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From Chapter 3 of C++ Template Metaprogramming by David Abrahams and Aleksey Gurtovoy. ISBN: 0321227255. Copyright (c) 2005 by Pearson Education, Inc. Reprinted with permission.
With the foundation laid so far, we're ready to explore one of the most basic uses of template metaprogramming techniques: adding static type checking to traditionally unchecked operations. We'll look at a practical example from science and engineering that can find applications in almost any numerical code. Along the way you'll learn some important new concepts and get a taste of metaprogramming at a high level using the MPL.
The first rule of doing physical calculations on paper is that the numbers being manipulated don't stand alone: most quantities have attached dimensions, to be ignored at our peril. As computations become more complex, keeping track of dimensions is what keeps us from inadvertently assigning a mass to what should be a length or adding acceleration to velocity—it establishes a type system for numbers.
Manual checking of types is tedious, and as a result, it's also errorprone. When human beings become bored, their attention wanders and they tend to make mistakes. Doesn't type checking seem like the sort of job a computer might be good at, though? If we could establish a framework of C++ types for dimensions and quantities, we might be able to catch errors in formulae before they cause serious problems in the real world.
Preventing quantities with different dimensions from interoperating isn't hard; we could simply represent dimensions as classes that only work with dimensions of the same type. What makes this problem interesting is that different dimensions can be combined, via multiplication or division, to produce arbitrarily complex new dimensions. For example, take Newton's law, which relates force to mass and acceleration:
F = ma
Since mass and acceleration have different dimensions, the dimensions of force must somehow capture their combination. In fact, the dimensions of acceleration are already just such a composite, a change in velocity over time:
dv/dt
Since velocity is just change in distance (l) over time (t), the fundamental dimensions of acceleration are:
(l/t)/t = l/t^{2}
And indeed, acceleration is commonly measured in "meters per second squared." It follows that the dimensions of force must be:
ml/t^{2}
and force is commonly measured in kg(m/s^{2}), or "kilogrammeters per second squared." When multiplying quantities of mass and acceleration, we multiply their dimensions as well and carry the result along, which helps us to ensure that the result is meaningful. The formal name for this bookkeeping is dimensional analysis, and our next task will be to implement its rules in the C++ type system. John Barton and Lee Nackman were the first to show how to do this in their seminal book, Scientific and Engineering C++ [BNack94]. We will recast their approach here in metaprogramming terms.
[BNack94]  John J. Barton and Lee R. Nackman, Scientific and Engineering C++: an introduction with advanced techniques and examples ISBN 0201533936, Addison Wesley, Reading Massachusetts, 1994 
An international standard called Système International d'Unites (SI), breaks every quantity down into a combination of the dimensions mass, length (or position), time, charge, temperature, intensity, and angle. To be reasonably general, our system would have to be able to represent seven or more fundamental dimensions. It also needs the ability to represent composite dimensions which, like force, are built through multiplication or division of the fundamental ones.
In general, a composite dimension is the product of powers of
fundamental dimensions.[1] If we were going to represent
these powers for manipulation at runtime, we could use an array
of seven int
s, with each position in the array
holding the power of a different fundamental dimension:
typedef int dimension[7]; // m l t ... dimension const mass = {1, 0, 0, 0, 0, 0, 0}; dimension const length = {0, 1, 0, 0, 0, 0, 0}; dimension const time = {0, 0, 1, 0, 0, 0, 0}; ...
In that representation, force would be:
dimension const force = {1, 1, 2, 0, 0, 0, 0};
that is, mlt^{2}. However, if we want to get dimensions into the type system, these arrays won't do the trick: they're all the same type! Instead, we need types that themselves represent sequences of numbers, so that two masses have the same type and a mass is a different type from a length.
