import { describe, expect, it } from '@jest/globals';
import { $, Term, _, _l, g, n, undef } from '../src/core';
import { toNOrd as $o, NOrd } from '../src/ord';
import { toBoolean as $b, iif } from '../src/bool';
import { toNumber as $n, Succ, Zero, fromNumber as _n, fromNumber as _nn, cmp as cmpn, eq as eqn, even, gt as ngt, odd, succ, sum } from '../src/num';
import { toArray as $a, Cons, Nil, fromArray as _a, all, any, append, cmp, concat, cons, eq, filter, foldl, foldlz, foldr, foldrz, ge, get, gt, head, intersperse, iterate, le, len, lt, map, nul, set, singleton, snoc, tail, update } from '../src/list';
import { toChar as $c } from '../src/char';
import { toString as $s } from '../src/string';
import { show as nshow } from '../src/num.show';
import { show } from '../src/list.show';

n('list.spec');

describe('List', () => {
  const infinite: Term = g('infinite', iterate._(Succ)._(Zero));

  const _na: (xs: number[]) => Term = xs => !xs.length ? Nil : Cons._(_n(xs[0]))._(_(() => _na(xs.slice(1))));

  const $na: (xs: Term) => number[] = xs => $(xs._(_([]))._(x => xs => _(({ x, xs }) => _([$n(x), ...$na(xs)]))));

  describe('toArray', () => {
    it('converts []', () => {
      expect($a(Nil)).toEqual([]);
    });

    it('converts [0]', () => {
      expect($a(Cons._(_n(0))._(Nil)).map($n)).toEqual([0]);
    });

    it('converts [0, 1]', () => {
      expect($a(Cons._(_n(0))._(Cons._(_n(1))._(Nil))).map($n)).toEqual([0, 1]);
    });
  });

  describe('fromArray', () => {
    it('converts []', () => {
      expect($a(_a([]))).toEqual([]);
    });

    it('converts [0]', () => {
      expect($a(_a([0].map(_n))).map($n)).toEqual([0]);
    });

    it('converts 2', () => {
      expect($a(_a([0, 1].map(_n))).map($n)).toEqual([0, 1]);
    });
  });

  describe('cons', () => {
    it('0 cons Nil is [0]', () => {
      expect($na(cons._(_n(0))._(Nil))).toEqual([0]);
    });

    it('0 cons [1] is [0, 1]', () => {
      expect($na(cons._(_n(0))._(_na([1])))).toEqual([0, 1]);
    });

    it('0 cons [1, 2] is [0, 1, 2]', () => {
      expect($na(cons._(_n(0))._(_na([1, 2])))).toEqual([0, 1, 2]);
    });

    it('handles infinite lists', () => {
      expect($n(cons._(_n(0))._(infinite)._(undef)._(x => _ => x))).toBe(0);
    });
  });

  describe('snoc', () => {
    it('Nil snoc 0 is [0]', () => {
      expect($na(snoc._(Nil)._(_n(0)))).toEqual([0]);
    });

    it('[1] snoc 0 is [1, 0]', () => {
      expect($na(snoc._(_na([1]))._(_n(0)))).toEqual([1, 0]);
    });

    it('[1, 2] snoc 0 is [1, 2, 0]', () => {
      expect($na(snoc._(_na([1, 2]))._(_n(0)))).toEqual([1, 2, 0]);
    });

    it('handles infinite lists', () => {
      expect($n(snoc._(infinite)._(_n(0))._(undef)._(x => _ => x))).toBe(0);
    });
  });

  describe('nul', () => {
    it('nul Nil is True', () => {
      expect($b(nul._(_na([])))).toEqual(true);
    });

    it('nul [1] is False', () => {
      expect($b(nul._(_na([1])))).toEqual(false);
    });

    it('nul [1, 2] is False', () => {
      expect($b(nul._(_na([1, 2])))).toEqual(false);
    });

    it('handles infinite lists', () => {
      expect($b(nul._(infinite))).toEqual(false);
    });
  });

  describe('len', () => {
    it('len Nil is 0', () => {
      expect($n(len._(_na([])))).toEqual(0);
    });

    it('len [1] is 1', () => {
      expect($n(len._(_na([1])))).toEqual(1);
    });

