Alphabet

Collaboration diagram for Alphabet:

Modules
	Adaptation
	Provides alphabet adaptions of some standard char and uint types.
	Aminoacid
	Provides the amino acid alphabets and functionality for translation from nucleotide.
	CIGAR
	Provides the CIGAR operation alphabet, along with the CIGAR cartesian composition.
	Composite
	Provides data structures joining multiple alphabets into a single alphabet.
	Gap
	Provides the gap alphabet and functionality to make an alphabet a gapped alphabet.
	Mask
	Provides the mask alphabet and functionality for creating masked composites.
	Nucleotide
	Provides the different DNA and RNA alphabet types.
	Quality
	Provides the various quality score types.
	Structure
	The structure module contains alphabets for RNA and protein structure.

Classes
interface	seqan3::Alphabet
	The generic alphabet concept that covers most data types used in ranges. More...
class	seqan3::alphabet_base< derived_type, size, char_t >
	A CRTP-base that makes defining a custom alphabet easier. More...
class	seqan3::alphabet_base< derived_type, 1ul, char_t >
	Specialisation of seqan3::alphabet_base for alphabets of size 1. More...
class	seqan3::alphabet_proxy< derived_type, alphabet_type >
	A CRTP-base that eases the definition of proxy types returned in place of regular alphabets. More...
struct	std::hash< alphabet_t >
	Struct for hashing a character. More...
struct	std::hash< urng_t >
	Struct for hashing a range of characters. More...
interface	seqan3::Semialphabet
	The basis for seqan3::Alphabet, but requires only rank interface (not char). More...
interface	seqan3::WritableAlphabet
	Refines seqan3::Alphabet and adds assignability. More...
interface	seqan3::WritableSemialphabet
	A refinement of seqan3::Semialphabet that adds assignability. More...

Typedefs
template<typename alphabet_type >
using	seqan3::alphabet_char_t = decltype(seqan3::to_char(std::declval< alphabet_type const >()))
	The char_type of the alphabet; defined as the return type of seqan3::to_char.
template<typename semi_alphabet_type >
using	seqan3::alphabet_rank_t = decltype(seqan3::to_rank(std::declval< semi_alphabet_type >()))
	The rank_type of the semi-alphabet; defined as the return type of seqan3::to_rank.

Functions
size_t	std::hash< alphabet_t >::operator() (alphabet_t const character) const noexcept
	Compute the hash for a character. More...
size_t	std::hash< urng_t >::operator() (urng_t const &range) const noexcept
	Compute the hash for a range of characters. More...

Variables
template<typename alph_t >
constexpr auto	seqan3::alphabet_size = detail::adl::only::alphabet_size_obj<alph_t>()
	A type trait that holds the size of a (semi-)alphabet. More...

Function objects
constexpr auto	seqan3::to_rank = detail::adl::only::to_rank_fn{}
	Return the rank representation of a (semi-)alphabet object. More...
constexpr auto	seqan3::assign_rank_to = detail::adl::only::assign_rank_to_fn{}
	Assign a rank to an alphabet object. More...
constexpr auto	seqan3::to_char = detail::adl::only::to_char_fn{}
	Return the char representation of an alphabet object. More...
constexpr auto	seqan3::assign_char_to = detail::adl::only::assign_char_to_fn{}
	Assign a character to an alphabet object. More...
template<typename alph_t >
constexpr auto	seqan3::char_is_valid_for = detail::adl::only::char_is_valid_for_fn<alph_t>{}
	Returns whether a character is in the valid set of a seqan3::Alphabet (usually implies a bijective mapping to an alphabet value). More...
constexpr auto	seqan3::assign_char_strictly_to = detail::adl::only::assign_char_strictly_to_fn{}
	Assign a character to an alphabet object, throw if the character is not valid. More...

Detailed Description

Introduction

Alphabets are a core component in SeqAn. They enable us to represent the smallest unit of biological sequence data, e.g. a nucleotide or an amino acid.