Fortunately, the MPL provides us with a collection of type sequences. For example, we can build a sequence of the builtin signed integral types this way:
#include <boost/mpl/vector.hpp> typedef boost::mpl::vector< signed char, short, int, long> signed_types;
How can we use a type sequence to represent numbers? Just as
numerical metafunctions pass and return wrapper types
having a nested ::value
, so numerical sequences are
really sequences of wrapper types (another example of
polymorphism). To make this sort of thing easier, MPL supplies
the int_<N>
class template, which presents its
integral argument as a nested ::value
:
#include <boost/mpl/int.hpp> namespace mpl = boost::mpl; // namespace alias static int const five = mpl::int_<5>::value;
namespace alias = namespacename;
declares alias to be a synonym for
namespacename. Many examples in this book will use
mpl::
to indicate boost::mpl::
, but
will omit the alias that makes it legal C++.
In fact, the library contains a whole suite of integral
constant wrappers such as long_
and
bool_
, each one wrapping a different type of
integral constant within a class template.
Now we can build our fundamental dimensions:
typedef mpl::vector< mpl::int_<1>, mpl::int_<0>, mpl::int_<0>, mpl::int_<0> , mpl::int_<0>, mpl::int_<0>, mpl::int_<0> > mass; typedef mpl::vector< mpl::int_<0>, mpl::int_<1>, mpl::int_<0>, mpl::int_<0> , mpl::int_<0>, mpl::int_<0>, mpl::int_<0> > length; ...
Whew! That's going to get tiring pretty quickly. Worse, it's hard to read and verify: The essential information, the powers of each fundamental dimension, is buried in repetitive syntactic "noise." Accordingly, MPL supplies integral sequence wrappers that allow us to write:
#include <boost/mpl/vector_c.hpp> typedef mpl::vector_c<int,1,0,0,0,0,0,0> mass; typedef mpl::vector_c<int,0,1,0,0,0,0,0> length; // or position typedef mpl::vector_c<int,0,0,1,0,0,0,0> time; typedef mpl::vector_c<int,0,0,0,1,0,0,0> charge; typedef mpl::vector_c<int,0,0,0,0,1,0,0> temperature; typedef mpl::vector_c<int,0,0,0,0,0,1,0> intensity; typedef mpl::vector_c<int,0,0,0,0,0,0,1> angle;
Even though they have different types, you can think of these
mpl::vector_c
specializations as being equivalent to
the more verbose versions above that use
mpl::vector
.
If we want, we can also define a few composite dimensions:
// base dimension: m l t ... typedef mpl::vector_c<int,0,1,1,0,0,0,0> velocity; // l/t typedef mpl::vector_c<int,0,1,2,0,0,0,0> acceleration; // l/(t^{2}) typedef mpl::vector_c<int,1,1,1,0,0,0,0> momentum; // ml/t typedef mpl::vector_c<int,1,1,2,0,0,0,0> force; // ml/(t^{2})
And, incidentally, the dimensions of scalars (like pi) can be described as:
typedef mpl::vector_c<int,0,0,0,0,0,0,0> scalar;
The types listed above are still pure metadata; to typecheck
real computations we'll need to somehow bind them to our runtime
data. A simple numeric value wrapper, parameterized on the
datatype T
and on its dimensions, fits the bill:
template <class T, class Dimensions> struct quantity { explicit quantity(T x) : m_value(x) {} T value() const { return m_value; } private: T m_value; };
Now we have a way to represent numbers associated with dimensions. For instance, we can say:
quantity<float,length> l( 1.0f ); quantity<float,mass> m( 2.0f );
Note that Dimensions
doesn't appear anywhere in
the definition of quantity
outside the template
parameter list; its only role is to ensure that
l
and m
have different types. Because
they do, we cannot make the mistake of assigning a length to a
mass:
m = l; // compiletime type error
We can now easily write the rules for addition and subtraction, since the dimensions of the arguments must always match.
