import type { Int } from ".";
import type { Arg0, Arg1, Fn } from "../../HKT";
import type { GT, 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";

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

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