[PySlice]

If programmers of functional languages were better at naming things, it would be easy. Let's rename g to callTwice and h to aFunction:

  function callTwice(aFunction) {

    return function(y) {
      return aFunction(aFunction(y));
    };

  }

  function square(x) { return x*x; }

  var squareTwice = callTwice(square);

  81 === squareTwice(3);

[hcarvalhoalves]

To be fair, the g and h names should obvious to anyone who studied function composition in high school.

Also, the names you gave don't help at all, as the idea of calling those g and h is to treat them anonymously. By calling it "callTwice", you are thinking about it as some sort of utility function, which is not the case. Shows you didn't grasped the idea behind it yet.

[meddlepal]

Might be obvious to you and other FPers, but when you're trying to teach FP to programmers who may only "sort of" or "not at all" grasp FP and spend most of their daily life writing CRUD business logic apps for a living but WANT to learn more about FP in order to be better programmers then it's totally useless. I found the other example immediately more understandable - even though I personally understood the content I sympathize with the people who are struggling. The FP community needs to take the academic context out of a lot of its teaching mechanisms.

[hamburglar]

It's actually very easy to see what is happening with g and f in this example. I think the part that is pretty opaque to non-FPers is why you would want to do that. Until something clicks, it is hard to see why this construct is anything beyond a very convoluted way of calculating 3 to the fourth power.

[PySlice]

So enlighten me.

[hcarvalhoalves]

In FP, you can treat all functions as "curryable" because that's how you achieve composition. So that would be the equivalent of naming all your functions "callTwice". Now that doesn't make sense.

[PySlice]

I don't see how that invalidates my explanation

In F# I would certainly call it "callTwice" too:

  let callTwice aFunction y = aFunction (aFunction y)