Reduce errors and compiletime in tree traversal

cmake/modules/AmdisCXXFeatures.cmake

-#include(CheckIncludeFileCXX)
 include(CheckCXXSourceCompiles)
-#include(CheckCXXSymbolExists)
 
 # fold expressions (a + ...)
 check_cxx_source_compiles("
@@ -30,4 +28,16 @@ check_cxx_source_compiles("
     return f<1>();
   }
 "  AMDIS_HAS_CXX_CONSTEXPR_IF
+)
+
+check_cxx_source_compiles("
+  #include <iostream>
+  #include <tuple>
+  int main()
+  {
+    auto tup = std::make_tuple(0, 'a', 3.14);
+    for... (auto elem : tup)
+      std::cout << elem << std::endl;
+  }
+"  AMDIS_HAS_EXPANSION_STATEMENTS
 )
\ No newline at end of file

config.h.cmake

@@ -49,6 +49,7 @@
 /* some detected compiler features may be used in AMDiS */
 #cmakedefine AMDIS_HAS_CXX_FOLD_EXPRESSIONS 1
 #cmakedefine AMDIS_HAS_CXX_CONSTEXPR_IF 1
+#cmakedefine AMDIS_HAS_EXPANSION_STATEMENTS 1
 
 /* end amdis
    Everything below here will be overwritten

examples/CMakeLists.txt

@@ -24,4 +24,4 @@ add_dependencies(examples
   stokes1.2d
   stokes3.2d
   navier_stokes.2d
-  convection_diffusion.2d)
\ No newline at end of file
+  convection_diffusion.2d)

src/amdis/BoundaryManager.hpp

@@ -146,9 +146,10 @@ namespace AMDiS
           if (!segment.boundary())
             continue;
 
-          auto index = segment.boundarySegmentIndex();
-          Dune::Hybrid::ifElse(Dune::Std::is_detected<HasBoundaryId, Segment>{},
-            [&](auto id) { boundaryIds_[index] = id(segment).boundaryId(); });
+          Dune::Hybrid::ifElse(Dune::Std::is_detected<HasBoundaryId, Segment>{}, [&](auto id) {
+            auto index = segment.boundarySegmentIndex();
+            boundaryIds_[index] = id(segment).boundaryId();
+          });
         }
       }
     }

src/amdis/DataTransfer.inc.hpp

@@ -22,8 +22,8 @@
 
 #include <amdis/Output.hpp>
 #include <amdis/common/ConcurrentCache.hpp>
+#include <amdis/typetree/Traversal.hpp>
 #include <amdis/typetree/TreeContainer.hpp>
-#include <amdis/typetree/Visitor.hpp>
 
 namespace AMDiS
 {
@@ -135,7 +135,7 @@ namespace AMDiS
     auto lv = basis_->localView();
     auto const& idSet = gv.grid().localIdSet();
 
-    forEachLeafNode_(lv.tree(), [&](auto const& node, auto const& tp) {
+    for_each_leaf_node(lv.tree(), [&](auto const& node, auto const& tp) {
       nodeDataTransfer_[tp].preAdaptInit(lv, coeff, node);
     });
 
@@ -148,7 +148,7 @@ namespace AMDiS
 
       lv.bind(e);
       auto& treeContainer = it.first->second;
-      forEachLeafNode_(lv.tree(), [&](auto const& node, auto const& tp) {
+      for_each_leaf_node(lv.tree(), [&](auto const& node, auto const& tp) {
         nodeDataTransfer_[tp].cacheLocal(treeContainer[tp]);
       });
     }
@@ -201,7 +201,7 @@ namespace AMDiS
                 };
 
                 restrictLocalCompleted = true;
-                forEachLeafNode_(lv.tree(), [&](auto const& node, auto const& tp) {
+                for_each_leaf_node(lv.tree(), [&](auto const& node, auto const& tp) {
                   restrictLocalCompleted &=
                     nodeDataTransfer_[tp].restrictLocal(father, treeContainer[tp], xInChildCached,
                                                         childContainer[tp], init);
@@ -224,7 +224,7 @@ namespace AMDiS
     auto gv = basis_->gridView();
     auto lv = basis_->localView();
     auto const& idSet = gv.grid().localIdSet();
-    forEachLeafNode_(lv.tree(), [&](auto const& node, auto const& tp) {
+    for_each_leaf_node(lv.tree(), [&](auto const& node, auto const& tp) {
       nodeDataTransfer_[tp].postAdaptInit(lv, coeff, node);
     });
 