In theory, these could just be represented as a char and this is how many people perceive them, but it makes sense to use a smaller, stricter and well-defined alphabet in almost all cases, because:

• Most of our sequences alphabets are actually smaller and can possibly be represented by less bits than a char, e.g. a char can have 256 values and thus must be represented by 8 bits of memory, but a DNA character could be represented by 2 bits, because it only has four values in the smallest representation ('A', 'C', 'G', 'T').
• From a programmer's point of view it is very important to also access the rank of a letter, i.e. we need to be able to convert 'A', 'C', 'G', 'T' to 0, 1, 2, 3 respectively. In fact the rank representation is used a lot more often than the visual representation which is only used in input/output.
• You may want to prevent the user from selecting letters that aren't part of that alphabet, e.g. 'J' is not part of any nucleotide definition so people shouldn't be able to select 'J'. With a specialised alphabet you could instead convert those to a special "unknown"-character, e.g. you might want 'J' to be always converted to 'N'.

In SeqAn there are alphabet types for typical sequence alphabets like DNA and amino acid, but also for qualities, RNA structures and alignment gaps. In addition there are templates for combining alphabet types into new alphabets, and wrappers for existing data types like the canonical char.

In addition to concrete alphabet types, SeqAn provides multiple concepts that describe groups of alphabets by their properties and can be used to constrain templates so that they only work with certain alphabet types. See the Tutorial on Concepts for a gentle introduction to the topic.

The alphabet concepts

Alphabet size

All alphabets in SeqAn have a fixed size. It can be queried via the seqan3::alphabet_size type trait and optionally also the alphabet_size static member of the alphabet (see below for "members VS free/global functions").

In some areas we provide alphabets types with different sizes for the same purpose, e.g. seqan3::dna4 ('A', 'C', 'G', 'T'), seqan3::dna5 (plus 'N') and seqan3::dna15 (plus ambiguous characters defined by IUPAC). By convention most of our alphabets carry their size in their name (seqan3::dna4 has size 4 a.s.o.).

A main reason for choosing a smaller alphabet over a bigger one is the possibility of optimising for space efficiency. Note, however, that a single letter by itself can never be smaller than a byte for architectural reasons. Actual space improvements are realised via secondary structures, e.g. when using a seqan3::bitcompressed_vector<seqan3::dna4> instead of std::vector<seqan3::dna4>. Also the single letter quality composite seqan3::qualified<seqan3::dna4, seqan3::phred42> fits into one byte, because the product of the alphabet sizes (4 * 42) is smaller than 256; whereas the same composite with seqan3::dna15 requires two bytes per letter (15 * 42 > 256).

Assigning and retrieving values

As mentioned above, we typically think of alphabets in their character representation, but we also require them in "rank representation" as programmers. In C and C++ it is quite difficult to cleanly differentiate between these, because the char type is considered an integral type and can be used to index an array (e.g. my_array['A'] translates to my_array[65]). Moreover the sign of char is implementation defined and on many platforms the smallest integer types int8_t and uint8_t are literally the same types as signed char and unsigned char respectively.

This leads to ambiguity when assigning and retrieving values:

// does not work:
// dna4 my_letter{0};      // we want to set the default, an A
// dna4 my_letter{'A'};    // we also want to set an A, but we are setting value 65

// std::cout << my_letter; // you expect 'A', but how would you access the number?

To solve this problem, alphabets in SeqAn define two interfaces:

1. a rank based interface with
   • seqan3::to_rank to produce the numerical representation;
   • seqan3::assign_rank_to to assign from the numerical representation;
   • the numerical representation is an unsigned integral type like size_t; the exact type can be retrieved via the seqan3::alphabet_rank_t.
2. a character based interface with
   • seqan3::to_char to produce the visual representation;
   • seqan3::assign_char_to to assign from the visual representation;
   • seqan3::char_is_valid_for that checks whether a character value has a one-to-one mapping to an alphabet value;
   • the visual representation is a character type (almost always char, but could be char16_t or char32_t, as well); the exact type can be retrieved via seqan3::alphabet_char_t.

To prevent the aforementioned ambiguity, you can neither assign from rank or char representation via operator=, nor can you cast the alphabet to either of it's representation forms, you need to explicitly use the interfaces:

dna4 my_letter;
assign_rank_to(0, my_letter);       // assign an A via rank interface
assign_char_to('A', my_letter);     // assign an A via char interface

For efficiency, the representation saved internally is normally the rank representation, and the character representation is generated via conversion tables. This is, however, not required as long as both interfaces are provided and all functions operate in constant time.

