n-ification

nify.js

const { pipe, compose, map, encase, K, range, pow } = require("sanctuary");

const ret = compose;
const repeat = n => x => map(K(x))(range(0, n));
const nify = n => pipe(repeat(n - 1)(ret));
const fail = () => {
  throw new Error();
};

// N-ifying encase
const ncs1 = nify(1)(encase);
const ncs2 = nify(2)(encase);
const ncs3 = nify(3)(encase);
// ...

ncs1(a => fail())(1);
// Nothing
ncs2(a => b => fail())(1)(2);
// Nothing
ncs3(a => b => c => fail())(1)(2)(3);
// Nothing
// ...

// N-ifying compose
// (y -> z) -> (a -> ... -> (x -> y))
//                           ^-- edit this
//             (a -> ... -> (x -> z))
//                           ^-- to this
// by composing with (y -> z)
const compose2 = f => nify(2)(compose(f));
const compose3 = f => nify(3)(compose(f));
const compose4 = f => nify(4)(compose(f));
// ...

compose2(pow(2))(x => y => x + y)(1)(2);
// 9
compose3(pow(2))(x => y => z => x + y + z)(1)(2)(3);
// 36
// ...