@@ -243,7 +243,7 @@ namespace AMDiS
       if (it != persistentContainer_.end()) {
         lv.bind(e);
         auto const& treeContainer = it->second;
-        forEachLeafNode_(lv.tree(), [&](auto const& node, auto const& tp) {
+        for_each_leaf_node(lv.tree(), [&](auto const& node, auto const& tp) {
           nodeDataTransfer_[tp].copyLocal(treeContainer[tp]);
         });
         finished_[index] = true;
@@ -275,7 +275,7 @@ namespace AMDiS
               return fatherGeo.local(childGeo.global(x));
             };
 
-            forEachLeafNode_(lv.tree(), [&](auto const& node, auto const& tp) {
+            for_each_leaf_node(lv.tree(), [&](auto const& node, auto const& tp) {
               nodeDataTransfer_[tp].prolongLocal(father, treeContainer[tp], xInFather, init);
             });
 

src/amdis/DirichletBC.hpp

@@ -11,8 +11,8 @@
 #include <amdis/BoundaryCondition.hpp>
 #include <amdis/common/Concepts.hpp>
 #include <amdis/typetree/RangeType.hpp>
+#include <amdis/typetree/Traversal.hpp>
 #include <amdis/typetree/TreeData.hpp>
-#include <amdis/typetree/Visitor.hpp>
 
 namespace AMDiS
 {

src/amdis/PeriodicBC.inc.hpp

@@ -196,7 +196,7 @@ std::vector<D> PeriodicBC<D,MI>::
 coords(Node const& tree, std::vector<std::size_t> const& localIndices) const
 {
   std::vector<D> dofCoords(localIndices.size());
-  AMDiS::forEachLeafNode_(tree, [&](auto const& node, auto const& tp)
+  for_each_leaf_node(tree, [&](auto const& node, auto const& tp)
   {
     std::size_t size = node.finiteElement().size();
     auto geometry = node.element().geometry();

src/amdis/ProblemStat.inc.hpp

@@ -177,7 +177,7 @@ void ProblemStat<Traits>::createMatricesAndVectors()
   rhs_ = std::make_shared<SystemVector>(*globalBasis_, NO_OPERATION);
 
   auto localView = globalBasis_->localView();
-  AMDiS::forEachNode_(localView.tree(), [&,this](auto const& node, auto treePath)
+  for_each_node(localView.tree(), [&,this](auto const& node, auto treePath)
   {
     std::string i = to_string(treePath);
     estimates_[i].resize(globalBasis_->gridView().indexSet().size(0));
@@ -205,7 +205,7 @@ void ProblemStat<Traits>::createMarker()
 {
   marker_.clear();
   auto localView = globalBasis_->localView();
-  AMDiS::forEachNode_(localView.tree(), [&,this](auto const& node, auto treePath)
+  for_each_node(localView.tree(), [&,this](auto const& node, auto treePath)
   {
     std::string componentName = name_ + "->marker[" + to_string(treePath) + "]";
 
@@ -232,7 +232,7 @@ void ProblemStat<Traits>::createFileWriter()
 {
   filewriter_.clear();
   auto localView = globalBasis_->localView();
-  forEachNode_(localView.tree(), [&,this](auto const& node, auto treePath)
+  for_each_node(localView.tree(), [&,this](auto const& node, auto treePath)
   {
     std::string componentName = name_ + "->output[" + to_string(treePath) + "]";
 
