How to compare two functions for equivalence, as in (λx.2*x) == (λx.x+x)?

Question

Is there a way to compare two functions for equality? For example, (λx.2*x) == (λx.x+x) should return true, because those are obviously equivalent.

Answer 1

In a language with symbolic computation like Mathematica:

Or C# with a computer algebra library:

MathObject f(MathObject x) => x + x;
MathObject g(MathObject x) => 2 * x;

{
    var x = new Symbol("x");

    Console.WriteLine(f(x) == g(x));
}

The above displays 'True' at the console.