The WriterMonad:

Accumulating Output Alongside Computations

Purpose

The Writer monad is a functional pattern designed for computations that, in addition to producing a primary result value, also need to accumulate some secondary output or log along the way. Think of scenarios like:

• Detailed logging of steps within a complex calculation.
• Collecting metrics or events during a process.
• Building up a sequence of results or messages.

A Writer<W, A> represents a computation that produces a main result of type A and simultaneously accumulates an output of type W. The key requirement is that the accumulated type W must form a Monoid.

The Role of Monoid<W>

A Monoid<W> is a type class that defines two things for type W:

1. empty(): Provides an identity element (like "" for String concatenation, 0 for addition, or an empty list).
2. combine(W w1, W w2): Provides an associative binary operation to combine two values of type W (like + for strings or numbers, or list concatenation).

The Writer monad uses the Monoid<W> to:

• Provide a starting point (the empty value) for the accumulation.
• Combine the accumulated outputs (W) from different steps using the combine operation when sequencing computations with flatMap or ap.

Common examples for W include String (using concatenation), Integer (using addition or multiplication), or List (using concatenation).

Structure

The Writer<W, A> record directly implements WriterKind<W, A>, which in turn extends Kind<WriterKind.Witness<W>, A>.

The Writer<W, A> Type

The core type is the Writer<W, A> record:

// From: org.higherkindedj.hkt.writer.Writer
public record Writer<W, A>(@NonNull W log, @Nullable A value) implements WriterKind<W, A> {
  // Static factories
  public static <W, A> @NonNull Writer<W, A> create(@NonNull W log, @Nullable A value);
  public static <W, A> @NonNull Writer<W, A> value(@NonNull Monoid<W> monoidW, @Nullable A value); // Creates (monoidW.empty(), value)
  public static <W> @NonNull Writer<W, Unit> tell(@NonNull W log); // Creates (log, Unit.INSTANCE) 

  // Instance methods (primarily for direct use, HKT versions via Monad instance)
  public <B> @NonNull Writer<W, B> map(@NonNull Function<? super A, ? extends B> f);
  public <B> @NonNull Writer<W, B> flatMap(
          @NonNull Monoid<W> monoidW, // Monoid needed for combining logs
          @NonNull Function<? super A, ? extends Writer<W, ? extends B>> f
  );
  public @Nullable A run(); // Get the value A, discard log
  public @NonNull W exec(); // Get the log W, discard value
}

• It simply holds a pair: the accumulated log (of type W) and the computed value (of type A).
• create(log, value): Basic constructor.
• value(monoid, value): Creates a Writer with the given value and an empty log according to the provided Monoid.
• tell(log): Creates a Writer with the given log, and Unit.INSTANCE as it's value, signifying that the operation's primary purpose is the accumulation of the log. Useful for just adding to the log. (Note: The original Writer.java might have tell(W log) and infer monoid elsewhere, or WriterMonad handles tell).
• map(...): Transforms the computed value A to B while leaving the log W untouched.
• flatMap(...): Sequences computations. It runs the first Writer, uses its value A to create a second Writer, and combines the logs from both using the provided Monoid.
• run(): Extracts only the computed value A, discarding the log.
• exec(): Extracts only the accumulated log W, discarding the value.

Writer Components

To integrate Writer with Higher-Kinded-J:

• WriterKind<W, A>: The HKT interface. Writer<W, A> itself implements WriterKind<W, A>. WriterKind<W, A> extends Kind<WriterKind.Witness<W>, A>.
  • It contains a nested final class Witness<LOG_W> {} which serves as the phantom type F_WITNESS for Writer<LOG_W, ?>.
• WriterKindHelper: The utility class with static methods:
  • widen(Writer<W, A>): Converts a Writer to Kind<WriterKind.Witness<W>, A>. Since Writer directly implements WriterKind, this is effectively a checked cast.
  • narrow(Kind<WriterKind.Witness<W>, A>): Converts Kind back to Writer<W,A>. This is also effectively a checked cast after an instanceof Writer check.
  • value(Monoid<W> monoid, A value): Factory method for a Kind representing a Writer with an empty log.
  • tell(W log): Factory method for a Kind representing a Writer that only logs.
  • runWriter(Kind<WriterKind.Witness<W>, A>): Unwraps to Writer<W,A> and returns the record itself.
  • run(Kind<WriterKind.Witness<W>, A>): Executes (unwraps) and returns only the value A.
  • exec(Kind<WriterKind.Witness<W>, A>): Executes (unwraps) and returns only the log W.

Type Class Instances (WriterFunctor, WriterApplicative, WriterMonad)

These classes provide the standard functional operations for Kind<WriterKind.Witness<W>, A>, allowing you to treat Writer computations generically. Crucially, WriterApplicative<W> and WriterMonad<W> require a Monoid<W> instance during construction.

