This project has a special dedicace to Tony Morris' blog post Debut with a catamorphism. I'm also very thankful to @sviperll and his adt4j project which was the initial inspiration for Derive4J.

So. What can this project do for us, poor functional programmers stuck with a legacy language called Java? A good deal of what is available for free in better languages like Haskell: pattern matching, laziness... An example being worth a thousand words...

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Programming language: Java
Latest version: v1.1.1

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Derive4J: Java 8 annotation processor for deriving algebraic data types constructors, pattern matching and more!

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tl;dr Show me how to write, say, the Either sum type with Derive4J!.

Table of contents

Caution: if you are not familiar with Algebraic Data Types or the "visitor pattern" then you may want to learn a bit about them.

So, what can this project do for us, poor functional programmers stuck with a legacy language called Java? A good deal of what is commonly available in better languages like Haskell, including:

Algebraic data types come in two flavours, product types and sum types. This readme focus on sum types because it is the more interesting case; product types being the well known common case in Java, but Derive4J handles product types in exactly the same fashion (ie. through a visitor interface with a single abstract method).

Example: a 'Visitor' for HTTP Request

Let's say we want to model an HTTP request. For the sake of the example let's say that an HTTP request can either be

  • a GET on a given path
  • a DELETE on a given path
  • a POST of a content body on a given path
  • a PUT of a content body on a given path

and nothing else!

You could then use the corrected visitor pattern and write the following class in Java:

package org.derive4j.example;

/** A data type to model an http request. */
public abstract class Request {

  /** the Request 'visitor' interface, R being the return type
   *  used by the 'accept' method : */
  interface Cases<R> {
    // A request can either be a 'GET' (of a path):
    R GET(String path);
    // or a 'DELETE' (of a path):
    R DELETE(String path);
    // or a 'PUT' (on a path, with a body):
    R PUT(String path, String body);
    // or a 'POST' (on a path, with a body):
    R POST(String path, String body);
    // and nothing else!

  // the 'accept' method of the visitor pattern:
  public abstract <R> R match(Cases<R> cases);

   * Alternatively and equivalently to the visitor pattern above, if you prefer a more FP style,
   * you can define a catamorphism instead. (see examples)
   * (most useful for standard data type like Option, Either, List...)


Without Derive4J, you would have to create subclasses of Request for all four cases. That is, write at the minimum something like:

  public static Request GET(String path) {
    return new Request() {
      public <R> R match(Cases<R> cases) {
        return cases.GET(path);

for each case. But thanks to the @Data annotation, Derive4j will do that for you! That is, it will generate a Requests class (the name is configurable, the class is generated by default in target/generated-sources/annotations when using Maven) with four static factory methods (what we call 'constructors' in FP):

  public static Request GET(String path) {...}
  public static Request DELETE(String path) {...}
  public static Request PUT(String path, String body) {...}
  public static Request POST(String path, String body) {...}

You can also ask Derive4J to generate null checks with:

@Data(arguments = ArgOption.checkedNotNull)

equals, hashCode, toString?

Derive4J philosophy is to be as safe and consistent as possible. That is why Object.{equals, hashCode, toString} are not implemented by generated classes by default (they are best kept ignored as they break parametricity). Nonetheless, as a concession to legacy, it is possible to force Derive4J to implement them, by declaring them abstract. Eg by adding the following in your annotated class:

  public abstract int hashCode();
  public abstract boolean equals(Object obj);
  public abstract String toString();

The safer solution would be to never use those methods and use 'type classes' instead, eg. Equal, Hash and Show. The project Derive4J for Functional Java aims to generate them automatically.

Pattern matching syntaxes

Now let's say that you want a function that returns the body size of a Request. Without Derive4J you would write something like:

  static final Function<Request, Integer> getBodySize = request -> 
      request.match(new Cases<Integer>() {
        public Integer GET(String path) {
          return 0;
        public Integer DELETE(String path) {
          return 0;
        public Integer PUT(String path, String body) {
          return body.length();
        public Integer POST(String path, String body) {
          return body.length();

With Derive4J you can do that a lot less verbosely, thanks to a generated fluent structural pattern matching syntaxes! And it does exhaustivity check! (you must handle all cases). The above can be rewritten into:

static final Function<Request, Integer> getBodySize = Requests.cases()
      .GET_(0) // shortcut for .Get(path -> 0)
      .PUT((path, body)  -> body.length())
      .POST((path, body) -> body.length())

or even (because you don't care of GET and DELETE cases):

static final Function<Request, Integer> getBodySize = Requests.cases()
      .PUT((path, body)  -> body.length())
      .POST((path, body) -> body.length())