    it('len [1, 2] is 2', () => {
      expect($n(len._(_na([1, 2])))).toEqual(2);
    });

    it('handles infinite lists', () => {
      expect($b(ngt._(len._(infinite))._(Zero))).toEqual(true);
    });

    it('ignores items', () => {
      expect($n(len._(cons._(undef)._(cons._(undef)._(Nil))))).toEqual(2);
    });
  });

  describe('singleton', () => {
    it('singleton 0 is [0]', () => {
      expect($na(singleton._(_n(0)))).toEqual([0]);
    });
  });

  describe('append', () => {
    it('Nil append Nil is Nil', () => {
      expect($na(append._(Nil)._(Nil))).toEqual([]);
    });

    it('[0] append [1] is [0, 1]', () => {
      expect($na(append._(_na([0]))._(_na([1])))).toEqual([0, 1]);
    });

    it('[0, 1] append [2, 3] is [0, 1, 2, 3]', () => {
      expect($na(append._(_na([0, 1]))._(_na([2, 3])))).toEqual([0, 1, 2, 3]);
    });

    it('handles infinite lists', () => {
      expect($n(append._(infinite)._(infinite)._(undef)._(x => _ => x))).toBe(0);
    });
  });

  describe('concat', () => {
    it('concat [Nil, Nil, Nil] is Nil', () => {
      expect($na(concat._(cons._(Nil)._(cons._(Nil)._(cons._(Nil)._(Nil)))))).toEqual([]);
    });

    it('concat [[0], [1], [2]] is [0, 1, 2]', () => {
      expect($na(concat._(cons._(_na([0]))._(cons._(_na([1]))._(cons._(_na([2]))._(Nil)))))).toEqual([0, 1, 2]);
    });

    it('concat [[0, 1], [2, 3], [4, 5]] is [0, 1, 2, 3, 4, 5]', () => {
      expect($na(concat._(cons._(_na([0, 1]))._(cons._(_na([2, 3]))._(cons._(_na([4, 5]))._(Nil)))))).toEqual([0, 1, 2, 3, 4, 5]);
    });

    it('handles infinite lists', () => {
      const dinfinite: Term = g('dinfinite', _(() => cons._(infinite)._(dinfinite)));
      expect($n(concat._(dinfinite)._(undef)._(x => _ => x))).toBe(0);
    });
  });

  // describe('repeat', () => {
  //   it('repeat 0 is [0, 0, 0, ...]', () => {
  //     expect($na(
  //       repeat._(_n(0))<List<Num>>(l((x0: Num) => l((x1s: List<Num>) =>
  //         x1s<List<Num>>(l((x1: Num) => l((x2s: List<Num>) =>
  //           x2s<List<Num>>(l((x2: Num) => l((_xrs: List<Num>): List<Num> => cons._(x0)._(cons._(x1)._(cons._(x2)._(Nil)))))))))))))).toEqual([0, 0, 0]);
  //   });
  // });

  // describe('iterate', () => {
  //   it('iterate succ 0 is [0, 1, 2, ...]', () => {
  //     expect($na(
  //       iterate._(_n(0))<List<Num>>(l((x0: Num) => l((x1s: List<Num>) =>
  //         x1s<List<Num>>(l((x1: Num) => l((x2s: List<Num>) =>
  //           x2s<List<Num>>(l((x2: Num) => l((_xrs: List<Num>): List<Num> => cons._(x0)._(cons._(x1)._(cons._(x2)._(Nil)))))))))))))).toEqual([0, 1, 2]);
  //   });
  // });

  describe('head', () => {
    it('returns nothing from Nil', () => {
      expect(() => $(head._(Nil))).toThrow();
    });

    it('returns only item', () => {
      expect($n(head._(_na([0])))).toBe(0);
    });

    it('returns first item', () => {
      expect($n(head._(_na([0, 1])))).toBe(0);
    });

    it('handles infinite lists', () => {
      expect($n(head._(infinite))).toBe(0);
    });
  });

  describe('tail', () => {
    it('drops nothing from Nil', () => {
      expect(() => $na(tail._(Nil))).toThrow();
    });

    it('drops only item', () => {
      expect($na(tail._(_na([0])))).toEqual([]);
    });

