JavaScript callbacks and functional programming

fs.readFile(file, (function cb(err,result){
    print(this.a+result);
}).bind({a: a});

Just inject context with variables and scope into the function if you must.

Because you complain about the API

fs.readFile(file, (function cb(a, err,result){
    print(a+result);
}).bind(null, a);

It's called currying. This is a lot more FP.

I think the problem is that you're misunderstanding what they mean by the use of an intermediate value (or they're misrepresenting it, I haven't read the link). Consider that a variable in a functional language is the definition of something, and that definition cannot change. It's perfectly acceptable to use names for values/formulas in functional programming, as long as they don't change.

function calculate(a,b,c) {
    // here we define an name to (a+b) so that we can use it later
    // there's nothing wrong with this "functionally", since we don't 
    // change it's definition later
    d = a + b;
    return c * d;
}

On the other hand, the following would not be ok, functionally

function sum(listofvalues) {
    sum = 0;
    foreach value in listofvalues
        // this is bad, since we're re-defining "sum"
        sum += value;
    return sum
}

For something closer to what you had in your code... consider you have a function call map that takes a list of things and a function to apply to a thing and returns a new list of things. It's perfectly acceptable to say:

function add_value(amount) {
    amount_to_incr = amount * 2;
    return function(amount, value) {
        // here we're using that "amount" value provided to us
        // the function returned will always return the same value for the same
        // input... its "referentially transparent"
        // and it uses the "intermediate" value of amount_to_incr... however, since 
        // that value doesn't change, it's fine
        return amount_to_incr + value;
    }
}
map [1,2,3] add_value(2) ;// -> [3,4,5]