template <class T, class D> quantity<T,D> operator+(quantity<T,D> x, quantity<T,D> y) { return quantity<T,D>(x.value() + y.value()); } template <class T, class D> quantity<T,D> operator(quantity<T,D> x, quantity<T,D> y) { return quantity<T,D>(x.value()  y.value()); }
These operators enable us to write code like:
quantity<float,length> len1( 1.0f ); quantity<float,length> len2( 2.0f ); len1 = len1 + len2; // OK
but prevent us from trying to add incompatible dimensions:
len1 = len2 + quantity<float,mass>( 3.7f ); // error
Multiplication is a bit more complicated than addition and subtraction. So far, the dimensions of the arguments and results have all been identical, but when multiplying, the result will usually have different dimensions from either of the arguments. For multiplication, the relation:
(x^{a})(x^{b}) == x ^{(a + b)}
implies that the exponents of the result dimensions should be the sum of corresponding exponents from the argument dimensions. Division is similar, except that the sum is replaced by a difference.
To combine corresponding elements from two sequences, we'll
use MPL's transform
algorithm.
transform
is a metafunction that iterates through
two input sequences in parallel, passing an element from each
sequence to an arbitrary binary metafunction, and placing the
result in an output sequence.
template <class Sequence1, class Sequence2, class BinaryOperation> struct transform; // returns a Sequence
The signature above should look familiar if you're acquainted
with the STL transform
algorithm that accepts two
runtime sequences as inputs:
template < class InputIterator1, class InputIterator2 , class OutputIterator, class BinaryOperation > void transform( InputIterator1 start1, InputIterator2 finish1 , InputIterator2 start2 , OutputIterator result, BinaryOperation func);
Now we just need to pass a BinaryOperation
that
adds or subtracts in order to multiply or divide dimensions with
mpl::transform
. If you look through the MPL
reference manual, you'll come across plus
and
minus
metafunctions that do just what you'd
expect:
#include <boost/static_assert.hpp> #include <boost/mpl/plus.hpp> #include <boost/mpl/int.hpp> namespace mpl = boost::mpl; BOOST_STATIC_ASSERT(( mpl::plus< mpl::int_<2> , mpl::int_<3> >::type::value == 5 ));
BOOST_STATIC_ASSERT
is a macro that causes a compilation error if its argument
is false. The double parentheses are required because the C++
preprocessor can't parse templates: it would otherwise be
fooled by the comma into treating the condition as two separate
macro arguments. Unlike its runtime analogue
assert(...)
, BOOST_STATIC_ASSERT
can
also be used at class scope, allowing us to put assertions in
our metafunctions. See Chapter 8 for an indepth
discussion.
At this point it might seem as though we have a solution, but
we're not quite there yet. A naive attempt to apply the
transform
algorithm in the implementation of
operator*
yields a compiler error:
#include <boost/mpl/transform.hpp> template <class T, class D1, class D2> quantity< T , typename mpl::transform<D1,D2,mpl::plus>::type > operator*(quantity<T,D1> x, quantity<T,D2> y) { ... }
It fails because the protocol says that metafunction arguments
must be types, and plus
is not a type, but a class
template. Somehow we need to make metafunctions like
plus
fit the metadata mold.
One natural way to introduce polymorphism between metafunctions and metadata is to employ the wrapper idiom that gave us polymorphism between types and integral constants. Instead of a nested integral constant, we can use a class template nested within a metafunction class:
struct plus_f { template <class T1, class T2> struct apply { typedef typename mpl::plus<T1,T2>::type type; }; };
A Metafunction Class is a class with a
publicly accessible nested metafunction called
apply
.
Whereas a metafunction is a template but not a type, a metafunction class wraps that template within an ordinary nontemplated class, which is a type. Since metafunctions operate on and return types, a metafunction class can be passed as an argument to, or returned from, another metafunction.
