <li><code>Lens</code></li> </ul> <p dir="auto">In addition to implementing <code>fmap</code> from <code>Functor</code>, implementing an applicative functor involves providing two methods: <code>pure</code>, a method that lifts a value into the functor; and <code>zip</code>, a method that applies a lifted function to a lifted value, returning a new lifted value. As usual, there are <a href="https://hackage.haskell.org/package/base-4.9.1.0/docs/Control-Applicative.html" rel="nofollow">some laws</a> that should be adhered to.</p> <div class="markdown-heading" dir="auto"><h3 tabindex="-1" class="heading-element" dir="auto"><a name="user-content-monads">Monads</a></h3><a id="user-content-monads" class="anchor" aria-label="Permalink: Monads" href="#monads"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <p dir="auto">Monads are applicative functors that additionally support a chaining operation, <code>flatMap :: (a -> f b) -> f a -> f b</code>: a function from the functor's parameter to a new instance of the same functor over a potentially different parameter. Because the function passed to <code>flatMap</code> can return a different instance of the same functor, functors can take advantage of multiple constructions that yield different functorial operations, like short-circuiting, as in the following example using <code>Either</code>:</p> <div class="highlight highlight-source-java notranslate position-relative overflow-auto" dir="auto" data-snippet-clipboard-copy-content="class Person { Optional<Occupation> occupation() { return Optional.empty(); } } class Occupation { } public static void main(String[] args) { Fn1<String, Either<String, Integer>> parseId = str -> Either.trying(() -> Integer.parseInt(str), __ -> str + " is not a valid id"); Map<Integer, Person> database = new HashMap<>(); Fn1<Integer, Either<String, Person>> lookupById = id -> Either.fromOptional(Optional.ofNullable(database.get(id)), () -> "No person found for id " + id); Fn1<Person, Either<String, Occupation>> getOccupation = p -> Either.fromOptional(p.occupation(), () -> "Person was unemployed"); Either<String, Occupation> occupationOrError = parseId.apply("12") // Either<String, Integer> .flatMap(lookupById) // Either<String, Person> .flatMap(getOccupation); // Either<String, Occupation> }"><pre><span class="pl-k">class</span> <span class="pl-smi">Person</span> { <span class="pl-smi">Optional</span><<span class="pl-smi">Occupation</span>> <span class="pl-en">occupation</span>() { <span class="pl-k">return</span> <span class="pl-smi">Optional</span>.<span class="pl-en">empty</span>(); } } <span class="pl-k">class</span> <span class="pl-smi">Occupation</span> { } <span class="pl-k">public</span> <span class="pl-k">static</span> <span class="pl-smi">void</span> <span class="pl-en">main</span>(<span class="pl-smi">String</span>[] <span class="pl-s1">args</span>) { <span class="pl-smi">Fn1</span><<span class="pl-smi">String</span>, <span class="pl-smi">Either</span><<span class="pl-smi">String</span>, <span class="pl-smi">Integer</span>>> <span class="pl-s1">parseId</span> = <span class="pl-s1">str</span> -> <span class="pl-smi">Either</span>.<span class="pl-en">trying</span>(() -> <span class="pl-smi">Integer</span>.<span class="pl-en">parseInt</span>(<span class="pl-s1">str</span>), <span class="pl-s1">__</span> -> <span class="pl-s1">str</span> + <span class="pl-s">" is not a valid id"</span>); <span class="pl-smi">Map</span><<span class="pl-smi">Integer</span>, <span class="pl-smi">Person</span>> <span class="pl-s1">database</span> = <span class="pl-k">new</span> <span class="pl-smi">HashMap</span><>(); <span class="pl-smi">Fn1</span><<span class="pl-smi">Integer</span>, <span class="pl-smi">Either</span><<span class="pl-smi">String</span>, <span class="pl-smi">Person</span>>> <span class="pl-s1">lookupById</span> = <span class="pl-s1">id</span> -> <span class="pl-smi">Either</span>.<span class="pl-en">fromOptional</span>(<span class="pl-smi">Optional</span>.<span class="pl-en">ofNullable</span>(<span class="pl-s1">database</span>.<span class="pl-en">get</span>(<span class="pl-s1">id</span>)), () -> <span class="pl-s">"No person found for id "</span> + <span class="pl-s1">id</span>); <span class="pl-smi">Fn1</span><<span class="pl-smi">Person</span>, <span class="pl-smi">Either</span><<span class="pl-smi">String</span>, <span class="pl-smi">Occupation</span>>> <span class="pl-s1">getOccupation</span> = <span class="pl-s1">p</span> -> <span class="pl-smi">Either</span>.<span class="pl-en">fromOptional</span>(<span class="pl-s1">p</span>.<span class="pl-en">occupation</span>(), () -> <span class="pl-s">"Person was unemployed"</span>); <span class="pl-smi">Either</span><<span class="pl-smi">String</span>, <span class="pl-smi">Occupation</span>> <span class="pl-s1">occupationOrError</span> = <span class="pl-s1">parseId</span>.<span class="pl-en">apply</span>(<span class="pl-s">"12"</span>) <span class="pl-c">// Either<String, Integer></span> .<span class="pl-en">flatMap</span>(<span class="pl-s1">lookupById</span>) <span class="pl-c">// Either<String, Person></span> .<span class="pl-en">flatMap</span>(<span class="pl-s1">getOccupation</span>); <span class="pl-c">// Either<String, Occupation></span> }</pre></div> <p dir="auto">In the previous example, if any of <code>parseId</code>, <code>lookupById</code>, or <code>getOccupation</code> fail, no further <code>flatMap</code> computations can succeed, so the result short-circuits to the first <code>left</code> value that is returned. This is completely predictable from the type signature of <code>Monad</code> and <code>Either</code>: <code>Either<L, R></code> is a <code>Monad<R></code>, so the single arity <code>flatMap</code> can have nothing to map in the case where there is no <code>R</code> value. With experience, it generally becomes quickly clear what the logical behavior of <code>flatMap</code> <em>must</em> be given the type signatures.</p> <p dir="auto">That's it. Monads are neither <a href="http://james-iry.blogspot.com/2007/09/monads-are-elephants-part-1.html" rel="nofollow">elephants</a> nor are they <a href="https://blog.plover.com/prog/burritos.html" rel="nofollow">burritos</a>; they're simply types that support a) the ability to lift a value into them, and b) a chaining function <code>flatMap :: (a -> f b) -> f a -> f b</code> that can potentially return different instances of the same monad. If a type can do those two things (and obeys <a href="https://wiki.haskell.org/Monad_laws" rel="nofollow">the laws</a>), it is a monad.</p> <p dir="auto">Further, if a type is a monad, it is necessarily an <code>Applicative</code>, which makes it necessarily a <code>Functor</code>, so <em>lambda</em> enforces this tautology via a hierarchical constraint.</p> <div class="markdown-heading" dir="auto"><h3 tabindex="-1" class="heading-element" dir="auto"><a name="user-content-traversables">Traversables</a></h3><a id="user-content-traversables" class="anchor" aria-label="Permalink: Traversables" href="#traversables"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <p dir="auto">Traversable functors -- functors that can be "traversed from left to right" -- are implemented via the <code>Traversable</code> interface.</p> <div class="highlight highlight-source-java notranslate position-relative overflow-auto" dir="auto" data-snippet-clipboard-copy-content="public abstract class Maybe<A> implements Traversable<A, Maybe> { private Maybe() { } @Override public abstract <B, App extends Applicative> Applicative<Maybe<B>, App> traverse( Function<? super A, ? extends Applicative<B, App>> fn, Function<? super Traversable<B, Maybe>, ? extends Applicative<? extends Traversable<B, Maybe>, App>> pure); @Override public abstract <B> Maybe<B> fmap(Function<? super A, ? extends B> fn); private static final class Just<A> extends Maybe<A> { private final A a; private Just(A a) { this.a = a; } @Override public <B, App extends Applicative> Applicative<Maybe<B>, App> traverse( Function<? super A, ? extends Applicative<B, App>> fn, Function<? super Traversable<B, Maybe>, ? extends Applicative<? extends Traversable<B, Maybe>, App>> pure) { return fn.apply(a).fmap(Just::new); } @Override public <B> Maybe<B> fmap(Function<? super A, ? extends B> fn) { return new Just<>(fn.apply(a)); } } private static final class Nothing<A> extends Maybe<A> { @Override @SuppressWarnings("unchecked") public <B, App extends Applicative> Applicative<Maybe<B>, App> traverse( Function<? super A, ? extends Applicative<B, App>> fn, Function<? super Traversable<B, Maybe>, ? extends Applicative<? extends Traversable<B, Maybe>, App>> pure) { return pure.apply((Maybe<B>) this).fmap(x -> (Maybe<B>) x); } @Override @SuppressWarnings("unchecked") public <B> Maybe<B> fmap(Function<? super A, ? extends B> fn) { return (Maybe<B>) this; } } } Maybe<Integer> just1 = Maybe.just(1); Maybe<Integer> nothing = Maybe.nothing(); Either<String, Maybe<Integer>> traversedJust = just1.traverse(x -> right(x + 1), empty -> left("empty")) .fmap(x -> (Maybe<Integer>) x) .coerce(); //-> Right(Just(2)) Either<String, Maybe<Integer>> traversedNothing = nothing.traverse(x -> right(x + 1), empty -> left("empty")) .fmap(x -> (Maybe<Integer>) x) .coerce(); //-> Left("empty")"><pre><span class="pl-k">public</span> <span class="pl-k">abstract</span> <span class="pl-k">class</span> <span class="pl-smi">Maybe</span><<span class="pl-smi">A</span>> <span class="pl-k">implements</span> <span class="pl-smi">Traversable</span><<span class="pl-smi">A</span>, <span class="pl-smi">Maybe</span>> { <span class="pl-k">private</span> <span