CTL (Compile Time Library)

Overview

This is a C++ library, created to include algorithms that can be worked out at compile time.
It uses template meta programming and functional programming techniques to execute many algorithms at compile time on one or more types.

The more work done at compile time, less time to complete the job at run time!

All algorithms/features are wrapped in namespace ctl

Features available to use:

Container
Utility

Note:

Container algorithms and utility are influenced by Boost::MP11.
This has been started as re-inventing wheel theory and taken personal approach to implement the APIs/Functions that MP11 library supports.
Many of the algorithms are having the same name as mentioned in library MP11.
_t next to algorithm name is implemented to avoid using ::type keyword with algorithm
_c next to algorithm name is implemented to take constants which are known at compile time (ex: true/false or numbers)
_f next to algorithm name is implemented to take template types as template parameter
_p next to algorithm name is implemented to take predicate as template parameter (predicate is a template type). It is same as _f, but _p is used to make it more clear to read
_qmf next to algorithm name is implemented to take Quoted meta functions as template parameter
- _qmf implementations are using its non _qmf counterparts
_v next to algorithm name is implemented to get the constant value (boolean or number). it is like using ::value on the integral_constant type

Container

There are 2 parts here.

List ⇒ the container which holds the type
Algorithms ⇒ used with list type. Not necessarily with ctl::list but any other compile time list as well. ex: std::tuple

List

It is a container which holds the types. It is an heterogenous container.

To use make sure to add #include <container/list.hpp> in source file.

There are 3 variants of list

clt::list<> ⇒ non-instantiable list
ctl::ilist<> ⇒ instantiable list
ctl::clist<> ⇒ instantiable and callable list.
It has many operator over-loadings which can be called at runtime.
Example for the same can be found in src/main.cpp file

Many algorithms can be applied on the created list type.
Even algorithms from MP11 can also be used with the list type.

Algorithms

Once the heterogenous list is created, algorithms are required to do some work with that list. like for example, to add new element to existing list, or to retrieve an element, or remove specific entry in the list like or even sorting the types in the list. Just like data structure std::vector<> (note that std::vector<> can be used to hold the values of homogenous type at runtime).

These algorithms can be used with any list of types like std::tuple<>. It is not restricted to ctl::list alone.

To use any algorithms make sure to add #include <container/algorithms.hpp> in source file.

All algorithms will result in new type. original type is never modified

Modifiers

Set of algorithms are used to get the new list from the original list by adding/removing one or more types.

General usage of the algorithm is:

using modified_type = _algo name_<L<Ts...>, U>::type

where,

_ algo name _ ⇒ name of the modifiable algorithms listed below
L<Ts…> ⇒ list which has to be modified
U ⇒ type of the interest. It could be single type or another list type!
This is optional parameter depending on algorithm.
::type ⇒ to access the type from the result of the modified list.
If algorithm name is postfixed with _t then there is no need of using ::type

Following are some of modifiable algorithms (replaced with _ algo name _):

rename

Usage:

using result = ctl::rename<L<Ts...>, Y>::type

if
  `L<Ts...> = ctl::list<T1, T2, T3>`
  `Y == std::tuple`
then
  `result = std::tuple<T2, T3, T1>`

Variants:

rename
rename_t ⇒ to avoid ::type

apply

Usage:

using result = ctl::apply<Y, L<Ts...>>::type

if
    `Y == std::tuple`
    `L<Ts...> = ctl::list<T1, T2, T3>`
then
    `result = std::tuple<T2, T3, T1>`

Variants:

apply ⇒ same as rename but template parameters reversed
apply_t ⇒ to avoid ::type

rotate left

Usage:

using result = rotate_left_c<L<Ts...>, _num_>::type

if
    `L<Ts...> = L<T1, T2, T3>`
    `_num_ = 1`
then
    `result = L<T2, T3, T1>`

