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Monadic Java

Monadic Java

Category Theory is to functional programming what GoF design patterns are to object oriented programming. Since Java introduced lambda expressions, time is arrived also for Java developers to learn something more about functional programming patterns. Monads are probably the most expressive (and very likely the most misunderstood) of these patterns. So the purpose of this talk is to explain monads, clarify with very practical examples how and when they should be used, underline their advantages and show how they can be implemented in Java 8.

Mario Fusco

May 08, 2022
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  1. Fortran C / C++ Java Lisp ML Haskell Add abstractions

    C# Algol Subtract abstractions Imperative languages Functional languages Scala F# Hybrid languages
  2. Learning a new language is relatively easy compared with learning

    a new paradigm. new language < new paradigm Functional Programming is more a new way of thinking than a new tool set
  3. What is a monad? A monad is a triple (T,

    η, μ) where T is an endofunctor T: X → X and η: I → T and μ: T x T → T are 2 natural transformations satisfying these laws: Identity law: μ(η(T)) = T = μ(T(η)) Associative law: μ(μ(T × T) × T)) = μ(T × μ(T × T)) In other words: "a monad in X is just a monoid in the category of endofunctors of X, with product × replaced by composition of endofunctors and unit set by the identity endofunctor" What's the problem?
  4. … really? do I need to know this? In order

    to understand monads you need to first learn Cathegory Theory In order to understand pizza you need to first learn Italian … it's like saying …
  5. … no seriously, what is a monad? A monad is

    a structure that puts a value in a computational context
  6. … and why should we care about? Reduce code duplication

    Improve maintainability Increase readability Remove side effects Hide complexity Encapsulate implementation details Allow composability
  7. { return flatMap( x -> unit( f.apply(x) ) ); }

    Monadic Methods M<A> unit(A a); M<B> bind(M<A> ma, Function<A, M<B>> f); interface M { M<B> map(Function<A, B> f); M<B> flatMap(Function<A, M<B>> f); } map can defined for every monad as a combination of flatMap and unit
  8. public class Person { private Car car; public Car getCar()

    { return car; } } public class Car { private Insurance insurance; public Insurance getInsurance() { return insurance; } } public class Insurance { private String name; public String getName() { return name; } } Finding Car's Insurance Name
  9. String getCarInsuranceName(Person person) { if (person != null) { Car

    car = person.getCar(); if (car != null) { Insurance insurance = car.getInsurance(); if (insurance != null) { return insurance.getName() } } } return "Unknown"; } Attempt 1: deep doubts
  10. Attempt 2: too many choices String getCarInsuranceName(Person person) { if

    (person == null) { return "Unknown"; } Car car = person.getCar(); if (car == null) { return "Unknown"; } Insurance insurance = car.getInsurance(); if (insurance == null) { return "Unknown"; } return insurance.getName() }
  11. What wrong with nulls? ✗ Errors source → NPE is

    by far the most common exception in Java ✗ Bloatware source → Worsen readability by making necessary to fill our code with null checks ✗ Breaks Java philosophy → Java always hides pointers to developers, except in one case: the null pointer ✗ A hole in the type system → Null has the bottom type, meaning that it can be assigned to any reference type: this is a problem because, when propagated to another part of the system, you have no idea what that null was initially supposed to be ✗ Meaningless → Don't have any semantic meaning and in particular are the wrong way to model the absence of a value in a statically typed language “Absence of a signal should never be used as a signal“ - J. Bigalow, 1947 Tony Hoare, who invented the null reference in 1965 while working on an object oriented language called ALGOL W, called its invention his “billion dollar mistake”
  12. Optional Monad to the rescue public class Optional<T> { private

    static final Optional<?> EMPTY = new Optional<>(null); private final T value; private Optional(T value) { this.value = value; } public<U> Optional<U> map(Function<? super T, ? extends U> f) { return value == null ? EMPTY : new Optional(f.apply(value)); } public<U> Optional<U> flatMap(Function<? super T, Optional<U>> f) { return value == null ? EMPTY : f.apply(value); } }
  13. public class Person { private Optional<Car> car; public Optional<Car> getCar()