class="pl-smi">Maybe</span>() { } <span class="pl-c1">@</span><span class="pl-c1">Override</span> <span class="pl-k">public</span> <span class="pl-k">abstract</span> <<span class="pl-smi">B</span>, <span class="pl-smi">App</span> <span class="pl-k">extends</span> <span class="pl-smi">Applicative</span>> <span class="pl-smi">Applicative</span><<span class="pl-smi">Maybe</span><<span class="pl-smi">B</span>>, <span class="pl-smi">App</span>> <span class="pl-en">traverse</span>( <span class="pl-smi">Function</span><? <span class="pl-en">super</span> <span class="pl-smi">A</span>, ? <span class="pl-k">extends</span> <span class="pl-smi">Applicative</span><<span class="pl-smi">B</span>, <span class="pl-smi">App</span>>> <span class="pl-s1">fn</span>, <span class="pl-smi">Function</span><? <span class="pl-en">super</span> <span class="pl-smi">Traversable</span><<span class="pl-smi">B</span>, <span class="pl-smi">Maybe</span>>, ? <span class="pl-k">extends</span> <span class="pl-smi">Applicative</span><? <span class="pl-k">extends</span> <span class="pl-smi">Traversable</span><<span class="pl-smi">B</span>, <span class="pl-smi">Maybe</span>>, <span class="pl-smi">App</span>>> <span class="pl-s1">pure</span>); <span class="pl-c1">@</span><span class="pl-c1">Override</span> <span class="pl-k">public</span> <span class="pl-k">abstract</span> <<span class="pl-smi">B</span>> <span class="pl-smi">Maybe</span><<span class="pl-smi">B</span>> <span class="pl-en">fmap</span>(<span class="pl-smi">Function</span><? <span class="pl-en">super</span> <span class="pl-smi">A</span>, ? <span class="pl-k">extends</span> <span class="pl-smi">B</span>> <span class="pl-s1">fn</span>); <span class="pl-k">private</span> <span class="pl-k">static</span> <span class="pl-k">final</span> <span class="pl-k">class</span> <span class="pl-smi">Just</span><<span class="pl-smi">A</span>> <span class="pl-k">extends</span> <span class="pl-smi">Maybe</span><<span class="pl-smi">A</span>> { <span class="pl-k">private</span> <span class="pl-k">final</span> <span class="pl-smi">A</span> <span class="pl-s1">a</span>; <span class="pl-k">private</span> <span class="pl-smi">Just</span>(<span class="pl-smi">A</span> <span class="pl-s1">a</span>) { <span class="pl-smi">this</span>.<span class="pl-s1">a</span> = <span class="pl-s1">a</span>; } <span class="pl-c1">@</span><span class="pl-c1">Override</span> <span class="pl-k">public</span> <<span class="pl-smi">B</span>, <span class="pl-smi">App</span> <span class="pl-k">extends</span> <span class="pl-smi">Applicative</span>> <span class="pl-smi">Applicative</span><<span class="pl-smi">Maybe</span><<span class="pl-smi">B</span>>, <span class="pl-smi">App</span>> <span class="pl-en">traverse</span>( <span class="pl-smi">Function</span><? <span class="pl-en">super</span> <span class="pl-smi">A</span>, ? <span class="pl-k">extends</span> <span class="pl-smi">Applicative</span><<span class="pl-smi">B</span>, <span class="pl-smi">App</span>>> <span class="pl-s1">fn</span>, <span class="pl-smi">Function</span><? <span class="pl-en">super</span> <span class="pl-smi">Traversable</span><<span class="pl-smi">B</span>, <span class="pl-smi">Maybe</span>>, ? <span class="pl-k">extends</span> <span class="pl-smi">Applicative</span><? <span class="pl-k">extends</span> <span class="pl-smi">Traversable</span><<span class="pl-smi">B</span>, <span class="pl-smi">Maybe</span>>, <span class="pl-smi">App</span>>> <span class="pl-s1">pure</span>) { <span class="pl-k">return</span> <span class="pl-s1">fn</span>.<span class="pl-en">apply</span>(<span class="pl-s1">a</span>).<span class="pl-en">fmap</span>(<span class="pl-smi">Just</span>::<span class="pl-k">new</span>); } <span class="pl-c1">@</span><span class="pl-c1">Override</span> <span class="pl-k">public</span> <<span class="pl-smi">B</span>> <span class="pl-smi">Maybe</span><<span class="pl-smi">B</span>> <span class="pl-en">fmap</span>(<span class="pl-smi">Function</span><? <span class="pl-en">super</span> <span class="pl-smi">A</span>, ? <span class="pl-k">extends</span> <span class="pl-smi">B</span>> <span class="pl-s1">fn</span>) { <span class="pl-k">return</span> <span class="pl-k">new</span> <span class="pl-smi">Just</span><>(<span class="pl-s1">fn</span>.<span class="pl-en">apply</span>(<span class="pl-s1">a</span>)); } } <span class="pl-k">private</span> <span class="pl-k">static</span> <span class="pl-k">final</span> <span class="pl-k">class</span> <span class="pl-smi">Nothing</span><<span class="pl-smi">A</span>> <span class="pl-k">extends</span> <span class="pl-smi">Maybe</span><<span class="pl-smi">A</span>> { <span class="pl-c1">@</span><span class="pl-c1">Override</span> <span class="pl-c1">@</span><span class="pl-c1">SuppressWarnings</span>(<span class="pl-s">"unchecked"</span>) <span class="pl-k">public</span> <<span class="pl-smi">B</span>, <span class="pl-smi">App</span> <span class="pl-k">extends</span> <span class="pl-smi">Applicative</span>> <span class="pl-smi">Applicative</span><<span class="pl-smi">Maybe</span><<span class="pl-smi">B</span>>, <span class="pl-smi">App</span>> <span class="pl-en">traverse</span>( <span class="pl-smi">Function</span><? <span class="pl-en">super</span> <span class="pl-smi">A</span>, ? <span class="pl-k">extends</span> <span class="pl-smi">Applicative</span><<span class="pl-smi">B</span>, <span class="pl-smi">App</span>>> <span class="pl-s1">fn</span>, <span class="pl-smi">Function</span><? <span class="pl-en">super</span> <span class="pl-smi">Traversable</span><<span class="pl-smi">B</span>, <span class="pl-smi">Maybe</span>>, ? <span class="pl-k">extends</span> <span class="pl-smi">Applicative</span><? <span class="pl-k">extends</span> <span class="pl-smi">Traversable</span><<span class="pl-smi">B</span>, <span class="pl-smi">Maybe</span>>, <span class="pl-smi">App</span>>> <span class="pl-s1">pure</span>) { <span class="pl-k">return</span> <span class="pl-s1">pure</span>.<span class="pl-en">apply</span>((<span class="pl-smi">Maybe</span><<span class="pl-smi">B</span>>) <span class="pl-smi">this</span>).<span class="pl-en">fmap</span>(<span class="pl-s1">x</span> -> (<span class="pl-smi">Maybe</span><<span class="pl-smi">B</span>>) <span class="pl-s1">x</span>); } <span class="pl-c1">@</span><span class="pl-c1">Override</span> <span class="pl-c1">@</span><span class="pl-c1">SuppressWarnings</span>(<span class="pl-s">"unchecked"</span>) <span class="pl-k">public</span> <<span class="pl-smi">B</span>> <span class="pl-smi">Maybe</span><<span class="pl-smi">B</span>> <span class="pl-en">fmap</span>(<span class="pl-smi">Function</span><? <span class="pl-en">super</span> <span class="pl-smi">A</span>, ? <span class="pl-k">extends</span> <span class="pl-smi">B</span>> <span class="pl-s1">fn</span>) { <span class="pl-k">return</span> (<span class="pl-smi">Maybe</span><<span class="pl-smi">B</span>>) <span class="pl-smi">this</span>; } } } <span class="pl-smi">Maybe</span><<span class="pl-smi">Integer</span>> <span class="pl-s1">just1</span> = <span class="pl-smi">Maybe</span>.<span class="pl-en">just</span>(<span class="pl-c1">1</span>); <span class="pl-smi">Maybe</span><<span class="pl-smi">Integer</span>> <span class="pl-s1">nothing</span> = <span class="pl-smi">Maybe</span>.<span class="pl-en">nothing</span>(); <span class="pl-smi">Either</span><<span class="pl-smi">String</span>, <span class="pl-smi">Maybe</span><<span class="pl-smi">Integer</span>>> <span class="pl-s1">traversedJust</span> = <span class="pl-s1">just1</span>.<span class="pl-en">traverse</span>(<span class="pl-s1">x</span> -> <span class="pl-en">right</span>(<span class="pl-s1">x</span> + <span class="pl-c1">1</span>), <span class="pl-s1">empty</span> -> <span class="pl-en">left</span>(<span class="pl-s">"empty"</span>)) .<span class="pl-en">fmap</span>(<span class="pl-s1">x</span> -> (<span class="pl-smi">Maybe</span><<span class="pl-smi">Integer</span>>) <span class="pl-s1">x</span>) .<span class="pl-en">coerce</span>(); <span class="pl-c">//-> Right(Just(2))</span> <span class="pl-smi">Either</span><<span class="pl-smi">String</span>, <span class="pl-smi">Maybe</span><<span class="pl-smi">Integer</span>>> <span class="pl-s1">traversedNothing</span> = <span class="pl-s1">nothing</span>.<span class="pl-en">traverse</span>(<span class="pl-s1">x</span> -> <span class="pl-en">right</span>(<span class="pl-s1">x</span> + <span class="pl-c1">1</span>), <span class="pl-s1">empty</span> -> <span class="pl-en">left</span>(<span class="pl-s">"empty"</span>)) .<span class="pl-en">fmap</span>(<span class="pl-s1">x</span> -> (<span class="pl-smi">Maybe</span><<span class="pl-smi">Integer</span>>) <span class="pl-s1">x</span>) .<span class="pl-en">coerce</span>(); <span class="pl-c">//-> Left("empty")</span></pre></div> <p dir="auto">Examples of traversable functors include:</p> <ul dir="auto"> <li><code>SingletonHList</code> and <code>Tuple*</code></li> <li><code>Choice*</code></li> <li><code>Either</code></li> <li><code>Const</code> and <code>Identity</code></li> <li><code>LambdaIterable</code> for wrapping <code>Iterable</code> in an instance of <code>Traversable</code></li> </ul> <p dir="auto">In addition to implementing <code>fmap</code> from <code>Functor</code>, implementing a traversable functor involves providing an implementation of <code>traverse</code>.</p> <p dir="auto">As always, there are <a href="https://hackage.haskell.org/package/base-4.9.1.0/docs/Data-Traversable.html" rel="nofollow">some laws</a> that should be observed.