package bjc.funcdata.theory;

import java.util.function.Function;

/**
 * A functor over a pair of heterogeneous types.
 *
 * @author ben
 *
 * @param <LeftType>
 *                    The type stored on the 'left' of the pair.
 *
 * @param <RightType>
 *                    The type stored on the 'right' of the pair.
 */
public interface Bifunctor<LeftType, RightType> {
	/**
	 * Alias for functor mapping.
	 *
	 * @author EVE
	 *
	 * @param <OldLeft>
	 *                   The old left type.
	 *
	 * @param <OldRight>
	 *                   The old right type.
	 *
	 * @param <NewLeft>
	 *                   The new left type.
	 *
	 * @param <NewRight>
	 *                   The new right type.
	 */
	public interface BifunctorMap<OldLeft, OldRight, NewLeft, NewRight>
			extends Function<Bifunctor<OldLeft, OldRight>, Bifunctor<NewLeft, NewRight>> {
		/*
		 * Alias
		 */
	}

	/**
	 * Alias for left functor mapping.
	 *
	 * @author EVE
	 *
	 * @param <OldLeft>
	 *                   The old left type.
	 *
	 * @param <OldRight>
	 *                   The old right type.
	 *
	 * @param <NewLeft>
	 *                   The new left type.
	 */
	public interface LeftBifunctorMap<OldLeft, OldRight, NewLeft>
			extends BifunctorMap<OldLeft, OldRight, NewLeft, OldRight> {
		/*
		 * Alias
		 */
	}

	/**
	 * Alias for right functor mapping.
	 *
	 * @author EVE
	 *
	 * @param <OldLeft>
	 *                   The old left type.
	 *
	 * @param <OldRight>
	 *                   The old right type.
	 *
	 * @param <NewRight>
	 *                   The new right type.
	 */
	public interface RightBifunctorMap<OldLeft, OldRight, NewRight>
			extends BifunctorMap<OldLeft, OldRight, OldLeft, NewRight> {
		/*
		 * Alias
		 */
	}

	/**
	 * Lift a pair of functions to a single function that maps over both parts of a
	 * pair.
	 *
	 * @param <OldLeft>
	 *                   The old left type of the pair.
	 *
	 * @param <OldRight>
	 *                   The old right type of the pair.
	 *
	 * @param <NewLeft>
	 *                   The new left type of the pair.
	 *
	 * @param <NewRight>
	 *                   The new right type of the pair.
	 *
	 * @param leftFunc
	 *                   The function that maps over the left of the pair.
	 *
	 * @param rightFunc
	 *                   The function that maps over the right of the pair.
	 *
	 * @return A function that maps over both parts of the pair.
	 */
	public default <OldLeft, OldRight, NewLeft, NewRight>
			BifunctorMap<OldLeft, OldRight, NewLeft, NewRight>
			bimap(final Function<OldLeft, NewLeft> leftFunc,
					final Function<OldRight, NewRight> rightFunc) {
		final BifunctorMap<OldLeft, OldRight, NewLeft, NewRight> bimappedFunc
				= argPair -> {
					final LeftBifunctorMap<OldLeft, OldRight, NewLeft> leftMapper
							= argPair.fmapLeft(leftFunc);

					final Bifunctor<NewLeft, OldRight> leftMappedFunctor
							= leftMapper.apply(argPair);
					final RightBifunctorMap<NewLeft, OldRight, NewRight> rightMapper
							= leftMappedFunctor.fmapRight(rightFunc);

					return rightMapper.apply(leftMappedFunctor);
				};

		return bimappedFunc;
	}

	/**
	 * Lift a function to operate over the left part of this pair.
	 *
	 * @param <OldLeft>
	 *                   The old left type of the pair.
	 *
	 * @param <OldRight>
	 *                   The old right type of the pair.
	 *
	 * @param <NewLeft>
	 *                   The new left type of the pair.
	 *
	 * @param func
	 *                   The function to lift to work over the left side of the
	 *                   pair.
	 *
	 * @return The function lifted to work over the left side of bifunctors.
	 */
	public <OldLeft, OldRight, NewLeft> LeftBifunctorMap<OldLeft, OldRight, NewLeft>
			fmapLeft(Function<OldLeft, NewLeft> func);

	/**
	 * Lift a function to operate over the right part of this pair.
	 *
	 * @param <OldLeft>
	 *                   The old left type of the pair.
	 *
	 * @param <OldRight>
	 *                   The old right type of the pair.
	 *
	 * @param <NewRight>
	 *                   The new right type of the pair.
	 *
	 * @param func
	 *                   The function to lift to work over the right side of the
	 *                   pair.
	 *
	 * @return The function lifted to work over the right side of bifunctors.
	 */
	public <OldLeft, OldRight, NewRight> RightBifunctorMap<OldLeft, OldRight, NewRight>
			fmapRight(Function<OldRight, NewRight> func);

	/**
	 * Get the value contained on the left of this bifunctor.
	 *
	 * @return The value on the left side of this bifunctor.
	 */
	public LeftType getLeft();

	/**
	 * Get the value contained on the right of this bifunctor.
	 *
	 * @return The value on the right of this bifunctor.
	 */
	public RightType getRight();
}