--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/main/java/fj/data/Tree.java	Fri Mar 20 21:04:03 2015 +0900
@@ -0,0 +1,379 @@
+package fj.data;
+
+import fj.F;
+import fj.F2;
+import fj.F2Functions;
+import fj.P;
+import fj.P1;
+import fj.P2;
+import static fj.Function.*;
+import static fj.data.Stream.*;
+import fj.Monoid;
+import fj.Show;
+
+import java.util.Collection;
+import java.util.Iterator;
+
+/**
+ * Provides a lazy, immutable, non-empty, multi-way tree (a rose tree).
+ *
+ * @version %build.number%
+ */
+public final class Tree<A> implements Iterable<A> {
+  /**
+   * Returns an iterator for this tree. This method exists to permit the use in a <code>for</code>-each loop.
+   *
+   * @return A iterator for this tree.
+   */
+  public Iterator<A> iterator() {
+    return flatten().iterator();
+  }
+
+  private final A root;
+  private final P1<Stream<Tree<A>>> subForest;
+
+  private Tree(final A root, final P1<Stream<Tree<A>>> subForest) {
+    this.root = root;
+    this.subForest = subForest;
+  }
+
+  /**
+   * Creates a nullary tree.
+   *
+   * @param root The root element of the tree.
+   * @return A nullary tree with the root element in it.
+   */
+  public static <A> Tree<A> leaf(final A root) {
+    return node(root, Stream.<Tree<A>>nil());
+  }
+
+  /**
+   * Creates a new tree given a root and a (potentially infinite) subforest.
+   *
+   * @param root   The root element of the tree.
+   * @param forest A stream of the tree's subtrees.
+   * @return A newly sprouted tree.
+   */
+  public static <A> Tree<A> node(final A root, final P1<Stream<Tree<A>>> forest) {
+    return new Tree<A>(root, forest);
+  }
+
+  /**
+   * Creates a new tree given a root and a (potentially infinite) subforest.
+   *
+   * @param root   The root element of the tree.
+   * @param forest A stream of the tree's subtrees.
+   * @return A newly sprouted tree.
+   */
+  public static <A> Tree<A> node(final A root, final Stream<Tree<A>> forest) {
+    return new Tree<A>(root, P.p(forest));
+  }
+
+  /**
+   * Creates a new n-ary given a root and a subforest of length n.
+   *
+   * @param root   The root element of the tree.
+   * @param forest A list of the tree's subtrees.
+   * @return A newly sprouted tree.
+   */
+  public static <A> Tree<A> node(final A root, final List<Tree<A>> forest) {
+    return node(root, forest.toStream());
+  }
+
+  /**
+   * First-class constructor of trees.
+   *
+   * @return A function that constructs an n-ary tree given a root and a subforest or length n.
+   */
+  public static <A> F<A, F<P1<Stream<Tree<A>>>, Tree<A>>> node() {
+    return curry(new F2<A, P1<Stream<Tree<A>>>, Tree<A>>() {
+      public Tree<A> f(final A a, final P1<Stream<Tree<A>>> p1) {
+        return node(a, p1);
+      }
+    });
+  }
+
+  /**
+   * Returns the root element of the tree.
+   *
+   * @return The root element of the tree.
+   */
+  public A root() {
+    return root;
+  }
+
+  /**
+   * Returns a stream of the tree's subtrees.
+   *
+   * @return A stream of the tree's subtrees.
+   */
+  public P1<Stream<Tree<A>>> subForest() {
+    return subForest;
+  }
+
+  /**
+   * Provides a transformation from a tree to its root.
+   *
+   * @return A transformation from a tree to its root.
+   */
+  public static <A> F<Tree<A>, A> root_() {
+    return new F<Tree<A>, A>() {
+      public A f(final Tree<A> a) {
+        return a.root();
+      }
+    };
+  }
+
+  /**
+   * Provides a transformation from a tree to its subforest.
+   *
+   * @return A transformation from a tree to its subforest.
+   */
+  public static <A> F<Tree<A>, P1<Stream<Tree<A>>>> subForest_() {
+    return new F<Tree<A>, P1<Stream<Tree<A>>>>() {
+      public P1<Stream<Tree<A>>> f(final Tree<A> a) {
+        return a.subForest();
+      }
+    };
+  }
+
+  /**
+   * Puts the elements of the tree into a Stream, in pre-order.
+   *
+   * @return The elements of the tree in pre-order.