</p> <div class="markdown-heading" dir="auto"><h2 tabindex="-1" class="heading-element" dir="auto"><a name="user-content-adts">ADTs</a></h2><a id="user-content-adts" class="anchor" aria-label="Permalink: ADTs" href="#adts"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <p dir="auto">Lambda also supports a few first-class <a href="https://www.wikiwand.com/en/Algebraic_data_type" rel="nofollow">algebraic data types</a>.</p> <div class="markdown-heading" dir="auto"><h3 tabindex="-1" class="heading-element" dir="auto"><a name="user-content-maybe">Maybe</a></h3><a id="user-content-maybe" class="anchor" aria-label="Permalink: Maybe" href="#maybe"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <p dir="auto"><code>Maybe</code> is the <em>lambda</em> analog to <code>java.util.Optional</code>. It behaves in much of the same way as <code>j.u.Optional</code>, except that it quite intentionally does not support the inherently unsafe <code>j.u.Optional#get</code>.</p> <div class="highlight highlight-source-java notranslate position-relative overflow-auto" dir="auto" data-snippet-clipboard-copy-content="Maybe<Integer> maybeInt = Maybe.just(1); // Just 1 Maybe<String> maybeString = Maybe.nothing(); // Nothing"><pre><span class="pl-smi">Maybe</span><<span class="pl-smi">Integer</span>> <span class="pl-s1">maybeInt</span> = <span class="pl-smi">Maybe</span>.<span class="pl-en">just</span>(<span class="pl-c1">1</span>); <span class="pl-c">// Just 1</span> <span class="pl-smi">Maybe</span><<span class="pl-smi">String</span>> <span class="pl-s1">maybeString</span> = <span class="pl-smi">Maybe</span>.<span class="pl-en">nothing</span>(); <span class="pl-c">// Nothing</span></pre></div> <p dir="auto">Also, because it's a <em>lambda</em> type, it takes advantage of the full functor hierarchy, as well as some helpful conversion functions:</p> <div class="highlight highlight-source-java notranslate position-relative overflow-auto" dir="auto" data-snippet-clipboard-copy-content="Maybe<String> just = Maybe.maybe("string"); // Just "string" Maybe<String> nothing = Maybe.maybe(null); // Nothing Maybe<Integer> maybeX = Maybe.just(1); Maybe<Integer> maybeY = Maybe.just(2); maybeY.zip(maybeX.fmap(x -> y -> x + y)); // Just 3 maybeY.zip(nothing()); // Nothing Maybe.<Integer>nothing().zip(maybeX.fmap(x -> y -> x + y)); // Nothing Either<String, Integer> right = maybeX.toEither(() -> "was empty"); // Right 1 Either<String, Integer> left = Maybe.<Integer>nothing().toEither(() -> "was empty"); // Left "was empty" Maybe.fromEither(right); // Just 1 Maybe.fromEither(left); // Nothing"><pre><span class="pl-smi">Maybe</span><<span class="pl-smi">String</span>> <span class="pl-s1">just</span> = <span class="pl-smi">Maybe</span>.<span class="pl-en">maybe</span>(<span class="pl-s">"string"</span>); <span class="pl-c">// Just "string"</span> <span class="pl-smi">Maybe</span><<span class="pl-smi">String</span>> <span class="pl-s1">nothing</span> = <span class="pl-smi">Maybe</span>.<span class="pl-en">maybe</span>(<span class="pl-c1">null</span>); <span class="pl-c">// Nothing</span> <span class="pl-smi">Maybe</span><<span class="pl-smi">Integer</span>> <span class="pl-s1">maybeX</span> = <span class="pl-smi">Maybe</span>.<span class="pl-en">just</span>(<span class="pl-c1">1</span>); <span class="pl-smi">Maybe</span><<span class="pl-smi">Integer</span>> <span class="pl-s1">maybeY</span> = <span class="pl-smi">Maybe</span>.<span class="pl-en">just</span>(<span class="pl-c1">2</span>); <span class="pl-s1">maybeY</span>.<span class="pl-en">zip</span>(<span class="pl-s1">maybeX</span>.<span class="pl-en">fmap</span>(<span class="pl-s1">x</span> -> <span class="pl-s1">y</span> -> <span class="pl-s1">x</span> + <span class="pl-s1">y</span>)); <span class="pl-c">// Just 3</span> <span class="pl-s1">maybeY</span>.<span class="pl-en">zip</span>(<span class="pl-en">nothing</span>()); <span class="pl-c">// Nothing</span> <span class="pl-smi">Maybe</span>.<<span class="pl-smi">Integer</span>><span class="pl-en">nothing</span>().<span class="pl-en">zip</span>(<span class="pl-s1">maybeX</span>.<span class="pl-en">fmap</span>(<span class="pl-s1">x</span> -> <span class="pl-s1">y</span> -> <span class="pl-s1">x</span> + <span class="pl-s1">y</span>)); <span class="pl-c">// Nothing</span> <span class="pl-smi">Either</span><<span class="pl-smi">String</span>, <span class="pl-smi">Integer</span>> <span class="pl-s1">right</span> = <span class="pl-s1">maybeX</span>.<span class="pl-en">toEither</span>(() -> <span class="pl-s">"was empty"</span>); <span class="pl-c">// Right 1</span> <span class="pl-smi">Either</span><<span class="pl-smi">String</span>, <span class="pl-smi">Integer</span>> <span class="pl-s1">left</span> = <span class="pl-smi">Maybe</span>.<<span class="pl-smi">Integer</span>><span class="pl-en">nothing</span>().<span class="pl-en">toEither</span>(() -> <span class="pl-s">"was empty"</span>); <span class="pl-c">// Left "was empty"</span> <span class="pl-smi">Maybe</span>.<span class="pl-en">fromEither</span>(<span class="pl-s1">right</span>); <span class="pl-c">// Just 1</span> <span class="pl-smi">Maybe</span>.<span class="pl-en">fromEither</span>(<span class="pl-s1">left</span>); <span class="pl-c">// Nothing</span></pre></div> <p dir="auto">Finally, for compatibility purposes, <code>Maybe</code> and <code>j.u.Optional</code> can be trivially converted back and forth:</p> <div class="highlight highlight-source-java notranslate position-relative overflow-auto" dir="auto" data-snippet-clipboard-copy-content="Maybe<Integer> just1 = Maybe.just(1); // Just 1 Optional<Integer> present1 = just1.toOptional(); // Optional.of(1) Optional<String> empty = Optional.empty(); // Optional.empty() Maybe<String> nothing = Maybe.fromOptional(empty); // Nothing"><pre><span class="pl-smi">Maybe</span><<span class="pl-smi">Integer</span>> <span class="pl-s1">just1</span> = <span class="pl-smi">Maybe</span>.<span class="pl-en">just</span>(<span class="pl-c1">1</span>); <span class="pl-c">// Just 1</span> <span class="pl-smi">Optional</span><<span class="pl-smi">Integer</span>> <span class="pl-s1">present1</span> = <span class="pl-s1">just1</span>.<span class="pl-en">toOptional</span>(); <span class="pl-c">// Optional.of(1)</span> <span class="pl-smi">Optional</span><<span class="pl-smi">String</span>> <span class="pl-s1">empty</span> = <span class="pl-smi">Optional</span>.<span class="pl-en">empty</span>(); <span class="pl-c">// Optional.empty()</span> <span class="pl-smi">Maybe</span><<span class="pl-smi">String</span>> <span class="pl-s1">nothing</span> = <span class="pl-smi">Maybe</span>.<span class="pl-en">fromOptional</span>(<span class="pl-s1">empty</span>); <span class="pl-c">// Nothing</span></pre></div> <p dir="auto"><em><strong>Note</strong></em>: One compatibility difference between <code>j.u.Optional</code> and <code>Maybe</code> is how <code>map</code>/<code>fmap</code> behave regarding functions that return <code>null</code>: <code>j.u.Optional</code> re-wraps <code>null</code> results from <code>map</code> operations in another <code>j.u.Optional</code>, whereas <code>Maybe</code> considers this to be an error, and throws an exception. The reason <code>Maybe</code> throws in this case is because <code>fmap</code> is not an operation to be called speculatively, and so any function that returns <code>null</code> in the context of an <code>fmap</code> operation is considered to be erroneous. Instead of calling <code>fmap</code> with a function that might return <code>null</code>, the function result should be wrapped in a <code>Maybe</code> and <code>flatMap</code> should be used, as illustrated in the following example:</p> <div class="highlight highlight-source-java notranslate position-relative overflow-auto" dir="auto" data-snippet-clipboard-copy-content="Function<Integer, Object> nullResultFn = __ -> null; Optional.of(1).map(nullResultFn); // Optional.empty() Maybe.just(1).fmap(nullResultFn); // throws NullPointerException Maybe.just(1).flatMap(nullResultFn.andThen(Maybe::maybe)); // Nothing"><pre><span class="pl-smi">Function</span><<span class="pl-smi">Integer</span>, <span class="pl-smi">Object</span>> <span class="pl-s1">nullResultFn</span> = <span class="pl-s1">__</span> -> <span class="pl-c1">null</span>; <span class="pl-smi">Optional</span>.<span class="pl-en">of</span>(<span class="pl-c1">1</span>).<span class="pl-en">map</span>(<span class="pl-s1">nullResultFn</span>); <span class="pl-c">// Optional.empty()</span> <span class="pl-smi">Maybe</span>.<span class="pl-en">just</span>(<span class="pl-c1">1</span>).<span class="pl-en">fmap</span>(<span class="pl-s1">nullResultFn</span>); <span class="pl-c">// throws NullPointerException</span> <span class="pl-smi">Maybe</span>.<span class="pl-en">just</span>(<span class="pl-c1">1</span>).<span class="pl-en">flatMap</span>(<span class="pl-s1">nullResultFn</span>.<span class="pl-en">andThen</span>(<span class="pl-smi">Maybe</span>::<span class="pl-s1">maybe</span>)); <span class="pl-c">// Nothing</span></pre></div> <div class="markdown-heading" dir="auto"><h3 tabindex="-1" class="heading-element" dir="auto"><a name="user-content-hlists">Heterogeneous Lists (HLists)</a></h3><a id="user-content-heterogeneous-lists-hlists" class="anchor" aria-label="Permalink: Heterogeneous Lists (HLists)" href="#heterogeneous-lists-hlists"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <p dir="auto">HLists are type-safe heterogeneous lists, meaning they can store elements of different types in the same list while facilitating certain type-safe interactions.