Finally, we have a BinaryOperation
type that we
can pass to transform
without causing a compilation
error:
template <class T, class D1, class D2> quantity< T , typename mpl::transform<D1,D2,plus_f>::type // new dimensions > operator*(quantity<T,D1> x, quantity<T,D2> y) { typedef typename mpl::transform<D1,D2,plus_f>::type dim; return quantity<T,dim>( x.value() * y.value() ); }
Now, if we want to compute the force exterted by gravity on a 5 kilogram laptop computer, that's just the acceleration due to gravity (9.8 m/sec^{2}) times the mass of the laptop:
quantity<float,mass> m(5.0f); quantity<float,acceleration> a(9.8f); std::cout << "force = " << (m * a).value();
Our operator*
multiplies the runtime values
(resulting in 6.0f), and our metaprogram code uses
transform
to sum the metasequences of fundamental
dimension exponents, so that the result type contains a
representation of a new list of exponents, something like:
vector_c<int,1,1,2,0,0,0,0>
However, if we try to write:
quantity<float,force> f = m * a;
we'll run into a little problem. Although the result of
m
* a does indeed represent a force with exponents of
mass, length, and time 1, 1, and 2 respectively, the type
returned by transform
isn't a specialization of
vector_c
. Instead, transform
works
generically on the elements of its inputs and builds a new
sequence with the appropriate elements: a type with many of the
same sequence properties as
vector_c<int,1,1,2,0,0,0,0>
, but with a
different C++ type altogether. If you want to see the type's full
name, you can try to compile the example yourself and look at the
error message, but the exact details aren't important. The point
is that force
names a different type, so the
assignment above will fail.
In order to resolve the problem, we can add an implicit
conversion from the multiplication's result type to
quantity<float,force>
. Since we can't predict
the exact types of the dimensions involved in any computation,
this conversion will have to be templated, something like:
template <class T, class Dimensions> struct quantity { // converting constructor template <class OtherDimensions> quantity(quantity<T,OtherDimensions> const& rhs) : m_value(rhs.value()) { } ...
Unfortunately, such a general conversion undermines our whole purpose, allowing nonsense such as:
// Should yield a force, not a mass! quantity<float,mass> bogus = m * a;
Luckily, we can correct that problem using another MPL
algorithm, equal
, which tests that two sequences
have the same elements:
template <class OtherDimensions> quantity(quantity<T,OtherDimensions> const& rhs) : m_value(rhs.value()) { BOOST_STATIC_ASSERT(( mpl::equal<Dimensions,OtherDimensions>::type::value )); }
Now, if the dimensions of the two quantities fail to match, the assertion will cause a compilation error.
Division is similar to multiplication, but instead of adding
exponents, we must subtract them. Rather than writing out a near
duplicate of plus_f
, we can use the following trick
to make minus_f
much simpler:
struct minus_f { template <class T1, class T2> struct apply : mpl::minus<T1,T2> {}; };
Here minus_f::apply
uses inheritance to expose
the nested type
of its base class,
mpl::minus
, so we don't have to write:
typedef typename ...::type type
We don't have to write typename
here (in fact, it
would be illegal), because the compiler knows that dependent
names in apply
's initializer list must be base
classes.[2] This powerful
simplification is known as metafunction
forwarding; we'll apply it often as the book goes
on.[3]
Syntactic tricks notwithstanding, writing trivial classes to
wrap existing metafunctions is going to get boring pretty
quickly. Even though the definition of minus_f
was
far less verbose than that of plus_f
, it's still an
awful lot to type. Fortunately, MPL gives us a much
simpler way to pass metafunctions around. Instead of building a
whole metafunction class, we can invoke transform
this way:
typename mpl::transform<D1,D2, mpl::minus<_1,_2> >::type
Those funny looking arguments (_1
and
_2
) are known as placeholders, and
they signify that when the transform
's
BinaryOperation
is invoked, its first and second
arguments will be passed on to minus
in the
positions indicated by _1
and _2
,
respectively. The whole type mpl::minus<_1,_2>
is known as a placeholder expression.
MPL's placeholders are in the mpl::placeholders
namespace and defined in
boost/mpl/placeholders.hpp
. In this book we will
usually assume that you have written:
#include<boost/mpl/placeholders.hpp> using namespace mpl::placeholders;
so that they can be accessed without qualification.
