W is a function space T^D — eval f(d), pointwise +, and scalar · over T. More...

Concept definition

template<typename W, typename D, typename T>
concept dedekind::geometry::IsFunctionSpace = 
    requires(W const& f, W const& g, D const& d, T const& s) {
      
      { f(d) } -> std::convertible_to<T>;
      
      { f + g } -> std::same_as<W>;
      
      { s * f } -> std::same_as<W>;
    }

Detailed Description

W is a function space T^D — eval f(d), pointwise +, and scalar · over T.

function__Concept

Template Parameters

W	Carrier type representing the function space.
D	Domain type (the index / argument type; `std::size_t` for `ℕ-indexed` function spaces, future `IsExtensionalCardinal` carriers for richer domains).
T	Codomain / scalar field type.

The concept value-side requires three operations:

Eval: f(d) yields a T-convertible value.
Pointwise +: f + g closes the carrier.
Scalar ·: s · f closes the carrier (left multiplication; carriers MAY also expose right multiplication f · s but it is not required by the concept).

The pointwise / scalar laws (associativity of +, distributivity over ·, identity elements) are documented but not encoded in this concept. Pinning them as static_asserts requires value-level witnesses on a constexpr-friendly inhabitant; today sequences::Path<T> uses std::function and is not constexpr, so the witness story is at the type level (concept inhabitation). Constexpr inhabitants (e.g. Diagonal<D, F>'s rule type) can pin the laws value-side in a follow-up.