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Getting started with Boost.Metaparse

1. Introduction
2. The text to parse
3. Creating a simple parser
4. Parsing simple expressions
5. Parsing longer expressions
6. Adding support for other operators
7. Dealing with precedence
8. Dealing with associativity
9. Dealing with unary operators
10. Dealing with parens
11. Dealing with invalid input
12. Summary
Copy-paste friendly code examples
Definitions before each section

This tutorial shows you how to build a parser for a small calculator language from the ground up. The goal is not to have a complete calculator, but to show you the most common situations one can face while building a parser using Metaparse. This tutorial assumes, that you have some template metaprogramming experience.

While you are using Metaparse, you will be writing parsers turning an input text into a type. These types can later be processed by further template metaprograms. While you are working on your parsers, you'll probably want to look at the result of parsing a test input. This tutorial assumes that you can use Metashell. Since the online demo makes the Boost headers available, you can use that in the tutorial as well.

If you install Metashell on your computer, make sure that you have the Boost libraries and the getting_started example of Metaparse on the include path. For example, you can start Metashell with the following arguments:

$ metashell -I$BOOST_ROOT -I$BOOST_ROOT/libs/metaparse/example/getting_started

$BOOST_ROOT refers to the boost root directory (where you have checked out the Boost source code).

This tutorial is long and therefore you might want to make shorter or longer breaks while reading it. To make it easy for you to stop at a certain point and continue later (or to start in the middle if you are already familiar with the basics) Metaparse has a getting_started directory in the examples. This contains the definitions for each section of this tutorial.

If you're about to start (or continue) this guide from section 5.2.1, you can include 5_2_1.hpp. This will define everything you need to start with that section.

[Note] Note

You have access to these headers in the online Metashell demo as well. For example you can include the <boost/metaparse/getting_started/5_2_1.hpp> header to start from section 5.2.1.

If you have no access to Metashell or you prefer using your regular C++ development environment while processing this tutorial, this is also possible.

The tutorial (and usually experimenting with Metaparse) requires that you evaluate different template metaprogramming expressions and check their result, which is a type. Thus, to try the examples of this tutorial you need a way to be able to display the result of evaluating a template metaprogram. This section shows you two options.

You can either use boost::mpl::print or mpllibs::metamonad::fail_with_type to enforce a warning or an error message containing the result of a metaprogram evaluation. For example to see what BOOST_METAPARSE_STRING("11 + 2") refers to, you can create a test.cpp with the following content:

#include <boost/metaparse/string.hpp>
#include <boost/mpl/print.hpp>

boost::mpl::print<BOOST_METAPARSE_STRING("11 + 2")> x;

If you try to compile it, the compiler will display warnings containing the type the expression BOOST_METAPARSE_STRING("11 + 2") constructs. To use this technique for this tutorial, you need to add all the includes and definitions the tutorial suggests typing in the shell to your test.cpp file. When the shell suggests to try to call some metafunction (or you'd like to try something out), you need to replace the template argument of boost::mpl::print with the expression in question and recompile the code.

You can also display the result of metaprograms at runtime. You can use the Boost.TypeIndex library to do this. For example to see what BOOST_METAPARSE_STRING("11 + 2") refers to, you can create a test.cpp with the following content:

#include <boost/metaparse/string.hpp>
#include <boost/type_index.hpp>
#include <iostream>

int main()
{
  std::cout
    << boost::typeindex::type_id_with_cvr<BOOST_METAPARSE_STRING("11 + 2")>()
    << std::endl;
}

If you compile and run this code, it will display the type on the standard output.

With Metaparse you can create template metaprograms parsing an input text. To pass the input text to the metaprograms, you need to represent them as types. For example let's represent the text "Hello world" as a type. The most straightforward way of doing it would be creating a variadic template class taking the characters of the text as template arguments:

template <char... Cs>
struct string;

The text "11 + 2" can be represented the following way:

string<'1', '1', ' ', '+', ' ', '2'>

Metaparse provides this type for you. Run the following command in Metashell:

> #include <boost/metaparse/string.hpp>
[Note] Note

Note that the > character at the beginning of the above code example is the prompt of Metashell. It is added to the code examples as a hint to what you should run in Metashell (or add to your test cpp file if you are using a regular development environment).

[Note] Note

Note that in the online-demo of Metashell you can paste code into the shell by right-clicking on the shell somewhere and choosing Paste from browser in the context menu.

This will make this type available for you. Now you can try running the following command:

> boost::metaparse::string<'1', '1', ' ', '+', ' ', '2'>

The shell will echo (almost) the same type back to you. The only difference is that it is in a sub-namespace indicating the version of Metaparse being used.

The nice thing about this representation is that metaprograms can easily access the individual characters of the text. The not so nice thing about this representation is that if you want to write the text "Hello world" in your source code, you have to type a lot.

Metaparse provides a macro that can turn a string literal into an instance of boost::metaparse::string. This is the BOOST_METAPARSE_STRING macro. You get it by including <boost/metaparse/string.hpp>. Let's try it by running the following command in Metashell:

> BOOST_METAPARSE_STRING("11 + 2")

You will get the same result as you got by instantiating boost::metaparse::string yourself.

[Note] Note

Note that you can find everything that has been included and defined so far here.

Let's try creating a parser. We will start with creating a parser for something simple: we will be parsing integer numbers, such as the text "13". You can think of this first parsing exercise as a template metaprogramming string-to-int conversion because we expect to get the value 13 as the result of parsing.

[Note] Note

You know the difference between "13" and 13 in C++. One of them is a character array, the other one is an integral value. But what is the difference between them in template metaprogramming? They are represented by different types. For example "13" is represented by string<'1', '3'> while 13 is represented by std::integral_constant<int, 13>.

To build a parser, we need to specify the grammar to use. Metaparse provides building blocks (called parsers) we can use to do this and one of them is the int_ parser which does exactly what we need: it parses integers. To make it available, we need to include it:

> #include <boost/metaparse/int_.hpp>

Our grammar is simple: int_. (Don't worry, we'll parse more complicated languages later).

A parser is a template metafunction class. It can be used directly, but its interface is designed for completeness and not for ease of use. Metaparse provides the build_parser metafunction that adds a wrapper to parsers with a simple interface.

[Note] Note

In this tutorial, we will always be wrapping our parsers with this. We will call these wrapped parsers parsers as well. If you are interested in it, you can learn about the complete interface of parsers here.

Let's create a parser using int_ and build_parser:

> #include <boost/metaparse/build_parser.hpp>
> using namespace boost::metaparse;
> using exp_parser1 = build_parser<int_>;

copy-paste friendly version

First we need to include build_parser.hpp to make build_parser available. Then we make our lives easier by running using namespace boost::metaparse;. The third command defines the parser: we need to instantiate the build_parser template class with our parser (int_ in this case) as argument.

Now that we have a parser, let's parse some text with it (if you haven't done it yet, include boost/metaparse/string.hpp):

> exp_parser1::apply<BOOST_METAPARSE_STRING("13")>::type
mpl_::integral_c<int, 13>

exp_parser1 is a template metafunction class taking the input text as it's argument and it returns the integral representation of the number in the string. Try it with different numbers and see how it converts them.

[Note] Note

Note that you can find everything that has been included and defined so far here.

Have you tried parsing an invalid input? Something that is not a number, such as:

> exp_parser1::apply<BOOST_METAPARSE_STRING("thirteen")>::type
<< compilation error >>

Well, "thirteen" is a number, but our parser does not speak English, so it is considered as invalid input. As a result of this, compilation fails and you get a compilation error from Metashell.

In the Dealing with invalid input section we will go into further details on error handling.

[Note] Note

Note that you can find everything that has been included and defined so far here.

Let's try to give the parser two numbers instead of one:

> exp_parser1::apply<BOOST_METAPARSE_STRING("11 13")>::type
mpl_::integral_c<int, 11>

You might be surprised by this: the parser did not return an error. It parsed the first number, 11 and ignored 13. The way int_ works is that it parses the number at the beginning of the input text and ignores the rest of the input.

So exp_parser1 has a bug: our little language consists of one number, not a list of numbers. Let's fix our parser to treat more than one numbers as an invalid input:

> #include <boost/metaparse/entire_input.hpp>

This gives us the entire_input template class. We can wrap int_ with entire_input indicating that the number we parse with int_ should be the entire input. Anything that comes after that is an error. So our parser is entire_input<int_> now. Let's wrap it with build_parser:

> using exp_parser2 = build_parser<entire_input<int_>>;

Let's try this new parser out:

> exp_parser2::apply<BOOST_METAPARSE_STRING("13")>::type
mpl_::integral_c<int, 13>

It can still parse numbers. Let's try to give it two numbers:

> exp_parser2::apply<BOOST_METAPARSE_STRING("11 13")>::type
<< compilation error >>

This generates a compilation error, since the parser failed.

[Note] Note

Note that you can find everything that has been included and defined so far here.

Our parser became a bit too restrictive now. It doesn't allow anything after the number, not even whitespaces:

> exp_parser2::apply<BOOST_METAPARSE_STRING("11 ")>::type
<< compilation error >>

Let's allow whitespaces after the number:

> #include <boost/metaparse/token.hpp>

This makes the token template class available. It takes a parser as its argument and allows optional whitespaces after that. Let's create a third parser allowing whitespaces after the number:

> using exp_parser3 = build_parser<entire_input<token<int_>>>;

We expect token<int_> to be the entire input in this case. We allow optional whitespaces after int_ but nothing else:

> exp_parser3::apply<BOOST_METAPARSE_STRING("11 ")>::type
mpl_::integral_c<int, 11>
[Note] Note

Note that you can find everything that has been included and defined so far here.

We can parse numbers. Let's try parsing something more complicated, such as "11 + 2". This is a number followed by a + symbol followed by another number. int_ (or token<int_>) implements the parser for one number.

First, let's write a parser for the + symbol. We can use the following:

> #include <boost/metaparse/lit_c.hpp>

This gives us lit_c which we can use to parse specific characters, such as +. The grammar parsing the + character can be represented by lit_c<'+'>. To allow optional whitespaces after it, we should use token<lit_c<'+'>>.

So to parse "11 + 2" we need the following sequence of parsers:

token<int_>    token<lit_c<'+'>>    token<int_>

Metaparse provides sequence for parsing the sequence of things:

> #include <boost/metaparse/sequence.hpp>

We can implement the parser for our expressions using sequence:

sequence<token<int_>, token<lit_c<'+'>>, token<int_>>

Let's create a parser using it:

> using exp_parser4 = build_parser<sequence<token<int_>, token<lit_c<'+'>>, token<int_>>>;

Try parsing a simple expression using it:

> exp_parser4::apply<BOOST_METAPARSE_STRING("11 + 2")>::type
boost::mpl::v_item<mpl_::integral_c<int, 2>, boost::mpl::v_item<mpl_::char_<'+'>
, boost::mpl::v_item<mpl_::integral_c<int, 11>, boost::mpl::vector0<mpl_::na>, 0
>, 0>, 0>

What you get might look strange to you. It is a vector from [Boost.MPL]( http://boost.org/libs/mpl). What you can see in the shell is the way this vector is represented. Metashell offers [pretty printing](metashell.org/manual/getting_started#data-structures-of-boostmpl) for Boost.MPL containers:

> #include <metashell/formatter.hpp>

After including this header, try parsing again:

> exp_parser4::apply<BOOST_METAPARSE_STRING("11 + 2")>::type
boost_::mpl::vector<mpl_::integral_c<int, 11>, mpl_::char_<'+'>, mpl_::integral_c<int, 2> >

What you get now looks more simple: this is a vector of three elements:

  • mpl_::integral_c<int, 11> This is the result of parsing with token<int_>.
  • mpl_::char_<'+'> This is the result of parsing with token<lit_c<'+'>>.
  • mpl_::integral_c<int, 2> > This is the result of parsing with token<int_>.

The result of parsing with a sequence is the vector of the individual parsing results.

[Note] Note

Note that you can find everything that has been included and defined so far here.

You might have noticed that our parsers have no separate tokenizers. Tokenization is part of the parsing process. However, it makes the code of the parsers cleaner if we separate the two layers. The previous example has two types of tokens:

  • a number (eg. 13)
  • a + symbol

In our last solution we parsed them by using the token<int_> and token<lit_c<'+'>> parsers. Have you noticed a pattern? We wrap the parsers of the tokens with token<...>. It is not just syntactic sugar. Our tokens might be followed (separated) by whitespaces, which can be ignored. That is what token<...> implements.

So let's make the implementation of exp_parser cleaner by separating the tokenization from the rest of the parser:

> using int_token = token<int_>;
> using plus_token = token<lit_c<'+'>>;

copy-paste friendly version

These two definitions create type aliases for the parsers of our tokens. For the compiler it doesn't matter if we use plus_token or token<lit_c<'+'>>, since they refer to the same type. But it makes the code of the parser easier to understand.

We can now define our expression parser using these tokens:

> using exp_parser5 = build_parser<sequence<int_token, plus_token, int_token>>;

We can use it the same way as exp_parser4:

> exp_parser5::apply<BOOST_METAPARSE_STRING("11 + 2")>::type
boost_::mpl::vector<mpl_::integral_c<int, 11>, mpl_::char_<'+'>, mpl_::integral_c<int, 2> >
[Note] Note

Note that you can find everything that has been included and defined so far here.

It would be nice if we could evaluate the expression as well. Instead of returning a vector as the result of parsing, we should return the evaluated expression. For example the result of parsing "11 + 2" should be mpl_::integral_c<int, 13>.

Metaparse provides transform which we can use to implement this:

> #include <boost/metaparse/transform.hpp>

This can be used to transform the result of a parser. For example we have the sequence<int_token, plus_token, int_token> parser which returns a vector. We want to transform this vector into a number, which is the result of evaluating the expression. We need to pass transform the sequence<...> parser and a function which turns the vector into the result we need. First let's create this metafunction:

> #include <boost/mpl/plus.hpp>
> #include <boost/mpl/at.hpp>
> template <class Vector> \
...> struct eval_plus : \
...>   boost::mpl::plus< \
...>     typename boost::mpl::at_c<Vector, 0>::type, \
...>     typename boost::mpl::at_c<Vector, 2>::type \
...>   > {};

copy-paste friendly version

[Note] Note

Note that if the last character of your command is the \ character in Metashell, then the shell assumes that you will continue typing the same command and waits for that before evaluating your command. When Metashell is waiting for the second (or third, or fourth, etc) line of a command, it uses a special prompt, ...>.

What it does is that using boost::mpl::at_c it takes the first (index 0) and the third (index 2) elements of the vector that is the result of parsing with sequence<...> and adds them. We can try it out with an example vector:

> eval_plus< \
...>  boost::mpl::vector< \
...>    mpl_::integral_c<int, 11>, \
...>    mpl_::char_<'+'>, \
...>    mpl_::integral_c<int, 2> \
...>  >>::type
mpl_::integral_c<int, 13>

copy-paste friendly version

We can use eval_plus to build a parser that evaluates the expression it parses:

> #include <boost/mpl/quote.hpp>
> using exp_parser6 = \
...> build_parser< \
...>   transform< \
...>     sequence<int_token, plus_token, int_token>, \
...>     boost::mpl::quote1<eval_plus> \
...>   > \
...> >;

copy-paste friendly version

[Note] Note

Note that we have to use boost::mpl::quote1 to turn our eval_plus metafunction into a metafunction class.

transform parses the input using sequence<int_token, plus_token, int_token> and transforms the result of that using eval_plus. Let's try it out:

> exp_parser6::apply<BOOST_METAPARSE_STRING("11 + 2")>::type
mpl_::integral_c<int, 13>

We have created a simple expression parser. The following diagram shows how it works:

The rounded boxes in the diagram are the parsers parsing the input, which are functions (template metafunction classes). The arrows represent how the results are passed around between these parsers (they are the return values of the function calls).

It uses sequence to parse the different elements (the first number, the + symbol and the second number) and builds a vector. The final result is calculated from that vector by the transform parser.

[Note] Note

Note that you can find everything that has been included and defined so far here.

We can parse simple expressions adding two numbers together. But we can't parse expressions adding three, four or maybe more numbers together. In this section we will implement a parser for expressions adding lots of numbers together.

[Note] Note

Note that you can find everything that has been included and defined so far here.

We can't solve this problem with sequence, since we don't know how many numbers the input will have. We need a parser that:

  • parses the first number
  • keeps parsing + <number> elements until the end of the input

Parsing the first number is something we can already do: the int_token parser does it for us. Parsing the + <number> elements is more tricky. Metaparse offers different tools for approaching this. The most simple is repeated:

> #include <boost/metaparse/any.hpp>

repeated needs a parser (which parses one + <number> element) and it keeps parsing the input with it as long as it can. This will parse the entire input for us. Let's create a parser for our expressions using it:

> using exp_parser7 = \
...> build_parser< \
...>   sequence< \
...>     int_token,                                /* The first <number> */ \
...>     repeated<sequence<plus_token, int_token>> /* The "+ <number>" elements */ \
...>   > \
...> >;

copy-paste friendly version

We have a sequence with two elements:

  • The first number (int_token)
  • The + <number> parts

The second part is an repeated, which parses the + <number> elements. One such element is parsed by sequence<plus_token, int_token>. This is just a sequence of the + symbol and the number.

Let's try parsing an expression using this:

> exp_parser7::apply<BOOST_METAPARSE_STRING("1 + 2 + 3 + 4")>::type

Here is a formatted version of the result which is easier to read:

boost_::mpl::vector<
  // The result of int_token
  mpl_::integral_c<int, 1>,

  // The result of repeated< sequence<plus_token, int_token> >
  boost_::mpl::vector<
    boost_::mpl::vector<mpl_::char_<'+'>, mpl_::integral_c<int, 2> >,
    boost_::mpl::vector<mpl_::char_<'+'>, mpl_::integral_c<int, 3> >,
    boost_::mpl::vector<mpl_::char_<'+'>, mpl_::integral_c<int, 4> >
  >
>

The result is a vector of two elements. The first element of this vector is the result of parsing the input with int_token, the second element of this vector is the result of parsing the input with repeated< sequence<plus_token, int_token>>. This second element is also a vector. Each element of this vector is the result of parsing the input with sequence<plus_token, int_token> once. Here is a diagram showing how exp_parser7 parses the input 1 + 2 + 3 + 4:

The diagram shows that the + <number> elements are parsed by sequence<plus_token, int_token> elements and their results are collected by repeated, which constructs a vector of these results. The value of the first <number> and this vector are placed in another vector, which is the result of parsing.

[Note] Note

Note that you can find everything that has been included and defined so far here.

The final result here is a pair of the first number and the vector of the rest of the values. To calculate the result we need to process that data structure. Let's give the example output we have just parsed a name. This will make it easier to test the code calculating the final result from this structure:

> using temp_result = exp_parser7::apply<BOOST_METAPARSE_STRING("1 + 2 + 3 + 4")>::type;

Now we can write a template metafunction turning this structure into the result of the calculation this structure represents.

[Note] Note

Note that you can find everything that has been included and defined so far here.

We have a vector containing another vector. Therefore, we will need to be able to summarise the elements of different vectors. We can use the boost::mpl::fold metafunction to do this:

> #include <boost/mpl/fold.hpp>

With this metafunction, we can iterate over a vector of parsed numbers and summarise them. We can provide it a metafunction taking two arguments: the sum we have so far and the next element of the vector. This metafunction will be called for every element of the vector.

[Note] Note

Note that this is very similar to the std::accumulate algorithm. Boost.MPL provides boost::mpl::accumulate as well, which is a synonym for boost::mpl::fold. This tutorial (and Metaparse) uses the name fold.

Let's start with a simple case: a vector of numbers. For example let's summarise the elements of the following vector:

> using vector_of_numbers = \
...> boost::mpl::vector< \
...>   boost::mpl::int_<2>, \
...>   boost::mpl::int_<5>, \
...>   boost::mpl::int_<6> \
...> >;

copy-paste friendly version

We will write a template metafunction, sum_vector for summarising the elements of a vector of numbers:

> template <class Vector> \
...> struct sum_vector : \
...>    boost::mpl::fold< \
...>      Vector, \
...>      boost::mpl::int_<0>, \
...>      boost::mpl::lambda< \
...>        boost::mpl::plus<boost::mpl::_1, boost::mpl::_2> \
...>      >::type \
...>    > \
...>  {};

copy-paste friendly version

This metafunction takes the vector to summarise the elements of as its argument and uses boost::mpl::fold to calculate the sum. boost::mpl::fold takes three arguments:

  • The container to summarise. This is Vector.
  • The starting value for the sum we have so far. Using 0 means that we want to start the sum from 0.
  • The function to call in every iteration while looping over the container. We are using a lambda expression in our example, which is the expression wrapped by boost::mpl::lambda. This expression adds its two arguments together using boost::mpl::plus. The lambda expression refers to its arguments by boost::mpl::_1 and boost::mpl::_2.

Let's try this metafunction out:

> sum_vector<vector_of_numbers>::type
mpl_::integral_c<int, 13>

It works as expected. Here is a diagram showing how it works:

As the diagram shows, boost::mpl::fold evaluates the lambda expression for each element of the vector and passes the result of the previous evaluation to the next lambda expression invocation.

We have a metafunction that can summarise a vector of numbers. The result of parsing the + <number> elements is a vector of vectors. As a recap, here is temp_result:

boost_::mpl::vector<
  // The result of int_token
  mpl_::integral_c<int, 1>,

  // The result of repeated< sequence<plus_token, int_token> >
  boost_::mpl::vector<
    boost_::mpl::vector<mpl_::char_<'+'>, mpl_::integral_c<int, 2> >,
    boost_::mpl::vector<mpl_::char_<'+'>, mpl_::integral_c<int, 3> >,
    boost_::mpl::vector<mpl_::char_<'+'>, mpl_::integral_c<int, 4> >
  >
>

First let's summarise the result of repeated<...> using boost::mpl::fold. This is a vector of vectors, but that's fine. boost::mpl::fold doesn't care about what the elements of the vector are. They can be numbers, vectors or something else as well. The function we use to add two numbers together (which was a lambda expression in our previous example) gets these elements as its argument and has to deal with them. So to summarise the elements of the vectors we get as the result of parsing with repeated<...>, we need to write a metafunction that can deal with these elements. One such element is boost_::mpl::vector<mpl_::char<'+'>, mpl_::integral_c<int, 2>>. Here is a metafunction that can be used in a boost::mpl::fold:

> template <class Sum, class Item> \
...>   struct sum_items : \
...>     boost::mpl::plus< \
...>       Sum, \
...>       typename boost::mpl::at_c<Item, 1>::type \
...>     > \
...> {};

copy-paste friendly version

This function takes two arguments:

  • Sum, which is a number. This is the summary of the already processed elements.
  • Item, the next item of the vector. These items are vectors of size two: the result of parsing the + symbol and the number.