Variants:

rotate_left_c
rotate_left_c_t ⇒ to avoid ::type
rotate_left ⇒ num is passed as type (It should have ::value to access the member). ::type is needed to access the type
rotate_left_t ⇒ to avoid ::type

rotate right

Usage:

using result = rotate_right_c<L<Ts...>, _num_>::type

if
    `L<Ts...> = L<T1, T2, T3>`
    `_num_ = 1`
then
    `result = L<T3, T1, T2>`

Variants:

rotate_right_c
rotate_right_c_t ⇒ to avoid ::type
rotate_right ⇒ num is passed as type (It should have ::value to access the member). ::type is needed to access the result type
rotate_right_t ⇒ to avoid ::type

sort

Usage:

using result = sort<L<Ts...>>::type

if
    `L<Ts...> = L<T3, T2, T1>`
then
    `result = L<T1, T2, T3>`

where `T1::value <= T2::value <= T3::value`.

Logic used here is Quick sort.

Variants:

sort
sort_t ⇒ to avoid ::type
sort_p ⇒ to provide comparator as predicate to compare 2 types. ::type is needed to access the result type
- comparator should return true if the first template parameter should be considered before the second template parameter
sort_p_t ⇒ to avoid ::type
sort_qmf_p ⇒ to provide comparator predicate as quoted meta function. ::type is needed to access the result type
sort_qmf_p_t ⇒ to avoid ::type

reverse

Usage:

using result = ctl::reverse<L<Ts...>>::type

if
    `L<Ts...> = L<T1, T2, T3>`
then
    `result = L<T3, T2, T1>`

Variants:

reverse
reverse_t ⇒ to avoid ::type

replace

Usage:

using result = ctl::replace<L<Ts...>, TR, RW>::type

if
    `L<Ts...> = L<T1, T2, T3>`
    `TR = T2`
    `RW = T4`
then
    `result = L<T1, T4, T3>`

Variants:

replace
replace_t ⇒ to avoid ::type
replace_at_c ⇒ to replace type at given position (position is a constant). ::type is needed to access the result type
replace_at_c_t ⇒ to avoid ::type
replace_at ⇒ to replace type at given position (position is a type, ::value is used to access the constant). ::type is needed to access the result type
replace_at_t ⇒ to avoid ::type
replace_if ⇒ to replace all types which results in true when passed to given predicate. ::type is needed to access the result type
replace_if_t ⇒ to avoid ::type
replace_if_qmf ⇒ predicate passed as quoted meta function. ::type is needed to access the result type
replace_if_qmf_t ⇒ to avoid ::type

push_front

Usage:

using result = ctl::push_front<L<Ts...>, T>::type

if
    `L<Ts...> = L<T1, T2, T3>`
    `L<T4, T5, T6>`
then
    `result = L<T4, T5, T6, T1, T2, T3>`

Variants:

push_front ⇒ to push another type/list to front of given list
push_front_t ⇒ used to avoid ::type

push_back

Usage:

using result = ctl::push_back<L<Ts...>, T>::type

if
    `L<Ts...> = L<T1, T2, T3>`
    `L<T4, T5, T6>`
then
    `result = L<T1, T2, T3, T4, T5, T6>`

Variants:

push_back ⇒ to push another type/list to back of given list
push_back_t ⇒ to avoid ::type

append

Usage:

using result = ctl::append<L<Ts...>, T>::type

if
    `L<Ts...> = L<T1, T2, T3>`
    `T = `L<T4, T5, T6>`
then
    `result = L<T1, T2, T3, T4, T5, T6>`

