Its been a while since I worked with this so this is kind of a shitty example out of the top of my head:

If you have code that looks like this:

    var user_list =
       fetch_json()
       .then(function(data){
           return data.users
       })

You can write it more succinctly using a combinator library instead of writing the callback out by hand:

   var user_list =
       fetch_json()
       .then(get('users'))

Similar things also apply on other code that uses callbacks like maps, filters, etc. I also had combinators for other common JS operators (set, "+", "==", ...)

The point where currying comes in is that it lets you define a single "get" function instead of a separate versions for one and two arguments:

    //curried
    x = get('users', data)
    y = get('users')(data)

    //non curried
    x = get2('users', data)
    y = get1('users')(data)

That said, there are some downsides to using combinators instead of writing the callbacks by hand. If you need to debug something the stack traces are harder to follow and currying doesn't play nice with functions like Array.prototype.forEach that pass "extra" parameters to the callbacks.

In the end the feeling I got was that trying to make JS more functional is not worth the trouble. If I could go back I would try to replace the promises with something less intrusive in terms of coding style, such as generators/coroutines.