The metafunction adds the sum we have so far and the next number together using the boost::mpl::plus metafunction. To get the next number out of Item, it uses boost::mpl::at_c. Let's try sum_items out:

> sum_items< \
...>   mpl_::integral_c<int, 1>, \
...>   boost::mpl::vector<mpl_::char_<'+'>, mpl_::integral_c<int, 2>> \
...> >::type
mpl_::integral_c<int, 3>

copy-paste friendly version

We have called sum_items with values from temp_result and saw that it works as expected: it added the partial sum (mpl_::integral_c<int, 1>) to the next number (mpl_::integral_c<int, 2>).

boost::mpl::fold can summarise the list we get as the result of parsing the + <number> elements of the input, so we need to extract this list from temp_result first:

> boost::mpl::at_c<temp_result, 1>::type

Here is the formatted version of the result:

boost_::mpl::vector<
  boost_::mpl::vector<mpl_::char_<'+'>, mpl_::integral_c<int, 2>>,
  boost_::mpl::vector<mpl_::char_<'+'>, mpl_::integral_c<int, 3>>,
  boost_::mpl::vector<mpl_::char_<'+'>, mpl_::integral_c<int, 4>>
>

This is the second element of the temp_result vector (the first one is the value of the first <number> element). Let's try fold out for this:

> \
...> boost::mpl::fold< \
...>   boost::mpl::at_c<temp_result, 1>::type, /* The vector to summarise */ \
...>   boost::mpl::int_<0>, /* The value to start the sum from */ \
...>   boost::mpl::quote2<sum_items> /* The function to call in each iteration */ \
...> >::type
mpl_::integral_c<int, 9>

copy-paste friendly version

[Note] Note

We are using sum_items as the function to call in each iteration. We are passing a metafunction (sum_items) to another metafunction (boost::mpl::fold) as an argument. To be able to do this, we need to turn it into a template metafunction class using boost::mpl::quote2 (2 means that it takes two arguments).

As we have seen, the result of this is the sum of the elements, which was 9 in our case. Here is a diagram showing how boost::mpl::fold works:

It starts with the value boost::mpl::int_<0> and adds the elements of the boost_::mpl::vector containing the parsing results one by one. The diagram shows how the subresults are calculated and then used for further calculations.

[Note] Note

Note that you can find everything that has been included and defined so far here.

Let's use sum_items with boost::mpl::fold to build the parser that summarises the values coming from the + <number> elements. We can extend the parser we were using in exp_parser7 by wrapping the repeated<...> part with transform, which transforms the result of repeated<...> with the folding expression we have just created:

> using exp_parser8 = \
...> build_parser< \
...>   sequence< \
...>     int_token, /* parse the first <number> */ \
...>     transform< \
...>       repeated<sequence<plus_token, int_token>>, /* parse the "+ <number>" elements */ \
...> \
...>       /* lambda expression summarising the "+ <number>" elements using fold */ \
...>       boost::mpl::lambda< \
...>         /* The folding expression we have just created */ \
...>         boost::mpl::fold< \
...>           boost::mpl::_1, /* the argument of the lambda expression, the result */ \
...>                           /* of the repeated<...> parser */ \
...>           boost::mpl::int_<0>, \
...>           boost::mpl::quote2<sum_items> \
...>         > \
...>       >::type \
...>     > \
...>   > \
...> >;

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It uses transform to turn the result of the previous version of our parser into one that summarises the + <number> elements. Let's try it out:

> exp_parser8::apply<BOOST_METAPARSE_STRING("1 + 2 + 3 + 4")>::type
boost_::mpl::vector<mpl_::integral_c<int, 1>, mpl_::integral_c<int, 9> >

This returns a pair of numbers as the result of parsing: the first number and the sum of the rest. To get the value of the entire expression we need to add these two numbers together. We can extend our parser to do this final addition as well:

> using exp_parser9 = \
...> build_parser< \
...>   transform< \
...>     /* What we had so far */ \
...>     sequence< \
...>       int_token, \
...>       transform< \
...>         repeated<sequence<plus_token, int_token>>, \
...>         boost::mpl::lambda< \
...>           boost::mpl::fold< \
...>             boost::mpl::_1, \
...>             boost::mpl::int_<0>, \
...>             boost::mpl::quote2<sum_items> \
...>           > \
...>         >::type \
...>       > \
...>     >, \
...>     boost::mpl::quote1<sum_vector> /* summarise the vector of numbers */ \
...>   > \
...> >;

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exp_parser9 wraps the parser we had so far (which gives us the two element vector as the result) with transform to add the elements of that two element vector together. Since that two element vector is a vector of numbers, we can (re)use the sum_vector metafunction for this. Let's try it out:

> exp_parser9::apply<BOOST_METAPARSE_STRING("1 + 2 + 3 + 4")>::type
mpl_::integral_c<int, 10>

It gives us the correct result, but it is very inefficient. Let's see why:

There are two loops in this process:

  • first repeated loops over the input to parse all of the + <number> elements. It builds a vector during this. (Loop 1 on the diagram)
  • then boost::mpl::fold loops over this vector to summarise the elements. (Loop 2 on the diagram)
[Note] Note

Note that we have been talking about loops while there is no such thing as a loop in template metaprogramming. Loops can be implemented using recursion: every recursive call is one iteration of the loop. The loop is stopped at the bottom of the recursive chain.

[Note] Note

Note that you can find everything that has been included and defined so far here.

It would be nice, if the two loops could be merged together and the temporary vector wouldn't have to be built in the middle (don't forget: there is no such thing as a garbage collector for template metaprogramming. Once you instantiate a template, it will be available until the end of ... the compilation).

Metaparse provides the foldl parser combinator:

> #include <boost/metaparse/foldl.hpp>

It is almost the same as boost::mpl::fold, but instead of taking the vector as its first argument, which was coming from the repeated application of a parser (sequence<plus_token, int_token>) on the input, it takes the parser itself. foldl parses the input and calculates the summary on the fly. Here is how we can write our parser using it:

> using exp_parser10 = \
...> build_parser< \
...>   transform< \
...>     sequence< \
...>       int_token, \
...>       foldl< \
...>         sequence<plus_token, int_token>, \
...>         boost::mpl::int_<0>, \
...>         boost::mpl::quote2<sum_items> \
...>       > \
...>     >, \
...>     boost::mpl::quote1<sum_vector>> \
...> >;

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Here are the formatted versions of exp_parser9 and exp_parser10 side-by-side:

//            exp_parser9                                       exp_parser10

build_parser<                                       build_parser<
  transform<                                          transform<
    sequence<                                           sequence<
      int_token,                                          int_token,


      transform<                                          foldl<
        repeated<sequence<plus_token, int_token>>,          sequence<plus_token, int_token>,
        boost::mpl::lambda<
          boost::mpl::fold<
            boost::mpl::_1,
            boost::mpl::int_<0>,                            boost::mpl::int_<0>,
            boost::mpl::quote2<sum_items>                   boost::mpl::quote2<sum_items>
          >
        >::type
      >                                                   >


    >,                                                  >,
    boost::mpl::quote1<sum_vector>                      boost::mpl::quote1<sum_vector>
  >                                                   >
>                                                   >

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In exp_parser10 the "_repeated and then transform with boost::mpl::fold_" part (the middle block of exp_parser9) has been replaced by one foldl parser that does the same thing but without building a vector in the middle. The same starting value (boost::mpl::int_<0>) and callback function (sum_items) could be used.

Here is a diagram showing how exp_parser10 works:

In this case, the results of the sequence<plus_token, int_token> parsers are passed directly to a folding algorithm without an intermediate vector. Here is a diagram showing exp_parser9 and exp_parser10 side-by-side to make it easier to see the difference:

[Note] Note

Note that you can find everything that has been included and defined so far here.

This solution can still be improved. The foldl summarising the + <number> elements starts from 0 and once this is done, we add the value of the first <number> of the input to it in the first iteration. It would be more straightforward if foldl could use the value of the first <number> as the initial value of the "sum we have so far". Metaparse provides foldl_start_with_parser for this:

> #include <boost/metaparse/foldl_start_with_parser.hpp>

foldl_start_with_parser is almost the same as foldl. The difference is that instead of taking a starting value for the sum it takes a parser. First it parses the input with this parser and uses the value it returns as the starting value. Here is how we can implement our parser using it:

> using exp_parser11 = \
...> build_parser< \
...>   foldl_start_with_parser< \
...>     sequence<plus_token, int_token>, /* apply this parser repeatedly */ \
...>     int_token, /* use this parser to get the initial value */ \
...>     boost::mpl::quote2<sum_items> /* use this function to add a new value to the summary */ \
...>   > \
...> >;

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This version of exp_parser uses foldl_start_with_parser. This implementation is more compact than the earlier versions. There is no sequence element in this: the first <number> is parsed by int_token and its value is used as the initial value for the summary. Let's try it out:

> exp_parser11::apply<BOOST_METAPARSE_STRING("1 + 2 + 3 + 4")>::type
mpl_::integral_c<int, 10>

It returns the same result as the earlier version but works differently. Here is a diagram showing how this implementation works:

[Note] Note

Note that you can find everything that has been included and defined so far here.

Our parsers now support expressions adding numbers together. In this section we will add support for the - operator, so expressions like 1 + 2 - 3 can be evaluated.

[Note] Note

Note that you can find everything that has been included and defined so far here.

Currently we use the plus_token for parsing "the" operator, which has to be +. We can define a new token for parsing the - symbol:

> using minus_token = token<lit_c<'-'>>;

We need to build a parser that accepts either a + or a - symbol. This can be implemented using one_of:

> #include <boost/metaparse/one_of.hpp>

one_of<plus_token, minus_token> is a parser which accepts either a + (using plus_token) or a - (using minus_token) symbol. The result of parsing is the result of the parser that succeeded.

[Note] Note

You can give any parser to one_of, therefore it is possible that more than one of them can parse the input. In those cases the order matters: one_of tries parsing the input with the parsers from left to right and the first one that succeeds, wins.

Using this, we can make our parser accept subtractions as well:

> using exp_parser12 = \
...> build_parser< \
...>   foldl_start_with_parser< \
...>     sequence<one_of<plus_token, minus_token>, int_token>, \
...>     int_token, \
...>     boost::mpl::quote2<sum_items> \
...>   > \
...> >;

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It uses one_of<plus_token, minus_token> as the separator for the numbers. Let's try it out:

> exp_parser12::apply<BOOST_METAPARSE_STRING("1 + 2 - 3")>::type
mpl_::integral_c<int, 6>

The result is not correct. The reason for this is that sum_items, the function we summarise with ignores which operator was used and assumes that it is always +.

[Note] Note

Note that you can find everything that has been included and defined so far here.

To fix the evaluation of expressions containing subtractions, we need to fix the function we use for summarising. We need to write a version that takes the operator being used into account.

First of all we will need the boost::mpl::minus metafunction for implementing subtraction:

> #include <boost/mpl/minus.hpp>

Let's write a helper metafunction that takes three arguments: the left operand, the operator and the right operand:

> template <class L, char Op, class R> struct eval_binary_op;
> template <class L, class R> struct eval_binary_op<L, '+', R> : boost::mpl::plus<L, R>::type {};
> template <class L, class R> struct eval_binary_op<L, '-', R> : boost::mpl::minus<L, R>::type {};

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The first command declares the eval_binary_op metafunction. The first and third arguments are the left and right operands and the second argument is the operator.

[Note] Note

Note that it does not satisfy the expectations of a template metafunction since it takes the operator as a char and not as a class (or typename) argument. For simplicity, we will still call it a metafunction.

The second and third commands define the operation for the cases when the operator is + and -. When the eval_binary_op metafunction is called, the C++ compiler chooses one of the definitions based on the operator. If you have functional programming experience this approach (pattern matching) might be familiar to you. Let's try eval_binary_op out:

> eval_binary_op<boost::mpl::int_<11>, '+', boost::mpl::int_<2>>::type
mpl_::integral_c<int, 13>
> eval_binary_op<boost::mpl::int_<13>, '-', boost::mpl::int_<2>>::type
mpl_::integral_c<int, 11>

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You might also try to use it with an operator it does not expect (yet). For example '*'. You will see the C++ compiler complaining about that the requested version of the eval_binary_op template has not been defined. This solution can be extended and support for the '*' operator can always be added later.

Let's write the metafunction we can use from the folding parser to evaluate the expressions using + and - operators. This takes two arguments:

  • The partial result we have evaluated so far. (This used to be the summary we have evaluated so far, but we are making it a more general evaluation now). This is the left operand, a number.
  • The result of parsing (+|-) <number>. This a vector containing two elements: a character representing the operator (+ or -) and the value of the <number>. The number is the right operand.

Let's write the metafunction binary_op that takes these arguments and calls eval_binary_op:

> template <class S, class Item> \
...> struct binary_op : \
...>   eval_binary_op< \
...>     S, \
...>     boost::mpl::at_c<Item, 0>::type::value, \
...>     typename boost::mpl::at_c<Item, 1>::type \
...>   > \
...>   {};

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This metafunction takes the operator (the first element) and the right operand (the second element) from Item. The operator is a class representing a character, such as mpl_::char_<'+'>. To get the character value out of it, one has to access its ::value. For example mpl_::char<'+'>::value is '+'. Since eval_binary_op takes this character value as its second argument, we had to pass boost::mpl::at_c<Item, 0>::type::value to it. Let's try it out:

> binary_op<boost::mpl::int_<11>, boost::mpl::vector<boost::mpl::char_<'+'>, boost::mpl::int_<2>>>::type
mpl_::integral_c<int, 13>

We passed it a number (11) and a vector of a character (+) and another number (2). It added the two numbers as expected. Let's use this function as the third argument of foldl_start_with_parser:

> using exp_parser13 = \
...> build_parser< \
...>   foldl_start_with_parser< \
...>     sequence<one_of<plus_token, minus_token>, int_token>, \
...>     int_token, \
...>     boost::mpl::quote2<binary_op> \
...>   > \
...> >;

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It uses binary_op instead of sum_items. Let's try it out:

> exp_parser13::apply<BOOST_METAPARSE_STRING("1 + 2 - 3")>::type
mpl_::integral_c<int, 0>

It returns the correct result.

[Note] Note

Note that you can find everything that has been included and defined so far here.

We support addition and subtraction. Let's support multiplication as well.

[Note] Note

Note that you can find everything that has been included and defined so far here.

We can extend the solution we have built for addition and subtraction. To do that, we need to add support for multiplication to eval_binary_op:

> #include <boost/mpl/times.hpp>
> template <class L, class R> struct eval_binary_op<L, '*', R> : boost::mpl::times<L, R>::type {};

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We had to include <boost/mpl/times.hpp> to get the boost::mpl::times metafunction and then we could extend eval_binary_op to support the * operator as well. We can try it out:

> eval_binary_op<boost::mpl::int_<3>, '*', boost::mpl::int_<4>>::type
mpl_::integral_c<int, 12>

This works as expected. Let's create a token for parsing the * symbol:

> using times_token = token<lit_c<'*'>>;

Now we can extend our parser to accept the * symbol as an operator:

> using exp_parser14 = \
...> build_parser< \
...>   foldl_start_with_parser< \
...>     sequence<one_of<plus_token, minus_token, times_token>, int_token>, \
...>     int_token, \
...>     boost::mpl::quote2<binary_op> \
...>   > \
...> >;

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This version accepts either a +, a - or a * symbol as the operator. Let's try this out:

> exp_parser14::apply<BOOST_METAPARSE_STRING("2 * 3")>::type
mpl_::integral_c<int, 6>

This works as expected. Let's try another, slightly more complicated expression:

> exp_parser14::apply<BOOST_METAPARSE_STRING("1 + 2 * 3")>::type
mpl_::integral_c<int, 9>

This returns a wrong result. The value of this expression should be 7, not 9. The problem with this is that our current implementation does not take operator precedence into account. It treats this expression as (1 + 2) * 3 while we expect it to be 1 + (2 * 3) since addition has higher precedence than multiplication.

[Note] Note

Note that you can find everything that has been included and defined so far here.

Let's make it possible for different operators to have different precedence. To do this, we define a new parser for parsing expressions containing only * operators (that is the operator with the lowest precedence):

> using mult_exp1 = foldl_start_with_parser<sequence<times_token, int_token>, int_token, boost::mpl::quote2<binary_op>>;

mult_exp1 can parse expressions containing only * operator. For example 3 * 2 or 6 * 7 * 8. Now we can create a parser supporting only the + and - operators but instead of separating numbers with these operators we will separate expressions containing only * operators. This means that the expression 1 * 2 + 3 * 4 is interpreted as the expressions 1 * 2 and 3 * 4 separated by a + operator. A number (eg. 13) is the special case of an expression containing only * operators.

Here is the parser implementing this:

> using exp_parser15 = \
...> build_parser< \
...>   foldl_start_with_parser< \
...>     sequence<one_of<plus_token, minus_token>, mult_exp1>, \
...>     mult_exp1, \
...>     boost::mpl::quote2<binary_op> \
...>   > \
...> >;

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Note that this is almost the same as exp_parser13. The only difference is that it uses mult_exp1 everywhere, where exp_parser13 was using int_token. Let's try it out:

> exp_parser15::apply<BOOST_METAPARSE_STRING("1 + 2 * 3")>::type
mpl_::integral_c<int, 7>

This takes the precedence rules into account. The following diagram shows how it works:

Subexpressions using * operators only are evaluated (by mult_exp1) and treated as single units while interpreting expressions using + and - operators. Numbers not surrounded by * operators are treated also as operators using * only (containing no operations but a number).

If you need more layers (eg. introducing the ^ operator) you can extend this solution with further layers. The order of the layers determine the precedence of the operators.

[Note] Note

Note that you can find everything that has been included and defined so far here.

Let's add division to our calculator language. Since it has the same precedence as multiplication, it should be added to that layer:

> #include <boost/mpl/divides.hpp>
> template <class L, class R> struct eval_binary_op<L, '/', R> : boost::mpl::divides<L, R>::type {};
> using divides_token = token<lit_c<'/'>>;
> using mult_exp2 = \
...> foldl_start_with_parser< \
...>   sequence<one_of<times_token, divides_token>, int_token>, \
...>   int_token, \
...>   boost::mpl::quote2<binary_op> \
...> >;
> using exp_parser16 = \
...> build_parser< \
...>   foldl_start_with_parser< \
...>     sequence<one_of<plus_token, minus_token>, mult_exp2>, \
...>     mult_exp2, \
...>     boost::mpl::quote2<binary_op> \
...>   > \
...> >;

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We have to include <boost/mpl/divides.hpp> to get a metafunction for doing a division. We need to extend the eval_binary_op metafunction to support division as well. We had to introduce a new token, divides_token that can parse the / symbol.

We have extended mult_exp1 to accept either a times_token or a divides_token as the operator. This extended parser is called mult_exp2.

We have written a new parser, exp_parser16 which is the same as exp_parser15 but uses mult_exp2 instead of mult_exp1. This can parse expressions using division as well (and this new operator has the right precedence). Let's try it out:

> exp_parser16::apply<BOOST_METAPARSE_STRING("8 / 4")>::type
mpl_::integral_c<int, 2>

This works as expected. But what should be the value of 8 / 4 / 2? The answer can be either 1 or 4 depending on the associativity of the division operator. If it is left associative, then this expressions is interpreted as (8 / 4) / 2 and the result is 1. If it is right associative, this expression is interpreted as 8 / (4 / 2) and the result is 4.

Try to guess which result our current implementation gives before trying it out. Once you have verified the current behaviour, continue reading.

[Note] Note

Note that you can find everything that has been included and defined so far here.

Here is a diagram showing how our current parser processes the expression 8 / 4 / 2:

It takes the first number, 8, divides it by the second one, 4 and then it divides the result with the third one, 2. This means, that in our current implementation, division is left associative: 8 / 4 / 2 means (8 / 4) / 2.

Another thing to note is that the initial value is 8 and the list of values foldl iterates over is "/ 4", "/ 2".

[Note] Note

Note that you can find everything that has been included and defined so far here.

foldl applies a parser repeatedly and iterates over the parsing results from left to right. (This is where the l in the name comes from). Metaparse provides another folding parser combinator, foldr. It applies a parser on the input as well but it iterates from right to left over the results.

Similarly to foldl_start_with_parser, Metaparse provides foldr_start_with_parser as well. A major difference between the two (foldl_start_with_parser and foldr_start_with-parser) solutions is that while foldl_start_with_parser treats the first number as a special one, foldr_start_with_parser treats the last number as a special one. This might sound strange, but think about it: if you want to summarise the elements from right to left, your starting value should be the last element, not the first one, as the first one is the one you visit last.

Due to the above difference foldr_start_with_parser is not a drop-in replacement of foldl_start_with_parser. While the list of values foldl was iterating over is "8", "/ 4", "/ 2", the list of values foldlr has to iterate over is "2", "4 /", "8 /".

This means that the function we use to "add" a new value to the already evaluated part of the expression (this has been binary_op so far) has to be prepared for taking the next operator and operand in a reverse order (eg. by taking "4 /" instead of "/ 4"). We write another metafunction for this purpose:

> template <class S, class Item> \
...> struct reverse_binary_op : \
...>   eval_binary_op< \
...>     typename boost::mpl::at_c<Item, 0>::type, \
...>     boost::mpl::at_c<Item, 1>::type::value, \
...>     S \
...>   > \
...>   {};

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There are multiple differences between binary_op and reverse_binary_op:

  • The Item argument, which is a vector is expected to be [operator, operand] in binary_op and [operand, operator] in reverse_binary_op.
  • Both versions use eval_binary_op to evaluate the subexpression, but binary_op treats S, the value representing the already evaluated part of the expression as the left operand, while reverse_binary_op treats it as the right operand. This is because in the first case we are going from left to right while in the second case we are going from right to left.

