dedekind::optimization::Relax< S, Cap, CostFn > Struct Template Reference

Fold step of the single-source semiring closure: relax the potential at e.head through the edge e, d(v) ← d(v) ⊕ d(u) ⊗ c(u,v). More...

Public Types
using	Add = typename dedekind::algebra::semiring_ops<S>::add
	The carrier's canonical additive op ⊕ (semiring_ops).
using	Mult = typename dedekind::algebra::semiring_ops<S>::mult
	The carrier's canonical multiplicative op ⊗ (semiring_ops).

Public Member Functions
constexpr FiniteNet< S, Cap >	operator() (FiniteNet< S, Cap > acc, const Edge &e) const
	Relax e.head: d(head) ← d(head) ⊕ d(tail) ⊗ c(tail,head), returning the new net — the fold step op(acc, Edge).

Public Attributes
CostFn	cost
	The edge-cost function c(tail,head); the only captured state.

Detailed Description

template<typename S, std::size_t Cap, typename CostFn = S (*)(std::size_t, std::size_t)>
requires dedekind::category::IsSemiring< S, typename dedekind::algebra::semiring_ops<S>::add, typename dedekind::algebra::semiring_ops<S>::mult> && requires(const CostFn& cost, std::size_t u) { { cost(u, u) } -> std::convertible_to<S>; }
struct dedekind::optimization::Relax< S, Cap, CostFn >

Fold step of the single-source semiring closure: relax the potential at e.head through the edge e, d(v) ← d(v) ⊕ d(u) ⊗ c(u,v).

The named replacement for the capturing relax lambda (#920): the closure structure — which cost the fold threads — is an inspectable type rather than a nameless closure. The semiring ops ⊕ / ⊗ are fixed by the carrier S itself (semiring_ops) rather than exposed as parameters, so cost is the only captured state. Models the fold step op(acc, Edge), returning the new net.

Note

The ops are the carrier's canonical semiring (the IsSemiring gate). cost is a bare BINARY callable (edge → weight, a raw lambda at the call site) with no Domain / Codomain, so it is gated structurally (a requires on cost), NOT by IsArrow, which models a unary morphism and would reject every caller.

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

• src/main/modules/dedekind/optimization/closure.cppm