funfix-types/dist/applicative.d.ts

Sub-package of Funfix defining type classes inspired by Haskell's standard library

/*!
 * Copyright (c) 2017 by The Funfix Project Developers.
 * Some rights reserved.
 *
 * Licensed under the Apache License, Version 2.0 (the "License");
 * you may not use this file except in compliance with the License.
 * You may obtain a copy of the License at
 *
 *     http://www.apache.org/licenses/LICENSE-2.0
 *
 * Unless required by applicable law or agreed to in writing, software
 * distributed under the License is distributed on an "AS IS" BASIS,
 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 * See the License for the specific language governing permissions and
 * limitations under the License.
 */
import { HK, Equiv, Constructor } from "./kinds";
import { Functor, FunctorLaws } from "./functor";
import { Either } from "funfix-core";
/**
 * The `Apply` type class, a weaker version of {@link Applicative},
 * exposing `ap` (apply), but not `pure`.
 *
 * This type class is exposed in addition to `Applicative` because
 * there are data types for which we can't implement `pure`, but
 * that could still benefit from an `ap` definition. For example
 * in case of a `Map<K, ?>` we couldn't define `pure` for it
 * because we don't have a `K` key.
 *
 * MUST obey the laws defined in {@link ApplyLaws}.
 *
 * Note that having an `Apply` instance implies that a
 * {@link Functor} implementation is also available, which is why
 * `Apply` is a subtype of `Functor`.
 *
 * ## Implementation notes
 *
 * Even though in TypeScript the Funfix library is using `abstract class` to
 * express type classes, when implementing this type class it is recommended
 * that you implement it as a mixin using "`implements`", instead of extending
 * it directly with "`extends`". See
 * [TypeScript: Mixins]{@link https://www.typescriptlang.org/docs/handbook/mixins.html}
 * for details and note that we already have `applyMixins` defined.
 *
 * Implementation example:
 *
 * ```typescript
 * import {
 *   HK, Apply,
 *   registerTypeClassInstance,
 *   applyMixins
 * } from "funfix"
 *
 * // Type alias defined for readability.
 * // HK is our encoding for higher-kinded types.
 * type BoxK<T> = HK<Box<any>, T>
 *
 * class Box<T> implements HK<Box<any>, T> {
 *   constructor(public value: T) {}
 *
 *   // Implements HK<Box<any>, A>, not really needed, but useful in order
 *   // to avoid type casts. Note these can and should be undefined:
 *   readonly _funKindF: Box<any>
 *   readonly _funKindA: T
 * }
 *
 * class BoxApply implements Apply<Box<any>> {
 *   map<A, B>(fa: BoxK<A>, f: (a: A) => B): Box<B> {
 *     const a = (fa as Box<A>).value
 *     return new Box(f(a))
 *   }
 *
 *   ap<A, B>(fa: BoxK<A>, ff: BoxK<(a: A) => B>): Box<B> {
 *     const a = (fa as Box<A>).value
 *     const f = (ff as Box<(a: A) => B>).value
 *     return new Box(f(a))
 *   }
 *
 *   // Mixed-in, as these have default implementations
 *   map2: <A, B, Z>(fa: BoxK<A>, fb: BoxK<B>, f: (a: A, b: B) => Z) => Box<Z>
 *   product: <A, B> (fa: BoxK<A>, fb: BoxK<B>) => Box<[A, B]>
 * }
 *
 * // Call needed in order to implement `map2` and `product` using
 * // the default implementations defined by `Apply`, because
 * // we are using `implements` instead of `extends` above and
 * // because in this sample we want the default implementations,
 * // but note that you can always provide your own definitions
 * applyMixins(BoxApply, [Apply])
 *
 * // Registering global Apply instance for Box, needed in order
 * // for the `applyOf(Box)` calls to work
 * registerTypeClassInstance(Apply)(Box, new BoxApply())
 * ```
 *
 * We are using `implements` in order to support multiple inheritance and to
 * avoid inheriting any `static` members. In the Flow definitions (e.g.
 * `.js.flow` files) for Funfix these type classes are defined with
 * "`interface`", as they are meant to be interfaces that sometimes have
 * default implementations and not classes.