Variants:

append ⇒ alias to push_back
append_t ⇒ alias to push_back_t

pop_front

Usage:

using result = ctl::pop_front<L<Ts...>>::type

if
    `L<Ts...> = L<T1, T2, T3>`
then
    `result = L<T2, T3>`

if list provided is empty, then it will result in error

Variants:

pop_front
pop_front_t ⇒ to avoid ::type

pop_back

Usage:

using result = ctl::pop_back<L<Ts...>>::type

if
    `L<Ts...> = L<T1, T2, T3>`
then
    `result = L<T1, T2>`

Variants:

pop_back
pop_back_t ⇒ to avoid ::type

insert

Usage:

using result = ctl::insert_c<L<Ts...>, _index_, Us...>::type

if
    `L<Ts...> = L<T1, T2, T3>`
    `_index_ = 1`
    `Us... = U1, U2, U3`
then
    `result = L<T1, U1, U2, U3, T2, T3>`

if index should be less than size of the L<Ts…>. otherwise it will result in compiler error

Variants:

insert_c
insert_c_t ⇒ to avoid ::type
insert ⇒ when index passed as type (::value is used to get the index value). ::type is needed to access the result type
insert_t ⇒ to avoid ::type

repeat

Usage:

using result = ctl::repeat_c<L<Ts...>, _count_>::type

if
    `L<Ts...> = L<T1, T2, T3>`
    _count_ = 2
then
    `result = L<T1, T2, T3, T1, T2, T3>`

if count == 0, then result = L<>

Variants:

repeat_c
repeat_c_t ⇒ to avoid ::type
repeat ⇒ when count passed as type (::value is used to get the count value). ::type is needed to access the result type
repeat_t ⇒ to avoid ::type

clear

Usage:

using result = ctl::repeat_c<L<Ts...>>::type

if
    `L<Ts...> = L<T1, T2, T3>`
then
    `result = L<>`

Variants:

clear
clear_t ⇒ to avoid ::type

erase

Usage:

using result = ctl::erase_c<L<Ts...>, _pos1_, _pos2_>::type

if
    `L<Ts...> = L<T1, T2, T3>`
    _pos1_ == 0
    _pos2_ == 1
then
    `result = L<T2, T3>`

if condition pos1 < L<Ts…> ⇐ pos2 fails, then results in compiler error.

Variants:

erase_c
erase_c_t ⇒ to avoid ::type
erase ⇒ when pos1 and pos2 are passed a types. ::type is needed to access the result type
erase_t ⇒ to avoid ::type

remove

Usage:

using result = ctl::remove_type<L<Ts...>, U>::type

if
    `L<Ts...> = L<T1, T2, T3>`
    `U = T2`
then
    `result = L<T1, T2>`

Variants:

remove_type
remove_type_t ⇒ to avoid ::type
remove_if ⇒ when U is a predicate. if P<T> results in true then type is removed. ::type is needed to access the result type
remove_if_t ⇒ to avoid ::type
remove_if_qmf
remove_if_qmf_t

filter

Usage:

using result = ctl::filter_if<P, L1, L2, ..., Ln>::type

if
    `L1 = L1<T1, T2, T3>,
    `L2 = L2<T4, T5, T6>`
    ...
    `Ln<Tn, Tn+1, Tn+2>`

    `P = P<T2, T5, ..., Tn+1> = true`
then
    `result = L<T2>`

Variants:

filter_if
filter_if_t ⇒ to avoid ::type
filter_if_qmf ⇒ when predicate is passed as quoted meta function. ::type is needed to access the result type
filter_if_qmf_t ⇒ to avoid ::type

copy_if

Usage:

using result = ctl::copy_if<L<Ts...>, P>::type

if
    `L<Ts...> = L<T1, T2, T3>`

    `P<T2> = true`
then
    `result = L<T2>`

Variants:

copy_if ⇒ alias to filter_if
copy_if_t ⇒ to avoid ::type
copy_if_qmf ⇒ alias to filter_if_qmf
copy_if_qmf_t ⇒ to avoid ::type

drop

Usage:

using result = ctl::drop_c<L<Ts...>, _count_>::type

if
    `L<Ts...> = L<T1, T2, T3>`
    _count_ = 2
then
    `result = L<T3>`

if count >= L<Ts…> size, then result = L<>

Variants:

drop_c
drop_c_t ⇒ to avoid ::type
drop ⇒ when count is a type. ::type is needed to access the result type
drop_t ⇒ to avoid ::type