We need to include foldr_start_with_parser:

> #include <boost/metaparse/foldr_start_with_parser.hpp>

We can rewrite mult_exp using foldr_start_with_parser:

> using mult_exp3 = \
...> foldr_start_with_parser< \
...>   sequence<int_token, one_of<times_token, divides_token>>, /* The parser applied repeatedly */ \
...>   int_token, /* The parser parsing the last number */ \
...>   boost::mpl::quote2<reverse_binary_op> /* The function called for every result */ \
...>                                         /* of applying the above parser */ \
...> >;

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It is almost the same as mult_exp2, but ...

  • ... the parser applied repeatedly parses <number> <operator> elements instead of <operator> <number> elements (what mult_exp2 did).
  • ... this version uses reverse_binary_op instead of binary_op as the function that is called for every result of applying the above parser.

We can create a new version of exp_parser that uses mult_exp3 instead of mult_exp2:

> using exp_parser17 = \
...> build_parser< \
...>   foldl_start_with_parser< \
...>     sequence<one_of<plus_token, minus_token>, mult_exp3>, \
...>     mult_exp3, \
...>     boost::mpl::quote2<binary_op> \
...>   > \
...> >;

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The only difference between exp_parser17 and the previous version, exp_parser16 is that it uses the updated version of mult_exp. Let's try this parser out:

> exp_parser17::apply<BOOST_METAPARSE_STRING("8 / 4 / 2")>::type
mpl_::integral_c<int, 4>

This version of the parser gives the other possible result. The one you get when division is right associative, which means that the above expression is evaluated as 8 / (4 / 2). Here is a diagram showing how the foldr_start_with_parser-based solution works:

To make it easier to compare the two solutions, here is a diagram showing the two approaches side-by-side:

As we have seen, the associativity of the operators can be controlled by choosing between folding solutions. The folding solutions going from left to right implement left associativity, while the solutions going from right to left implement right associativity.

[Note] Note

Note that folding solutions going from left to right is implemented in a more efficient way than folding from right to left. Therefore when both solutions can be used you should prefer folding from left to right.

[Note] Note

Note that you can find everything that has been included and defined so far here.

Our calculator language provides no direct support for negative numbers. To get a negative number, we need to do a subtraction. For example to get the number -13 we need to evaluate the expression 0 - 13.

We will implement - as a unary operator. Therefore the expression -13 won't be a negative number. It will be the unary - operator applied on the number 13.

Since - is an operator, it might be used multiple times. So the expression ---13 is also valid and gives the same result as -13. This means that any number of - symbols are valid before a number.

Our parser can be extended to support the unary - operator by adding a new layer to the list of precedence layers. This should have the lowest precedence, which means that we should use this new layer where we have been using int_token. Let's write a new parser:

> #include <boost/mpl/negate.hpp>
> using unary_exp1 = \
...> foldr_start_with_parser< \
...>   minus_token, \
...>   int_token, \
...>   boost::mpl::lambda<boost::mpl::negate<boost::mpl::_1>>::type \
...> >;

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We had to include <boost/mpl/negate.hpp> to get a metafunction we can negate a value with.

unary_exp1 is implemented with right to left folding: it starts from the number (parsed by int_token) and processes the - symbols one by one. The function to be called for each - symbol is a lambda expression that negates the number. So the number is negated for every - symbol.

We can implement a new version of mult_exp and exp_parser. They are the same as mult_exp2 and exp_parser16. The only difference is that they (directly only exp_parser18) use unary_exp1 instead of int_token.

> using mult_exp4 = \
...> foldl_start_with_parser< \
...>   sequence<one_of<times_token, divides_token>, unary_exp1>, \
...>   unary_exp1, \
...>   boost::mpl::quote2<binary_op> \
...> >;
> using exp_parser18 = \
...> build_parser< \
...>   foldl_start_with_parser< \
...>     sequence<one_of<plus_token, minus_token>, mult_exp4>, \
...>     mult_exp4, \
...>     boost::mpl::quote2<binary_op> \
...>   > \
...> >;

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Let's try these new parsers out:

> exp_parser18::apply<BOOST_METAPARSE_STRING("---13")>::type
mpl_::integral_c<int, -13>
> exp_parser18::apply<BOOST_METAPARSE_STRING("13")>::type
mpl_::integral_c<int, 13>

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It can deal with negative numbers correctly.

Our parsers already support the precedence of the different operators. Let's add support for parens as well, so users can override the precedence rules when they need to.

We can add a new parser for parsing (and evaluating) expressions in parens. First we introduce tokens for parsing the ( and ) symbols:

> using lparen_token = token<lit_c<'('>>;
> using rparen_token = token<lit_c<')'>>;

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A paren can contain an expression with any operators in it, so we add a parser for parsing (and evaluating) an expression containing operators of the highest precedence:

> using plus_exp1 = \
...> foldl_start_with_parser< \
...>   sequence<one_of<plus_token, minus_token>, mult_exp4>, \
...>   mult_exp4, \
...>   boost::mpl::quote2<binary_op> \
...> >;

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This was just a refactoring of our last parser for the calculator language. We can build the parser for our calculator language by using build_parser<plus_exp1> now. Let's write a parser for a paren expression:

> using paren_exp1 = sequence<lparen_token, plus_exp1, rparen_token>;

This definition parses a left paren, then a complete expression followed by a right paren. The result of parsing a paren expression is a vector of three elements: the ( character, the value of the expression and the ) character. We only need the value of the expression, which is the middle element. We could wrap the whole thing with a transform that gets the middle element and throws the rest away, but we don't need to. This is such a common pattern, that Metaparse provides middle_of for this:

> #include <boost/metaparse/middle_of.hpp>
> using paren_exp2 = middle_of<lparen_token, plus_exp1, rparen_token>;

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This implementation is almost the same as paren_exp1. The difference is that the result of parsing will be the value of the wrapped expression (the result of the plus_exp1 parser).

Let's define a parser for a primary expression which is either a number or an expression in parens:

> using primary_exp1 = one_of<int_token, paren_exp2>;

This parser accepts either a number using int_token or an expression in parens using paren_exp1.

Everywhere, where one can write a number (parsed by int_token), one can write a complete expression in parens as well. Our current parser implementation parses int_tokens in unary_exp, therefore we need to change that to use primary_exp instead of int_token.

There is a problem here: this makes the definitions of our parsers recursive. Think about it:

  • plus_exp uses mult_exp
  • mult_exp uses unary_exp
  • unary_exp uses primary_exp
  • primary_exp uses paren_exp
  • paren_exp uses plus_exp
[Note] Note

Since we are versioning the different parser implementations in Metashell (paren_exp1, paren_exp2, etc) you might try to define these recursive parsers and it might seem to work for the first time. In that case, when you later try creating a parser as part of a library (save your Metashell environment to a file or re-implement the important/successful elements) you face this issue.

We have been using type aliases (typedef and using) for defining the parsers. We can do it as long as their definition is not recursive. We can not refer to a type alias until we have defined it and type aliases can not be forward declared, so we can't find a point in the recursive cycle where we could start defining things.

A solution for this is making one of the parsers a new class instead of a type alias. Classes can be forward declared, therefore we can declare the class, implement the rest of the parsers as they can refer to that class and then define the class at the end.

Let's make plus_exp a class. So as a first step, let's forward declare it:

> struct plus_exp2;

Now we can write the rest of the parsers and they can refer to plus_exp2:

> using paren_exp3 = middle_of<lparen_token, plus_exp2, rparen_token>;
> using primary_exp2 = one_of<int_token, paren_exp2>;
> using unary_exp2 = \
...> foldr_start_with_parser< \
...>   minus_token, \
...>   primary_exp2, \
...>   boost::mpl::lambda<boost::mpl::negate<boost::mpl::_1>>::type \
...> >;
> using mult_exp5 = \
...> foldl_start_with_parser< \
...>   sequence<one_of<times_token, divides_token>, unary_exp2>, \
...>   unary_exp2, \
...>   boost::mpl::quote2<binary_op> \
...> >;

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There is nothing new in the definition of these parsers. They build up the hierarchy we have worked out in the earlier sections of this tutorial. The only element missing is plus_exp2:

> struct plus_exp2 : \
...> foldl_start_with_parser< \
...>   sequence<one_of<plus_token, minus_token>, mult_exp5>, \
...>   mult_exp5, \
...>   boost::mpl::quote2<binary_op> \
...> > {};

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This definition makes use of inheritance instead of type aliasing. Now we can write the parser for the calculator that supports parens as well:

> using exp_parser19 = build_parser<plus_exp2>;

Let's try this parser out:

> exp_parser19::apply<BOOST_METAPARSE_STRING("(1 + 2) * 3")>::type
mpl_::integral_c<int, 9>

Our parser accepts and can deal with parens in the expressions.

So far we have been focusing on parsing valid user input. However, users of our parsers will make mistakes and we should help them finding the source of the problem. And we should make this process not too painful.

The major difficulty in error reporting is that we have no direct way of showing error messages to the user. The parsers are template metaprograms. When they detect that the input is invalid, they can make the compilation fail and the compiler (running the metaprogram) display an error message. What we can do is making those error messages short and contain all information about the parsing error. We should make it easy to find this information in whatever the compiler displays.

So let's try to parse some invalid expression and let's see what happens:

> exp_parser19::apply<BOOST_METAPARSE_STRING("hello")>::type
<< compilation error >>

You will get a lot (if you have seen error messages coming from template metaprograms you know: this is not a lot.) of error messages. Take a closer look. It contains this:

x__________________PARSING_FAILED__________________x<
  1, 1,
  boost::metaparse::v1::error::literal_expected<'('>
>

You can see a formatted version above. There are no line breaks in the real output. This is relatively easy to spot (thanks to the ____________ part) and contains answers to the main questions one has when parsing fails:

  • where is the error? It is column 1 in line 1 (inside BOOST_METAPARSE_STRING). This is the 1, 1 part.
  • what is the problem? literal_expected<'('>. This is a bit misleading, as it contains only a part of the problem. An open paren is not the only acceptable token here, a number would also be fine. This misleading error message is our fault: we (the parser authors) need to make the parsing errors more descriptive.

So how can we improve the error messages? Let's look at what went wrong in the previous case:

  • The input was hello.
  • plus_exp2 tried to parse it.
  • plus_exp2 tried to parse it using mult_exp5 (assuming that this is the initial mult_exp in the list of + / - separated mult_exps).
  • so mult_exp5 tried to parse it.
  • mult_exp5 tried to parse it using unary_exp2 (assuming that this is the initial unary_exp in the list of * / / separated unary_exps).
  • so unary_exp2 tried to parse it.
  • unary_exp2 parsed all of the - symbols using minus_token. There were none of them (the input started with an h character).
  • so unary_exp2 tried to parse it using primary_exp2.
  • primary_exp2 is: one_of<int_token, paren_exp2>. It tried parsing the input with int_token (which failed) and then with paren_exp2 (which failed as well). So one_of could not parse the input with any of the choices and therefore it failed as well. In such situations one_of checks which parser made the most progress (consumed the most characters of the input) before failing and assumes, that that is the parser the user intended to use, thus it returns the error message coming from that parser. In this example none of the parsers could make any progress, in which case one_of returns the error coming from the last parser in the list. This was paren_exp2, and it expects the expression to start with an open paren. This is where the error message came from. The rest of the layers did not change or improve this error message so this was the error message displayed to the user.

We, the parser authors know: we expect a primary expression there. When one_of fails, it means that none was found.

To be able to return custom error messages (like missing_primary_expression) to the user, we need to define those error messages first. The error messages are represented by classes with some requirements:

  • It should have a static method called get_value() returning a std::string containing the description of the error.
  • It should be a template metaprogramming value.

These classes are called parsing error messages. To make it easy to implement such classes and to make it difficult (if not impossible) to forget to fulfill a requirement, Metaparse provides a macro for defining these classes. To get this macro, include the following header:

> #include <boost/metaparse/define_error.hpp>

Let's define the parsing error message:

> BOOST_METAPARSE_DEFINE_ERROR(missing_primary_expression, "Missing primary expression");

This defines a class called missing_primary_expression representing this error message. What we need to do is making our parser return this error message when one_of fails.

Let's define plus_exp and paren_exp first. Their definition does not change:

> struct plus_exp3;
> using paren_exp4 = middle_of<lparen_token, plus_exp3, rparen_token>;

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When the input contains no number (parsed by int_token) and no paren expression (parsed by paren_exp4), we should return the missing_primary_expression error message. We can do it by adding a third parser to one_of<int_token, paren_exp4, ...> which always fails with this error message. Metaparse provides fail for this:

> #include <boost/metaparse/fail.hpp>

Now we can define the primary_exp parser using it:

> using primary_exp3 = one_of<int_token, paren_exp4, fail<missing_primary_expression>>;

It adds fail<missing_primary_expression> to one_of as the last element. Therefore if none of the "real" cases parse the input and none of them makes any progress before failing, the error message will be missing_primary_expression.

We need to define the rest of the parsers. Their definition is the same as before:

> using unary_exp3 = \
...> foldr_start_with_parser< \
...>   minus_token, \
...>   primary_exp3, \
...>   boost::mpl::lambda<boost::mpl::negate<boost::mpl::_1>>::type \
...> >;
> using mult_exp6 = \
...> foldl_start_with_parser< \
...>   sequence<one_of<times_token, divides_token>, unary_exp3>, \
...>   unary_exp3, \
...>   boost::mpl::quote2<binary_op> \
...> >;
> struct plus_exp3 : \
...> foldl_start_with_parser< \
...>   sequence<one_of<plus_token, minus_token>, mult_exp6>, \
...>   mult_exp6, \
...>   boost::mpl::quote2<binary_op> \
...> > {};
> using exp_parser20 = build_parser<plus_exp3>;

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We can try to give our new parser an invalid input:

> exp_parser20::apply<BOOST_METAPARSE_STRING("hello")>::type
<< compilation error >>
..... x__________________PARSING_FAILED__________________x<1, 1, missing_primary_expression> ....
<< compilation error >>

The error message is now more specific to the calculator language. This covers only one case, where the error messages can be improved. Other cases (eg. missing closing parens, missing operators, etc) can be covered in a similar way.

Missing closing parens are common errors. Let's see how our parsers report them:

> exp_parser20::apply<BOOST_METAPARSE_STRING("(1+2")>::type
<< compilation error >>
..... x__________________PARSING_FAILED__________________x<1, 5, unpaired<1, 1, literal_expected<')'>>> ....
<< compilation error >>

The parser could detect that there is a missing paren and the error report points to the open paren which is not closed. This looks great, but we are not done yet. Let's try a slightly more complex input:

> exp_parser20::apply<BOOST_METAPARSE_STRING("0+(1+2")>::type
mpl_::integral_c<int, 0>

This is getting strange now. We parse the + <mult_exp> elements using foldl_start_with_parser (see the definition of plus_exp3). foldl_start_with_parser parses the input as long as it can and stops when it fails to parse it. In the above input, it parses 0 as the initial element and then it tries to parse the first + <mult_exp> element. But parsing the <mult_exp> part fails because of the missing closing paren. So foldl_start_with_parser stops and ignores this failing part of the input.

The result of the above is that we parse only the 0 part of the input, ignore the "garbage" at the end and assume that the value of the expression is 0. This could be fixed by using entire_input. Our parser would reject the input (because of the "garbage" at the end), but the error message would not be useful. So we take a different approach.

When foldl_start_with_parser stops, we should check if there is an extra broken + <mult_exp> there or not. When there is, we should report what is wrong with that broken + <mult_exp> (eg. a missing closing paren). Metaparse provides fail_at_first_char_expected to implement such validations. fail_at_first_char_expected<parser> checks how parser fails to parse the input: when it fails right at the first character, fail_at_first_char_expected assumes that there is no garbage and accepts the input. When parser consumes characters from the input before failing, fail_at_first_char_expected assumes that there is a broken expression and propagates the error. It can be used the following way:

> #include <boost/metaparse/fail_at_first_char_expected.hpp>
> #include <boost/metaparse/first_of.hpp>
> struct plus_exp4 : \
...> first_of< \
...>   foldl_start_with_parser< \
...>     sequence<one_of<plus_token, minus_token>, mult_exp6>, \
...>     mult_exp6, \
...>     boost::mpl::quote2<binary_op> \
...>   >, \
...>   fail_at_first_char_expected< \
...>     sequence<one_of<plus_token, minus_token>, mult_exp6> \
...>   > \
...> > {};
> using exp_parser21 = build_parser<plus_exp4>;

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first_of is similar to middle_of, but keeps the result of the first element, not the middle one. We use it to keep the "real" result (the result of foldl_start_with_parser) and to throw the dummy result coming from fail_at_first_char_expected away when there is no broken expression at the end. first_of propagates any error coming from fail_at_first_char_expected.

Let's try this new expression parser out with a missing closing paren:

> exp_parser21::apply<BOOST_METAPARSE_STRING("0+(1+2")>::type
<< compilation error >>
..... x__________________PARSING_FAILED__________________x<1, 7, unpaired<1, 3, literal_expected<')'>>> ....
<< compilation error >>

This works as expected now: it tells us that there is a missing paren and it points us the open paren which is not closed.

Our parser provides useful error messages for missing closing parens, however, the implementation of the parser (plus_exp4) is long and repetitive: it contains the parser for the repeated element (sequence<one_of<plus_token, minus_token>, mult_exp6>) twice, and that is not ideal.

plus_exp4 uses foldl_start_with_parser to implement repetition. Metaparse provides foldl_reject_incomplete_start_with_parser which does the same we did with first_of, foldl_start_with_parser and fail_at_first_char_expected together:

> #include <boost/metaparse/foldl_reject_incomplete_start_with_parser.hpp>
> struct plus_exp5 : \
...> foldl_reject_incomplete_start_with_parser< \
...>   sequence<one_of<plus_token, minus_token>, mult_exp6>, \
...>   mult_exp6, \
...>   boost::mpl::quote2<binary_op> \
...> > {};
> using exp_parser22 = build_parser<plus_exp5>;

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It parses the input using sequence<one_of<plus_token, minus_token>, mult_exp6>) repeatedly. When it fails, foldl_reject_incomplete_start_with_parser checks if it consumed any character before failing (the same as what fail_at_first_char_expected does), and if yes, then foldl_reject_incomplete_start_with_parser fails.

This makes the implementation of the repetition with advanced error reporting simpler. Let's try it out:

> exp_parser22::apply<BOOST_METAPARSE_STRING("0+(1+2")>::type
<< compilation error >>
..... x__________________PARSING_FAILED__________________x<1, 7, unpaired<1, 3, literal_expected<')'>>> ....
<< compilation error >>

Note that other folding parsers have their f versions as well (eg. foldr_reject_incomplete, foldl_reject_incomplete1, etc).

We have replaced one foldl_start_with_parser with foldl_reject_incomplete_start_with_parser. Other layers (mult_exp, unary_exp, etc) use folding as well. Let's use it at all layers:

> struct plus_exp6;
> using paren_exp5 = middle_of<lparen_token, plus_exp6, rparen_token>;
> using primary_exp4 = one_of<int_token, paren_exp5, fail<missing_primary_expression>>;
> using unary_exp4 = \
...> foldr_start_with_parser< \
...>   minus_token, \
...>   primary_exp4, \
...>   boost::mpl::lambda<boost::mpl::negate<boost::mpl::_1>>::type \
...> >;
> using mult_exp7 = \
...> foldl_reject_incomplete_start_with_parser< \
...>   sequence<one_of<times_token, divides_token>, unary_exp4>, \
...>   unary_exp4, \
...>   boost::mpl::quote2<binary_op> \
...> >;
> struct plus_exp6 : \
...> foldl_reject_incomplete_start_with_parser< \
...>   sequence<one_of<plus_token, minus_token>, mult_exp7>, \
...>   mult_exp7, \
...>   boost::mpl::quote2<binary_op> \
...> > {};
> using exp_parser23 = build_parser<plus_exp6>;

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[Note] Note

Note that unary_exp4 uses foldr_start_with_parser instead of foldr_reject_incomplete_start_with_parser. The reason behind it is that there is no foldr_reject_incomplete_start_with_parser. foldr_start_with_parser applies the primary_exp4 parser when minus_token does not accept the input any more. Therefore, it is supposed to catch the errors of incomplete expressions after the repetition.

Let's try different invalid expressions:

> exp_parser23::apply<BOOST_METAPARSE_STRING("1+(2*")>::type
<< compilation error >>
..... x__________________PARSING_FAILED__________________x<1, 6, missing_primary_expression> ....
<< compilation error >>

> exp_parser23::apply<BOOST_METAPARSE_STRING("1+(2*3")>::type
<< compilation error >>
..... x__________________PARSING_FAILED__________________x<1, 7, unpaired<1, 3, literal_expected<')'>>> ....
<< compilation error >>

This tutorial showed you how to build a parser for a calculator language. Now that you understand how to do this, you should be able to use the same techniques and building blocks presented here to build a parser for your own language. You should start building the parser and once you face a problem (eg. you need to add parens or you need better error messages) you can always return to this tutorial and read the section showing you how to deal with those situations.

