/**
 * @since 2.0.0
 */
import { Applicative, Applicative1, Applicative2, Applicative2C, Applicative3 } from './Applicative'
import { HKT, Kind, Kind2, Kind3, URIS, URIS2, URIS3, URIS4, Kind4 } from './HKT'
import { Monad, Monad1, Monad2, Monad2C, Monad3, Monad3C } from './Monad'
import { Monoid } from './Monoid'
/**
 * @category type classes
 * @since 2.0.0
 */
export interface Foldable<F> {
  readonly URI: F
  readonly reduce: <A, B>(fa: HKT<F, A>, b: B, f: (b: B, a: A) => B) => B
  readonly foldMap: <M>(M: Monoid<M>) => <A>(fa: HKT<F, A>, f: (a: A) => M) => M
  readonly reduceRight: <A, B>(fa: HKT<F, A>, b: B, f: (a: A, b: B) => B) => B
}
/**
 * @category type classes
 * @since 2.0.0
 */
export interface Foldable1<F extends URIS> {
  readonly URI: F
  readonly reduce: <A, B>(fa: Kind<F, A>, b: B, f: (b: B, a: A) => B) => B
  readonly foldMap: <M>(M: Monoid<M>) => <A>(fa: Kind<F, A>, f: (a: A) => M) => M
  readonly reduceRight: <A, B>(fa: Kind<F, A>, b: B, f: (a: A, b: B) => B) => B
}
/**
 * @category type classes
 * @since 2.0.0
 */
export interface Foldable2<F extends URIS2> {
  readonly URI: F
  readonly reduce: <E, A, B>(fa: Kind2<F, E, A>, b: B, f: (b: B, a: A) => B) => B
  readonly foldMap: <M>(M: Monoid<M>) => <E, A>(fa: Kind2<F, E, A>, f: (a: A) => M) => M
  readonly reduceRight: <E, A, B>(fa: Kind2<F, E, A>, b: B, f: (a: A, b: B) => B) => B
}
/**
 * @category type classes
 * @since 2.0.0
 */
export interface Foldable2C<F extends URIS2, E> {
  readonly URI: F
  readonly _E: E
  readonly reduce: <A, B>(fa: Kind2<F, E, A>, b: B, f: (b: B, a: A) => B) => B
  readonly foldMap: <M>(M: Monoid<M>) => <A>(fa: Kind2<F, E, A>, f: (a: A) => M) => M
  readonly reduceRight: <A, B>(fa: Kind2<F, E, A>, b: B, f: (a: A, b: B) => B) => B
}
/**
 * @category type classes
 * @since 2.0.0
 */
export interface Foldable3<F extends URIS3> {
  readonly URI: F
  readonly reduce: <R, E, A, B>(fa: Kind3<F, R, E, A>, b: B, f: (b: B, a: A) => B) => B
  readonly foldMap: <M>(M: Monoid<M>) => <R, E, A>(fa: Kind3<F, R, E, A>, f: (a: A) => M) => M
  readonly reduceRight: <R, E, A, B>(fa: Kind3<F, R, E, A>, b: B, f: (a: A, b: B) => B) => B
}
/**
 * @category type classes
 * @since 2.2.0
 */
export interface Foldable3C<F extends URIS3, E> {
  readonly URI: F
  readonly _E: E
  readonly reduce: <R, A, B>(fa: Kind3<F, R, E, A>, b: B, f: (b: B, a: A) => B) => B
  readonly foldMap: <M>(M: Monoid<M>) => <R, A>(fa: Kind3<F, R, E, A>, f: (a: A) => M) => M
  readonly reduceRight: <R, A, B>(fa: Kind3<F, R, E, A>, b: B, f: (a: A, b: B) => B) => B
}
/**
 * @category type classes
 * @since 2.0.0
 */
export interface Foldable4<F extends URIS4> {
  readonly URI: F
  readonly reduce: <S, R, E, A, B>(fa: Kind4<F, S, R, E, A>, b: B, f: (b: B, a: A) => B) => B
  readonly foldMap: <M>(M: Monoid<M>) => <S, R, E, A>(fa: Kind4<F, S, R, E, A>, f: (a: A) => M) => M
  readonly reduceRight: <S, R, E, A, B>(fa: Kind4<F, S, R, E, A>, b: B, f: (a: A, b: B) => B) => B
}
/**
 * @since 2.0.0
 */
export interface FoldableComposition<F, G> {