remove_duplicates

Usage:

using result = ctl::remove_duplicates<L<Ts...>>::type

if
    `L<Ts...> = L<T1, T1, T2>`
    _count_ = 2
then
    `result = L<T1, T2>`

Variants:

remove_duplicates
remove_duplicates_t ⇒ to avoid ::type

unique

Usage:

using result = ctl::unique<L<Ts...>>::type

if
    `L<Ts...> = L<T1, T1, T2>`
    _count_ = 2
then
    `result = L<T1, T2>`

Variants:

unique ⇒ alias to remove_duplicates
unique_t ⇒ to avoid ::type

unique_if

Usage:

using result = ctl::unique_if<L<Ts...>, P>::type

if
    `L<Ts...> = L<T1, T2, T3>`
    `P<T> = T2`
then
    `result = L<T1, T2>`

Variants:

unique_if ⇒ alias to remove_if
unique_if_t ⇒ to avoid ::type
unique_if_qmf ⇒ alias to remove_if_qmf
unique_if_qmf_t ⇒ to avoid ::type

transform

Usage:

using result = ctl::transform<F, L1, L2, ..., Ln>::type

if
    `L1 = L1<T1, T2, T3>
    `L2 = L2<T4, T5, T6> `
    ...
    `Ln<Tn, Tn+1, Tn+2>`
then
    `result = L<F<T1, T4, ..., Tn>, F<T2, T5, ..., Tn+1>, F<T3, T6, ..., Tn+2>>`.
    where, F is templated type.

Variants:

transform
transform_t ⇒ to avoid ::type
transform_qmf ⇒ when F is provided as quoted meta function. ::type is needed to access the result type
transform_qmf_t ⇒ to avoid ::type
transform_if ⇒ when predicate P is passed as 3rd template argument. result will have F<T> only when P<T> is true. ::type is needed to access the result type
transform_if_t ⇒ to avoid ::type
transform_if_qmf ⇒ when F and predicate provided as quoted meta function
transform_if_qmf_t ⇒ to avoid ::type

flatten

Usage:

using result = ctl::flatten<L1, L2=clear_t<L1>>::type

if
    `L1 = L1<T1, T2, std::tuple<T3>>
    `L2 = std::tuple<>`
then
    `result = L1<T1, T2, T3>

L2 is optional. If L2 is not provided, then L2 will be assumed as L1<>

Variants:

flatten
flatten_t ⇒ to avoid ::type

Accessors

Set of algorithms are used to retrieve the one or more types from the original list. In some case conditional retrieval is possible. These algorithms will result in compiler error if the provided list is empty.

General usage of the algorithm is:

using result = _algo name_<L<Ts...>, P>::type

where,

_ algo name _ ⇒ name of the accessor algorithms listed below
L<Ts…> ⇒ list from which one or more type is retrieved
P ⇒ predicate/function which is applied on each type to access/retrieve.
It is optional, not every algorithm needs this parameter
::type ⇒ to access the type from the result.
If algorithm name is postfixed with _t then there is no need of using ::type

Following are some of accessor algorithms (replaced with _ algo name _):

at

Usage:

using result = ctl::at_c<L<Ts...>, _pos_>::type

if
    `L<Ts...> = L<T1, T2, T3>`
    _pos_ == 2
then
    `result = T3`

If condition pos < size of L<Ts…> then it will result in compiler error

Variants:

at_c
at_c_t ⇒ to avoid ::type
at ⇒ when pos is passed as type. ::type is needed to access the result type
at_t ⇒ to avoid ::type

first

Usage:

using result = ctl::first<L<Ts...>>::type

if
    `L<Ts...> = L<T1, T2, T3>`
then
    `result = T1`

If list provided is empty, then it will result in compiler error

Variants:

first ⇒ to get the first type from the list
first_t ⇒ to avoid ::type

front

Usage:

