import type { Nat } from ".";
import type { _CompareDigit } from "./internal/_CompareDigit";
import type { _CompareSDigit } from "./internal/_CompareSDigit";
import type { _CompareStrLength } from "./internal/_CompareStrLength";
import type { SDigit } from "..";
import type { Arg0, Arg1, Fn } from "../../HKT";
import type { AssertOrdering } from "../../helpers";
import type { EQ, Ordering } from "../../typeclass/Ord";

/**
 * Compare two string representations of {@link Nat}s.
 *
 * **⚠️ Warning:** `N` must be of the same length as `M`.
 * @private
 */
type _CompareSNatRec<N extends string, M extends string> =
  N extends `${infer F extends SDigit}${infer R}` ?
    M extends `${infer G extends SDigit}${infer S}` ?
      _CompareSDigit<F, G> extends EQ ?
        _CompareSNatRec<R, S>
      : _CompareSDigit<F, G>
    : never
  : EQ;

/**
 * Compare two {@link Nat}s.
 *
 * Sig: `(n: Nat, m: Nat) => Ordering`
 */
export type Compare<N extends Nat, M extends Nat> = AssertOrdering<
  N extends M ? EQ
  : _CompareStrLength<`${N}`, `${M}`> extends infer O extends Ordering ?
    O extends EQ ?
      _CompareSNatRec<`${N}`, `${M}`>
    : O
  : never
>;

/**
 * [Fn] Compare two {@link Nat}s.
 *
 * Sig: `(n: Nat, m: Nat) => Ordering`
 */
export default interface CompareFn extends Fn<[Nat, Nat], Ordering> {
  def: () => Compare<Arg0<this>, Arg1<this>>;
}