</p> <p dir="auto">The following illustrates how the linear expansion of the recursive type signature for <code>HList</code> prevents ill-typed expressions:</p> <div class="highlight highlight-source-java notranslate position-relative overflow-auto" dir="auto" data-snippet-clipboard-copy-content="HCons<Integer, HCons<String, HNil>> hList = HList.cons(1, HList.cons("foo", HList.nil())); System.out.println(hList.head()); // prints 1 System.out.println(hList.tail().head()); // prints "foo" HNil nil = hList.tail().tail(); //nil.head() won't type-check"><pre><span class="pl-smi">HCons</span><<span class="pl-smi">Integer</span>, <span class="pl-smi">HCons</span><<span class="pl-smi">String</span>, <span class="pl-smi">HNil</span>>> <span class="pl-s1">hList</span> = <span class="pl-smi">HList</span>.<span class="pl-en">cons</span>(<span class="pl-c1">1</span>, <span class="pl-smi">HList</span>.<span class="pl-en">cons</span>(<span class="pl-s">"foo"</span>, <span class="pl-smi">HList</span>.<span class="pl-en">nil</span>())); <span class="pl-smi">System</span>.<span class="pl-s1">out</span>.<span class="pl-en">println</span>(<span class="pl-s1">hList</span>.<span class="pl-en">head</span>()); <span class="pl-c">// prints 1</span> <span class="pl-smi">System</span>.<span class="pl-s1">out</span>.<span class="pl-en">println</span>(<span class="pl-s1">hList</span>.<span class="pl-en">tail</span>().<span class="pl-en">head</span>()); <span class="pl-c">// prints "foo"</span> <span class="pl-smi">HNil</span> <span class="pl-s1">nil</span> = <span class="pl-s1">hList</span>.<span class="pl-en">tail</span>().<span class="pl-en">tail</span>(); <span class="pl-c">//nil.head() won't type-check</span></pre></div> <div class="markdown-heading" dir="auto"><h4 tabindex="-1" class="heading-element" dir="auto"><a name="user-content-tuples">Tuples</a></h4><a id="user-content-tuples" class="anchor" aria-label="Permalink: Tuples" href="#tuples"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <p dir="auto">One of the primary downsides to using <code>HList</code>s in Java is how quickly the type signature grows.</p> <p dir="auto">To address this, tuples in lambda are specializations of <code>HList</code>s up to 8 elements deep, with added support for index-based accessor methods.</p> <div class="highlight highlight-source-java notranslate position-relative overflow-auto" dir="auto" data-snippet-clipboard-copy-content="HNil nil = HList.nil(); SingletonHList<Integer> singleton = nil.cons(8); Tuple2<Integer, Integer> tuple2 = singleton.cons(7); Tuple3<Integer, Integer, Integer> tuple3 = tuple2.cons(6); Tuple4<Integer, Integer, Integer, Integer> tuple4 = tuple3.cons(5); Tuple5<Integer, Integer, Integer, Integer, Integer> tuple5 = tuple4.cons(4); Tuple6<Integer, Integer, Integer, Integer, Integer, Integer> tuple6 = tuple5.cons(3); Tuple7<Integer, Integer, Integer, Integer, Integer, Integer, Integer> tuple7 = tuple6.cons(2); Tuple8<Integer, Integer, Integer, Integer, Integer, Integer, Integer, Integer> tuple8 = tuple7.cons(1); System.out.println(tuple2._1()); // prints 7 System.out.println(tuple8._8()); // prints 8"><pre><span class="pl-smi">HNil</span> <span class="pl-s1">nil</span> = <span class="pl-smi">HList</span>.<span class="pl-en">nil</span>(); <span class="pl-smi">SingletonHList</span><<span class="pl-smi">Integer</span>> <span class="pl-s1">singleton</span> = <span class="pl-s1">nil</span>.<span class="pl-en">cons</span>(<span class="pl-c1">8</span>); <span class="pl-smi">Tuple2</span><<span class="pl-smi">Integer</span>, <span class="pl-smi">Integer</span>> <span class="pl-s1">tuple2</span> = <span class="pl-s1">singleton</span>.<span class="pl-en">cons</span>(<span class="pl-c1">7</span>); <span class="pl-smi">Tuple3</span><<span class="pl-smi">Integer</span>, <span class="pl-smi">Integer</span>, <span class="pl-smi">Integer</span>> <span class="pl-s1">tuple3</span> = <span class="pl-s1">tuple2</span>.<span class="pl-en">cons</span>(<span class="pl-c1">6</span>); <span class="pl-smi">Tuple4</span><<span class="pl-smi">Integer</span>, <span class="pl-smi">Integer</span>, <span class="pl-smi">Integer</span>, <span class="pl-smi">Integer</span>> <span class="pl-s1">tuple4</span> = <span class="pl-s1">tuple3</span>.<span class="pl-en">cons</span>(<span class="pl-c1">5</span>); <span class="pl-smi">Tuple5</span><<span class="pl-smi">Integer</span>, <span class="pl-smi">Integer</span>, <span class="pl-smi">Integer</span>, <span class="pl-smi">Integer</span>, <span class="pl-smi">Integer</span>> <span class="pl-s1">tuple5</span> = <span class="pl-s1">tuple4</span>.<span class="pl-en">cons</span>(<span class="pl-c1">4</span>); <span class="pl-smi">Tuple6</span><<span class="pl-smi">Integer</span>, <span class="pl-smi">Integer</span>, <span class="pl-smi">Integer</span>, <span class="pl-smi">Integer</span>, <span class="pl-smi">Integer</span>, <span class="pl-smi">Integer</span>> <span class="pl-s1">tuple6</span> = <span class="pl-s1">tuple5</span>.<span class="pl-en">cons</span>(<span class="pl-c1">3</span>); <span class="pl-smi">Tuple7</span><<span class="pl-smi">Integer</span>, <span class="pl-smi">Integer</span>, <span class="pl-smi">Integer</span>, <span class="pl-smi">Integer</span>, <span class="pl-smi">Integer</span>, <span class="pl-smi">Integer</span>, <span class="pl-smi">Integer</span>> <span class="pl-s1">tuple7</span> = <span class="pl-s1">tuple6</span>.<span class="pl-en">cons</span>(<span class="pl-c1">2</span>); <span class="pl-smi">Tuple8</span><<span class="pl-smi">Integer</span>, <span class="pl-smi">Integer</span>, <span class="pl-smi">Integer</span>, <span class="pl-smi">Integer</span>, <span class="pl-smi">Integer</span>, <span class="pl-smi">Integer</span>, <span class="pl-smi">Integer</span>, <span class="pl-smi">Integer</span>> <span class="pl-s1">tuple8</span> = <span class="pl-s1">tuple7</span>.<span class="pl-en">cons</span>(<span class="pl-c1">1</span>); <span class="pl-smi">System</span>.<span class="pl-s1">out</span>.<span class="pl-en">println</span>(<span class="pl-s1">tuple2</span>.<span class="pl-en">_1</span>()); <span class="pl-c">// prints 7</span> <span class="pl-smi">System</span>.<span class="pl-s1">out</span>.<span class="pl-en">println</span>(<span class="pl-s1">tuple8</span>.<span class="pl-en">_8</span>()); <span class="pl-c">// prints 8</span></pre></div> <p dir="auto">Additionally, <code>HList</code> provides convenience static factory methods for directly constructing lists of up to 8 elements:</p> <div class="highlight highlight-source-java notranslate position-relative overflow-auto" dir="auto" data-snippet-clipboard-copy-content="SingletonHList<Integer> singleton = HList.singletonHList(1); Tuple2<Integer, Integer> tuple2 = HList.tuple(1, 2); Tuple3<Integer, Integer, Integer> tuple3 = HList.tuple(1, 2, 3); Tuple4<Integer, Integer, Integer, Integer> tuple4 = HList.tuple(1, 2, 3, 4); Tuple5<Integer, Integer, Integer, Integer, Integer> tuple5 = HList.tuple(1, 2, 3, 4, 5); Tuple6<Integer, Integer, Integer, Integer, Integer, Integer> tuple6 = HList.tuple(1, 2, 3, 4, 5, 6); Tuple7<Integer, Integer, Integer, Integer, Integer, Integer, Integer> tuple7 = HList.tuple(1, 2, 3, 4, 5, 6, 7); Tuple8<Integer, Integer, Integer, Integer, Integer, Integer, Integer, Integer> tuple8 = HList.tuple(1, 2, 3, 4, 5, 6, 7, 8);"><pre><span class="pl-smi">SingletonHList</span><<span class="pl-smi">Integer</span>> <span class="pl-s1">singleton</span> = <span class="pl-smi">HList</span>.<span class="pl-en">singletonHList</span>(<span class="pl-c1">1</span>); <span class="pl-smi">Tuple2</span><<span class="pl-smi">Integer</span>, <span class="pl-smi">Integer</span>> <span class="pl-s1">tuple2</span> = <span class="pl-smi">HList</span>.<span class="pl-en">tuple</span>(<span class="pl-c1">1</span>, <span class="pl-c1">2</span>); <span class="pl-smi">Tuple3</span><<span class="pl-smi">Integer</span>, <span class="pl-smi">Integer</span>, <span class="pl-smi">Integer</span>> <span class="pl-s1">tuple3</span> = <span class="pl-smi">HList</span>.<span class="pl-en">tuple</span>(<span class="pl-c1">1</span>, <span class="pl-c1">2</span>, <span class="pl-c1">3</span>); <span class="pl-smi">Tuple4</span><<span class="pl-smi">Integer</span>, <span class="pl-smi">Integer</span>, <span class="pl-smi">Integer</span>, <span class="pl-smi">Integer</span>> <span class="pl-s1">tuple4</span> = <span class="pl-smi">HList</span>.<span class="pl-en">tuple</span>(<span class="pl-c1">1</span>, <span class="pl-c1">2</span>, <span class="pl-c1">3</span>, <span class="pl-c1">4</span>); <span class="pl-smi">Tuple5</span><<span class="pl-smi">Integer</span>, <span class="pl-smi">Integer</span>, <span class="pl-smi">Integer</span>, <span class="pl-smi">Integer</span>, <span class="pl-smi">Integer</span>> <span class="pl-s1">tuple5</span> = <span class="pl-smi">HList</span>.<span class="pl-en">tuple</span>(<span class="pl-c1">1</span>, <span class="pl-c1">2</span>, <span class="pl-c1">3</span>, <span class="pl-c1">4</span>, <span class="pl-c1">5</span>); <span class="pl-smi">Tuple6</span><<span class="pl-smi">Integer</span>, <span class="pl-smi">Integer</span>, <span class="pl-smi">Integer</span>, <span class="pl-smi">Integer</span>, <span class="pl-smi">Integer</span>, <span class="pl-smi">Integer</span>> <span class="pl-s1">tuple6</span> = <span class="pl-smi">HList</span>.<span class="pl-en">tuple</span>(<span class="pl-c1">1</span>, <span class="pl-c1">2</span>, <span class="pl-c1">3</span>, <span class="pl-c1">4</span>, <span class="pl-c1">5</span>, <span class="pl-c1">6</span>); <span class="pl-smi">Tuple7</span><<span class="pl-smi">Integer</span>, <span class="pl-smi">Integer</span>, <span class="pl-smi">Integer</span>, <span class="pl-smi">Integer</span>, <span class="pl-smi">Integer</span>, <span class="pl-smi">Integer</span>, <span class="pl-smi">Integer</span>> <span class="pl-s1">tuple7</span> = <span class="pl-smi">HList</span>.