03_functions.txt

:chap_num: 3
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= Functions =

[chapterquote="true"]
[quote, Donald Knuth]
____
People think that computer science is the art of
geniuses but the actual reality is the opposite, just many people
doing things that build on each other, like a wall of mini stones.
____

(((Knuth+++,+++ Donald)))(((function)))(((code structure)))You've seen function values, such
as `alert`, and how to call them. Functions are the bread and butter
of JavaScript programming. The concept of wrapping a piece of program
in a value has many uses. It is a tool to structure larger programs,
to reduce repetition, to associate names with subprograms, and to
isolate these subprograms from each other.

(((human language)))The most obvious application of functions is
defining new ((vocabulary)). Creating new words in regular,
human-language prose is usually bad style. But in programming, it is
indispensable.

(((abstraction)))Typical adult English speakers have some 20,000 words
in their vocabulary. Few programming languages come with 20,000
commands built in. And the vocabulary that _is_ available tends to be
more precisely defined, and thus less flexible, than in human
language. Therefore, we usually _have_ to add some of our own
vocabulary to avoid repeating ourselves too much.

== Defining a function ==

(((square)))(((function,definition)))A function definition is just a
regular ((variable)) definition where the value given to the variable
happens to be a function. For example, the following code defines the
variable `square` to refer to a function that produces the square of a
given number:

[source,javascript]
----
var square = function(x) {
  return x * x;
};

console.log(square(12));
// → 144
----

indexsee:[braces,curly braces]
(((curly braces)))(((block)))(((syntax)))(((function
keyword)))(((function,body)))(((function,as value)))A function is
created by an expression that starts with the keyword `function`.
Functions have a set of _((parameter))s_ (in this case, only `x`) and
a _body_, which contains the statements that are to be executed when
the function is called. The function body must always be wrapped in
braces, even when it consists of only a single ((statement)) (as
in the previous example).

(((power example)))A function can have multiple parameters or no
parameters at all. In the following example, `makeNoise` does not list
any parameter names, whereas `power` lists two:

[source,javascript]
----
var makeNoise = function() {
  console.log("Pling!");
};

makeNoise();
// → Pling!

var power = function(base, exponent) {
  var result = 1;
  for (var count = 0; count < exponent; count++)
    result *= base;
  return result;
};

console.log(power(2, 10));
// → 1024
----

(((return value)))(((return keyword)))(((undefined)))Some functions
produce a value, such as `power` and `square`, and some don't, such as
`makeNoise`, which produces only a ((side effect)). A `return`
statement determines the value the function returns. When control
comes across such a statement, it immediately jumps out of the current
function and gives the returned value to the code that called the
function. The `return` keyword without an expression after it will
cause the function to return `undefined`.

== Parameters and scopes ==

(((function,application)))(((variable,from parameter)))The
((parameter))s to a function behave like regular variables, but their
initial values are given by the _caller_ of the function, not the code
in the function itself.

(((function,scope)))(((scope)))(((local variable)))An
important property of functions is that the variables created inside
of them, including their parameters, are _local_ to the function. This
means, for example, that the `result` variable in the `power` example
will be newly created every time the function is called, and these
separate incarnations do not interfere with each other.

indexsee:[top-level scope,global scope]
(((var keyword)))(((global scope)))(((variable,global)))This
“localness” of variables applies only to the parameters and to variables
declared with the `var` keyword inside the function body. Variables
declared outside of any function are called _global_, because they are
visible throughout the program. It is possible to access such
variables from inside a function, as long as you haven't declared a
local variable with the same name.

(((variable,assignment)))The following code demonstrates this. It
defines and calls two functions that both assign a value to the
variable `x`. The first one declares the variable as local and thus
changes only the local variable. The second does not declare `x`
locally, so references to `x` inside of it refer to the global
variable `x` defined at the top of the example.

[source,javascript]
----
var x = "outside";

var f1 = function() {
  var x = "inside f1";
};
f1();
console.log(x);
// → outside

var f2 = function() {
  x = "inside f2";
};
f2();
console.log(x);
// → inside f2
----

(((variable,naming)))(((scope)))(((global scope)))(((code,structure
of)))This behavior helps prevent accidental interference between
functions. If all variables were shared by the whole program, it'd
take a lot of effort to make sure no name is ever used for two
different purposes. And if you _did_ reuse a variable name, you might
see strange effects from unrelated code messing with the value of your
variable. By treating function-local variables as existing only within
the function, the language makes it possible to read and understand
functions as small universes, without having to worry about all the
code at once.

