export const chain: <B>(E: Eq<B>) => <A>(f: (x: A) => Set<B>) => (set: Set<A>) => Set<B> = ...

export const compact: <A>(E: Eq<A>) => (fa: Set<Option<A>>) => Set<A> = ...

export const difference: <A>(E: Eq<A>) => (x: Set<A>, y: Set<A>) => Set<A> = ...

import { difference } from 'fp-ts/lib/Set'
import { eqNumber } from 'fp-ts/lib/Eq'

assert.deepStrictEqual(difference(eqNumber)(new Set([1, 2]), new Set([1, 3])), new Set([2]))

export const elem: <A>(E: Eq<A>) => (a: A, set: Set<A>) => boolean = ...

export const empty: Set<never> = ...

export const every: <A>(predicate: Predicate<A>) => (set: Set<A>) => boolean = ...

export function filter<A, B extends A>(refinement: Refinement<A, B>): (set: Set<A>) => Set<B>
export function filter<A>(predicate: Predicate<A>): (set: Set<A>) => Set<A> { ... }

export const filterMap: <B>(E: Eq<B>) => <A>(f: (a: A) => Option<B>) => (fa: Set<A>) => Set<B> = ...

export const foldMap: <A, M>(O: Ord<A>, M: Monoid<M>) => (f: (a: A) => M) => (fa: Set<A>) => M = ...

export const fromArray: <A>(E: Eq<A>) => (as: Array<A>) => Set<A> = ...

export const getEq: <A>(E: Eq<A>) => Eq<Set<A>> = ...

export const getIntersectionSemigroup: <A>(E: Eq<A>) => Semigroup<Set<A>> = ...

export const getShow: <A>(S: Show<A>) => Show<Set<A>> = ...

export const getUnionMonoid: <A>(E: Eq<A>) => Monoid<Set<A>> = ...

export const insert: <A>(E: Eq<A>) => (a: A) => (set: Set<A>) => Set<A> = ...

export const intersection: <A>(E: Eq<A>) => (set: Set<A>, y: Set<A>) => Set<A> = ...

export const map: <B>(E: Eq<B>) => <A>(f: (x: A) => B) => (set: Set<A>) => Set<B> = ...

export function partition<A, B extends A>(refinement: Refinement<A, B>): (set: Set<A>) => Separated<Set<A>, Set<B>>
export function partition<A>(predicate: Predicate<A>): (set: Set<A>) => Separated<Set<A>, Set<A>> { ... }

export const partitionMap: <B, C>(
  EB: Eq<B>,
  EC: Eq<C>
) => <A>(f: (a: A) => Either<B, C>) => (set: Set<A>) => Separated<Set<B>, Set<C>> = ...

export const reduce: <A>(O: Ord<A>) => <B>(b: B, f: (b: B, a: A) => B) => (fa: Set<A>) => B = ...

export const remove: <A>(E: Eq<A>) => (a: A) => (set: Set<A>) => Set<A> = ...

export const separate: <E, A>(
  EE: Eq<E>,
  EA: Eq<A>
) => (fa: Set<Either<E, A>>) => Separated<Set<E>, Set<A>> = ...

export const singleton: <A>(a: A) => Set<A> = ...

export const some: <A>(predicate: Predicate<A>) => (set: Set<A>) => boolean = ...

export const subset: <A>(E: Eq<A>) => (x: Set<A>, y: Set<A>) => boolean = ...

export const toArray: <A>(O: Ord<A>) => (set: Set<A>) => Array<A> = ...

export function toggle<A>(E: Eq<A>): (a: A) => (set: Set<A>) => Set<A> { ... }

export const union: <A>(E: Eq<A>) => (set: Set<A>, y: Set<A>) => Set<A> = ...