boost/hana/fwd/concept/constant.hpp
/*! @file Forward declares `boost::hana::Constant`. @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_CONSTANT_HPP #define BOOST_HANA_FWD_CONCEPT_CONSTANT_HPP #include <boost/hana/config.hpp> BOOST_HANA_NAMESPACE_BEGIN //! @ingroup group-concepts //! @defgroup group-Constant Constant //! The `Constant` concept represents data that can be manipulated at //! compile-time. //! //! At its core, `Constant` is simply a generalization of the principle //! behind `std::integral_constant` to all types that can be constructed //! at compile-time, i.e. to all types with a `constexpr` constructor //! (also called [Literal types][1]). More specifically, a `Constant` is //! an object from which a `constexpr` value may be obtained (through the //! `value` method) regardless of the `constexpr`ness of the object itself. //! //! All `Constant`s must be somewhat equivalent, in the following sense. //! Let `C(T)` and `D(U)` denote the tags of `Constant`s holding objects //! of type `T` and `U`, respectively. Then, an object with tag `D(U)` //! must be convertible to an object with tag `C(T)` whenever `U` is //! convertible to `T`, as determined by `is_convertible`. The //! interpretation here is that a `Constant` is just a box holding //! an object of some type, and it should be possible to swap between //! boxes whenever the objects inside the boxes can be swapped. //! //! Because of this last requirement, one could be tempted to think that //! specialized "boxes" like `std::integral_constant` are prevented from //! being `Constant`s because they are not able to hold objects of any //! type `T` (`std::integral_constant` may only hold integral types). //! This is false; the requirement should be interpreted as saying that //! whenever `C(T)` is _meaningful_ (e.g. only when `T` is integral for //! `std::integral_constant`) _and_ there exists a conversion from `U` //! to `T`, then a conversion from `D(U)` to `C(T)` should also exist. //! The precise requirements for being a `Constant` are embodied in the //! following laws. //! //! //! Minimal complete definition //! --------------------------- //! `value` and `to`, satisfying the laws below. //! //! //! Laws //! ---- //! Let `c` be an object of with tag `C`, which represents a `Constant` //! holding an object with tag `T`. The first law ensures that the value //! of the wrapped object is always a constant expression by requiring //! the following to be well-formed: //! @code //! constexpr auto x = hana::value<decltype(c)>(); //! @endcode //! //! This means that the `value` function must return an object that can //! be constructed at compile-time. It is important to note how `value` //! only receives the type of the object and not the object itself. //! This is the core of the `Constant` concept; it means that the only //! information required to implement `value` must be stored in the _type_ //! of its argument, and hence be available statically. //! //! The second law that must be satisfied ensures that `Constant`s are //! basically dumb boxes, which makes it possible to provide models for //! many concepts without much work from the user. The law simply asks //! for the following expression to be valid: //! @code //! to<C>(i) //! @endcode //! where, `i` is an _arbitrary_ `Constant` holding an internal value //! with a tag that can be converted to `T`, as determined by the //! `hana::is_convertible` metafunction. In other words, whenever `U` is //! convertible to `T`, a `Constant` holding a `U` is convertible to //! a `Constant` holding a `T`, if such a `Constant` can be created. //! //! Finally, the tag `C` must provide a nested `value_type` alias to `T`, //! which allows us to query the tag of the inner value held by objects //! with tag `C`. In other words, the following must be true for any //! object `c` with tag `C`: //! @code //! std::is_same< //! C::value_type, //! tag_of<decltype(hana::value(c))>::type //! >::value //! @endcode //! //! //! Refined concepts //! ---------------- //! In certain cases, a `Constant` can automatically be made a model of //! another concept. In particular, if a `Constant` `C` is holding an //! object of tag `T`, and if `T` models a concept `X`, then `C` may //! in most cases model `X` by simply performing whatever operation is //! required on its underlying value, and then wrapping the result back //! in a `C`. //! //! More specifically, if a `Constant` `C` has an underlying value //! (`C::value_type`) which is a model of `Comparable`, `Orderable`, //! `Logical`, or `Monoid` up to `EuclideanRing`, then `C` must also //! be a model of