    { return car; } } public class Car { private Optional<Insurance> insurance; public Optional<Insurance> getInsurance() { return insurance; } } public class Insurance { private String name; public String getName() { return name; } } Rethinking our model Using the type system to model nullable value
  14. String getCarInsuranceName(Optional<Person> person) { return person.flatMap(person -> person.getCar()) .flatMap(car ->

    car.getInsurance()) .map(insurance -> insurance.getName()) .orElse("Unknown"); } Restoring the sanity
  15. String getCarInsuranceName(Optional<Person> person) { return person.flatMap(person -> person.getCar()) .flatMap(car ->

    car.getInsurance()) .map(insurance -> insurance.getName()) .orElse("Unknown"); } Restoring the sanity Person Optional
  16. String getCarInsuranceName(Optional<Person> person) { return person.flatMap(person -> person.getCar()) .flatMap(car ->

    car.getInsurance()) .map(insurance -> insurance.getName()) .orElse("Unknown"); } Restoring the sanity Person Optional flatMap(person -> person.getCar())
  17. String getCarInsuranceName(Optional<Person> person) { return person.flatMap(person -> person.getCar()) .flatMap(car ->

    car.getInsurance()) .map(insurance -> insurance.getName()) .orElse("Unknown"); } Restoring the sanity Optional flatMap(person -> person.getCar()) Optional Car
  18. String getCarInsuranceName(Optional<Person> person) { return person.flatMap(person -> person.getCar()) .flatMap(car ->

    car.getInsurance()) .map(insurance -> insurance.getName()) .orElse("Unknown"); } Restoring the sanity Optional flatMap(car -> car.getInsurance()) Car
  19. String getCarInsuranceName(Optional<Person> person) { return person.flatMap(person -> person.getCar()) .flatMap(car ->

    car.getInsurance()) .map(insurance -> insurance.getName()) .orElse("Unknown"); } Restoring the sanity Optional flatMap(car -> car.getInsurance()) Optional Insurance
  20. String getCarInsuranceName(Optional<Person> person) { return person.flatMap(person -> person.getCar()) .flatMap(car ->

    car.getInsurance()) .map(insurance -> insurance.getName()) .orElse("Unknown"); } Restoring the sanity Optional map(insurance -> insurance.getName()) Insurance
  21. String getCarInsuranceName(Optional<Person> person) { return person.flatMap(person -> person.getCar()) .flatMap(car ->

    car.getInsurance()) .map(insurance -> insurance.getName()) .orElse("Unknown"); } Restoring the sanity Optional orElse("Unknown") String
  22. person .flatMap(Person::getCar) .flatMap(Car::getInsurance) .map(Insurance::getName) .orElse("Unknown"); Why map and flatMap ?

    map defines monad's policy for function application flatMap defines monad's policy for monads composition
  23. The Optional Monad The Optional monad makes the possibility of

    missing data explicit in the type system, while hiding the boilerplate of "if non-null" logic
  24. Given n>0 find all pairs i and j where 1

    ≤ j ≤ i ≤ n and i+j is prime Stream.iterate(1, i -> i+1).limit(n) .flatMap(i -> Stream.iterate(1, j -> j+1).limit(n) .map(j -> new int[]{i, j})) .filter(pair -> isPrime(pair[0] + pair[1])) .collect(toList()); public boolean isPrime(int n) { return Stream.iterate(2, i -> i+1) .limit((long) Math.sqrt(n)) .noneMatch(i -> n % i == 0); }
  25. The Stream Monad The Stream monad makes the possibility of

    multiple data explicit in the type system, while hiding the boilerplate of nested loops
  26. No Monads syntactic sugar in Java :( for { i