 *
 * ## Credits
 *
 * This type class is inspired by the equivalent in Haskell's
 * standard library and the implementation is inspired by the
 * [Typelevel Cats]{@link http://typelevel.org/cats/} project.
 */
export declare abstract class Apply<F> implements Functor<F> {
    /**
     * Given a value and a function in the `Apply` context,
     * applies the function to the value.
     */
    abstract ap<A, B>(fa: HK<F, A>, ff: HK<F, (a: A) => B>): HK<F, B>;
    /** Inherited from {@link Functor.map}. */
    abstract map<A, B>(fa: HK<F, A>, f: (a: A) => B): HK<F, B>;
    /**
     * Applies the pure (binary) function `f` to the effectful values
     * `fa` and `fb`.
     *
     * `map2` can be seen as a binary version of {@link Functor.map}.
     */
    map2<A, B, Z>(fa: HK<F, A>, fb: HK<F, B>, f: (a: A, b: B) => Z): HK<F, Z>;
    /**
     * Captures the idea of composing independent effectful values.
     *
     * It is of particular interest when taken together with [[Functor]].
     * Where [[Functor]] captures the idea of applying a unary pure
     * function to an effectful value, calling `product` with `map`
     * allows one to apply a function of arbitrary arity to multiple
     * independent effectful values.
     *
     * This operation is equivalent with:
     *
     * ```typescript
     * map2(fa, fb, (a, b) => [a, b])
     * ```
     */
    product<A, B>(fa: HK<F, A>, fb: HK<F, B>): HK<F, [A, B]>;
    /** @hidden */
    static readonly _funTypeId: string;
    /** @hidden */
    static readonly _funSupertypeIds: string[];
    /** @hidden */
    static readonly _funErasure: Apply<any>;
}
/**
 * Type class laws defined for {@link Apply}.
 *
 * This is an abstract definition. In order to use it in unit testing,
 * the implementor must think of a strategy to evaluate the truthiness
 * of the returned `Equiv` values.
 *
 * Even though in TypeScript the Funfix library is using classes to
 * express these laws, when implementing this class it is recommended
 * that you implement it as a mixin using `implements`, instead of extending
 * it directly with `extends`. See
 * [TypeScript: Mixins]{@link https://www.typescriptlang.org/docs/handbook/mixins.html}
 * for details and note that we already have `applyMixins` defined.
 *
 * We are doing this in order to support multiple inheritance and to
 * avoid inheriting any `static` members. In the Flow definitions (e.g.
 * `.js.flow` files) for Funfix these classes are defined with
 * `interface`, as they are meant to be interfaces that sometimes have
 * default implementations and not classes.
 */
export declare abstract class ApplyLaws<F> implements FunctorLaws<F> {
    /**
     * The {@link Apply} designated instance for `F`,
     * to be tested.
     */
    readonly F: Apply<F>;
    applyComposition<A, B, C>(fa: HK<F, A>, fab: HK<F, (a: A) => B>, fbc: HK<F, (b: B) => C>): Equiv<HK<F, C>>;
    applyProductConsistency<A, B>(fa: HK<F, A>, f: HK<F, (a: A) => B>): Equiv<HK<F, B>>;
    applyMap2Consistency<A, B>(fa: HK<F, A>, f: HK<F, (a: A) => B>): Equiv<HK<F, B>>;
    /** Mixed-in from {@link FunctorLaws.covariantIdentity}. */
    covariantIdentity: <A>(fa: HK<F, A>) => Equiv<HK<F, A>>;
    /** Mixed-in from {@link FunctorLaws.covariantComposition}. */
    covariantComposition: <A, B, C>(fa: HK<F, A>, f: (a: A) => B, g: (b: B) => C) => Equiv<HK<F, C>>;
}
/**
 * Given a {@link Constructor} reference, returns its associated
 * {@link Apply} instance if it exists, or throws a `NotImplementedError`
 * in case there's no such association.
