export interface Profunctor<F> {
  readonly URI: F
  readonly map: <L, A, B>(fa: HKT2<F, L, A>, f: (a: A) => B) => HKT2<F, L, B>
  readonly promap: <A, B, C, D>(fbc: HKT2<F, B, C>, f: (a: A) => B, g: (c: C) => D) => HKT2<F, A, D>
}

export interface Profunctor2<F extends URIS2> extends Functor2<F> {
  readonly promap: <A, B, C, D>(fbc: Type2<F, B, C>, f: (a: A) => B, g: (c: C) => D) => Type2<F, A, D>
}

export interface Profunctor3<F extends URIS3> extends Functor3<F> {
  readonly promap: <U, A, B, C, D>(fbc: Type3<F, U, B, C>, f: (a: A) => B, g: (c: C) => D) => Type3<F, U, A, D>
}

export interface Profunctor4<F extends URIS4> extends Functor4<F> {
  readonly promap: <X, U, A, B, C, D>(fbc: Type4<F, X, U, B, C>, f: (a: A) => B, g: (c: C) => D) => Type4<F, X, U, A, D>
}

export function lmap<F extends URIS3>(
  profunctor: Profunctor3<F>
): <U, A, B, C>(fbc: Type3<F, U, B, C>, f: (a: A) => B) => Type3<F, U, A, C>
export function lmap<F extends URIS2>(
  profunctor: Profunctor2<F>
): <A, B, C>(fbc: Type2<F, B, C>, f: (a: A) => B) => Type2<F, A, C>
export function lmap<F>(profunctor: Profunctor<F>): <A, B, C>(fbc: HKT2<F, B, C>, f: (a: A) => B) => HKT2<F, A, C> { ... }

export function rmap<F extends URIS3>(
  profunctor: Profunctor3<F>
): <U, B, C, D>(fbc: Type3<F, U, B, C>, g: (c: C) => D) => Type3<F, U, B, D>
export function rmap<F extends URIS2>(
  profunctor: Profunctor2<F>
): <B, C, D>(fbc: Type2<F, B, C>, g: (c: C) => D) => Type2<F, B, D>
export function rmap<F>(profunctor: Profunctor<F>): <B, C, D>(fbc: HKT2<F, B, C>, g: (c: C) => D) => HKT2<F, B, D> { ... }