@@ -428,9 +428,9 @@ buildAfterAdapt(AdaptInfo& /*adaptInfo*/, Flag /*flag*/, bool asmMatrix, bool as
   rhs_->init(asmVector);
 
   auto localView = globalBasis_->localView();
-  forEachNode_(localView.tree(), [&,this](auto const& rowNode, auto rowTp) {
+  for_each_node(localView.tree(), [&,this](auto const& rowNode, auto rowTp) {
     auto rowBasis = Dune::Functions::subspaceBasis(*globalBasis_, rowTp);
-    forEachNode_(localView.tree(), [&,this](auto const& colNode, auto colTp) {
+    for_each_node(localView.tree(), [&,this](auto const& colNode, auto colTp) {
       auto colBasis = Dune::Functions::subspaceBasis(*globalBasis_, colTp);
       for (auto bc : dirichletBCs_[rowNode][colNode])
         bc->init(rowBasis, colBasis);
@@ -456,8 +456,8 @@ buildAfterAdapt(AdaptInfo& /*adaptInfo*/, Flag /*flag*/, bool asmMatrix, bool as
   systemMatrix_->finish(asmMatrix);
   rhs_->finish(asmVector);
 
-  forEachNode_(localView.tree(), [&,this](auto const& rowNode, auto) {
-    forEachNode_(localView.tree(), [&,this](auto const& colNode, auto) {
+  for_each_node(localView.tree(), [&,this](auto const& rowNode, auto) {
+    for_each_node(localView.tree(), [&,this](auto const& colNode, auto) {
       // finish boundary condition
       for (auto bc : dirichletBCs_[rowNode][colNode])
         bc->fillBoundaryCondition(*systemMatrix_, *solution_, *rhs_, rowNode, colNode);

src/amdis/common/ForEach.hpp

@@ -2,7 +2,6 @@
 
 #include <initializer_list>
 
-#include <amdis/common/Apply.hpp>
 #include <amdis/common/Index.hpp>
 #include <amdis/common/Range.hpp>
 
@@ -16,34 +15,52 @@ namespace AMDiS
       void ignored_evaluation(std::initializer_list<T>&&) { /* do nothing */ }
     }
 
+    template <std::size_t... I, class Tuple, class Functor>
+    constexpr void for_each(std::index_sequence<I...>, Tuple&& tuple, Functor&& f)
+    {
+      using std::get;
+#if AMDIS_HAS_EXPANSION_STATEMENTS
+      for... (auto&& t : tuple) { f(FWD(t)); }
+#elif AMDIS_HAS_CXX_FOLD_EXPRESSIONS
+      (f(get<I>(tuple)),...);
+#else
+      Impl_::ignored_evaluation<int>({0, (f(get<I>(tuple)), 0)...});
+#endif
+    }
+
     template <class Tuple, class Functor>
     constexpr void for_each(Tuple&& tuple, Functor&& f)
     {
-  #if AMDIS_HAS_CXX_FOLD_EXPRESSIONS
-      Tools::apply([f=std::move(f)](auto&&... t) { (f(FWD(t)),...); }, tuple);
-  #else
-      Tools::apply([f=std::move(f)](auto&&... t) {
-        Impl_::ignored_evaluation<int>({0, (f(FWD(t)), 0)...});
-      }, tuple);
-  #endif
+      Tools::for_each(std::make_index_sequence<Size_v<std::remove_reference_t<Tuple>>>{}, FWD(tuple), FWD(f));
+    }
+
+
+    template <std::size_t I0 = 0, std::size_t... I, class Functor>
+    constexpr void for_range(std::index_sequence<I...>, Functor&& f)
+    {
+#if AMDIS_HAS_CXX_FOLD_EXPRESSIONS
+      (f(index_t<I0+I>{}),...);
+#else
+      Impl_::ignored_evaluation<int>({0, (f(index_t<I0+I>{}), 0)...});
+#endif
     }
 
