How to correctly express arbitrary Promise chains without "indentation pyramids"?

Because of the way that subsequent operations rely on multiple bits of previous operations, your choices are:

1. Do what you've done

2. Put the variables outside the chain and assign them as you go

3. Have the entire thing passing around an object with a, b, and such on it as properties

#1 is what I'd stick with, barring a really good reason to do either of the other two. Fortunately, that kind of accumulation rarely goes as deep as shown in your question.

async/await is the way to do it here some years later (and may have been when the question was posted, the proposal was finished and they could be used with a transpiler), see Sterling's answer for how they could simplify it. Here's a working example:

const F = x => {
    return new Promise(resolve => {
        setTimeout(() => {
            resolve(x);
        }, 100);
    });
};
(async () => {
    const a = await F(100);
    const b = await F(200);
    const c = await F(a+b);
    const d = await F(a+c);
    const e = await F(b+c);
    const f = await F(d+e);
    console.log(f);
})()
.catch(error => {
    // ...handle/report error...
});

Live on Babel's REPL for those with outdated environments.

Second try. @Luggage in the JS chat suggested using Async/Await to keep the scope of your params.

let a = await F(200);
let b = await F(a + 100);
let c = await F(a + b);
//... etc, all inside an async function

You could also use Promise.all or (this is my experience) I've used the async lib to help waterfall these issues.

async.waterfall([
   (callback) => {
        let a = F(200);
        callback(null, a)
    }, (a, callback) => {
        let b = F(a+b);
        callback(null, b);
    }, //etc down the chain
]);

I think Promise.all would manage it better than an async lib, but async/await is the prettiest method here, though it will require ES2017 support/transpiling.

Async/await solve this issue quite nicely I think;

async function runAsync(){
  const F = async (x) => x;
  const a = await F(1);
  const b = await F(2);
  const c = await F(a + b);
  const d = await F(a + c);
  const e = await F(b + c);
  console.log(e);
}

function runSync(){
  const F = (x) => x;
  const a = F(1);
  const b = F(2);
  const c = F(a + b);
  const d = F(a + c);
  const e = F(b + c);
  console.log(e);
}

runSync(); //5
runAsync(); //5

this will run natively with node 7 using node --harmony-async-await example

Unfortunately, you'll likely need to transpile down for general use and the output can get quite large.