stabilize build system: depends, installer, boost/bdb fixes, cross targets groundwork

2026-02-24 18:38:47 +00:00
parent da8c28aaeb
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+/*!
+@file
+Forward declares `boost::hana::Monoid`.
+
+@copyright Louis Dionne 2013-2017
+Distributed under the Boost Software License, Version 1.0.
+(See accompanying file LICENSE.md or copy at http://boost.org/LICENSE_1_0.txt)
+ */
+
+#ifndef BOOST_HANA_FWD_CONCEPT_MONOID_HPP
+#define BOOST_HANA_FWD_CONCEPT_MONOID_HPP
+
+#include <boost/hana/config.hpp>
+
+
+BOOST_HANA_NAMESPACE_BEGIN
+    //! @ingroup group-concepts
+    //! @defgroup group-Monoid Monoid
+    //! The `Monoid` concept represents data types with an associative
+    //! binary operation that has an identity.
+    //!
+    //! Specifically, a [Monoid][1] is a basic algebraic structure typically
+    //! used in mathematics to construct more complex algebraic structures
+    //! like `Group`s, `Ring`s and so on. They are useful in several contexts,
+    //! notably to define the properties of numbers in a granular way. At its
+    //! core, a `Monoid` is a set `S` of objects along with a binary operation
+    //! (let's say `+`) that is associative and that has an identity in `S`.
+    //! There are many examples of `Monoid`s:
+    //! - strings with concatenation and the empty string as the identity
+    //! - integers with addition and `0` as the identity
+    //! - integers with multiplication and `1` as the identity
+    //! - many others...
+    //!
+    //! As you can see with the integers, there are some sets that can be
+    //! viewed as a monoid in more than one way, depending on the choice
+    //! of the binary operation and identity. The method names used here
+    //! refer to the monoid of integers under addition; `plus` is the binary
+    //! operation and `zero` is the identity element of that operation.
+    //!
+    //!
+    //! Minimal complete definition
+    //! ---------------------------
+    //! `plus` and `zero` satisfying the laws
+    //!
+    //!
+    //! Laws
+    //! ----
+    //! For all objects `x`, `y` and `z` of a `Monoid` `M`, the following
+    //! laws must be satisfied:
+    //! @code
+    //!     plus(zero<M>(), x) == x                    // left zero
+    //!     plus(x, zero<M>()) == x                    // right zero
+    //!     plus(x, plus(y, z)) == plus(plus(x, y), z) // associativity
+    //! @endcode
+    //!
+    //!
+    //! Concrete models
+    //! ---------------
+    //! `hana::integral_constant`
+    //!
+    //!
+    //! Free model for non-boolean arithmetic data types
+    //! ------------------------------------------------
+    //! A data type `T` is arithmetic if `std::is_arithmetic<T>::%value` is
+    //! true. For a non-boolean arithmetic data type `T`, a model of `Monoid`
+    //! is automatically defined by setting
+    //! @code
+    //!     plus(x, y) = (x + y)
+    //!     zero<T>() = static_cast<T>(0)
+    //! @endcode
+    //!
+    //! > #### Rationale for not making `bool` a `Monoid` by default
+    //! > First, it makes no sense whatsoever to define an additive `Monoid`
+    //! > over the `bool` type. Also, it could make sense to define a `Monoid`
+    //! > with logical conjunction or disjunction. However, C++ allows `bool`s
+    //! > to be added, and the method names of this concept really suggest
+    //! > addition. In line with the principle of least surprise, no model
+    //! > is provided by default.
+    //!
+    //!
+    //! Structure-preserving functions
+    //! ------------------------------
+    //! Let `A` and `B` be two `Monoid`s. A function `f : A -> B` is said
+    //! to be a [Monoid morphism][2] if it preserves the monoidal structure
+    //! between `A` and `B`. Rigorously, for all objects `x, y` of data
+    //! type `A`,
+    //! @code
+    //!     f(plus(x, y)) == plus(f(x), f(y))
+    //!     f(zero<A>()) == zero<B>()
+    //! @endcode
+    //! Functions with these properties interact nicely with `Monoid`s, which
+    //! is why they are given such a special treatment.
+    //!
+    //!
+    //! [1]: http://en.wikipedia.org/wiki/Monoid
+    //! [2]: http://en.wikipedia.org/wiki/Monoid#Monoid_homomorphisms
+    template <typename M>
+    struct Monoid;
+BOOST_HANA_NAMESPACE_END
+
+#endif // !BOOST_HANA_FWD_CONCEPT_MONOID_HPP