Here's our division operator written using placeholder expressions:
template <class T, class D1, class D2> quantity< T , typename mpl::transform<D1,D2,mpl::minus<_1,_2> >::type > operator/(quantity<T,D1> x, quantity<T,D2> y) { typedef typename mpl::transform<D1,D2,mpl::minus<_1,_2> >::type dim; return quantity<T,dim>( x.value() / y.value() ); }
This code is considerably simpler. We can simplify it even further by factoring the code that calculates the new dimensions into its own metafunction:
template <class D1, class D2> struct divide_dimensions : mpl::transform<D1,D2,mpl::minus<_1,_2> > // forwarding again {}; template <class T, class D1, class D2> quantity<T, typename divide_dimensions<D1,D2>::type> operator/(quantity<T,D1> x, quantity<T,D2> y) { return quantity<T, typename divide_dimensions<D1,D2>::type>( x.value() / y.value()); }
Now we can verify our "forceonalaptop" computation by reversing it, as follows:
quantity<float,mass> m2 = f/a; float rounding_error = std::abs((m2  m).value());
If we got everything right, rounding_error
should
be very close to zero. These are boring calculations, but they're
just the sort of thing that could ruin a whole program (or worse)
if you got them wrong. If we had written a/f
instead
of f/a
, there would have been a compilation error,
preventing a mistake from propagating throughout our program.
In the previous section we used two different
forms—metafunction classes and placeholder expressions—to pass
and return metafunctions just like any other metadata. Bundling
metafunctions into "first class metadata" allows
transform
to perform an infinite variety of
different operations: in our case, multiplication and division of
dimensions. Though the idea of using functions to manipulate
other functions may seem simple, its great power and flexibility
[Hudak89] has earned it a fancy title:
higherorder functional programming. A function
that operates on another function is known as a
higherorder function. It follows that
transform
is a higherorder metafunction: a
metafunction that operates on another metafunction.
[Hudak89]  Paul Hudak, "Conception, evolution, and application of functional programming languages," ACM Press New York, NY, USA Pages: 359  411, 1989 ISSN:03600300 http://doi.acm.org/10.1145/72551.72554 
Now that we've seen the power of higherorder metafunctions at
work, it would be good to be able to create new ones. In order to
explore the basic mechanisms, let's try a simple example. Our
task is to write a metafunction called twice
,
which—given a unary metafunction f and arbitrary
metadata x—computes:
twice(f, x) := f(f(x))
This might seem like a trivial example, and in fact it is. You
won't find much use for twice
in real code. We hope
you'll bear with us anyway: Because it doesn't do much more than
accept and invoke a metafunction, twice
captures all
the essential elements of "higherorderness" without any
distracting details.
If f is a metafunction class, the definition of
twice
is straightforward:
template <class F, class X> struct twice { typedef typename F::template apply<X>::type once; // f(x) typedef typename F::template apply<once>::type type; // f(f(x)) };
Or, applying metafunction forwarding:
template <class F, class X> struct twice : F::template apply< typename F::template apply<X>::type > {};
The C++ standard requires the template
keyword
when we use a dependent name that refers to a
member template. F::apply
may or may not name a
template, depending on the particular F
that is passed. See Appendix B for more information about
template
.
Given the need to sprinkle our code with the
template
keyword, it would be nice to reduce the
syntactic burden of invoking metafunction classes. As usual, the
solution is to factor the pattern into a metafunction:
template <class UnaryMetaFunctionClass, class Arg> struct apply1 : UnaryMetaFunctionClass::template apply<Arg> {};
Now twice
is just:
template <class F, class X> struct twice : apply1<F, typename apply1<F,X>::type> {};
To see twice
at work, we can apply it to a little
metafunction class built around the add_pointer
metafunction:
struct add_pointer_f { template <class T> struct apply : boost::add_pointer<T> {}; };
Now we can use twice
with
add_pointer_f
to build pointerstopointers:
BOOST_STATIC_ASSERT(( boost::is_same< twice<add_pointer_f, int>::type , int** >::value ));
Our implementation of twice
already works with
metafunction classes. Ideally, we would like it to work with
placeholder expressions too, much the same as
mpl::transform
allows us to pass either form. For
example, we would like to be able to write:
template <class X> struct two_pointers : twice<boost::add_pointer<_1>, X> {};
But when we look at the implementation of
boost::add_pointer
, it becomes clear that the
current definition of twice
can't work that way.