     template <std::size_t I0, std::size_t I1, class Functor>
     constexpr void for_range(index_t<I0> i0, index_t<I1> i1, Functor&& f)
     {
-      Tools::for_each(range_t<I0,I1>{}, FWD(f));
+      Tools::for_range<I0>(std::make_index_sequence<std::size_t(I1-I0)>{}, FWD(f));
     }
 
     template <std::size_t N, class Functor>
     constexpr void for_range(index_t<N>, Functor&& f)
     {
-      Tools::for_each(range_t<0,N>{}, FWD(f));
+      Tools::for_range(std::make_index_sequence<N>{}, FWD(f));
     }
 
     template <std::size_t I0, std::size_t I1, class Functor>
     constexpr void for_range(Functor&& f)
     {
-      Tools::for_each(range_t<I0,I1>{}, FWD(f));
+      Tools::for_range<I0>(std::make_index_sequence<std::size_t(I1-I0)>{}, FWD(f));
     }
 
   } // end namespace Tools

src/amdis/common/TypeTraits.hpp

@@ -65,6 +65,12 @@ namespace AMDiS
   template <class T>
   using owner = T;
 
+  /// A functor with no operation
+  struct NoOp
+  {
+    template <class... T>
+    constexpr void operator()(T&&...) const { /* no nothing */ }
+  };
 
   /// Create a unique_ptr by copy/move construction
   template <class Obj>

src/amdis/gridfunctions/DiscreteFunction.inc.hpp

@@ -147,7 +147,7 @@ LocalFunction::operator()(Domain const& x) const
 
   auto&& coefficients = *globalFunction_.dofVector_;
   auto&& nodeToRangeEntry = globalFunction_.nodeToRangeEntry_;
-  forEachLeafNode_(*subTree_, [&,this](auto const& node, auto const& tp)
+  for_each_leaf_node(*subTree_, [&,this](auto const& node, auto const& tp)
   {
     auto&& fe = node.finiteElement();
     auto&& localBasis = fe.localBasis();
@@ -193,7 +193,7 @@ GradientLocalFunction::operator()(Domain const& x) const
 
   auto&& coefficients = *globalFunction_.dofVector_;
   auto&& nodeToRangeEntry = globalFunction_.nodeToRangeEntry_;
-  forEachLeafNode_(*subTree_, [&,this](auto const& node, auto const& tp)
+  for_each_leaf_node(*subTree_, [&,this](auto const& node, auto const& tp)
   {
     // TODO: may DOFVectorView::Range to FieldVector type if necessary
     using LocalDerivativeTraits

src/amdis/linearalgebra/DOFMatrixBase.inc.hpp

@@ -2,7 +2,7 @@
 
 #include <amdis/Assembler.hpp>
 #include <amdis/LocalOperator.hpp>
-#include <amdis/typetree/Visitor.hpp>
+#include <amdis/typetree/Traversal.hpp>
 #include <amdis/utility/AssembleOperators.hpp>
 
 namespace AMDiS {
@@ -75,8 +75,8 @@ assemble(RowLocalView const& rowLocalView, ColLocalView const& colLocalView)
   auto const& element = rowLocalView.element();
   auto geometry = element.geometry();
 
-  forEachNode_(rowLocalView.tree(), [&](auto const& rowNode, auto) {
-    forEachNode_(colLocalView.tree(), [&](auto const& colNode, auto) {
+  for_each_node(rowLocalView.tree(), [&](auto const& rowNode, auto) {
+    for_each_node(colLocalView.tree(), [&](auto const& colNode, auto) {
       auto& matOp = operators_[rowNode][colNode];
       if (matOp) {
         matOp.bind(element, geometry);

src/amdis/linearalgebra/DOFVectorBase.inc.hpp

@@ -2,7 +2,7 @@
 
 #include <amdis/Assembler.hpp>
 #include <amdis/LocalOperator.hpp>
-#include <amdis/typetree/Visitor.hpp>
+#include <amdis/typetree/Traversal.hpp>
 #include <amdis/utility/AssembleOperators.hpp>
 
 namespace AMDiS {
@@ -66,7 +66,7 @@ assemble(LocalView const& localView)
   auto const& element = localView.element();
   auto geometry = element.geometry();
 