 *
 * ```typescript
 * import { Option, Apply, applyOf } from "funfix"
 *
 * const F: Apply<Option<any>> = applyOf(Option)
 * ```
 */
export declare const applyOf: <F>(c: Constructor<F>) => Apply<F>;
/**
 * Given an {@link Apply} instance, returns the {@link ApplyLaws}
 * associated with it.
 */
export declare function applyLawsOf<F>(instance: Apply<F>): ApplyLaws<F>;
/**
 * `Applicative` functor type class.
 *
 * Allows application of a function in an Applicative context to a
 * value in an `Applicative` context.
 *
 * References:
 *
 * - [The Essence of the Iterator Pattern]{@link https://www.cs.ox.ac.uk/jeremy.gibbons/publications/iterator.pdf}
 * - [Applicative programming with effects]{@link http://staff.city.ac.uk/~ross/papers/Applicative.pdf}
 *
 * Example:
 *
 * ```typescript
 * const F = applicativeOf(Option)
 *
 * F.ap(F.pure(1), F.pure((x: number) => x + 1)) // Some(2)
 * ```
 *
 * Note that having an `Applicative` instance implies
 * {@link Functor} and {@link Apply} implementations are also
 * available, which is why `Applicative` is a subtype of
 * `Functor` and `Apply`.
 *
 * ## Implementation notes
 *
 * Even though in TypeScript the Funfix library is using `abstract class` to
 * express type classes, when implementing this type class it is recommended
 * that you implement it as a mixin using "`implements`", instead of extending
 * it directly with "`extends`". See
 * [TypeScript: Mixins]{@link https://www.typescriptlang.org/docs/handbook/mixins.html}
 * for details and note that we already have `applyMixins` defined.
 *
 * Implementation example:
 *
 * ```typescript
 * import {
 *   HK, Applicative,
 *   registerTypeClassInstance,
 *   applyMixins
 * } from "funfix"
 *
 * // Type alias defined for readability.
 * // HK is our encoding for higher-kinded types.
 * type BoxK<T> = HK<Box<any>, T>
 *
 * class Box<T> implements HK<Box<any>, T> {
 *   constructor(public value: T) {}
 *
 *   // Implements HK<Box<any>, A>, not really needed, but useful in order
 *   // to avoid type casts. Note they can and should be undefined:
 *   readonly _funKindF: Box<any>
 *   readonly _funKindA: T
 * }
 *
 * class BoxApplicative implements Applicative<Box<any>> {
 *   pure<A>(a: A): Box<A> { return new Box(a) }
 *
 *   ap<A, B>(fa: BoxK<A>, ff: BoxK<(a: A) => B>): Box<B> {
 *     const a = (fa as Box<A>).value
 *     const f = (ff as Box<(a: A) => B>).value
 *     return new Box(f(a))
 *   }
 *
 *   // Mixed-in, as these have default implementations
 *   map: <A, B>(fa: BoxK<A>, f: (a: A) => B) => Box<B>
 *   map2: <A, B, Z>(fa: BoxK<A>, fb: BoxK<B>, f: (a: A, b: B) => Z) => Box<Z>
 *   product: <A, B> (fa: BoxK<A>, fb: BoxK<B>) => Box<[A, B]>
 *   unit: () => Box<void>
 * }
 *
 * // Call needed in order to implement `map`, `map2`, `product` and `unit`,
 * // using the default implementations defined by `Applicative`, because
 * // we are using `implements` instead of `extends` above and
 * // because in this sample we want the default implementations,
 * // but note that you can always provide your own
 * applyMixins(BoxApplicative, [Applicative])
 *
 * // Registering global Applicative instance for Box, needed in order
 * // for the `functorOf(Box)`, `applyOf(Box)` and `applicativeOf(Box)`
 * // calls to work
 * registerTypeClassInstance(Applicative)(Box, new BoxApplicative())
 * ```
 *
 * We are using `implements` in order to support multiple inheritance and to
 * avoid inheriting any `static` members. In the Flow definitions (e.g.
 * `.js.flow` files) for Funfix these type classes are defined with
 * "`interface`", as they are meant to be interfaces that sometimes have
 * default implementations and not classes.
 *
 * ## Credits
 *
 * This type class is inspired by the equivalent in Haskell's
 * standard library and the implementation is inspired by the
 * [Typelevel Cats]{@link http://typelevel.org/cats/} project.