using result = ctl::front<L<Ts...>>::type

if
    `L<Ts...> = L<T1, T2, T3>`
then
    `result = T1`

If list provided is empty, then it will result in compiler error

Variants:

front ⇒ alias to first
front_t ⇒ to avoid ::type

last

Usage:

using result = ctl::last<L<Ts...>>::type

if
    `L<Ts...> = L<T1, T2, T3>`
then
    `result = T3`

If list provided is empty, then it will result in compiler error

Variants:

last ⇒ to get the last type from the list
last_t ⇒ to avoid ::type

back

Usage:

using result = ctl::back<L<Ts...>>::type

if
    `L<Ts...> = L<T1, T2, T3>`
then
    `result = T3`

If list provided is empty, then it will result in compiler error

Variants:

back ⇒ alias to last
back_t ⇒ to avoid ::type

head

Usage:

using result = ctl::head<L<Ts...>>::type

if
    `L<Ts...> = L<T1, T2, T3>`
then
    `result = L<T1, T2>`

If list provided is empty, then it will result in compiler error.
If there is only one entry in the list, then result = L<>

Variants:

head
head_t ⇒ to avoid ::type

tail

Usage:

using result = ctl::tail<L<Ts...>>::type

if
    `L<Ts...> = L<T1, T2, T3>`
then
    `result = L<T2, T3>`

If list provided is empty, then it will result in compiler error.
If there is only one entry in the list, then result = L<>

Variants:

tail
tail_t ⇒ to avoid ::type

take

Usage:

using result = ctl::take<L<Ts...>, _count_>::type

if
    `L<Ts...> = L<T1, T2, T3>`
    _count_ = 2,
then
    `result = L<T1, T2>`

If count >= size of L<Ts…> then result = L<Ts…>

Variants:

take_c
take_c_t ⇒ to avoid ::type
take ⇒ when count is provided as type. ::type is needed to access the result type
take_t ⇒ to avoid ::type

Miscellaneous

Set of algorithms used for miscellaneous stuffs which are not listed above! like for ex, creating the integer sequence, getting the position of the type in a list, getting the size of the list, etc.

Following are some of algorithms:

size

Usage:

using result = ctl::size<L<Ts...>>::type

if
    `L<Ts...> = L<T1, T2, T3>`
then
    `result = std::integral_constant<uint32_t, 3>`

Variants:

size
size_t ⇒ to avoid ::type
size_v ⇒ to avoid ::value

count

Usage:

using result = ctl::count<L<Ts...>>::type

if
    `L<Ts...> = L<T1, T2, T3>`
then
    `result = std::integral_constant<uint32_t, 3>`

Variants:

count ⇒ alias to size
count_t ⇒ to avoid ::type
count_v ⇒ to avoid ::value
count_if ⇒ when predicate P is passed as second template argument. type will be counted only if P<T> is true. ::type is needed to access the result type
count_if_t ⇒ to avoid ::type
count_if_v ⇒ to avoid ::value
count_if_qmf ⇒ when predicate is passed as quoted meta function
count_if_qmf_t ⇒ to avoid ::type
count_if_qmf_v ⇒ to avoid ::value

empty

Usage:

using result = ctl::empty<L<Ts...>>::type

if
    `L<Ts...> = L<T1, T2, T3>`
then
    `result = std::false_type`

If L<Ts…> = L<> then result = std::true_type

Variants:

empty
empty_t ⇒ to avoid ::type
empty_v ⇒ to avoid ::value

contains

Usage:

using result = ctl::contains<L<Ts...>, U>::type

if
    `L<Ts...> = L<T1, T2, T3>`
    `U == T2`
then
    `result = std::true_type`

If U == T4 then result = std::false_type

Variants:

contains
contains_t ⇒ to avoid ::type
contains_v ⇒ to avoid ::value

find

Usage:

using result = ctl::find<L<Ts...>, U>::type

if
    `L<Ts...> = L<T1, T2, T3>`
    `U == T2`
then
    `result = std::integral_constant<uint32_t, 1>`.

