2.5.1   Syntax

We can make any of the parameters optional by following its keyword with the | operator and the parameter's default value within the square brackets. In the following example, we've given root_vertex a default of 42 and color_map a default of "hello, world".

namespace graphs { namespace core
{
  template <class ArgumentPack>
  void depth_first_search(ArgumentPack const& args)
  {
      std::cout << "graph:\t" << args[graph] << std::endl;
      std::cout << "visitor:\t" << args[visitor] << std::endl;
      std::cout << "root_vertex:\t" << args[root_vertex|42] << std::endl;
      std::cout << "index_map:\t" << args[index_map] << std::endl;
      std::cout << "color_map:\t" << args[color_map|"hello, world"] << std::endl;
  }
}} // graphs::core

Now we can invoke the function without supplying color_map or root_vertex:

core::depth_first_search((
  graph = 'G', index_map = "index", visitor = 6));

The call above would print:

graph:       G
visitor:     6
root_vertex: 42
index_map:   index
color_map:   hello, world

2.5.2   Getting More Realistic

Now it's time to put some more realistic defaults in place. We'll have to give up our print statements—at least if we want to see the defaults work—since, the default values of these parameters generally aren't printable.

Instead, we'll connect local variables to the arguments and use those in our algorithm:

namespace graphs { namespace core
{
  template <class ArgumentPack>
  void depth_first_search(ArgumentPack const& args)
  {
      Graph   g = args[graph];
      Visitor v = args[visitor|default-expression1];
      Vertex  s = args[root_vertex|default-expression2];
      Index   i = args[index_map|default-expression3];
      Color   c = args[visitor|default-expression4];

      …use g, v, s, i, and c to implement the algorithm…
  }
}} // graphs::core

We'll insert the default expressions in a moment, but first we need to come up with the types Graph, Visitor, Vertex, Index, and Color.

2.5.3   The binding Metafunction

To compute the type of a parameter we can use a Metafunction called binding:

binding<ArgumentPack, Keyword, Default = void>
{ typedef see text type; };

where Default is the type of the default argument, if any.

For example, to declare and initialize g above, we could write:

typedef typename parameter::binding<
  ArgumentPack,tag::graph
>::type Graph;

Graph g = args[graph];

As shown in the parameter table, graph has no default, so the binding invocation for Graph takes only two arguments. The default visitor is boost::dfs_visitor<>(), so the binding invocation for Visitor takes three arguments:

typedef typename parameter::binding<
  ArgumentPack,tag::visitor,boost::dfs_visitor<>
>::type Visitor;

Visitor v = args[visitor|boost::dfs_visitor<>()];

Note that the default visitor is supplied as a temporary instance of dfs_visitor. Because args[…] always yields a reference, making v a reference would cause it to bind to that temporary, and immediately dangle. Therefore, it's crucial that we passed dfs_visitor<>, and not dfs_visitor<> const&, as the last argument to binding.

Sometimes there's no need to use binding at all. The root_vertex argument is required to be of the graph's vertex_descriptor type,³ so we can just use that knowledge to bypass binding altogether.

typename boost::graph_traits<Graph>::vertex_descriptor
  s = args[root_vertex|*vertices(g).first];

2.5.4   Beyond Ordinary Default Arguments

Here's how you might write the declaration for the index_map parameter:

typedef typename parameter::binding<
    ArgumentPack
  , tag::index_map
  , typename boost::property_map<Graph, vertex_index_t>::const_type
>::type Index;

Index i = args[index_map|get(boost::vertex_index,g)];

Notice two capabilities we've gained over what plain C++ default arguments provide:

1. The default value of the index parameter depends on the value of the graph parameter. That's illegal in plain C++:

   void f(int graph, int index = graph + 1); // error
   

2. The index parameter has a useful default, yet it is templated and its type can be deduced when an index argument is explicitly specified by the caller. In plain C++, you can specify a default value for a parameter with deduced type, but it's not very useful:

   template <class Index>
   int f(Index index = 42);  // OK
   int y = f();                // error; can't deduce Index
   

