import { Functor } from '../data/Functor';

export interface ChainFunction<A, B> {

    (a: A): Monad<B>

}

/**
 * Monad 
 */
export interface Monad<A> extends Functor<A> {

    of(t: A): Monad<A>;
    chain<B>(f: (a: A) => Monad<B>): Monad<B>;

}

/**
 * composeK two monadic functions into one.
 */
export const composeK = <A, B, C>(f: ChainFunction<B, C>, g: ChainFunction<A, B>): ChainFunction<A, C> =>
    x => g(x).chain(f);

/**
 * pipeK the result of one monadic function into another. 
 */
export const pipeK = <A, B, C>(f: ChainFunction<A, B>, g: ChainFunction<B, C>): ChainFunction<A, C> =>
    (x: A) => (f(x) as Monad<B>).chain(g);

/**
 * chain is a partially applied version of a Monad's chain.
 * It allows us to avoid anonymous functions when chaining monads.
 */
export const chain = <A, B>(f: ChainFunction<A, B>) => (m: Monad<A>) => m.chain(f);