#include <boost/metaparse/build_parser.hpp>
using namespace boost::metaparse;
using exp_parser1 = build_parser<int_>;
using int_token = token<int_>;
using plus_token = token<lit_c<'+'>>;
#include <boost/mpl/plus.hpp>
#include <boost/mpl/at.hpp>
template <class Vector> struct eval_plus : boost::mpl::plus< typename boost::mpl::at_c<Vector, 0>::type, typename boost::mpl::at_c<Vector, 2>::type > {};
eval_plus< boost::mpl::vector< mpl_::integral_c<int, 11>, mpl_::char_<'+'>, mpl_::integral_c<int, 2> >>::type
#include <boost/mpl/quote.hpp>
using exp_parser6 = build_parser< transform< sequence<int_token, plus_token, int_token>, boost::mpl::quote1<eval_plus> > >;
using exp_parser7 = build_parser< sequence< int_token,                                /* The first <number> */ repeated<sequence<plus_token, int_token>> /* The "+ <number>" elements */ > >;
using vector_of_numbers = boost::mpl::vector< boost::mpl::int_<2>, boost::mpl::int_<5>, boost::mpl::int_<6> >;
template <class Vector> struct sum_vector : boost::mpl::fold< Vector, boost::mpl::int_<0>, boost::mpl::lambda< boost::mpl::plus<boost::mpl::_1, boost::mpl::_2> >::type > {};
template <class Sum, class Item> struct sum_items : boost::mpl::plus< Sum, typename boost::mpl::at_c<Item, 1>::type > {};
sum_items< mpl_::integral_c<int, 1>, boost::mpl::vector<mpl_::char_<'+'>, mpl_::integral_c<int, 2>> >::type
boost::mpl::fold< boost::mpl::at_c<temp_result, 1>::type, /* The vector to summarise */ boost::mpl::int_<0>, /* The value to start the sum from */ boost::mpl::quote2<sum_items> /* The function to call in each iteration */ >::type
using exp_parser8 = build_parser< sequence< int_token, /* parse the first <number> */ transform< repeated<sequence<plus_token, int_token>>, /* parse the "+ <number>" elements */ /* lambda expression summarising the "+ <number>" elements using fold */ boost::mpl::lambda< /* The folding expression we have just created */ boost::mpl::fold< boost::mpl::_1, /* the argument of the lambda expression, the result */ /* of the repeated<...> parser */ boost::mpl::int_<0>, boost::mpl::quote2<sum_items> > >::type > > >;
using exp_parser9 = build_parser< transform< /* What we had so far */ sequence< int_token, transform< repeated<sequence<plus_token, int_token>>, boost::mpl::lambda< boost::mpl::fold< boost::mpl::_1, boost::mpl::int_<0>, boost::mpl::quote2<sum_items> > >::type > >, boost::mpl::quote1<sum_vector> /* summarise the vector of numbers */ > >;
using exp_parser10 = build_parser< transform< sequence< int_token, foldl< sequence<plus_token, int_token>, boost::mpl::int_<0>, boost::mpl::quote2<sum_items> > >, boost::mpl::quote1<sum_vector>> >;
>
using exp_parser11 = build_parser< foldl_start_with_parser< sequence<plus_token, int_token>, /* apply this parser repeatedly */ int_token, /* use this parser to get the initial value */ boost::mpl::quote2<sum_items> /* use this function to add a new value to the summary */ > >;
using exp_parser12 = build_parser< foldl_start_with_parser< sequence<one_of<plus_token, minus_token>, int_token>, int_token, boost::mpl::quote2<sum_items> > >;
template <class L, char Op, class R> struct eval_binary_op;
template <class L, class R> struct eval_binary_op<L, '+', R> : boost::mpl::plus<L, R>::type {};
template <class L, class R> struct eval_binary_op<L, '-', R> : boost::mpl::minus<L, R>::type {};
eval_binary_op<boost::mpl::int_<11>, '+', boost::mpl::int_<2>>::type
eval_binary_op<boost::mpl::int_<13>, '-', boost::mpl::int_<2>>::type
template <class S, class Item> struct binary_op : eval_binary_op< S, boost::mpl::at_c<Item, 0>::type::value, typename boost::mpl::at_c<Item, 1>::type > {};
using exp_parser13 = build_parser< foldl_start_with_parser< sequence<one_of<plus_token, minus_token>, int_token>, int_token, boost::mpl::quote2<binary_op> > >;
#include <boost/mpl/times.hpp>
template <class L, class R> struct eval_binary_op<L, '*', R> : boost::mpl::times<L, R>::type {};
using exp_parser14 = build_parser< foldl_start_with_parser< sequence<one_of<plus_token, minus_token, times_token>, int_token>, int_token, boost::mpl::quote2<binary_op> > >;
using exp_parser15 = build_parser< foldl_start_with_parser< sequence<one_of<plus_token, minus_token>, mult_exp1>, mult_exp1, boost::mpl::quote2<binary_op> > >;
#include <boost/mpl/divides.hpp>
template <class L, class R> struct eval_binary_op<L, '/', R> : boost::mpl::divides<L, R>::type {};
using divides_token = token<lit_c<'/'>>;
using mult_exp2 = foldl_start_with_parser< sequence<one_of<times_token, divides_token>, int_token>, int_token, boost::mpl::quote2<binary_op> >;
using exp_parser16 = build_parser< foldl_start_with_parser< sequence<one_of<plus_token, minus_token>, mult_exp2>, mult_exp2, boost::mpl::quote2<binary_op> > >;
template <class S, class Item> struct reverse_binary_op : eval_binary_op< typename boost::mpl::at_c<Item, 0>::type, boost::mpl::at_c<Item, 1>::type::value, S > {};
using mult_exp3 = foldr_start_with_parser< sequence<int_token, one_of<times_token, divides_token>>, /* The parser applied repeatedly */ int_token, /* The parser parsing the last number */ boost::mpl::quote2<reverse_binary_op> /* The function called for every result */ /* of applying the above parser */ >;
using exp_parser17 = build_parser< foldl_start_with_parser< sequence<one_of<plus_token, minus_token>, mult_exp3>, mult_exp3, boost::mpl::quote2<binary_op> > >;
#include <boost/mpl/negate.hpp>
using unary_exp1 = foldr_start_with_parser< minus_token, int_token, boost::mpl::lambda<boost::mpl::negate<boost::mpl::_1>>::type >;
using mult_exp4 = foldl_start_with_parser< sequence<one_of<times_token, divides_token>, unary_exp1>, unary_exp1, boost::mpl::quote2<binary_op> >;
using exp_parser18 = build_parser< foldl_start_with_parser< sequence<one_of<plus_token, minus_token>, mult_exp4>, mult_exp4, boost::mpl::quote2<binary_op> > >;
exp_parser18::apply<BOOST_METAPARSE_STRING("---13")>::type
exp_parser18::apply<BOOST_METAPARSE_STRING("13")>::type
using lparen_token = token<lit_c<'('>>;
using rparen_token = token<lit_c<')'>>;
using plus_exp1 = foldl_start_with_parser< sequence<one_of<plus_token, minus_token>, mult_exp4>, mult_exp4, boost::mpl::quote2<binary_op> >;
#include <boost/metaparse/middle_of.hpp>
using paren_exp2 = middle_of<lparen_token, plus_exp1, rparen_token>;
using paren_exp3 = middle_of<lparen_token, plus_exp2, rparen_token>;
using primary_exp2 = one_of<int_token, paren_exp2>;
using unary_exp2 = foldr_start_with_parser< minus_token, primary_exp2, boost::mpl::lambda<boost::mpl::negate<boost::mpl::_1>>::type >;
using mult_exp5 = foldl_start_with_parser< sequence<one_of<times_token, divides_token>, unary_exp2>, unary_exp2, boost::mpl::quote2<binary_op> >;
struct plus_exp2 : foldl_start_with_parser< sequence<one_of<plus_token, minus_token>, mult_exp5>, mult_exp5, boost::mpl::quote2<binary_op> > {};
struct plus_exp3;
using paren_exp4 = middle_of<lparen_token, plus_exp3, rparen_token>;
using unary_exp3 = foldr_start_with_parser< minus_token, primary_exp3, boost::mpl::lambda<boost::mpl::negate<boost::mpl::_1>>::type >;
using mult_exp6 = foldl_start_with_parser< sequence<one_of<times_token, divides_token>, unary_exp3>, unary_exp3, boost::mpl::quote2<binary_op> >;
struct plus_exp3 : foldl_start_with_parser< sequence<one_of<plus_token, minus_token>, mult_exp6>, mult_exp6, boost::mpl::quote2<binary_op> > {};
using exp_parser20 = build_parser<plus_exp3>;
#include <boost/metaparse/fail_at_first_char_expected.hpp>
#include <boost/metaparse/first_of.hpp>
struct plus_exp4 : first_of< foldl_start_with_parser< sequence<one_of<plus_token, minus_token>, mult_exp6>, mult_exp6, boost::mpl::quote2<binary_op> >, fail_at_first_char_expected< sequence<one_of<plus_token, minus_token>, mult_exp6> > > {};
using exp_parser21 = build_parser<plus_exp4>;
#include <boost/metaparse/foldl_reject_incomplete_start_with_parser.hpp>
struct plus_exp5 : foldl_reject_incomplete_start_with_parser< sequence<one_of<plus_token, minus_token>, mult_exp6>, mult_exp6, boost::mpl::quote2<binary_op> > {};
using exp_parser22 = build_parser<plus_exp5>;
struct plus_exp6;
using paren_exp5 = middle_of<lparen_token, plus_exp6, rparen_token>;
using primary_exp4 = one_of<int_token, paren_exp5, fail<missing_primary_expression>>;
using unary_exp4 = foldr_start_with_parser< minus_token, primary_exp4, boost::mpl::lambda<boost::mpl::negate<boost::mpl::_1>>::type >;
using mult_exp7 = foldl_reject_incomplete_start_with_parser< sequence<one_of<times_token, divides_token>, unary_exp4>, unary_exp4, boost::mpl::quote2<binary_op> >;
struct plus_exp6 : foldl_reject_incomplete_start_with_parser< sequence<one_of<plus_token, minus_token>, mult_exp7>, mult_exp7, boost::mpl::quote2<binary_op> > {};
using exp_parser23 = build_parser<plus_exp6>;

Definitions before section 3.

#include <boost/metaparse/string.hpp>

Definitions before section 3.1.

#include <boost/metaparse/string.hpp>
#include <boost/metaparse/int_.hpp>

#include <boost/metaparse/build_parser.hpp>

using namespace boost::metaparse;

using exp_parser1 = build_parser<int_>;

Definitions before section 3.2.

#include <boost/metaparse/string.hpp>
#include <boost/metaparse/int_.hpp>

#include <boost/metaparse/build_parser.hpp>

using namespace boost::metaparse;

using exp_parser1 = build_parser<int_>;

Definitions before section 3.3.

#include <boost/metaparse/string.hpp>
#include <boost/metaparse/int_.hpp>

#include <boost/metaparse/build_parser.hpp>

using namespace boost::metaparse;

using exp_parser1 = build_parser<int_>;
#include <boost/metaparse/entire_input.hpp>

using exp_parser2 = build_parser<entire_input<int_>>;

Definitions before section 4.

#include <boost/metaparse/string.hpp>
#include <boost/metaparse/int_.hpp>

#include <boost/metaparse/build_parser.hpp>

using namespace boost::metaparse;

using exp_parser1 = build_parser<int_>;
#include <boost/metaparse/entire_input.hpp>

using exp_parser2 = build_parser<entire_input<int_>>;
#include <boost/metaparse/token.hpp>

using exp_parser3 = build_parser<entire_input<token<int_>>>;

Definitions before section 4.1.

#include <boost/metaparse/string.hpp>
#include <boost/metaparse/int_.hpp>

#include <boost/metaparse/build_parser.hpp>

using namespace boost::metaparse;

using exp_parser1 = build_parser<int_>;
#include <boost/metaparse/entire_input.hpp>

using exp_parser2 = build_parser<entire_input<int_>>;
#include <boost/metaparse/token.hpp>

using exp_parser3 = build_parser<entire_input<token<int_>>>;
#include <boost/metaparse/lit_c.hpp>

#include <boost/metaparse/sequence.hpp>

using exp_parser4 = build_parser<sequence<token<int_>, token<lit_c<'+'>>, token<int_>>>;

#include <metashell/formatter.hpp>

Definitions before section 4.2.

#include <boost/metaparse/string.hpp>
#include <boost/metaparse/int_.hpp>

#include <boost/metaparse/build_parser.hpp>

using namespace boost::metaparse;

using exp_parser1 = build_parser<int_>;
#include <boost/metaparse/entire_input.hpp>

using exp_parser2 = build_parser<entire_input<int_>>;
#include <boost/metaparse/token.hpp>

using exp_parser3 = build_parser<entire_input<token<int_>>>;
#include <boost/metaparse/lit_c.hpp>

#include <boost/metaparse/sequence.hpp>

using exp_parser4 = build_parser<sequence<token<int_>, token<lit_c<'+'>>, token<int_>>>;

#include <metashell/formatter.hpp>

using int_token = token<int_>;

using plus_token = token<lit_c<'+'>>;

using exp_parser5 = build_parser<sequence<int_token, plus_token, int_token>>;

Definitions before section 5.

#include <boost/metaparse/string.hpp>
#include <boost/metaparse/int_.hpp>

#include <boost/metaparse/build_parser.hpp>

using namespace boost::metaparse;

using exp_parser1 = build_parser<int_>;
#include <boost/metaparse/entire_input.hpp>

using exp_parser2 = build_parser<entire_input<int_>>;
#include <boost/metaparse/token.hpp>

using exp_parser3 = build_parser<entire_input<token<int_>>>;
#include <boost/metaparse/lit_c.hpp>

#include <boost/metaparse/sequence.hpp>

using exp_parser4 = build_parser<sequence<token<int_>, token<lit_c<'+'>>, token<int_>>>;

#include <metashell/formatter.hpp>

using int_token = token<int_>;

using plus_token = token<lit_c<'+'>>;

using exp_parser5 = build_parser<sequence<int_token, plus_token, int_token>>;
#include <boost/metaparse/transform.hpp>

#include <boost/mpl/plus.hpp>

#include <boost/mpl/at.hpp>

template <class Vector>
 struct eval_plus :
   boost::mpl::plus<
     typename boost::mpl::at_c<Vector, 0>::type,
     typename boost::mpl::at_c<Vector, 2>::type
   > {};

#include <boost/mpl/quote.hpp>

using exp_parser6 =
 build_parser<
   transform<
     sequence<int_token, plus_token, int_token>,
     boost::mpl::quote1<eval_plus>
   >
 >;

Definitions before section 5.1.

#include <boost/metaparse/string.hpp>
#include <boost/metaparse/int_.hpp>

#include <boost/metaparse/build_parser.hpp>

using namespace boost::metaparse;

using exp_parser1 = build_parser<int_>;
#include <boost/metaparse/entire_input.hpp>

using exp_parser2 = build_parser<entire_input<int_>>;
#include <boost/metaparse/token.hpp>

using exp_parser3 = build_parser<entire_input<token<int_>>>;
#include <boost/metaparse/lit_c.hpp>

#include <boost/metaparse/sequence.hpp>

using exp_parser4 = build_parser<sequence<token<int_>, token<lit_c<'+'>>, token<int_>>>;

#include <metashell/formatter.hpp>

using int_token = token<int_>;

using plus_token = token<lit_c<'+'>>;

using exp_parser5 = build_parser<sequence<int_token, plus_token, int_token>>;
#include <boost/metaparse/transform.hpp>

#include <boost/mpl/plus.hpp>

#include <boost/mpl/at.hpp>

template <class Vector>
 struct eval_plus :
   boost::mpl::plus<
     typename boost::mpl::at_c<Vector, 0>::type,
     typename boost::mpl::at_c<Vector, 2>::type
   > {};

#include <boost/mpl/quote.hpp>

using exp_parser6 =
 build_parser<
   transform<
     sequence<int_token, plus_token, int_token>,
     boost::mpl::quote1<eval_plus>
   >
 >;

Definitions before section 5.2.

#include <boost/metaparse/string.hpp>
#include <boost/metaparse/int_.hpp>

#include <boost/metaparse/build_parser.hpp>

using namespace boost::metaparse;

using exp_parser1 = build_parser<int_>;
#include <boost/metaparse/entire_input.hpp>

using exp_parser2 = build_parser<entire_input<int_>>;
#include <boost/metaparse/token.hpp>

using exp_parser3 = build_parser<entire_input<token<int_>>>;
#include <boost/metaparse/lit_c.hpp>

#include <boost/metaparse/sequence.hpp>

using exp_parser4 = build_parser<sequence<token<int_>, token<lit_c<'+'>>, token<int_>>>;

#include <metashell/formatter.hpp>

using int_token = token<int_>;

using plus_token = token<lit_c<'+'>>;

using exp_parser5 = build_parser<sequence<int_token, plus_token, int_token>>;
#include <boost/metaparse/transform.hpp>

#include <boost/mpl/plus.hpp>

#include <boost/mpl/at.hpp>

template <class Vector>
 struct eval_plus :
   boost::mpl::plus<
     typename boost::mpl::at_c<Vector, 0>::type,
     typename boost::mpl::at_c<Vector, 2>::type
   > {};

#include <boost/mpl/quote.hpp>

using exp_parser6 =
 build_parser<
   transform<
     sequence<int_token, plus_token, int_token>,
     boost::mpl::quote1<eval_plus>
   >
 >;
#include <boost/metaparse/any.hpp>

using exp_parser7 =
 build_parser<
   sequence<
     int_token,                                /* The first <number> */
     repeated<sequence<plus_token, int_token>> /* The "+ <number>" elements */
   >
 >;

Definitions before section 5.2.1.

#include <boost/metaparse/string.hpp>
#include <boost/metaparse/int_.hpp>

#include <boost/metaparse/build_parser.hpp>

using namespace boost::metaparse;

using exp_parser1 = build_parser<int_>;
#include <boost/metaparse/entire_input.hpp>

using exp_parser2 = build_parser<entire_input<int_>>;
#include <boost/metaparse/token.hpp>

using exp_parser3 = build_parser<entire_input<token<int_>>>;
#include <boost/metaparse/lit_c.hpp>

#include <boost/metaparse/sequence.hpp>

using exp_parser4 = build_parser<sequence<token<int_>, token<lit_c<'+'>>, token<int_>>>;

#include <metashell/formatter.hpp>

using int_token = token<int_>;

using plus_token = token<lit_c<'+'>>;

using exp_parser5 = build_parser<sequence<int_token, plus_token, int_token>>;
#include <boost/metaparse/transform.hpp>

#include <boost/mpl/plus.hpp>

#include <boost/mpl/at.hpp>

template <class Vector>
 struct eval_plus :
   boost::mpl::plus<
     typename boost::mpl::at_c<Vector, 0>::type,
     typename boost::mpl::at_c<Vector, 2>::type
   > {};

#include <boost/mpl/quote.hpp>

using exp_parser6 =
 build_parser<
   transform<
     sequence<int_token, plus_token, int_token>,
     boost::mpl::quote1<eval_plus>
   >
 >;
#include <boost/metaparse/any.hpp>

using exp_parser7 =
 build_parser<
   sequence<
     int_token,                                /* The first <number> */
     repeated<sequence<plus_token, int_token>> /* The "+ <number>" elements */
   >
 >;
using temp_result = exp_parser7::apply<BOOST_METAPARSE_STRING("1 + 2 + 3 + 4")>::type;

Definitions before section 5.2.2.

#include <boost/metaparse/string.hpp>
#include <boost/metaparse/int_.hpp>

#include <boost/metaparse/build_parser.hpp>

using namespace boost::metaparse;

using exp_parser1 = build_parser<int_>;
#include <boost/metaparse/entire_input.hpp>

using exp_parser2 = build_parser<entire_input<int_>>;
#include <boost/metaparse/token.hpp>

using exp_parser3 = build_parser<entire_input<token<int_>>>;
#include <boost/metaparse/lit_c.hpp>

#include <boost/metaparse/sequence.hpp>

using exp_parser4 = build_parser<sequence<token<int_>, token<lit_c<'+'>>, token<int_>>>;

#include <metashell/formatter.hpp>

using int_token = token<int_>;

using plus_token = token<lit_c<'+'>>;

using exp_parser5 = build_parser<sequence<int_token, plus_token, int_token>>;
#include <boost/metaparse/transform.hpp>

#include <boost/mpl/plus.hpp>

#include <boost/mpl/at.hpp>

template <class Vector>
 struct eval_plus :
   boost::mpl::plus<
     typename boost::mpl::at_c<Vector, 0>::type,
     typename boost::mpl::at_c<Vector, 2>::type
   > {};

#include <boost/mpl/quote.hpp>

using exp_parser6 =
 build_parser<
   transform<
     sequence<int_token, plus_token, int_token>,
     boost::mpl::quote1<eval_plus>
   >
 >;
#include <boost/metaparse/any.hpp>

using exp_parser7 =
 build_parser<
   sequence<
     int_token,                                /* The first <number> */
     repeated<sequence<plus_token, int_token>> /* The "+ <number>" elements */
   >
 >;
using temp_result = exp_parser7::apply<BOOST_METAPARSE_STRING("1 + 2 + 3 + 4")>::type;
#include <boost/mpl/fold.hpp>

using vector_of_numbers =
 boost::mpl::vector<
   boost::mpl::int_<2>,
   boost::mpl::int_<5>,
   boost::mpl::int_<6>
 >;

template <class Vector>
 struct sum_vector :
    boost::mpl::fold<
      Vector,
      boost::mpl::int_<0>,
      boost::mpl::lambda<
        boost::mpl::plus<boost::mpl::_1, boost::mpl::_2>
      >::type
    >
  {};

template <class Sum, class Item>
   struct sum_items :
     boost::mpl::plus<
       Sum,
       typename boost::mpl::at_c<Item, 1>::type
     >
 {};

Definitions before section 5.2.3.