template <class T> struct add_pointer { typedef T* type; };
To be invokable by twice
,
boost::add_pointer<_1>
would have to be a
metafunction class, along the lines of
add_pointer_f
. Instead, it's just a nullary
metafunction returning the almost senseless type
_1*
. Any attempt to use two_pointers
will fail when apply1
reaches for a nested
::apply
metafunction in
boost::add_pointer<_1>
and finds that it
doesn't exist.
We've determined that we don't get the behavior we want
automatically, so what next? Since mpl::transform
can do this sort of thing, there ought to be a way for us to do
it too—and so there is.
lambda
MetafunctionWe can generate a metafunction class from
boost::add_pointer<_1>
, using MPL's
lambda
metafunction:
template <class X> struct two_pointers : twice<typename mpl::lambda<boost::add_pointer<_1> >::type, X> {}; BOOST_STATIC_ASSERT(( boost::is_same< typename two_pointers<int>::type , int** >::value ));
We'll refer to metafunction classes like
add_pointer_f
and placeholder expressions like
boost::add_pointer<_1>
as lambda
expressions. The term, meaning "unnamed function
object," was introduced in the 1930s by the logician Alonzo
Church as part of a fundamental theory of computation he called
the lambdacalculus.[4] MPL uses the somewhat obscure
word lambda
because of its wellestablished
precedent in functional programming languages.
Although its primary purpose is to turn placeholder
expressions into metafunction classes, mpl::lambda
can accept any lambda expression, even if it's already a
metafunction class. In that case, lambda
returns its
argument unchanged. MPL algorithms like transform
call lambda
internally, before invoking the
resulting metafunction class, so that they work equally well with
either kind of lambda expression. We can apply the same strategy
to twice
:
template <class F, class X> struct twice : apply1< typename mpl::lambda<F>::type , typename apply1< typename mpl::lambda<F>::type , X >::type > {};
Now we can use twice
with metafunction classes
and placeholder expressions:
int* x; twice<add_pointer_f, int>::type p = &x; twice<boost::add_pointer<_1>, int>::type q = &x;
apply
MetafunctionInvoking the result of lambda
is such a common
pattern that MPL provides an apply
metafunction to
do just that. Using mpl::apply
, our flexible version
of twice
becomes:
#include <boost/mpl/apply.hpp> template <class F, class X> struct twice : mpl::apply<F, typename mpl::apply<F,X>::type> {};
You can think of mpl::apply
as being just like
the apply1
template that we wrote, with two
additional features:
While apply1
operates only on
metafunction classes, the first argument to
mpl::apply
can be any lambda expression
(including those built with placeholders).
While apply1
accepts only one
additional argument to which the metafunction class will be
applied, mpl::apply
can invoke its first
argument on any number from zero to five additional
arguments.[5] For
example:
// binary lambda expression applied to 2 additional arguments mpl::apply< mpl::plus<_1,_2> , mpl::int_<6> , mpl::int_<7> >::type::value // == 13
When writing a metafunction that invokes one of its
arguments, use mpl::apply
so that it works with
lambda expressions.
Lambda expressions provide much more than just the ability to pass a metafunction as an argument. The two capabilities described next combine to make lambda expressions an invaluable part of almost every metaprogramming task.
Consider the lambda expression
mpl::plus<_1,_1>
. A single argument is
directed to both of plus
's parameters, thereby
adding a number to itself. Thus, a binary metafunction,
plus
, is used to build a unary lambda
expression. In other words, we've created a whole new
computation! We're not done yet, though: By supplying a
nonplaceholder as one of the arguments, we can build a unary
lambda expression that adds a fixed value, say 42, to its
argument:
mpl::plus<_1, mpl::int_<42> >
The process of binding argument values to a subset of a function's parameters is known in the world of functional programming as partial function application.