    it('drops first item', () => {
      expect($na(tail._(_na([0, 1])))).toEqual([1]);
    });

    it('handles infinite lists', () => {
      expect($n(head._(tail._(infinite)))).toBe(1);
    });
  });

  describe('foldl', () => {
    it('folds Nil', () => {
      expect($n(foldl._(sum)._(Zero)._(_na([])))).toBe(0);
    });

    it('folds single item', () => {
      expect($n(foldl._(sum)._(Zero)._(_na([1])))).toBe(1);
    });

    it('folds several items', () => {
      expect($n(foldl._(sum)._(Zero)._(_na([1, 2])))).toBe(3);
    });
  });

  describe('foldlz', () => {
    it('does not fold Nil', () => {
      expect(() => $n(foldlz._(sum)._(Nil))).toThrow();
    });

    it('folds single item', () => {
      expect($n(foldlz._(sum)._(_na([1])))).toBe(1);
    });

    it('folds several items', () => {
      expect($n(foldlz._(sum)._(_na([1, 2])))).toBe(3);
    });
  });

  describe('foldr', () => {
    it('folds Nil', () => {
      expect($n(foldr._(sum)._(Zero)._(_na([])))).toBe(0);
    });

    it('folds single item', () => {
      expect($n(foldr._(sum)._(Zero)._(_na([1])))).toBe(1);
    });

    it('folds several items', () => {
      expect($n(foldr._(sum)._(Zero)._(_na([1, 2])))).toBe(3);
    });

    it('handles infinite lists', () => {
      expect($n(
        foldr
          ._(x => a => sum._(x)._(iif._(eqn._(_n(5))._(x))._(Zero)._(a)))
          ._(Zero)
          ._(infinite)))
        .toBe(15);
    });
  });

  describe('foldrz', () => {
    it('does not fold Nil', () => {
      expect(() => $n(foldrz._(sum)._(Nil))).toThrow();
    });

    it.failing('folds single item', () => {
      expect($n(foldrz._(sum)._(_na([1])))).toBe(1);
    });

    it.failing('folds several items', () => {
      expect($n(foldrz._(sum)._(_na([1, 2])))).toBe(3);
    });

    it.failing('handles infinite lists', () => {
      expect($n(
        foldrz
          ._(x => a => sum._(x)._(iif._(eqn._(_n(5))._(x))._(Zero)._(a)))
          ._(infinite)))
        .toBe(15);
    });
  });

  describe('cmp', () => {
    it('Nil cmp Nil is EQ', () => {
      expect($o(cmp._(cmpn)._(_na([]))._(_na([])))).toEqual(NOrd.EQ);
    });

    it('Nil cmp [0, 1, 2] is LT', () => {
      expect($o(cmp._(cmpn)._(_na([]))._(_na([0, 1, 2])))).toEqual(NOrd.LT);
    });

    it('[0, 1, 2] cmp Nil is GT', () => {
      expect($o(cmp._(cmpn)._(_na([0, 1, 2]))._(_na([])))).toEqual(NOrd.GT);
    });

    it('[0] cmp [0, 1, 2] is LT', () => {
      expect($o(cmp._(cmpn)._(_na([0]))._(_na([0, 1, 2])))).toEqual(NOrd.LT);
    });

    it('[0, 1, 2] cmp [0] is GT', () => {
      expect($o(cmp._(cmpn)._(_na([0, 1, 2]))._(_na([0])))).toEqual(NOrd.GT);
    });

    it('[1, 2, 0] cmp [0, 1, 2] is GT', () => {
      expect($o(cmp._(cmpn)._(_na([1, 2, 0]))._(_na([0, 1, 2])))).toEqual(NOrd.GT);
    });

    it('[0, 1, 2] cmp [1, 2, 0] is LT', () => {
      expect($o(cmp._(cmpn)._(_na([0, 1, 2]))._(_na([1, 2, 0])))).toEqual(NOrd.LT);
    });

    it('[0, 1, 2] cmp [0, 1, 2] is EQ', () => {
      expect($o(cmp._(cmpn)._(_na([0, 1, 2]))._(_na([0, 1, 2])))).toEqual(NOrd.EQ);
    });

