import type * as P from "@principia/prelude";
import type { IO, URI, V } from "./model";
/**
 * ```haskell
 * ap_ :: Apply f => (f (a -> b), f a) -> f b
 * ```
 *
 * Apply a function to an argument under a type constructor
 *
 * @category Apply
 * @since 1.0.0
 */
export declare const ap_: <A, B>(fab: IO<(a: A) => B>, fa: IO<A>) => IO<B>;
/**
 * ```haskell
 * ap :: Apply f => f a -> f (a -> b) -> f b
 * ```
 *
 * Apply a function to an argument under a type constructor
 *
 * @category Apply
 * @since 1.0.0
 */
export declare const ap: <A>(fa: IO<A>) => <B>(fab: IO<(a: A) => B>) => IO<B>;
/**
 * ```haskell
 * apFirst_ :: Apply f => (f a, f b) -> f a
 * ```
 *
 * Combine two effectful actions, keeping only the result of the first
 *
 * @category Apply
 * @since 1.0.0
 */
export declare const apFirst_: <A, B>(fa: IO<A>, fb: IO<B>) => IO<A>;
/**
 * ```haskell
 * apFirst :: Apply f => f b -> f a -> f a
 * ```
 *
 * Combine two effectful actions, keeping only the result of the first
 *
 * @category Apply
 * @since 1.0.0
 */
export declare const apFirst: <B>(fb: IO<B>) => <A>(fa: IO<A>) => IO<A>;
/**
 * ```haskell
 * apSecond_ :: Apply f => (f a, f b) -> f b
 * ```
 *
 * Combine two effectful actions, keeping only the result of the second
 *
 * @category Apply
 * @since 1.0.0
 */
export declare const apSecond_: <A, B>(fa: IO<A>, fb: IO<B>) => IO<B>;
/**
 * ```haskell
 * apSecond :: Apply f => f b -> f a -> f b
 * ```
 *
 * Combine two effectful actions, keeping only the result of the second
 *
 * @category Apply
 * @since 1.0.0
 */
export declare const apSecond: <B>(fb: IO<B>) => <A>(fa: IO<A>) => IO<B>;
/**
 * ```haskell
 * mapBoth_ :: Apply f => (f a, f b, ((a, b) -> c)) -> f c
 * ```
 *
 * Applies both `IO`s and maps their results with function `f`
 *
 * @category Apply
 * @since 1.0.0
 */
export declare const mapBoth_: <A, B, C>(fa: IO<A>, fb: IO<B>, f: (a: A, b: B) => C) => IO<C>;
/**
 * ```haskell
 * mapBoth :: Apply f => (f b, ((a, b) -> c)) -> f a -> f c
 * ```
 *
 * Applies both `IO`s and maps their results with function `f`
 *
 * @category Apply
 * @since 1.0.0
 */
export declare const mapBoth: <A, B, C>(fb: IO<B>, f: (a: A, b: B) => C) => (fa: IO<A>) => IO<C>;
/**
 * ```haskell
 * lift2 :: Apply f => (a -> b -> c) -> f a -> f b -> f c
 * ```
 *
 * Lifts a binary function to actions
 *
 * @category Apply
 * @since 1.0.0
 */
export declare const liftA2: <A, B, C>(f: (a: A) => (b: B) => C) => (fa: IO<A>) => (fb: IO<B>) => IO<C>;
/**
 * ```haskell
 * apS :: (Apply f, Nominal n) =>
 *    (n n3, f c)
 *    -> f ({ n1: a, n2: b, ... })
 *    -> f ({ n1: a, n2: b, n3: c })
 * ```
 *
 * A pipeable version of `sequenceS`
 *
 * @category Apply
 * @since 1.0.0
 */
export declare const apS: <N extends string, A, B>(
   name: Exclude<N, keyof A>,
   fb: IO<B>
) => (fa: IO<A>) => IO<{ [K in N | keyof A]: K extends keyof A ? A[K] : B }>;
export declare const Apply: P.Apply<[URI], V>;
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