The same applies for printing characters although seqan3::debug_stream provides some convenience:

std::cout << to_char(my_letter);            // prints 'A'
std::cout << (unsigned)to_rank(my_letter);  // prints 0
// we have to add the cast here, because uint8_t is also treated as a char type by default :(

// Using SeqAn's debug_stream:
debug_stream << to_char(my_letter);         // prints 'A'
debug_stream << my_letter;                  // prints 'A' (calls to_char() automatically!)
debug_stream << to_rank(my_letter);         // prints 0   (casts uint8_t to unsigned automatically!)

To reduce the burden of calling assign_char often, most alphabets in SeqAn3 provide custom literals for the alphabet and sequences over the alphabet:

dna4        my_letter = 'A'_dna4;           // identical to assign_char_to('A', my_letter);
dna4_vector my_seq    = "ACGT"_dna4;        // identical to calling assign_char for each element

Note, however, that literals are not required by the concept.

Different concepts

All types that have valid implementations of the functions/functors described above model the concept seqan3::WritableAlphabet. This is the strongest (i.e. most refined) general case concept. There are more refined concepts for specific biological applications (like seqan3::NucleotideAlphabet), and there are less refined concepts that only model part of an alphabet:

• seqan3::Semialphabet and derived concepts only require the rank interface;
• seqan3::Alphabet (without Writable*) and derived concepts only require readability and not assignability.

Typically you will use seqan3::Alphabet in "read-only" situations (e.g. const parameters) and seqan3::WritableAlphabet whenever the values might be changed. Semi-alphabets are less useful in application code.

	Semialphabet	WritableSemialphabet	Alphabet	WritableAlphabet	Aux
alphabet_size	✅	✅	✅	✅
to_rank	✅	✅	✅	✅
alphabet_rank_t	✅	✅	✅	✅	🔗
assign_rank_to		✅		✅
to_char			✅	✅
alphabet_char_t			✅	✅	🔗
assign_char_to				✅
char_is_valid_for				✅
assign_char_strictly_to				✅	🔗

The above table shows all alphabet concepts and related functions and type traits. The entities marked as "auxiliary" provide shortcuts to the other "essential" entitities. This difference is only relevant if you want to create your own alphabet (you do not need to provide an implementation for the "auxiliary" entities, they are provided automatically).

Members VS free/global functions

The alphabet concept (as most concepts in SeqAn) looks for free/global functions, i.e. you need to be able to call seqan3::to_rank(my_letter), however most alphabets also provide a member function, i.e. my_letter.to_rank(). The same is true for the type trait seqan3::alphabet_size vs the static data member alphabet_size.

Members are provided for convenience and if you are an application developer who works with a single concrete alphabet type you are fine with using the member functions. If you, however, implement a generic function that accepts different alphabet types, you need to use the free function / type trait interface, because it is the only interface guaranteed to exist (member functions are not required/enforced by the concept).

Containers over alphabets

In SeqAn3 it is recommended you use the STL container classes like std::vector for storing sequence data, but you can use other class templates if they satisfy the respective seqan3::Container, e.g. std::deque or folly::fbvector or even Qt::QVector.

std::basic_string is also supported, however, we recommend against using it, because it is not safe (and not useful) to call certain members like .c_str() if our alphabets are used as value type.

We provide specialised containers with certain properties in the Range module.

Function Documentation

operator()() [1/2]

template<typename alphabet_t >

size_t std::hash< alphabet_t >::operator() ( alphabet_t const  character ) const

inlinenoexcept

Compute the hash for a character.

Parameters

[in]

character

The character to process. Must model seqan3::Semialphabet.

Returns

size_t.

See also

seqan3::to_rank.

operator()() [2/2]

template<ranges::InputRange urng_t>

size_t std::hash< urng_t >::operator() ( urng_t const &  range ) const

inlinenoexcept

Compute the hash for a range of characters.

Parameters

[in]

range

The input range to process. Must model std::ranges::InputRange and the reference type of the range of the range must model seqan3::Semialphabet.

Returns

size_t.

Variable Documentation

alphabet_size

template<typename alph_t >

constexpr auto seqan3::alphabet_size = detail::adl::only::alphabet_size_obj<alph_t>()

inline

A type trait that holds the size of a (semi-)alphabet.

Template Parameters

your_type

The (semi-)alphabet type being queried.

This type trait is implemented as a global variable template.

