import type * as P from "@principia/prelude";
import type { LazyPromise, 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: LazyPromise<(a: A) => B>, fa: LazyPromise<A>) => LazyPromise<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: LazyPromise<A>) => <B>(fab: LazyPromise<(a: A) => B>) => LazyPromise<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: LazyPromise<A>, fb: LazyPromise<B>) => LazyPromise<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: LazyPromise<B>) => <A>(fa: LazyPromise<A>) => LazyPromise<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: LazyPromise<A>, fb: LazyPromise<B>) => LazyPromise<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: LazyPromise<B>) => <A>(fa: LazyPromise<A>) => LazyPromise<B>;
/**
 * ```haskell
 * liftA2 :: 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: LazyPromise<A>) => (fb: LazyPromise<B>) => LazyPromise<C>;
/**
 * ```haskell
 * mapBoth_ :: Apply f => (f a, f b, ((a, b) -> c)) -> f c
 * ```
 *
 * Applies both `LazyPromise`s and maps their results with function `f`
 *
 * @category Apply
 * @since 1.0.0
 */
export declare const mapBoth_: <A, B, C>(
   fa: LazyPromise<A>,
   fb: LazyPromise<B>,
   f: (a: A, b: B) => C
) => LazyPromise<C>;
/**
 * ```haskell
 * mapBoth :: Apply f => (f b, ((a, b) -> c)) -> f a -> f c
 * ```
 *
 * Applies both `LazyPromise`s and maps their results with function `f`
 *
 * @category Apply
 * @since 1.0.0
 */
export declare const mapBoth: <A, B, C>(
   fb: LazyPromise<B>,
   f: (a: A, b: B) => C
) => (fa: LazyPromise<A>) => LazyPromise<C>;
/**
 * ```haskell
 * apSeq_ :: Apply f => (f (a -> b), f a) -> f b
 * ```
 *
 * Sequentially apply a function to an argument under a type constructor. For a parallel version, see `ap_`
 *
 * @category Apply
 * @since 1.0.0
 */
export declare const apSeq_: <A, B>(fab: LazyPromise<(a: A) => B>, fa: LazyPromise<A>) => LazyPromise<B>;
/**
 * ```haskell
 * apSeq :: Apply f => f a -> f (a -> b) -> f b
 * ```
 *
 * Sequentially apply a function to an argument under a type constructor. For a parallel version, see `ap`
 *
 * @category Apply
 * @since 1.0.0
 */
export declare const apSeq: <A>(fa: LazyPromise<A>) => <B>(fab: LazyPromise<(a: A) => B>) => LazyPromise<B>;
/**
 * ```haskell
 * apFirstSeq_ :: Apply f => (f a, f b) -> f a
 * ```
 *
 * Sequentially combine two effectful actions, keeping only the result of the first. For a parallel version, see `apFirst_`
 *
 * @category Uncurried Apply
 * @since 1.0.0
 */
export declare const apFirstSeq_: <A, B>(fa: LazyPromise<A>, fb: LazyPromise<B>) => LazyPromise<A>;
/**
 * ```haskell
 * apFirst :: Apply f => f b -> f a -> f a
 * ```
 *
 * Sequentially combine two effectful actions, keeping only the result of the first. For a parallel version, see `apFirst`
 *
 * @category Apply
 * @since 1.0.0
 */
export declare const apFirstSeq: <B>(fb: LazyPromise<B>) => <A>(fa: LazyPromise<A>) => LazyPromise<A>;
/**
 * ```haskell
 * apSecondSeq_ :: Apply f => (f a, f b) -> f b
 * ```
 *
 * Sequentially combine two effectful actions, keeping only the result of the second. For a parallel version, see `apSecond_`
 *
 * @category Apply
 * @since 1.0.0
 */
export declare const apSecondSeq_: <A, B>(fa: LazyPromise<A>, fb: LazyPromise<B>) => LazyPromise<B>;
/**
 * ```haskell
 * apSecondSeq :: Apply f => f b -> f a -> f b
 * ```
 *
 * Sequentially combine two effectful actions, keeping only the result of the second. For a parallel version, see `apSecond`
 *
 * @category Apply
 * @since 1.0.0
 */
export declare const apSecondSeq: <B>(fb: LazyPromise<B>) => <A>(fa: LazyPromise<A>) => LazyPromise<B>;
/**
 * ```haskell
 * mapBothSeq_ :: Apply f => (f a, f b, ((a, b) -> c)) -> f c
 * ```
 *
 * Sequentially applies both `LazyPromise`s and maps their results with function `f`. For a parallel version, see `mapBoth_`
 *
 * @category Apply
 * @since 1.0.0
 */
export declare const mapBothSeq_: <A, B, C>(
   fa: LazyPromise<A>,
   fb: LazyPromise<B>,
   f: (a: A, b: B) => C
) => LazyPromise<C>;
/**
 * ```haskell
 * mapBoth :: Apply f => (f b, ((a, b) -> c)) -> f a -> f c
 * ```
 *
 * Sequentially applies both `LazyPromise`s and maps their results with function `f`. For a parallel version, see `mapBoth`
 *
 * @category Apply
 * @since 1.0.0
 */
export declare const mapBothSeq: <A, B, C>(
   fb: LazyPromise<B>,
   f: (a: A, b: B) => C
) => (fa: LazyPromise<A>) => LazyPromise<C>;
/**
 * ```haskell
 * liftA2Seq :: Apply f => (a -> b -> c) -> f a -> f b -> f c
 * ```
 *
 * Lifts a binary function to actions. `LazyPromise`s will be evaluated sequentially. For a parallel version, see `lift2`
 *
 * @category Apply
 * @since 1.0.0
 */
export declare const liftA2Seq: <A, B, C>(
   f: (a: A) => (b: B) => C
) => (fa: LazyPromise<A>) => (fb: LazyPromise<B>) => LazyPromise<C>;
export declare const ApplyPar: P.Apply<[URI], V>;
export declare const ApplySeq: P.Apply<[URI], V>;
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