declare const productMany: <F extends TypeLambda>(
  map: Covariant<F>["map"],
  product: SemiProduct<F>["product"]
) => SemiProduct<F>["productMany"]

declare const andThenBind: <F extends TypeLambda>(
  F: SemiProduct<F>
) => {
  <N extends string, A extends object, R2, O2, E2, B>(
    name: Exclude<N, keyof A>,
    that: Kind<F, R2, O2, E2, B>
  ): <R1, O1, E1>(
    self: Kind<F, R1, O1, E1, A>
  ) => Kind<F, R1 & R2, O1 | O2, E1 | E2, { [K in keyof A | N]: K extends keyof A ? A[K] : B }>
  <R1, O1, E1, A extends object, N extends string, R2, O2, E2, B>(
    self: Kind<F, R1, O1, E1, A>,
    name: Exclude<N, keyof A>,
    that: Kind<F, R2, O2, E2, B>
  ): Kind<F, R1 & R2, O1 | O2, E1 | E2, { [K in keyof A | N]: K extends keyof A ? A[K] : B }>
}

export interface SemiProduct<F extends TypeLambda> extends Invariant<F> {
  readonly product: <R1, O1, E1, A, R2, O2, E2, B>(
    self: Kind<F, R1, O1, E1, A>,
    that: Kind<F, R2, O2, E2, B>
  ) => Kind<F, R1 & R2, O1 | O2, E1 | E2, [A, B]>

  readonly productMany: <R, O, E, A>(
    self: Kind<F, R, O, E, A>,
    collection: Iterable<Kind<F, R, O, E, A>>
  ) => Kind<F, R, O, E, [A, ...Array<A>]>
}

declare const appendElement: <F extends TypeLambda>(
  F: SemiProduct<F>
) => {
  <R2, O2, E2, B>(
    that: Kind<F, R2, O2, E2, B>
  ): <R1, O1, E1, A extends ReadonlyArray<any>>(
    self: Kind<F, R1, O1, E1, A>
  ) => Kind<F, R1 & R2, O2 | O1, E2 | E1, [...A, B]>
  <R1, O1, E1, A extends ReadonlyArray<any>, R2, O2, E2, B>(
    self: Kind<F, R1, O1, E1, A>,
    that: Kind<F, R2, O2, E2, B>
  ): Kind<F, R1 & R2, O1 | O2, E1 | E2, [...A, B]>
}

declare const nonEmptyStruct: <F extends TypeLambda>(
  F: SemiProduct<F>
) => <R extends { readonly [x: string]: Kind<F, any, any, any, any> }>(
  fields: EnforceNonEmptyRecord<R> & { readonly [x: string]: Kind<F, any, any, any, any> }
) => Kind<
  F,
  [R[keyof R]] extends [Kind<F, infer R, any, any, any>] ? R : never,
  [R[keyof R]] extends [Kind<F, any, infer O, any, any>] ? O : never,
  [R[keyof R]] extends [Kind<F, any, any, infer E, any>] ? E : never,
  { [K in keyof R]: [R[K]] extends [Kind<F, any, any, any, infer A>] ? A : never }
>

declare const nonEmptyTuple: <F extends TypeLambda>(
  F: SemiProduct<F>
) => <T extends readonly [Kind<F, any, any, any, any>, ...Array<Kind<F, any, any, any, any>>]>(
  ...elements: T
) => Kind<
  F,
  [T[number]] extends [Kind<F, infer R, any, any, any>] ? R : never,
  [T[number]] extends [Kind<F, any, infer O, any, any>] ? O : never,
  [T[number]] extends [Kind<F, any, any, infer E, any>] ? E : never,
  { [I in keyof T]: [T[I]] extends [Kind<F, any, any, any, infer A>] ? A : never }
>

declare const productComposition: <F extends TypeLambda, G extends TypeLambda>(
  F: SemiApplicative<F>,
  G: SemiProduct<G>
) => <FR1, FO1, FE1, GR1, GO1, GE1, A, FR2, FO2, FE2, GR2, GO2, GE2, B>(
  self: Kind<F, FR1, FO1, FE1, Kind<G, GR1, GO1, GE1, A>>,
  that: Kind<F, FR2, FO2, FE2, Kind<G, GR2, GO2, GE2, B>>
) => Kind<F, FR1 & FR2, FO1 | FO2, FE1 | FE2, Kind<G, GR1 & GR2, GO1 | GO2, GE1 | GE2, [A, B]>>

declare const productManyComposition: <F extends TypeLambda, G extends TypeLambda>(
  F: SemiApplicative<F>,
  G: SemiProduct<G>
) => <FR, FO, FE, GR, GO, GE, A>(
  self: Kind<F, FR, FO, FE, Kind<G, GR, GO, GE, A>>,
  collection: Iterable<Kind<F, FR, FO, FE, Kind<G, GR, GO, GE, A>>>
) => Kind<F, FR, FO, FE, Kind<G, GR, GO, GE, [A, ...Array<A>]>>