+   */
+  public Stream<A> flatten() {
+    final F2<Tree<A>, P1<Stream<A>>, Stream<A>> squish = new F2<Tree<A>, P1<Stream<A>>, Stream<A>>() {
+      public Stream<A> f(final Tree<A> t, final P1<Stream<A>> xs) {
+        return cons(t.root(), t.subForest().map(Stream.<Tree<A>, Stream<A>>foldRight().f(F2Functions.curry(this)).f(xs._1())));
+      }
+    };
+    return squish.f(this, P.p(Stream.<A>nil()));
+  }
+
+  /**
+   * flatten :: Tree a -> [a]
+   * flatten t = squish t []
+   * where squish (Node x ts) xs = x:Prelude.foldr squish xs ts
+   * Puts the elements of the tree into a Stream, in pre-order.
+   *
+   * @return The elements of the tree in pre-order.
+   */
+  public static <A> F<Tree<A>, Stream<A>> flatten_() {
+    return new F<Tree<A>, Stream<A>>() {
+      public Stream<A> f(final Tree<A> t) {
+        return t.flatten();
+      }
+    };
+  }
+
+  /**
+   * Provides a stream of the elements of the tree at each level, in level order.
+   *
+   * @return The elements of the tree at each level.
+   */
+  public Stream<Stream<A>> levels() {
+    final F<Stream<Tree<A>>, Stream<Tree<A>>> flatSubForests =
+        Stream.<Tree<A>, Tree<A>>bind_().f(compose(P1.<Stream<Tree<A>>>__1(), Tree.<A>subForest_()));
+    final F<Stream<Tree<A>>, Stream<A>> roots = Stream.<Tree<A>, A>map_().f(Tree.<A>root_());
+    return iterateWhile(flatSubForests, Stream.<Tree<A>>isNotEmpty_(), single(this)).map(roots);
+  }
+
+  /**
+   * Maps the given function over this tree.
+   *
+   * @param f The function to map over this tree.
+   * @return The new Tree after the function has been applied to each element in this Tree.
+   */
+  public <B> Tree<B> fmap(final F<A, B> f) {
+    return node(f.f(root()), subForest().map(Stream.<Tree<A>, Tree<B>>map_().f(Tree.<A, B>fmap_().f(f))));
+  }
+
+  /**
+   * Provides a transformation to lift any function so that it maps over Trees.
+   *
+   * @return A transformation to lift any function so that it maps over Trees.
+   */
+  public static <A, B> F<F<A, B>, F<Tree<A>, Tree<B>>> fmap_() {
+    return new F<F<A, B>, F<Tree<A>, Tree<B>>>() {
+      public F<Tree<A>, Tree<B>> f(final F<A, B> f) {
+        return new F<Tree<A>, Tree<B>>() {
+          public Tree<B> f(final Tree<A> a) {
+            return a.fmap(f);
+          }
+        };
+      }
+    };
+  }
+
+  /**
+   * Folds this tree using the given monoid.
+   *
+   * @param f A transformation from this tree's elements, to the monoid.
+   * @param m The monoid to fold this tree with.
+   * @return The result of folding the tree with the given monoid.
+   */
+  public <B> B foldMap(final F<A, B> f, final Monoid<B> m) {
+    return m.sum(f.f(root()), m.sumRight(subForest()._1().map(foldMap_(f, m)).toList()));
+  }
+
+  /**
+   * Projects an immutable collection of this tree.
+   *
+   * @return An immutable collection of this tree.
+   */
+  public Collection<A> toCollection() {
+    return flatten().toCollection();
+  }
+
+  /**
+   * Provides a function that folds a tree with the given monoid.
+   *
+   * @param f A transformation from a tree's elements to the monoid.
+   * @param m A monoid to fold the tree with.
+   * @return A function that, given a tree, folds it with the given monoid.
+   */
+  public static <A, B> F<Tree<A>, B> foldMap_(final F<A, B> f, final Monoid<B> m) {
+    return new F<Tree<A>, B>() {
+      public B f(final Tree<A> t) {
+        return t.foldMap(f, m);
+      }
+    };
+  }
+
+  /**
+   * Builds a tree from a seed value.
+   *
+   * @param f A function with which to build the tree.
+   * @return A function which, given a seed value, yields a tree.
+   */
+  public static <A, B> F<B, Tree<A>> unfoldTree(final F<B, P2<A, P1<Stream<B>>>> f) {
+    return new F<B, Tree<A>>() {
+      public Tree<A> f(final B b) {
+        final P2<A, P1<Stream<B>>> p = f.f(b);
+        return node(p._1(), p._2().map(Stream.<B, Tree<A>>map_().f(unfoldTree(f))));
+      }
+    };
+  }
+
+  /**
+   * Applies the given function to all subtrees of this tree, returning a tree of the results (comonad pattern).
+   *
+   * @param f A function to bind across all the subtrees of this tree.
+   * @return A new tree, with the results of applying the given function to each subtree of this tree. The result
+   *         of applying the function to the entire tree is the root label, and the results of applying to the
+   *         root's children are labels of the root's subforest, etc.