<span class="pl-en">tuple</span>(<span class="pl-c1">1</span>, <span class="pl-c1">2</span>, <span class="pl-c1">3</span>, <span class="pl-c1">4</span>, <span class="pl-c1">5</span>, <span class="pl-c1">6</span>, <span class="pl-c1">7</span>); <span class="pl-smi">Tuple8</span><<span class="pl-smi">Integer</span>, <span class="pl-smi">Integer</span>, <span class="pl-smi">Integer</span>, <span class="pl-smi">Integer</span>, <span class="pl-smi">Integer</span>, <span class="pl-smi">Integer</span>, <span class="pl-smi">Integer</span>, <span class="pl-smi">Integer</span>> <span class="pl-s1">tuple8</span> = <span class="pl-smi">HList</span>.<span class="pl-en">tuple</span>(<span class="pl-c1">1</span>, <span class="pl-c1">2</span>, <span class="pl-c1">3</span>, <span class="pl-c1">4</span>, <span class="pl-c1">5</span>, <span class="pl-c1">6</span>, <span class="pl-c1">7</span>, <span class="pl-c1">8</span>);</pre></div> <p dir="auto"><code>Index</code> can be used for type-safe retrieval and updating of elements at specific indexes:</p> <div class="highlight highlight-source-java notranslate position-relative overflow-auto" dir="auto" data-snippet-clipboard-copy-content="HCons<Integer, HCons<String, HCons<Character, HNil>>> hList = cons(1, cons("2", cons('3', nil()))); HCons<Integer, Tuple2<String, Character>> tuple = tuple(1, "2", '3'); Tuple5<Integer, String, Character, Double, Boolean> longerHList = tuple(1, "2", '3', 4.0d, false); Index<Character, HCons<Integer, ? extends HCons<String, ? extends HCons<Character, ?>>>> characterIndex = Index.<Character>index().<String>after().after(); characterIndex.get(hList); // '3' characterIndex.get(tuple); // '3' characterIndex.get(longerHList); // '3' characterIndex.set('4', hList); // HList{ 1 :: "2" :: '4' }"><pre><span class="pl-smi">HCons</span><<span class="pl-smi">Integer</span>, <span class="pl-smi">HCons</span><<span class="pl-smi">String</span>, <span class="pl-smi">HCons</span><<span class="pl-smi">Character</span>, <span class="pl-smi">HNil</span>>>> <span class="pl-s1">hList</span> = <span class="pl-en">cons</span>(<span class="pl-c1">1</span>, <span class="pl-en">cons</span>(<span class="pl-s">"2"</span>, <span class="pl-en">cons</span>(<span class="pl-s">'3'</span>, <span class="pl-en">nil</span>()))); <span class="pl-smi">HCons</span><<span class="pl-smi">Integer</span>, <span class="pl-smi">Tuple2</span><<span class="pl-smi">String</span>, <span class="pl-smi">Character</span>>> <span class="pl-s1">tuple</span> = <span class="pl-en">tuple</span>(<span class="pl-c1">1</span>, <span class="pl-s">"2"</span>, <span class="pl-s">'3'</span>); <span class="pl-smi">Tuple5</span><<span class="pl-smi">Integer</span>, <span class="pl-smi">String</span>, <span class="pl-smi">Character</span>, <span class="pl-smi">Double</span>, <span class="pl-smi">Boolean</span>> <span class="pl-s1">longerHList</span> = <span class="pl-en">tuple</span>(<span class="pl-c1">1</span>, <span class="pl-s">"2"</span>, <span class="pl-s">'3'</span>, <span class="pl-c1">4.0d</span>, <span class="pl-c1">false</span>); <span class="pl-smi">Index</span><<span class="pl-smi">Character</span>, <span class="pl-smi">HCons</span><<span class="pl-smi">Integer</span>, ? <span class="pl-k">extends</span> <span class="pl-smi">HCons</span><<span class="pl-smi">String</span>, ? <span class="pl-k">extends</span> <span class="pl-smi">HCons</span><<span class="pl-smi">Character</span>, ?>>>> <span class="pl-s1">characterIndex</span> = <span class="pl-smi">Index</span>.<<span class="pl-smi">Character</span>><span class="pl-en">index</span>().<<span class="pl-smi">String</span>><span class="pl-en">after</span>().<span class="pl-en">after</span>(); <span class="pl-s1">characterIndex</span>.<span class="pl-en">get</span>(<span class="pl-s1">hList</span>); <span class="pl-c">// '3'</span> <span class="pl-s1">characterIndex</span>.<span class="pl-en">get</span>(<span class="pl-s1">tuple</span>); <span class="pl-c">// '3'</span> <span class="pl-s1">characterIndex</span>.<span class="pl-en">get</span>(<span class="pl-s1">longerHList</span>); <span class="pl-c">// '3'</span> <span class="pl-s1">characterIndex</span>.<span class="pl-en">set</span>(<span class="pl-s">'4'</span>, <span class="pl-s1">hList</span>); <span class="pl-c">// HList{ 1 :: "2" :: '4' }</span></pre></div> <p dir="auto">Finally, all <code>Tuple*</code> classes are instances of both <code>Functor</code> and <code>Bifunctor</code>:</p> <div class="highlight highlight-source-java notranslate position-relative overflow-auto" dir="auto" data-snippet-clipboard-copy-content="Tuple2<Integer, String> mappedTuple2 = tuple(1, 2).biMap(x -> x + 1, Object::toString); System.out.println(mappedTuple2._1()); // prints 2 System.out.println(mappedTuple2._2()); // prints "2" Tuple3<String, Boolean, Integer> mappedTuple3 = tuple("foo", true, 1).biMap(x -> !x, x -> x + 1); System.out.println(mappedTuple3._1()); // prints "foo" System.out.println(mappedTuple3._2()); // prints false System.out.println(mappedTuple3._3()); // prints 2"><pre><span class="pl-smi">Tuple2</span><<span class="pl-smi">Integer</span>, <span class="pl-smi">String</span>> <span class="pl-s1">mappedTuple2</span> = <span class="pl-en">tuple</span>(<span class="pl-c1">1</span>, <span class="pl-c1">2</span>).<span class="pl-en">biMap</span>(<span class="pl-s1">x</span> -> <span class="pl-s1">x</span> + <span class="pl-c1">1</span>, <span class="pl-smi">Object</span>::<span class="pl-s1">toString</span>); <span class="pl-smi">System</span>.<span class="pl-s1">out</span>.<span class="pl-en">println</span>(<span class="pl-s1">mappedTuple2</span>.<span class="pl-en">_1</span>()); <span class="pl-c">// prints 2</span> <span class="pl-smi">System</span>.<span class="pl-s1">out</span>.<span class="pl-en">println</span>(<span class="pl-s1">mappedTuple2</span>.<span class="pl-en">_2</span>()); <span class="pl-c">// prints "2"</span> <span class="pl-smi">Tuple3</span><<span class="pl-smi">String</span>, <span class="pl-smi">Boolean</span>, <span class="pl-smi">Integer</span>> <span class="pl-s1">mappedTuple3</span> = <span class="pl-en">tuple</span>(<span class="pl-s">"foo"</span>, <span class="pl-c1">true</span>, <span class="pl-c1">1</span>).<span class="pl-en">biMap</span>(<span class="pl-s1">x</span> -> !<span class="pl-s1">x</span>, <span class="pl-s1">x</span> -> <span class="pl-s1">x</span> + <span class="pl-c1">1</span>); <span class="pl-smi">System</span>.<span class="pl-s1">out</span>.<span class="pl-en">println</span>(<span class="pl-s1">mappedTuple3</span>.<span class="pl-en">_1</span>()); <span class="pl-c">// prints "foo"</span> <span class="pl-smi">System</span>.<span class="pl-s1">out</span>.<span class="pl-en">println</span>(<span class="pl-s1">mappedTuple3</span>.<span class="pl-en">_2</span>()); <span class="pl-c">// prints false</span> <span class="pl-smi">System</span>.<span class="pl-s1">out</span>.<span class="pl-en">println</span>(<span class="pl-s1">mappedTuple3</span>.<span class="pl-en">_3</span>()); <span class="pl-c">// prints 2</span></pre></div> <div class="markdown-heading" dir="auto"><h3 tabindex="-1" class="heading-element" dir="auto"><a name="user-content-hmaps">Heterogeneous Maps</a></h3><a id="user-content-heterogeneous-maps" class="anchor" aria-label="Permalink: Heterogeneous Maps" href="#heterogeneous-maps"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <p dir="auto">HMaps are type-safe heterogeneous maps, meaning they can store mappings to different value types in the same map; however, whereas HLists encode value types in their type signatures, HMaps rely on the keys to encode the value type that they point to.</p> <div class="highlight highlight-source-java notranslate position-relative overflow-auto" dir="auto" data-snippet-clipboard-copy-content="TypeSafeKey<String> stringKey = TypeSafeKey.typeSafeKey(); TypeSafeKey<Integer> intKey = TypeSafeKey.typeSafeKey(); HMap hmap = HMap.hMap(stringKey, "string value", intKey, 1); Optional<String> stringValue = hmap.get(stringKey); // Optional["string value"] Optional<Integer> intValue = hmap.get(intKey); // Optional[1] Optional<Integer> anotherIntValue = hmap.get(anotherIntKey); // Optional.empty"><pre><span class="pl-smi">TypeSafeKey</span><<span class="pl-smi">String</span>> <span class="pl-s1">stringKey</span> = <span class="pl-smi">TypeSafeKey</span>.<span class="pl-en">typeSafeKey</span>(); <span class="pl-smi">TypeSafeKey</span><<span class="pl-smi">Integer</span>> <span class="pl-s1">intKey</span> = <span class="pl-smi">TypeSafeKey</span>.<span class="pl-en">typeSafeKey</span>(); <span class="pl-smi">HMap</span> <span class="pl-s1">hmap</span> = <span class="pl-smi">HMap</span>.<span class="pl-en">hMap</span>(<span class="pl-s1">stringKey</span>, <span class="pl-s">"string value"</span>, <span class="pl-s1">intKey</span>, <span class="pl-c1">1</span>); <span class="pl-smi">Optional</span><<span class="pl-smi">String</span>> <span class="pl-s1">stringValue</span> = <span class="pl-s1">hmap</span>.<span class="pl-en">get</span>(<span class="pl-s1">stringKey</span>); <span class="pl-c">// Optional["string value"]</span> <span class="pl-smi">Optional</span><<span class="pl-smi">Integer</span>> <span class="pl-s1">intValue</span> = <span class="pl-s1">hmap</span>.