    it('handles infinite lists', () => {
      expect($o(cmp._(cmpn)._(_na([0, 1, 2]))._(infinite))).toEqual(NOrd.LT);
      expect($o(cmp._(cmpn)._(infinite)._(_na([0, 1, 2])))).toEqual(NOrd.GT);
    });
  });

  describe('lt', () => {
    it('Nil lt Nil is False', () => {
      expect($b(lt._(cmpn)._(_na([]))._(_na([])))).toEqual(false);
    });

    it('Nil lt [0, 1, 2] is True', () => {
      expect($b(lt._(cmpn)._(_na([]))._(_na([0, 1, 2])))).toEqual(true);
    });

    it('[0, 1, 2] lt Nil is False', () => {
      expect($b(lt._(cmpn)._(_na([0, 1, 2]))._(_na([])))).toEqual(false);
    });

    it('[0] lt [0, 1, 2] is True', () => {
      expect($b(lt._(cmpn)._(_na([0]))._(_na([0, 1, 2])))).toEqual(true);
    });

    it('[0, 1, 2] lt [0] is False', () => {
      expect($b(lt._(cmpn)._(_na([0, 1, 2]))._(_na([0])))).toEqual(false);
    });

    it('[1, 2, 0] lt [0, 1, 2] is False', () => {
      expect($b(lt._(cmpn)._(_na([1, 2, 0]))._(_na([0, 1, 2])))).toEqual(false);
    });

    it('[0, 1, 2] lt [1, 2, 0] is True', () => {
      expect($b(lt._(cmpn)._(_na([0, 1, 2]))._(_na([1, 2, 0])))).toEqual(true);
    });

    it('[0, 1, 2] lt [0, 1, 2] is False', () => {
      expect($b(lt._(cmpn)._(_na([0, 1, 2]))._(_na([0, 1, 2])))).toEqual(false);
    });

    it('handles infinite lists', () => {
      expect($b(lt._(cmpn)._(_na([0, 1, 2]))._(infinite))).toEqual(true);
      expect($b(lt._(cmpn)._(infinite)._(_na([0, 1, 2])))).toEqual(false);
    });
  });

  describe('le', () => {
    it('Nil le Nil is True', () => {
      expect($b(le._(cmpn)._(_na([]))._(_na([])))).toEqual(true);
    });

    it('Nil le [0, 1, 2] is True', () => {
      expect($b(le._(cmpn)._(_na([]))._(_na([0, 1, 2])))).toEqual(true);
    });

    it('[0, 1, 2] le Nil is False', () => {
      expect($b(le._(cmpn)._(_na([0, 1, 2]))._(_na([])))).toEqual(false);
    });

    it('[0] le [0, 1, 2] is True', () => {
      expect($b(le._(cmpn)._(_na([0]))._(_na([0, 1, 2])))).toEqual(true);
    });

    it('[0, 1, 2] le [0] is False', () => {
      expect($b(le._(cmpn)._(_na([0, 1, 2]))._(_na([0])))).toEqual(false);
    });

    it('[1, 2, 0] le [0, 1, 2] is False', () => {
      expect($b(le._(cmpn)._(_na([1, 2, 0]))._(_na([0, 1, 2])))).toEqual(false);
    });

    it('[0, 1, 2] le [1, 2, 0] is True', () => {
      expect($b(le._(cmpn)._(_na([0, 1, 2]))._(_na([1, 2, 0])))).toEqual(true);
    });

    it('[0, 1, 2] le [0, 1, 2] is True', () => {
      expect($b(le._(cmpn)._(_na([0, 1, 2]))._(_na([0, 1, 2])))).toEqual(true);
    });

    it('handles infinite lists', () => {
      expect($b(le._(cmpn)._(_na([0, 1, 2]))._(infinite))).toEqual(true);
      expect($b(le._(cmpn)._(infinite)._(_na([0, 1, 2])))).toEqual(false);
    });
  });

  describe('eq', () => {
    it('Nil eq Nil is True', () => {
      expect($b(eq._(eqn)._(_na([]))._(_na([])))).toEqual(true);
    });

    it('Nil eq [0, 1, 2] is False', () => {
      expect($b(eq._(eqn)._(_na([]))._(_na([0, 1, 2])))).toEqual(false);
    });

