Functional patterns for Java

Programming language: Java
License: MIT License
Tags: Functional Programming     Monad     Optics    
Latest version: v5.4.0

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Functional patterns for Java

Table of Contents


Lambda was born out of a desire to use some of the same canonical functions (e.g. unfoldr, takeWhile, zipWith) and functional patterns (e.g. Functor and friends) that are idiomatic in other languages and make them available for Java.

Some things a user of lambda most likely values:

  • Lazy evaluation
  • Immutability by design
  • Composition
  • Higher-level abstractions
  • Parametric polymorphism

Generally, everything that lambda produces is lazily-evaluated (except for terminal operations like reduce), immutable (except for Iterators, 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).

Although the library is currently (very) small, these values should always be the driving forces behind future growth.


Add the following dependency to your:

pom.xml (Maven):


build.gradle (Gradle):

compile group: 'com.jnape.palatable', name: 'lambda', version: '5.4.0'


First, the obligatory map/filter/reduce example:

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

Every function in lambda is curried, so we could have also done this:

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

How about the positive squares below 100:

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]

We could have also used unfoldr:

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]

What if we want the cross product of a domain and codomain:

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")]

Let's compose two functions:

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);

And partially apply some:

Fn2<Integer, Integer, Integer> add = (x, y) -> x + y;

Fn1<Integer, Integer> add1 = add.apply(1);
//-> 3

And have fun with 3s:

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]]

Check out the tests or javadoc for more examples.


Semigroups are supported via Semigroup<A>, a subtype of Fn2<A,A,A>, and add left and right folds over an Iterable<A>.

Semigroup<Integer> add = (augend, addend) -> augend + addend;
add.apply(1, 2); //-> 3
add.foldLeft(0, asList(1, 2, 3)); //-> 6

Lambda ships some default logical semigroups for lambda types and core JDK types. Common examples are:

  • AddAll for concatenating two Collections
  • Collapse for collapsing two Tuple2s together
  • Merge for merging two Eithers using left-biasing semantics

Check out the semigroup package for more examples.


Monoids are supported via Monoid<A>, a subtype of Semigroup<A> with an A #identity() method, and add left and right reduces over an Iterable<A>, as well as foldMap.

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

Some commonly used lambda monoid implementations include:

  • Present for merging together two Optionals
  • Join for joining two Strings
  • And for logical conjunction of two Booleans
  • Or for logical disjunction of two Booleans

Additionally, instances of Monoid<A> can be trivially synthesized from instances of Semigroup<A> via the Monoid#monoid static factory method, taking the Semigroup and the identity element A or a supplier of the identity element Supplier<A>.

Check out the monoid package for more examples.


Functors are implemented via the Functor interface, and are sub-typed by every function type that lambda exports, as well as many of the ADTs.

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;

    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"

Examples of functors include:

  • Fn*, Semigroup, and Monoid
  • SingletonHList and Tuple*
  • Choice*
  • Either
  • Const, Identity, and Compose
  • Lens

Implementing Functor is as simple as providing a definition for the covariant mapping function #fmap (ideally satisfying the two laws).


Bifunctors -- functors that support two parameters that can be covariantly mapped over -- are implemented via the Bifunctor interface.

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;

    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

Examples of bifunctors include:

  • Tuple*
  • Choice*
  • Either
  • Const

Implementing Bifunctor requires implementing either biMapL and biMapR or biMap. As with Functor, there are a few laws that well-behaved instances of Bifunctor should adhere to.


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 Profunctor interface.

Fn1<Integer, Integer> add2 = (x) -> x + 2;
add2.<String, String>diMap(Integer::parseInt, Object::toString).apply("1"); //-> "3"

Examples of profunctors include:

  • Fn*
  • Lens

Implementing Profunctor requires implementing either diMapL and diMapR or diMap. As with Functor and Bifunctor, there are some laws that well behaved instances of Profunctor should adhere to.


Applicative functors -- functors that can be applied together with a 2-arity or higher function -- are implemented via the Applicative interface.