<span class="pl-en">get</span>(<span class="pl-s1">intKey</span>); <span class="pl-c">// Optional[1]</span> <span class="pl-smi">Optional</span><<span class="pl-smi">Integer</span>> <span class="pl-s1">anotherIntValue</span> = <span class="pl-s1">hmap</span>.<span class="pl-en">get</span>(<span class="pl-s1">anotherIntKey</span>); <span class="pl-c">// Optional.empty</span></pre></div> <div class="markdown-heading" dir="auto"><h3 tabindex="-1" class="heading-element" dir="auto"><a name="user-content-coproducts">CoProducts</a></h3><a id="user-content-coproducts" class="anchor" aria-label="Permalink: CoProducts" href="#coproducts"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <p dir="auto"><code>CoProduct</code>s generalize unions of disparate types in a single consolidated type, and the <code>ChoiceN</code> ADTs represent canonical implementations of these coproduct types.</p> <div class="highlight highlight-source-java notranslate position-relative overflow-auto" dir="auto" data-snippet-clipboard-copy-content="CoProduct3<String, Integer, Character, ?> string = Choice3.a("string"); CoProduct3<String, Integer, Character, ?> integer = Choice3.b(1); CoProduct3<String, Integer, Character, ?> character = Choice3.c('a');"><pre><span class="pl-smi">CoProduct3</span><<span class="pl-smi">String</span>, <span class="pl-smi">Integer</span>, <span class="pl-smi">Character</span>, ?> <span class="pl-s1">string</span> = <span class="pl-smi">Choice3</span>.<span class="pl-en">a</span>(<span class="pl-s">"string"</span>); <span class="pl-smi">CoProduct3</span><<span class="pl-smi">String</span>, <span class="pl-smi">Integer</span>, <span class="pl-smi">Character</span>, ?> <span class="pl-s1">integer</span> = <span class="pl-smi">Choice3</span>.<span class="pl-en">b</span>(<span class="pl-c1">1</span>); <span class="pl-smi">CoProduct3</span><<span class="pl-smi">String</span>, <span class="pl-smi">Integer</span>, <span class="pl-smi">Character</span>, ?> <span class="pl-s1">character</span> = <span class="pl-smi">Choice3</span>.<span class="pl-en">c</span>(<span class="pl-s">'a'</span>);</pre></div> <p dir="auto">Rather than supporting explicit value unwrapping, which would necessarily jeopardize type safety, <code>CoProduct</code>s support a <code>match</code> method that takes one function per possible value type and maps it to a final common result type:</p> <div class="highlight highlight-source-java notranslate position-relative overflow-auto" dir="auto" data-snippet-clipboard-copy-content="CoProduct3<String, Integer, Character, ?> string = Choice3.a("string"); CoProduct3<String, Integer, Character, ?> integer = Choice3.b(1); CoProduct3<String, Integer, Character, ?> character = Choice3.c('a'); Integer result = string.<Integer>match(String::length, identity(), Character::charCount); // 6"><pre><span class="pl-smi">CoProduct3</span><<span class="pl-smi">String</span>, <span class="pl-smi">Integer</span>, <span class="pl-smi">Character</span>, ?> <span class="pl-s1">string</span> = <span class="pl-smi">Choice3</span>.<span class="pl-en">a</span>(<span class="pl-s">"string"</span>); <span class="pl-smi">CoProduct3</span><<span class="pl-smi">String</span>, <span class="pl-smi">Integer</span>, <span class="pl-smi">Character</span>, ?> <span class="pl-s1">integer</span> = <span class="pl-smi">Choice3</span>.<span class="pl-en">b</span>(<span class="pl-c1">1</span>); <span class="pl-smi">CoProduct3</span><<span class="pl-smi">String</span>, <span class="pl-smi">Integer</span>, <span class="pl-smi">Character</span>, ?> <span class="pl-s1">character</span> = <span class="pl-smi">Choice3</span>.<span class="pl-en">c</span>(<span class="pl-s">'a'</span>); <span class="pl-smi">Integer</span> <span class="pl-s1">result</span> = <span class="pl-s1">string</span>.<<span class="pl-smi">Integer</span>><span class="pl-en">match</span>(<span class="pl-smi">String</span>::<span class="pl-s1">length</span>, <span class="pl-en">identity</span>(), <span class="pl-smi">Character</span>::<span class="pl-s1">charCount</span>); <span class="pl-c">// 6</span></pre></div> <p dir="auto">Additionally, because a <code>CoProduct2<A, B, ?></code> guarantees a subset of a <code>CoProduct3<A, B, C, ?></code>, the <code>diverge</code> method exists between <code>CoProduct</code> types of single magnitude differences to make it easy to use a more convergent <code>CoProduct</code> where a more divergent <code>CoProduct</code> is expected:</p> <div class="highlight highlight-source-java notranslate position-relative overflow-auto" dir="auto" data-snippet-clipboard-copy-content="CoProduct2<String, Integer, ?> coProduct2 = Choice2.a("string"); CoProduct3<String, Integer, Character, ?> coProduct3 = coProduct2.diverge(); // still just the coProduct2 value, adapted to the coProduct3 shape"><pre><span class="pl-smi">CoProduct2</span><<span class="pl-smi">String</span>, <span class="pl-smi">Integer</span>, ?> <span class="pl-s1">coProduct2</span> = <span class="pl-smi">Choice2</span>.<span class="pl-en">a</span>(<span class="pl-s">"string"</span>); <span class="pl-smi">CoProduct3</span><<span class="pl-smi">String</span>, <span class="pl-smi">Integer</span>, <span class="pl-smi">Character</span>, ?> <span class="pl-s1">coProduct3</span> = <span class="pl-s1">coProduct2</span>.<span class="pl-en">diverge</span>(); <span class="pl-c">// still just the coProduct2 value, adapted to the coProduct3 shape</span></pre></div> <p dir="auto">There are <code>CoProduct</code> and <code>Choice</code> specializations for type unions of up to 8 different types: <code>CoProduct2</code> through <code>CoProduct8</code>, and <code>Choice2</code> through <code>Choice8</code>, respectively.</p> <div class="markdown-heading" dir="auto"><h3 tabindex="-1" class="heading-element" dir="auto"><a name="user-content-either">Either</a></h3><a id="user-content-either" class="anchor" aria-label="Permalink: Either" href="#either"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <p dir="auto"><code>Either<L, R></code> represents a specialized <code>CoProduct2<L, R></code>, which resolve to one of two possible values: a left value wrapping an <code>L</code>, or a right value wrapping an <code>R</code> (typically an exceptional value or a successful value, respectively).</p> <p dir="auto">As with <code>CoProduct2</code>, rather than supporting explicit value unwrapping, <code>Either</code> supports many useful comprehensions to help facilitate type-safe interactions:</p> <div class="highlight highlight-source-java notranslate position-relative overflow-auto" dir="auto" data-snippet-clipboard-copy-content="Either<String, Integer> right = Either.right(1); Either<String, Integer> left = Either.left("Head fell off"); Integer result = right.orElse(-1); //-> 1 List<Integer> values = left.match(l -> Collections.emptyList(), Collections::singletonList); //-> [] "><pre><span class="pl-smi">Either</span><<span class="pl-smi">String</span>, <span class="pl-smi">Integer</span>> <span class="pl-s1">right</span> = <span class="pl-smi">Either</span>.<span class="pl-en">right</span>(<span class="pl-c1">1</span>); <span class="pl-smi">Either</span><<span class="pl-smi">String</span>, <span class="pl-smi">Integer</span>> <span class="pl-s1">left</span> = <span class="pl-smi">Either</span>.<span class="pl-en">left</span>(<span class="pl-s">"Head fell off"</span>); <span class="pl-smi">Integer</span> <span class="pl-s1">result</span> = <span class="pl-s1">right</span>.<span class="pl-en">orElse</span>(-<span class="pl-c1">1</span>); <span class="pl-c">//-> 1</span> <span class="pl-smi">List</span><<span class="pl-smi">Integer</span>> <span class="pl-s1">values</span> = <span class="pl-s1">left</span>.<span class="pl-en">match</span>(<span class="pl-s1">l</span> -> <span class="pl-smi">Collections</span>.<span class="pl-en">emptyList</span>(), <span class="pl-smi">Collections</span>::<span class="pl-s1">singletonList</span>); <span class="pl-c">//-> [] </span></pre></div> <p dir="auto">Check out the tests for <a href="https://github.com/palatable/lambda/blob/master/src/test/java/com/jnape/palatable/lambda/adt/EitherTest.java">more examples</a> of ways to interact with <code>Either</code>.</p> <div class="markdown-heading" dir="auto"><h2 tabindex="-1" class="heading-element" dir="auto"><a name="user-content-lenses">Lenses</a></h2><a id="user-content-lenses" class="anchor" aria-label="Permalink: Lenses" href="#lenses"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <p dir="auto">Lambda also ships with a first-class <a href="https://www.youtube.com/watch?v=cefnmjtAolY&feature=youtu.be&hd=1" rel="nofollow">lens</a> type, as well as a small library of useful general lenses:</p> <div class="highlight highlight-source-java notranslate position-relative overflow-auto" dir="auto" data-snippet-clipboard-copy-content="Lens<List<String>, List<String>, Optional<String>, String> stringAt0 = ListLens.at(0); List<String> strings = asList("foo", "bar", "baz"); view(stringAt0, strings); // Optional[foo] set(stringAt0, "quux", strings); // [quux, bar, baz] over(stringAt0, s -> s.map(String::toUpperCase).orElse(""), strings); // [FOO, bar, baz]"><pre><span class="pl-smi">Lens</span><<span class="pl-smi">List</span><<span class="pl-smi">String</span>>, <span class="pl-smi">List</span><<span class="pl-smi">String</span>>, <span class="pl-smi">Optional</span><<span class="pl-smi">String</span>>, <span class="pl-smi">String</span>> <span class="pl-s1">stringAt0</span> = <span class="pl-smi">ListLens</span>.