#include <boost/metaparse/string.hpp>
#include <boost/metaparse/int_.hpp>

#include <boost/metaparse/build_parser.hpp>

using namespace boost::metaparse;

using exp_parser1 = build_parser<int_>;
#include <boost/metaparse/entire_input.hpp>

using exp_parser2 = build_parser<entire_input<int_>>;
#include <boost/metaparse/token.hpp>

using exp_parser3 = build_parser<entire_input<token<int_>>>;
#include <boost/metaparse/lit_c.hpp>

#include <boost/metaparse/sequence.hpp>

using exp_parser4 = build_parser<sequence<token<int_>, token<lit_c<'+'>>, token<int_>>>;

#include <metashell/formatter.hpp>

using int_token = token<int_>;

using plus_token = token<lit_c<'+'>>;

using exp_parser5 = build_parser<sequence<int_token, plus_token, int_token>>;
#include <boost/metaparse/transform.hpp>

#include <boost/mpl/plus.hpp>

#include <boost/mpl/at.hpp>

template <class Vector>
 struct eval_plus :
   boost::mpl::plus<
     typename boost::mpl::at_c<Vector, 0>::type,
     typename boost::mpl::at_c<Vector, 2>::type
   > {};

#include <boost/mpl/quote.hpp>

using exp_parser6 =
 build_parser<
   transform<
     sequence<int_token, plus_token, int_token>,
     boost::mpl::quote1<eval_plus>
   >
 >;
#include <boost/metaparse/any.hpp>

using exp_parser7 =
 build_parser<
   sequence<
     int_token,                                /* The first <number> */
     repeated<sequence<plus_token, int_token>> /* The "+ <number>" elements */
   >
 >;
using temp_result = exp_parser7::apply<BOOST_METAPARSE_STRING("1 + 2 + 3 + 4")>::type;
#include <boost/mpl/fold.hpp>

using vector_of_numbers =
 boost::mpl::vector<
   boost::mpl::int_<2>,
   boost::mpl::int_<5>,
   boost::mpl::int_<6>
 >;

template <class Vector>
 struct sum_vector :
    boost::mpl::fold<
      Vector,
      boost::mpl::int_<0>,
      boost::mpl::lambda<
        boost::mpl::plus<boost::mpl::_1, boost::mpl::_2>
      >::type
    >
  {};

template <class Sum, class Item>
   struct sum_items :
     boost::mpl::plus<
       Sum,
       typename boost::mpl::at_c<Item, 1>::type
     >
 {};
using exp_parser8 =
 build_parser<
   sequence<
     int_token, /* parse the first <number> */
     transform<
       repeated<sequence<plus_token, int_token>>, /* parse the "+ <number>" elements */
       /* lambda expression summarising the "+ <number>" elements using fold */
       boost::mpl::lambda<
         /* The folding expression we have just created */
         boost::mpl::fold<
           boost::mpl::_1, /* the argument of the lambda expression, the result */
                           /* of the repeated<...> parser */
           boost::mpl::int_<0>,
           boost::mpl::quote2<sum_items>
         >
       >::type
     >
   >
 >;

using exp_parser9 =
 build_parser<
   transform<
     /* What we had so far */
     sequence<
       int_token,
       transform<
         repeated<sequence<plus_token, int_token>>,
         boost::mpl::lambda<
           boost::mpl::fold<
             boost::mpl::_1,
             boost::mpl::int_<0>,
             boost::mpl::quote2<sum_items>
           >
         >::type
       >
     >,
     boost::mpl::quote1<sum_vector> /* summarise the vector of numbers */
   >
 >;

Definitions before section 5.2.4.

#include <boost/metaparse/string.hpp>
#include <boost/metaparse/int_.hpp>

#include <boost/metaparse/build_parser.hpp>

using namespace boost::metaparse;

using exp_parser1 = build_parser<int_>;
#include <boost/metaparse/entire_input.hpp>

using exp_parser2 = build_parser<entire_input<int_>>;
#include <boost/metaparse/token.hpp>

using exp_parser3 = build_parser<entire_input<token<int_>>>;
#include <boost/metaparse/lit_c.hpp>

#include <boost/metaparse/sequence.hpp>

using exp_parser4 = build_parser<sequence<token<int_>, token<lit_c<'+'>>, token<int_>>>;

#include <metashell/formatter.hpp>

using int_token = token<int_>;

using plus_token = token<lit_c<'+'>>;

using exp_parser5 = build_parser<sequence<int_token, plus_token, int_token>>;
#include <boost/metaparse/transform.hpp>

#include <boost/mpl/plus.hpp>

#include <boost/mpl/at.hpp>

template <class Vector>
 struct eval_plus :
   boost::mpl::plus<
     typename boost::mpl::at_c<Vector, 0>::type,
     typename boost::mpl::at_c<Vector, 2>::type
   > {};

#include <boost/mpl/quote.hpp>

using exp_parser6 =
 build_parser<
   transform<
     sequence<int_token, plus_token, int_token>,
     boost::mpl::quote1<eval_plus>
   >
 >;
#include <boost/metaparse/any.hpp>

using exp_parser7 =
 build_parser<
   sequence<
     int_token,                                /* The first <number> */
     repeated<sequence<plus_token, int_token>> /* The "+ <number>" elements */
   >
 >;
using temp_result = exp_parser7::apply<BOOST_METAPARSE_STRING("1 + 2 + 3 + 4")>::type;
#include <boost/mpl/fold.hpp>

using vector_of_numbers =
 boost::mpl::vector<
   boost::mpl::int_<2>,
   boost::mpl::int_<5>,
   boost::mpl::int_<6>
 >;

template <class Vector>
 struct sum_vector :
    boost::mpl::fold<
      Vector,
      boost::mpl::int_<0>,
      boost::mpl::lambda<
        boost::mpl::plus<boost::mpl::_1, boost::mpl::_2>
      >::type
    >
  {};

template <class Sum, class Item>
   struct sum_items :
     boost::mpl::plus<
       Sum,
       typename boost::mpl::at_c<Item, 1>::type
     >
 {};
using exp_parser8 =
 build_parser<
   sequence<
     int_token, /* parse the first <number> */
     transform<
       repeated<sequence<plus_token, int_token>>, /* parse the "+ <number>" elements */
       /* lambda expression summarising the "+ <number>" elements using fold */
       boost::mpl::lambda<
         /* The folding expression we have just created */
         boost::mpl::fold<
           boost::mpl::_1, /* the argument of the lambda expression, the result */
                           /* of the repeated<...> parser */
           boost::mpl::int_<0>,
           boost::mpl::quote2<sum_items>
         >
       >::type
     >
   >
 >;

using exp_parser9 =
 build_parser<
   transform<
     /* What we had so far */
     sequence<
       int_token,
       transform<
         repeated<sequence<plus_token, int_token>>,
         boost::mpl::lambda<
           boost::mpl::fold<
             boost::mpl::_1,
             boost::mpl::int_<0>,
             boost::mpl::quote2<sum_items>
           >
         >::type
       >
     >,
     boost::mpl::quote1<sum_vector> /* summarise the vector of numbers */
   >
 >;
#include <boost/metaparse/foldl.hpp>

using exp_parser10 =
 build_parser<
   transform<
     sequence<
       int_token,
       foldl<
         sequence<plus_token, int_token>,
         boost::mpl::int_<0>,
         boost::mpl::quote2<sum_items>
       >
     >,
     boost::mpl::quote1<sum_vector>>
 >;

Definitions before section 6.

#include <boost/metaparse/string.hpp>
#include <boost/metaparse/int_.hpp>

#include <boost/metaparse/build_parser.hpp>

using namespace boost::metaparse;

using exp_parser1 = build_parser<int_>;
#include <boost/metaparse/entire_input.hpp>

using exp_parser2 = build_parser<entire_input<int_>>;
#include <boost/metaparse/token.hpp>

using exp_parser3 = build_parser<entire_input<token<int_>>>;
#include <boost/metaparse/lit_c.hpp>

#include <boost/metaparse/sequence.hpp>

using exp_parser4 = build_parser<sequence<token<int_>, token<lit_c<'+'>>, token<int_>>>;

#include <metashell/formatter.hpp>

using int_token = token<int_>;

using plus_token = token<lit_c<'+'>>;

using exp_parser5 = build_parser<sequence<int_token, plus_token, int_token>>;
#include <boost/metaparse/transform.hpp>

#include <boost/mpl/plus.hpp>

#include <boost/mpl/at.hpp>

template <class Vector>
 struct eval_plus :
   boost::mpl::plus<
     typename boost::mpl::at_c<Vector, 0>::type,
     typename boost::mpl::at_c<Vector, 2>::type
   > {};

#include <boost/mpl/quote.hpp>

using exp_parser6 =
 build_parser<
   transform<
     sequence<int_token, plus_token, int_token>,
     boost::mpl::quote1<eval_plus>
   >
 >;
#include <boost/metaparse/any.hpp>

using exp_parser7 =
 build_parser<
   sequence<
     int_token,                                /* The first <number> */
     repeated<sequence<plus_token, int_token>> /* The "+ <number>" elements */
   >
 >;
using temp_result = exp_parser7::apply<BOOST_METAPARSE_STRING("1 + 2 + 3 + 4")>::type;
#include <boost/mpl/fold.hpp>

using vector_of_numbers =
 boost::mpl::vector<
   boost::mpl::int_<2>,
   boost::mpl::int_<5>,
   boost::mpl::int_<6>
 >;

template <class Vector>
 struct sum_vector :
    boost::mpl::fold<
      Vector,
      boost::mpl::int_<0>,
      boost::mpl::lambda<
        boost::mpl::plus<boost::mpl::_1, boost::mpl::_2>
      >::type
    >
  {};

template <class Sum, class Item>
   struct sum_items :
     boost::mpl::plus<
       Sum,
       typename boost::mpl::at_c<Item, 1>::type
     >
 {};
using exp_parser8 =
 build_parser<
   sequence<
     int_token, /* parse the first <number> */
     transform<
       repeated<sequence<plus_token, int_token>>, /* parse the "+ <number>" elements */
       /* lambda expression summarising the "+ <number>" elements using fold */
       boost::mpl::lambda<
         /* The folding expression we have just created */
         boost::mpl::fold<
           boost::mpl::_1, /* the argument of the lambda expression, the result */
                           /* of the repeated<...> parser */
           boost::mpl::int_<0>,
           boost::mpl::quote2<sum_items>
         >
       >::type
     >
   >
 >;

using exp_parser9 =
 build_parser<
   transform<
     /* What we had so far */
     sequence<
       int_token,
       transform<
         repeated<sequence<plus_token, int_token>>,
         boost::mpl::lambda<
           boost::mpl::fold<
             boost::mpl::_1,
             boost::mpl::int_<0>,
             boost::mpl::quote2<sum_items>
           >
         >::type
       >
     >,
     boost::mpl::quote1<sum_vector> /* summarise the vector of numbers */
   >
 >;
#include <boost/metaparse/foldl.hpp>

using exp_parser10 =
 build_parser<
   transform<
     sequence<
       int_token,
       foldl<
         sequence<plus_token, int_token>,
         boost::mpl::int_<0>,
         boost::mpl::quote2<sum_items>
       >
     >,
     boost::mpl::quote1<sum_vector>>
 >;
#include <boost/metaparse/foldl_start_with_parser.hpp>

using exp_parser11 =
 build_parser<
   foldl_start_with_parser<
     sequence<plus_token, int_token>, /* apply this parser repeatedly */
     int_token, /* use this parser to get the initial value */
     boost::mpl::quote2<sum_items> /* use this function to add a new value to the summary */
   >
 >;

Definitions before section 6.1.

#include <boost/metaparse/string.hpp>
#include <boost/metaparse/int_.hpp>

#include <boost/metaparse/build_parser.hpp>

using namespace boost::metaparse;

using exp_parser1 = build_parser<int_>;
#include <boost/metaparse/entire_input.hpp>

using exp_parser2 = build_parser<entire_input<int_>>;
#include <boost/metaparse/token.hpp>

using exp_parser3 = build_parser<entire_input<token<int_>>>;
#include <boost/metaparse/lit_c.hpp>

#include <boost/metaparse/sequence.hpp>

using exp_parser4 = build_parser<sequence<token<int_>, token<lit_c<'+'>>, token<int_>>>;

#include <metashell/formatter.hpp>

using int_token = token<int_>;

using plus_token = token<lit_c<'+'>>;

using exp_parser5 = build_parser<sequence<int_token, plus_token, int_token>>;
#include <boost/metaparse/transform.hpp>

#include <boost/mpl/plus.hpp>

#include <boost/mpl/at.hpp>

template <class Vector>
 struct eval_plus :
   boost::mpl::plus<
     typename boost::mpl::at_c<Vector, 0>::type,
     typename boost::mpl::at_c<Vector, 2>::type
   > {};

#include <boost/mpl/quote.hpp>

using exp_parser6 =
 build_parser<
   transform<
     sequence<int_token, plus_token, int_token>,
     boost::mpl::quote1<eval_plus>
   >
 >;
#include <boost/metaparse/any.hpp>

using exp_parser7 =
 build_parser<
   sequence<
     int_token,                                /* The first <number> */
     repeated<sequence<plus_token, int_token>> /* The "+ <number>" elements */
   >
 >;
using temp_result = exp_parser7::apply<BOOST_METAPARSE_STRING("1 + 2 + 3 + 4")>::type;
#include <boost/mpl/fold.hpp>

using vector_of_numbers =
 boost::mpl::vector<
   boost::mpl::int_<2>,
   boost::mpl::int_<5>,
   boost::mpl::int_<6>
 >;

template <class Vector>
 struct sum_vector :
    boost::mpl::fold<
      Vector,
      boost::mpl::int_<0>,
      boost::mpl::lambda<
        boost::mpl::plus<boost::mpl::_1, boost::mpl::_2>
      >::type
    >
  {};

template <class Sum, class Item>
   struct sum_items :
     boost::mpl::plus<
       Sum,
       typename boost::mpl::at_c<Item, 1>::type
     >
 {};
using exp_parser8 =
 build_parser<
   sequence<
     int_token, /* parse the first <number> */
     transform<
       repeated<sequence<plus_token, int_token>>, /* parse the "+ <number>" elements */
       /* lambda expression summarising the "+ <number>" elements using fold */
       boost::mpl::lambda<
         /* The folding expression we have just created */
         boost::mpl::fold<
           boost::mpl::_1, /* the argument of the lambda expression, the result */
                           /* of the repeated<...> parser */
           boost::mpl::int_<0>,
           boost::mpl::quote2<sum_items>
         >
       >::type
     >
   >
 >;

using exp_parser9 =
 build_parser<
   transform<
     /* What we had so far */
     sequence<
       int_token,
       transform<
         repeated<sequence<plus_token, int_token>>,
         boost::mpl::lambda<
           boost::mpl::fold<
             boost::mpl::_1,
             boost::mpl::int_<0>,
             boost::mpl::quote2<sum_items>
           >
         >::type
       >
     >,
     boost::mpl::quote1<sum_vector> /* summarise the vector of numbers */
   >
 >;
#include <boost/metaparse/foldl.hpp>

using exp_parser10 =
 build_parser<
   transform<
     sequence<
       int_token,
       foldl<
         sequence<plus_token, int_token>,
         boost::mpl::int_<0>,
         boost::mpl::quote2<sum_items>
       >
     >,
     boost::mpl::quote1<sum_vector>>
 >;
#include <boost/metaparse/foldl_start_with_parser.hpp>

using exp_parser11 =
 build_parser<
   foldl_start_with_parser<
     sequence<plus_token, int_token>, /* apply this parser repeatedly */
     int_token, /* use this parser to get the initial value */
     boost::mpl::quote2<sum_items> /* use this function to add a new value to the summary */
   >
 >;

Definitions before section 6.2.

#include <boost/metaparse/string.hpp>
#include <boost/metaparse/int_.hpp>

#include <boost/metaparse/build_parser.hpp>

using namespace boost::metaparse;

using exp_parser1 = build_parser<int_>;
#include <boost/metaparse/entire_input.hpp>

using exp_parser2 = build_parser<entire_input<int_>>;
#include <boost/metaparse/token.hpp>

using exp_parser3 = build_parser<entire_input<token<int_>>>;
#include <boost/metaparse/lit_c.hpp>

#include <boost/metaparse/sequence.hpp>

using exp_parser4 = build_parser<sequence<token<int_>, token<lit_c<'+'>>, token<int_>>>;

#include <metashell/formatter.hpp>

using int_token = token<int_>;

using plus_token = token<lit_c<'+'>>;

using exp_parser5 = build_parser<sequence<int_token, plus_token, int_token>>;
#include <boost/metaparse/transform.hpp>

#include <boost/mpl/plus.hpp>

#include <boost/mpl/at.hpp>

template <class Vector>
 struct eval_plus :
   boost::mpl::plus<
     typename boost::mpl::at_c<Vector, 0>::type,
     typename boost::mpl::at_c<Vector, 2>::type
   > {};

#include <boost/mpl/quote.hpp>

using exp_parser6 =
 build_parser<
   transform<
     sequence<int_token, plus_token, int_token>,
     boost::mpl::quote1<eval_plus>
   >
 >;
#include <boost/metaparse/any.hpp>

using exp_parser7 =
 build_parser<
   sequence<
     int_token,                                /* The first <number> */
     repeated<sequence<plus_token, int_token>> /* The "+ <number>" elements */
   >
 >;
using temp_result = exp_parser7::apply<BOOST_METAPARSE_STRING("1 + 2 + 3 + 4")>::type;
#include <boost/mpl/fold.hpp>

using vector_of_numbers =
 boost::mpl::vector<
   boost::mpl::int_<2>,
   boost::mpl::int_<5>,
   boost::mpl::int_<6>
 >;

template <class Vector>
 struct sum_vector :
    boost::mpl::fold<
      Vector,
      boost::mpl::int_<0>,
      boost::mpl::lambda<
        boost::mpl::plus<boost::mpl::_1, boost::mpl::_2>
      >::type
    >
  {};

template <class Sum, class Item>
   struct sum_items :
     boost::mpl::plus<
       Sum,
       typename boost::mpl::at_c<Item, 1>::type
     >
 {};
using exp_parser8 =
 build_parser<
   sequence<
     int_token, /* parse the first <number> */
     transform<
       repeated<sequence<plus_token, int_token>>, /* parse the "+ <number>" elements */
       /* lambda expression summarising the "+ <number>" elements using fold */
       boost::mpl::lambda<
         /* The folding expression we have just created */
         boost::mpl::fold<
           boost::mpl::_1, /* the argument of the lambda expression, the result */
                           /* of the repeated<...> parser */
           boost::mpl::int_<0>,
           boost::mpl::quote2<sum_items>
         >
       >::type
     >
   >
 >;

using exp_parser9 =
 build_parser<
   transform<
     /* What we had so far */
     sequence<
       int_token,
       transform<
         repeated<sequence<plus_token, int_token>>,
         boost::mpl::lambda<
           boost::mpl::fold<
             boost::mpl::_1,
             boost::mpl::int_<0>,
             boost::mpl::quote2<sum_items>
           >
         >::type
       >
     >,
     boost::mpl::quote1<sum_vector> /* summarise the vector of numbers */
   >
 >;
#include <boost/metaparse/foldl.hpp>

using exp_parser10 =
 build_parser<
   transform<
     sequence<
       int_token,
       foldl<
         sequence<plus_token, int_token>,
         boost::mpl::int_<0>,
         boost::mpl::quote2<sum_items>
       >
     >,
     boost::mpl::quote1<sum_vector>>
 >;
#include <boost/metaparse/foldl_start_with_parser.hpp>

using exp_parser11 =
 build_parser<
   foldl_start_with_parser<
     sequence<plus_token, int_token>, /* apply this parser repeatedly */
     int_token, /* use this parser to get the initial value */
     boost::mpl::quote2<sum_items> /* use this function to add a new value to the summary */
   >
 >;
using minus_token = token<lit_c<'-'>>;

#include <boost/metaparse/one_of.hpp>

using exp_parser12 =
 build_parser<
   foldl_start_with_parser<
     sequence<one_of<plus_token, minus_token>, int_token>,
     int_token,
     boost::mpl::quote2<sum_items>
   >
 >;

Definitions before section 7.

#include <boost/metaparse/string.hpp>
#include <boost/metaparse/int_.hpp>

#include <boost/metaparse/build_parser.hpp>

using namespace boost::metaparse;

using exp_parser1 = build_parser<int_>;
#include <boost/metaparse/entire_input.hpp>

using exp_parser2 = build_parser<entire_input<int_>>;
#include <boost/metaparse/token.hpp>

using exp_parser3 = build_parser<entire_input<token<int_>>>;
#include <boost/metaparse/lit_c.hpp>

#include <boost/metaparse/sequence.hpp>

using exp_parser4 = build_parser<sequence<token<int_>, token<lit_c<'+'>>, token<int_>>>;

#include <metashell/formatter.hpp>

using int_token = token<int_>;

using plus_token = token<lit_c<'+'>>;

using exp_parser5 = build_parser<sequence<int_token, plus_token, int_token>>;
#include <boost/metaparse/transform.hpp>

#include <boost/mpl/plus.hpp>

#include <boost/mpl/at.hpp>

template <class Vector>
 struct eval_plus :
   boost::mpl::plus<
     typename boost::mpl::at_c<Vector, 0>::type,
     typename boost::mpl::at_c<Vector, 2>::type
   > {};

#include <boost/mpl/quote.hpp>

using exp_parser6 =
 build_parser<
   transform<
     sequence<int_token, plus_token, int_token>,
     boost::mpl::quote1<eval_plus>
   >
 >;
#include <boost/metaparse/any.hpp>

using exp_parser7 =
 build_parser<
   sequence<
     int_token,                                /* The first <number> */
     repeated<sequence<plus_token, int_token>> /* The "+ <number>" elements */
   >
 >;
using temp_result = exp_parser7::apply<BOOST_METAPARSE_STRING("1 + 2 + 3 + 4")>::type;
#include <boost/mpl/fold.hpp>

using vector_of_numbers =
 boost::mpl::vector<
   boost::mpl::int_<2>,
   boost::mpl::int_<5>,
   boost::mpl::int_<6>
 >;

template <class Vector>
 struct sum_vector :
    boost::mpl::fold<
      Vector,
      boost::mpl::int_<0>,
      boost::mpl::lambda<
        boost::mpl::plus<boost::mpl::_1, boost::mpl::_2>
      >::type
    >
  {};

template <class Sum, class Item>
   struct sum_items :
     boost::mpl::plus<
       Sum,
       typename boost::mpl::at_c<Item, 1>::type
     >
 {};
using exp_parser8 =
 build_parser<
   sequence<
     int_token, /* parse the first <number> */
     transform<
       repeated<sequence<plus_token, int_token>>, /* parse the "+ <number>" elements */
       /* lambda expression summarising the "+ <number>" elements using fold */
       boost::mpl::lambda<
         /* The folding expression we have just created */
         boost::mpl::fold<
           boost::mpl::_1, /* the argument of the lambda expression, the result */
                           /* of the repeated<...> parser */
           boost::mpl::int_<0>,
           boost::mpl::quote2<sum_items>
         >
       >::type
     >
   >
 >;

using exp_parser9 =
 build_parser<
   transform<
     /* What we had so far */
     sequence<
       int_token,
       transform<
         repeated<sequence<plus_token, int_token>>,
         boost::mpl::lambda<
           boost::mpl::fold<
             boost::mpl::_1,
             boost::mpl::int_<0>,
             boost::mpl::quote2<sum_items>
           >
         >::type
       >
     >,
     boost::mpl::quote1<sum_vector> /* summarise the vector of numbers */
   >
 >;
#include <boost/metaparse/foldl.hpp>

using exp_parser10 =
 build_parser<
   transform<
     sequence<
       int_token,
       foldl<
         sequence<plus_token, int_token>,
         boost::mpl::int_<0>,
         boost::mpl::quote2<sum_items>
       >
     >,
     boost::mpl::quote1<sum_vector>>
 >;
#include <boost/metaparse/foldl_start_with_parser.hpp>

using exp_parser11 =
 build_parser<
   foldl_start_with_parser<
     sequence<plus_token, int_token>, /* apply this parser repeatedly */
     int_token, /* use this parser to get the initial value */
     boost::mpl::quote2<sum_items> /* use this function to add a new value to the summary */
   >
 >;
using minus_token = token<lit_c<'-'>>;

#include <boost/metaparse/one_of.hpp>

using exp_parser12 =
 build_parser<
   foldl_start_with_parser<
     sequence<one_of<plus_token, minus_token>, int_token>,
     int_token,
     boost::mpl::quote2<sum_items>
   >
 >;
#include <boost/mpl/minus.hpp>

template <class L, char Op, class R> struct eval_binary_op;

template <class L, class R> struct eval_binary_op<L, '+', R> : boost::mpl::plus<L, R>::type {};

template <class L, class R> struct eval_binary_op<L, '-', R> : boost::mpl::minus<L, R>::type {};

template <class S, class Item>
 struct binary_op :
   eval_binary_op<
     S,
     boost::mpl::at_c<Item, 0>::type::value,
     typename boost::mpl::at_c<Item, 1>::type
   >
   {};

using exp_parser13 =
 build_parser<
   foldl_start_with_parser<
     sequence<one_of<plus_token, minus_token>, int_token>,
     int_token,
     boost::mpl::quote2<binary_op>
   >
 >;

Definitions before section 7.1.

