/**
 * A `Traversable` with an additional index.
 * A `TraversableWithIndex` instance must be compatible with its `Traversable` instance
 *
 * ```ts
 * traverse(F)(ta, f) = traverseWithIndex(F)(ta, (_, a) => f(a))
 * ```
 *
 * with its `FoldableWithIndex` instance
 *
 * ```ts
 * foldMapWithIndex(M)(ta, f) = traverseWithIndex(getApplicative(M))(ta, (i, a) => new Const(f(i, a))).value
 * ```
 *
 * and with its `FunctorWithIndex` instance
 *
 * ```purescript
 * mapWithIndex(ta, f) = traverseWithIndex(identity)(ta, (i, a) => new Identity(f(i, a))).value
 * ```
 *
 * @since 2.0.0
 */
import { Applicative, Applicative1, Applicative2, Applicative2C, Applicative3, Applicative3C } from './Applicative'
import { FoldableWithIndex, FoldableWithIndex1, FoldableWithIndex2, FoldableWithIndex2C } from './FoldableWithIndex'
import { FunctorWithIndex, FunctorWithIndex1, FunctorWithIndex2, FunctorWithIndex2C } from './FunctorWithIndex'
import { HKT, Kind, Kind2, Kind3, URIS, URIS2, URIS3 } from './HKT'
import { Traversable, Traversable1, Traversable2, Traversable2C } from './Traversable'
/**
 * @since 2.0.0
 */
export interface TraversableWithIndex<T, I> extends FunctorWithIndex<T, I>, FoldableWithIndex<T, I>, Traversable<T> {
  readonly traverseWithIndex: TraverseWithIndex<T, I>
}
/**
 * @since 2.0.0
 */
export interface TraversableWithIndex1<T extends URIS, I>
  extends FunctorWithIndex1<T, I>,
    FoldableWithIndex1<T, I>,
    Traversable1<T> {
  readonly traverseWithIndex: TraverseWithIndex1<T, I>
}
/**
 * @since 2.0.0
 */
export interface TraversableWithIndex2<T extends URIS2, I>
  extends FunctorWithIndex2<T, I>,
    FoldableWithIndex2<T, I>,
    Traversable2<T> {
  readonly traverseWithIndex: TraverseWithIndex2<T, I>
}
/**
 * @since 2.0.0
 */
export interface TraversableWithIndex2C<T extends URIS2, I, E>
  extends FunctorWithIndex2C<T, I, E>,
    FoldableWithIndex2C<T, I, E>,
    Traversable2C<T, E> {
  readonly traverseWithIndex: TraverseWithIndex2C<T, I, E>
}
/**
 * @since 2.0.0
 */
export interface TraverseWithIndex<T, I> {
  <F extends URIS3>(F: Applicative3<F>): <A, R, E, B>(
    ta: HKT<T, A>,
    f: (i: I, a: A) => Kind3<F, R, E, B>
  ) => Kind3<F, R, E, HKT<T, B>>
  <F extends URIS3, E>(F: Applicative3C<F, E>): <A, R, B>(
    ta: HKT<T, A>,
    f: (i: I, a: A) => Kind3<F, R, E, B>
  ) => Kind3<F, R, E, HKT<T, B>>
  <F extends URIS2>(F: Applicative2<F>): <A, E, B>(
    ta: HKT<T, A>,
    f: (i: I, a: A) => Kind2<F, E, B>
  ) => Kind2<F, E, HKT<T, B>>
  <F extends URIS2, E>(F: Applicative2C<F, E>): <A, B>(
    ta: HKT<T, A>,
    f: (i: I, a: A) => Kind2<F, E, B>
  ) => Kind2<F, E, HKT<T, B>>
  <F extends URIS>(F: Applicative1<F>): <A, B>(ta: HKT<T, A>, f: (i: I, a: A) => Kind<F, B>) => Kind<F, HKT<T, B>>
  <F>(F: Applicative<F>): <A, B>(ta: HKT<T, A>, f: (i: I, a: A) => HKT<F, B>) => HKT<F, HKT<T, B>>
}
/**
 * @since 2.0.0
 */
export interface TraverseWithIndex1<T extends URIS, I> {
  <F extends URIS3>(F: Applicative3<F>): <A, R, E, B>(
    ta: Kind<T, A>,
    f: (i: I, a: A) => Kind3<F, R, E, B>
  ) => Kind3<F, R, E, Kind<T, B>>
  <F extends URIS3, E>(F: Applicative3C<F, E>): <A, R, B>(
    ta: Kind<T, A>,
    f: (i: I, a: A) => Kind3<F, R, E, B>
  ) => Kind3<F, R, E, Kind<T, B>>
  <F extends URIS2>(F: Applicative2<F>): <A, E, B>(
    ta: Kind<T, A>,
    f: (i: I, a: A) => Kind2<F, E, B>
  ) => Kind2<F, E, Kind<T, B>>
  <F extends URIS2, E>(F: Applicative2C<F, E>): <A, B>(
    ta: Kind<T, A>,
    f: (i: I, a: A) => Kind2<F, E, B>
  ) => Kind2<F, E, Kind<T, B>>
  <F extends URIS>(F: Applicative1<F>): <A, B>(ta: Kind<T, A>, f: (i: I, a: A) => Kind<F, B>) => Kind<F, Kind<T, B>>
