to<InversePresentation>

This file contains documentation for creating inverse semigroup and monoid presentations in libsemigroups from other types of objects.

See also

The `to` function for an overview of possible conversions between libsemigroups types.

Functions
template<typename Result, typename Word>
auto	to (InversePresentation< Word > const &ip) noexcept -> std::enable_if_t< std::is_same_v< InversePresentation< typename Result::word_type >, Result > &&!std::is_same_v< Word, typename Result::word_type >, Result >
	Make an inverse presentation from a different type of inverse presentation.
template<typename Result, typename Word, typename Func>
auto	to (InversePresentation< Word > const &ip, Func &&f) -> std::enable_if_t< std::is_same_v< InversePresentation< typename Result::word_type >, Result >, Result >
	Make an inverse presentation from a different type of inverse presentation.
template<template< typename... > typename Thing, typename Word>
auto	to (Presentation< Word > cont &p) -> std::enable_if_t< std::is_same_v< InversePresentation< Word >, Thing< Word > >, InversePresentation< Word > >
	Make an inverse presentation from a presentation.

Function Documentation

to() [1/3]

template<typename Result, typename Word>

auto to ( InversePresentation< Word > const & ip ) -> std::enable_if_t< std::is_same_v<InversePresentation<typename Result::word_type>, Result> && !std::is_same_v<Word, typename Result::word_type>, Result>

noexcept

Defined in to-presentation.hpp.

Despite the hideous signature, this function should be invoked as follows:

to<InversePresentation<Word>>(ip);

There are 2 versions of this function:

1. When typename Result::word_type and Word are not the same, this function returns an inverse presentation equivalent to the input inverse presentation but of a different type (for example, can be used to convert from std::string to word_type).
2. When typename Result::word_type and Word are the same, this function just returns its argument ip (as a reference), and is included solely for the purpose of simplifying certain client code, where inverse presentations must be converted from one type to another sometimes, but not other times.

If the alphabet of of ip is \(\{a_0, a_1, \dots a_{n-1}\}\), then the conversion from InversePresentation<WordInput>::letter_type to InversePresentation<WordOutput>::letter_type is \(a_i \mapsto\) human_readable_letter<WordOutput>(size_t i).

Template Parameters

Result	the return type, also used for SFINAE, should be InversePresentation<T> for some type T.
Word	the type of the words in the input inverse presentation.

Parameters

ip	the input inverse presentation.

Returns

A value of type InversePresentation<WordOutput>.

Exceptions

LibsemigroupsException

if typename Result::word_type and Word are not the same and p.throw_if_bad_alphabet_or_rules() throws. If typename Result::word_type and Word are the same, then this function is noexcept.

to() [2/3]

template<typename Result, typename Word, typename Func>

auto to	(	InversePresentation< Word > const &	ip,
		Func &&	f ) -> std::enable_if_t< std::is_same_v< InversePresentation< typename Result::word_type >, Result >, Result >

Defined in to-presentation.hpp.

Despite the hideous signature, this function should be invoked as follows:

to<InversePresentation<Word>>(p, func);

This function returns an inverse presentation equivalent to the input inverse presentation but of a different type (for example, can be used to convert from std::string to word_type). The second parameter specifies how to map the letters of one inverse presentation to the other.

Template Parameters

Result	the return type, also used for SFINAE, should be InversePresentation<T> for some type T.
Word	the type of the words in the input inverse presentation.
Func	the type of a function for transforming letters.

Parameters

ip	the input inverse presentation.
f	a function mapping InversePresentation<Word>::letter_type to Result::letter_type.

Returns

A value of type InversePresentation<WordOutput>.

Exceptions

LibsemigroupsException

if p.throw_if_bad_alphabet_or_rules() throws.

Note

Func must be a function type that is invocable with values of Presentation<Word>::letter_type. If this is not true, then template substitution will fail.

to() [3/3]

template<template< typename... > typename Thing, typename Word>

auto to

(

Presentation< Word > cont &

p

)

-> std::enable_if_t< std::is_same_v< InversePresentation< Word >, Thing< Word > >, InversePresentation< Word > >

Defined in to-presentation.hpp.

Despite the hideous signature, this function should be invoked as follows:

to<InversePresentation>(p);

This function returns an inverse presentation with rules equivalent to those of the input presentation, but over a normalised alphabet. If the alphabet of p is \(\{a_0, a_1, \dots, a_{n-1}\}\), then the alphabet of the returned inverse presentation will be \(\{0, 1, \dots, n-1, n, \dots, 2n-1\}\), where the inverse of letter \(i\) is the letter \(i + n\, (\text{mod }2n)\).

Template Parameters

Thing	used for SFINAE, must be InversePresentation.
Word	the type of the words in the input presentation.

Parameters

p	the input presentation.

Returns

A value of type InversePresentation<Word>.

Exceptions

LibsemigroupsException

if p.throw_if_bad_alphabet_or_rules() throws.