[[scoping]]
== Nested scope ==

(((nesting,of functions)))(((nesting,of
scope)))(((scope)))(((inner function)))(((lexical
scoping)))JavaScript distinguishes not just between _global_ and
_local_ variables. Functions can be created inside other functions,
producing several degrees of locality.

(((landscape example)))For example, this rather nonsensical function
has two functions inside of it:

[source,javascript]
----
var landscape = function() {
  var result = "";
  var flat = function(size) {
    for (var count = 0; count < size; count++)
      result += "_";
  };
  var mountain = function(size) {
    result += "/";
    for (var count = 0; count < size; count++)
      result += "'";
    result += "\\";
  };
 
  flat(3);
  mountain(4);
  flat(6);
  mountain(1);
  flat(1);
  return result;
};

console.log(landscape());
// → ___/''''\______/'\_
----

(((function,scope)))(((scope)))The `flat` and `mountain` functions
can “see” the variable called `result`, since they are inside the
function that defines it. But they cannot see each other's `count`
variables since they are outside each other's scope. The environment
outside of the `landscape` function doesn't see any of the variables
defined inside `landscape`.

In short, each local scope can also see all the local scopes that
contain it. The set of variables visible inside a function is
determined by the place of that function in the program text. All
variables from blocks _around_ a function's definition are
visible—meaning both those in function bodies that enclose it and
those at the top level of the program. This approach to variable
visibility is called _((lexical scoping))_.

((({} (block))))People who have experience with other programming
languages might expect that any block of code between braces produces
a new local environment. But in JavaScript, functions are the only
things that create a new scope. You are allowed to use free-standing
blocks.

[source,javascript]
----
var something = 1;
{
  var something = 2;
  // Do stuff with variable something...
}
// Outside of the block again...
----

But the `something` inside the block refers to the same variable as
the one outside the block. In fact, although blocks like this are
allowed, they are useful only to group the body of an `if` statement
or a loop.

(((let keyword)))(((ECMAScript 6)))If you find this odd, you're not
alone. The next version of JavaScript will introduce a `let` keyword,
which works like `var` but creates a variable that is local to the
enclosing _block_, not the enclosing _function_.

== Functions as values ==

(((function,as value)))Function ((variable))s usually simply act as
names for a specific piece of the program. Such a variable is defined
once and never changed. This makes it easy to start confusing the
function and its name.

(((variable,assignment)))But the two are different. A function value
can do all the things that other values can do—you can use it in
arbitrary ((expression))s, not just call it. It is possible to store a
function value in a new place, pass it as an argument to a function,
and so on. Similarly, a variable that holds a function is still just a
regular variable and can be assigned a new value, like so:

// test: no

[source,javascript]
----
var launchMissiles = function(value) {
  missileSystem.launch("now");
};
if (safeMode)
  launchMissiles = function(value) {/* do nothing */};
----

(((function,higher-order)))In
link:05_higher_order.html#higher_order[Chapter 5], we will discuss the
wonderful things that can be done by passing around function values to
other functions.

== Declaration notation ==

(((syntax)))(((square example)))(((function
keyword)))(((function,definition)))(((function,declaration)))There is
a slightly shorter way to say “++var square = function…++”. The
`function` keyword can also be used at the start of a statement, as in
the following:

[source,javascript]
----
function square(x) {
  return x * x;
}
----

(((future)))(((execution order)))This is a function _declaration_. The
statement defines the variable `square` and points it at the given
function. So far so good. There is one subtlety with this form of
function definition, however.

[source,javascript]
----
console.log("The future says:", future());

function future() {
  return "We STILL have no flying cars.";
}
----

This code works, even though the function is defined _below_ the code
that uses it. This is because function declarations are not part of
the regular top-to-bottom flow of control. They are conceptually moved
to the top of their scope and can be used by all the code in that
scope. This is sometimes useful because it gives us the freedom to
order code in a way that seems meaningful, without worrying about
having to define all functions above their first use.

(((function,declaration)))What happens when you put such a function
definition inside a conditional (`if`) block or a loop? Well, don't do
that. Different JavaScript platforms in different browsers have
traditionally done different things in that situation, and the latest
((standard)) actually forbids it. If you want your programs to behave
consistently, only use this form of function-defining statements in
the outermost block of a function or program.