 */
export declare abstract class Applicative<F> implements Apply<F> {
    /**
     * Lifts a strict value `A` into the `F<A>` context.
     */
    abstract pure<A>(a: A): HK<F, A>;
    /** Inherited from {@link Apply.ap}. */
    abstract ap<A, B>(fa: HK<F, A>, ff: HK<F, (a: A) => B>): HK<F, B>;
    /**
     * Shorthand for `pure<void>(undefined)`, provided for convenience
     * and because implementations can override the default for
     * optimization purposes.
     */
    unit(): HK<F, void>;
    /** Inherited from {@link Functor.map}. */
    map<A, B>(fa: HK<F, A>, f: (a: A) => B): HK<F, B>;
    /** Mixed-in from {@link Apply.map2}. */
    map2: <A, B, Z>(fa: HK<F, A>, fb: HK<F, B>, f: (a: A, b: B) => Z) => HK<F, Z>;
    /** Mixed-in from {@link Apply.product}. */
    product: <A, B>(fa: HK<F, A>, fb: HK<F, B>) => HK<F, [A, B]>;
    /** @hidden */
    static readonly _funTypeId: string;
    /** @hidden */
    static readonly _funSupertypeIds: string[];
    /** @hidden */
    static readonly _funErasure: Applicative<any>;
}
/**
 * Type class laws defined for {@link Applicative}.
 *
 * This is an abstract definition. In order to use it in unit testing,
 * the implementor must think of a strategy to evaluate the truthiness
 * of the returned `Equiv` values.
 *
 * Even though in TypeScript the Funfix library is using classes to
 * express these laws, when implementing this class it is recommended
 * that you implement it as a mixin using `implements`, instead of extending
 * it directly with `extends`. See
 * [TypeScript: Mixins]{@link https://www.typescriptlang.org/docs/handbook/mixins.html}
 * for details and note that we already have `applyMixins` defined.
 *
 * We are doing this in order to support multiple inheritance and to
 * avoid inheriting any `static` members. In the Flow definitions (e.g.
 * `.js.flow` files) for Funfix these classes are defined with
 * `interface`, as they are meant to be interfaces that sometimes have
 * default implementations and not classes.
 */
export declare abstract class ApplicativeLaws<F> implements ApplyLaws<F> {
    /**
     * The {@link Applicative} designated instance for `F`,
     * to be tested.
     */
    readonly F: Applicative<F>;
    applicativeIdentity<A>(fa: HK<F, A>): Equiv<HK<F, A>>;
    applicativeHomomorphism<A, B>(a: A, f: (a: A) => B): Equiv<HK<F, B>>;
    applicativeInterchange<A, B>(a: A, ff: HK<F, (a: A) => B>): Equiv<HK<F, B>>;
    applicativeMap<A, B>(fa: HK<F, A>, f: (a: A) => B): Equiv<HK<F, B>>;
    applicativeComposition<A, B, C>(fa: HK<F, A>, fab: HK<F, (a: A) => B>, fbc: HK<F, (b: B) => C>): Equiv<HK<F, C>>;
    applicativeUnit<A>(a: A): Equiv<HK<F, A>>;
    /** Mixed-in from {@link FunctorLaws.covariantIdentity}. */
    covariantIdentity: <A>(fa: HK<F, A>) => Equiv<HK<F, A>>;
    /** Mixed-in from {@link FunctorLaws.covariantComposition}. */
    covariantComposition: <A, B, C>(fa: HK<F, A>, f: (a: A) => B, g: (b: B) => C) => Equiv<HK<F, C>>;
    /** Mixed-in from {@link ApplyLaws.applyComposition}. */
    applyComposition: <A, B, C>(fa: HK<F, A>, fab: HK<F, (a: A) => B>, fbc: HK<F, (b: B) => C>) => Equiv<HK<F, C>>;
    /** Mixed-in from {@link ApplyLaws.applyProductConsistency}. */
    applyProductConsistency: <A, B>(fa: HK<F, A>, f: HK<F, (a: A) => B>) => Equiv<HK<F, B>>;
    /** Mixed-in from {@link ApplyLaws.applyMap2Consistency}. */
    applyMap2Consistency: <A, B>(fa: HK<F, A>, f: HK<F, (a: A) => B>) => Equiv<HK<F, B>>;
}
/**
 * Given a {@link Constructor} reference, returns its associated
 * {@link Applicative} instance if it exists, or throws a `NotImplementedError`
 * in case there's no such association.