-  forEachNode_(localView.tree(), [&](auto const& node, auto) {
+  for_each_node(localView.tree(), [&](auto const& node, auto) {
     auto& rhsOp = operators_[node];
     if (rhsOp) {
       rhsOp.bind(element, geometry);

src/amdis/typetree/CMakeLists.txt

@@ -7,5 +7,4 @@ install(FILES
     TreeContainer.hpp
     TreeData.hpp
     TreePath.hpp
-    Visitor.hpp
 DESTINATION ${CMAKE_INSTALL_INCLUDEDIR}/amdis/typetree)

src/amdis/typetree/Traversal.hpp

@@ -3,139 +3,257 @@
 #include <dune/common/hybridutilities.hh>
 #include <dune/common/rangeutilities.hh>
 
+#include <dune/typetree/childextraction.hh>
 #include <dune/typetree/nodetags.hh>
 #include <dune/typetree/treepath.hh>
 #include <dune/typetree/visitor.hh>
 
 #include <amdis/common/ForEach.hpp>
+#include <amdis/common/Logical.hpp>
+#include <amdis/common/Range.hpp>
 #include <amdis/common/TypeTraits.hpp>
 
-namespace AMDiS
-{
-  // forward declaration of main engine struct
-  template <typename NodeTag, bool visit = true>
-  struct TraverseTree;
-
-
-  // Do not visit nodes the visitor is not interested in
-  template <typename NodeTag>
-  struct TraverseTree<NodeTag, false>
-  {
-    template <typename Node, typename Visitor, typename TreePath>
-    static void apply(const Node& node, const Visitor& visitor, TreePath const& tp)
-    {}
-  };
-
-#ifndef DOXYGEN
-
-  // some implementation details
-
-  template <class Node, class Index>
-  struct HybridChildType
-      : HybridChildType<std::remove_const_t<Node>, std::remove_const_t<Index>> {};
-
-  template <class Node>
-  struct HybridChildType<Node, std::size_t>
-  {
-    using type = typename Node::template Child<0>::Type;
-  };
-
-  template <class Node, std::size_t K>
-  struct HybridChildType<Node, Dune::index_constant<K>>
-  {
-    using type = typename Node::template Child<K>::Type;
-  };
-
-  template <class NodeTag, class Node>
-  constexpr std::size_t hybridDegree(NodeTag, Node const& node)
-  {
-    return Dune::TypeTree::degree(node);
-  }
-
-  template <class Node>
-  constexpr auto hybridDegree(Dune::TypeTree::CompositeNodeTag, Node const& node)
-  {
-    return Dune::index_constant<Node::CHILDREN>{};
-  }
-
-
-  template <std::size_t k, std::size_t n>
-  constexpr bool notLastChild(Dune::index_constant<k> const&, Dune::index_constant<n> const&)
-  {
-    return k < n-1;
-  }
-
-  constexpr bool notLastChild(std::size_t k, std::size_t n)
-  {
-    return k < n-1;
-  }
-
-#endif
-
-
-  template <class NodeTag>
-  struct TraverseTree<NodeTag, true>
-  {
-    template <typename N, typename V, typename TreePath>
-    static void apply(N&& n, V&& v, TreePath const& tp)
+// NOTE: backport of dune/typetree/traversal.hpp from Dune 2.7
+
+namespace AMDiS {
+
+    enum class TreePathType
     {
-      using Node = std::remove_reference_t<N>;
-      using Visitor = std::remove_reference_t<V>;
+      DYNAMIC, STATIC
+    };
+
+    namespace Impl {
+
+      // This is a constexpr version of the ternery operator c?t1:t1.
+      // In contrast to the latter the type of t1 and t2 can be different.
+      // Notice that std::conditional would not do the trick, because
+      // it only selects between types.
+      template<bool c, class T1, class T2,
+        std::enable_if_t<c, int> = 0>
+      constexpr auto conditionalValue(T1&& t1, T2&& t2) {
+        return std::forward<T1>(t1);
+      }
+
+      template<bool c, class T1, class T2,
+        std::enable_if_t<not c, int> = 0>
+      constexpr auto conditionalValue(T1&& t1, T2&& t2) {
+        return std::forward<T2>(t2);
+      }
+
+
+      /* The signature is the same as for the public applyToTree
+       * function in Dune::Typetree, despite the additionally passed
+       * treePath argument. The path passed here is associated to