It is only defined for types that provide one of the following (checked in this order):

1. A free function alphabet_size(your_type const &) in the namespace of your type (or as friend) that returns the size as an integral value. The function must be marked constexpr and noexcept and the return type needs to be implicitly convertible to size_t. The value of the argument to the function shall be ignored, it is only used to select the function via argument-dependent lookup.
2. A free function alphabet_size(your_type const &) in namespace seqan3::custom that returns the size as an integral value. The same restrictions apply as above.
3. A static constexpr data member called alphabet_size that is the size. It must be implicitly convertible to size_t.

Every (semi-)alphabet type must provide one of the above.

Note that if the (semi-)alphabet type with cvref removed is not std::is_nothrow_default_constructible or not seqan3::is_constexpr_default_constructible, this object will instead look for alphabet_size(std::type_identity<your_type> const &) with the same semantics (in cases 1. and 2.).

Example

#include <seqan3/alphabet/nucleotide/dna5.hpp>
#include <seqan3/alphabet/adaptation/char.hpp>
#include <seqan3/alphabet/concept.hpp>

int main()
{
    auto r2 = seqan3::alphabet_size<char>;            // calls seqan3::custom::alphabet_size(char{}); r2 == 256
    auto r3 = seqan3::alphabet_size<seqan3::dna5>;    // returns dna5::alphabet_size; r3 == 5
}

For an example of a full alphabet definition with free function implementations (solution 1. above), see seqan3::Alphabet.

Customisation point

This is a customisation point (see Customisation). To specify the behaviour for your own alphabet type, simply provide one of the three functions specified above.

assign_char_strictly_to

constexpr auto seqan3::assign_char_strictly_to = detail::adl::only::assign_char_strictly_to_fn{}

inline

Assign a character to an alphabet object, throw if the character is not valid.

Template Parameters

your_type

Type of the target object.

Parameters

chr	The character being assigned; must be of the seqan3::alphabet_char_t of the target object.
alph	The target object; its type must model seqan3::Alphabet.

Returns

Reference to alph if alph was given as lvalue, otherwise a copy.

Exceptions

seqan3::invalid_char_assignment

If seqan3::char_is_valid_for<decltype(alph)>(chr) == false.

This is a function object. Invoke it with the parameters specified above.

Note that this is not a customisation point and it cannot be "overloaded". It simply invokes seqan3::char_is_valid_for and seqan3::assign_char_to.

Example

#include <seqan3/alphabet/nucleotide/dna5.hpp>
#include <seqan3/alphabet/adaptation/char.hpp>
#include <seqan3/alphabet/concept.hpp>

int main()
{
    char c = '!';
    seqan3::assign_char_strictly_to('?', c);     // calls seqan3::custom::assign_char_strictly_to('A', c)

    seqan3::dna5 d{};
    seqan3::assign_char_strictly_to('A', d);     // calls .assign_char('A') member

    // also works for temporaries:
    seqan3::dna5 d2 = seqan3::assign_char_strictly_to('A', seqan3::dna5{});

    // invalid/unknown characters throw
//     seqan3::dna5 d3 = seqan3::assign_char_strictly_to('!', seqan3::dna5{});
}

assign_char_to

constexpr auto seqan3::assign_char_to = detail::adl::only::assign_char_to_fn{}

inline

Assign a character to an alphabet object.

Template Parameters

your_type

Type of the target object.

Parameters

chr	The character being assigned; must be of the seqan3::alphabet_char_t of the target object.
alph	The target object; its type must model seqan3::Alphabet.

Returns

Reference to alph if alph was given as lvalue, otherwise a copy.

This is a function object. Invoke it with the parameter(s) specified above.

It acts as a wrapper and looks for three possible implementations (in this order):

1. A free function assign_char_to(char_type const chr, your_type & a) in the namespace of your type (or as friend). The function must be marked noexcept (constexpr is not required, but recommended) and the return type be your_type &.
2. A free function assign_char_to(char_type const chr, your_type & a) in namespace seqan3::custom. The same restrictions apply as above.
3. A member function called assign_char(char_type const chr) (not assign_char_to). It must be marked noexcept (constexpr is not required, but recommended) and the return type be your_type &.

Every alphabet type must provide one of the above. Note that temporaries of your_type are handled by this function object and do not require an additional overload.

