Currying

package ch.claude_martin.java8;

import java.util.*;
import java.util.function.Function;
import java.util.stream.*;

/**
 * Currying examples.
 *
 * @author Claude Martin
 *
 */
public class Currying {
  /** A 2-Tuple with two values. */
  static class Pair<A, B> {
    public Pair(final A first, final B second) {
      super();
      this._1 = first;
      this._2 = second;
    }

    final A _1;
    final B _2;
  }

  /** A 3-Tuple with three values. */
  static class Triple<A, B, C> extends Pair<A, B> {
    public Triple(final A first, final B second, final C third) {
      super(first, second);
      this._3 = third;
    }

    final C _3;
  }

  /** A 4-Tuple with four values. */
  static class Quad<A, B, C, D> extends Triple<A, B, C> {
    public Quad(final A first, final B second, final C third, final D fourth) {
      super(first, second, third);
      this._4 = fourth;
    }

    final D _4;
  }

  /**
   * Run this to see what it does. I recommend using a debugger for this.
   */
  public static void main(final String... args) {
    {
      // A function always consumes only one parameter!
      // If you want more parameters you must return a function to consume more
      // parameters.
      // This is the "add"-function (addition):
      final Function<Integer, Function<Integer, Integer>> add = i -> j -> i + j;
      Integer result = add.apply(1).apply(2); // = apply(add, 1, 2);
      System.out.println(result);// =3

      // But you can just claim that the two parameters are really just one.
      // Just create a Pair and pass it as one parameter:
      final Function<Pair<Integer, Integer>, Integer> add2 = p -> add.apply(p._1).apply(p._2);
      result = add2.apply(new Pair<>(1, 2));
      System.out.println(result);// =3

      // Each function that consumes just one pair can be converted to a
      // function that returns a function:
      final Function<Integer, Function<Integer, Integer>> add3 = i -> j -> add2.apply(new Pair<>(i, j));
      result = apply(add3, 1, 2);
      System.out.println(result);// =3

      // curry2 is a function that "curries" a function that takes a pair:
      result = curry2(add2).apply(1).apply(2);
      System.out.println(result);// =3

      // curry2(uncurry2(x)) = x
      result = curry2(uncurry2(curry2(uncurry2(curry2(uncurry2(curry2(add2))))))).apply(1).apply(2);
      System.out.println(result);// =3

      // uncurry does the opposite:
      result = uncurry2(add).apply(new Pair<>(1, 2));
      System.out.println(result);// =3

      // The same is true for more than two parameter:
      final Function<Integer, Function<Integer, Function<Integer, Integer>>> f = a -> b -> c -> a * b + c;
      result = uncurry3(f).apply(new Triple<>(1, 2, 3));
      System.out.println(result);
      result = apply(f, 1, 2, 3);
      System.out.println(result);// =5

      // You can only apply some parameters and get a function, then you can
      // later apply the rest.
      // partial application:
      Function<Integer, Integer> part = apply(f, 1, 2);
      System.out.println(part); // ...$$Lambda$...
      // apply last argument:
      result = apply(part, 3);
      System.out.println(result); // =5

      // applyR does exactly the same as apply, but it is recursive.
      part = applyR(f, 1); // only one argument this time
      System.out.println(part); // ...$$Lambda$...
      // apply last two arguments:
      result = applyR(part, 2, 3);
      System.out.println(result); // =5

      // Some functions even consume a 4-Tuple!
      final Function<Quad<Integer, String, Boolean, Integer>, Integer> f2 = q -> q._1 * q._2.length() + (q._3 ? q._4 : 0);
      result = apply(curry4(f2), 1, "hallo", true, 4);
      System.out.println(result);// =9
      result = curry4(f2).apply(1).apply("hallo").apply(true).apply(4);
      System.out.println(result);// =9
    }

    { // Some fun with Collections:
      final Collection<Integer> list = Arrays.asList(1, 2, 3, 4);
      final Function<Integer, Function<Integer, Integer>> add = i -> j -> i + j;
      // partially apply all integers to add:
      final Stream<Function<Integer, Integer>> list2 = list.stream().map(add);
      // Now apply 42 as the "second" parameter:
      final Stream<Integer> list3 = list2.map(f2 -> f2.apply(42));
      // Print to console:
      System.out.println(Arrays.toString(list3.toArray())); // = [43, 44, 45, 46]
    }

