The base class for functor traits. More...

#include <FunctorTraits.hpp>

Inheritance diagram for sp::f::TraitsBase< CRTP, F >:

Public Types
using	Functor = F
	The described functor. More...

using	Inverse = void
	The inverse of this functor. More...

using	GroupInverseOf = void
	The functor defining a group that this functor is an inverse of. More...

using	UnaryGroupInverse = void
	The functor that acts as the unary inverse for this functor. More...

using	BinaryGroupInverse = void
	The functor that acts as the binary inverse for this functor. More...

Static Public Attributes
static constexpr bool	Total = false
	The function is defined for all input tuples (division is not). More...

static constexpr bool	Even = false
	f(-x) = f(x). More...

static constexpr bool	Odd = false
	f(-x) = -f(x). More...

static constexpr bool	Associative = false
	f(f(a, b), c) = f(a, f(b, c)). More...

static constexpr bool	Commutative = false
	f(a, b) = f(b, a). More...

static constexpr bool	Anticommutative = false
	f(a, b) = -f(b, a). More...

static constexpr bool	Invertible = false
	For all x, there exists y such that f(x, y) = f(y, x) = IdentityValue. More...

static constexpr bool	HasIdentity = false
	The functor has an identity, c, such that f(x, c) = x. More...

static constexpr bool	HasAbsorbingElement = false
	The functor has an absorbing element, c, such that f(c, x) = c. More...

template<typename G >
static constexpr bool	LeftDistributiveOver = CRTP::template RightDistributiveOver<G> && CRTP::Commutative
	The functor is left-distributes under g. More...

template<typename G >
static constexpr bool	RightDistributiveOver = false
	The functor is right-distributes under g. More...

static constexpr bool	Involutory = std::is_same_v<typename CRTP::Inverse, Functor>
	f(f(x)) = x. More...

static constexpr bool	Monoid = CRTP::Total && CRTP::Associative && CRTP::HasIdentity
	Simultaneously total, associative, and with identity. More...

static constexpr bool	Group = Monoid && Invertible
	An invertible monoid. More...

static constexpr bool	AbelianMonoid = Monoid && CRTP::Commutative
	A commutative monoid. More...

static constexpr bool	AbelianGroup = Group && CRTP::Commutative
	A commutative group. More...

Detailed Description

template<typename CRTP, typename F>
struct sp::f::TraitsBase< CRTP, F >

The base class for functor traits.

The function being described is documented as being called f.

This should only be subclassed by Traits and its specializations, which should override any members for which the default is not appropriate. The defaults are chosen so that failure to override represents "no information".

See also: sp::f::Traits.

Template Parameters

CRTP	A curiously recurring template parameter.
F	The functor being described.

Member Typedef Documentation

◆ BinaryGroupInverse

template<typename CRTP , typename F >

using sp::f::TraitsBase< CRTP, F >::BinaryGroupInverse = void

The functor that acts as the binary inverse for this functor.

BinaryGroupInverse(x, y) = f(x, UnaryGroupInverse(y)).

◆ Functor

template<typename CRTP , typename F >

using sp::f::TraitsBase< CRTP, F >::Functor = F

The described functor.

◆ GroupInverseOf

template<typename CRTP , typename F >

using sp::f::TraitsBase< CRTP, F >::GroupInverseOf = void

The functor defining a group that this functor is an inverse of.

That functor such that InvertOf::UnaryGroupInverse is f, or InvertOf::BinaryGroupInverse is f.

◆ Inverse

template<typename CRTP , typename F >

using sp::f::TraitsBase< CRTP, F >::Inverse = void

The inverse of this functor.

The functor, g, such that g(f(x)) = x.

Not to be confused with UnaryGroupInverse or Invertible.

◆ UnaryGroupInverse

template<typename CRTP , typename F >

using sp::f::TraitsBase< CRTP, F >::UnaryGroupInverse = void

The functor that acts as the unary inverse for this functor.

f(x, UnaryGroupInverse(x)) = IdentityValue and UnaryGroupInverse is involutory.

Not to be confused with Inverse.

Member Data Documentation

◆ AbelianGroup

template<typename CRTP , typename F >

constexpr bool sp::f::TraitsBase< CRTP, F >::AbelianGroup = Group && CRTP::Commutative

staticconstexpr

A commutative group.

◆ AbelianMonoid

template<typename CRTP , typename F >

constexpr bool sp::f::TraitsBase< CRTP, F >::AbelianMonoid = Monoid && CRTP::Commutative

staticconstexpr

A commutative monoid.