If U is not found in list, then result is size of the list

Variants:

find
find_t ⇒ to avoid ::type
find_v ⇒ to avoid ::value
find_if ⇒ when U is a predicate. result will have the first position for which P<T> will result in true. ::type is needed to access the result type
find_if_t ⇒ to avoid ::type
find_if_v ⇒ to avoid ::value
find_if_qmf ⇒ when predicate is passed as quoted meta function. ::type is needed to access the result type
find_if_qmf_t ⇒ to avoid ::type
find_if_qmf_v ⇒ to avoid ::value

all_of

Usage:

using result = ctl::all_of<L<Ts...>, P>::type

if
    `L<Ts...> = L<T1, T2, T3>`
    `P<T> == true` for all T1, T2, T3 types
then
    `result = std::true_type`,
    `result = std::false_type`, if P<T> == false for any one of the types

Variants:

all_of
all_of_t ⇒ to avoid ::type
all_of_v ⇒ to avoid ::value
all_of_qmf ⇒ when predicate is passed as quoted meta function. ::type is needed to access the result type
all_of_qmf_t ⇒ to avoid ::type
all_of_qmf_v ⇒ to avoid ::value

any_of

Usage:

using result = ctl::any_of<L<Ts...>, P>::type

if
    `L<Ts...> = L<T1, T2, T3>`
    `P<T> == true` for any T1, T2, T3 types
then
    `result = std::true_type`,
    `result = std::false_type`, if P<T> == false for all types

Variants:

any_of
any_of_t ⇒ to avoid ::type
any_of_v ⇒ to avoid ::value
any_of_qmf ⇒ when predicate is passed as quoted meta function. ::type is needed to access the result type
any_of_qmf_t ⇒ to avoid ::type
any_of_qmf_v ⇒ to avoid ::value

none_of

Usage:

using result = ctl::none_of<L<Ts...>, P>::type

if
    `L<Ts...> = L<T1, T2, T3>`
    `P<T> == false` for all T1, T2, T3 types
then
    `result = std::true_type`,
    `result = std::false_type`, if P<T> for any one of the types

Variants:

none_of
none_of_t ⇒ to avoid ::type
none_of_v ⇒ to avoid ::value
none_of_qmf ⇒ when predicate is passed as quoted meta function. ::type is needed to access the result type
none_of_qmf_t ⇒ to avoid ::type
none_of_qmf_v ⇒ to avoid ::value

from integer sequence

Usage:

using result = ctl::from_integer_sequence<sequence, RT>::type

if
    `sequence = std::integer_sequence<unsigned int, 9, 2, 5>`
    `RT == ctl::list`
then
    `result = ctl::list<std::integral_constant<unsigned int, 9>, std::integral_constant<unsigned int, 2>, std::integral_constant<unsigned int, 5> >`

RT default type is ctl::list.

Variants:

from_integer_sequence
from_integer_sequence_t ⇒ to avoid ::type

iota

Usage:

using result = ctl::iota_c<_count_, DT, RT>::type

if
    _count_ = 3,
    `DT = uint32_t`
    `RT == ctl::list`
then
    `result = ctl::list<std::integral_constant<uint32_t, 0>, std::integral_constant<uint32_t, 1>, std::integral_constant<uint32_t, 2> >`

DT default type is uint32_t.
RT default type is ctl::list.

iota_c
iota_c_t ⇒ to avoid ::type
iota ⇒ when count is provided as type. ::type is needed to access the result type
iota_t ⇒ to avoid ::type

is_similar

Usage:

using result = ctl::is_similar<T1, T2>::type

if
    T1 = std::tuple<Ts...>,
    T2 = std::tuple<Us...>
then
    `result = std::integral_constant<bool, true>

if T1 or T2 are not similar list, then result will be false type

is_similar
is_similar_t ⇒ to avoid ::type
is_similar_v ⇒ to avoid ::value

equal

Usage:

using result = ctl::equal<T1, T2>::type

if
    T1 = std::tuple<Ts...>,
    T2 = std::tuple<Ts...>
then
    `result = std::integral_constant<bool, true>

if T1 or T2 are not similar list or any entry in the list is not same or list are of different length, then result will be false type

equal
equal_t ⇒ to avoid ::type
equal_v ⇒ to avoid ::value

Utility

Following struct(s)/algorithm(s) can be applied on the types. To use algorithms make sure to add #include <utils.hpp> in source file.

