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Boost.Hana
1.6.0
Your standard library for metaprogramming
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Boost.Hana
1.6.0
Your standard library for metaprogramming
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The Iterable concept represents data structures supporting external iteration.
Intuitively, an Iterable can be seen as a kind of container whose elements can be pulled out one at a time. An Iterable also provides a way to know when the container is empty, i.e. when there are no more elements to pull out.
Whereas Foldable represents data structures supporting internal iteration with the ability to accumulate a result, the Iterable concept allows inverting the control of the iteration. This is more flexible than Foldable, since it allows iterating over only some part of the structure. This, in turn, allows Iterable to work on infinite structures, while trying to fold such a structure would never finish.
at, drop_front and is_empty
Iterable Intuitively, for an Iterable structure xs, the linearization of xs is the sequence of all the elements in xs as if they had been put in a (possibly infinite) list:
The nth element of the linearization of an Iterable can be accessed with the at function. In other words, at(xs, n) == xn.
Note that this notion is precisely the extension of the linearization notion of Foldables to the infinite case. This notion is useful for expressing various properties of Iterables, and is used for that elsewhere in the documentation.
Iterables A compile-time Iterable is an Iterable for which is_empty returns a compile-time Logical. These structures allow iteration to be done at compile-time, in the sense that the "loop" doing the iteration can be unrolled because the total length of the structure is kown at compile-time.
In particular, note that being a compile-time Iterable has nothing to do with being finite or infinite. For example, it would be possible to create a sequence representing the Pythagorean triples as integral_constants. Such a sequence would be infinite, but iteration on the sequence would still be done at compile-time. However, if one tried to iterate over all the elements of the sequence, the compiler would loop indefinitely, in contrast to your program looping indefinitely if the sequence was a runtime one.
In the current version of the library, only compile-time Iterables are supported. While it would be possible in theory to support runtime Iterables, doing it efficiently is the subject of some research. In particular, follow this issue for the current status of runtime Iterables.
First, we require the equality of two Iterables to be related to the equality of the elements in their linearizations. More specifically, if xs and ys are two Iterables of data type It, then
This conveys that two Iterables must have the same linearization in order to be considered equal.
Secondly, since every Iterable is also a Searchable, we require the models of Iterable and Searchable to be consistent. This is made precise by the following laws. For any Iterable xs with a linearization of [x1, x2, x3, ...],
for some finite index i. Furthermore,
or nothing if no such xi exists.
Searchable (free model)Iterable gives rise to a model of Searchable, where the keys and the values are both the elements in the structure. Searching for a key is just doing a linear search through the elements of the structure. Foldable for finite IterablesIterable gives rise to a model of Foldable. For these models to be consistent, we require the models of both Foldable and Iterable to have the same linearization.Iterables are also Searchables and their models have to be consistent. By the laws presented here, it also means that the Foldable model for finite Iterables has to be consistent with the Searchable model.For convenience, finite Iterables must only provide a definition of length to model the Foldable concept; defining the more powerful unpack or fold_left is not necessary (but still possible). The default implementation of unpack derived from Iterable + length uses the fact that at(xs, i) denotes the ith element of xs's linearization, and that the linearization of a finite Iterable must be the same as its linearization as a Foldable.
hana::tuple, hana::string, hana::range
Variables | |
| constexpr auto | boost::hana::at |
Returns the nth element of an iterable.Given an Iterable and an IntegralConstant index, at returns the element located at the index in the linearization of the iterable. Specifically, given an iterable xs with a linearization of [x1, ..., xN], at(xs, k) is equivalent to xk. More... | |
| template<std::size_t n> | |
| constexpr auto | boost::hana::at_c |
Equivalent to at; provided for convenience. More... | |
| constexpr auto | boost::hana::back |
Returns the last element of a non-empty and finite iterable.Given a non-empty and finite iterable xs with a linearization of [x1, ..., xN], back(xs) is equal to xN. Equivalently, back(xs) must be equivalent to at_c<N-1>(xs), and that regardless of the value category of xs (back must respect the reference semantics of at). More... | |
| constexpr auto | boost::hana::drop_front |
Drop the first n elements of an iterable, and return the rest.Given an Iterable xs with a linearization of [x1, x2, ...] and a non-negative IntegralConstant n, drop_front(xs, n) is an iterable with the same tag as xs whose linearization is [xn+1, xn+2, ...]. In particular, note that this function does not mutate the original iterable in any way. If n is not given, it defaults to an IntegralConstant with a value equal to 1. More... | |