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;

    public <B> Slot<B> fmap(Function<? super A, ? extends B> fn) {
        return pure(fn.apply(a));

    public <B> Slot<B> pure(B b) {
        return new Slot<>(b);

    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}

Examples of applicative functors include:

  • Fn*, Semigroup, and Monoid
  • SingletonHList and Tuple*
  • Choice*
  • Either
  • Const, Identity, and Compose
  • Lens

In addition to implementing fmap from Functor, implementing an applicative functor involves providing two methods: pure, a method that lifts a value into the functor; and zip, a method that applies a lifted function to a lifted value, returning a new lifted value. As usual, there are some laws that should be adhered to.


Monads are applicative functors that additionally support a chaining operation, flatMap :: (a -> f b) -> f a -> f b: 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 flatMap 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 Either:

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>

In the previous example, if any of parseId, lookupById, or getOccupation fail, no further flatMap computations can succeed, so the result short-circuits to the first left value that is returned. This is completely predictable from the type signature of Monad and Either: Either<L, R> is a Monad<R>, so the single arity flatMap can have nothing to map in the case where there is no R value. With experience, it generally becomes quickly clear what the logical behavior of flatMap must be given the type signatures.

That's it. Monads are neither elephants nor are they burritos; they're simply types that support a) the ability to lift a value into them, and b) a chaining function flatMap :: (a -> f b) -> f a -> f b that can potentially return different instances of the same monad. If a type can do those two things (and obeys the laws), it is a monad.

Further, if a type is a monad, it is necessarily an Applicative, which makes it necessarily a Functor, so lambda enforces this tautology via a hierarchical constraint.


Traversable functors -- functors that can be "traversed from left to right" -- are implemented via the Traversable interface.

public abstract class Maybe<A> implements Traversable<A, Maybe> {
    private Maybe() {

    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);

    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;

        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);

        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> {
        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);

        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")

Examples of traversable functors include:

  • SingletonHList and Tuple*
  • Choice*
  • Either
  • Const and Identity
  • LambdaIterable for wrapping Iterable in an instance of Traversable

In addition to implementing fmap from Functor, implementing a traversable functor involves providing an implementation of traverse.

As always, there are some laws that should be observed.


Lambda also supports a few first-class algebraic data types.


Maybe is the lambda analog to java.util.Optional. It behaves in much of the same way as j.u.Optional, except that it quite intentionally does not support the inherently unsafe j.u.Optional#get.

Maybe<Integer> maybeInt = Maybe.just(1); // Just 1
Maybe<String> maybeString = Maybe.nothing(); // Nothing

Also, because it's a lambda type, it takes advantage of the full functor hierarchy, as well as some helpful conversion functions:

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

Finally, for compatibility purposes, Maybe and j.u.Optional can be trivially converted back and forth:

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

Note: One compatibility difference between j.u.Optional and Maybe is how map/fmap behave regarding functions that return null: j.u.Optional re-wraps null results from map operations in another j.u.Optional, whereas Maybe considers this to be an error, and throws an exception. The reason Maybe throws in this case is because fmap is not an operation to be called speculatively, and so any function that returns null in the context of an fmap operation is considered to be erroneous. Instead of calling fmap with a function that might return null, the function result should be wrapped in a Maybe and flatMap should be used, as illustrated in the following example:

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

Heterogeneous Lists (HLists)

HLists are type-safe heterogeneous lists, meaning they can store elements of different types in the same list while facilitating certain type-safe interactions.

The following illustrates how the linear expansion of the recursive type signature for HList prevents ill-typed expressions:

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


One of the primary downsides to using HLists in Java is how quickly the type signature grows.

To address this, tuples in lambda are specializations of HLists up to 8 elements deep, with added support for index-based accessor methods.

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

Additionally, HList provides convenience static factory methods for directly constructing lists of up to 8 elements:

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);

Index can be used for type-safe retrieval and updating of elements at specific indexes:

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 =

characterIndex.get(hList); // '3'
characterIndex.get(tuple); // '3'
characterIndex.get(longerHList); // '3'

characterIndex.set('4', hList); // HList{ 1 :: "2" :: '4' }

Finally, all Tuple* classes are instances of both Functor and Bifunctor:

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

Heterogeneous Maps

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.