quote

This helps to wrap template type inside a structure called quote.
Template type can be accessed with the help of nested type fn.

template <template <typename...> typename F>
struct quote {
    template <typename... Ts>
    using fn = F<Ts...>;
};

invert

This helps to invert the provided type/value.

template <bool C>
struct invert_c {
  ...
};

variants of invert are:

invert_c
invert_c_t ⇒ to avoid ::type
invert_c_v ⇒ to avoid ::value
invert ⇒ to pass typename as template parameter.
boolean value is accessed with the help of C::value
invert_t ⇒ to avoid ::type
invert_v ⇒ to avoid ::value

is_same

This helps to Check if the given 2 types are same

template <typename T1, typename T2>
struct is_same {
  ...
};

It results in std::true_type if T1 and T2 are same. std::false_type otherwise.

variants of is_same are:

is_same
is_same_t ⇒ to avoid using ::type
is_same_v ⇒ to avoid using ::value

valid

This helps to validate if the provided template type is valid or not.

template <template <typename...> typename F, typename... Ts>
struct valid {
  ...
};

It results in std::true_type if F<Ts…>::type is valid. std::false_type otherwise.

variants of valid are:

valid
valid_t ⇒ to avoid using ::type
valid_v ⇒ to avoid using ::value
valid_qmf ⇒ to pass template function as a quoted meta function
valid_qmf_t ⇒ to avoid using ::type
valid_qmf_v ⇒ to avoid using ::value

select

This is equivalent of ternary operator but for types.

template <bool C, typename T, typename F>
struct select_c {
  ...
};

If condition C is true, select_c<>::type will be alias to T, to F otherwise.

variants of select are:

select_c ⇒ when condition is true/false value. ::type required to retrieve the type
select_c_t ⇒ to avoid ::type
select ⇒ when condition is a type.
boolean value is accessed with the help of C::value
select_t ⇒ to avoid ::type

Following variants of select is used to get the false type as templated function.
i.e. if condition results in false then selected type is F<Ts…>.

template <bool C, typename T, template <typename...> typename F, typename... Ts>
using select_f_c_t {
  ...
};

select_f_c ⇒ when condition is true/false value. ::type required to retrieve the type
select_f_c_t ⇒ to avoid ::type
select_f ⇒ when condition is a type. boolean value is accessed with the help of C::value
select_f_t ⇒ to avoid ::type
select_qmf_c ⇒ when false type is captured with quoted meta function, and condition is true/false value
select_qmf_c_t ⇒ to avoid ::type
select_qmf ⇒ when false type is captured with quoted meta function, and condition is a type
select_qmf_t ⇒ to avoid ::type

is_function

This will check if the provided type is a function or not.

template <typename T>
struct is_function {
  ...
};

If the provided type is not a reference and adding const to type will not result in the const, then it is considered as function.

variants of is_function are:

is_function_t ⇒ to avoid using ::type
is_function_v ⇒ to avoid using ::value

is_invocable

This will check if the provided type is a function OR a class which implements operator()

template <typename T>
struct is_invocable {
  ...
};

It makes use of the CPP member detection idiom technique.

If the provided T is a function, then it will result in std::true_type
If the provided T is a class, if it implements operator() then it will result in std::true_type
otherwise it will result in std::false_type

variants of is_invocable are:

is_invocable_t ⇒ to avoid using ::type
is_invocable_v ⇒ to avoid using ::value