Lambda Calculus w/o Parenthesis

OpenClose.js

//// Implementation
OPEN = Symbol("open")
CLOSE = Symbol("close")
function run(program) {
    function applyUntilClose(continuation = x => x) {
        function iter(f) {
            if (f === OPEN) { 
                return applyUntilClose(r => iter(r))
            } else if (f == CLOSE) {
                throw new Error("Unexpected empty grouping")
            } else {
                return function (x) {
                    if (x === OPEN) {
                        return applyUntilClose(r => iter(f(r)))
                    } else if (x === CLOSE) {
                        return continuation(f)
                    } else {
                        return iter(f(x))
                    }
                }
            }
        }
        return iter;
    }
    return program(applyUntilClose())(CLOSE)
}

//// Example
// Boring helpers:
let min = x => y => x < y ? x : y;
let plus = x => y => x + y;
let square = x => x * x;

// Cool part:
// equivalent to `square (plus (min 2 (plus 1 2)) 5)` 
let program = x => x(square)(OPEN)(plus)(OPEN)(min)(2)(OPEN)(plus)(1)(2)(CLOSE)(CLOSE)(5)(CLOSE)
console.log(run(program)) // -> 49