  <F>(F: Applicative<F>): <A, B>(ta: Kind<T, A>, f: (i: I, a: A) => HKT<F, B>) => HKT<F, Kind<T, B>>
}
/**
 * @since 2.0.0
 */
export interface TraverseWithIndex2<T extends URIS2, I> {
  <F extends URIS3>(F: Applicative3<F>): <TE, A, R, FE, B>(
    ta: Kind2<T, TE, A>,
    f: (i: I, a: A) => Kind3<F, R, FE, B>
  ) => Kind3<F, R, FE, Kind2<T, TE, B>>
  <F extends URIS2>(F: Applicative2<F>): <TE, A, FE, B>(
    ta: Kind2<T, TE, A>,
    f: (i: I, a: A) => Kind2<F, FE, B>
  ) => Kind2<F, FE, Kind2<T, TE, B>>
  <F extends URIS2, FE>(F: Applicative2C<F, FE>): <TE, A, B>(
    ta: Kind2<T, TE, A>,
    f: (i: I, a: A) => Kind2<F, FE, B>
  ) => Kind2<F, FE, Kind2<T, TE, B>>
  <F extends URIS>(F: Applicative1<F>): <E, A, B>(
    ta: Kind2<T, E, A>,
    f: (i: I, a: A) => Kind<F, B>
  ) => Kind<F, Kind2<T, E, B>>
  <F>(F: Applicative<F>): <E, A, B>(ta: Kind2<T, E, A>, f: (i: I, a: A) => HKT<F, B>) => HKT<F, Kind2<T, E, B>>
}
/**
 * @since 2.0.0
 */
export interface TraverseWithIndex2C<T extends URIS2, I, E> {
  <F extends URIS3>(F: Applicative3<F>): <A, R, FE, B>(
    ta: Kind2<T, E, A>,
    f: (i: I, a: A) => Kind3<F, R, FE, B>
  ) => Kind3<F, R, FE, Kind2<T, E, B>>
  <F extends URIS3>(F: Applicative3C<F, E>): <A, R, B>(
    ta: Kind2<T, E, A>,
    f: (i: I, a: A) => Kind3<F, R, E, B>
  ) => Kind3<F, R, E, Kind2<T, E, B>>
  <F extends URIS2>(F: Applicative2<F>): <A, FE, B>(
    ta: Kind2<T, E, A>,
    f: (i: I, a: A) => Kind2<F, FE, B>
  ) => Kind2<F, FE, Kind2<T, E, B>>
  <F extends URIS2>(F: Applicative2C<F, E>): <A, B>(
    ta: Kind2<T, E, A>,
    f: (i: I, a: A) => Kind2<F, E, B>
  ) => Kind2<F, E, Kind2<T, E, B>>
  <F extends URIS>(F: Applicative1<F>): <A, B>(
    ta: Kind2<T, E, A>,
    f: (i: I, a: A) => Kind<F, B>
  ) => Kind<F, Kind2<T, E, B>>
  <F>(F: Applicative<F>): <A, B>(ta: Kind2<T, E, A>, f: (i: I, a: A) => HKT<F, B>) => HKT<F, Kind2<T, E, B>>
}
/**
 * @since 2.6.3
 */
export interface PipeableTraverseWithIndex1<T extends URIS, I> {
  <F extends URIS3>(F: Applicative3<F>): <A, R, E, B>(
    f: (i: I, a: A) => Kind3<F, R, E, B>
  ) => (ta: Kind<T, A>) => Kind3<F, R, E, Kind<T, B>>
  <F extends URIS3, E>(F: Applicative3C<F, E>): <A, R, B>(
    f: (i: I, a: A) => Kind3<F, R, E, B>
  ) => (ta: Kind<T, A>) => Kind3<F, R, E, Kind<T, B>>
  <F extends URIS2>(F: Applicative2<F>): <A, E, B>(
    f: (i: I, a: A) => Kind2<F, E, B>
  ) => (ta: Kind<T, A>) => Kind2<F, E, Kind<T, B>>
  <F extends URIS2, E>(F: Applicative2C<F, E>): <A, B>(
    f: (i: I, a: A) => Kind2<F, E, B>
  ) => (ta: Kind<T, A>) => Kind2<F, E, Kind<T, B>>
  <F extends URIS>(F: Applicative1<F>): <A, B>(f: (i: I, a: A) => Kind<F, B>) => (ta: Kind<T, A>) => Kind<F, Kind<T, B>>
  <F>(F: Applicative<F>): <A, B>(f: (i: I, a: A) => HKT<F, B>) => (ta: Kind<T, A>) => HKT<F, Kind<T, B>>
}
/**
 * @since 2.6.3
 */
export interface PipeableTraverseWithIndex2<T extends URIS2, I> {
  <F extends URIS3>(F: Applicative3<F>): <A, R, FE, B>(
    f: (i: I, a: A) => Kind3<F, R, FE, B>
  ) => <TE>(ta: Kind2<T, TE, A>) => Kind3<F, R, FE, Kind2<T, TE, B>>
  <F extends URIS2>(F: Applicative2<F>): <A, FE, B>(
    f: (i: I, a: A) => Kind2<F, FE, B>
  ) => <TE>(ta: Kind2<T, TE, A>) => Kind2<F, FE, Kind2<T, TE, B>>
  <F extends URIS2, FE>(F: Applicative2C<F, FE>): <A, B>(
    f: (i: I, a: A) => Kind2<F, FE, B>
  ) => <TE>(ta: Kind2<T, TE, A>) => Kind2<F, FE, Kind2<T, TE, B>>
  <F extends URIS>(F: Applicative1<F>): <A, B>(
    f: (i: I, a: A) => Kind<F, B>
  ) => <E>(ta: Kind2<T, E, A>) => Kind<F, Kind2<T, E, B>>
  <F>(F: Applicative<F>): <A, B>(f: (i: I, a: A) => HKT<F, B>) => <E>(ta: Kind2<T, E, A>) => HKT<F, Kind2<T, E, B>>
}