monoid

Synopsis

template <class MonoidTag>
struct monoid;
  // Requires:
  //   publicly inherit from monoid_defaults<MonoidTag>
  //   struct mempty;
  //   struct mappend { template <class, class> struct apply; };

template <class MonadTag>
struct monoid_defaults
{
  struct mconcat
  {
    template <class L>
    struct apply
    {
      // unspecified
    };
  };
};

Description

This is a typeclass for monoids. A monoid is an abstraction of a type and an associative operation (mappend) on it. The operation is required to have an identity element (mempty). Examples:

• integers with 0 as identity and addition as operation
• integers with 1 as identity and multiplication as operation
• lists with empty list as identity and concatenation as operation

Monoids have a mconcat operation that takes a sequence of values and produces as sum value from it by repeatedly calling mappend.

For any MonoidTag, the operations are expected to meet the following requirements:

• mappend<mempty, X> is equivalent to X
• mappend<X, mempty> is equivalent to X
• mappend<X, mappend<Y, Z>> is equivalent to mappend<mappend<X, Y>, Z>
• mconcat<L> is equivalent to boost::mpl::reverse_fold<L, mempty, mappend>

Due to the way Metamonad handles versioning, the monoid template class has to be specialised in the mpllibs::metamonad::v1 namespace.

Header

#include <mpllibs/metamonad/monoid.hpp>

Example

using boost::mpl;

struct plus_tag : mpllibs::metamonad::tmp_tag<plus_tag> {};

template <>
struct monoid<plus_tag> : monoid_defaults<plus_tag>
{
  typedef int0 mempty;
  typedef lambda_c<a, b, plus<a, b>> mappend;
};

Copyright Abel Sinkovics (abel at elte dot hu) 2011. Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt

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