Types

This file contains functionality for various types used in libsemigroups.

Classes
struct	SmallestInteger< N >
	Type giving the smallest unsigned integer type that can represent a template. More...

Typedefs
template<typename Given, typename Expected>
using	enable_if_is_same = std::enable_if_t<std::is_same_v<Given, Expected>, Expected>
	Alias equal to the second template parameter if both template parameters are equal.
using	letter_type = size_t
	Type for the index of a generator of a semigroup.
using	relation_type = std::pair<word_type, word_type>
	Type for a pair of word_type (a relation) of a semigroup.
using	word_type = std::vector<letter_type>
	Type for a word over the generators of a semigroup.

Enumerations
enum class	congruence_kind { onesided = 1 , twosided = 2 }
	Enum to indicate the sided-ness of a congruence. More...
enum class	Order : uint8_t { none = 0 , shortlex , lex , recursive }
	The possible orderings of words and strings. More...
enum class	side { left , right }
	Enum class indicating the handedness or side of an action. More...
enum class	tril { FALSE = 0 , TRUE = 1 , unknown = 2 }
	Enum to indicate true, false or not currently knowable. More...

Typedef Documentation

enable_if_is_same

template<typename Given, typename Expected>

using enable_if_is_same = std::enable_if_t<std::is_same_v<Given, Expected>, Expected>

Alias equal to the second template parameter if both template parameters are equal.

Enumeration Type Documentation

congruence_kind

enum class congruence_kind

strong

The values in this enum can be used to indicate that a congruence should be 2-sided, left, or right.

Enumerator
onesided	Value representing a one-sided congruence.
twosided	Value representing a two-sided congruence.

Order

enum class Order : uint8_t

strong

The values in this enum can be used as the arguments for functions such as standardize(Order) or order(Order) to specify which ordering should be used. The normal forms for congruence classes are given with respect to one of the orders specified by the values in this enum.

See also

Orders

Enumerator
none	No ordering.
shortlex	The short-lex ordering. Words are first ordered by length, and then lexicographically.
lex	The lexicographic ordering. Note that this is not a well-order, so there may not be a lexicographically least word in a given congruence class of words.
recursive	The recursive-path ordering, as described in [37] (Definition 1.2.14, page 24).

side

enum class side

strong

The values in this enum can be used as a template parameter for the Action class to specify whether the action of the Action is a left or right action.

See also

Actions

Enumerator
left	This value indicates that the action in an Action instance should be a left action.
right	This value indicates that the action in an Action instance should be a right action.

tril

enum class tril

strong

The values in this enum can be used to indicate a result is true, false, or not currently knowable.

Enumerator
FALSE	Value representing false.
TRUE	Value representing true.
unknown	Value representing unknown (either true or false).