How to interpret bind/>>= of the function instance?

Question

I\'m trying to improve my understanding of Applicatives and Monads by implementing their function instances in Javascript. My knowledge of Haskell

Answer 1

The values in the monad instance for functions have type r -> a for some fixed type r. The function (a -> (r -> b)) given to (>>=) allows you to choose the next function to return given the result from the current value (a function r -> a). f r has type a and k (f r) has type r -> b which is the next function to apply.

In your code g(f(x)) is therefore a function which expects a single argument of type r. The caller of bind can choose this function based on the value returned by the previous function e.g.

var inc = x => x + 1;
var f = bind(inc)(function(i) {
   if(i <= 5) { return x => x * 2; }
   else { return x => x * 3; }
});

The function will be given x as an input and can choose the next stage in the computation based on the result of inc(x) e.g.

f(2) //4;
f(5) //15;