import type { Kind } from '../../kinds/index.js';
import { TypeSkell } from '../../typeskell/index.js';
export declare namespace Functor {
    type $map<F extends Kind> = TypeSkell<'(a -> b) -> F a ..e -> F b ..e', {
        F: F;
    }>;
    type $mapCompose<F extends Kind, G extends Kind> = TypeSkell<'(a -> b) -> F (G a ..x) ..y -> F (G b ..x) ..y', {
        F: F;
        G: G;
    }>;
    type $flap<F extends Kind> = TypeSkell<'a -> F (a -> b) ..x -> F b ..x', {
        F: F;
    }>;
    type $as<F extends Kind> = TypeSkell<'b -> F a ..x -> F b ..x', {
        F: F;
    }>;
    type $let<F extends Kind> = TypeSkell<'(DoName n a) (a -> b) -> F a ..e -> F (Do n a b) ..e', {
        DoName: Kind.DoName;
        Do: Kind.Do;
        F: F;
    }>;
    type $tap<F extends Kind> = TypeSkell<'(a -> empty) -> F a ..e -> F a ..e', {
        F: F;
    }, ['empty'], [void]>;
}
/**
 * Functor is a typeclass that defines a single operation, map.
 *
 * Laws:
 *  - Identity: map id = id
 *  - Composition: map (f . g) = map f . map g
 */
export interface Functor<F extends Kind> {
    /**
     * map :: `(a -> b) -> F a -> F b`
     *
     * @param f `a -> b`
     * @returns `F a -> F b`
     */
    map: Functor.$map<F>;
}
/**
 * mapCompose :: `Functor<F> Functor<G> -> (a -> b) -> F (G a) -> F (G b)`
 *
 * @param FunctorF `Functor<F>`
 * @param FunctorG `Functor<G>`
 * @returns `(a -> b) -> F (G a) -> F (G b)`
 */
export declare const mapCompose: <F extends Kind, G extends Kind>(FunctorF: Functor<F>, FunctorG: Functor<G>) => Functor.$mapCompose<F, G>;
/**
 * flap :: `Functor F -> a -> F (a -> b) -> F b`
 *
 * @param functor `Functor<F>`
 * @returns `a -> F (a -> b) -> F b`
 */
export declare const flap: <F extends Kind>(functor: Functor<F>) => Functor.$flap<F>;
/**
 * as :: `Functor F -> b -> F a -> F b`
 *
 * @param functor `Functor<F>`
 * @returns `b -> F a -> F b`
 */
export declare const as: <F extends Kind>(functor: Functor<F>) => Functor.$as<F>;
export declare const tap: <F extends Kind>(functor: Functor<F>) => Functor.$tap<F>;
declare const $$let: <F extends Kind>(functor: Functor<F>) => Functor.$let<F>;
export { $$let as let };