export interface Contravariant<F> {
  readonly URI: F
  readonly contramap: <A, B>(fa: HKT<F, A>, f: (b: B) => A) => HKT<F, B>
}

export interface Contravariant1<F extends URIS> {
  readonly URI: F
  readonly contramap: <A, B>(fa: Type<F, A>, f: (b: B) => A) => Type<F, B>
}

export interface Contravariant2<F extends URIS2> {
  readonly URI: F
  readonly contramap: <L, A, B>(fa: Type2<F, L, A>, f: (b: B) => A) => Type2<F, L, B>
}

export interface Contravariant2C<F extends URIS2, L> {
  readonly URI: F
  readonly _L: L
  readonly contramap: <A, B>(fa: Type2<F, L, A>, f: (b: B) => A) => Type2<F, L, B>
}

export interface Contravariant3<F extends URIS3> {
  readonly URI: F
  readonly contramap: <U, L, A, B>(fa: Type3<F, U, L, A>, f: (b: B) => A) => Type3<F, U, L, B>
}

export interface Contravariant3C<F extends URIS3, U, L> {
  readonly URI: F
  readonly _L: L
  readonly _U: U
  readonly contramap: <A, B>(fa: Type3<F, U, L, A>, f: (b: B) => A) => Type3<F, U, L, B>
}

export function lift<F extends URIS3>(
  contravariant: Contravariant3<F>
): <A, B>(f: (b: B) => A) => <U, L>(fa: Type3<F, U, L, A>) => Type3<F, U, L, B>
export function lift<F extends URIS3, U, L>(
  contravariant: Contravariant3C<F, U, L>
): <A, B>(f: (b: B) => A) => (fa: Type3<F, U, L, A>) => Type3<F, U, L, B>
export function lift<F extends URIS2>(
  contravariant: Contravariant2<F>
): <A, B>(f: (b: B) => A) => <L>(fa: Type2<F, L, A>) => Type2<F, L, B>
export function lift<F extends URIS2, L>(
  contravariant: Contravariant2C<F, L>
): <A, B>(f: (b: B) => A) => (fa: Type2<F, L, A>) => Type2<F, L, B>
export function lift<F extends URIS>(
  contravariant: Contravariant1<F>
): <A, B>(f: (b: B) => A) => (fa: Type<F, A>) => Type<F, B>
export function lift<F>(contravariant: Contravariant<F>): <A, B>(f: (b: B) => A) => (fa: HKT<F, A>) => HKT<F, B> { ... }