    { // More fun with Collections:
      final Collection<Integer> listA = Arrays.asList(1, 2, 3, 4);
      final Collection<Integer> listB = Arrays.asList(5, 6, 7, 8);
      final Function<Integer, Function<Integer, Integer>> add = i -> j -> i + j;

      // Where did Stream::zip go?! Not available in this beta release...
      // listA.stream().zip(listB.stream()).map(...

      final Collection<Pair<Integer, Integer>> zip = new LinkedList<>();
      final Iterator<Integer> iteratorA = listA.iterator();
      final Iterator<Integer> iteratorB = listB.iterator();
      while (iteratorA.hasNext() && iteratorB.hasNext())
        zip.add(new Pair<>(iteratorA.next(), iteratorB.next()));

      final List<Integer> results = zip.stream().map(uncurry2(add)).collect(Collectors.<Integer> toList());
      System.out.println(results.toString()); // = [6, 8, 10, 12]
    }
  }

  /**
   * Applies the first argument to the function and then the next to the
   * returned function. The application of all given parameters must result in a
   * complete application of the given function.
   *
   * @param f
   *          Curried Function.
   * @param arg0
   *          The first argument is type checked.
   * @param args
   *          More arguments.
   * @return Returns the value of the last function.
   * @throws IllegalArgumentException
   *           Thrown when the arguments don't match.
   * @throws ClassCastException
   *           The return value will be cast implicitly, which could cause a
   *           ClassCastException.
   */
  @SuppressWarnings({ "unchecked", "rawtypes" })
  static <T, X> T apply(final Function<? super X, ?> f, final X arg0, final Object... args) throws ClassCastException, IllegalArgumentException {
    Objects.requireNonNull(f, "The function argument must not be null.");
    Object result = f.apply(arg0);
    if (args != null && args.length > 0) {
      Function f2 = requireFunction(result);
      for (int i = 0; i < args.length - 1; i++)
        f2 = requireFunction(f2.apply(args[i]));
      result = f2.apply(args[args.length - 1]);
    }
    return (T) result;
  }

  /** Cast to function or throw IllegalArgumentException. */
  @SuppressWarnings("rawtypes")
  private static Function requireFunction(final Object x) {
    if (!(x instanceof Function))
      throw new IllegalArgumentException("Result was not a function, but more arguments remain.");
    return (Function) x;
  }

  /** The same as {@link #apply(Function, Object, Object...)}, but recursive. */
  @SafeVarargs
  @SuppressWarnings("unchecked")
  static <T, X, Y> T applyR(final Function<? super X, ?> f, final X arg0, final Y... args) throws ClassCastException, IllegalArgumentException {
    if (args == null || args.length == 0)
      return (T) f.apply(arg0);
    else
      return (T) applyR(requireFunction(f.apply(arg0)), args[0], Arrays.copyOfRange(args, 1, args.length));
  }

  /** Converts an uncurried function to a curried function. */
  static <A, B, C> Function<A, Function<B, C>> curry2(final Function<Pair<A, B>, C> f) {
    return a -> b -> f.apply(new Pair<>(a, b));
  }

  /** Converts a curried function to a function on pairs. */
  static <A, B, C> Function<Pair<A, B>, C> uncurry2(final Function<A, Function<B, C>> f) {
    return (Pair<A, B> p) -> f.apply(p._1).apply(p._2);
  }

  /** Converts an uncurried function to a curried function. */
  static <A, B, C, D> Function<A, Function<B, Function<C, D>>> curry3(final Function<Triple<A, B, C>, D> f) {
    return a -> b -> c -> f.apply(new Triple<>(a, b, c));
  }

  /** Converts a curried function to a function on triples. */
  static <A, B, C, D> Function<Triple<A, B, C>, D> uncurry3(final Function<A, Function<B, Function<C, D>>> f) {
    return (Triple<A, B, C> p) -> f.apply(p._1).apply(p._2).apply(p._3);
  }

  /** Converts an uncurried function to a curried function. */
  static <A, B, C, D, E> Function<A, Function<B, Function<C, Function<D, E>>>> curry4(final Function<Quad<A, B, C, D>, E> f) {
    return a -> b -> c -> d -> f.apply(new Quad<>(a, b, c, d));
  }

  /** Converts a curried function to a function on quads. */
  static <A, B, C, D, E> Function<Quad<A, B, C, D>, E> uncurry4(final Function<A, Function<B, Function<C, Function<D, E>>>> f) {
    return (Quad<A, B, C, D> p) -> f.apply(p._1).apply(p._2).apply(p._3).apply(p._4);
  }

}