  readonly reduce: <A, B>(fga: HKT<F, HKT<G, A>>, b: B, f: (b: B, a: A) => B) => B
  readonly foldMap: <M>(M: Monoid<M>) => <A>(fa: HKT<F, HKT<G, A>>, f: (a: A) => M) => M
  readonly reduceRight: <A, B>(fa: HKT<F, HKT<G, A>>, b: B, f: (a: A, b: B) => B) => B
}
/**
 * @since 2.0.0
 */
export interface FoldableComposition11<F extends URIS, G extends URIS> {
  readonly reduce: <A, B>(fga: Kind<F, Kind<G, A>>, b: B, f: (b: B, a: A) => B) => B
  readonly foldMap: <M>(M: Monoid<M>) => <A>(fa: Kind<F, Kind<G, A>>, f: (a: A) => M) => M
  readonly reduceRight: <A, B>(fa: Kind<F, Kind<G, A>>, b: B, f: (a: A, b: B) => B) => B
}
/**
 * @since 2.0.0
 */
export interface FoldableComposition12<F extends URIS, G extends URIS2> {
  readonly reduce: <E, A, B>(fga: Kind<F, Kind2<G, E, A>>, b: B, f: (b: B, a: A) => B) => B
  readonly foldMap: <M>(M: Monoid<M>) => <E, A>(fa: Kind<F, Kind2<G, E, A>>, f: (a: A) => M) => M
  readonly reduceRight: <E, A, B>(fa: Kind<F, Kind2<G, E, A>>, b: B, f: (a: A, b: B) => B) => B
}
/**
 * @since 2.0.0
 */
export interface FoldableComposition12C<F extends URIS, G extends URIS2, E> {
  readonly reduce: <A, B>(fga: Kind<F, Kind2<G, E, A>>, b: B, f: (b: B, a: A) => B) => B
  readonly foldMap: <M>(M: Monoid<M>) => <A>(fa: Kind<F, Kind2<G, E, A>>, f: (a: A) => M) => M
  readonly reduceRight: <A, B>(fa: Kind<F, Kind2<G, E, A>>, b: B, f: (a: A, b: B) => B) => B
}
/**
 * @since 2.0.0
 */
export interface FoldableComposition21<F extends URIS2, G extends URIS> {
  readonly reduce: <E, A, B>(fga: Kind2<F, E, Kind<G, A>>, b: B, f: (b: B, a: A) => B) => B
  readonly foldMap: <M>(M: Monoid<M>) => <E, A>(fa: Kind2<F, E, Kind<G, A>>, f: (a: A) => M) => M
  readonly reduceRight: <E, A, B>(fa: Kind2<F, E, Kind<G, A>>, b: B, f: (a: A, b: B) => B) => B
}
/**
 * @since 2.0.0
 */
export interface FoldableComposition2C1<F extends URIS2, G extends URIS, E> {
  readonly reduce: <A, B>(fga: Kind2<F, E, Kind<G, A>>, b: B, f: (b: B, a: A) => B) => B
  readonly foldMap: <M>(M: Monoid<M>) => <A>(fa: Kind2<F, E, Kind<G, A>>, f: (a: A) => M) => M
  readonly reduceRight: <A, B>(fa: Kind2<F, E, Kind<G, A>>, b: B, f: (a: A, b: B) => B) => B
}
/**
 * @since 2.0.0
 */
export interface FoldableComposition22<F extends URIS2, G extends URIS2> {
  readonly reduce: <FE, GE, A, B>(fga: Kind2<F, FE, Kind2<G, GE, A>>, b: B, f: (b: B, a: A) => B) => B
  readonly foldMap: <M>(M: Monoid<M>) => <FE, GE, A>(fa: Kind2<F, FE, Kind2<G, GE, A>>, f: (a: A) => M) => M
  readonly reduceRight: <FE, GE, A, B>(fa: Kind2<F, FE, Kind2<G, GE, A>>, b: B, f: (a: A, b: B) => B) => B
}
/**
 * @since 2.0.0
 */
export interface FoldableComposition22C<F extends URIS2, G extends URIS2, E> {
  readonly reduce: <FE, A, B>(fga: Kind2<F, FE, Kind2<G, E, A>>, b: B, f: (b: B, a: A) => B) => B
  readonly foldMap: <M>(M: Monoid<M>) => <FE, A>(fa: Kind2<F, FE, Kind2<G, E, A>>, f: (a: A) => M) => M
  readonly reduceRight: <FE, A, B>(fa: Kind2<F, FE, Kind2<G, E, A>>, b: B, f: (a: A, b: B) => B) => B
}
/**
