import { L, P, _ } from './core';
import { GT, LT, Ord } from './ord';
import { Bool, False, True, and } from './bool';
import { Nil, concat, cons } from './list';
import { String, fromString as _s } from './string';

export type Pair<F extends P, S extends P> = L<<R extends P>(f: L<(f: F) => L<(s: S) => R>>) => R>;

export const Pair: L<<F extends P, S extends P>(f: F) => L<(s: S) => Pair<F, S>>>
  = _(<F extends P, S extends P>(f: F) =>
    _((s: S) =>
      _(<R extends P>(p: L<(f: F) => L<(s: S) => R>>) => p(f)(s))));

export const fst: L<<F extends P, S extends P>(p: Pair<F, S>) => F>
  = _(p => p(_(f => _(_s => f))));

export const snd: L<<F extends P, S extends P>(p: Pair<F, S>) => S>
  = _(p => p(_(_f => _(s => s))));

export const first: L<<F extends P, FR extends P, S extends P>(t: L<(f: F) => FR>) => L<(p: Pair<F, S>) => Pair<FR, S>>>
  = _(<F extends P, FR extends P>(t: L<(f: F) => FR>) =>
    _(<S extends P>(p: Pair<F, S>) => p(_(f => _(s => Pair(t(f))(s))))));

export const second: L<<F extends P, S extends P, SR extends P>(t: L<(s: S) => SR>) => L<(p: Pair<F, S>) => Pair<F, SR>>>
  = _(<S extends P, SR extends P>(t: L<(s: S) => SR>) =>
    _(<F extends P>(p: Pair<F, S>) => p(_(f => _(s => Pair(f)(t(s)))))));

export const both: L<<F extends P, FR extends P, S extends P, SR extends P>(tf: L<(f: F) => FR>) => L<(ts: L<(s: S) => SR>) => L<(p: Pair<F, S>) => Pair<FR, SR>>>>
  = _(<F extends P, FR extends P>(tf: L<(f: F) => FR>) =>
    _(<S extends P, SR extends P>(ts: L<(s: S) => SR>) =>
      _((p: Pair<F, S>) => p(_(f => _(s => Pair(tf(f))(ts(s))))))));

export const uncurry: L<<F extends P, S extends P, R extends P>(t: L<(f: F) => L<(s: S) => R>>) => L<(p: Pair<F, S>) => R>>
  = _(<F extends P, S extends P, R extends P>(t: L<(f: F) => L<(s: S) => R>>) =>
    _((p: Pair<F, S>) => p(t)));

export const cmp: L<<F extends P, S extends P>(fcmp: L<(l: F) => L<(r: F) => Ord>>) => L<(scmp: L<(l: S) => L<(r: S) => Ord>>) => L<(l: Pair<F, S>) => L<(r: Pair<F, S>) => Ord>>>>
  = _(<F extends P, S extends P>(fcmp: L<(l: F) => L<(r: F) => Ord>>) =>
    _((scmp: L<(l: S) => L<(r: S) => Ord>>) =>
      uncurry(_((lf: F) => _((ls: S) =>
        uncurry(_((rf: F) => _((rs: S) =>
          fcmp(lf)(rf)(LT)(scmp(ls)(rs))(GT)))))))));

export const lt: L<<F extends P, S extends P>(fcmp: L<(l: F) => L<(r: F) => Ord>>) => L<(scmp: L<(l: S) => L<(r: S) => Bool>>) => L<(l: Pair<F, S>) => L<(r: Pair<F, S>) => Bool>>>>
  = _(<F extends P, S extends P>(fcmp: L<(l: F) => L<(r: F) => Ord>>) =>
    _((scmp: L<(l: S) => L<(r: S) => Ord>>) =>
      uncurry(_((lf: F) => _((ls: S) =>
        uncurry(_((rf: F) => _((rs: S) =>
          fcmp(lf)(rf)(True)(scmp(ls)(rs)(True)(False)(False))(False)))))))));

export const le: L<<F extends P, S extends P>(fcmp: L<(l: F) => L<(r: F) => Ord>>) => L<(scmp: L<(l: S) => L<(r: S) => Bool>>) => L<(l: Pair<F, S>) => L<(r: Pair<F, S>) => Bool>>>>
  = _(<F extends P, S extends P>(fcmp: L<(l: F) => L<(r: F) => Ord>>) =>
    _((scmp: L<(l: S) => L<(r: S) => Ord>>) =>
      uncurry(_((lf: F) => _((ls: S) =>
        uncurry(_((rf: F) => _((rs: S) =>
          fcmp(lf)(rf)(True)(scmp(ls)(rs)(True)(True)(False))(False)))))))));

export const eq: L<<F extends P, S extends P>(feq: L<(l: F) => L<(r: F) => Bool>>) => L<(seq: L<(l: S) => L<(r: S) => Bool>>) => L<(l: Pair<F, S>) => L<(r: Pair<F, S>) => Bool>>>>
  = _(<F extends P, S extends P>(feq: L<(l: F) => L<(r: F) => Bool>>) =>
    _((seq: L<(l: S) => L<(r: S) => Bool>>) =>
      uncurry(_((lf: F) => _((ls: S) =>
        uncurry(_((rf: F) => _((rs: S) =>
          and(feq(lf)(rf))(seq(ls)(rs))))))))));

export const ge: L<<F extends P, S extends P>(fcmp: L<(l: F) => L<(r: F) => Ord>>) => L<(scmp: L<(l: S) => L<(r: S) => Bool>>) => L<(l: Pair<F, S>) => L<(r: Pair<F, S>) => Bool>>>>
  = _(<F extends P, S extends P>(fcmp: L<(l: F) => L<(r: F) => Ord>>) =>
    _((scmp: L<(l: S) => L<(r: S) => Ord>>) =>
      uncurry(_((lf: F) => _((ls: S) =>
        uncurry(_((rf: F) => _((rs: S) =>
          fcmp(lf)(rf)(False)(scmp(ls)(rs)(False)(True)(True))(True)))))))));

export const gt: L<<F extends P, S extends P>(fcmp: L<(l: F) => L<(r: F) => Ord>>) => L<(scmp: L<(l: S) => L<(r: S) => Bool>>) => L<(l: Pair<F, S>) => L<(r: Pair<F, S>) => Bool>>>>
  = _(<F extends P, S extends P>(fcmp: L<(l: F) => L<(r: F) => Ord>>) =>
    _((scmp: L<(l: S) => L<(r: S) => Ord>>) =>
      uncurry(_((lf: F) => _((ls: S) =>
        uncurry(_((rf: F) => _((rs: S) =>
          fcmp(lf)(rf)(False)(scmp(ls)(rs)(False)(False)(True))(True)))))))));

export const show: L<<F extends P, S extends P>(fshow: L<(f: F) => String>) => L<(sshow: L<(s: S) => String>) => L<(p: Pair<F, S>) => String>>>
  = _(<F extends P>(fshow: L<(f: F) => String>) =>
    _(<S extends P>(sshow: L<(s: S) => String>) =>
      uncurry(_((f: F) => _((s: S) => concat(cons(_s('('))(cons(fshow(f))(cons(_s(', '))(cons(sshow(s))(cons(_s(')'))(Nil)))))))))));