[source,javascript]
----
function example() {
  function a() {} // Okay
  if (something) {
    function b() {} // Danger!
  }
}
----

[[stack]]
== The call stack ==

indexsee:[stack,call stack]
(((call stack)))(((function,application)))It will be helpful to take a
closer look at the way control flows through functions. Here is a
simple program that makes a few function calls:

[source,javascript]
----
function greet(who) {
  console.log("Hello " + who);
}
greet("Harry");
console.log("Bye");
----

(((control flow)))(((execution order)))(((console.log)))A run through
this program goes roughly like this: the call to `greet` causes
control to jump to the start of that function (line 2). It calls
`console.log` (a built-in browser function), which takes control, does
its job, and then returns control to line 2. Then it reaches the end
of the `greet` function, so it returns to the place that called it, at
line 4. The line after that calls `console.log` again.

We could show the flow of control schematically like this:

----
top
   greet
        console.log
   greet
top
   console.log
top
----

(((return keyword)))(((memory)))Because a function has to jump back to
the place of the call when it returns, the computer must remember the
context from which the function was called. In one case, `console.log`
has to jump back to the `greet` function. In the other case, it jumps
back to the end of the program.

The place where the computer stores this context is the _((call
stack))_. Every time a function is called, the current context is put
on top of this “stack”. When the function returns, it removes the top
context from the stack and uses it to continue execution.

(((infinite loop)))(((stack overflow)))(((recursion)))Storing this
stack requires space in the computer's memory. When the stack grows
too big, the computer will fail with a message like “out of stack
space” or “too much recursion”. The following code illustrates this by
asking the computer a really hard question, which causes an infinite
back-and-forth between two functions. Rather, it _would_ be infinite,
if the computer had an infinite stack. As it is, we will run out of
space, or “blow the stack”.

// test: no

[source,javascript]
----
function chicken() {
  return egg();
}
function egg() {
  return chicken();
}
console.log(chicken() + " came first.");
// → ??
----

== Optional Arguments ==

(((argument)))(((function,application)))The following code is allowed
and executes without any problem:

[source,javascript]
----
alert("Hello", "Good Evening", "How do you do?");
----

(((alert function)))The function `alert` officially accepts only one
argument. Yet when you call it like this, it doesn't complain. It
simply ignores the other arguments and shows you “Hello”.

(((undefined)))(((parameter)))JavaScript is extremely broad-minded
about the number of arguments you pass to a function. If you pass too
many, the extra ones are ignored. If you pass too few, the missing
parameters simply get assigned the value `undefined`.

The downside of this is that it is possible—likely, even—that you'll
accidentally pass the wrong number of arguments to functions and no
one will tell you about it.

[[power]]
(((power example)))(((optional argument)))The
upside is that this behavior can be used to have a function take
“optional” arguments. For example, the following version of `power`
can be called either with two arguments or with a single argument, in
which case the exponent is assumed to be two, and the function behaves
like `square`.

// test: wrap

[source,javascript]
----
function power(base, exponent) {
  if (exponent == undefined)
    exponent = 2;
  var result = 1;
  for (var count = 0; count < exponent; count++)
    result *= base;
  return result;
}

console.log(power(4));
// → 16
console.log(power(4, 3));
// → 64
----

(((console.log)))In the link:04_data.html#arguments_object[next
chapter], we will see a way in which a function body can get at the
exact list of arguments that were passed. This is helpful because it
makes it possible for a function to accept any number of arguments.
For example, `console.log` makes use of this—it outputs all of the
values it is given.

[source,javascript]
----
console.log("R", 2, "D", 2);
// → R 2 D 2
----

== Closure ==

(((call stack)))(((local variable)))(((function,as
value)))(((closure)))(((scope)))The ability to treat functions as
values, combined with the fact that local variables are “re-created”
every time a function is called, brings up an interesting question.
What happens to local variables when the function call that created
them is no longer active?

The following code shows an example of this. It defines a function,
`wrapValue`, which creates a local variable. It then returns a function
that accesses and returns this local variable.