    it('[0, 1, 2] eq Nil is False', () => {
      expect($b(eq._(eqn)._(_na([0, 1, 2]))._(_na([])))).toEqual(false);
    });

    it('[0] eq [0, 1, 2] is False', () => {
      expect($b(eq._(eqn)._(_na([0]))._(_na([0, 1, 2])))).toEqual(false);
    });

    it('[0, 1, 2] eq [0] is False', () => {
      expect($b(eq._(eqn)._(_na([0, 1, 2]))._(_na([0])))).toEqual(false);
    });

    it('[1, 2, 0] eq [0, 1, 2] is False', () => {
      expect($b(eq._(eqn)._(_na([1, 2, 0]))._(_na([0, 1, 2])))).toEqual(false);
    });

    it('[0, 1, 2] eq [1, 2, 0] is False', () => {
      expect($b(eq._(eqn)._(_na([0, 1, 2]))._(_na([1, 2, 0])))).toEqual(false);
    });

    it('[0, 1, 2] eq [0, 1, 2] is True', () => {
      expect($b(eq._(eqn)._(_na([0, 1, 2]))._(_na([0, 1, 2])))).toEqual(true);
    });

    it('handles infinite lists', () => {
      expect($b(eq._(eqn)._(_na([0, 1, 2]))._(infinite))).toEqual(false);
      expect($b(eq._(eqn)._(infinite)._(_na([0, 1, 2])))).toEqual(false);
    });
  });

  describe('ge', () => {
    it('Nil ge Nil is True', () => {
      expect($b(ge._(cmpn)._(_na([]))._(_na([])))).toEqual(true);
    });

    it('Nil ge [0, 1, 2] is False', () => {
      expect($b(ge._(cmpn)._(_na([]))._(_na([0, 1, 2])))).toEqual(false);
    });

    it('[0, 1, 2] ge Nil is True', () => {
      expect($b(ge._(cmpn)._(_na([0, 1, 2]))._(_na([])))).toEqual(true);
    });

    it('[0] ge [0, 1, 2] is False', () => {
      expect($b(ge._(cmpn)._(_na([0]))._(_na([0, 1, 2])))).toEqual(false);
    });

    it('[0, 1, 2] ge [0] is True', () => {
      expect($b(ge._(cmpn)._(_na([0, 1, 2]))._(_na([0])))).toEqual(true);
    });

    it('[1, 2, 0] ge [0, 1, 2] is True', () => {
      expect($b(ge._(cmpn)._(_na([1, 2, 0]))._(_na([0, 1, 2])))).toEqual(true);
    });

    it('[0, 1, 2] ge [1, 2, 0] is False', () => {
      expect($b(ge._(cmpn)._(_na([0, 1, 2]))._(_na([1, 2, 0])))).toEqual(false);
    });

    it('[0, 1, 2] ge [0, 1, 2] is True', () => {
      expect($b(ge._(cmpn)._(_na([0, 1, 2]))._(_na([0, 1, 2])))).toEqual(true);
    });

    it('handles infinite lists', () => {
      expect($b(ge._(cmpn)._(_na([0, 1, 2]))._(infinite))).toEqual(false);
      expect($b(ge._(cmpn)._(infinite)._(_na([0, 1, 2])))).toEqual(true);
    });
  });

  describe('gt', () => {
    it('Nil gt Nil is False', () => {
      expect($b(gt._(cmpn)._(_na([]))._(_na([])))).toEqual(false);
    });

    it('Nil gt [0, 1, 2] is False', () => {
      expect($b(gt._(cmpn)._(_na([]))._(_na([0, 1, 2])))).toEqual(false);
    });

    it('[0, 1, 2] gt Nil is True', () => {
      expect($b(gt._(cmpn)._(_na([0, 1, 2]))._(_na([])))).toEqual(true);
    });

    it('[0] gt [0, 1, 2] is False', () => {
      expect($b(gt._(cmpn)._(_na([0]))._(_na([0, 1, 2])))).toEqual(false);
    });

    it('[0, 1, 2] gt [0] is True', () => {
      expect($b(gt._(cmpn)._(_na([0, 1, 2]))._(_na([0])))).toEqual(true);
    });

