import type { Int } from ".";
import type { Arg0, Arg1, Fn } from "../../HKT";
import type { LT } from "../../typeclass/Ord";
import type { Abs } from "../Abs";
import type { IsPos } from "../IsPos";
import type { Add as AddNat } from "../Nat/Add";
import type { Compare as CompareNat } from "../Nat/Compare";
import type { Sub as SubNat } from "../Nat/Sub";
import type { _StrToNum } from "../internal/_StrToNum";

/**
 * Add two {@link Int}s.
 *
 * Sig: `(n: Int, m: Int) => Int`
 */
export type Add<N extends Int, M extends Int> =
  Int extends N | M ? number
  : IsPos<N> extends true ?
    IsPos<M> extends true ? AddNat<N, M>
    : CompareNat<N, Abs<M>> extends LT ? _StrToNum<`-${SubNat<Abs<M>, N>}`>
    : SubNat<N, Abs<M>>
  : IsPos<M> extends true ?
    CompareNat<M, Abs<N>> extends LT ?
      _StrToNum<`-${SubNat<Abs<N>, M>}`>
    : SubNat<M, Abs<N>>
  : _StrToNum<`-${AddNat<Abs<N>, Abs<M>>}`>;

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