[source,javascript]
----
function wrapValue(n) {
  var localVariable = n;
  return function() { return localVariable; };
}

var wrap1 = wrapValue(1);
var wrap2 = wrapValue(2);
console.log(wrap1());
// → 1
console.log(wrap2());
// → 2
----

This is allowed and works as you'd hope—the variable can still be
accessed. In fact, multiple instances of the variable can be alive at
the same time, which is another good illustration of the concept that
local variables really are re-created for every call—different calls
can't trample on one another's local variables.

This feature—being able to reference a specific instance of local
variables in an enclosing function—is called _closure_. A function
that “closes over” some local variables is called _a_ closure. This
behavior not only frees you from having to worry about lifetimes of
variables but also allows for some creative use of function values.

(((multiplier function)))With a slight change, we can turn the
previous example into a way to create functions that multiply by an
arbitrary amount.

[source,javascript]
----
function multiplier(factor) {
  return function(number) {
    return number * factor;
  };
}

var twice = multiplier(2);
console.log(twice(5));
// → 10
----

(((variable,from parameter)))The explicit `localVariable` from the
`wrapValue` example isn't needed since a parameter is itself a local
variable.

(((function,model of)))Thinking about programs like this takes some
practice. A good mental model is to think of the `function` keyword as
“freezing” the code in its body and wrapping it into a package (the
function value). So when you read `return function(...) {...}`, think
of it as returning a handle to a piece of computation, frozen for
later use.

In the example, `multiplier` returns a frozen chunk of code that gets
stored in the `twice` variable. The last line then calls the value in
this variable, causing the frozen code (`return number * factor;`) to
be activated. It still has access to the `factor` variable from the
`multiplier` call that created it, and in addition it gets access to
the argument passed when unfreezing it, 5, through its `number`
parameter.

== Recursion ==

(((power example)))(((stack
overflow)))(((recursion)))(((function,application)))It is perfectly
okay for a function to call itself, as long as it takes care not to
overflow the stack. A function that calls itself is called
_recursive_. Recursion allows some functions to be written in a
different style. Take, for example, this alternative implementation of
`power`:

// test: wrap

[source,javascript]
----
function power(base, exponent) {
  if (exponent == 0)
    return 1;
  else
    return base * power(base, exponent - 1);
}

console.log(power(2, 3));
// → 8
----

(((loop)))(((readability)))(((mathematics)))This is rather
close to the way mathematicians define exponentiation and arguably
describes the concept in a more elegant way than the looping variant
does. The function calls itself multiple times with different
arguments to achieve the repeated multiplication.

(((function,application)))(((efficiency)))But this implementation has
one important problem: in typical JavaScript implementations, it's
about 10 times slower than the looping version. Running through a
simple loop is a lot cheaper than calling a function multiple times.

(((optimization)))The dilemma of speed versus ((elegance)) is an
interesting one. You can see it as a kind of continuum between
human-friendliness and machine-friendliness. Almost any program can be
made faster by making it bigger and more convoluted. The programmer
must decide on an appropriate balance.

In the case of the link:03_functions.html#power[earlier] `power`
function, the inelegant (looping) version is still fairly simple and
easy to read. It doesn't make much sense to replace it with the
recursive version. Often, though, a program deals with such complex
concepts that giving up some efficiency in order to make the program
more straightforward becomes an attractive choice.

(((profiling)))The basic rule, which has been repeated by many
programmers and with which I wholeheartedly agree, is to not worry
about efficiency until you know for sure that the program is too slow.
If it is, find out which parts are taking up the most time, and start
exchanging elegance for efficiency in those parts.

Of course, this rule doesn't mean one should start ignoring
performance altogether. In many cases, like the `power` function, not
much simplicity is gained from the “elegant” approach. And sometimes
an experienced programmer can see right away that a simple approach is
never going to be fast enough.

(((premature optimization)))The reason I'm stressing this is that
surprisingly many beginning programmers focus fanatically on
efficiency, even in the smallest details. The result is bigger, more
complicated, and often less correct programs, that take longer to
write than their more straightforward equivalents and that usually run
only marginally faster.

(((branching recursion)))But recursion is not always just a
less-efficient alternative to looping. Some problems are much easier
to solve with recursion than with loops. Most often these are problems
that require exploring or processing several “branches”, each of which
might branch out again into more branches.

