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# 2.5. Functional Programming - Scope, Closures, Higher-order Functions, Static vs. Dynamic Binding¶

## 2.5.1. 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 contained in the location).

In the statement x = x + 1, the leftmost x refers to a location or a value? The rightmost “x” refers 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 ** 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 typed into the read-eval-print loop of node:

var x = "outside";                              // what is the scope of this x?
var f1 = function() { var x = "inside f1"; };   // what is the scope of this x?
f1();
// what is the value of x right here?
var f2 = function() { x = "inside f2"; };       // what is the scope of this x?
// is this a trick question?
f2();
// what is the value of x right here?


What about the following code? Remember 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:

var x = 10;
var f = function(y) {
console.log(y);
if (true) {
var x = 20;      // what is the scope of this x?
}
console.log(x);
}
f(x);


Inside the body of a JavaScript 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.

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.

In the following code, what is the value returned by the call f(2,3)? What is the value of x on line A? What is the value of x on line B?

var f = function (x,y) {

var g = function (x) {     // what is the scope of g?

return x + y;    // line A
}

return g(10*x);            // line B
}


When an expression refers to a variable x but there is no declaration of x in the smallest scope containing the expression, how is the use of x bound to a declaration? The following code illustrates this situation.

var x = 1;
var f = function () {  return x; }   // the variable x is bound to which declaration of x?
x = 2;
var g = function () {
var x = 20;              // which type of binding does JS use?
return f();
}
x = 3;
g();       // what is the value returned here with dynamic binding? with static binding?


With dynamic binding, 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.

With static binding, the use of x in expression $e$ is bound to the declaration of x that appears in the smallest scope that contains $e$ in the source program, that is, at the time the function was defined.

Static binding is also called static scoping or lexical scoping.

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; }
}
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,

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; }
}
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 is that it allows us to easily build new functions at run-time as in the following example.

var makeIncrementer = function (x) {
var incr = function (y)  {return y + x;}
return incr;
}
var incrBy1 = makeIncrementer(1);
var incrBy5 = makeIncrementer(5);
incrBy1(10);             // returns 11
incrBy5(10);             // returns 15


In the previous example, we returned a function from makeIncrementer by first assigning it to a variable that was consequently returned. However, doing this was unnecessary, and we also could have written makeIncrementer as follows:

var makeIncrementer = function (x) {
return function (y) {return y + x;}
}
var incrBy1 = makeIncrementer(1);
var incrBy5 = makeIncrementer(5);
incrBy1(10);             // returns 11
incrBy5(10);             // returns 15


The code above represents an example of an anonymous function.

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.

## 2.5.2. Scope, Closures, Higher-order Functions (2)¶

This problem is about higher-order functions and scoping rules. It uses closures and anonymous functions.

## 2.5.3. Scope, Closures, Higher-order Functions (3)¶

This problem uses the same code as the previous problem and illustrates the same topics.

## 2.5.4. 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.