Functional Programming - Scope, Closures, Higher-order Functions, Static vs. Dynamic Binding¶
1. Scope, Closures, Higher-order Functions (1)¶
Every variable is a memory location. Each variable has a name, by which you can refer to this location in your program, and a value that is associated with the location.
In the statement x = x + 1, does the leftmost x refer to a location or a value? Does the rightmost “x” refer to a location or a value?
Additionally every variable also has a scope which comprises all of the sections of the program where the variable is visible. So, when the variable x is in scope, you can refer to it by name. Anywhere else, using the name x is an error (unless there exists another variable also called x that is in scope, as considered below).
In JavaScript, there are only two kinds of scopes: the global scope and local scopes. A local scope is always defined by the body of a function. This is different from languages like C and Java, where scope is defined by a block enclosed in curly braces. Suppose for example, the following code is loaded into the read-eval-print loop of an interpreter like node.
In most other languages, it is better to give each variable the smallest scope possible, by declaring the variable as close as possible to its uses. Not so in JavaScript, because JavaScript does not have block scope and variable declarations are always hoisted to the top of the function. Consider how this plays out in the following example, remembering to take into account what was said earlier about scope in JavaScript being defined by the body of a function and not by an inner set of curly braces.
The prior example illustrates something allowed but considered a bad practice in JavaScript. Inside the body of a function, you should never declare a variable inside any nested block. You should always declare your variables in the outermost block (that is, the block defining the body of the function). Furthermore, always declare your variables at the beginning of that body.
When an expression refers to a variable for which there is no declaration in the smallest scope containing the expression, how is the use of that variable bound to a declaration? The following code illustrates this situation.
Here is another example illustrating the nuances of using variables of the same name at different levels of scope. Consider what happens when this code is loaded into a read-eval-print interpreter.
The example above indicates that JavaScript (and most other functional languages) use static binding. That is, the use of x in expression \(e\) is bound to the declaration of x that appears in the smallest scope that contains \(e\) at the time the function was defined.
Static binding is also called static scoping or lexical scoping.
There is a different type of binding called dynamic binding, in which the declaration that binds a use of x in expression \(e\) is first looked for in the function (say, f) that contains \(e\), then, if needed, in the function (say, g) that called f, then in the function that called g, etc. Note that, if JavaScript used dynamic binding, the value returned in the previous example would have been 20 instead of 3.
We saw that a function can be declared inside another function. Furthermore, recall that, in functional languages (and in the subset of JavaScript we are considering), functions are first-class values. This implies that a function, like any other value, can be the return value of a function call. Hence a function can return the value of any one of its local variables. It makes no difference whether that returned variable is bound to an integer, a boolean, or a function. A function that returns another function (or that takes in a function as an argument) is called a higher-order function, as illustrated in the following example.
var f = function () {
var add1 = function (x) { return x + 1; };
return add1;
}
var g = f(); // g is now the function that takes in one argument and adds 1 to it
g(5); // returns 6
f()(5); // same thing
Here, f is a higher-order function. However, add1 is not a higher-order function. What about g?
What happens when a function f returns a local function that refers to a parameter or a local variable of f as in the following example?
var f = function () {
var y = 1;
var addY = function (x) { return x + y; };
return addY;
}
var g = f(); // after f returns, the variable y
// in f is gone from the stack
g(5); // but g can still access it!
f()(5); // still returns 6
When a local function refers to a variable defined in an enclosing function, the local function is implemented as a closure, that is, the local function contains not only its own code, but also the variables its code refers to that were defined in the environment at the time the local function was created.
So far, we have seen three distinct and independent concepts that are central to functional programming:
- Functions as first-class values and higher-order functions,
- Closures, and
- Static binding.
Since JavaScript implements all of these, it is quite natural and powerful to use the functional programming paradigm in JavaScript. One powerful aspect of it is that it allows us to easily build new functions at run-time as in the following example.
Once you become comfortable with the notion of functions as first-class values, you will find the use of anonymous functions as illustrated in the final slide in the above example is a technique that often enhances the readability of your code. Why use a "temporary variable" such as incr to store something that could just as well be returned directly?
This first problem is about higher-order functions and uses closures and anonymous functions. This problem is randomized. You must solve it correctly three times in a row.
2. Scope, Closures, Higher-order Functions (2)¶
This problem is about higher-order functions and scoping rules. It uses closures and anonymous functions.
3. Scope, Closures, Higher-order Functions (3)¶
This problem uses the same code as the previous problem and illustrates the same topics.
4. Static vs. Dynamic Binding¶
This problem uses the same code as the previous two problems but focuses on the difference between static and dynamic binding rules.
