'use strict';

// Church logic
const If = p => a => b => p(a)(b);
const And = p => q => p(q)(p);
const Or = p => q => p(p)(q);
const Not = p => p(False)(True);

// Church numerals
const show = lambda => lambda(x => x + 1)(0);
const zero = f => x => x;
const one = f => x => f(x);
const two = f => x => f(f(x));
const three = f => x => f(f(f(x)));
const four = f => x => f(f(f(f(x))));
const five = f => x => f(f(f(f(f(x)))));

// Simple arithmetic
const succ = n => f => x => f(n(f)(x));
const plus = (m, n) => f => x => m(f)(n(f)(x));
const mult = (m, n) => f => x => m(n(f))(x);
const pred = n => f => x => n(g => h => h(g(f)))(u => x)(u => u);

// y-combinator: canonical definition recur f = f (recur f)
const recur = f => n => f(recur(f))(n);
const sumTo = recur(f => n => n == 0 ? 0 : n + f(n - 1));
const fact = recur(f => n => n <= 1 ? 1 : n * f(n - 1));

console.log(show(one)); // 1