import { toNative as $$, L, P, _, fromNative as __ } from './core';
import { Bool, False, True } from './bool';

export type Ord = L<<T extends P>(lt: T) => L<(eq: T) => L<(gt: T) => T>>>;

export const enum NOrd {
  LT,
  EQ,
  GT,
};

export const LT: Ord
  = _(lt => _(_eq => _(_gt => lt))) as Ord;

export const EQ: Ord
  = _(_lt => _(eq => _(_gt => eq)));

export const GT: Ord
  = _(_lt => _(_eq => _(gt => gt)));

export const eq: L<(l: Ord) => L<(r: Ord) => Bool>>
  = _(l => _(r => l
    ._(r._(True)._(False)._(False))
    ._(r._(False)._(True)._(False))
    ._(r._(False)._(False)._(True))));

export const fromNOrd: (b: NOrd) => Ord
  = o => o === NOrd.LT ? LT : o === NOrd.EQ ? EQ : GT;

export const toNOrd: (b: Ord) => NOrd
  = o => $$(o._(__(NOrd.LT))._(__(NOrd.EQ))._(__(NOrd.GT)));