#include <boost/metaparse/string.hpp>
#include <boost/metaparse/int_.hpp>

#include <boost/metaparse/build_parser.hpp>

using namespace boost::metaparse;

using exp_parser1 = build_parser<int_>;
#include <boost/metaparse/entire_input.hpp>

using exp_parser2 = build_parser<entire_input<int_>>;
#include <boost/metaparse/token.hpp>

using exp_parser3 = build_parser<entire_input<token<int_>>>;
#include <boost/metaparse/lit_c.hpp>

#include <boost/metaparse/sequence.hpp>

using exp_parser4 = build_parser<sequence<token<int_>, token<lit_c<'+'>>, token<int_>>>;

#include <metashell/formatter.hpp>

using int_token = token<int_>;

using plus_token = token<lit_c<'+'>>;

using exp_parser5 = build_parser<sequence<int_token, plus_token, int_token>>;
#include <boost/metaparse/transform.hpp>

#include <boost/mpl/plus.hpp>

#include <boost/mpl/at.hpp>

template <class Vector>
 struct eval_plus :
   boost::mpl::plus<
     typename boost::mpl::at_c<Vector, 0>::type,
     typename boost::mpl::at_c<Vector, 2>::type
   > {};

#include <boost/mpl/quote.hpp>

using exp_parser6 =
 build_parser<
   transform<
     sequence<int_token, plus_token, int_token>,
     boost::mpl::quote1<eval_plus>
   >
 >;
#include <boost/metaparse/any.hpp>

using exp_parser7 =
 build_parser<
   sequence<
     int_token,                                /* The first <number> */
     repeated<sequence<plus_token, int_token>> /* The "+ <number>" elements */
   >
 >;
using temp_result = exp_parser7::apply<BOOST_METAPARSE_STRING("1 + 2 + 3 + 4")>::type;
#include <boost/mpl/fold.hpp>

using vector_of_numbers =
 boost::mpl::vector<
   boost::mpl::int_<2>,
   boost::mpl::int_<5>,
   boost::mpl::int_<6>
 >;

template <class Vector>
 struct sum_vector :
    boost::mpl::fold<
      Vector,
      boost::mpl::int_<0>,
      boost::mpl::lambda<
        boost::mpl::plus<boost::mpl::_1, boost::mpl::_2>
      >::type
    >
  {};

template <class Sum, class Item>
   struct sum_items :
     boost::mpl::plus<
       Sum,
       typename boost::mpl::at_c<Item, 1>::type
     >
 {};
using exp_parser8 =
 build_parser<
   sequence<
     int_token, /* parse the first <number> */
     transform<
       repeated<sequence<plus_token, int_token>>, /* parse the "+ <number>" elements */
       /* lambda expression summarising the "+ <number>" elements using fold */
       boost::mpl::lambda<
         /* The folding expression we have just created */
         boost::mpl::fold<
           boost::mpl::_1, /* the argument of the lambda expression, the result */
                           /* of the repeated<...> parser */
           boost::mpl::int_<0>,
           boost::mpl::quote2<sum_items>
         >
       >::type
     >
   >
 >;

using exp_parser9 =
 build_parser<
   transform<
     /* What we had so far */
     sequence<
       int_token,
       transform<
         repeated<sequence<plus_token, int_token>>,
         boost::mpl::lambda<
           boost::mpl::fold<
             boost::mpl::_1,
             boost::mpl::int_<0>,
             boost::mpl::quote2<sum_items>
           >
         >::type
       >
     >,
     boost::mpl::quote1<sum_vector> /* summarise the vector of numbers */
   >
 >;
#include <boost/metaparse/foldl.hpp>

using exp_parser10 =
 build_parser<
   transform<
     sequence<
       int_token,
       foldl<
         sequence<plus_token, int_token>,
         boost::mpl::int_<0>,
         boost::mpl::quote2<sum_items>
       >
     >,
     boost::mpl::quote1<sum_vector>>
 >;
#include <boost/metaparse/foldl_start_with_parser.hpp>

using exp_parser11 =
 build_parser<
   foldl_start_with_parser<
     sequence<plus_token, int_token>, /* apply this parser repeatedly */
     int_token, /* use this parser to get the initial value */
     boost::mpl::quote2<sum_items> /* use this function to add a new value to the summary */
   >
 >;
using minus_token = token<lit_c<'-'>>;

#include <boost/metaparse/one_of.hpp>

using exp_parser12 =
 build_parser<
   foldl_start_with_parser<
     sequence<one_of<plus_token, minus_token>, int_token>,
     int_token,
     boost::mpl::quote2<sum_items>
   >
 >;
#include <boost/mpl/minus.hpp>

template <class L, char Op, class R> struct eval_binary_op;

template <class L, class R> struct eval_binary_op<L, '+', R> : boost::mpl::plus<L, R>::type {};

template <class L, class R> struct eval_binary_op<L, '-', R> : boost::mpl::minus<L, R>::type {};

template <class S, class Item>
 struct binary_op :
   eval_binary_op<
     S,
     boost::mpl::at_c<Item, 0>::type::value,
     typename boost::mpl::at_c<Item, 1>::type
   >
   {};

using exp_parser13 =
 build_parser<
   foldl_start_with_parser<
     sequence<one_of<plus_token, minus_token>, int_token>,
     int_token,
     boost::mpl::quote2<binary_op>
   >
 >;

Definitions before section 7.2.

#include <boost/metaparse/string.hpp>
#include <boost/metaparse/int_.hpp>

#include <boost/metaparse/build_parser.hpp>

using namespace boost::metaparse;

using exp_parser1 = build_parser<int_>;
#include <boost/metaparse/entire_input.hpp>

using exp_parser2 = build_parser<entire_input<int_>>;
#include <boost/metaparse/token.hpp>

using exp_parser3 = build_parser<entire_input<token<int_>>>;
#include <boost/metaparse/lit_c.hpp>

#include <boost/metaparse/sequence.hpp>

using exp_parser4 = build_parser<sequence<token<int_>, token<lit_c<'+'>>, token<int_>>>;

#include <metashell/formatter.hpp>

using int_token = token<int_>;

using plus_token = token<lit_c<'+'>>;

using exp_parser5 = build_parser<sequence<int_token, plus_token, int_token>>;
#include <boost/metaparse/transform.hpp>

#include <boost/mpl/plus.hpp>

#include <boost/mpl/at.hpp>

template <class Vector>
 struct eval_plus :
   boost::mpl::plus<
     typename boost::mpl::at_c<Vector, 0>::type,
     typename boost::mpl::at_c<Vector, 2>::type
   > {};

#include <boost/mpl/quote.hpp>

using exp_parser6 =
 build_parser<
   transform<
     sequence<int_token, plus_token, int_token>,
     boost::mpl::quote1<eval_plus>
   >
 >;
#include <boost/metaparse/any.hpp>

using exp_parser7 =
 build_parser<
   sequence<
     int_token,                                /* The first <number> */
     repeated<sequence<plus_token, int_token>> /* The "+ <number>" elements */
   >
 >;
using temp_result = exp_parser7::apply<BOOST_METAPARSE_STRING("1 + 2 + 3 + 4")>::type;
#include <boost/mpl/fold.hpp>

using vector_of_numbers =
 boost::mpl::vector<
   boost::mpl::int_<2>,
   boost::mpl::int_<5>,
   boost::mpl::int_<6>
 >;

template <class Vector>
 struct sum_vector :
    boost::mpl::fold<
      Vector,
      boost::mpl::int_<0>,
      boost::mpl::lambda<
        boost::mpl::plus<boost::mpl::_1, boost::mpl::_2>
      >::type
    >
  {};

template <class Sum, class Item>
   struct sum_items :
     boost::mpl::plus<
       Sum,
       typename boost::mpl::at_c<Item, 1>::type
     >
 {};
using exp_parser8 =
 build_parser<
   sequence<
     int_token, /* parse the first <number> */
     transform<
       repeated<sequence<plus_token, int_token>>, /* parse the "+ <number>" elements */
       /* lambda expression summarising the "+ <number>" elements using fold */
       boost::mpl::lambda<
         /* The folding expression we have just created */
         boost::mpl::fold<
           boost::mpl::_1, /* the argument of the lambda expression, the result */
                           /* of the repeated<...> parser */
           boost::mpl::int_<0>,
           boost::mpl::quote2<sum_items>
         >
       >::type
     >
   >
 >;

using exp_parser9 =
 build_parser<
   transform<
     /* What we had so far */
     sequence<
       int_token,
       transform<
         repeated<sequence<plus_token, int_token>>,
         boost::mpl::lambda<
           boost::mpl::fold<
             boost::mpl::_1,
             boost::mpl::int_<0>,
             boost::mpl::quote2<sum_items>
           >
         >::type
       >
     >,
     boost::mpl::quote1<sum_vector> /* summarise the vector of numbers */
   >
 >;
#include <boost/metaparse/foldl.hpp>

using exp_parser10 =
 build_parser<
   transform<
     sequence<
       int_token,
       foldl<
         sequence<plus_token, int_token>,
         boost::mpl::int_<0>,
         boost::mpl::quote2<sum_items>
       >
     >,
     boost::mpl::quote1<sum_vector>>
 >;
#include <boost/metaparse/foldl_start_with_parser.hpp>

using exp_parser11 =
 build_parser<
   foldl_start_with_parser<
     sequence<plus_token, int_token>, /* apply this parser repeatedly */
     int_token, /* use this parser to get the initial value */
     boost::mpl::quote2<sum_items> /* use this function to add a new value to the summary */
   >
 >;
using minus_token = token<lit_c<'-'>>;

#include <boost/metaparse/one_of.hpp>

using exp_parser12 =
 build_parser<
   foldl_start_with_parser<
     sequence<one_of<plus_token, minus_token>, int_token>,
     int_token,
     boost::mpl::quote2<sum_items>
   >
 >;
#include <boost/mpl/minus.hpp>

template <class L, char Op, class R> struct eval_binary_op;

template <class L, class R> struct eval_binary_op<L, '+', R> : boost::mpl::plus<L, R>::type {};

template <class L, class R> struct eval_binary_op<L, '-', R> : boost::mpl::minus<L, R>::type {};

template <class S, class Item>
 struct binary_op :
   eval_binary_op<
     S,
     boost::mpl::at_c<Item, 0>::type::value,
     typename boost::mpl::at_c<Item, 1>::type
   >
   {};

using exp_parser13 =
 build_parser<
   foldl_start_with_parser<
     sequence<one_of<plus_token, minus_token>, int_token>,
     int_token,
     boost::mpl::quote2<binary_op>
   >
 >;
#include <boost/mpl/times.hpp>

template <class L, class R> struct eval_binary_op<L, '*', R> : boost::mpl::times<L, R>::type {};

using times_token = token<lit_c<'*'>>;

using exp_parser14 =
 build_parser<
   foldl_start_with_parser<
     sequence<one_of<plus_token, minus_token, times_token>, int_token>,
     int_token,
     boost::mpl::quote2<binary_op>
   >
 >;

Definitions before section 8.

#include <boost/metaparse/string.hpp>
#include <boost/metaparse/int_.hpp>

#include <boost/metaparse/build_parser.hpp>

using namespace boost::metaparse;

using exp_parser1 = build_parser<int_>;
#include <boost/metaparse/entire_input.hpp>

using exp_parser2 = build_parser<entire_input<int_>>;
#include <boost/metaparse/token.hpp>

using exp_parser3 = build_parser<entire_input<token<int_>>>;
#include <boost/metaparse/lit_c.hpp>

#include <boost/metaparse/sequence.hpp>

using exp_parser4 = build_parser<sequence<token<int_>, token<lit_c<'+'>>, token<int_>>>;

#include <metashell/formatter.hpp>

using int_token = token<int_>;

using plus_token = token<lit_c<'+'>>;

using exp_parser5 = build_parser<sequence<int_token, plus_token, int_token>>;
#include <boost/metaparse/transform.hpp>

#include <boost/mpl/plus.hpp>

#include <boost/mpl/at.hpp>

template <class Vector>
 struct eval_plus :
   boost::mpl::plus<
     typename boost::mpl::at_c<Vector, 0>::type,
     typename boost::mpl::at_c<Vector, 2>::type
   > {};

#include <boost/mpl/quote.hpp>

using exp_parser6 =
 build_parser<
   transform<
     sequence<int_token, plus_token, int_token>,
     boost::mpl::quote1<eval_plus>
   >
 >;
#include <boost/metaparse/any.hpp>

using exp_parser7 =
 build_parser<
   sequence<
     int_token,                                /* The first <number> */
     repeated<sequence<plus_token, int_token>> /* The "+ <number>" elements */
   >
 >;
using temp_result = exp_parser7::apply<BOOST_METAPARSE_STRING("1 + 2 + 3 + 4")>::type;
#include <boost/mpl/fold.hpp>

using vector_of_numbers =
 boost::mpl::vector<
   boost::mpl::int_<2>,
   boost::mpl::int_<5>,
   boost::mpl::int_<6>
 >;

template <class Vector>
 struct sum_vector :
    boost::mpl::fold<
      Vector,
      boost::mpl::int_<0>,
      boost::mpl::lambda<
        boost::mpl::plus<boost::mpl::_1, boost::mpl::_2>
      >::type
    >
  {};

template <class Sum, class Item>
   struct sum_items :
     boost::mpl::plus<
       Sum,
       typename boost::mpl::at_c<Item, 1>::type
     >
 {};
using exp_parser8 =
 build_parser<
   sequence<
     int_token, /* parse the first <number> */
     transform<
       repeated<sequence<plus_token, int_token>>, /* parse the "+ <number>" elements */
       /* lambda expression summarising the "+ <number>" elements using fold */
       boost::mpl::lambda<
         /* The folding expression we have just created */
         boost::mpl::fold<
           boost::mpl::_1, /* the argument of the lambda expression, the result */
                           /* of the repeated<...> parser */
           boost::mpl::int_<0>,
           boost::mpl::quote2<sum_items>
         >
       >::type
     >
   >
 >;

using exp_parser9 =
 build_parser<
   transform<
     /* What we had so far */
     sequence<
       int_token,
       transform<
         repeated<sequence<plus_token, int_token>>,
         boost::mpl::lambda<
           boost::mpl::fold<
             boost::mpl::_1,
             boost::mpl::int_<0>,
             boost::mpl::quote2<sum_items>
           >
         >::type
       >
     >,
     boost::mpl::quote1<sum_vector> /* summarise the vector of numbers */
   >
 >;
#include <boost/metaparse/foldl.hpp>

using exp_parser10 =
 build_parser<
   transform<
     sequence<
       int_token,
       foldl<
         sequence<plus_token, int_token>,
         boost::mpl::int_<0>,
         boost::mpl::quote2<sum_items>
       >
     >,
     boost::mpl::quote1<sum_vector>>
 >;
#include <boost/metaparse/foldl_start_with_parser.hpp>

using exp_parser11 =
 build_parser<
   foldl_start_with_parser<
     sequence<plus_token, int_token>, /* apply this parser repeatedly */
     int_token, /* use this parser to get the initial value */
     boost::mpl::quote2<sum_items> /* use this function to add a new value to the summary */
   >
 >;
using minus_token = token<lit_c<'-'>>;

#include <boost/metaparse/one_of.hpp>

using exp_parser12 =
 build_parser<
   foldl_start_with_parser<
     sequence<one_of<plus_token, minus_token>, int_token>,
     int_token,
     boost::mpl::quote2<sum_items>
   >
 >;
#include <boost/mpl/minus.hpp>

template <class L, char Op, class R> struct eval_binary_op;

template <class L, class R> struct eval_binary_op<L, '+', R> : boost::mpl::plus<L, R>::type {};

template <class L, class R> struct eval_binary_op<L, '-', R> : boost::mpl::minus<L, R>::type {};

template <class S, class Item>
 struct binary_op :
   eval_binary_op<
     S,
     boost::mpl::at_c<Item, 0>::type::value,
     typename boost::mpl::at_c<Item, 1>::type
   >
   {};

using exp_parser13 =
 build_parser<
   foldl_start_with_parser<
     sequence<one_of<plus_token, minus_token>, int_token>,
     int_token,
     boost::mpl::quote2<binary_op>
   >
 >;
#include <boost/mpl/times.hpp>

template <class L, class R> struct eval_binary_op<L, '*', R> : boost::mpl::times<L, R>::type {};

using times_token = token<lit_c<'*'>>;

using exp_parser14 =
 build_parser<
   foldl_start_with_parser<
     sequence<one_of<plus_token, minus_token, times_token>, int_token>,
     int_token,
     boost::mpl::quote2<binary_op>
   >
 >;
using mult_exp1 = foldl_start_with_parser<sequence<times_token, int_token>, int_token, boost::mpl::quote2<binary_op>>;

using exp_parser15 =
 build_parser<
   foldl_start_with_parser<
     sequence<one_of<plus_token, minus_token>, mult_exp1>,
     mult_exp1,
     boost::mpl::quote2<binary_op>
   >
 >;

Definitions before section 8.1.

#include <boost/metaparse/string.hpp>
#include <boost/metaparse/int_.hpp>

#include <boost/metaparse/build_parser.hpp>

using namespace boost::metaparse;

using exp_parser1 = build_parser<int_>;
#include <boost/metaparse/entire_input.hpp>

using exp_parser2 = build_parser<entire_input<int_>>;
#include <boost/metaparse/token.hpp>

using exp_parser3 = build_parser<entire_input<token<int_>>>;
#include <boost/metaparse/lit_c.hpp>

#include <boost/metaparse/sequence.hpp>

using exp_parser4 = build_parser<sequence<token<int_>, token<lit_c<'+'>>, token<int_>>>;

#include <metashell/formatter.hpp>

using int_token = token<int_>;

using plus_token = token<lit_c<'+'>>;

using exp_parser5 = build_parser<sequence<int_token, plus_token, int_token>>;
#include <boost/metaparse/transform.hpp>

#include <boost/mpl/plus.hpp>

#include <boost/mpl/at.hpp>

template <class Vector>
 struct eval_plus :
   boost::mpl::plus<
     typename boost::mpl::at_c<Vector, 0>::type,
     typename boost::mpl::at_c<Vector, 2>::type
   > {};

#include <boost/mpl/quote.hpp>

using exp_parser6 =
 build_parser<
   transform<
     sequence<int_token, plus_token, int_token>,
     boost::mpl::quote1<eval_plus>
   >
 >;
#include <boost/metaparse/any.hpp>

using exp_parser7 =
 build_parser<
   sequence<
     int_token,                                /* The first <number> */
     repeated<sequence<plus_token, int_token>> /* The "+ <number>" elements */
   >
 >;
using temp_result = exp_parser7::apply<BOOST_METAPARSE_STRING("1 + 2 + 3 + 4")>::type;
#include <boost/mpl/fold.hpp>

using vector_of_numbers =
 boost::mpl::vector<
   boost::mpl::int_<2>,
   boost::mpl::int_<5>,
   boost::mpl::int_<6>
 >;

template <class Vector>
 struct sum_vector :
    boost::mpl::fold<
      Vector,
      boost::mpl::int_<0>,
      boost::mpl::lambda<
        boost::mpl::plus<boost::mpl::_1, boost::mpl::_2>
      >::type
    >
  {};

template <class Sum, class Item>
   struct sum_items :
     boost::mpl::plus<
       Sum,
       typename boost::mpl::at_c<Item, 1>::type
     >
 {};
using exp_parser8 =
 build_parser<
   sequence<
     int_token, /* parse the first <number> */
     transform<
       repeated<sequence<plus_token, int_token>>, /* parse the "+ <number>" elements */
       /* lambda expression summarising the "+ <number>" elements using fold */
       boost::mpl::lambda<
         /* The folding expression we have just created */
         boost::mpl::fold<
           boost::mpl::_1, /* the argument of the lambda expression, the result */
                           /* of the repeated<...> parser */
           boost::mpl::int_<0>,
           boost::mpl::quote2<sum_items>
         >
       >::type
     >
   >
 >;

using exp_parser9 =
 build_parser<
   transform<
     /* What we had so far */
     sequence<
       int_token,
       transform<
         repeated<sequence<plus_token, int_token>>,
         boost::mpl::lambda<
           boost::mpl::fold<
             boost::mpl::_1,
             boost::mpl::int_<0>,
             boost::mpl::quote2<sum_items>
           >
         >::type
       >
     >,
     boost::mpl::quote1<sum_vector> /* summarise the vector of numbers */
   >
 >;
#include <boost/metaparse/foldl.hpp>

using exp_parser10 =
 build_parser<
   transform<
     sequence<
       int_token,
       foldl<
         sequence<plus_token, int_token>,
         boost::mpl::int_<0>,
         boost::mpl::quote2<sum_items>
       >
     >,
     boost::mpl::quote1<sum_vector>>
 >;
#include <boost/metaparse/foldl_start_with_parser.hpp>

using exp_parser11 =
 build_parser<
   foldl_start_with_parser<
     sequence<plus_token, int_token>, /* apply this parser repeatedly */
     int_token, /* use this parser to get the initial value */
     boost::mpl::quote2<sum_items> /* use this function to add a new value to the summary */
   >
 >;
using minus_token = token<lit_c<'-'>>;

#include <boost/metaparse/one_of.hpp>

using exp_parser12 =
 build_parser<
   foldl_start_with_parser<
     sequence<one_of<plus_token, minus_token>, int_token>,
     int_token,
     boost::mpl::quote2<sum_items>
   >
 >;
#include <boost/mpl/minus.hpp>

template <class L, char Op, class R> struct eval_binary_op;

template <class L, class R> struct eval_binary_op<L, '+', R> : boost::mpl::plus<L, R>::type {};

template <class L, class R> struct eval_binary_op<L, '-', R> : boost::mpl::minus<L, R>::type {};

template <class S, class Item>
 struct binary_op :
   eval_binary_op<
     S,
     boost::mpl::at_c<Item, 0>::type::value,
     typename boost::mpl::at_c<Item, 1>::type
   >
   {};

using exp_parser13 =
 build_parser<
   foldl_start_with_parser<
     sequence<one_of<plus_token, minus_token>, int_token>,
     int_token,
     boost::mpl::quote2<binary_op>
   >
 >;
#include <boost/mpl/times.hpp>

template <class L, class R> struct eval_binary_op<L, '*', R> : boost::mpl::times<L, R>::type {};

using times_token = token<lit_c<'*'>>;

using exp_parser14 =
 build_parser<
   foldl_start_with_parser<
     sequence<one_of<plus_token, minus_token, times_token>, int_token>,
     int_token,
     boost::mpl::quote2<binary_op>
   >
 >;
using mult_exp1 = foldl_start_with_parser<sequence<times_token, int_token>, int_token, boost::mpl::quote2<binary_op>>;

using exp_parser15 =
 build_parser<
   foldl_start_with_parser<
     sequence<one_of<plus_token, minus_token>, mult_exp1>,
     mult_exp1,
     boost::mpl::quote2<binary_op>
   >
 >;
#include <boost/mpl/divides.hpp>

template <class L, class R> struct eval_binary_op<L, '/', R> : boost::mpl::divides<L, R>::type {};

using divides_token = token<lit_c<'/'>>;

using mult_exp2 =
 foldl_start_with_parser<
   sequence<one_of<times_token, divides_token>, int_token>,
   int_token,
   boost::mpl::quote2<binary_op>
 >;

using exp_parser16 =
 build_parser<
   foldl_start_with_parser<
     sequence<one_of<plus_token, minus_token>, mult_exp2>,
     mult_exp2,
     boost::mpl::quote2<binary_op>
   >
 >;

Definitions before section 8.2.

