/// <summary> /// Binds a value in monadic space M(X) to a function that carries a value /// from the base space X into the monadic space M(Y) /// </summary> /// <typeparam name="X">The base space for the function domain</typeparam> /// <typeparam name="Y">The base space for the function codomain</typeparam> /// <returns>A point in M(Y) that originated in M(X)</returns> public static LinqMonad <Y> Bind <X, Y>(this LinqMonad <X> mx, Func <X, LinqMonad <Y> > f) => LinqMonad.bind(mx, f);
/// <summary> /// 1. Drops a point x from monadic X-space to the base /// 2. Applies a selector to x which yields a value m(y) that lives in monadic Y-space /// 3. Binds the point m(y) to a function F:X x Y -> Z that is evaluated over the point (x,y) to yield a point in Z /// 4. Finally, lifts the point z into monadic Z-space /// </summary> /// <typeparam name="X">The domain of the selector</typeparam> /// <typeparam name="Y">The base space for the range of the selector</typeparam> /// <typeparam name="Z">The domain for the projector</typeparam> /// <param name="select">The selection function</param> /// <param name="project">The projection function</param> /// <returns>A point in M(Z) that originated in M(X)</returns> public static LinqMonad <Z> SelectMany <X, Y, Z>(this LinqMonad <X> mx, Func <X, LinqMonad <Y> > select, Func <X, Y, Z> project) => LinqMonad.bind <Y, Z>(select((X)mx), y => project((X)mx, y));
/// <summary> /// Drops a value from monadic X-space to its base, applies a selection function F:X->Y that yields /// a point y in the base space Y and finally lifts the point y to m(y) in monadic Y-space M(Y) /// </summary> /// <typeparam name="X">The domain of the selector</typeparam> /// <typeparam name="Y">The range of the selector</typeparam> /// <param name="selector">The function to apply</param> /// <returns>A point in M(Y) that originated in M(X)</returns> public static LinqMonad <Y> Select <X, Y>(this LinqMonad <X> mx, Func <X, Y> selector) => LinqMonad.fmap(mx, selector);
/// <summary> /// Drops a doubly-monadic value into the base space /// </summary> /// <typeparam name="X">The base space</typeparam> /// <param name="x"></param> /// <returns></returns> /// <remarks> /// This effectively represents a duality operator, that establishes a vector space /// isomorphism between a space and the double-dual: the dual of a dual value is just /// the original value /// </remarks> public static X dual <X>(LinqMonad <LinqMonad <X> > x) => (X)((LinqMonad <X>)x);
public static LinqMonad <Y> fmap <X, Y>(LinqMonad <X> mx, Func <X, Y> f) => f((X)mx);
public static LinqMonad <Z> bind <X, Y, Z>(LinqMonad <X> mx, Func <X, LinqMonad <Y> > f, Func <X, Y, Z> compose) => bind <Y, Z>(f((X)mx), y => compose((X)mx, y));
public static LinqMonad <Y> bind <X, Y>(LinqMonad <X> mx, Func <X, LinqMonad <Y> > f) => f((X)mx);