    <- List.range(1, n) j <- List.range(1, i) if isPrime(i + j) } yield {i, j} List.range(1, n) .flatMap(i => List.range(1, i) .filter(j => isPrime(i+j)) .map(j => (i, j))) Scala's for-comprehension is just syntactic sugar to manipulate monads translated by the compiler in
  27. Promise: a monadic CompletableFuture public class Promise<A> implements Future<A> {

    private final CompletableFuture<A> future; private Promise(CompletableFuture<A> future) { this.future = future; } public static final <A> Promise<A> promise(Supplier<A> supplier) { return new Promise<A>(CompletableFuture.supplyAsync(supplier)); } public <B> Promise<B> map(Function<? super A,? extends B> f) { return new Promise<B>(future.thenApplyAsync(f)); } public <B> Promise<B> flatMap(Function<? super A, Promise<B>> f) { return new Promise<B>( future.thenComposeAsync(a -> f.apply(a).future)); } // ... omitting methods delegating the wrapped future }
  28. public int slowLength(String s) { someLongComputation(); return s.length(); } public

    int slowDouble(int i) { someLongComputation(); return i*2; } String s = "Hello"; Promise<Integer> p = promise(() -> slowLength(s)) .flatMap(i -> promise(() -> slowDouble(i))); Composing long computations
  29. The Promise Monad The Promise monad makes asynchronous computation explicit

    in the type system, while hiding the boilerplate thread logic
  30. Lost in Exceptions public Person validateAge(Person p) throws ValidationException {

    if (p.getAge() > 0 && p.getAge() < 130) return p; throw new ValidationException("Age must be between 0 and 130"); } public Person validateName(Person p) throws ValidationException { if (Character.isUpperCase(p.getName().charAt(0))) return p; throw new ValidationException("Name must start with uppercase"); } List<String> errors = new ArrayList<String>(); try { validateAge(person); } catch (ValidationException ex) { errors.add(ex.getMessage()); } try { validateName(person); } catch (ValidationException ex) { errors.add(ex.getMessage()); }
  31. public abstract class Validation<L, A> { protected final A value;

    private Validation(A value) { this.value = value; } public abstract <B> Validation<L, B> map( Function<? super A, ? extends B> mapper); public abstract <B> Validation<L, B> flatMap( Function<? super A, Validation<?, ? extends B>> mapper); public abstract boolean isSuccess(); } Defining a Validation Monad
  32. Success !!! public class Success<L, A> extends Validation<L, A> {

    private Success(A value) { super(value); } public <B> Validation<L, B> map( Function<? super A, ? extends B> mapper) { return success(mapper.apply(value)); } public <B> Validation<L, B> flatMap( Function<? super A, Validation<?, ? extends B>> mapper) { return (Validation<L, B>) mapper.apply(value); } public boolean isSuccess() { return true; } public static <L, A> Success<L, A> success(A value) { return new Success<L, A>(value); } }
  33. Failure :((( public class Failure<L, A> extends Validation<L, A> {

    protected final L left; public Failure(A value, L left) {super(value); this.left = left;} public <B> Validation<L, B> map( Function<? super A, ? extends B> mapper) { return failure(left, mapper.apply(value)); } public <B> Validation<L, B> flatMap( Function<? super A, Validation<?, ? extends B>> mapper) { Validation<?, ? extends B> result = mapper.apply(value); return result.isSuccess() ? failure(left, result.value) : failure(((Failure<L, B>)result).left, result.value); } public boolean isSuccess() { return false; } }
  34. The Validation Monad The Validation monad makes the possibility of

    errors explicit in the type system, while hiding the boilerplate of "try/catch" logic
  35. Rewriting validating methods public Validation<String, Person> validateAge(Person p) { return

    (p.getAge() > 0 && p.getAge() < 130) ? success(p) : failure("Age must be between 0 and 130", p); } public Validation<String, Person> validateName(Person p) { return Character.isUpperCase(p.getName().charAt(0)) ? success(p) : failure("Name must start with uppercase", p); }
  36. Gathering multiple errors - Success public class SuccessList<L, A> extends

    Success<List<L>, A> { public SuccessList(A value) { super(value); } public <B> Validation<List<L>, B> map( Function<? super A, ? extends B> mapper) { return new SuccessList(mapper.apply(value)); } public <B> Validation<List<L>, B> flatMap( Function<? super A, Validation<?, ? extends B>> mapper) { Validation<?, ? extends B> result = mapper.apply(value); return (Validation<List<L>, B>)(result.isSuccess() ? new SuccessList(result.value) : new FailureList<L, B>(((Failure<L, B>)result).left, result.value)); } }
  37. Gathering multiple errors - Failure public class FailureList<L, A> extends