2.6.1   Describing the Positional Argument Order

First, we'll need to build a type that describes the allowed parameters and their ordering when passed positionally. This type is known as a ParameterSpec (MSVC6.x users see this note):

namespace graphs
{
  typedef parameter::parameters<
      tag::graph
    , tag::visitor
    , tag::root_vertex
    , tag::index_map
    , tag::color_map
  > dfs_params;
}

The parameters template supplies a function-call operator that groups all its arguments into an ArgumentPack. Any arguments passed to it without a keyword label will be associated with a parameter according to its position in the ParameterSpec. So for example, given an object p of type dfs_params,

p('G', index_map=1)

yields an ArgumentPack whose graph parameter has a value of 'G', and whose index_map parameter has a value of 1.

2.6.2   Forwarding Functions

Next we need a family of overloaded depth_first_search function templates that can be called with anywhere from one to five arguments. These forwarding functions will invoke an instance of dfs_params as a function object, passing their parameters to its operator() and forwarding the result on to core::depth_first_search:

namespace graphs
{
  template <class A0>
  void depth_first_search(A0 const& a0)
  {
     core::depth_first_search(dfs_params()(a0));
  }

  template <class A0, class A1>
  void depth_first_search(A0 const& a0, A1 const& a1)
  {
     core::depth_first_search(dfs_params()(a0,a1));
  } 
  .
  .
  .
 
  template <class A0, class A1, …class A4>
  void depth_first_search(A0 const& a0, A1 const& a1, …A4 const& a4)
  {
     core::depth_first_search(dfs_params()(a0,a1,a2,a3,a4));
  }
}

That's it! We can now call graphs::depth_first_search with from one to five arguments passed positionally or via keyword.

2.6.3   “Out” Parameters

Well, that's not quite it. When passing arguments by keyword, the keyword object's assignment operator yields a temporary ArgumentPack object. A conforming C++ compiler will refuse to bind a non-const reference to a temporary, so to support a keyword interface for all arguments, the overload set above must take its arguments by const reference. On the other hand—as you may recall from the parameter table—color_map is an “out” parameter, so it really should be passed by non-const reference.

A keyword object has a pair of operator= overloads that ensure we can pass anything—temporary or not, const or not—by name, while preserving the mutability of non-temporaries:

template <class A>                  // handles non-const, 
ArgumentPack operator=(A&);       // non-temporary objects

template <class A>                  // handles const objects
ArgumentPack operator=(A const&); // and temporaries

However, when an “out” parameter is passed positionally, there's no keyword object involved. With our depth_first_search overload set above, the color_map will be passed by const reference, and compilation will fail when mutating operations are used on it. The simple solution is to add another overload that takes a non-const reference in the position of the “out” parameter:

template <class A0, class A1, …class A4>
void depth_first_search(A0 const& a0, A1 const& a1, …A4& a4)
{
    core::depth_first_search(dfs_params()(a0,a1,a2,a3,a4));
}

That approach works nicely because there is only one “out” parameter and it is in the last position. If color_map had been the first parameter, we would have needed ten overloads. In the worst case—where the function has five “out” parameters—2⁵ or 32 overloads would be required. This “forwarding problem” is well-known to generic library authors, and the C++ standard committee is working on a proposal to address it. In the meantime, you might consider using Boost.Preprocessor to generate the overloads you need.

If it is impractical for you to generate or write the overloads that would be required for positional “out” arguments to be passed directly, you still have the option to ask users to pass them through boost::ref, which will ensure that the algorithm implementation sees a non-const reference:

depth_first_search(g, v, s, i, boost::ref(c));

2.6.4   Generating Forwarding Functions with Macros

To remove some of the tedium of writing overloaded forwarding functions, the library supplies a macro, suitably located in boost/parameter/macros.hpp, that will generate free function overloads for you:

BOOST_PARAMETER_FUN(void, depth_first_search, 1, 5, dfs_params);

will generate a family of five depth_first_search overloads, in the current scope, that pass their arguments through dfs_params. Instead of core::depth_first_search, these overloads will forward the ArgumentPack on to a function called depth_first_search_with_named_params, also in the current scope. It's up to you to implement that function. You could simply transplant the body of core::depth_first_search into depth_first_search_with_named_params if you were going to use this approach.

