'use strict';

const suc = a => b => c => b(a(b)(c));
const add = a => b => c => d => a(c)(b(c)(d));
const mul = a => b => c => a(b(c));
const exp = a => b => b(a);
const pre = a => b => c => a(d => e => e(d(b)))(f => c)(g => g);
const sub = a => b => b(pre)(a);
const ntc = n => n > 0 ? a => b => a(ntc(n - 1)(a)(b)) : a => b => b;
const ctn = a => a(x => x + 1)(0);

module.exports = {
  suc,
  add,
  mul,
  exp,
  pre,
  sub,
  ntc,
  ctn,
};