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diff --git a/src/main/java/bjc/funcdata/theory/Bifunctor.java b/src/main/java/bjc/funcdata/theory/Bifunctor.java
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+++ b/src/main/java/bjc/funcdata/theory/Bifunctor.java
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+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();
+}