#include <boost/metaparse/string.hpp>
#include <boost/metaparse/int_.hpp>

#include <boost/metaparse/build_parser.hpp>

using namespace boost::metaparse;

using exp_parser1 = build_parser<int_>;
#include <boost/metaparse/entire_input.hpp>

using exp_parser2 = build_parser<entire_input<int_>>;
#include <boost/metaparse/token.hpp>

using exp_parser3 = build_parser<entire_input<token<int_>>>;
#include <boost/metaparse/lit_c.hpp>

#include <boost/metaparse/sequence.hpp>

using exp_parser4 = build_parser<sequence<token<int_>, token<lit_c<'+'>>, token<int_>>>;

#include <metashell/formatter.hpp>

using int_token = token<int_>;

using plus_token = token<lit_c<'+'>>;

using exp_parser5 = build_parser<sequence<int_token, plus_token, int_token>>;
#include <boost/metaparse/transform.hpp>

#include <boost/mpl/plus.hpp>

#include <boost/mpl/at.hpp>

template <class Vector>
 struct eval_plus :
   boost::mpl::plus<
     typename boost::mpl::at_c<Vector, 0>::type,
     typename boost::mpl::at_c<Vector, 2>::type
   > {};

#include <boost/mpl/quote.hpp>

using exp_parser6 =
 build_parser<
   transform<
     sequence<int_token, plus_token, int_token>,
     boost::mpl::quote1<eval_plus>
   >
 >;
#include <boost/metaparse/any.hpp>

using exp_parser7 =
 build_parser<
   sequence<
     int_token,                                /* The first <number> */
     repeated<sequence<plus_token, int_token>> /* The "+ <number>" elements */
   >
 >;
using temp_result = exp_parser7::apply<BOOST_METAPARSE_STRING("1 + 2 + 3 + 4")>::type;
#include <boost/mpl/fold.hpp>

using vector_of_numbers =
 boost::mpl::vector<
   boost::mpl::int_<2>,
   boost::mpl::int_<5>,
   boost::mpl::int_<6>
 >;

template <class Vector>
 struct sum_vector :
    boost::mpl::fold<
      Vector,
      boost::mpl::int_<0>,
      boost::mpl::lambda<
        boost::mpl::plus<boost::mpl::_1, boost::mpl::_2>
      >::type
    >
  {};

template <class Sum, class Item>
   struct sum_items :
     boost::mpl::plus<
       Sum,
       typename boost::mpl::at_c<Item, 1>::type
     >
 {};
using exp_parser8 =
 build_parser<
   sequence<
     int_token, /* parse the first <number> */
     transform<
       repeated<sequence<plus_token, int_token>>, /* parse the "+ <number>" elements */
       /* lambda expression summarising the "+ <number>" elements using fold */
       boost::mpl::lambda<
         /* The folding expression we have just created */
         boost::mpl::fold<
           boost::mpl::_1, /* the argument of the lambda expression, the result */
                           /* of the repeated<...> parser */
           boost::mpl::int_<0>,
           boost::mpl::quote2<sum_items>
         >
       >::type
     >
   >
 >;

using exp_parser9 =
 build_parser<
   transform<
     /* What we had so far */
     sequence<
       int_token,
       transform<
         repeated<sequence<plus_token, int_token>>,
         boost::mpl::lambda<
           boost::mpl::fold<
             boost::mpl::_1,
             boost::mpl::int_<0>,
             boost::mpl::quote2<sum_items>
           >
         >::type
       >
     >,
     boost::mpl::quote1<sum_vector> /* summarise the vector of numbers */
   >
 >;
#include <boost/metaparse/foldl.hpp>

using exp_parser10 =
 build_parser<
   transform<
     sequence<
       int_token,
       foldl<
         sequence<plus_token, int_token>,
         boost::mpl::int_<0>,
         boost::mpl::quote2<sum_items>
       >
     >,
     boost::mpl::quote1<sum_vector>>
 >;
#include <boost/metaparse/foldl_start_with_parser.hpp>

using exp_parser11 =
 build_parser<
   foldl_start_with_parser<
     sequence<plus_token, int_token>, /* apply this parser repeatedly */
     int_token, /* use this parser to get the initial value */
     boost::mpl::quote2<sum_items> /* use this function to add a new value to the summary */
   >
 >;
using minus_token = token<lit_c<'-'>>;

#include <boost/metaparse/one_of.hpp>

using exp_parser12 =
 build_parser<
   foldl_start_with_parser<
     sequence<one_of<plus_token, minus_token>, int_token>,
     int_token,
     boost::mpl::quote2<sum_items>
   >
 >;
#include <boost/mpl/minus.hpp>

template <class L, char Op, class R> struct eval_binary_op;

template <class L, class R> struct eval_binary_op<L, '+', R> : boost::mpl::plus<L, R>::type {};

template <class L, class R> struct eval_binary_op<L, '-', R> : boost::mpl::minus<L, R>::type {};

template <class S, class Item>
 struct binary_op :
   eval_binary_op<
     S,
     boost::mpl::at_c<Item, 0>::type::value,
     typename boost::mpl::at_c<Item, 1>::type
   >
   {};

using exp_parser13 =
 build_parser<
   foldl_start_with_parser<
     sequence<one_of<plus_token, minus_token>, int_token>,
     int_token,
     boost::mpl::quote2<binary_op>
   >
 >;
#include <boost/mpl/times.hpp>

template <class L, class R> struct eval_binary_op<L, '*', R> : boost::mpl::times<L, R>::type {};

using times_token = token<lit_c<'*'>>;

using exp_parser14 =
 build_parser<
   foldl_start_with_parser<
     sequence<one_of<plus_token, minus_token, times_token>, int_token>,
     int_token,
     boost::mpl::quote2<binary_op>
   >
 >;
using mult_exp1 = foldl_start_with_parser<sequence<times_token, int_token>, int_token, boost::mpl::quote2<binary_op>>;

using exp_parser15 =
 build_parser<
   foldl_start_with_parser<
     sequence<one_of<plus_token, minus_token>, mult_exp1>,
     mult_exp1,
     boost::mpl::quote2<binary_op>
   >
 >;
#include <boost/mpl/divides.hpp>

template <class L, class R> struct eval_binary_op<L, '/', R> : boost::mpl::divides<L, R>::type {};

using divides_token = token<lit_c<'/'>>;

using mult_exp2 =
 foldl_start_with_parser<
   sequence<one_of<times_token, divides_token>, int_token>,
   int_token,
   boost::mpl::quote2<binary_op>
 >;

using exp_parser16 =
 build_parser<
   foldl_start_with_parser<
     sequence<one_of<plus_token, minus_token>, mult_exp2>,
     mult_exp2,
     boost::mpl::quote2<binary_op>
   >
 >;

Definitions before section 9.

#include <boost/metaparse/string.hpp>
#include <boost/metaparse/int_.hpp>

#include <boost/metaparse/build_parser.hpp>

using namespace boost::metaparse;

using exp_parser1 = build_parser<int_>;
#include <boost/metaparse/entire_input.hpp>

using exp_parser2 = build_parser<entire_input<int_>>;
#include <boost/metaparse/token.hpp>

using exp_parser3 = build_parser<entire_input<token<int_>>>;
#include <boost/metaparse/lit_c.hpp>

#include <boost/metaparse/sequence.hpp>

using exp_parser4 = build_parser<sequence<token<int_>, token<lit_c<'+'>>, token<int_>>>;

#include <metashell/formatter.hpp>

using int_token = token<int_>;

using plus_token = token<lit_c<'+'>>;

using exp_parser5 = build_parser<sequence<int_token, plus_token, int_token>>;
#include <boost/metaparse/transform.hpp>

#include <boost/mpl/plus.hpp>

#include <boost/mpl/at.hpp>

template <class Vector>
 struct eval_plus :
   boost::mpl::plus<
     typename boost::mpl::at_c<Vector, 0>::type,
     typename boost::mpl::at_c<Vector, 2>::type
   > {};

#include <boost/mpl/quote.hpp>

using exp_parser6 =
 build_parser<
   transform<
     sequence<int_token, plus_token, int_token>,
     boost::mpl::quote1<eval_plus>
   >
 >;
#include <boost/metaparse/any.hpp>

using exp_parser7 =
 build_parser<
   sequence<
     int_token,                                /* The first <number> */
     repeated<sequence<plus_token, int_token>> /* The "+ <number>" elements */
   >
 >;
using temp_result = exp_parser7::apply<BOOST_METAPARSE_STRING("1 + 2 + 3 + 4")>::type;
#include <boost/mpl/fold.hpp>

using vector_of_numbers =
 boost::mpl::vector<
   boost::mpl::int_<2>,
   boost::mpl::int_<5>,
   boost::mpl::int_<6>
 >;

template <class Vector>
 struct sum_vector :
    boost::mpl::fold<
      Vector,
      boost::mpl::int_<0>,
      boost::mpl::lambda<
        boost::mpl::plus<boost::mpl::_1, boost::mpl::_2>
      >::type
    >
  {};

template <class Sum, class Item>
   struct sum_items :
     boost::mpl::plus<
       Sum,
       typename boost::mpl::at_c<Item, 1>::type
     >
 {};
using exp_parser8 =
 build_parser<
   sequence<
     int_token, /* parse the first <number> */
     transform<
       repeated<sequence<plus_token, int_token>>, /* parse the "+ <number>" elements */
       /* lambda expression summarising the "+ <number>" elements using fold */
       boost::mpl::lambda<
         /* The folding expression we have just created */
         boost::mpl::fold<
           boost::mpl::_1, /* the argument of the lambda expression, the result */
                           /* of the repeated<...> parser */
           boost::mpl::int_<0>,
           boost::mpl::quote2<sum_items>
         >
       >::type
     >
   >
 >;

using exp_parser9 =
 build_parser<
   transform<
     /* What we had so far */
     sequence<
       int_token,
       transform<
         repeated<sequence<plus_token, int_token>>,
         boost::mpl::lambda<
           boost::mpl::fold<
             boost::mpl::_1,
             boost::mpl::int_<0>,
             boost::mpl::quote2<sum_items>
           >
         >::type
       >
     >,
     boost::mpl::quote1<sum_vector> /* summarise the vector of numbers */
   >
 >;
#include <boost/metaparse/foldl.hpp>

using exp_parser10 =
 build_parser<
   transform<
     sequence<
       int_token,
       foldl<
         sequence<plus_token, int_token>,
         boost::mpl::int_<0>,
         boost::mpl::quote2<sum_items>
       >
     >,
     boost::mpl::quote1<sum_vector>>
 >;
#include <boost/metaparse/foldl_start_with_parser.hpp>

using exp_parser11 =
 build_parser<
   foldl_start_with_parser<
     sequence<plus_token, int_token>, /* apply this parser repeatedly */
     int_token, /* use this parser to get the initial value */
     boost::mpl::quote2<sum_items> /* use this function to add a new value to the summary */
   >
 >;
using minus_token = token<lit_c<'-'>>;

#include <boost/metaparse/one_of.hpp>

using exp_parser12 =
 build_parser<
   foldl_start_with_parser<
     sequence<one_of<plus_token, minus_token>, int_token>,
     int_token,
     boost::mpl::quote2<sum_items>
   >
 >;
#include <boost/mpl/minus.hpp>

template <class L, char Op, class R> struct eval_binary_op;

template <class L, class R> struct eval_binary_op<L, '+', R> : boost::mpl::plus<L, R>::type {};

template <class L, class R> struct eval_binary_op<L, '-', R> : boost::mpl::minus<L, R>::type {};

template <class S, class Item>
 struct binary_op :
   eval_binary_op<
     S,
     boost::mpl::at_c<Item, 0>::type::value,
     typename boost::mpl::at_c<Item, 1>::type
   >
   {};

using exp_parser13 =
 build_parser<
   foldl_start_with_parser<
     sequence<one_of<plus_token, minus_token>, int_token>,
     int_token,
     boost::mpl::quote2<binary_op>
   >
 >;
#include <boost/mpl/times.hpp>

template <class L, class R> struct eval_binary_op<L, '*', R> : boost::mpl::times<L, R>::type {};

using times_token = token<lit_c<'*'>>;

using exp_parser14 =
 build_parser<
   foldl_start_with_parser<
     sequence<one_of<plus_token, minus_token, times_token>, int_token>,
     int_token,
     boost::mpl::quote2<binary_op>
   >
 >;
using mult_exp1 = foldl_start_with_parser<sequence<times_token, int_token>, int_token, boost::mpl::quote2<binary_op>>;

using exp_parser15 =
 build_parser<
   foldl_start_with_parser<
     sequence<one_of<plus_token, minus_token>, mult_exp1>,
     mult_exp1,
     boost::mpl::quote2<binary_op>
   >
 >;
#include <boost/mpl/divides.hpp>

template <class L, class R> struct eval_binary_op<L, '/', R> : boost::mpl::divides<L, R>::type {};

using divides_token = token<lit_c<'/'>>;

using mult_exp2 =
 foldl_start_with_parser<
   sequence<one_of<times_token, divides_token>, int_token>,
   int_token,
   boost::mpl::quote2<binary_op>
 >;

using exp_parser16 =
 build_parser<
   foldl_start_with_parser<
     sequence<one_of<plus_token, minus_token>, mult_exp2>,
     mult_exp2,
     boost::mpl::quote2<binary_op>
   >
 >;
template <class S, class Item>
 struct reverse_binary_op :
   eval_binary_op<
     typename boost::mpl::at_c<Item, 0>::type,
     boost::mpl::at_c<Item, 1>::type::value,
     S
   >
   {};

#include <boost/metaparse/foldr_start_with_parser.hpp>

using mult_exp3 =
 foldr_start_with_parser<
   sequence<int_token, one_of<times_token, divides_token>>, /* The parser applied repeatedly */
   int_token, /* The parser parsing the last number */
   boost::mpl::quote2<reverse_binary_op> /* The function called for every result */
                                         /* of applying the above parser */
 >;

using exp_parser17 =
 build_parser<
   foldl_start_with_parser<
     sequence<one_of<plus_token, minus_token>, mult_exp3>,
     mult_exp3,
     boost::mpl::quote2<binary_op>
   >
 >;

Definitions before section 10.

#include <boost/metaparse/string.hpp>
#include <boost/metaparse/int_.hpp>

#include <boost/metaparse/build_parser.hpp>

using namespace boost::metaparse;

using exp_parser1 = build_parser<int_>;
#include <boost/metaparse/entire_input.hpp>

using exp_parser2 = build_parser<entire_input<int_>>;
#include <boost/metaparse/token.hpp>

using exp_parser3 = build_parser<entire_input<token<int_>>>;
#include <boost/metaparse/lit_c.hpp>

#include <boost/metaparse/sequence.hpp>

using exp_parser4 = build_parser<sequence<token<int_>, token<lit_c<'+'>>, token<int_>>>;

#include <metashell/formatter.hpp>

using int_token = token<int_>;

using plus_token = token<lit_c<'+'>>;

using exp_parser5 = build_parser<sequence<int_token, plus_token, int_token>>;
#include <boost/metaparse/transform.hpp>

#include <boost/mpl/plus.hpp>

#include <boost/mpl/at.hpp>

template <class Vector>
 struct eval_plus :
   boost::mpl::plus<
     typename boost::mpl::at_c<Vector, 0>::type,
     typename boost::mpl::at_c<Vector, 2>::type
   > {};

#include <boost/mpl/quote.hpp>

using exp_parser6 =
 build_parser<
   transform<
     sequence<int_token, plus_token, int_token>,
     boost::mpl::quote1<eval_plus>
   >
 >;
#include <boost/metaparse/any.hpp>

using exp_parser7 =
 build_parser<
   sequence<
     int_token,                                /* The first <number> */
     repeated<sequence<plus_token, int_token>> /* The "+ <number>" elements */
   >
 >;
using temp_result = exp_parser7::apply<BOOST_METAPARSE_STRING("1 + 2 + 3 + 4")>::type;
#include <boost/mpl/fold.hpp>

using vector_of_numbers =
 boost::mpl::vector<
   boost::mpl::int_<2>,
   boost::mpl::int_<5>,
   boost::mpl::int_<6>
 >;

template <class Vector>
 struct sum_vector :
    boost::mpl::fold<
      Vector,
      boost::mpl::int_<0>,
      boost::mpl::lambda<
        boost::mpl::plus<boost::mpl::_1, boost::mpl::_2>
      >::type
    >
  {};

template <class Sum, class Item>
   struct sum_items :
     boost::mpl::plus<
       Sum,
       typename boost::mpl::at_c<Item, 1>::type
     >
 {};
using exp_parser8 =
 build_parser<
   sequence<
     int_token, /* parse the first <number> */
     transform<
       repeated<sequence<plus_token, int_token>>, /* parse the "+ <number>" elements */
       /* lambda expression summarising the "+ <number>" elements using fold */
       boost::mpl::lambda<
         /* The folding expression we have just created */
         boost::mpl::fold<
           boost::mpl::_1, /* the argument of the lambda expression, the result */
                           /* of the repeated<...> parser */
           boost::mpl::int_<0>,
           boost::mpl::quote2<sum_items>
         >
       >::type
     >
   >
 >;

using exp_parser9 =
 build_parser<
   transform<
     /* What we had so far */
     sequence<
       int_token,
       transform<
         repeated<sequence<plus_token, int_token>>,
         boost::mpl::lambda<
           boost::mpl::fold<
             boost::mpl::_1,
             boost::mpl::int_<0>,
             boost::mpl::quote2<sum_items>
           >
         >::type
       >
     >,
     boost::mpl::quote1<sum_vector> /* summarise the vector of numbers */
   >
 >;
#include <boost/metaparse/foldl.hpp>

using exp_parser10 =
 build_parser<
   transform<
     sequence<
       int_token,
       foldl<
         sequence<plus_token, int_token>,
         boost::mpl::int_<0>,
         boost::mpl::quote2<sum_items>
       >
     >,
     boost::mpl::quote1<sum_vector>>
 >;
#include <boost/metaparse/foldl_start_with_parser.hpp>

using exp_parser11 =
 build_parser<
   foldl_start_with_parser<
     sequence<plus_token, int_token>, /* apply this parser repeatedly */
     int_token, /* use this parser to get the initial value */
     boost::mpl::quote2<sum_items> /* use this function to add a new value to the summary */
   >
 >;
using minus_token = token<lit_c<'-'>>;

#include <boost/metaparse/one_of.hpp>

using exp_parser12 =
 build_parser<
   foldl_start_with_parser<
     sequence<one_of<plus_token, minus_token>, int_token>,
     int_token,
     boost::mpl::quote2<sum_items>
   >
 >;
#include <boost/mpl/minus.hpp>

template <class L, char Op, class R> struct eval_binary_op;

template <class L, class R> struct eval_binary_op<L, '+', R> : boost::mpl::plus<L, R>::type {};

template <class L, class R> struct eval_binary_op<L, '-', R> : boost::mpl::minus<L, R>::type {};

template <class S, class Item>
 struct binary_op :
   eval_binary_op<
     S,
     boost::mpl::at_c<Item, 0>::type::value,
     typename boost::mpl::at_c<Item, 1>::type
   >
   {};

using exp_parser13 =
 build_parser<
   foldl_start_with_parser<
     sequence<one_of<plus_token, minus_token>, int_token>,
     int_token,
     boost::mpl::quote2<binary_op>
   >
 >;
#include <boost/mpl/times.hpp>

template <class L, class R> struct eval_binary_op<L, '*', R> : boost::mpl::times<L, R>::type {};

using times_token = token<lit_c<'*'>>;

using exp_parser14 =
 build_parser<
   foldl_start_with_parser<
     sequence<one_of<plus_token, minus_token, times_token>, int_token>,
     int_token,
     boost::mpl::quote2<binary_op>
   >
 >;
using mult_exp1 = foldl_start_with_parser<sequence<times_token, int_token>, int_token, boost::mpl::quote2<binary_op>>;

using exp_parser15 =
 build_parser<
   foldl_start_with_parser<
     sequence<one_of<plus_token, minus_token>, mult_exp1>,
     mult_exp1,
     boost::mpl::quote2<binary_op>
   >
 >;
#include <boost/mpl/divides.hpp>

template <class L, class R> struct eval_binary_op<L, '/', R> : boost::mpl::divides<L, R>::type {};

using divides_token = token<lit_c<'/'>>;

using mult_exp2 =
 foldl_start_with_parser<
   sequence<one_of<times_token, divides_token>, int_token>,
   int_token,
   boost::mpl::quote2<binary_op>
 >;

using exp_parser16 =
 build_parser<
   foldl_start_with_parser<
     sequence<one_of<plus_token, minus_token>, mult_exp2>,
     mult_exp2,
     boost::mpl::quote2<binary_op>
   >
 >;
template <class S, class Item>
 struct reverse_binary_op :
   eval_binary_op<
     typename boost::mpl::at_c<Item, 0>::type,
     boost::mpl::at_c<Item, 1>::type::value,
     S
   >
   {};

#include <boost/metaparse/foldr_start_with_parser.hpp>

using mult_exp3 =
 foldr_start_with_parser<
   sequence<int_token, one_of<times_token, divides_token>>, /* The parser applied repeatedly */
   int_token, /* The parser parsing the last number */
   boost::mpl::quote2<reverse_binary_op> /* The function called for every result */
                                         /* of applying the above parser */
 >;

using exp_parser17 =
 build_parser<
   foldl_start_with_parser<
     sequence<one_of<plus_token, minus_token>, mult_exp3>,
     mult_exp3,
     boost::mpl::quote2<binary_op>
   >
 >;
#include <boost/mpl/negate.hpp>

using unary_exp1 =
 foldr_start_with_parser<
   minus_token,
   int_token,
   boost::mpl::lambda<boost::mpl::negate<boost::mpl::_1>>::type
 >;

using mult_exp4 =
 foldl_start_with_parser<
   sequence<one_of<times_token, divides_token>, unary_exp1>,
   unary_exp1,
   boost::mpl::quote2<binary_op>
 >;

using exp_parser18 =
 build_parser<
   foldl_start_with_parser<
     sequence<one_of<plus_token, minus_token>, mult_exp4>,
     mult_exp4,
     boost::mpl::quote2<binary_op>
   >
 >;

Definitions before section 11.