+       * the tree and the relative paths of the children (wrt. to tree)
+       * are appended to this.  Hence the behavior of the public function
+       * is resembled by passing an empty treePath.
+       */
+
+      /*
+       * This is the overload for leaf traversal
+       */
+      template<class T, class TP, class V,
+        std::enable_if_t<remove_cvref_t<T>::isLeaf, int> = 0>
+      void apply_to_tree(T&& tree, TP treePath, V&& visitor)
+      {
+        visitor.leaf(tree, treePath);
+      }
+
+      /*
+       * This is the general overload doing child traversal.
+       */
+      template<class T, class TP, class V,
+        std::enable_if_t<not remove_cvref_t<T>::isLeaf, int> = 0>
+      void apply_to_tree(T&& tree, TP treePath, V&& visitor)
+      {
+        // Do we really want to take care for const-ness of the Tree
+        // when instantiating VisitChild below? I'd rather expect this:
+        // using Tree = remove_cvref_t<T>;
+        // using Visitor = remove_cvref_t<V>;
+        using Tree = std::remove_reference_t<T>;
+        using Visitor = std::remove_reference_t<V>;
+        visitor.pre(tree, treePath);
+
+        // Use statically encoded degree unless tree
+        // is a power node and dynamic traversal is requested.
+        constexpr auto useDynamicTraversal = (Tree::isPower and Visitor::treePathType==TreePathType::DYNAMIC);
+        auto degree = conditionalValue<useDynamicTraversal>(Tree::degree(), Dune::index_constant<Tree::degree()>{});
+
+        auto indices = Dune::range(degree);
+        Dune::Hybrid::forEach(indices, [&](auto i) {
+          auto childTP = Dune::TypeTree::push_back(treePath, i);
+          auto&& child = tree.child(i);
+          using Child = TYPEOF(child);
+
+          visitor.beforeChild(tree, child, treePath, i);
+
+          // This requires that visiotor.in(...) can always be instantiated,
+          // even if there's a single child only.
+          if (i>0)
+            visitor.in(tree, treePath);
+          static constexpr auto visitChild = Visitor::template VisitChild<Tree,Child,TP>::value;
+          #if AMDIS_HAS_CXX_CONSTEXPR_IF
+          if constexpr(visitChild)
+            applyToTree(child, childTP, visitor);
+          #else // AMDIS_HAS_CXX_CONSTEXPR_IF
+          Dune::Hybrid::ifElse(bool_t<visitChild>{}, [&] (auto /*id*/) {
+            applyToTree(child, childTP, visitor);
+          });
+          #endif // AMDIS_HAS_CXX_CONSTEXPR_IF
+          visitor.afterChild(tree, child, treePath, i);
+        });
+        visitor.post(tree, treePath);
+      }
+
+      // Overload for leaf nodes
+      template<class Tree, class TP, class Pre, class Leaf, class Post,
+        std::enable_if_t<remove_cvref_t<Tree>::isLeaf, int> = 0>
+      void for_each_node(Tree&& tree, TP treePath, Pre&& /*preFunc*/, Leaf&& leafFunc, Post&& /*postFunc*/)
+      {
+        leafFunc(tree, treePath);
+      }
+
+      // Overload for non-leaf nodes
+      // Forward declaration needed for recursion
+      template<class Tree, class TP, class Pre, class Leaf, class Post,
+        std::enable_if_t<not remove_cvref_t<Tree>::isLeaf,int> = 0>
+      void for_each_node(Tree&& tree, TP treePath, Pre&& preFunc, Leaf&& leafFunc, Post&& postFunc);
+
+      // Helper for power nodes
+      template<class Tree, class TP, class Pre, class Leaf, class Post, std::size_t... I,
+        std::enable_if_t<remove_cvref_t<Tree>::isPower, int> = 0>
+      void for_each_node_unfold(Tree&& tree, TP treePath, Pre&& preFunc, Leaf&& leafFunc, Post&& postFunc, std::index_sequence<I...>)
+      {
+        for (std::size_t i = 0; i < sizeof...(I); ++i)
+          Impl::for_each_node(tree.child(i), Dune::TypeTree::push_back(treePath, i), preFunc, leafFunc, postFunc);
+      }
 