+   */
+  public <B> Tree<B> cobind(final F<Tree<A>, B> f) {
+    return unfoldTree(new F<Tree<A>, P2<B, P1<Stream<Tree<A>>>>>() {
+      public P2<B, P1<Stream<Tree<A>>>> f(final Tree<A> t) {
+        return P.p(f.f(t), t.subForest());
+      }
+    }).f(this);
+  }
+
+  /**
+   * Expands this tree into a tree of trees, with this tree as the root label, and subtrees as the labels of
+   * child nodes (comonad pattern).
+   *
+   * @return A tree of trees, with this tree as its root label, and subtrees of this tree as the labels of
+   *         its child nodes.
+   */
+  public Tree<Tree<A>> cojoin() {
+    final F<Tree<A>, Tree<A>> id = identity();
+    return cobind(id);
+  }
+
+  private static <A> Stream<String> drawSubTrees(final Show<A> s, final Stream<Tree<A>> ts) {
+    return ts.isEmpty() ? Stream.<String>nil()
+                        : ts.tail()._1().isEmpty() ? shift("`- ", "   ", ts.head().drawTree(s)).cons("|")
+                                                   : shift("+- ", "|  ", ts.head().drawTree(s))
+                                                       .append(drawSubTrees(s, ts.tail()._1()));
+  }
+
+  private static Stream<String> shift(final String f, final String o, final Stream<String> s) {
+    return Stream.repeat(o).cons(f).zipWith(s, Monoid.stringMonoid.sum());
+  }
+
+  private Stream<String> drawTree(final Show<A> s) {
+    return drawSubTrees(s, subForest._1()).cons(s.showS(root));
+  }
+
+  /**
+   * Draws a 2-dimensional representation of a tree.
+   *
+   * @param s A show instance for the elements of the tree.
+   * @return a String showing this tree in two dimensions.
+   */
+  public String draw(final Show<A> s) {
+    return Monoid.stringMonoid.join(drawTree(s), "\n");
+  }
+
+  /**
+   * Provides a show instance that draws a 2-dimensional representation of a tree.
+   *
+   * @param s A show instance for the elements of the tree.
+   * @return a show instance that draws a 2-dimensional representation of a tree.
+   */
+  public static <A> Show<Tree<A>> show2D(final Show<A> s) {
+    return Show.showS(new F<Tree<A>, String>() {
+      public String f(final Tree<A> tree) {
+        return tree.draw(s);
+      }
+    });
+  }
+
+  /**
+   * Zips this tree with another, using the given function. The resulting tree is the structural intersection
+   * of the two trees.
+   *
+   * @param bs A tree to zip this tree with.
+   * @param f  A function with which to zip together the two trees.
+   * @return A new tree of the results of applying the given function over this tree and the given tree, position-wise.
+   */
+  public <B, C> Tree<C> zipWith(final Tree<B> bs, final F2<A, B, C> f) {
+    return F2Functions.zipTreeM(f).f(this, bs);
+  }
+
+  /**
+   * Zips this tree with another, using the given function. The resulting tree is the structural intersection
+   * of the two trees.
+   *
+   * @param bs A tree to zip this tree with.
+   * @param f  A function with which to zip together the two trees.
+   * @return A new tree of the results of applying the given function over this tree and the given tree, position-wise.
+   */
+  public <B, C> Tree<C> zipWith(final Tree<B> bs, final F<A, F<B, C>> f) {
+    return zipWith(bs, uncurryF2(f));
+  }
+  
+  /**
+   * Folds a Tree<A> into a Tree<B> by applying the function f from the bottom of the Tree to the top
+   *
+   * @param t A tree to fold from the bottom to the top.
+   * @param f  A function transforming the current node and a stream of already transformed nodes (its children) into a new node
+   * @return The folded tree
+   */
+  public static <A, B> Tree<B> bottomUp(Tree<A> t, final F<P2<A, Stream<B>>, B> f) {
+    final F<Tree<A>, Tree<B>> recursiveCall = new F<Tree<A>, Tree<B>>() {
+      @Override public Tree<B> f(Tree<A> a) {
+        return bottomUp(a, f);
+      }
+    };
+ 
+    final Stream<Tree<B>> tbs = t.subForest()._1().map(recursiveCall);
+    return Tree.node(f.f(P.p(t.root(), tbs.map(Tree.<B> getRoot()))), tbs);
+   }
+ 
+   /**
+    * @return a function getting the root of a Tree 
+	*/
+   private static <A> F<Tree<A>, A> getRoot() {
+     return new F<Tree<A>, A>() {
+       @Override public A f(Tree<A> a) {
+         return a.root();
+       }
+     };
+   }
+
+}
\ No newline at end of file