Derive4j also allows to match directly against a value:

static int getBodyLength(Request request) {
  return Requests.caseOf(request)
      .PUT((path, body)  -> body.length())
      .POST((path, body) -> body.length())

Accessors (getters)

Now, pattern matching every time you want to inspect an instance of Request is a bit tedious. For this reason Derive4J generates 'getter' static methods for all fields. For the path and body fields, Derive4J will generate the following methods in the Requests class:

  public static String getPath(Request request){
    return Requests.cases()
        .GET(path          -> path)
        .DELETE(path       -> path)
        .PUT((path, body)  -> path)
        .POST((path, body) -> path)
  // return an Optional because the body is not present in the GET and DELETE cases:
  static Optional<String> getBody(Request request){
    return Requests.cases()
        .PUT((path, body)  -> body)
        .POST((path, body) -> body)

(Actually the generated code is equivalent but more efficient)

Using the generated getBody methods, we can rewrite our getBodySize function into:

static final Function<Request, Integer> getBodySize = request ->

Functional setters ('withers')

The most painful part of immutable data structures (like the one generated by Derive4J) is updating them. Scala case classes have copy methods for that. Derive4J generates similar modifier and setter methods in the Requests class:

  public static Function<Request, Request> setPath(String newPath){
    return Requests.cases()
            .GET(path          -> Requests.GET(newPath))
            .DELETE(path       -> Requests.DELETE(newPath))
            .PUT((path, body)  -> Requests.PUT(newPath, body))
            .POST((path, body) -> Requests.POST(newPath, body)));
  public static Function<Request, Request> modPath(Function<String, String> pathMapper){
    return Requests.cases()
            .GET(path          -> Requests.GET(pathMapper.apply(path)))
            .DELETE(path       -> Requests.DELETE(pathMapper.apply(path)))
            .PUT((path, body)  -> Requests.PUT(pathMapper.apply(path), body))
            .POST((path, body) -> Requests.POST(pathMapper.apply(path), body)));
  public static Function<Request, Request> setBody(String newBody){
    return Requests.cases()
            .GET(path          -> Requests.GET(path))    // identity function for GET
            .DELETE(path       -> Requests.DELETE(path)) // and DELETE cases.
            .PUT((path, body)  -> Requests.PUT(path, newBody))
            .POST((path, body) -> Requests.POST(path, newBody)));

By returning a function, modifiers and setters allow for a lightweight syntax when updating deeply nested immutable data structures.

First class laziness

Languages like Haskell provide laziness by default, which simplifies a lot of algorithms. In traditional Java you would have to declare a method argument as Supplier<Request> (and do memoization) to emulate laziness. With Derive4J that is no more necessary as it generates a lazy constructor that gives you transparent lazy evaluation for all consumers of your data type:

  // the requestExpression will be lazy-evaluated on the first call
  // to the 'match' method of the returned Request instance:
  public static Request lazy(Supplier<Request> requestExpression) {

Have a look at List for how to implement a lazy cons list in Java using Derive4J (you may also want to see the associated generated code).


In the example above, we have used the default JDK flavour. Also available are FJ (Functional Java), Fugue (Fugue), Javaslang/Vavr (Vavr), HighJ (HighJ), Guava and Cyclops (Cyclops-react) flavours. When using those alternative flavours, Derive4J will use eg. the specific Option implementations from those projects instead of the jdk Optional class.

Optics (functional lenses)

If you are not familiar with optics, have a look at Monocle (for Scala, but Functional Java provides similar abstraction).

Using Derive4J generated code, defining optics is a breeze (you need to use the FJ flavour by specifying @Data(flavour = Flavour.FJ):

   * Lenses: optics focused on a field present for all data type constructors
   * (getter cannot 'failed'):
  public static final Lens<Request, String> _path = lens(
   * Optional: optics focused on a field that may not be present for all constructors
   * (getter return an 'Option'):
  public static final Optional<Request, String> _body = optional(
   * Prism: optics focused on a specific constructor:
  public static final Prism<Request, String> _GET = prism(
      // Getter function
      // Reverse Get function (aka constructor)

  // If there is more than one field, we use a tuple as the prism target:
  public static final Prism<Request, P2<String, String>> _POST = prism(
      // Getter:
          .POST((path, body) -> p(path, body))
      // reverse get (construct a POST request given a P2<String, String>):
      p2 -> Requests.POST(p2._1(), p2._2()));

Smart constructors

Sometimes you want to validate the constructors parameters before returning an instance of a type. When using the Smart visibity (@Data(@Derive(withVisibility = Visibility.Smart))), Derive4J will not expose "raw" constructors and setter as public, but will use package private visibility for those methods instead (getters will still be public).