<span class="pl-en">at</span>(<span class="pl-c1">0</span>); <span class="pl-smi">List</span><<span class="pl-smi">String</span>> <span class="pl-s1">strings</span> = <span class="pl-en">asList</span>(<span class="pl-s">"foo"</span>, <span class="pl-s">"bar"</span>, <span class="pl-s">"baz"</span>); <span class="pl-en">view</span>(<span class="pl-s1">stringAt0</span>, <span class="pl-s1">strings</span>); <span class="pl-c">// Optional[foo]</span> <span class="pl-en">set</span>(<span class="pl-s1">stringAt0</span>, <span class="pl-s">"quux"</span>, <span class="pl-s1">strings</span>); <span class="pl-c">// [quux, bar, baz]</span> <span class="pl-en">over</span>(<span class="pl-s1">stringAt0</span>, <span class="pl-s1">s</span> -> <span class="pl-s1">s</span>.<span class="pl-en">map</span>(<span class="pl-smi">String</span>::<span class="pl-s1">toUpperCase</span>).<span class="pl-en">orElse</span>(<span class="pl-s">""</span>), <span class="pl-s1">strings</span>); <span class="pl-c">// [FOO, bar, baz]</span></pre></div> <p dir="auto">There are three functions that lambda provides that interface directly with lenses: <code>view</code>, <code>over</code>, and <code>set</code>. As the name implies, <code>view</code> and <code>set</code> are used to retrieve values and store values, respectively, whereas <code>over</code> is used to apply a function to the value a lens is focused on, alter it, and store it (you can think of <code>set</code> as a specialization of <code>over</code> using <code>constantly</code>).</p> <p dir="auto">Lenses can be easily created. Consider the following <code>Person</code> class:</p> <div class="highlight highlight-source-java notranslate position-relative overflow-auto" dir="auto" data-snippet-clipboard-copy-content="public final class Person { private final int age; public Person(int age) { this.age = age; } public int getAge() { return age; } public Person setAge(int age) { return new Person(age); } public Person setAge(LocalDate dob) { return setAge((int) YEARS.between(dob, LocalDate.now())); } }"><pre><span class="pl-k">public</span> <span class="pl-k">final</span> <span class="pl-k">class</span> <span class="pl-smi">Person</span> { <span class="pl-k">private</span> <span class="pl-k">final</span> <span class="pl-smi">int</span> <span class="pl-s1">age</span>; <span class="pl-k">public</span> <span class="pl-smi">Person</span>(<span class="pl-smi">int</span> <span class="pl-s1">age</span>) { <span class="pl-smi">this</span>.<span class="pl-s1">age</span> = <span class="pl-s1">age</span>; } <span class="pl-k">public</span> <span class="pl-smi">int</span> <span class="pl-en">getAge</span>() { <span class="pl-k">return</span> <span class="pl-s1">age</span>; } <span class="pl-k">public</span> <span class="pl-smi">Person</span> <span class="pl-en">setAge</span>(<span class="pl-smi">int</span> <span class="pl-s1">age</span>) { <span class="pl-k">return</span> <span class="pl-k">new</span> <span class="pl-smi">Person</span>(<span class="pl-s1">age</span>); } <span class="pl-k">public</span> <span class="pl-smi">Person</span> <span class="pl-en">setAge</span>(<span class="pl-smi">LocalDate</span> <span class="pl-s1">dob</span>) { <span class="pl-k">return</span> <span class="pl-en">setAge</span>((<span class="pl-smi">int</span>) <span class="pl-c1">YEARS</span>.<span class="pl-en">between</span>(<span class="pl-s1">dob</span>, <span class="pl-smi">LocalDate</span>.<span class="pl-en">now</span>())); } }</pre></div> <p dir="auto">...and a lens for getting and setting <code>age</code> as an <code>int</code>:</p> <div class="highlight highlight-source-java notranslate position-relative overflow-auto" dir="auto" data-snippet-clipboard-copy-content="Lens<Person, Person, Integer, Integer> ageLensWithInt = Lens.lens(Person::getAge, Person::setAge); //or, when each pair of type arguments match... Lens.Simple<Person, Integer> alsoAgeLensWithInt = Lens.simpleLens(Person::getAge, Person::setAge);"><pre><span class="pl-smi">Lens</span><<span class="pl-smi">Person</span>, <span class="pl-smi">Person</span>, <span class="pl-smi">Integer</span>, <span class="pl-smi">Integer</span>> <span class="pl-s1">ageLensWithInt</span> = <span class="pl-smi">Lens</span>.<span class="pl-en">lens</span>(<span class="pl-smi">Person</span>::<span class="pl-s1">getAge</span>, <span class="pl-smi">Person</span>::<span class="pl-s1">setAge</span>); <span class="pl-c">//or, when each pair of type arguments match...</span> <span class="pl-smi">Lens</span>.<span class="pl-smi">Simple</span><<span class="pl-smi">Person</span>, <span class="pl-smi">Integer</span>> <span class="pl-s1">alsoAgeLensWithInt</span> = <span class="pl-smi">Lens</span>.<span class="pl-en">simpleLens</span>(<span class="pl-smi">Person</span>::<span class="pl-s1">getAge</span>, <span class="pl-smi">Person</span>::<span class="pl-s1">setAge</span>);</pre></div> <p dir="auto">If we wanted a lens for the <code>LocalDate</code> version of <code>setAge</code>, we could use the same method references and only alter the type signature:</p> <div class="highlight highlight-source-java notranslate position-relative overflow-auto" dir="auto" data-snippet-clipboard-copy-content="Lens<Person, Person, Integer, LocalDate> ageLensWithLocalDate = Lens.lens(Person::getAge, Person::setAge);"><pre><span class="pl-smi">Lens</span><<span class="pl-smi">Person</span>, <span class="pl-smi">Person</span>, <span class="pl-smi">Integer</span>, <span class="pl-smi">LocalDate</span>> <span class="pl-s1">ageLensWithLocalDate</span> = <span class="pl-smi">Lens</span>.<span class="pl-en">lens</span>(<span class="pl-smi">Person</span>::<span class="pl-s1">getAge</span>, <span class="pl-smi">Person</span>::<span class="pl-s1">setAge</span>);</pre></div> <p dir="auto">Compatible lenses can be trivially composed:</p> <div class="highlight highlight-source-java notranslate position-relative overflow-auto" dir="auto" data-snippet-clipboard-copy-content="Lens<List<Integer>, List<Integer>, Optional<Integer>, Integer> at0 = ListLens.at(0); Lens<Map<String, List<Integer>>, Map<String, List<Integer>>, List<Integer>, List<Integer>> atFoo = MapLens.atKey("foo", emptyList()); view(atFoo.andThen(at0), singletonMap("foo", asList(1, 2, 3))); // Optional[1]"><pre><span class="pl-smi">Lens</span><<span class="pl-smi">List</span><<span class="pl-smi">Integer</span>>, <span class="pl-smi">List</span><<span class="pl-smi">Integer</span>>, <span class="pl-smi">Optional</span><<span class="pl-smi">Integer</span>>, <span class="pl-smi">Integer</span>> <span class="pl-s1">at0</span> = <span class="pl-smi">ListLens</span>.<span class="pl-en">at</span>(<span class="pl-c1">0</span>); <span class="pl-smi">Lens</span><<span class="pl-smi">Map</span><<span class="pl-smi">String</span>, <span class="pl-smi">List</span><<span class="pl-smi">Integer</span>>>, <span class="pl-smi">Map</span><<span class="pl-smi">String</span>, <span class="pl-smi">List</span><<span class="pl-smi">Integer</span>>>, <span class="pl-smi">List</span><<span class="pl-smi">Integer</span>>, <span class="pl-smi">List</span><<span class="pl-smi">Integer</span>>> <span class="pl-s1">atFoo</span> = <span class="pl-smi">MapLens</span>.<span class="pl-en">atKey</span>(<span class="pl-s">"foo"</span>, <span class="pl-en">emptyList</span>()); <span class="pl-en">view</span>(<span class="pl-s1">atFoo</span>.<span class="pl-en">andThen</span>(<span class="pl-s1">at0</span>), <span class="pl-en">singletonMap</span>(<span class="pl-s">"foo"</span>, <span class="pl-en">asList</span>(<span class="pl-c1">1</span>, <span class="pl-c1">2</span>, <span class="pl-c1">3</span>))); <span class="pl-c">// Optional[1]</span></pre></div> <p dir="auto">Lens provides independent <code>map</code> operations for each parameter, so incompatible lenses can also be composed:</p> <div class="highlight highlight-source-java notranslate position-relative overflow-auto" dir="auto" data-snippet-clipboard-copy-content="Lens<List<Integer>, List<Integer>, Optional<Integer>, Integer> at0 = ListLens.at(0); Lens<Map<String, List<Integer>>, Map<String, List<Integer>>, Optional<List<Integer>>, List<Integer>> atFoo = MapLens.atKey("foo"); Lens<Map<String, List<Integer>>, Map<String, List<Integer>>, Optional<Integer>, Integer> composed = atFoo.mapA(optL -> optL.orElse(singletonList(-1))) .andThen(at0); view(composed, singletonMap("foo", emptyList())); // Optional.empty"><pre><span class="pl-smi">Lens</span><<span class="pl-smi">List</span><<span class="pl-smi">Integer</span>>, <span class="pl-smi">List</span><<span class="pl-smi">Integer</span>>, <span class="pl-smi">Optional</span><<span class="pl-smi">Integer</span>>, <span class="pl-smi">Integer</span>> <span class="pl-s1">at0</span> = <span class="pl-smi">ListLens</span>.<span class="pl-en">at</span>(<span class="pl-c1">0</span>); <span class="pl-smi">Lens</span><<span class="pl-smi">Map</span><<span class="pl-smi">String</span>, <span class="pl-smi">List</span><<span class="pl-smi">Integer</span>>>, <span class="pl-smi">Map</span><<span class="pl-smi">String</span>, <span class="pl-smi">List</span><<span class="pl-smi">Integer</span>>>, <span class="pl-smi">Optional</span><<span class="pl-smi">List</span><<span class="pl-smi">Integer</span>>>, <span class="pl-smi">List</span><<span class="pl-smi">Integer</span>>> <span class="pl-s1">atFoo</span> = <span class="pl-smi">MapLens</span>.<span class="pl-en">atKey</span>(<span class="pl-s">"foo"</span>); <span class="pl-smi">Lens</span><<span class="pl-smi">Map</span><<span class="pl-smi">String</span>, <span class="pl-smi">List</span><<span class="pl-smi">Integer</span>>>, <span class="pl-smi">Map</span><<span class="pl-smi">String</span>, <span class="pl-smi">List</span><<span class="pl-smi">Integer</span>>>, <span class="pl-smi">Optional</span><<span class="pl-smi">Integer</span>>, <span class="pl-smi">Integer</span>> <span class="pl-s1">composed</span> = <span class="pl-s1">atFoo</span>.