    Failure<List<L>, A> { private FailureList(List<L> left, A value) { super(left, value); } public <B> Validation<List<L>, B> map( Function<? super A, ? extends B> mapper) { return new FailureList(left, mapper.apply(value)); } public <B> Validation<List<L>, B> flatMap( Function<? super A, Validation<?, ? extends B>> mapper) { Validation<?, ? extends B> result = mapper.apply(value); return (Validation<List<L>, B>)(result.isSuccess() ? new FailureList(left, result.value) : new FailureList<L, B>(new ArrayList<L>(left) {{ add(((Failure<L, B>)result).left); }}, result.value)); } }
  38. Homework: develop your own Transaction Monad The Transaction monad makes

    transactionally explicit in the type system, while hiding the boilerplate propagation of invoking rollbacks
  39. Alternative Monads Definitions Monads are parametric types with two operations

    flatMap and unit that obey some algebraic laws Monads are structures that represent computations defined as sequences of steps Monads are chainable containers types that confine values defining how to transform and combine them Monads are return types that guide you through the happy path
  40. A OOP BankAccount ... public class Balance { final BigDecimal

    amount; public Balance( BigDecimal amount ) { this.amount = amount; } } public class Account { private final String owner; private final String number; private Balance balance = new Balance(BigDecimal.ZERO); public Account( String owner, String number ) { this.owner = owner; this.number = number; } public void credit(BigDecimal value) { balance = new Balance( balance.amount.add( value ) ); } public void debit(BigDecimal value) throws InsufficientBalanceException { if (balance.amount.compareTo( value ) < 0) throw new InsufficientBalanceException(); balance = new Balance( balance.amount.subtract( value ) ); } } Mutability Error handling using Exception
  41. … and how we can use it Account a =

    new Account("Alice", "123"); Account b = new Account("Bob", "456"); Account c = new Account("Charlie", "789"); List<Account> unpaid = new ArrayList<>(); for (Account account : Arrays.asList(a, b, c)) { try { account.debit( new BigDecimal( 100.00 ) ); } catch (InsufficientBalanceException e) { unpaid.add(account); } } List<Account> unpaid = new ArrayList<>(); Stream.of(a, b, c).forEach( account -> { try { account.debit( new BigDecimal( 100.00 ) ); } catch (InsufficientBalanceException e) { unpaid.add(account); } } ); Mutation of enclosing scope Cannot use a parallel Stream Ugly syntax
  42. Error handling with Try monad public interface Try<A> { <B>

    Try<B> map(Function<A, B> f); <B> Try<B> flatMap(Function<A, Try<B>> f); boolean isFailure(); } public Success<A> implements Try<A> { private final A value; public Success(A value) { this.value = value; } public boolean isFailure() { return false; } public <B> Try<B> map(Function<A, B> f) { return new Success<>(f.apply(value)); } public <B> Try<B> flatMap(Function<A, Try<B>> f) { return f.apply(value); } } public Failure<A> implements Try<T> { private final Object error; public Failure(Object error) { this.error = error; } public boolean isFailure() { return false; } public <B> Try<B> map(Function<A, B> f) { return (Failure<B>)this; } public <B> Try<B> flatMap(Function<A, Try<B>> f) { return (Failure<B>)this; } }
  43. A functional BankAccount ... public class Account { private final

