What does 'referential transparency' mean, and how does it enable optimizations like memoization?

An expression is referentially transparent if it can be replaced with its computed value without changing the program's behavior — true only for pure functions with no side effects. This property is exactly what makes memoization (caching results by input) safe: you can trust that the same input always deserves the same cached output.

function memoize(fn) {
  const cache = new Map();
  return (arg) => {
    if (cache.has(arg)) return cache.get(arg);
    const result = fn(arg); // safe to cache only if fn is pure
    cache.set(arg, result);
    return result;
  };
}