to<Presentation>

This file contains documentation for creating 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>
auto	to (FroidurePinBase &fp) -> std::enable_if_t< std::is_same_v< Presentation< typename Result::word_type >, Result >, Result >
	Make a presentation from a FroidurePin object.
template<template< typename... > typename Thing, typename Word, typename Rewriter, typename ReductionOrder>
auto	to (KnuthBendix< Word, Rewriter, ReductionOrder > &kb) -> std::enable_if_t< std::is_same_v< Thing< Word >, Presentation< Word > >, Presentation< Word > >
	Make a presentation from a KnuthBendix object.
template<typename Result, typename Word>
auto	to (Presentation< Word > const &p) -> std::enable_if_t< std::is_same_v< Presentation< typename Result::word_type >, Result > &&!std::is_same_v< typename Result::word_type, Word >, Result >
	Make a presentation from a different type of presentation.
template<typename Result, typename Word, typename Func>
auto	to (Presentation< Word > const &p, Func &&f) -> std::enable_if_t< std::is_same_v< Presentation< typename Result::word_type >, Result >, Result >
	Make a presentation from a different type of presentation.

Function Documentation

to() [1/4]

template<typename Result>

auto to

(

FroidurePinBase &

fp

)

-> std::enable_if_t< std::is_same_v< Presentation< typename Result::word_type >, Result >, Result >

Defined in to-presentation.hpp.

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

to<Presentation<Word>>(fp);

This function constructs and returns a Presentation object using the rules of a FroidurePin object, accessed via FroidurePin::cbegin_rules and FroidurePin::cend_rules.

No enumeration of the argument fp is performed, so it might be the case that the resulting presentation does not define the same semigroup as fp. To ensure that the resulting presentation defines the same semigroup as fp, run FroidurePin::run (or any other function that fully enumerates fp) prior to calling this function.

Template Parameters

Result

the return type, also used for SFINAE, should be Presentation<Word> for some type Word.

Parameters

fp	the FroidurePin object from which to obtain the rules.

Returns

An object of type Presentation<Word>.

Exceptions

This function guarantees not to throw a LibsemigroupsException.

to() [2/4]

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

auto to

(

KnuthBendix< Word, Rewriter, ReductionOrder > &

kb

)

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

Defined in to-presentation.hpp.

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

to<Presentation>(kb);

This function constructs and returns a Presentation object using the currently active rules of kb.

No enumeration of the argument kb is performed, so it might be the case that the resulting presentation does not define the same semigroup/monoid as kb. To ensure that the resulting presentation defines the same semigroup as kb, run run (or any other function that fully enumerates kb) prior to calling this function.

Template Parameters

Thing	used for SFINAE, must be Presentation.
Word	the type of the rules in the presentation of the KnuthBendix object kb.
Rewriter	the second template parameter for KnuthBendix.
ReductionOrder	the third template parameter for KnuthBendix. constructed.

Parameters

kb	the KnuthBendix object from which to obtain the rules.

Returns

An object of type Presentation<Word>.

Exceptions

This function guarantees not to throw a LibsemigroupsException.

to() [3/4]

template<typename Result, typename Word>

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

noexcept

Defined in to-presentation.hpp.

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

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

There are 2 versions of this function:

1. When typename Result::word_type and Word are not the same, this function returns a presentation equivalent to the input 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 p (as a reference), and is included solely for the purpose of simplifying certain client code, where presentations must be converted from one type to another sometimes, but not other times.

If the alphabet of of p is \(\{a_0, a_1, \dots a_{n-1}\}\), then the conversion from Presentation<WordInput>::letter_type to Presentation<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 Presentation<T> for some type T.
Word	the type of the words in the input presentation.

Parameters

p	the input presentation.

Returns

A value of type Result.

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() [4/4]

template<typename Result, typename Word, typename Func>

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

Defined in to-presentation.hpp.

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

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

This function returns a presentation equivalent to the input 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 presentation to the other.

Template Parameters

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

Parameters

p	the input presentation.
f	a function mapping Presentation<Word>::letter_type to Result::letter_type.

Returns

A value of type Result.

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.