Lambda expressions can also be used to assemble more
interesting computations from simple metafunctions. For example,
the following expression, which multiplies the sum of two numbers
by their difference, is a composition of the
three metafunctions multiplies
, plus
,
and minus
:
mpl::multiplies<mpl::plus<_1,_2>, mpl::minus<_1,_2> >
When evaluating a lambda expression, MPL checks to see if any of its arguments are themselves lambda expressions, and evaluates each one that it finds. The results of these inner evaluations are substituted into the outer expression before it is evaluated.
Now that you have an idea of the semantics of MPL's
lambda
facility, let's formalize that understanding
and look at things a little more deeply.
The definition of "placeholder" may surprise you:
A placeholder is a metafunction class of
the form mpl::arg<X>
.
The convenient names _1
, _2
,...
_5
are actually typedef
s for
specializations of mpl::arg
that simply select the
Nth argument for any N. [6] The implementation of
placeholders looks something like this:
namespace boost { namespace mpl { namespace placeholders { template <int N> struct arg; // forward declarations struct void_; template <> struct arg<1> { template < class A1, class A2 = void_, ... class Am = void_> struct apply { typedef A1 type; // return the first argument }; }; typedef arg<1> _1; template <> struct arg<2> { template < class A1, class A2, class A3 = void_, ...class Am = void_ > struct apply { typedef A2 type; // return the second argument }; }; typedef arg<2> _2; more specializations and typedefs... }}}
Remember that invoking a metafunction class is the same as
invoking its nested apply
metafunction. When a
placeholder in a lambda expression is evaluated, it is invoked on
the expression's actual arguments, returning just one of them.
The results are then substituted back into the lambda expression
and the evaluation process continues.
There's one special placeholder, known as the unnamed placeholder, that we haven't yet defined:
namespace boost { namespace mpl { namespace placeholders { typedef arg<1> _; // the unnamed placeholder }}}
The details of its implementation aren't important; all you
really need to know about the unnamed placeholder is that it gets
special treatment. When a lambda expression is being transformed
into a metafunction class by mpl::lambda
,
the nth appearance of the unnamed placeholder in a
given template specialization is replaced with
_
n.
So, for example, every row of Table 3.1 below contains two equivalent lambda expressions.
mpl::plus<_,_> 
mpl::plus<_1,_2> 
boost::is_same< _ , boost::add_pointer<_> > 
boost::is_same< _1 , boost::add_pointer<_1> > 
mpl::multiplies< mpl::plus<_,_> , mpl::minus<_,_> > 
mpl::multiplies< mpl::plus<_1,_2> , mpl::minus<_1,_2> > 
Especially when used in simple lambda expressions, the unnamed placeholder often eliminates just enough syntactic "noise" to significantly improve readability.
Now that you know just what placeholder means, we can define placeholder expression:
A placeholder expression is either:
 a placeholder
or
 a template specialization with at least one argument that is a placeholder expression.
In other words, a placeholder expression always involves a placeholder.
There is just one detail of placeholder expressions that we
haven't discussed yet. MPL uses a special rule to make it easier
to integrate ordinary templates into metaprograms: After all of
the placeholders have been replaced with actual arguments, if the
resulting template specialization X doesn't have a
nested ::type
, the result is just X
itself.
For example, mpl::apply<std::vector<_>,
T> is always just
std::vector<T>
. If it weren't for this
behavior, we would have to build trivial metafunctions to create
ordinary template specializations in lambda expressions:
// trivial std::vector generator template<class U> struct make_vector { typedef std::vector<U> type; }; typedef mpl::apply<make_vector<_>, T>::type vector_of_t;
Instead, we can simply write:
typedef mpl::apply<std::vector<_>, T>::type vector_of_t;
Recall the definition of always_int
from the
previous chapter:
struct always_int { typedef int type; };
Nullary metafunctions might not seem very important at first,
since something like add_pointer<int>
could be
replaced by int*
in any lambda expression where it
appears. Not all nullary metafunctions are that simple,
though:
struct add_pointer_f { template <class T> struct apply : boost::add_pointer<T> {}; }; typedef mpl::vector<int, char*, double&> seq; typedef mpl::transform<seq, add_pointer_f> calc_ptr_seq;
Note that calc_ptr_seq
is a nullary metafunction,
since it has transform
's nested ::type
.
