import type { Kind } from '../../kinds/index.js';
import { TypeSkell } from '../../typeskell/index.js';
export declare namespace BiFunctor {
    type $bimap<F extends Kind> = TypeSkell<'(a -> b) (c -> d) -> F a c ..e -> F b d ..e', {
        F: F;
    }>;
    type $mapLeft<F extends Kind> = TypeSkell<'(a -> b) -> F a c ..e -> F b c ..e', {
        F: F;
    }>;
    type $mapRight<F extends Kind> = TypeSkell<'(a -> b) -> F c a ..e -> F c b ..e', {
        F: F;
    }>;
    type $bitap<F extends Kind> = TypeSkell<'(a -> empty) (b -> empty) -> F a b ..e -> F a b ..e', {
        F: F;
    }, ['empty'], [void]>;
    type $tapLeft<F extends Kind> = TypeSkell<'(a -> empty) -> F a b ..e -> F a b ..e', {
        F: F;
    }, ['empty'], [void]>;
    type $tapRight<F extends Kind> = TypeSkell<'(b -> empty) -> F a b ..e -> F a b ..e', {
        F: F;
    }, ['empty'], [void]>;
}
/**
 * BiFunctor is a typeclass that defines a single operation, bimap.
 * It is a generalization of Functor.
 *
 * Definition for mapLeft and mapRight are derived from bimap.
 *  - mapLeft f  = bimap f id
 *  - mapRight f = bimap id f
 *
 * Laws:
 * - Identity: bimap id id = id
 * - Composition: bimap (f . g) (h . i) = bimap f h  . bimap g i
 */
export interface BiFunctor<F extends Kind> {
    /**
     * bimap :: `(a -> b) (c -> d) -> F a c -> F b d`
     */
    bimap: BiFunctor.$bimap<F>;
}
/**
 * mapLeft :: `BiFunctor F -> (a -> b) -> F a c -> F b c`
 */
export declare const mapLeft: <F extends Kind>(bifunctor: BiFunctor<F>) => BiFunctor.$mapLeft<F>;
/**
 * mapRight :: `BiFunctor F  -> (a -> b) -> F c a -> F c b`
 */
export declare const mapRight: <F extends Kind>(bifunctor: BiFunctor<F>) => BiFunctor.$mapRight<F>;
export declare const bitap: <F extends Kind>(bifunctor: BiFunctor<F>) => BiFunctor.$bitap<F>;
export declare const tapLeft: <F extends Kind>(bifunctor: BiFunctor<F>) => BiFunctor.$tapLeft<F>;
export declare const tapRight: <F extends Kind>(bifunctor: BiFunctor<F>) => BiFunctor.$tapRight<F>;