    String owner; private final String number; private final Balance balance; public Account( String owner, String number, Balance balance ) { this.owner = owner; this.number = number; this.balance = balance; } public Account credit(BigDecimal value) { return new Account( owner, number, new Balance( balance.amount.add( value ) ) ); } public Try<Account> debit(BigDecimal value) { if (balance.amount.compareTo( value ) < 0) return new Failure<>( new InsufficientBalanceError() ); return new Success<>( new Account( owner, number, new Balance( balance.amount.subtract( value ) ) ) ); } } Immutable Error handling without Exceptions
  44. … and how we can use it Account a =

    new Account("Alice", "123"); Account b = new Account("Bob", "456"); Account c = new Account("Charlie", "789"); List<Account> unpaid = Stream.of( a, b, c ) .map( account -> new Tuple2<>( account, account.debit( new BigDecimal( 100.00 ) ) ) ) .filter( t -> t._2.isFailure() ) .map( t -> t._1 ) .collect( toList() ); List<Account> unpaid = Stream.of( a, b, c ) .filter( account -> account.debit( new BigDecimal( 100.00 ) ) .isFailure() ) .collect( toList() );
  45. From Methods to Functions public class BankService { public static

    Try<Account> open(String owner, String number, BigDecimal balance) { if (initialBalance.compareTo( BigDecimal.ZERO ) < 0) return new Failure<>( new InsufficientBalanceError() ); return new Success<>( new Account( owner, number, new Balance( balance ) ) ); } public static Account credit(Account account, BigDecimal value) { return new Account( account.owner, account.number, new Balance( account.balance.amount.add( value ) ) ); } public static Try<Account> debit(Account account, BigDecimal value) { if (account.balance.amount.compareTo( value ) < 0) return new Failure<>( new InsufficientBalanceError() ); return new Success<>( new Account( account.owner, account.number, new Balance( account.balance.amount.subtract( value ) ) ) ); } }
  46. Decoupling state and behavior import static BankService.* Try<Account> account =

    open( "Alice", "123", new BigDecimal( 100.00 ) ) .map( acc -> credit( acc, new BigDecimal( 200.00 ) ) ) .map( acc -> credit( acc, new BigDecimal( 300.00 ) ) ) .flatMap( acc -> debit( acc, new BigDecimal( 400.00 ) ) ); The object-oriented paradigm couples state and behavior Functional programming decouples them
  47. A naïve solution public class BankService { public static Try<Account>

    open(String owner, String number, BigDecimal balance, BankConnection bankConnection) { ... } public static Account credit(Account account, BigDecimal value, BankConnection bankConnection) { ... } public static Try<Account> debit(Account account, BigDecimal value, BankConnection bankConnection) { ... } } BankConnection bconn = new BankConnection(); Try<Account> account = open( "Alice", "123", new BigDecimal( 100.00 ), bconn ) .map( acc -> credit( acc, new BigDecimal( 200.00 ), bconn ) ) .map( acc -> credit( acc, new BigDecimal( 300.00 ), bconn ) ) .flatMap( acc -> debit( acc, new BigDecimal( 400.00 ), bconn ) ); Necessary to create the BankConnection in advance ... … and pass it to all methods
  48. Making it lazy public class BankService { public static Function<BankConnection,

    Try<Account>> open(String owner, String number, BigDecimal balance) { return (BankConnection bankConnection) -> ... } public static Function<BankConnection, Account> credit(Account account, BigDecimal value) { return (BankConnection bankConnection) -> ... } public static Function<BankConnection, Try<Account>> debit(Account account, BigDecimal value) { return (BankConnection bankConnection) -> ... } } Function<BankConnection, Try<Account>> f = (BankConnection conn) -> open( "Alice", "123", new BigDecimal( 100.00 ) ) .apply( conn ) .map( acc -> credit( acc, new BigDecimal( 200.00 ) ).apply( conn ) ) .map( acc -> credit( acc, new BigDecimal( 300.00 ) ).apply( conn ) ) .flatMap( acc -> debit( acc, new BigDecimal( 400.00 ) ).apply( conn ) ); Try<Account> account = f.apply( new BankConnection() );
  49. open Ctx -> S1 S1 A, B credit Ctx S2

