import { $, $N, Kind, NaturalNumber, Conditional, List, Function } from '..';
/**
 * Check whether a natural number `N` is divisible by another number `M`.
 *
 * i.e. determine whether `N % M === 0`.
 *
 * @template M - The number to divide by.
 * @template N - The number to check divisibility for.
 *
 * This function 'lifts' the modulo parameters (M and N) out of the pipe via
 * the curry and uncurry operators.
 *
 * For optimal performance, this should be implemented as a 'native' type-level
 * function - however this example is pedagogically valuable for demonstrating
 * the lifting technique.
 */
type DivisibleBy = $N<Kind.Curry, [
    2,
    $<Kind.Pipe, [
        $<Kind.Uncurry, NaturalNumber.ModuloBy>,
        $<Conditional.Equals, 0>
    ]>
]>;
/**
 * A type-level function that returns "FizzBuzz" if the input is divisible by
 * both 3 and 5, "Fizz" if the input is divisible by 3, "Buzz" if the input is
 * divisible by 5, and the input otherwise.
 *
 * This function uses the `Conditional.If` type-level function to encode an
 * if-then-else statement.
 *
 * @template N - The number to compute the FizzBuzz result for.
 *
 * @example
 * ```ts
 * import { $, NaturalNumberTheory } from "hkt-toolbelt"
 *
 * type R15 = $<NaturalNumberTheory.FizzBuzz, 15> // "FizzBuzz"
 * type R4 = $<NaturalNumberTheory.FizzBuzz, 4> // 4
 * ```
 */
export type FizzBuzz = $N<Conditional.If, [
    $<DivisibleBy, 15>,
    $<Function.Constant, 'FizzBuzz'>,
    $N<Conditional.If, [
        $<DivisibleBy, 3>,
        $<Function.Constant, 'Fizz'>,
        $N<Conditional.If, [
            $<DivisibleBy, 5>,
            $<Function.Constant, 'Buzz'>,
            Function.Identity
        ]>
    ]>
]>;
/**
 * A type-level function that returns a list of the FizzBuzz results for the
 * first `N` natural numbers, from 1 to `N` inclusive.
 *
 * @template N - The number of FizzBuzz results to compute.
 *
 * @example
 * ```ts
 * import { $, NaturalNumberTheory } from "hkt-toolbelt"
 *
 * // ["1", "2", "Fizz", "4", "Buzz", "Fizz", "7", "8", "Fizz", "Buzz"]
 * type R10 = $<NaturalNumberTheory.FizzBuzzSequence, 10>
 * ```
 */
export type FizzBuzzSequence = $<Kind.Pipe, [
    List.Times,
    $<List.Map, $<Kind.Pipe, [NaturalNumber.Increment, FizzBuzz]>>
]>;
export {};