import { $, Term, _, _l, g, n } from './core';
import { False, True } from './bool';

n('ord');

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

export const LT = g('LT', _l(lt => _l(_ => _l(_ => lt))));

export const EQ = g('EQ', _l(_ => _l(eq => _l(_ => eq))));

export const GT = g('GT', _l(_ => _l(_ => _l(gt => gt))));

export const eq = g('eq', _l(l => _l(r => l
  ._(r._(True)._(False)._(False))
  ._(r._(False)._(True)._(False))
  ._(r._(False)._(False)._(True)))));

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

export const toNOrd: (o: Term) => NOrd
  = o => $(o._(_(NOrd.LT))._(_(NOrd.EQ))._(_(NOrd.GT)).reduce());