import type AddFn from "./Add";
import type CompareFn from "./Compare";
import type IsNatFn from "./IsNat";
import type SubFn from "./Sub";
import type { PartialApply } from "../../HKT";

/**
 * Alias for `number` to represent natural numbers.
 */
export type Nat = number;

/***********
 * Methods *
 ***********/
/**
 * Methods for `Nat`.
 */
export namespace Nat {
  /**
   * [Fn] Compare two {@link Nat}s.
   *
   * Sig: `(n: Nat, m: Nat) => Ordering`
   */
  export type Compare = CompareFn;
  /**
   * [Fn] Compare a {@link Nat} with another {@link Nat}.
   *
   * Sig: `[m: Nat](n: Nat) => Ordering`
   */
  export type CompareWith<M extends Nat> = PartialApply<CompareFn, [M], "_1">;
  /**
   * [Fn] Compare a {@link Nat} with another {@link Nat}.
   *
   * Sig: `[n: Nat](m: Nat) => Ordering`
   */
  export type CompareAgainst<N extends Nat> = PartialApply<CompareFn, [N]>;

  /**
   * [Fn] Add two {@link Nat}s.
   *
   * Sig: `(n: Nat, m: Nat) => Nat`
   */
  export type Add2 = AddFn;
  /**
   * [Fn] Add two {@link Nat}s.
   *
   * Sig: `[m: Nat](n: Nat) => Nat`
   */
  export type Add<M extends Nat> = PartialApply<AddFn, [M], "_1">;

  /**
   * [Fn] Subtract two {@link Nat}s.
   *
   * Sig: `(n: Nat, m: Nat) => Nat`
   *
   * **⚠️ Warning:** `n` must be greater than or equal to `m`.
   */
  export type Sub2 = SubFn;
  /**
   * [Fn] Subtract two {@link Nat}s.
   *
   * Sig: `[m: Nat](n: Nat) => Nat`
   *
   * **⚠️ Warning:** `n` must be greater than or equal to `m`.
   */
  export type Sub<M extends Nat> = PartialApply<SubFn, [M], "_1">;
}

/******************
 * Static members *
 ******************/
/**
 * [Fn] Check if a value is {@link Nat}.
 *
 * Sig: `(x: unknown) => boolean`
 */
export type Nat$$IsNat = IsNatFn;