#include <boost/metaparse/string.hpp>
#include <boost/metaparse/int_.hpp>

#include <boost/metaparse/build_parser.hpp>

using namespace boost::metaparse;

using exp_parser1 = build_parser<int_>;
#include <boost/metaparse/entire_input.hpp>

using exp_parser2 = build_parser<entire_input<int_>>;
#include <boost/metaparse/token.hpp>

using exp_parser3 = build_parser<entire_input<token<int_>>>;
#include <boost/metaparse/lit_c.hpp>

#include <boost/metaparse/sequence.hpp>

using exp_parser4 = build_parser<sequence<token<int_>, token<lit_c<'+'>>, token<int_>>>;

#include <metashell/formatter.hpp>

using int_token = token<int_>;

using plus_token = token<lit_c<'+'>>;

using exp_parser5 = build_parser<sequence<int_token, plus_token, int_token>>;
#include <boost/metaparse/transform.hpp>

#include <boost/mpl/plus.hpp>

#include <boost/mpl/at.hpp>

template <class Vector>
 struct eval_plus :
   boost::mpl::plus<
     typename boost::mpl::at_c<Vector, 0>::type,
     typename boost::mpl::at_c<Vector, 2>::type
   > {};

#include <boost/mpl/quote.hpp>

using exp_parser6 =
 build_parser<
   transform<
     sequence<int_token, plus_token, int_token>,
     boost::mpl::quote1<eval_plus>
   >
 >;
#include <boost/metaparse/any.hpp>

using exp_parser7 =
 build_parser<
   sequence<
     int_token,                                /* The first <number> */
     repeated<sequence<plus_token, int_token>> /* The "+ <number>" elements */
   >
 >;
using temp_result = exp_parser7::apply<BOOST_METAPARSE_STRING("1 + 2 + 3 + 4")>::type;
#include <boost/mpl/fold.hpp>

using vector_of_numbers =
 boost::mpl::vector<
   boost::mpl::int_<2>,
   boost::mpl::int_<5>,
   boost::mpl::int_<6>
 >;

template <class Vector>
 struct sum_vector :
    boost::mpl::fold<
      Vector,
      boost::mpl::int_<0>,
      boost::mpl::lambda<
        boost::mpl::plus<boost::mpl::_1, boost::mpl::_2>
      >::type
    >
  {};

template <class Sum, class Item>
   struct sum_items :
     boost::mpl::plus<
       Sum,
       typename boost::mpl::at_c<Item, 1>::type
     >
 {};
using exp_parser8 =
 build_parser<
   sequence<
     int_token, /* parse the first <number> */
     transform<
       repeated<sequence<plus_token, int_token>>, /* parse the "+ <number>" elements */
       /* lambda expression summarising the "+ <number>" elements using fold */
       boost::mpl::lambda<
         /* The folding expression we have just created */
         boost::mpl::fold<
           boost::mpl::_1, /* the argument of the lambda expression, the result */
                           /* of the repeated<...> parser */
           boost::mpl::int_<0>,
           boost::mpl::quote2<sum_items>
         >
       >::type
     >
   >
 >;

using exp_parser9 =
 build_parser<
   transform<
     /* What we had so far */
     sequence<
       int_token,
       transform<
         repeated<sequence<plus_token, int_token>>,
         boost::mpl::lambda<
           boost::mpl::fold<
             boost::mpl::_1,
             boost::mpl::int_<0>,
             boost::mpl::quote2<sum_items>
           >
         >::type
       >
     >,
     boost::mpl::quote1<sum_vector> /* summarise the vector of numbers */
   >
 >;
#include <boost/metaparse/foldl.hpp>

using exp_parser10 =
 build_parser<
   transform<
     sequence<
       int_token,
       foldl<
         sequence<plus_token, int_token>,
         boost::mpl::int_<0>,
         boost::mpl::quote2<sum_items>
       >
     >,
     boost::mpl::quote1<sum_vector>>
 >;
#include <boost/metaparse/foldl_start_with_parser.hpp>

using exp_parser11 =
 build_parser<
   foldl_start_with_parser<
     sequence<plus_token, int_token>, /* apply this parser repeatedly */
     int_token, /* use this parser to get the initial value */
     boost::mpl::quote2<sum_items> /* use this function to add a new value to the summary */
   >
 >;
using minus_token = token<lit_c<'-'>>;

#include <boost/metaparse/one_of.hpp>

using exp_parser12 =
 build_parser<
   foldl_start_with_parser<
     sequence<one_of<plus_token, minus_token>, int_token>,
     int_token,
     boost::mpl::quote2<sum_items>
   >
 >;
#include <boost/mpl/minus.hpp>

template <class L, char Op, class R> struct eval_binary_op;

template <class L, class R> struct eval_binary_op<L, '+', R> : boost::mpl::plus<L, R>::type {};

template <class L, class R> struct eval_binary_op<L, '-', R> : boost::mpl::minus<L, R>::type {};

template <class S, class Item>
 struct binary_op :
   eval_binary_op<
     S,
     boost::mpl::at_c<Item, 0>::type::value,
     typename boost::mpl::at_c<Item, 1>::type
   >
   {};

using exp_parser13 =
 build_parser<
   foldl_start_with_parser<
     sequence<one_of<plus_token, minus_token>, int_token>,
     int_token,
     boost::mpl::quote2<binary_op>
   >
 >;
#include <boost/mpl/times.hpp>

template <class L, class R> struct eval_binary_op<L, '*', R> : boost::mpl::times<L, R>::type {};

using times_token = token<lit_c<'*'>>;

using exp_parser14 =
 build_parser<
   foldl_start_with_parser<
     sequence<one_of<plus_token, minus_token, times_token>, int_token>,
     int_token,
     boost::mpl::quote2<binary_op>
   >
 >;
using mult_exp1 = foldl_start_with_parser<sequence<times_token, int_token>, int_token, boost::mpl::quote2<binary_op>>;

using exp_parser15 =
 build_parser<
   foldl_start_with_parser<
     sequence<one_of<plus_token, minus_token>, mult_exp1>,
     mult_exp1,
     boost::mpl::quote2<binary_op>
   >
 >;
#include <boost/mpl/divides.hpp>

template <class L, class R> struct eval_binary_op<L, '/', R> : boost::mpl::divides<L, R>::type {};

using divides_token = token<lit_c<'/'>>;

using mult_exp2 =
 foldl_start_with_parser<
   sequence<one_of<times_token, divides_token>, int_token>,
   int_token,
   boost::mpl::quote2<binary_op>
 >;

using exp_parser16 =
 build_parser<
   foldl_start_with_parser<
     sequence<one_of<plus_token, minus_token>, mult_exp2>,
     mult_exp2,
     boost::mpl::quote2<binary_op>
   >
 >;
template <class S, class Item>
 struct reverse_binary_op :
   eval_binary_op<
     typename boost::mpl::at_c<Item, 0>::type,
     boost::mpl::at_c<Item, 1>::type::value,
     S
   >
   {};

#include <boost/metaparse/foldr_start_with_parser.hpp>

using mult_exp3 =
 foldr_start_with_parser<
   sequence<int_token, one_of<times_token, divides_token>>, /* The parser applied repeatedly */
   int_token, /* The parser parsing the last number */
   boost::mpl::quote2<reverse_binary_op> /* The function called for every result */
                                         /* of applying the above parser */
 >;

using exp_parser17 =
 build_parser<
   foldl_start_with_parser<
     sequence<one_of<plus_token, minus_token>, mult_exp3>,
     mult_exp3,
     boost::mpl::quote2<binary_op>
   >
 >;
#include <boost/mpl/negate.hpp>

using unary_exp1 =
 foldr_start_with_parser<
   minus_token,
   int_token,
   boost::mpl::lambda<boost::mpl::negate<boost::mpl::_1>>::type
 >;

using mult_exp4 =
 foldl_start_with_parser<
   sequence<one_of<times_token, divides_token>, unary_exp1>,
   unary_exp1,
   boost::mpl::quote2<binary_op>
 >;

using exp_parser18 =
 build_parser<
   foldl_start_with_parser<
     sequence<one_of<plus_token, minus_token>, mult_exp4>,
     mult_exp4,
     boost::mpl::quote2<binary_op>
   >
 >;
using lparen_token = token<lit_c<'('>>;

using rparen_token = token<lit_c<')'>>;

using plus_exp1 =
 foldl_start_with_parser<
   sequence<one_of<plus_token, minus_token>, mult_exp4>,
   mult_exp4,
   boost::mpl::quote2<binary_op>
 >;

using paren_exp1 = sequence<lparen_token, plus_exp1, rparen_token>;

#include <boost/metaparse/middle_of.hpp>

using paren_exp2 = middle_of<lparen_token, plus_exp1, rparen_token>;

using primary_exp1 = one_of<int_token, paren_exp2>;

struct plus_exp2;

using paren_exp3 = middle_of<lparen_token, plus_exp2, rparen_token>;

using primary_exp2 = one_of<int_token, paren_exp2>;

using unary_exp2 =
 foldr_start_with_parser<
   minus_token,
   primary_exp2,
   boost::mpl::lambda<boost::mpl::negate<boost::mpl::_1>>::type
 >;

using mult_exp5 =
 foldl_start_with_parser<
   sequence<one_of<times_token, divides_token>, unary_exp2>,
   unary_exp2,
   boost::mpl::quote2<binary_op>
 >;

struct plus_exp2 :
 foldl_start_with_parser<
   sequence<one_of<plus_token, minus_token>, mult_exp5>,
   mult_exp5,
   boost::mpl::quote2<binary_op>
 > {};

using exp_parser19 = build_parser<plus_exp2>;

Definitions before section 11.1.

#include <boost/metaparse/string.hpp>
#include <boost/metaparse/int_.hpp>

#include <boost/metaparse/build_parser.hpp>

using namespace boost::metaparse;

using exp_parser1 = build_parser<int_>;
#include <boost/metaparse/entire_input.hpp>

using exp_parser2 = build_parser<entire_input<int_>>;
#include <boost/metaparse/token.hpp>

using exp_parser3 = build_parser<entire_input<token<int_>>>;
#include <boost/metaparse/lit_c.hpp>

#include <boost/metaparse/sequence.hpp>

using exp_parser4 = build_parser<sequence<token<int_>, token<lit_c<'+'>>, token<int_>>>;

#include <metashell/formatter.hpp>

using int_token = token<int_>;

using plus_token = token<lit_c<'+'>>;

using exp_parser5 = build_parser<sequence<int_token, plus_token, int_token>>;
#include <boost/metaparse/transform.hpp>

#include <boost/mpl/plus.hpp>

#include <boost/mpl/at.hpp>

template <class Vector>
 struct eval_plus :
   boost::mpl::plus<
     typename boost::mpl::at_c<Vector, 0>::type,
     typename boost::mpl::at_c<Vector, 2>::type
   > {};

#include <boost/mpl/quote.hpp>

using exp_parser6 =
 build_parser<
   transform<
     sequence<int_token, plus_token, int_token>,
     boost::mpl::quote1<eval_plus>
   >
 >;
#include <boost/metaparse/any.hpp>

using exp_parser7 =
 build_parser<
   sequence<
     int_token,                                /* The first <number> */
     repeated<sequence<plus_token, int_token>> /* The "+ <number>" elements */
   >
 >;
using temp_result = exp_parser7::apply<BOOST_METAPARSE_STRING("1 + 2 + 3 + 4")>::type;
#include <boost/mpl/fold.hpp>

using vector_of_numbers =
 boost::mpl::vector<
   boost::mpl::int_<2>,
   boost::mpl::int_<5>,
   boost::mpl::int_<6>
 >;

template <class Vector>
 struct sum_vector :
    boost::mpl::fold<
      Vector,
      boost::mpl::int_<0>,
      boost::mpl::lambda<
        boost::mpl::plus<boost::mpl::_1, boost::mpl::_2>
      >::type
    >
  {};

template <class Sum, class Item>
   struct sum_items :
     boost::mpl::plus<
       Sum,
       typename boost::mpl::at_c<Item, 1>::type
     >
 {};
using exp_parser8 =
 build_parser<
   sequence<
     int_token, /* parse the first <number> */
     transform<
       repeated<sequence<plus_token, int_token>>, /* parse the "+ <number>" elements */
       /* lambda expression summarising the "+ <number>" elements using fold */
       boost::mpl::lambda<
         /* The folding expression we have just created */
         boost::mpl::fold<
           boost::mpl::_1, /* the argument of the lambda expression, the result */
                           /* of the repeated<...> parser */
           boost::mpl::int_<0>,
           boost::mpl::quote2<sum_items>
         >
       >::type
     >
   >
 >;

using exp_parser9 =
 build_parser<
   transform<
     /* What we had so far */
     sequence<
       int_token,
       transform<
         repeated<sequence<plus_token, int_token>>,
         boost::mpl::lambda<
           boost::mpl::fold<
             boost::mpl::_1,
             boost::mpl::int_<0>,
             boost::mpl::quote2<sum_items>
           >
         >::type
       >
     >,
     boost::mpl::quote1<sum_vector> /* summarise the vector of numbers */
   >
 >;
#include <boost/metaparse/foldl.hpp>

using exp_parser10 =
 build_parser<
   transform<
     sequence<
       int_token,
       foldl<
         sequence<plus_token, int_token>,
         boost::mpl::int_<0>,
         boost::mpl::quote2<sum_items>
       >
     >,
     boost::mpl::quote1<sum_vector>>
 >;
#include <boost/metaparse/foldl_start_with_parser.hpp>

using exp_parser11 =
 build_parser<
   foldl_start_with_parser<
     sequence<plus_token, int_token>, /* apply this parser repeatedly */
     int_token, /* use this parser to get the initial value */
     boost::mpl::quote2<sum_items> /* use this function to add a new value to the summary */
   >
 >;
using minus_token = token<lit_c<'-'>>;

#include <boost/metaparse/one_of.hpp>

using exp_parser12 =
 build_parser<
   foldl_start_with_parser<
     sequence<one_of<plus_token, minus_token>, int_token>,
     int_token,
     boost::mpl::quote2<sum_items>
   >
 >;
#include <boost/mpl/minus.hpp>

template <class L, char Op, class R> struct eval_binary_op;

template <class L, class R> struct eval_binary_op<L, '+', R> : boost::mpl::plus<L, R>::type {};

template <class L, class R> struct eval_binary_op<L, '-', R> : boost::mpl::minus<L, R>::type {};

template <class S, class Item>
 struct binary_op :
   eval_binary_op<
     S,
     boost::mpl::at_c<Item, 0>::type::value,
     typename boost::mpl::at_c<Item, 1>::type
   >
   {};

using exp_parser13 =
 build_parser<
   foldl_start_with_parser<
     sequence<one_of<plus_token, minus_token>, int_token>,
     int_token,
     boost::mpl::quote2<binary_op>
   >
 >;
#include <boost/mpl/times.hpp>

template <class L, class R> struct eval_binary_op<L, '*', R> : boost::mpl::times<L, R>::type {};

using times_token = token<lit_c<'*'>>;

using exp_parser14 =
 build_parser<
   foldl_start_with_parser<
     sequence<one_of<plus_token, minus_token, times_token>, int_token>,
     int_token,
     boost::mpl::quote2<binary_op>
   >
 >;
using mult_exp1 = foldl_start_with_parser<sequence<times_token, int_token>, int_token, boost::mpl::quote2<binary_op>>;

using exp_parser15 =
 build_parser<
   foldl_start_with_parser<
     sequence<one_of<plus_token, minus_token>, mult_exp1>,
     mult_exp1,
     boost::mpl::quote2<binary_op>
   >
 >;
#include <boost/mpl/divides.hpp>

template <class L, class R> struct eval_binary_op<L, '/', R> : boost::mpl::divides<L, R>::type {};

using divides_token = token<lit_c<'/'>>;

using mult_exp2 =
 foldl_start_with_parser<
   sequence<one_of<times_token, divides_token>, int_token>,
   int_token,
   boost::mpl::quote2<binary_op>
 >;

using exp_parser16 =
 build_parser<
   foldl_start_with_parser<
     sequence<one_of<plus_token, minus_token>, mult_exp2>,
     mult_exp2,
     boost::mpl::quote2<binary_op>
   >
 >;
template <class S, class Item>
 struct reverse_binary_op :
   eval_binary_op<
     typename boost::mpl::at_c<Item, 0>::type,
     boost::mpl::at_c<Item, 1>::type::value,
     S
   >
   {};

#include <boost/metaparse/foldr_start_with_parser.hpp>

using mult_exp3 =
 foldr_start_with_parser<
   sequence<int_token, one_of<times_token, divides_token>>, /* The parser applied repeatedly */
   int_token, /* The parser parsing the last number */
   boost::mpl::quote2<reverse_binary_op> /* The function called for every result */
                                         /* of applying the above parser */
 >;

using exp_parser17 =
 build_parser<
   foldl_start_with_parser<
     sequence<one_of<plus_token, minus_token>, mult_exp3>,
     mult_exp3,
     boost::mpl::quote2<binary_op>
   >
 >;
#include <boost/mpl/negate.hpp>

using unary_exp1 =
 foldr_start_with_parser<
   minus_token,
   int_token,
   boost::mpl::lambda<boost::mpl::negate<boost::mpl::_1>>::type
 >;

using mult_exp4 =
 foldl_start_with_parser<
   sequence<one_of<times_token, divides_token>, unary_exp1>,
   unary_exp1,
   boost::mpl::quote2<binary_op>
 >;

using exp_parser18 =
 build_parser<
   foldl_start_with_parser<
     sequence<one_of<plus_token, minus_token>, mult_exp4>,
     mult_exp4,
     boost::mpl::quote2<binary_op>
   >
 >;
using lparen_token = token<lit_c<'('>>;

using rparen_token = token<lit_c<')'>>;

using plus_exp1 =
 foldl_start_with_parser<
   sequence<one_of<plus_token, minus_token>, mult_exp4>,
   mult_exp4,
   boost::mpl::quote2<binary_op>
 >;

using paren_exp1 = sequence<lparen_token, plus_exp1, rparen_token>;

#include <boost/metaparse/middle_of.hpp>

using paren_exp2 = middle_of<lparen_token, plus_exp1, rparen_token>;

using primary_exp1 = one_of<int_token, paren_exp2>;

struct plus_exp2;

using paren_exp3 = middle_of<lparen_token, plus_exp2, rparen_token>;

using primary_exp2 = one_of<int_token, paren_exp2>;

using unary_exp2 =
 foldr_start_with_parser<
   minus_token,
   primary_exp2,
   boost::mpl::lambda<boost::mpl::negate<boost::mpl::_1>>::type
 >;

using mult_exp5 =
 foldl_start_with_parser<
   sequence<one_of<times_token, divides_token>, unary_exp2>,
   unary_exp2,
   boost::mpl::quote2<binary_op>
 >;

struct plus_exp2 :
 foldl_start_with_parser<
   sequence<one_of<plus_token, minus_token>, mult_exp5>,
   mult_exp5,
   boost::mpl::quote2<binary_op>
 > {};

using exp_parser19 = build_parser<plus_exp2>;

Definitions before section 11.2.

#include <boost/metaparse/string.hpp>
#include <boost/metaparse/int_.hpp>

#include <boost/metaparse/build_parser.hpp>

using namespace boost::metaparse;

using exp_parser1 = build_parser<int_>;
#include <boost/metaparse/entire_input.hpp>

using exp_parser2 = build_parser<entire_input<int_>>;
#include <boost/metaparse/token.hpp>

using exp_parser3 = build_parser<entire_input<token<int_>>>;
#include <boost/metaparse/lit_c.hpp>

#include <boost/metaparse/sequence.hpp>

using exp_parser4 = build_parser<sequence<token<int_>, token<lit_c<'+'>>, token<int_>>>;

#include <metashell/formatter.hpp>

using int_token = token<int_>;