Then you expose a public static factory method that will do the necessary validation of the arguments before returning an instance (typically wrapped in a Option/Either/Validation), and that public factory will be the only way to get an instance of that type.

See usage of this feature in PersonName.

Static methods export

It is generally considered good style to keep static methods and instance methods separated, especially because overloads could cause ambiguities on usage as method references.

The Java file generated by derive4j contains only static methods, so it makes sense to use this class as main entry point for the static part of the data type API.

To this end, Derive4J support re-exporting of your own manually-written static methods as part of the generated class API. It can do so in two ways (that can be combined):

  1. by specifying that the main generated class must extends a given class eg. MyStaticMethods.class, thus exposing all its static methods through inheritance.
  2. by annotating your package-private static methods with @ExportAsPublic: Derive4J will generate public forwarding methods in the generated class, and, as bonus, it will memoize the result of nullary methods. ```java @Data(@Derive(extend = MyStaticMethods.class)) public abstract class List { // package-private static class with public static methods: static abstract class MyStaticMethods { public static List singleton(A a) { return Lists.cons(a, Lists.nil()) } } // Or use the annotation, either in the above MyStaticMethods class // or directly in the data type class: @ExportAsPublic static List singleton(A a) { return Lists.cons(a, Lists.nil()) } }

public static void main(final String[] args) { // enjoy single access points for all static methods: List a = Lists.singleton("a"); }

See usage of this feature in [PersonName](https://github.com/derive4j/derive4j/blob/master/examples/src/main/java/org/derive4j/example/PersonName.java#L49).

# Updating deeply nested immutable data structure
Let's say you want to model a CRM. Each client is a ```Person``` who can be contacted by email, by telephone or by postal mail. With Derive4J you could write the following:
import org.derive4j.*;
import java.util.function.BiFunction;

public abstract class Address {
  public abstract <R> R match(@FieldNames({"number", "street"}) 
                  BiFunction<Integer, String, R> Address);
import org.derive4j.Data;

public abstract class Contact {
    interface Cases<R> {
      R byEmail(String email);
      R byPhone(String phoneNumber);
      R byMail(Address postalAddress);
    public abstract <R> R match(Cases<R> cases);
import org.derive4j.*;
import java.util.function.BiFunction;

public abstract class Person {
  public abstract <R> R match(@FieldNames({"name", "contact"})
                              BiFunction<String, Contact, R> Person);

But now we have a problem: All the clients have been imported from a legacy database with an off-by-one error for the street number! We must create a function that increments each Person's street number (if it exists) by one. And we have to do this without modifying the original data structure (because it is immutable). With Derive4J, writing such a function is trivial:

import java.util.Optional;
import java.util.function.Function;

import static org.derive4j.example.Addresss.Address;
import static org.derive4j.example.Addresss.getNumber;
import static org.derive4j.example.Addresss.modNumber;
import static org.derive4j.example.Contacts.getPostalAddress;
import static org.derive4j.example.Contacts.modPostalAddress;
import static org.derive4j.example.Persons.Person;
import static org.derive4j.example.Persons.getContact;
import static org.derive4j.example.Persons.modContact;

  public static void main(String[] args) {

    Person joe = Person("Joe", Contacts.byMail(Address(10, "Main St")));

    Function<Person, Person> incrementStreetNumber = modContact(
                                     modNumber(number -> number + 1)));

    // correctedJoe is a copy of joe with the street number incremented:
    Person correctedJoe = incrementStreetNumber.apply(joe);

    Optional<Integer> newStreetNumber = getPostalAddress(getContact(correctedJoe))
        .map(postalAddress -> getNumber(postalAddress));

    System.out.println(newStreetNumber); // print "Optional[11]" !!