◆ Anticommutative

template<typename CRTP , typename F >

constexpr bool sp::f::TraitsBase< CRTP, F >::Anticommutative = false

staticconstexpr

f(a, b) = -f(b, a).

◆ Associative

template<typename CRTP , typename F >

constexpr bool sp::f::TraitsBase< CRTP, F >::Associative = false

staticconstexpr

f(f(a, b), c) = f(a, f(b, c)).

◆ Commutative

template<typename CRTP , typename F >

constexpr bool sp::f::TraitsBase< CRTP, F >::Commutative = false

staticconstexpr

f(a, b) = f(b, a).

◆ Even

template<typename CRTP , typename F >

constexpr bool sp::f::TraitsBase< CRTP, F >::Even = false

staticconstexpr

f(-x) = f(x).

◆ Group

template<typename CRTP , typename F >

constexpr bool sp::f::TraitsBase< CRTP, F >::Group = Monoid && Invertible

staticconstexpr

An invertible monoid.

◆ HasAbsorbingElement

template<typename CRTP , typename F >

constexpr bool sp::f::TraitsBase< CRTP, F >::HasAbsorbingElement = false

staticconstexpr

The functor has an absorbing element, c, such that f(c, x) = c.

E.g: 0 for multiplication.

If this is true, the identity itself must be specified as follows:

template <typename T>

static constexpr T AbsorbingElement = T{...};

◆ HasIdentity

template<typename CRTP , typename F >

constexpr bool sp::f::TraitsBase< CRTP, F >::HasIdentity = false

staticconstexpr

The functor has an identity, c, such that f(x, c) = x.

E.g: 0 for addition and subtraction, and 1 for multiplication and division.

If this is true, the identity itself must be specified as follows:

template <typename T>

static constexpr T Identity = T{...};

◆ Invertible

template<typename CRTP , typename F >

constexpr bool sp::f::TraitsBase< CRTP, F >::Invertible = false

staticconstexpr

For all x, there exists y such that f(x, y) = f(y, x) = IdentityValue.

Not to be confused with whether Inverse is non-void.

◆ Involutory

template<typename CRTP , typename F >

constexpr bool sp::f::TraitsBase< CRTP, F >::Involutory = std::is_same_v<typename CRTP::Inverse, Functor>

staticconstexpr

f(f(x)) = x.

◆ LeftDistributiveOver

template<typename CRTP , typename F >

template<typename G >

constexpr bool sp::f::TraitsBase< CRTP, F >::LeftDistributiveOver = CRTP::template RightDistributiveOver<G> && CRTP::Commutative

staticconstexpr

The functor is left-distributes under g.

I.e: True only if g(f(x, a), f(x, b)) = f(x, g(a, b)).

This only needs to be overridden for operators that are left-distributive and aren't both right distributive and commutative. Matrix multiplication over addition is an example, because it's not commutative, but is both left and right distributive.

◆ Monoid

template<typename CRTP , typename F >

constexpr bool sp::f::TraitsBase< CRTP, F >::Monoid = CRTP::Total && CRTP::Associative && CRTP::HasIdentity

staticconstexpr

Simultaneously total, associative, and with identity.

◆ Odd

template<typename CRTP , typename F >

constexpr bool sp::f::TraitsBase< CRTP, F >::Odd = false

staticconstexpr

f(-x) = -f(x).

◆ RightDistributiveOver

template<typename CRTP , typename F >

template<typename G >

constexpr bool sp::f::TraitsBase< CRTP, F >::RightDistributiveOver = false

staticconstexpr

The functor is right-distributes under g.

I.e: True only if g(f(a, x), f(b, x)) = f(g(a, b), x). e.g: If the functor is multiplication, RightDistributiveOver for addition is true.

◆ Total

template<typename CRTP , typename F >

constexpr bool sp::f::TraitsBase< CRTP, F >::Total = false

staticconstexpr

The function is defined for all input tuples (division is not).

Public Types

Static Public Attributes

Detailed Description

Member Typedef Documentation

◆ BinaryGroupInverse

◆ Functor

◆ GroupInverseOf

◆ Inverse

◆ UnaryGroupInverse

Member Data Documentation

◆ AbelianGroup

◆ AbelianMonoid

◆ Anticommutative

◆ Associative

◆ Commutative

◆ Even

◆ Group

◆ HasAbsorbingElement

◆ HasIdentity

◆ Invertible

◆ Involutory

◆ LeftDistributiveOver

◆ Monoid

◆ Odd

◆ RightDistributiveOver

◆ Total