    it('[1, 2, 0] gt [0, 1, 2] is True', () => {
      expect($b(gt._(cmpn)._(_na([1, 2, 0]))._(_na([0, 1, 2])))).toEqual(true);
    });

    it('[0, 1, 2] gt [1, 2, 0] is False', () => {
      expect($b(gt._(cmpn)._(_na([0, 1, 2]))._(_na([1, 2, 0])))).toEqual(false);
    });

    it('[0, 1, 2] gt [0, 1, 2] is False', () => {
      expect($b(gt._(cmpn)._(_na([0, 1, 2]))._(_na([0, 1, 2])))).toEqual(false);
    });

    it('handles infinite lists', () => {
      expect($b(gt._(cmpn)._(_na([0, 1, 2]))._(infinite))).toEqual(false);
      expect($b(gt._(cmpn)._(infinite)._(_na([0, 1, 2])))).toEqual(true);
    });
  });

  describe('map', () => {
    it('maps Nil', () => {
      expect($na(map._(succ)._(_na([])))).toEqual([]);
    });

    it('maps only item', () => {
      expect($na(map._(succ)._(_na([0])))).toEqual([1]);
    });

    it('maps several items', () => {
      expect($na(map._(succ)._(_na([0, 1])))).toEqual([1, 2]);
    });

    it('handles infinite lists', () => {
      expect($n(head._(map._(succ)._(infinite)))).toBe(1);
    });
  });

  describe('filter', () => {
    it('filter Nil', () => {
      expect($na(filter._(odd)._(_na([])))).toEqual([]);
    });

    it('filters only item', () => {
      expect($na(filter._(odd)._(_na([])))).toEqual([]);
    });

    it('filters several items', () => {
      expect($na(filter._(odd)._(_na([0, 1])))).toEqual([1]);
    });

    it('handles infinite lists', () => {
      expect($n(head._(filter._(odd)._(infinite)))).toBe(1);
    });
  });

  describe('any', () => {
    it('any Nil is False', () => {
      expect($b(any._(odd)._(_na([])))).toEqual(false);
    });

    it('any for no matching item is False', () => {
      expect($b(any._(odd)._(_na([0, 2])))).toEqual(false);
    });

    it('any for matching item is True', () => {
      expect($b(any._(odd)._(_na([0, 1, 2])))).toEqual(true);
    });

    it('handles infinite lists', () => {
      expect($b(any._(odd)._(infinite))).toEqual(true);
    });
  });

  describe('all', () => {
    it('all Nil is True', () => {
      expect($b(all._(even)._(_na([])))).toEqual(true);
    });

    it('all for non-matching item is False', () => {
      expect($b(all._(even)._(_na([0, 1, 2])))).toEqual(false);
    });

    it('all for no non-matching item is True', () => {
      expect($b(all._(even)._(_na([0, 2])))).toEqual(true);
    });

    it('handles infinite lists', () => {
      expect($b(all._(even)._(infinite))).toEqual(false);
    });
  });

  describe('get', () => {
    it('returns nothing from Nil', () => {
      expect(() => $n(get._(_n(0))._(Nil))).toThrow();
    });

    it('returns nothing with out of bounds index', () => {
      expect(() => $n(get._(_n(100))._(_na([0, 1, 2, 3])))).toThrow();
    });

    it('[0, 1, 2, 3][0] is 0', () => {
      expect($n(get._(_n(0))._(_na([0, 1, 2, 3])))).toBe(0);
    });

    it('[0, 1, 2, 3][1] is 1', () => {
      expect($n(get._(_n(1))._(_na([0, 1, 2, 3])))).toBe(1);
    });

    it('[0, 1, 2, 3][2] is 2', () => {
      expect($n(get._(_n(2))._(_na([0, 1, 2, 3])))).toBe(2);
    });

    it('[0, 1, 2, 3][3] get 3 is 3', () => {
      expect($n(get._(_n(3))._(_na([0, 1, 2, 3])))).toBe(3);
    });

    it('handles infinite lists', () => {
      expect($n(get._(_n(4))._(infinite))).toBe(4);
    });
  });