• WriterFunctor<W>: Implements Functor<WriterKind.Witness<W>>. Provides map (operates only on the value A).
• WriterApplicative<W>: Extends WriterFunctor<W>, implements Applicative<WriterKind.Witness<W>>. Requires a Monoid<W>. Provides of (lifting a value with an empty log) and ap (applying a wrapped function to a wrapped value, combining logs).
• WriterMonad<W>: Extends WriterApplicative<W>, implements Monad<WriterKind.Witness<W>>. Requires a Monoid<W>. Provides flatMap for sequencing computations, automatically combining logs using the Monoid.

class StringMonoid implements Monoid<String> {
  @Override public String empty() { return ""; }
  @Override public String combine(String x, String y) { return x + y; }
}

Monoid<String> stringMonoid = new StringMonoid(); 

import org.higherkindedj.hkt.writer.WriterMonad;

// Monad instance for computations logging Strings
// F_WITNESS here is WriterKind.Witness<String>
WriterMonad<String> writerMonad = new WriterMonad<>(stringMonoid);

// Writer with an initial value and empty log
Kind<WriterKind.Witness<String>, Integer> initialValue = WRITER.value(stringMonoid, 5); // Log: "", Value: 5

// Writer that just logs a message (value is Unit.INSTANCE)
Kind<WriterKind.Witness<String>, Unit> logStart = WRITER.tell("Starting calculation; "); // Log: "Starting calculation; ", Value: ()

// A function that performs a calculation and logs its step
Function<Integer, Kind<WriterKind.Witness<String>, Integer>> addAndLog =
        x -> {
          int result = x + 10;
          String logMsg = "Added 10 to " + x + " -> " + result + "; ";
          // Create a Writer directly then wrap with helper or use helper factory
          return WRITER.widen(Writer.create(logMsg, result));
        };

Function<Integer, Kind<WriterKind.Witness<String>, String>> multiplyAndLogToString =
        x -> {
          int result = x * 2;
          String logMsg = "Multiplied " + x + " by 2 -> " + result + "; ";
          return WRITER.widen(Writer.create(logMsg, "Final:" + result));
        };

// Chain the operations:
// Start with a pure value 0 in the Writer context (empty log)
Kind<WriterKind.Witness<String>, Integer> computationStart = writerMonad.of(0);

// 1. Log the start
Kind<WriterKind.Witness<String>, Integer> afterLogStart  = writerMonad.flatMap(ignoredUnit -> initialValue, logStart);

Kind<WriterKind.Witness<String>, Integer> step1Value = WRITER.value(stringMonoid, 5); // ("", 5)
Kind<WriterKind.Witness<String>, Unit> step1Log = WRITER.tell("Initial value set to 5; "); // ("Initial value set to 5; ", ())


// Start -> log -> transform value -> log -> transform value ...
Kind<WriterKind.Witness<String>, Integer> calcPart1 = writerMonad.flatMap(
        ignored -> addAndLog.apply(5), // Apply addAndLog to 5, after logging "start"
        WRITER.tell("Starting with 5; ")
);
// calcPart1: Log: "Starting with 5; Added 10 to 5 -> 15; ", Value: 15

Kind<WriterKind.Witness<String>, String> finalComputation = writerMonad.flatMap(
        intermediateValue -> multiplyAndLogToString.apply(intermediateValue),
        calcPart1
);
// finalComputation: Log: "Starting with 5; Added 10 to 5 -> 15; Multiplied 15 by 2 -> 30; ", Value: "Final:30"


// Using map: Only transforms the value, log remains unchanged from the input Kind
Kind<WriterKind.Witness<String>, Integer> initialValForMap = value(stringMonoid, 100); // Log: "", Value: 100
Kind<WriterKind.Witness<String>, String> mappedVal = writerMonad.map(
        i -> "Value is " + i,
        initialValForMap
); // Log: "", Value: "Value is 100"

import org.higherkindedj.hkt.writer.Writer; 

// Get the final Writer record (log and value)
Writer<String, String> finalResultWriter = runWriter(finalComputation);
String finalLog = finalResultWriter.log();
String finalValue = finalResultWriter.value();

System.out.println("Final Log: " + finalLog);
// Output: Final Log: Starting with 5; Added 10 to 5 -> 15; Multiplied 15 by 2 -> 30;
System.out.println("Final Value: " + finalValue);
// Output: Final Value: Final:30

// Or get only the value or log
String justValue = WRITER.run(finalComputation); // Extracts value from finalResultWriter
String justLog = WRITER.exec(finalComputation);  // Extracts log from finalResultWriter

System.out.println("Just Value: " + justValue); // Output: Just Value: Final:30
System.out.println("Just Log: " + justLog);     // Output: Just Log: Starting with 5; Added 10 to 5 -> 15; Multiplied 15 by 2 -> 30;

Writer<String, String> mappedResult = WRITER.runWriter(mappedVal);
System.out.println("Mapped Log: " + mappedResult.log());   // Output: Mapped Log
System.out.println("Mapped Value: " + mappedResult.value()); // Output: Mapped Value: Value is 100