Example

#include <seqan3/alphabet/nucleotide/dna5.hpp>
#include <seqan3/alphabet/adaptation/char.hpp>
#include <seqan3/alphabet/concept.hpp>

int main()
{
    char c = '!';
    seqan3::assign_char_to('?', c);     // calls seqan3::custom::assign_char_to('A', c)

    seqan3::dna5 d{};
    seqan3::assign_char_to('A', d);     // calls .assign_char('A') member

    // also works for temporaries:
    seqan3::dna5 d2 = seqan3::assign_char_to('A', seqan3::dna5{});

    // invalid/unknown characters are converted:
    seqan3::dna5 d3 = seqan3::assign_char_to('!', seqan3::dna5{}); // == 'N'_dna5
}

For an example of a full alphabet definition with free function implementations (solution 1. above), see seqan3::Alphabet.

Customisation point

This is a customisation point (see Customisation). To specify the behaviour for your own alphabet type, simply provide one of the three functions specified above.

assign_rank_to

constexpr auto seqan3::assign_rank_to = detail::adl::only::assign_rank_to_fn{}

inline

Assign a rank to an alphabet object.

Template Parameters

your_type

Type of the target object.

Parameters

chr	The rank being assigned; must be of the seqan3::alphabet_rank_t of the target object.
alph	The target object.

Returns

Reference to alph if alph was given as lvalue, otherwise a copy.

This is a function object. Invoke it with the parameter(s) specified above.

It acts as a wrapper and looks for three possible implementations (in this order):

1. A free function assign_rank_to(rank_type const chr, your_type & a) in the namespace of your type (or as friend). The function must be marked noexcept (constexpr is not required, but recommended) and the return type be your_type &.
2. A free function assign_rank_to(rank_type const chr, your_type & a) in namespace seqan3::custom. The same restrictions apply as above.
3. A member function called assign_rank(rank_type const chr) (not assign_rank_to). It must be marked noexcept (constexpr is not required, but recommended) and the return type be your_type &.

Every (semi-)alphabet type must provide one of the above. Note that temporaries of your_type are handled by this function object and do not require an additional overload.

Example

#include <seqan3/alphabet/nucleotide/dna5.hpp>
#include <seqan3/alphabet/adaptation/char.hpp>
#include <seqan3/alphabet/concept.hpp>

int main()
{
    char c = '!';
    seqan3::assign_rank_to(66, c);     // calls seqan3::custom::assign_rank_to(66, c); == 'B'

    seqan3::dna5 d{};
    seqan3::assign_rank_to(2, d);     // calls .assign_rank(2) member; == 'G'_dna5

    // also works for temporaries:
    seqan3::dna5 d2 = seqan3::assign_rank_to(2, seqan3::dna5{});

    // too-large ranks are undefined behaviour:
//    seqan3::dna5 d3 = seqan3::assign_rank_to(50, seqan3::dna5{});
}

For an example of a full alphabet definition with free function implementations (solution 1. above), see seqan3::Alphabet.

Customisation point

This is a customisation point (see Customisation). To specify the behaviour for your own alphabet type, simply provide one of the three functions specified above.

char_is_valid_for

template<typename alph_t >

constexpr auto seqan3::char_is_valid_for = detail::adl::only::char_is_valid_for_fn<alph_t>{}

inline

Returns whether a character is in the valid set of a seqan3::Alphabet (usually implies a bijective mapping to an alphabet value).

Template Parameters

your_type

The alphabet type being queried.

Parameters

chr	The character being checked; must be convertible to seqan3::alphabet_char_t<your_type>.
alph	The target object; its type must model seqan3::Alphabet.

Returns

true or false.

This is a function object. Invoke it with the parameter(s) specified above.

It acts as a wrapper and looks for three possible implementations (in this order):

1. A free function char_is_valid_for(char_type const chr, your_type const &) in the namespace of your type (or as friend). The function must be marked noexcept (constexpr is not required, but recommended) and the return type be bool. The value of the second argument to the function shall be ignored, it is only used to select the function via argument-dependent lookup.
2. A free function char_is_valid_for(char_type const chr, your_type const &) in namespace seqan3::custom. The same restrictions apply as above.
3. A static member function called char_is_valid(char_type) (not char_is_valid_for). It must be marked noexcept (constexpr is not required, but recommended) and the return type be bool.