| constexpr auto | boost::hana::drop_front_exactly |
Drop the first n elements of an iterable, and return the rest.Given an Iterable xs with a linearization of [x1, x2, ...] and a non-negative IntegralConstant n, drop_front_exactly(xs, n) is an iterable with the same tag as xs whose linearization is [xn+1, xn+2, ...]. In particular, note that this function does not mutate the original iterable in any way. If n is not given, it defaults to an IntegralConstant with a value equal to 1. More... | |
| constexpr auto | boost::hana::drop_while |
Drop elements from an iterable up to, but excluding, the first element for which the predicate is not satisfied.Specifically, drop_while returns an iterable containing all the elements of the original iterable except for those in the range delimited by [head, e), where head is the first element and e is the first element for which the predicate is not satisfied. If the iterable is not finite, the predicate has to return a false- valued Logical at a finite index for this method to return. More... | |
| constexpr auto | boost::hana::front |
Returns the first element of a non-empty iterable.Given a non-empty Iterable xs with a linearization of [x1, ..., xN], front(xs) is equal to x1. If xs is empty, it is an error to use this function. Equivalently, front(xs) must be equivalent to at_c<0>(xs), and that regardless of the value category of xs (front must respect the reference semantics of at). More... | |
| constexpr auto | boost::hana::index_if |
Finds the value associated to the first key satisfying a predicate.Given an Iterable structure xs and a predicate pred, index_if(xs, pred) returns a hana::optional containing an IntegralConstant of the index of the first element that satisfies the predicate or nothing if no element satisfies the predicate. More... | |
| constexpr auto | boost::hana::is_empty |
Returns whether the iterable is empty.Given an Iterable xs, is_empty returns whether xs contains no more elements. In other words, it returns whether trying to extract the tail of xs would be an error. In the current version of the library, is_empty must return an IntegralConstant holding a value convertible to bool. This is because only compile-time Iterables are supported right now. More... | |
| constexpr auto | boost::hana::lexicographical_compare |
Short-circuiting lexicographical comparison of two Iterables with an optional custom predicate, by default hana::less.Given two Iterables xs and ys and a binary predicate pred, lexicographical_compare returns whether xs is to be considered less than ys in a lexicographical ordering. Specifically, let's denote the linearizations of xs and ys by [x1, x2, ...] and [y1, y2, ...], respectively. If the first couple satisfying the predicate is of the form xi, yi, lexicographical_compare returns true. Otherwise, if the first couple to satisfy the predicate is of the form yi, xi, lexicographical_compare returns false. If no such couple can be found, lexicographical_compare returns whether xs has fewer elements than ys. More... | |
| constexpr auto boost::hana::at |
#include <boost/hana/fwd/at.hpp>
Returns the nth element of an iterable.Given an Iterable and an IntegralConstant index, at returns the element located at the index in the linearization of the iterable. Specifically, given an iterable xs with a linearization of [x1, ..., xN], at(xs, k) is equivalent to xk.
If the Iterable actually stores the elements it contains, at is required to return a lvalue reference, a lvalue reference to const or a rvalue reference to the matching element, where the type of reference must match that of the iterable passed to at. If the Iterable does not store the elements it contains (i.e. it generates them on demand), this requirement is dropped.
| xs | The iterable in which an element is retrieved. The iterable must contain at least n + 1 elements. |
| n | A non-negative IntegralConstant representing the 0-based index of the element to return. It is an error to call at with an index that out of bounds of the iterable. |
| constexpr auto boost::hana::at_c |
#include <boost/hana/fwd/at.hpp>
Equivalent to at; provided for convenience.
hana::at_c<n> is an overloaded function, not a function object. Hence, it can't be passed to higher-order algorithms. This is done for compile-time performance reasons.| constexpr auto boost::hana::back |
#include <boost/hana/fwd/back.hpp>
Returns the last element of a non-empty and finite iterable.Given a non-empty and finite iterable xs with a linearization of [x1, ..., xN], back(xs) is equal to xN. Equivalently, back(xs) must be equivalent to at_c<N-1>(xs), and that regardless of the value category of xs (back must respect the reference semantics of at).
| constexpr auto boost::hana::drop_front |
#include <boost/hana/fwd/drop_front.hpp>
Drop the first n elements of an iterable, and return the rest.Given an Iterable xs with a linearization of [x1, x2, ...] and a non-negative IntegralConstant n, drop_front(xs, n) is an iterable with the same tag as xs whose linearization is [xn+1, xn+2, ...]. In particular, note that this function does not mutate the original iterable in any way. If n is not given, it defaults to an IntegralConstant with a value equal to 1.