  describe('set', () => {
    it('can not update Nil', () => {
      expect(() => $na(set._(_n(10))._(_n(0))._(Nil))).toThrow();
    });

    it('can not update out of bounds index', () => {
      expect(() => $na(set._(_n(10))._(_n(100))._(_na([0, 1, 2, 3])))).toThrow();
    });

    it('[0, 1, 2, 3][0] = 10 is [10, 1, 2, 3]', () => {
      expect($na(set._(_n(10))._(_n(0))._(_na([0, 1, 2, 3])))).toEqual([10, 1, 2, 3]);
    });

    it('[0, 1, 2, 3][1] = 10 is [0, 10, 2, 3]', () => {
      expect($na(set._(_n(10))._(_n(1))._(_na([0, 1, 2, 3])))).toEqual([0, 10, 2, 3]);
    });

    it('[0, 1, 2, 3][2] = 10 is [0, 1, 10, 3]', () => {
      expect($na(set._(_n(10))._(_n(2))._(_na([0, 1, 2, 3])))).toEqual([0, 1, 10, 3]);
    });

    it('[0, 1, 2, 3][3] = 10 is [0, 1, 2, 10]', () => {
      expect($na(set._(_n(10))._(_n(3))._(_na([0, 1, 2, 3])))).toEqual([0, 1, 2, 10]);
    });

    it('handles infinite lists', () => {
      expect($n(get._(_n(4))._(set._(_n(10))._(_n(4))._(infinite)))).toBe(10);
    });
  });

  describe('update', () => {
    it('can not update Nil', () => {
      expect(() => $na(update._(succ)._(_n(0))._(Nil))).toThrow();
    });

    it('can not update out of bounds index', () => {
      expect(() => $na(update._(succ)._(_n(100))._(_na([0, 1, 2, 3])))).toThrow();
    });

    it('[0, 1, 2, 3][0]++ is [10, 1, 2, 3]', () => {
      expect($na(update._(succ)._(_n(0))._(_na([0, 1, 2, 3])))).toEqual([1, 1, 2, 3]);
    });

    it('[0, 1, 2, 3][1]++ is [0, 10, 2, 3]', () => {
      expect($na(update._(succ)._(_n(1))._(_na([0, 1, 2, 3])))).toEqual([0, 2, 2, 3]);
    });

    it('[0, 1, 2, 3][2]++ is [0, 1, 10, 3]', () => {
      expect($na(update._(succ)._(_n(2))._(_na([0, 1, 2, 3])))).toEqual([0, 1, 3, 3]);
    });

    it('[0, 1, 2, 3][3]++ is [0, 1, 2, 10]', () => {
      expect($na(update._(succ)._(_n(3))._(_na([0, 1, 2, 3])))).toEqual([0, 1, 2, 4]);
    });

    it('handles infinite lists', () => {
      expect($n(get._(_n(4))._(update._(succ)._(_n(4))._(infinite)))).toBe(5);
    });
  });

  describe('intersperse', () => {
    it('0 intersperse Nil is Nil', () => {
      expect($na(intersperse._(_n(0))._(Nil))).toEqual([]);
    });

    it('0 intersperse [1] is [1]', () => {
      expect($na(intersperse._(_n(0))._(_na([1])))).toEqual([1]);
    });

    it('0 intersperse [1, 2, 3] is [1, 0, 2, 0, 3]', () => {
      expect($na(intersperse._(_n(0))._(_na([1, 2, 3])))).toEqual([1, 0, 2, 0, 3]);
    });

    it('handles infinite lists', () => {
      expect($n(head._(intersperse._(_n(0))._(infinite)))).toBe(0);
    });
  });

  describe('show', () => {
    it('show Nil is "[]"', () => {
      expect($s(show._(nshow)._(_na([])))).toBe('[]');
    });

    it('show [0] is "[0]"', () => {
      expect($s(show._(nshow)._(_na([0])))).toBe('[0]');
    });

    it('show [0, 1, 2] is "[0, 1, 2]"', () => {
      expect($s(show._(nshow)._(_na([0, 1, 2])))).toBe('[0, 1, 2]');
    });

    it('handles infinite lists', () => {
      expect($c(head._(show._(nshow)._(infinite)))).toBe('[');
    });
  });
});