<span class="pl-en">mapA</span>(<span class="pl-s1">optL</span> -> <span class="pl-s1">optL</span>.<span class="pl-en">orElse</span>(<span class="pl-en">singletonList</span>(-<span class="pl-c1">1</span>))) .<span class="pl-en">andThen</span>(<span class="pl-s1">at0</span>); <span class="pl-en">view</span>(<span class="pl-s1">composed</span>, <span class="pl-en">singletonMap</span>(<span class="pl-s">"foo"</span>, <span class="pl-en">emptyList</span>())); <span class="pl-c">// Optional.empty</span></pre></div> <p dir="auto">Check out the tests or the <a href="http://palatable.github.io/lambda/javadoc/" rel="nofollow">javadoc</a> for more info.</p> <div class="markdown-heading" dir="auto"><h2 tabindex="-1" class="heading-element" dir="auto"><a name="user-content-notes">Notes</a></h2><a id="user-content-notes" class="anchor" aria-label="Permalink: Notes" href="#notes"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <p dir="auto">Wherever possible, <em>lambda</em> maintains interface compatibility with similar, familiar core Java types. Some examples of where this works well is with both <code>Fn1</code> and <code>Predicate</code>, which extend <code>j.u.f.Function</code> and <code>j.u.f.Predicate</code>, respectively. In these examples, they also override any implemented methods to return their <em>lambda</em>-specific counterparts (<code>Fn1.compose</code> returning <code>Fn1</code> instead of <code>j.u.f.Function</code> as an example).</p> <p dir="auto">Unfortunately, due to Java's type hierarchy and inheritance inconsistencies, this is not always possible. One surprising example of this is how <code>Fn1</code> extends <code>j.u.f.Function</code>, but <code>Fn2</code> does not extend <code>j.u.f.BiFunction</code>. This is because <code>j.u.f.BiFunction</code> itself does not extend <code>j.u.f.Function</code>, but it does define methods that collide with <code>j.u.f.Function</code>. For this reason, both <code>Fn1</code> and <code>Fn2</code> cannot extend their Java counterparts without sacrificing their own inheritance hierarchy. These types of asymmetries are, unfortunately, not uncommon; however, wherever these situations arise, measures are taken to attempt to ease the transition in and out of core Java types (in the case of <code>Fn2</code>, a supplemental <code>#toBiFunction</code> method is added). I do not take these inconveniences for granted, and I'm regularly looking for ways to minimize the negative impact of this as much as possible. Suggestions and use cases that highlight particular pain points here are particularly appreciated.</p> <div class="markdown-heading" dir="auto"><h2 tabindex="-1" class="heading-element" dir="auto"><a name="user-content-ecosystem">Ecosystem</a></h2><a id="user-content-ecosystem" class="anchor" aria-label="Permalink: Ecosystem" href="#ecosystem"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <div class="markdown-heading" dir="auto"><h3 tabindex="-1" class="heading-element" dir="auto">Official extension libraries:</h3><a id="user-content-official-extension-libraries" class="anchor" aria-label="Permalink: Official extension libraries:" href="#official-extension-libraries"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <p dir="auto">These are officially supported libraries that extend lambda's core functionality and are developed under the same governance and processes as lambda.</p> <ul dir="auto"> <li><a href="https://github.com/palatable/shoki">Shōki</a> - Purely functional, persistent data structures for the JVM</li> </ul> <div class="markdown-heading" dir="auto"><h3 tabindex="-1" class="heading-element" dir="auto">Third-party community libraries:</h3><a id="user-content-third-party-community-libraries" class="anchor" aria-label="Permalink: Third-party community libraries:" href="#third-party-community-libraries"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <p dir="auto">These are open-sourced community projects that rely on <em>lambda</em> for significant functionality, but are not necessarily affiliated with lambda and have their own separate maintainers. If you use <em>lambda</em> in your own open-sourced project, feel free to create an issue and I'll be happy to review the project and add it to this section!</p> <ul dir="auto"> <li><a href="https://github.com/kschuetz/enhanced-iterables">Enhanced Iterables</a> - Kevin Schuetz <a href="https://github.com/kschuetz">@kschuetz</a></li> <li><a href="https://github.com/kschuetz/collection-views">Collection Views</a> - Kevin Schuetz <a href="https://github.com/kschuetz">@kschuetz</a></li> <li><a href="https://github.com/nomicflux/WuWei">WuWei</a> - Michael Anderson <a href="https://github.com/nomicflux">@nomicflux</a> - <code>ST</code> monad for safe mutability</li> <li><a href="https://github.com/kschuetz/kraftwerk">Kraftwerk</a> - Kevin Schuetz <a href="https://github.com/kschuetz">@kschuetz</a> - random data generators and combinators</li> </ul> <div class="markdown-heading" dir="auto"><h2 tabindex="-1" class="heading-element" dir="auto"><a name="user-content-license">License</a></h2><a id="user-content-license" class="anchor" aria-label="Permalink: License" href="#license"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <p dir="auto"><em>lambda</em> is part of <a href="http://www.github.com/palatable">palatable</a>, which is distributed under <a href="http://choosealicense.com/licenses/mit/" rel="nofollow">The MIT License</a>.</p> </article></div></div></div></div></div> <!-- --> <!-- --> <script type="application/json" id="__PRIMER_DATA_:R0:__">{"resolvedServerColorMode":"day"}</script></div> </react-partial> <input type="hidden" data-csrf="true" value="yEV/BmERc/dTnikyUFwEVB69qr38IzSIdr2B3kQcB6vZ0vYxvoBewnQGVQOJAKt1kesR2HiQ2CFc5Kw2H2GNCw==" /> </div> <div data-view-component="true" class="Layout-sidebar"> <div class="BorderGrid about-margin" data-pjax> <div class="BorderGrid-row"> <div class="BorderGrid-cell"> <div class="hide-sm hide-md"> <h2 class="mb-3 h4">About</h2> <p class="f4 my-3"> Functional patterns for Java </p> <div class="my-3 d-flex flex-items-center"> <svg aria-hidden="true" height="16" viewBox="0 0 16 16" version="1.1" width="16" data-view-component="true" class="octicon octicon-link flex-shrink-0 mr-2"> <path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 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aria-label="Close dialog"></summary> <details-dialog class="Box Box--overlay d-flex flex-column anim-fade-in fast hx_rsm-dialog hx_rsm-modal"> <button class="Box-btn-octicon m-0 btn-octicon position-absolute right-0 top-0" type="button" aria-label="Close dialog" data-close-dialog> <svg aria-hidden="true" height="16" viewBox="0 0 16 16" version="1.1" width="16" data-view-component="true" class="octicon octicon-x"> <path d="M3.72 3.72a.75.75 0 0 1 1.06 0L8 6.94l3.22-3.22a.749.749 0 0 1 1.275.326.749.749 0 0 1-.215.734L9.06 8l3.22 3.22a.749.749 0 0 1-.326 1.275.749.749 0 0 1-.734-.215L8 9.06l-3.22 3.22a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042L6.94 8 3.72 4.78a.75.75 0 0 1 0-1.06Z"></path> </svg> </button> <div class="octocat-spinner my-6 js-details-dialog-spinner"></div> </details-dialog> </details> </template> <div class="Popover js-hovercard-content position-absolute" style="display: none; outline: none;"> <div class="Popover-message Popover-message--bottom-left 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aria-hidden="true" height="16" viewBox="0 0 16 16" version="1.1" width="16" data-view-component="true" class="octicon octicon-check js-clipboard-check-icon color-fg-success d-none m-2"> <path d="M13.78 4.22a.75.75 0 0 1 0 1.06l-7.25 7.25a.75.75 0 0 1-1.06 0L2.22 9.28a.751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018L6 10.94l6.72-6.72a.75.75 0 0 1 1.06 0Z"></path> </svg> </clipboard-copy> </div> </template> <template id="snippet-clipboard-copy-button-unpositioned"> <div class="zeroclipboard-container"> <clipboard-copy aria-label="Copy" class="ClipboardButton btn btn-invisible js-clipboard-copy m-2 p-0 d-flex flex-justify-center flex-items-center" data-copy-feedback="Copied!" data-tooltip-direction="w"> <svg aria-hidden="true" height="16" viewBox="0 0 16 16" version="1.1" width="16" data-view-component="true" class="octicon octicon-copy js-clipboard-copy-icon"> <path d="M0 6.75C0 5.784.784 5 1.75 5h1.5a.75.75 0 0 1 0 1.5h-1.5a.25.25 0 0 0-.25.25v7.5c0 .138.112.25.25.25h7.5a.25.25 0 0 0 .25-.25v-1.5a.75.75 0 0 1 1.5 0v1.5A1.75 1.75 0 0 1 9.25 16h-7.5A1.75 1.75 0 0 1 0 14.25Z"></path><path d="M5 1.75C5 .784 5.784 0 6.75 0h7.5C15.216 0 16 .784 16 1.75v7.5A1.75 1.75 0 0 1 14.25 11h-7.5A1.75 1.75 0 0 1 5 9.25Zm1.75-.25a.25.25 0 0 0-.25.25v7.5c0 .138.112.25.25.25h7.5a.25.25 0 0 0 .25-.25v-7.5a.25.25 0 0 0-.25-.25Z"></path> </svg> <svg aria-hidden="true" height="16" viewBox="0 0 16 16" version="1.1" width="16" data-view-component="true" class="octicon octicon-check js-clipboard-check-icon color-fg-success d-none"> <path d="M13.78 4.22a.75.75 0 0 1 0 1.06l-7.25 7.25a.75.75 0 0 1-1.06 0L2.22 9.28a.751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018L6 10.94l6.72-6.72a.75.75 0 0 1 1.06 0Z"></path> </svg> </clipboard-copy> </div> </template> </div> <div id="js-global-screen-reader-notice" class="sr-only mt-n1" aria-live="polite" aria-atomic="true" ></div> <div id="js-global-screen-reader-notice-assertive" class="sr-only mt-n1" aria-live="assertive" aria-atomic="true"></div> </body> </html>