Note that BOOST_PARAMETER_FUN only takes arguments by const reference, so you will have to add any additional overloads required to handle positional “out” parameters yourself. We are looking into providing a more sophisticated set of macros to address this problem and others, for an upcoming release of Boost.

2.7.1   Updating the ParameterSpec

This sort of overload control can be accomplished in C++ by taking advantage of the SFINAE (Substitution Failure Is Not An Error) rule.⁶ You can take advantage of the Parameter library's built-in SFINAE support by using the following class templates in your ParameterSpec:

template< class KeywordTag, class Predicate = unspecified >
struct required;

template< class KeywordTag, class Predicate = unspecified >
struct optional;

Instead of using keyword tags directly, we can wrap them in required and optional to indicate which function parameters are required, and optionally pass Predicates to describe the type requirements for each function parameter. The Predicate argument must be a unary MPL lambda expression that, when applied to the actual type of the argument, indicates whether that argument type meets the function's requirements for that parameter position.

For example, let's say we want to restrict depth_first_search() so that the graph parameter is required and the root_vertex parameter is convertible to int. We might write:

#include <boost/type_traits/is_convertible.hpp>
#include <boost/mpl/placeholders.hpp>
namespace graphs
{
  using namespace boost::mpl::placeholders;

  struct dfs_params
    : parameter::parameters<
          parameter::required<tag::graph>
        , parameter::optional<tag::visitor>
        , parameter::optional<
              tag::root_vertex, boost::is_convertible<_,int>
          >
        , parameter::optional<tag::index_map>
        , parameter::optional<tag::color_map>
      >
  {};
}

2.7.2   Applying SFINAE to the Overload Set

Now we add a special defaulted argument to each of our depth_first_search overloads:

namespace graphs
{
  template <class A0>
  void depth_first_search(
      A0 const& a0
    , typename dfs_params::match<A0>::type p = dfs_params())
  {
     core::depth_first_search(p(a0));
  }

  template <class A0, class A1>
  void depth_first_search(
      A0 const& a0, A1 const& a1
    , typename dfs_params::match<A0,A1>::type p = dfs_params())
  {
     core::depth_first_search(p(a0,a1));
  } 
  .
  .
  .
 
  template <class A0, class A1, …class A4>
  void depth_first_search(
      A0 const& a0, A1 const& a1, …A4 const& A4
    , typename dfs_params::match<A0,A1,A2,A3,A4>::type p = dfs_params())
  {
     core::depth_first_search(p(a0,a1,a2,a3,a4));
  }
}

These additional parameters are not intended to be used directly by callers; they merely trigger SFINAE by becoming illegal types when the name argument is not convertible to const char*. The BOOST_PARAMETER_FUN macro described earlier adds these extra function parameters for you (Borland users see this note).

2.7.3   Reducing Boilerplate With Macros

The library provides a macro you can use to eliminate some of the repetetiveness of the declaring the optional parameters. BOOST_PARAMETER_MATCH takes three arguments: the ParameterSpec, a Boost.Preprocessor sequence of the function argument types, and a name for the defaulted function parameter (p, above), and it generates the appropriate defaulted argument. So we could shorten the overload set definition as follows:

namespace graphs
{
  template <class A0>
  void depth_first_search(
      A0 const& a0
    , BOOST_PARAMETER_MATCH(dfs_params, (A0), p))
  {
     core::depth_first_search(p(a0));
  }

  template <class A0, class A1>
  void depth_first_search(
      A0 const& a0, A1 const& a1
    , BOOST_PARAMETER_MATCH(dfs_params, (A0)(A1), p))
  {
     core::depth_first_search(p(a0,a1));
  } 
  .
  .
  .
 
  template <class A0, class A1, …class A4>
  void depth_first_search(
      A0 const& a0, A1 const& a1, …A4 const& A4
    , BOOST_PARAMETER_MATCH(dfs_params, (A0)(A1)…(A4), p))
  {
     core::depth_first_search(p(a0,a1,a2,a3,a4));
  }
}

2.8.1   Eliminating Copies

The library has no way to know whether an explicitly-supplied argument is expensive to copy (or even if it is copyable at all), so binding<…,k,…>::type is always a reference type when the k parameter is supplied by the caller. Since args[…] yields a reference to the actual argument, color will be bound to the actual color_map argument and no copying will be done.