 * Returns the composition of two foldables
 *
 * @example
 * import { getFoldableComposition } from 'fp-ts/Foldable'
 * import { array } from 'fp-ts/Array'
 * import { option, some, none } from 'fp-ts/Option'
 * import { monoidString } from 'fp-ts/Monoid'
 *
 * const F = getFoldableComposition(array, option)
 * assert.strictEqual(F.reduce([some('a'), some('b'), some('c')], '', monoidString.concat), 'abc')
 * assert.strictEqual(F.reduce([some('a'), none, some('c')], '', monoidString.concat), 'ac')
 *
 * @since 2.0.0
 */
export declare function getFoldableComposition<F extends URIS2, G extends URIS2, E>(
  F: Foldable2<F>,
  G: Foldable2C<G, E>
): FoldableComposition22C<F, G, E>
export declare function getFoldableComposition<F extends URIS2, G extends URIS2>(
  F: Foldable2<F>,
  G: Foldable2<G>
): FoldableComposition22<F, G>
export declare function getFoldableComposition<F extends URIS2, G extends URIS, E>(
  F: Foldable2C<F, E>,
  G: Foldable1<G>
): FoldableComposition2C1<F, G, E>
export declare function getFoldableComposition<F extends URIS2, G extends URIS>(
  F: Foldable2<F>,
  G: Foldable1<G>
): FoldableComposition21<F, G>
export declare function getFoldableComposition<F extends URIS, G extends URIS2, E>(
  F: Foldable1<F>,
  G: Foldable2C<G, E>
): FoldableComposition12C<F, G, E>
export declare function getFoldableComposition<F extends URIS, G extends URIS2>(
  F: Foldable1<F>,
  G: Foldable2<G>
): FoldableComposition12<F, G>
export declare function getFoldableComposition<F extends URIS, G extends URIS>(
  F: Foldable1<F>,
  G: Foldable1<G>
): FoldableComposition11<F, G>
export declare function getFoldableComposition<F, G>(F: Foldable<F>, G: Foldable<G>): FoldableComposition<F, G>
/**
 * Use `reduceM` instead
 *
 * @since 2.0.0
 * @deprecated
 */
export declare function foldM<M extends URIS3, F extends URIS>(
  M: Monad3<M>,
  F: Foldable1<F>
): <R, E, A, B>(fa: Kind<F, A>, b: B, f: (b: B, a: A) => Kind3<M, R, E, B>) => Kind3<M, R, E, B>
/** @deprecated */
export declare function foldM<M extends URIS3, F extends URIS, E>(
  M: Monad3C<M, E>,
  F: Foldable1<F>
): <R, A, B>(fa: Kind<F, A>, b: B, f: (b: B, a: A) => Kind3<M, R, E, B>) => Kind3<M, R, E, B>
/** @deprecated */
export declare function foldM<M extends URIS2, F extends URIS>(
  M: Monad2<M>,
  F: Foldable1<F>
): <E, A, B>(fa: Kind<F, A>, b: B, f: (b: B, a: A) => Kind2<M, E, B>) => Kind2<M, E, B>
/** @deprecated */
export declare function foldM<M extends URIS2, F extends URIS, E>(
  M: Monad2C<M, E>,
  F: Foldable1<F>
): <A, B>(fa: Kind<F, A>, b: B, f: (b: B, a: A) => Kind2<M, E, B>) => Kind2<M, E, B>
/** @deprecated */
export declare function foldM<M extends URIS, F extends URIS>(
  M: Monad1<M>,
  F: Foldable1<F>
): <A, B>(fa: Kind<F, A>, b: B, f: (b: B, a: A) => Kind<M, B>) => Kind<M, B>
/** @deprecated */
export declare function foldM<M, F>(
  M: Monad<M>,
  F: Foldable<F>
): <A, B>(fa: HKT<F, A>, b: B, f: (b: B, a: A) => HKT<M, B>) => HKT<M, B>
/**
 * Similar to 'reduce', but the result is encapsulated in a monad.
