dedekind::sequences::Path< T, Cardinality, Index > Class Template Reference

A sequence F: ℕ → T. More...

Inheritance diagram for dedekind::sequences::Path< T, Cardinality, Index >:

Classes
struct	const_iterator

Public Types
using	Domain = Index
using	Codomain = T
using	cardinality_type = Cardinality
using	index_type = Index

Public Member Functions
constexpr Codomain	operator() (Index i) const
constexpr T	at (Index i) const
constexpr std::size_t	size () const noexcept
constexpr auto	begin () const noexcept
constexpr auto	end () const noexcept
constexpr auto	cardinality () const noexcept
	The Path is generally viewed as a mapping from N.

Public Attributes
std::function< T(Index)>	generator
	The underlying mapping f(n).
std::size_t	extent = 0

Friends
constexpr Path	operator+ (Path const &a, Path const &b)
constexpr Path	operator- (Path const &a, Path const &b)
constexpr Path	operator- (Path const &a)
constexpr Path	operator* (T const &s, Path const &a)
constexpr Path	operator* (Path const &a, T const &s)
template<typename F> requires dedekind::category::IsArrow<std::remove_cvref_t<F>> && std::same_as<dedekind::category::Dom<std::remove_cvref_t<F>>, T> && requires { typename dedekind::category::Cod< std::remove_cvref_t<F>>::Codomain; } && std::same_as<dedekind::category::Cod<std::remove_cvref_t<F>>, Path<typename dedekind::category::Cod< std::remove_cvref_t<F>>::Codomain, Cardinality, Index>>
constexpr auto	operator>>= (const Path &m, F &&f)
	Bind (>>=): m >>= f, for a Kleisli arrow f: T → Path, a path of this one's cardinality and index.
template<typename F> requires dedekind::category::IsArrow<std::remove_cvref_t<F>> && std::same_as<dedekind::category::Dom<std::remove_cvref_t<F>>, Path<T, Cardinality, Index>>
constexpr auto	operator<<= (const Path &w, F &&f)
	Extend (<<=): w <<= f, for a co-Kleisli arrow f: Path<T> → U.

Detailed Description

template<typename T, typename Cardinality = ℵ_0, dedekind::sets::IsRingIntegral Index = std::size_t>
class dedekind::sequences::Path< T, Cardinality, Index >

A sequence F: ℕ → T.

Template Parameters

T	The Species being enumerated.
Cardinality	The cardinality tag (ℵ_0 for infinite, Finite for bounded).
Index	The carrier of the Domain — any IsRingIntegral inhabitant, defaulting to std::size_t for back-compat with all existing call sites. The Form-shaped choices are dedekind::sets::ExtensionalCardinal<> (the algebraically-certified finite ℕ carrier) and dedekind::sets::Cardinality (the variant ℕ Form). Closes the Sollbruchstelle documented on this struct historically ("Path::Domain currently @c std::size_t — once generalised, @c Cardinality is what makes the @c size_t choice principled rather than accidental").

Member Function Documentation

at()

template<typename T, typename Cardinality = ℵ_0, dedekind::sets::IsRingIntegral Index = std::size_t>

T dedekind::sequences::Path< T, Cardinality, Index >::at ( Index i ) const

inlineconstexpr

path__Sequence_Interface

Friends And Related Symbol Documentation

operator+

template<typename T, typename Cardinality = ℵ_0, dedekind::sets::IsRingIntegral Index = std::size_t>

Path operator+ ( Path< T, Cardinality, Index > const & a, Path< T, Cardinality, Index > const & b )

friend

path__Pointwise_Operators

Path<T, Cardinality> is a function space T^ℕ (or T^[0..N) in the finite case): pointwise +, scalar ·, and unary - give the vector-space surface a function space carries. This is the operator anchor for #537's IsFunctionSpace<W, D, T> concept. Each operation produces a fresh Path whose generator captures the operands intensionally — no eager materialisation of values.

operator<<=

template<typename T, typename Cardinality = ℵ_0, dedekind::sets::IsRingIntegral Index = std::size_t>

template<typename F>
requires dedekind::category::IsArrow<std::remove_cvref_t<F>> && std::same_as<dedekind::category::Dom<std::remove_cvref_t<F>>, Path<T, Cardinality, Index>>

auto operator<<= ( const Path< T, Cardinality, Index > & w, F && f )

friend

Extend (<<=): w <<= f, for a co-Kleisli arrow f: Path<T> → U.

path__Co_Kleisli_Triple

operator>>=

template<typename T, typename Cardinality = ℵ_0, dedekind::sets::IsRingIntegral Index = std::size_t>

template<typename F>
requires dedekind::category::IsArrow<std::remove_cvref_t<F>> && std::same_as<dedekind::category::Dom<std::remove_cvref_t<F>>, T> && requires { typename dedekind::category::Cod< std::remove_cvref_t<F>>::Codomain; } && std::same_as<dedekind::category::Cod<std::remove_cvref_t<F>>, Path<typename dedekind::category::Cod< std::remove_cvref_t<F>>::Codomain, Cardinality, Index>>

auto operator>>= ( const Path< T, Cardinality, Index > & m, F && f )

friend

Bind (>>=): m >>= f, for a Kleisli arrow f: T → Path, a path of this one's cardinality and index.

path__Kleisli_Triple

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The documentation for this class was generated from the following file:

• src/main/modules/dedekind/sequences/path.cppm