Calling a Function defined inside another function in Javascript

The scoping is correct as you've noted. However, you are not calling the inner function anywhere.

You can do either:

function outer() { 

    // when you define it this way, the inner function will be accessible only from 
    // inside the outer function

    function inner() {
        alert("hi");
    }
    inner(); // call it
}

Or

function outer() { 
    this.inner = function() {
        alert("hi");
    }
}

<input type="button" onclick="(new outer()).inner();" value="ACTION">​

You could make it into a module and expose your inner function by returning it in an Object.

function outer() { 
    function inner() {
        console.log("hi");
    }
    return {
        inner: inner
    };
}
var foo = outer();
foo.inner();

You are not calling the function inner, just defining it.

function outer() { 
    function inner() {
        alert("hi");
    }

    inner(); //Call the inner function

}