An alphabet type may provide one of the above. If none is provided, this function will declare every character c as valid for whom it holds that seqan3::to_char(seqan3::assign_char_to(c, alph_t{})) == c, i.e. converting back and forth results in the same value.

Note that if the alphabet type with cvref removed is not std::is_nothrow_default_constructible, this function object will instead look for char_is_valid_for(char_type const chr, std::type_identity<your_type> const &) with the same semantics. In that case the "fallback" above also does not work and you are required to provide such an implementation.

Example

#include <seqan3/alphabet/nucleotide/dna5.hpp>
#include <seqan3/alphabet/adaptation/char.hpp>
#include <seqan3/alphabet/concept.hpp>

int main()
{
    bool b = seqan3::char_is_valid_for<char>('A');  // calls seqan3::custom::char_is_valid_for<char>('A'); always true

    bool c = seqan3::char_is_valid_for<seqan3::dna5>('A');  // calls dna5::char_is_valid('A') member; == true

    // for some alphabets, characters that are not uniquely mappable are still valid:
    bool d = seqan3::char_is_valid_for<seqan3::dna5>('a');  // lower case also true
}

Customisation point

This is a customisation point (see Customisation). To specify the behaviour for your own alphabet type, simply provide one of the three functions specified above.

to_char

constexpr auto seqan3::to_char = detail::adl::only::to_char_fn{}

inline

Return the char representation of an alphabet object.

Template Parameters

your_type

Type of the argument.

Parameters

alph	The alphabet object.

Returns

The char representation; usually char.

This is a function object. Invoke it with the parameter(s) specified above.

It acts as a wrapper and looks for three possible implementations (in this order):

1. A free function to_char(your_type const a) in the namespace of your type (or as friend). The function must be marked noexcept (constexpr is not required, but recommended) and the return type be of the respective char representation (usually a small integral type).
2. A free function to_char(your_type const a) in namespace seqan3::custom. The same restrictions apply as above.
3. A member function called to_char(). It must be marked noexcept (constexpr is not required, but recommended) and the return type be of the respective char representation.

Every alphabet type must provide one of the above.

Example

#include <seqan3/alphabet/nucleotide/dna5.hpp>
#include <seqan3/alphabet/adaptation/char.hpp>
#include <seqan3/alphabet/concept.hpp>

using seqan3::operator""_dna5;

int main()
{
    auto r2 = seqan3::to_char('A');         // calls seqan3::custom::to_char('A'); r2 == 'A'
    auto r3 = seqan3::to_char('A'_dna5);    // calls .to_char() member; r3 == 'A'
}

For an example of a full alphabet definition with free function implementations (solution 1. above), see seqan3::Alphabet.

Customisation point

This is a customisation point (see Customisation). To specify the behaviour for your own alphabet type, simply provide one of the three functions specified above.

to_rank

constexpr auto seqan3::to_rank = detail::adl::only::to_rank_fn{}

inline

Return the rank representation of a (semi-)alphabet object.

Template Parameters

your_type

Type of the argument.

Parameters

alph	The (semi-)alphabet object.

Returns

The rank representation; an integral type.

This is a function object. Invoke it with the parameter(s) specified above.

It acts as a wrapper and looks for three possible implementations (in this order):

1. A free function to_rank(your_type const a) in the namespace of your type (or as friend). The function must be marked noexcept (constexpr is not required, but recommended) and the return type be of the respective rank representation (usually a small integral type).
2. A free function to_rank(your_type const a) in namespace seqan3::custom. The same restrictions apply as above.
3. A member function called to_rank(). It must be marked noexcept (constexpr is not required, but recommended) and the return type be of the respective rank representation.

Every (semi-)alphabet type must provide one of the above.

Example

#include <seqan3/alphabet/nucleotide/dna5.hpp>
#include <seqan3/alphabet/adaptation/char.hpp>
#include <seqan3/alphabet/concept.hpp>

using seqan3::operator""_dna5;

int main()
{
    auto r2 = seqan3::to_rank('A');         // calls seqan3::custom::to_rank('A'); r2 == 65
    auto r3 = seqan3::to_rank('A'_dna5);    // calls .to_char() member; r3 == 0
}

For an example of a full alphabet definition with free function implementations (solution 1. above), see seqan3::Alphabet.

Customisation point

This is a customisation point (see Customisation). To specify the behaviour for your own alphabet type, simply provide one of the three functions specified above.