    C, D result open S1 A, B, Ctx injection credit C, D, Ctx, S1 result S2 Pure OOP implementation Static Methods open A, B apply(Ctx) S1 Ctx -> S2 apply(Ctx) S2 C, D Lazy evaluation Ctx credit result
  50. Introducing the Reader monad ... public class Reader<R, A> {

    private final Function<R, A> run; public Reader( Function<R, A> run ) { this.run = run; } public <B> Reader<R, B> map(Function<A, B> f) { ... } public <B> Reader<R, B> flatMap(Function<A, Reader<R, B>> f) { ... } public A apply(R r) { return run.apply( r ); } } The reader monad provides an environment to wrap an abstract computation without evaluating it
  51. Introducing the Reader monad ... public class Reader<R, A> {

    private final Function<R, A> run; public Reader( Function<R, A> run ) { this.run = run; } public <B> Reader<R, B> map(Function<A, B> f) { return new Reader<>((R r) -> f.apply( apply( r ) )); } public <B> Reader<R, B> flatMap(Function<A, Reader<R, B>> f) { return new Reader<>((R r) -> f.apply( apply( r ) ).apply( r )); } public A apply(R r) { return run.apply( r ); } } The reader monad provides an environment to wrap an abstract computation without evaluating it
  52. The Reader Monad The Reader monad makes a lazy computation

    explicit in the type system, while hiding the logic to apply it In other words the reader monad allows us to treat functions as values with a context We can act as if we already know what the functions will return.
  53. … and combining it with Try public class TryReader<R, A>

    { private final Function<R, Try<A>> run; public TryReader( Function<R, Try<A>> run ) { this.run = run; } public <B> TryReader<R, B> map(Function<A, B> f) { ... } public <B> TryReader<R, B> mapReader(Function<A, Reader<R, B>> f) { ... } public <B> TryReader<R, B> flatMap(Function<A, TryReader<R, B>> f) { ... } public Try<A> apply(R r) { return run.apply( r ); } }
  54. … and combining it with Try public class TryReader<R, A>

    { private final Function<R, Try<A>> run; public TryReader( Function<R, Try<A>> run ) { this.run = run; } public <B> TryReader<R, B> map(Function<A, B> f) { return new TryReader<R, B>((R r) -> apply( r ) .map( a -> f.apply( a ) )); } public <B> TryReader<R, B> mapReader(Function<A, Reader<R, B>> f) { return new TryReader<R, B>((R r) -> apply( r ) .map( a -> f.apply( a ).apply( r ) )); } public <B> TryReader<R, B> flatMap(Function<A, TryReader<R, B>> f) { return new TryReader<R, B>((R r) -> apply( r ) .flatMap( a -> f.apply( a ).apply( r ) )); } public Try<A> apply(R r) { return run.apply( r ); } }
  55. A more user-friendly API public class BankService { public static

    TryReader<BankConnection, Account> open(String owner, String number, BigDecimal balance) { return new TryReader<>( (BankConnection bankConnection) -> ... ) } public static Reader<BankConnection, Account> credit(Account account, BigDecimal value) { return new Reader<>( (BankConnection bankConnection) -> ... ) } public static TryReader<BankConnection, Account> debit(Account account, BigDecimal value) { return new TryReader<>( (BankConnection bankConnection) -> ... ) } } TryReader<BankConnection, Account> reader = open( "Alice", "123", new BigDecimal( 100.00 ) ) .mapReader( acc -> credit( acc, new BigDecimal( 200.00 ) ) ) .mapReader( acc -> credit( acc, new BigDecimal( 300.00 ) ) ) .flatMap( acc -> debit( acc, new BigDecimal( 400.00 ) ) ); Try<Account> account = reader.apply( new BankConnection() );
  56. open Ctx -> S1 S1 A, B credit Ctx S2

    C, D result open S1 A, B, Ctx injection credit C, D, Ctx, S1 result S2 Pure OOP implementation Static Methods open A, B apply(Ctx) S1 Ctx -> S2 apply(Ctx) S2 C, D Lazy evaluation Ctx credit Reader monad result Ctx -> S1 A, B C, D map(credit) Ctx -> result apply(Ctx) open Ctx -> S2
  57. To recap: a Monad is a design pattern Alias 

    flatMap that shit Intent  Put a value in a computational context defining the policy on how to operate on it Motivations  Reduce code duplication  Improve maintainability  Increase readability  Remove side effects  Hide complexity  Encapusalate implementation details  Allow composability Known Uses  Optional, Stream, Promise, Validation, Transaction, State, …