A C++ template is not instantiated until we actually "look inside
it," though. Just naming calc_ptr_seq
does not cause
it to be evaluated, since we haven't accessed its
::type
yet.
Metafunctions can be invoked lazily, rather than
immediately upon supplying all of their arguments. We can use
lazy evaluation to improve compilation time when
a metafunction result is only going to be used conditionally. We
can sometimes also avoid contorting program structure by
naming an invalid computation without actually
performing it. That's what we've done with
calc_ptr_seq
above, since you can't legally form
double&*
. Laziness and all of its virtues will
be a recurring theme throughout this book.
By now you should have a fairly complete view of the fundamental concepts and language of both template metaprogramming in general and of the Boost Metaprogramming Library. This section reviews the highlights.
type
of a metafunction by accessing the one
provided by its base class.apply
.#include <boost/mpl/componentname.hpp>
If the component's name ends in an
underscore, however, the corresponding MPL header name does
not include the trailing underscore. For example,
mpl::bool_
can be found in
<boost/mpl/bool.hpp>
. Where the library
deviates from this convention, we'll be sure to point it out
to you.
A kind of lambda expression that, through the use of placeholders, enables inplace partial metafunction application and metafunction composition. As you will see throughout this book, these features give us the truly amazing ability to build up almost any kind of complex type computation from more primitive metafunctions, right at its point of use:
// find the position of a type x in some_sequence such that: // x is convertible to 'int' // && x is not 'char' // && x is not a floating type typedef mpl::find_if< some_sequence , mpl::and_< boost::is_convertible<_1,int> , mpl::not_<boost::is_same<_1,char> > , mpl::not_<boost::is_float<_1> > > >::type iter;
Placeholder expressions make good on the promise of algorithm reuse without forcing us to write new metafunction classes. The corresponding capability is often sorely missed in the runtime world of the STL, since it is often much easier to write a loop by hand than it is to use standard algorithms, despite their correctness and efficiency advantages.
lambda
metafunction.lambda
and the lambda evaluation process, please
see the MPL reference manual.apply
metafunction.mpl::apply
along with the arguments you want to
apply it to in lieu of using lambda
and invoking
the result "manually."::type
s, so we can
supply all of their arguments without performing any
computation and delay evaluation to the last possible
moment.plus_f
, but since it's a little subtle,
we introduced the straightforward but verbose formulation
first.__EDG_VERSION__
, which is defined by all EDGbased
compilers.mpl::apply
.Discuss this article in the Articles Forum topic, A Deeper Look at Metafunctions.
David Abrahams and Aleksey Gurtovoy are the authors of
Template Metaprogramming, which can be preordered from
on Amazon.com at:
http://www.amazon.com/exec/obidos/ASIN/0321227255/
David Abrahams is a leading authority on C++ software development. His company, Boost Consulting (http://www.boostconsulting.com), provides support and development services for the opensource Boost C++ libraries, and delivers professional training in the practice of software construction. As a founding member of Boost (http://www.boost.org), David has worked with some of the best developers from all over the world in designing and building widelyused, reliable, maintainable software components. David has been an ANSI/ISO C++ committee member since 1996, where he is best known for developing the theory, and implementation of exception safety in the C++ standard.
Aleksey Gurtovoy is a technical lead at MetaCommunications, Inc, and a contributing member of the C++ Boost community. He holds a MS degree in Computer Science from Krasnoyarsk Technical State University, Russia. He can be reached at agurtovoy@metacomm.com.
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