import { _, _l, g, n } from './core';
import { GT, LT } from './ord';
import { False, True, and } from './bool';
import { fromString as _s } from './string';

n('pair');

export const Pair = g('Pair', _l(f => _l(s => _l(p => p._(f)._(s)))));

export const fst = g('fst', _l(p => p._(_l(f => _l(_ => f)))));

export const snd = g('snd', _l(p => p._(_l(_ => _l(s => s)))));

export const first = g('first', _l(t => _l(p => p._(_l(f => _l(s => Pair._(t._(f))._(s)))))));

export const second = g('second', _l(t => _l(p => p._(_l(f => _l(s => Pair._(f)._(t._(s))))))));

export const both = g('both', _l(tf => _l(ts => _l(p => p._(_l(f => _l(s => Pair._(tf._(f))._(ts._(s)))))))));

export const uncurry = g('uncurry', _l(t => _l(p => p._(t))));

export const cmp = g('cmp', _l(fcmp => _l(scmp => uncurry._(_l(lf => _l(ls => uncurry._(_l(rf => _l(rs => fcmp._(lf)._(rf)._(LT)._(scmp._(ls)._(rs))._(GT))))))))));

export const lt = g('lt', _l(fcmp => _l(scmp => uncurry._(_l(lf => _l(ls => uncurry._(_l(rf => _l(rs => fcmp._(lf)._(rf)._(True)._(scmp._(ls)._(rs)._(True)._(False)._(False))._(False))))))))));

export const le = g('le', _l(fcmp => _l(scmp => uncurry._(_l(lf => _l(ls => uncurry._(_l(rf => _l(rs => fcmp._(lf)._(rf)._(True)._(scmp._(ls)._(rs)._(True)._(True)._(False))._(False))))))))));

export const eq = g('eq', _l(feq => _l(seq => uncurry._(_l(lf => _l(ls => uncurry._(_l(rf => _l(rs => and._(feq._(lf)._(rf))._(seq._(ls)._(rs)))))))))));

export const ge = g('ge', _l(fcmp => _l(scmp => uncurry._(_l(lf => _l(ls => uncurry._(_l(rf => _l(rs => fcmp._(lf)._(rf)._(False)._(scmp._(ls)._(rs)._(False)._(True)._(True))._(True))))))))));

export const gt = g('gt', _l(fcmp => _l(scmp => uncurry._(_l(lf => _l(ls => uncurry._(_l(rf => _l(rs => fcmp._(lf)._(rf)._(False)._(scmp._(ls)._(rs)._(False)._(False)._(True))._(True))))))))));