 *
 * ```typescript
 * import { Option, Applicative, applicativeOf } from "funfix"
 *
 * const F: Applicative<Option<any>> = applicativeOf(Option)
 * ```
 */
export declare const applicativeOf: <F>(c: Constructor<F>) => Applicative<F>;
/**
 * Given an {@link Applicative} instance, returns the {@link ApplicativeLaws}
 * associated with it.
 */
export declare function applicativeLawsOf<F>(instance: Applicative<F>): ApplicativeLaws<F>;
/**
 * The `ApplicativeError` type class is a {@link Applicative} that
 * also allows you to raise and or handle an error value.
 *
 * This type class allows one to abstract over error-handling
 * applicative types.
 *
 * MUST follow the law defined in {@link ApplicativeErrorLaws}.
 *
 * ## Implementation notes
 *
 * Even though in TypeScript the Funfix library is using `abstract class` to
 * express type classes, when implementing this type class it is recommended
 * that you implement it as a mixin using "`implements`", instead of extending
 * it directly with "`extends`". See
 * [TypeScript: Mixins]{@link https://www.typescriptlang.org/docs/handbook/mixins.html}
 * for details and note that we already have `applyMixins` defined.
 *
 * Implementation example:
 *
 * ```typescript
 * import {
 *   HK,
 *   ApplicativeError,
 *   registerTypeClassInstance,
 *   applyMixins,
 *   Try
 * } from "funfix"
 *
 * // Type alias defined for readability.
 * // HK is our encoding for higher-kinded types.
 * type BoxK<T> = HK<Box<any>, T>
 *
 * class Box<T> implements HK<Box<any>, T> {
 *   constructor(public value: Try<T>) {}
 *
 *   // Implements HK<Box<any>, A>, not really needed, but useful in order
 *   // to avoid type casts. Note they can and should be undefined:
 *   readonly _funKindF: Box<any>
 *   readonly _funKindA: T
 * }
 *
 * class BoxApplicativeError implements ApplicativeError<Box<any>, any> {
 *   pure<A>(a: A): Box<A> { return new Box(Try.success(a)) }
 *
 *   ap<A, B>(fa: BoxK<A>, ff: BoxK<(a: A) => B>): Box<B> {
 *     const ta = (fa as Box<A>).value
 *     const tf = (ff as Box<(a: A) => B>).value
 *     return new Box(Try.map2(ta, tf, (a, f) => f(a)))
 *   }
 *
 *   raise<A>(e: any): HK<Box<any>, A> {
 *     return new Box(Try.failure(e))
 *   }
 *
 *   recoverWith<A>(fa: BoxK<A>, f: (e: any) => BoxK<A>): HK<Box<any>, A> {
 *     return new Box((fa as Box<A>).value.recoverWith(e => (f(e) as Box<A>).value))
 *   }
 *
 *   // Mixed-in, as these have default implementations
 *   map: <A, B>(fa: BoxK<A>, f: (a: A) => B) => Box<B>
 *   map2: <A, B, Z>(fa: BoxK<A>, fb: BoxK<B>, f: (a: A, b: B) => Z) => Box<Z>
 *   product: <A, B> (fa: BoxK<A>, fb: BoxK<B>) => Box<[A, B]>
 *   unit: () => Box<void>
 *   recover: <A>(fa: HK<Box<any>, A>, f: (e: any) => A) => HK<Box<any>, A>
 *   attempt: <A>(fa: HK<Box<any>, A>) => HK<Box<any>, Either<any, A>>
 * }
 *
 * // Call needed in order to implement `map`, `map2`, `product`, etc.