Popular use-case: domain specific languages

Algebraic data types are particulary well fitted for creating DSLs. A calculator for arithmetic expressions could be built like this:

import java.util.function.Function;
import org.derive4j.Data;
import static org.derive4j.example.Expressions.*;

public abstract class Expression {

    interface Cases<R> {
        R Const(Integer value);
        R Add(Expression left, Expression right);
        R Mult(Expression left, Expression right);
        R Neg(Expression expr);

    public abstract <R> R match(Cases<R> cases);

    private static Function<Expression, Integer> eval = Expressions
            .Const(value        -> value)
            .Add((left, right)  -> eval(left) + eval(right))
            .Mult((left, right) -> eval(left) * eval(right))
            .Neg(expr           -> -eval(expr));

    public static Integer eval(Expression expression) {
        return eval.apply(expression);

    public static void main(String[] args) {
        Expression expr = Add(Const(1), Mult(Const(2), Mult(Const(3), Const(3))));
        System.out.println(eval(expr)); // (1+(2*(3*3))) = 19


are generated for recursively defined datatypes. So that you can rewrite the above eval method into:

    public static Integer eval(Expression expression) {
                value -> value,
                (left, right) -> left + right,
                (left, right) -> left * right,
                expr -> -expr,

The last parameter (Supplier::get above) specify how recursive calls are suspended. Using Supplier::get means that the computation is not suspended: for deep structures it may blow the stack!

To be safe, use the lazy, (or delay or suspend or defer...) constructor of your result type, such as the lazy constructor generated by Derive4J.

If no such constructor is available then your safe option is to use a Trampoline, such as the one provided by FunctionalJava:

public static Integer stackSafeEval(Expression expression) {
        value -> Trampoline.pure(value),
        (left, right) -> left.zipWith(right, (l, r) -> l + r),
        (left, right) -> left.zipWith(right, (l, r) -> l * r),
        expr -> expr.map(i -> -i),

Extensible algebraic data types

Algebraic data types defined as fix-point (aka initial algebra) of an object algebras can enjoy their extensibility properties.

When the data type is not inductive the extensibility property comes directly from covariance

Eg. an event type for an inventory service:

  interface EventV1 {

    interface Cases<R> {
      R newItem(Long ref, String itemName);
      R itemRemoved(Long ref);

    <R> R match(Cases<R> cases);

Then comes a new version of the service, with enriched events and new cases. If the visitor for the new event type extend the old visitor interface then old events can be easily converted to new events, without change to the old classes:

  interface EventV2 {

    interface Cases<R> extends EventV1.Cases<R> { // extends V1 with:

      // new `initialStock` field in `newItem` event:
      R newItem(Long ref, String itemName, int initialStock);
      // default to 0 for old events:
      default R newItem(Long ref, String itemName) {
        return newItem(ref, itemName, 0);
      // new event:
      R itemRenamed(Long ref, String newName);

    <R> R match(Cases<R> cases);

    static EventV2 fromV1(EventV1 v1Event) {
      // Events are (polymorphic) functions!
      // And functions are contra-variant in type argument,
      // thus we can use method reference to convert from V1 to V2:
      return v1Event::match;

Extensible inductive data types via hylomorphisms

Aka solving the expression problem via object-algebras used as visitor. For this, we need to slightly change the visitor of the above Expression so that a type variable (E) is used instead of the self-reference:

interface Exp {

  interface ExpAlg<E, R> {
    R Lit(int lit);
    R Add(E e1, E e2);

  <R> R accept(ExpAlg<Exp, R> alg);

When data types are defined is such a way (as a fix-point of the algebra), Derive4J generate (by default) an instance of the visitor/algebra that can serve as factory (aka. anamorphism). Using this factory as an argument to compatible catamorphism (thus creating a hylomorphism) we obtain a conversion function from one ADT to another.

Eg. we can create a new data type that add a multiplication case to the above data type, and still be able to maximally reuse the existing code without modification:

interface ExpMul {

  interface ExpMulAlg<E, R> extends Exp.ExpAlg<E, R> {
    R Mul(E e1, E e2);

  <R> R accept(ExpMulAlg<ExpMul, R> alg);

  static Function<Exp, ExpMul> fromExp() {
    ExpMulAlg<ExpMul, ExpMul> factory = ExpMuls.factory();
    return Exps.cata(factory, ExpMuls::lazy);

To ensure smooth extensibility across compilation unit (or even during incremental compilation), it is best to use the -parameters option of javac.

But what exactly is generated?

This is a very legitimate question. Here is the ExpMuls.java file that is generated for the above @Data ExpMul type.