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


CoProducts generalize unions of disparate types in a single consolidated type, and the ChoiceN ADTs represent canonical implementations of these coproduct types.

CoProduct3<String, Integer, Character, ?> string = Choice3.a("string");
CoProduct3<String, Integer, Character, ?> integer = Choice3.b(1);
CoProduct3<String, Integer, Character, ?> character = Choice3.c('a');

Rather than supporting explicit value unwrapping, which would necessarily jeopardize type safety, CoProducts support a match method that takes one function per possible value type and maps it to a final common result type:

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

Additionally, because a CoProduct2<A, B, ?> guarantees a subset of a CoProduct3<A, B, C, ?>, the diverge method exists between CoProduct types of single magnitude differences to make it easy to use a more convergent CoProduct where a more divergent CoProduct is expected:

CoProduct2<String, Integer, ?> coProduct2 = Choice2.a("string");
CoProduct3<String, Integer, Character, ?> coProduct3 = coProduct2.diverge(); // still just the coProduct2 value, adapted to the coProduct3 shape

There are CoProduct and Choice specializations for type unions of up to 8 different types: CoProduct2 through CoProduct8, and Choice2 through Choice8, respectively.


Either<L, R> represents a specialized CoProduct2<L, R>, which resolve to one of two possible values: a left value wrapping an L, or a right value wrapping an R (typically an exceptional value or a successful value, respectively).

As with CoProduct2, rather than supporting explicit value unwrapping, Either supports many useful comprehensions to help facilitate type-safe interactions:

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);
//-> [] 

Check out the tests for more examples of ways to interact with Either.


Lambda also ships with a first-class lens type, as well as a small library of useful general lenses:

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]

There are three functions that lambda provides that interface directly with lenses: view, over, and set. As the name implies, view and set are used to retrieve values and store values, respectively, whereas over is used to apply a function to the value a lens is focused on, alter it, and store it (you can think of set as a specialization of over using constantly).

Lenses can be easily created. Consider the following Person class:

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()));

...and a lens for getting and setting age as an int:

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);

If we wanted a lens for the LocalDate version of setAge, we could use the same method references and only alter the type signature:

Lens<Person, Person, Integer, LocalDate> ageLensWithLocalDate = Lens.lens(Person::getAge, Person::setAge);

Compatible lenses can be trivially composed:

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]

Lens provides independent map operations for each parameter, so incompatible lenses can also be composed:

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)))

view(composed, singletonMap("foo", emptyList())); // Optional.empty

Check out the tests or the javadoc for more info.


Wherever possible, lambda maintains interface compatibility with similar, familiar core Java types. Some examples of where this works well is with both Fn1 and Predicate, which extend j.u.f.Function and j.u.f.Predicate, respectively. In these examples, they also override any implemented methods to return their lambda-specific counterparts (Fn1.compose returning Fn1 instead of j.u.f.Function as an example).

Unfortunately, due to Java's type hierarchy and inheritance inconsistencies, this is not always possible. One surprising example of this is how Fn1 extends j.u.f.Function, but Fn2 does not extend j.u.f.BiFunction. This is because j.u.f.BiFunction itself does not extend j.u.f.Function, but it does define methods that collide with j.u.f.Function. For this reason, both Fn1 and Fn2 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 Fn2, a supplemental #toBiFunction 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.


Official extension libraries:

These are officially supported libraries that extend lambda's core functionality and are developed under the same governance and processes as lambda.

  • Shōki - Purely functional, persistent data structures for the JVM

Third-party community libraries:

These are open-sourced community projects that rely on lambda for significant functionality, but are not necessarily affiliated with lambda and have their own separate maintainers. If you use lambda 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!


lambda is part of palatable, which is distributed under The MIT License.

*Note that all licence references and agreements mentioned in the λ README section above are relevant to that project's source code only.