those concepts. In other words, when `C::value_type` //! models one of the listed concepts, `C` itself must also model that //! concept. However, note that free models are provided for all of //! those concepts, so no additional work must be done. //! //! While it would be possible in theory to provide models for concepts //! like `Foldable` too, only a couple of concepts are useful to have as //! `Constant` in practice. Providing free models for the concepts listed //! above is useful because it allows various types of integral constants //! (`std::integral_constant`, `mpl::integral_c`, etc...) to easily have //! models for them just by defining the `Constant` concept. //! //! @remark //! An interesting observation is that `Constant` is actually the //! canonical embedding of the subcategory of `constexpr` things //! into the Hana category, which contains everything in this library. //! Hence, whatever is true in that subcategory is also true here, via //! this functor. This is why we can provide models of any concept that //! works on `constexpr` things for Constants, by simply passing them //! through that embedding. //! //! //! Concrete models //! --------------- //! `hana::integral_constant` //! //! //! Provided conversion to the tag of the underlying value //! ------------------------------------------------------ //! Any `Constant` `c` holding an underlying value of tag `T` is //! convertible to any tag `U` such that `T` is convertible to `U`. //! Specifically, the conversion is equivalent to //! @code //! to<U>(c) == to<U>(value<decltype(c)>()) //! @endcode //! //! Also, those conversions are marked as an embedding whenever the //! conversion of underlying types is an embedding. This is to allow //! Constants to inter-operate with `constexpr` objects easily: //! @code //! plus(int_c<1>, 1) == 2 //! @endcode //! //! Strictly speaking, __this is sometimes a violation__ of what it means //! to be an embedding. Indeed, while there exists an embedding from any //! Constant to a `constexpr` object (since Constant is just the canonical //! inclusion), there is no embedding from a Constant to a runtime //! object since we would lose the ability to define the `value` method //! (the `constexpr`ness of the object would have been lost). Since there //! is no way to distinguish `constexpr` and non-`constexpr` objects based //! on their type, Hana has no way to know whether the conversion is to a //! `constexpr` object of not. In other words, the `to` method has no way //! to differentiate between //! @code //! constexpr int i = hana::to<int>(int_c<1>); //! @endcode //! which is an embedding, and //! @code //! int i = hana::to<int>(int_c<1>); //! @endcode //! //! which isn't. To be on the safer side, we could mark the conversion //! as not-an-embedding. However, if e.g. the conversion from //! `integral_constant_tag<int>` to `int` was not marked as an embedding, //! we would have to write `plus(to<int>(int_c<1>), 1)` instead of just //! `plus(int_c<1>, 1)`, which is cumbersome. Hence, the conversion is //! marked as an embedding, but this also means that code like //! @code //! int i = 1; //! plus(int_c<1>, i); //! @endcode //! will be considered valid, which implicitly loses the fact that //! `int_c<1>` is a Constant, and hence does not follow the usual rules //! for cross-type operations in Hana. //! //! //! Provided common data type //! ------------------------- //! Because of the requirement that `Constant`s be interchangeable when //! their contents are compatible, two `Constant`s `A` and `B` will have //! a common data type whenever `A::value_type` and `B::value_type` have //! one. Their common data type is an unspecified `Constant` `C` such //! that `C::value_type` is exactly `common_t<A::value_type, B::value_type>`. //! A specialization of the `common` metafunction is provided for //! `Constant`s to reflect this. //! //! In the same vein, a common data type is also provided from any //! constant `A` to a type `T` such that `A::value_type` and `T` share //! a common type. The common type between `A` and `T` is obviously the //! common type between `A::value_type` and `T`. As explained above in //! the section on conversions, this is sometimes a violation of the //! definition of a common type, because there must be an embedding //! to the common type, which is not always the case. For the same //! reasons as explained above, this common type is still provided. //! //! //! [1]: http://en.cppreference.com/w/cpp/concept/LiteralType template <typename C> struct Constant; BOOST_HANA_NAMESPACE_END #endif // !BOOST_HANA_FWD_CONCEPT_CONSTANT_HPP