-      v.pre(FWD(n),tp);
+      // Helper for composite nodes
+      template<class Tree, class TP, class Pre, class Leaf, class Post, std::size_t... I,
+        std::enable_if_t<not remove_cvref_t<Tree>::isPower, int> = 0>
+      void for_each_node_unfold(Tree&& tree, TP treePath, Pre&& preFunc, Leaf&& leafFunc, Post&& postFunc, std::index_sequence<I...>)
+      {
+        (void)std::initializer_list<int>{(
+          Impl::for_each_node(tree.child(Dune::index_constant<I>{}),
+            Dune::TypeTree::push_back(treePath, Dune::index_constant<I>{}), preFunc, leafFunc, postFunc),0)...
+        };
+      }
 
-      auto const deg = hybridDegree(NodeTag{}, n);
-      Dune::Hybrid::forEach(Dune::range(deg), [&](auto const _k)
+      /*
+       * Traverse tree and visit each node. The signature is the same
+       * as for the public for_each_node function in Dune::Typtree,
+       * despite the additionally passed treePath argument. The path
+       * passed here is associated to the tree and the relative
+       * paths of the children (wrt. to tree) are appended to this.
+       * Hence the behavior of the public function is resembled
+       * by passing an empty treePath.
+       *
+       * See also the specialization for leaf-nodes.
+       */
+      template<class Tree, class TP, class Pre, class Leaf, class Post,
+        std::enable_if_t<not remove_cvref_t<Tree>::isLeaf,int>>
+      void for_each_node(Tree&& tree, TP treePath, Pre&& preFunc, Leaf&& leafFunc, Post&& postFunc)
       {
-        // always call beforeChild(), regardless of the value of visit
-        v.beforeChild(FWD(n),n.child(_k),tp,_k);
+        auto indices = std::make_index_sequence<TYPEOF(tree)::degree()>{};
+        preFunc(tree, treePath);
+        Impl::for_each_node_unfold(tree, treePath, preFunc, leafFunc, postFunc, indices);
+        postFunc(tree, treePath);
+      }
+
+    } // namespace Impl
+
+
+    // ********************************************************************************
+    // Public Interface
+    // ********************************************************************************
 
-        // descend to child
-        using C = typename HybridChildType<Node, decltype(_k)>::type;
-        const bool visit = Visitor::template VisitChild<Node,C,TreePath>::value;
-        TraverseTree<Dune::TypeTree::NodeTag<C>,visit>::apply(n.child(_k),FWD(v),push_back(tp, _k));
+    //! Apply visitor to TypeTree.
+    /**
+     * \code
+     * #include <amdis/typetree/Traversal.hpp>
+     * \endcode
+     * This function applies the given visitor to the given tree. Both visitor and tree may be const
+     * or non-const (if the compiler supports rvalue references, they may even be a non-const temporary).
+     *