 *
 * Note: this function is not generally stack-safe, e.g., for monads which build up thunks a la `IO`.
 *
 * @example
 * import { reduceM } from 'fp-ts/Foldable'
 * import { Monad, some } from 'fp-ts/Option'
 * import { make, Foldable } from 'fp-ts/Tree'
 * import { pipe } from 'fp-ts/function'
 *
 * const t = make(1, [make(2, []), make(3, []), make(4, [])])
 * assert.deepStrictEqual(pipe(t, reduceM(Monad, Foldable)(0, (b, a) => (a > 2 ? some(b + a) : some(b)))), some(7))
 *
 * @since 2.8.0
 */
export declare function reduceM<M extends URIS3, F extends URIS>(
  M: Monad3<M>,
  F: Foldable1<F>
): <B, A, R, E>(b: B, f: (b: B, a: A) => Kind3<M, R, E, B>) => (fa: Kind<F, A>) => Kind3<M, R, E, B>
export declare function reduceM<M extends URIS3, F extends URIS, E>(
  M: Monad3C<M, E>,
  F: Foldable1<F>
): <B, A, R>(b: B, f: (b: B, a: A) => Kind3<M, R, E, B>) => (fa: Kind<F, A>) => Kind3<M, R, E, B>
export declare function reduceM<M extends URIS2, F extends URIS>(
  M: Monad2<M>,
  F: Foldable1<F>
): <B, A, E>(b: B, f: (b: B, a: A) => Kind2<M, E, B>) => (fa: Kind<F, A>) => Kind2<M, E, B>
export declare function reduceM<M extends URIS2, F extends URIS, E>(
  M: Monad2C<M, E>,
  F: Foldable1<F>
): <B, A>(b: B, f: (b: B, a: A) => Kind2<M, E, B>) => (fa: Kind<F, A>) => Kind2<M, E, B>
export declare function reduceM<M extends URIS, F extends URIS>(
  M: Monad1<M>,
  F: Foldable1<F>
): <B, A>(b: B, f: (b: B, a: A) => Kind<M, B>) => (fa: Kind<F, A>) => Kind<M, B>
export declare function reduceM<M, F>(
  M: Monad<M>,
  F: Foldable<F>
): <B, A>(b: B, f: (b: B, a: A) => HKT<M, B>) => (fa: HKT<F, A>) => HKT<M, B>
/**
 * Fold a data structure, accumulating values in some `Monoid`, combining adjacent elements using the specified separator
 *
 * @example
 * import { intercalate } from 'fp-ts/Foldable'
 * import { monoidString } from 'fp-ts/Monoid'
 * import { make, tree } from 'fp-ts/Tree'
 *
 * const t = make('a', [make('b', []), make('c', []), make('d', [])])
 * assert.strictEqual(intercalate(monoidString, tree)('|', t), 'a|b|c|d')
 *
 * @since 2.0.0
 */
export declare function intercalate<M, F extends URIS3>(
  M: Monoid<M>,
  F: Foldable3<F>
): <R, E>(sep: M, fm: Kind3<F, R, E, M>) => M
export declare function intercalate<M, F extends URIS2>(
  M: Monoid<M>,
  F: Foldable2<F>
): <E>(sep: M, fm: Kind2<F, E, M>) => M
export declare function intercalate<M, F extends URIS2, E>(
  M: Monoid<M>,
  F: Foldable2C<F, E>
): (sep: M, fm: Kind2<F, E, M>) => M
export declare function intercalate<M, F extends URIS>(M: Monoid<M>, F: Foldable1<F>): (sep: M, fm: Kind<F, M>) => M
export declare function intercalate<M, F>(M: Monoid<M>, F: Foldable<F>): (sep: M, fm: HKT<F, M>) => M
/**
 * Transforms a `Foldable` into a read-only array.
