import { NaturalNumber, Type, Number, Kind } from '..';
/**
 * `_$moduloBy` is a type-level function that takes in two natural number types,
 * `A` and `B`, and returns the remainder of `B` divided by `A`.
 *
 * @template A - The number to divide by to calculate the remainder.
 * @template B - The numerator.
 *
 * The parameters are reversed from `_$modulo`. This is useful for partial
 * application, i.e. to test divisibility.
 */
export type _$moduloBy<
/**
 * The number to divide by to calculate the remainder.
 */
A extends number, 
/**
 * The numerator.
 */
B extends number> = NaturalNumber._$modulo<B, A>;
export interface ModuloBy_T<A extends number> extends Kind.Kind {
    f(x: Type._$cast<this[Kind._], number>): Number._$isNatural<typeof x> extends true ? _$moduloBy<A, typeof x> : never;
}
/**
 * `ModuloBy` is a type-level function that takes in two natural number types,
 * `A` and `B`, and returns the remainder of `B` divided by `A`.
 *
 * @template A - The number to divide by to calculate the remainder.
 * @template B - The numerator.
 *
 * The parameters are reversed from `Modulo`. This is useful for partial
 * application, i.e. to test divisibility.
 *
 * ## Usage Examples
 *
 * @example
 * For example, we can use `ModuloBy` to determine the remainder of a natural
 * number divided by another natural number. In this example, `3` and `4` are
 * passed as type arguments to the type-level function:
 *
 * ```ts
 * import { $, NaturalNumber } from "hkt-toolbelt";
 *
 * type ModuloByThree = $<NaturalNumber.ModuloBy, 3>;
 *
 * type Result = $<ModuloByThree, 4>; // 4 % 3 = 1
 * ```
 */
export interface ModuloBy extends Kind.Kind {
    f(x: Type._$cast<this[Kind._], number>): ModuloBy_T<typeof x>;
}
/**
 * Given two natural numbers, return the remainder of the second divided by the
 * first.
 *
 * @param {number} a - The denominator.
 * @param {number} b - The numerator.
 *
 * @example
 * ```ts
 * import { NaturalNumber } from "hkt-toolbelt";
 *
 * const result = NaturalNumber.moduloBy(3)(10)
 * //    ^? 1
 * ```
 */
export declare const moduloBy: Kind._$reify<ModuloBy>;