 * // using the default implementations defined by `ApplicativeError`,
 * // because we are using `implements` instead of `extends` above and
 * // because in this sample we want the default implementations,
 * // but note that you can always provide your own
 * applyMixins(BoxApplicativeError, [ApplicativeError])
 *
 * // Registering global ApplicativeError instance for Box, needed in order
 * // for the `functorOf(Box)`, `applyOf(Box)`, `applicativeOf(Box)`
 * // and `applicativeErrorOf(Box)` calls to work
 * registerTypeClassInstance(ApplicativeError)(Box, new BoxApplicativeError())
 * ```
 *
 * We are using `implements` in order to support multiple inheritance and to
 * avoid inheriting any `static` members. In the Flow definitions (e.g.
 * `.js.flow` files) for Funfix these type classes are defined with
 * "`interface`", as they are meant to be interfaces that sometimes have
 * default implementations and not classes.
 *
 * ## Credits
 *
 * This type class is inspired by the equivalent in Haskell's
 * standard library and the implementation is inspired by the
 * [Typelevel Cats]{@link http://typelevel.org/cats/} project.
 */
export declare abstract class ApplicativeError<F, E> implements Applicative<F> {
    /**
     * Lift an error into the `F` context.
     */
    abstract raise<A>(e: E): HK<F, A>;
    /**
     * Handle any error, potentially recovering from it, by mapping it to an
     * `F<A>` value.
     *
     * @see {@link recover} to handle any error by simply mapping it to an `A`
     * value instead of an `F<A>`.
     */
    abstract recoverWith<A>(fa: HK<F, A>, f: (e: E) => HK<F, A>): HK<F, A>;
    /**
     * Handle any error by mapping it to an `A` value.
     *
     * @see {@link recoverWith} to map to an `F[A]` value instead of
     * simply an `A` value.
     */
    recover<A>(fa: HK<F, A>, f: (e: E) => A): HK<F, A>;
    /**
     * Handle errors by turning them into `Either` values.
     *
     * If there is no error, then a `Right` value will be returned.
     * All non-fatal errors should be handled by this method.
     */
    attempt<A>(fa: HK<F, A>): HK<F, Either<E, A>>;
    /** Inherited from {@link Applicative.pure}. */
    abstract pure<A>(a: A): HK<F, A>;
    /** Inherited from {@link Applicative.ap}. */
    abstract ap<A, B>(fa: HK<F, A>, ff: HK<F, (a: A) => B>): HK<F, B>;
    /** Mixed-in from {@link Applicative.unit}. */
    unit: () => HK<F, void>;
    /** Mixed-in from {@link Applicative.map}. */
    map: <A, B>(fa: HK<F, A>, f: (a: A) => B) => HK<F, B>;
    /** Mixed-in from {@link Apply.map2}. */
    map2: <A, B, Z>(fa: HK<F, A>, fb: HK<F, B>, f: (a: A, b: B) => Z) => HK<F, Z>;
    /** Mixed-in from {@link Apply.product}. */
    product: <A, B>(fa: HK<F, A>, fb: HK<F, B>) => HK<F, [A, B]>;
    /** @hidden */
    static readonly _funTypeId: string;
    /** @hidden */
    static readonly _funSupertypeIds: string[];
    /** @hidden */
    static readonly _funErasure: ApplicativeError<any, any>;
}
/**
 * Type class laws defined for {@link ApplicativeError}.
 *
 * This is an abstract definition. In order to use it in unit testing,
 * the implementor must think of a strategy to evaluate the truthiness
 * of the returned `Equiv` values.
 *
 * Even though in TypeScript the Funfix library is using classes to
 * express these laws, when implementing this class it is recommended
 * that you implement it as a mixin using `implements`, instead of extending
 * it directly with `extends`. See
 * [TypeScript: Mixins]{@link https://www.typescriptlang.org/docs/handbook/mixins.html}
 * for details and note that we already have `applyMixins` defined.
 *
 * We are doing this in order to support multiple inheritance and to
 * avoid inheriting any `static` members. In the Flow definitions (e.g.
 * `.js.flow` files) for Funfix these classes are defined with
 * `interface`, as they are meant to be interfaces that sometimes have
 * default implementations and not classes.