 *
 * @example
 * import { toArray } from 'fp-ts/Foldable'
 * import { tree, make } from 'fp-ts/Tree'
 *
 * const t = make(1, [make(2, []), make(3, []), make(4, [])])
 * assert.deepStrictEqual(toArray(tree)(t), [1, 2, 3, 4])
 *
 * @since 2.8.0
 */
export declare function toArray<F extends URIS4>(
  F: Foldable4<F>
): <S, R, E, A>(fa: Kind4<F, S, R, E, A>) => ReadonlyArray<A>
export declare function toArray<F extends URIS3>(F: Foldable3<F>): <R, E, A>(fa: Kind3<F, R, E, A>) => ReadonlyArray<A>
export declare function toArray<F extends URIS3, E>(
  F: Foldable3C<F, E>
): <R, A>(fa: Kind3<F, R, E, A>) => ReadonlyArray<A>
export declare function toArray<F extends URIS2>(F: Foldable2<F>): <E, A>(fa: Kind2<F, E, A>) => ReadonlyArray<A>
export declare function toArray<F extends URIS2, E>(F: Foldable2C<F, E>): <A>(fa: Kind2<F, E, A>) => ReadonlyArray<A>
export declare function toArray<F extends URIS>(F: Foldable1<F>): <A>(fa: Kind<F, A>) => ReadonlyArray<A>
export declare function toArray<F>(F: Foldable<F>): <A>(fa: HKT<F, A>) => ReadonlyArray<A>
/**
 * Traverse a data structure, performing some effects encoded by an `Applicative` functor at each value, ignoring the
 * final result.
 *
 * @example
 * import { array } from 'fp-ts/Array'
 * import { traverse_ } from 'fp-ts/Foldable'
 * import { io } from 'fp-ts/IO'
 *
 * let log = ''
 * const append = (s: string) => () => (log += s)
 * traverse_(io, array)(['a', 'b', 'c'], append)()
 * assert.strictEqual(log, 'abc')
 *
 * @since 2.0.0
 */
export declare function traverse_<M extends URIS3, F extends URIS>(
  M: Applicative3<M>,
  F: Foldable1<F>
): <R, E, A, B>(fa: Kind<F, A>, f: (a: A) => Kind3<M, R, E, B>) => Kind3<M, R, E, void>
export declare function traverse_<M extends URIS2, F extends URIS>(
  M: Applicative2<M>,
  F: Foldable1<F>
): <E, A, B>(fa: Kind<F, A>, f: (a: A) => Kind2<M, E, B>) => Kind2<M, E, void>
export declare function traverse_<M extends URIS2, F extends URIS, E>(
  M: Applicative2C<M, E>,
  F: Foldable1<F>
): <A, B>(fa: Kind<F, A>, f: (a: A) => Kind2<M, E, B>) => Kind2<M, E, void>
export declare function traverse_<M extends URIS, F extends URIS>(
  M: Applicative1<M>,
  F: Foldable1<F>
): <A, B>(fa: Kind<F, A>, f: (a: A) => Kind<M, B>) => Kind<M, void>
export declare function traverse_<M, F>(
  M: Applicative<M>,
  F: Foldable<F>
): <A, B>(fa: HKT<F, A>, f: (a: A) => HKT<M, B>) => HKT<M, void>