Parametric polymorphism

... works as expected. For example, you can write the following:

import java.util.function.Function;
import java.util.function.Supplier;
import org.derive4j.Data;

public abstract class Option<A> {

    public abstract <R> R cata(Supplier<R> none, Function<A, R> some);

    public final <B> Option<B> map(final Function<A, B> mapper) {
        return Options.modSome(mapper).apply(this);

The generated modifier method modSome allows polymorphic update and is incidentaly the functor for our Option!

Generalized Algebraic Data Types

GADTs are also supported out of the box by Derive4J (within the limitations of the Java type system). Here is how you can translate the example from Fun with phantom types:

import org.derive4j.hkt.TypeEq;

public abstract class Term<T> {
  interface Cases<A, R> {
    R Zero(TypeEq<Integer, A> id);
    R Succ(Term<Integer> pred, TypeEq<Integer, A> id);
    R Pred(Term<Integer> succ, TypeEq<Integer, A> id);
    R IsZero(Term<Integer> a, TypeEq<Boolean, A> id);
    R If(Term<Boolean> cond, Term<A> then, Term<A> otherwise);

  public abstract <X> X match(Cases<T, X> cases);

  public static <T> T eval(final Term<T> term) {

    return Terms.caseOf(term).
        Zero(id -> id.coerce(0)).
        Succ((t, id) -> id.coerce(eval(t) + 1)).
        Pred((t, id) -> id.coerce(eval(t) - 1)).
        IsZero((t, id) -> id.coerce(eval(t) == 0)).
        If((cond, then, otherwise) -> eval(cond)
            ? eval(then)
            : eval(otherwise));

  public static void main(final String[] args) {

    Term<Integer> one = Succ(Zero());
    out.println(eval(one)); // "1"
    out.println(eval(IsZero(one))); // "false"
    // IsZero(IsZero(one)); // does not compile:
    // "The method IsZero(Term<Integer>) in the type Term<T> is not
    // applicable for the arguments (Term<Boolean>)"
    out.println(eval(If(IsZero(one), Zero(), one))); // "1"
    Term<Boolean> True = IsZero(Zero());
    Term<Boolean> False = IsZero(one);
    out.println(eval(If(True, True, False))); // "true"
    // out.println(prettyPrint(If(True, True, False), 0)); // "if IsZero(0)
    //  then IsZero(0)
    //  else IsZero(Succ(0))"

For GADT you will need to add a dependency on derive4j/hkt which provides TypeEq<A, B>: a witness of the equality of two types, A and B.

DRY annotation configuration

By default the @Data annotation triggers the generation of everything which is available, in a file whose name is the English plural of the annotated class. But you may want to restrict the scope of what is generated, or change the name of the file, and you usually want all you ADTs to use the same flavour. You may even dislike the name of the annotation because it clashes with another framework...

For example, let's say that you want to always use the FJ flavour (FunctionalJava), make the generated code package private in a class suffixed by Impl and only generate the pattern matching syntax and the constructors. Then all you have to do is to create the following annotation:

@Data(flavour = Flavour.FJ, value = @Derive(
    inClass = "{ClassName}Impl",
    withVisibility = Visibility.Package,
    make = { Make.constructors, Make.caseOfMatching }
public @interface myADT {}

And you annotate your classes with @myADT instead of @Data, saving on that configuration every time.

But now for some of your ADTs you may want to also generate getters and functional setters. In order to not lose the benefits of your @myADT, derive4j allows you to do this:

@Derive(make = { Make.getters, Make.modifiers }) // add-up to the @myADT configuration
public abstract class Adt {...}

Use it in your project

Derive4J should be declared as a compile-time only dependency (not needed at runtime). So while derive4j is (L)GPL-licensed, the generated code is not linked to derive4j, and thus derive4j can be used in any project (proprietary or not).




compile(group: 'org.derive4j', name: 'derive4j', version: '1.1.1', ext: 'jar')

or better using the gradle-apt-plugin:

compileOnly "org.derive4j:derive4j-annotation:1.1.1"
apt "org.derive4j:derive4j:1.1.1"


Bug reports and feature requests are welcome, as well as contributions to improve documentation.

Right now the codebase is not ready for external contribution (many blocks of code are more complicated than they should be). So you might be better off waiting for the resolution of #2 before trying to dig into the codebase.


[email protected], @jb9i or use the project GitHub issues.

Further reading


This project has a special dedication to Tony Morris' blog post Debut with a catamorphism. I'm also very thankful to @sviperll and his adt4j project which was the initial inspiration for Derive4J.

*Note that all licence references and agreements mentioned in the derive4j README section above are relevant to that project's source code only.