dedekind::category::detail_kleisli Namespace Reference

Classes
struct	StepAt
	The step at one element, a Kleisli arrow \(A \to T(A)\). More...
struct	Extending
	A fold step on \(T(A)\): the step at the element, by κ. More...
struct	Halved
	A witness's step that may fail: half of an even count. More...

Concepts
concept	IsKleisliStep
	A step from A and an element into TA, the monad on A.

Functions
template<typename MA, IsArrow F> requires requires { typename functor_of_t<MA>; } && std::same_as<Dom<F>, typename functor_of_t<MA>::Σ_cat::Species>
constexpr auto	lifted (const MA &ma, F f)
	\(T(f)\) applied to ma: the arrow f, from the value's element, under T's action, at the value.

Detailed Description

The fold in the Kleisli category

A step that may fail, \(A \times X \to T(A)\), folds a range from \(a : T(A)\): at each element, the step there as a Kleisli arrow \(A \to T(A)\), extended by κ, so a hole passes through to the end and no step cases on it (Haskell's foldM).

Function Documentation

lifted()

template<typename MA, IsArrow F>
requires requires { typename functor_of_t<MA>; } && std::same_as<Dom<F>, typename functor_of_t<MA>::Σ_cat::Species>

auto dedekind::category::detail_kleisli::lifted ( const MA & ma, F f )

constexpr

\(T(f)\) applied to ma: the arrow f, from the value's element, under T's action, at the value.

Parameters

ma	the value.
f	the arrow.