As described above, because the default is a temporary, it's important that color be a non-reference when the default is used. In that case, the default value will be copied into color. If we store the default in a named variable, though, color can be a reference, thereby eliminating the copy:

default_color_map default_color(num_vertices(g),i);

typename parameter::binding<
    ArgumentPack
  , tag::color_map
  , default_color_map&
>::type color = args[color_map|default_color];

2.8.2   Lazy Default Computation

Of course it's nice to avoid copying default_color, but the more important cost is that of constructing it in the first place. A vector_property_map is cheap to copy, since it holds its elements via a shared_ptr. On the other hand, construction of default_color costs at least two dynamic memory allocations and num_vertices(g) copies; it would be better to avoid doing this work when the default value won't be needed.

To that end, the library allows us to supply a callable object that—if no argument was supplied by the caller—will be invoked to construct the default value. Instead of following the keyword with the | operator, we'll use || and follow it with a nullary (zero-argument) function object that constructs a default_color_map. Here, we build the function object using Boost.Lambda:⁴

// After #include <boost/lambda/construct.hpp>
typename parameter::binding<
    ArgumentPack
  , tag::color_map
  , default_color_map
>::type color = args[
  color_map
  || boost::lambda::construct<default_color_map>(num_vertices(g),i)
];

2.8.3   Default Forwarding

Types that are expensive to construct yet cheap to copy aren't all that typical, and even copying the color map is more expensive than we might like. It might be nice to avoid both needless construction and needless copying of the default color map. The simplest way to achieve that is to avoid naming it altogether, at least not in core::depth_first_search. Instead, we'll introduce another function template to implement the actual algorithm:

namespace graphs { namespace core
{
  template <class G, class V, class S, class I, class C>
  void dfs_impl(G& g, V& v, S& s, I& i, C& c)
  {
      …actual algorithm implementation…
  }
}}

Then, in core::depth_first_search, we'll simply forward the result of indexing args to core::dfs_impl:

core::dfs_impl( 
    g,v,s,i
  , args[
      color_map
      || boost::lambda::construct<default_color_map>(num_vertices(g),i)
    ]);

In real code, after going to the trouble to write dfs_impl, we'd probably just forward all the arguments.

2.8.4   Dispatching Based on the Presence of a Default

In fact, the Graph library itself constructs a slightly different color_map, to avoid even the overhead of initializing a shared_ptr:

std::vector<boost::default_color_type> 
  color_vec(num_vertices(g));

boost::iterator_property_map<
    typename std::vector<
       boost::default_color_type
    >::iterator
  , Index
> c(color_vec.begin(), i);

To avoid instantiating that code when it isn't needed, we'll have to find a way to select different function implementations, at compile time, based on whether a color_map argument was supplied. By using tag dispatching on the presence of a color_map argument, we can do just that:

#include <boost/type_traits/is_same.hpp>
#include <boost/mpl/bool.hpp>

namespace graphs { namespace core {

  template <class ArgumentPack>
  void dfs_dispatch(ArgumentPack& args, mpl::true_)
  {
      …use the color map computed in the previous example…
  }
  
  template <class ArgumentPack>
  void dfs_dispatch(ArgumentPack& args, mpl::false_)
  {
      …use args[color]…
  }
  
  template <class ArgumentPack>
  void depth_first_search(ArgumentPack& args)
  {
      typedef typename binding<args,tag::color>::type color_;
      core::dfs_dispatch(args, boost::is_same<color_,void>());
  }
}}

We've used the fact that the default for binding's third argument is void: because specializations of is_same are bool-valued MPL Integral Constants derived either from mpl::true_ or mpl::false_, the appropriate dfs_dispatch implementation will be selected.