 */
export declare abstract class ApplicativeErrorLaws<F, E> implements ApplicativeLaws<F> {
    /**
     * The {@link Applicative} designated instance for `F`,
     * to be tested.
     */
    readonly F: ApplicativeError<F, E>;
    applicativeErrorRecoverWith<A>(e: E, f: (e: E) => HK<F, A>): Equiv<HK<F, A>>;
    applicativeErrorRecover<A>(e: E, f: (e: E) => A): Equiv<HK<F, A>>;
    recoverWithPure<A>(a: A, f: (e: E) => HK<F, A>): Equiv<HK<F, A>>;
    recoverPure<A>(a: A, f: (e: E) => A): Equiv<HK<F, A>>;
    raiseErrorAttempt(e: E): Equiv<HK<F, Either<E, void>>>;
    pureAttempt<A>(a: A): Equiv<HK<F, Either<E, A>>>;
    /** Mixed-in from {@link ApplicativeLaws.applicativeIdentity}. */
    applicativeIdentity: <A>(fa: HK<F, A>) => Equiv<HK<F, A>>;
    /** Mixed-in from {@link ApplicativeLaws.applicativeHomomorphism}. */
    applicativeHomomorphism: <A, B>(a: A, f: (a: A) => B) => Equiv<HK<F, B>>;
    /** Mixed-in from {@link ApplicativeLaws.applicativeInterchange}. */
    applicativeInterchange: <A, B>(a: A, ff: HK<F, (a: A) => B>) => Equiv<HK<F, B>>;
    /** Mixed-in from {@link ApplicativeLaws.applicativeMap}. */
    applicativeMap: <A, B>(fa: HK<F, A>, f: (a: A) => B) => Equiv<HK<F, B>>;
    /** Mixed-in from {@link ApplicativeLaws.applicativeComposition}. */
    applicativeComposition: <A, B, C>(fa: HK<F, A>, fab: HK<F, (a: A) => B>, fbc: HK<F, (b: B) => C>) => Equiv<HK<F, C>>;
    /** Mixed-in from {@link ApplicativeLaws.applicativeUnit}. */
    applicativeUnit: <A>(a: A) => Equiv<HK<F, A>>;
    /** Mixed-in from {@link FunctorLaws.covariantIdentity}. */
    covariantIdentity: <A>(fa: HK<F, A>) => Equiv<HK<F, A>>;
    /** Mixed-in from {@link FunctorLaws.covariantComposition}. */
    covariantComposition: <A, B, C>(fa: HK<F, A>, f: (a: A) => B, g: (b: B) => C) => Equiv<HK<F, C>>;
    /** Mixed-in from {@link ApplyLaws.applyComposition}. */
    applyComposition: <A, B, C>(fa: HK<F, A>, fab: HK<F, (a: A) => B>, fbc: HK<F, (b: B) => C>) => Equiv<HK<F, C>>;
    /** Mixed-in from {@link ApplyLaws.applyProductConsistency}. */
    applyProductConsistency: <A, B>(fa: HK<F, A>, f: HK<F, (a: A) => B>) => Equiv<HK<F, B>>;
    /** Mixed-in from {@link ApplyLaws.applyMap2Consistency}. */
    applyMap2Consistency: <A, B>(fa: HK<F, A>, f: HK<F, (a: A) => B>) => Equiv<HK<F, B>>;
}
/**
 * Given a {@link Constructor} reference, returns its associated
 * {@link ApplicativeError} instance if it exists, or throws a `NotImplementedError`
 * in case there's no such association.
 *
 * ```typescript
 * import { Eval, ApplicativeError, applicativeErrorOf } from "funfix"
 *
 * const F: ApplicativeError<Option<any>> = applicativeErrorOf(Eval)
 * ```
 */
export declare const applicativeErrorOf: <F, E>(c: Constructor<F>) => ApplicativeError<F, E>;
/**
 * Given an {@link ApplicativeError} instance, returns the
 * {@link ApplicativeErrorLaws} associated with it.
 */
export declare function applicativeErrorLawsOf<F, E>(instance: ApplicativeError<F, E>): ApplicativeErrorLaws<F, E>;