In case length(xs) <= n, drop_front will simply drop the whole iterable without failing, thus returning an empty iterable. This is different from drop_front_exactly, which expects n <= length(xs) but can be better optimized because of this additional guarantee.
| xs | The iterable from which elements are dropped. |
| n | A non-negative IntegralConstant representing the number of elements to be dropped from the iterable. If n is not given, it defaults to an IntegralConstant with a value equal to 1. |
| constexpr auto boost::hana::drop_front_exactly |
#include <boost/hana/fwd/drop_front_exactly.hpp>
Drop the first n elements of an iterable, and return the rest.Given an Iterable xs with a linearization of [x1, x2, ...] and a non-negative IntegralConstant n, drop_front_exactly(xs, n) is an iterable with the same tag as xs whose linearization is [xn+1, xn+2, ...]. In particular, note that this function does not mutate the original iterable in any way. If n is not given, it defaults to an IntegralConstant with a value equal to 1.
It is an error to use drop_front_exactly with n > length(xs). This additional guarantee allows drop_front_exactly to be better optimized than the drop_front function, which allows n > length(xs).
| xs | The iterable from which elements are dropped. |
| n | A non-negative IntegralConstant representing the number of elements to be dropped from the iterable. In addition to being non-negative, n must be less than or equal to the number of elements in xs. If n is not given, it defaults to an IntegralConstant with a value equal to 1. |
| constexpr auto boost::hana::drop_while |
#include <boost/hana/fwd/drop_while.hpp>
Drop elements from an iterable up to, but excluding, the first element for which the predicate is not satisfied.Specifically, drop_while returns an iterable containing all the elements of the original iterable except for those in the range delimited by [head, e), where head is the first element and e is the first element for which the predicate is not satisfied. If the iterable is not finite, the predicate has to return a false- valued Logical at a finite index for this method to return.
| iterable | The iterable from which elements are dropped. |
| predicate | A function called as predicate(x), where x is an element of the structure, and returning a Logical representing whether x should be dropped from the structure. In the current version of the library, predicate should return a compile-time Logical. |
| constexpr auto boost::hana::front |
#include <boost/hana/fwd/front.hpp>
Returns the first element of a non-empty iterable.Given a non-empty Iterable xs with a linearization of [x1, ..., xN], front(xs) is equal to x1. If xs is empty, it is an error to use this function. Equivalently, front(xs) must be equivalent to at_c<0>(xs), and that regardless of the value category of xs (front must respect the reference semantics of at).
| constexpr auto boost::hana::index_if |
#include <boost/hana/fwd/index_if.hpp>
Finds the value associated to the first key satisfying a predicate.Given an Iterable structure xs and a predicate pred, index_if(xs, pred) returns a hana::optional containing an IntegralConstant of the index of the first element that satisfies the predicate or nothing if no element satisfies the predicate.
| xs | The structure to be searched. |
| predicate | A function called as predicate(x), where x is an element of the Iterable structure and returning whether x is the element being searched for. In the current version of the library, the predicate has to return an IntegralConstant holding a value that can be converted to bool. |
| constexpr auto boost::hana::is_empty |
#include <boost/hana/fwd/is_empty.hpp>
Returns whether the iterable is empty.Given an Iterable xs, is_empty returns whether xs contains no more elements. In other words, it returns whether trying to extract the tail of xs would be an error. In the current version of the library, is_empty must return an IntegralConstant holding a value convertible to bool. This is because only compile-time Iterables are supported right now.
| constexpr auto boost::hana::lexicographical_compare |
#include <boost/hana/fwd/lexicographical_compare.hpp>
Short-circuiting lexicographical comparison of two Iterables with an optional custom predicate, by default hana::less.Given two Iterables xs and ys and a binary predicate pred, lexicographical_compare returns whether xs is to be considered less than ys in a lexicographical ordering. Specifically, let's denote the linearizations of xs and ys by [x1, x2, ...] and [y1, y2, ...], respectively. If the first couple satisfying the predicate is of the form xi, yi, lexicographical_compare returns true. Otherwise, if the first couple to satisfy the predicate is of the form yi, xi, lexicographical_compare returns false. If no such couple can be found, lexicographical_compare returns whether xs has fewer elements than ys.
Given two Iterables It1(T) and It2(T) and a predicate \( pred : T \times T \to Bool \) (where Bool is some Logical), lexicographical_compare has the following signatures. For the variant with a provided predicate,
\[ \mathtt{lexicographical\_compare} : It1(T) \times It2(T) \times (T \times T \to Bool) \to Bool \]
for the variant without a custom predicate, T is required to be Orderable. The signature is then
\[ \mathtt{lexicographical\_compare} : It1(T) \times It2(T) \to Bool \]
| xs,ys | Two Iterables to compare lexicographically. |
| pred | A binary function called as pred(x, y) and pred(y, x), where x and y are elements of xs and ys, respectively. pred must return a Logical representing whether its first argument is to be considered as less than its second argument. Also note that pred must define a total ordering as defined by the Orderable concept. When pred is not provided, it defaults to less. |