[[recursive_puzzle]]

(((recursion)))(((number puzzle example)))Consider this puzzle: by
starting from the number 1 and repeatedly either adding 5 or
multiplying by 3, an infinite amount of new numbers can be produced.
How would you write a function that, given a number, tries to find a
sequence of such additions and multiplications that produce that
number? For example, the number 13 could be reached by first
multiplying by 3 and then adding 5 twice, whereas the number 15 cannot
be reached at all.

Here is a recursive solution:

[source,javascript]
----
function findSolution(target) {
  function find(start, history) {
    if (start == target)
      return history;
    else if (start > target)
      return null;
    else
      return find(start + 5, "(" + history + " + 5)") ||
             find(start * 3, "(" + history + " * 3)");
  }
  return find(1, "1");
}

console.log(findSolution(24));
// → (((1 * 3) + 5) * 3)
----

Note that this program doesn't necessarily find the _shortest_
sequence of operations. It is satisfied when it finds any sequence at
all.

I don't necessarily expect you to see how it works right away. But
let's work through it, since it makes for a great exercise in
recursive thinking.

The inner function `find` does the actual recursing. It takes two
((argument))s—the current number and a string that records how we
reached this number—and returns either a string that shows how to get
to the target or `null`.

(((null)))(((|| operator)))(((short-circuit evaluation)))To do this, the
function performs one of three actions. If the current number is the
target number, the current history is a way to reach that target, so
it is simply returned. If the current number is greater than the
target, there's no sense in further exploring this history since both
adding and multiplying will only make the number bigger. And finally,
if we're still below the target, the function tries both possible
paths that start from the current number, by calling itself twice,
once for each of the allowed next steps. If the first call returns
something that is not `null`, it is returned. Otherwise, the second
call is returned—regardless of whether it produces a string or `null`.

(((call stack)))To better understand how this function produces the
effect we're looking for, let's look at all the calls to `find` that
are made when searching for a solution for the number 13.

----
find(1, "1")
  find(6, "(1 + 5)")
    find(11, "((1 + 5) + 5)")
      find(16, "(((1 + 5) + 5) + 5)")
        too big
      find(33, "(((1 + 5) + 5) * 3)")
        too big
    find(18, "((1 + 5) * 3)")
      too big
  find(3, "(1 * 3)")
    find(8, "((1 * 3) + 5)")
      find(13, "(((1 * 3) + 5) + 5)")
        found!
----

The indentation suggests the depth of the call stack. The first time
`find` is called it calls itself twice to explore the solutions that start with
`(1 + 5)` and `(1 * 3)`. The first call tries to find a solution that
starts with `(1 + 5)` and, using recursion, explores _every_ solution
that yields a number less than or equal to the target number. Since
it doesn't find a solution that hits the target, it returns `null`
back to the first call. There the `||` operator causes the call that
explores `(1 * 3)` to happen. This search has more luck because its
first recursive call, through yet _another_ recursive call, hits upon
the target number, 13. This innermost recursive call returns a string,
and each of the `||` operators in the intermediate calls pass that
string along, ultimately returning our solution.

== Growing functions ==

(((function,definition)))There are two more or less natural ways for
functions to be introduced into programs.

(((repetition)))The first is that you find yourself writing very
similar code multiple times. We want to avoid doing that since having
more code means more space for mistakes to hide and more material to
read for people trying to understand the program. So we take the
repeated functionality, find a good name for it, and put it into a
function.

The second way is that you find you need some functionality that you
haven't written yet and that sounds like it deserves its own function.
You'll start by naming the function, and you'll then write its body.
You might even start writing code that uses the function before you
actually define the function itself.

(((function,naming)))(((variable,naming)))How difficult it is to find
a good name for a function is a good indication of how clear a concept
it is that you're trying to wrap. Let's go through an example.

(((farm example)))We want to write a program that prints two numbers,
the numbers of cows and chickens on a farm, with the words `Cows` and
`Chickens` after them, and zeros padded before both numbers so that
they are always three digits long.

----
007 Cows
011 Chickens
----

That clearly asks for a function of two arguments. Let's get coding.

[source,javascript]
----
function printFarmInventory(cows, chickens) {
  var cowString = String(cows);
  while (cowString.length < 3)
    cowString = "0" + cowString;
  console.log(cowString + " Cows");
  var chickenString = String(chickens);
  while (chickenString.length < 3)
    chickenString = "0" + chickenString;
  console.log(chickenString + " Chickens");
}
printFarmInventory(7, 11);
----

(((length property,for string)))(((while loop)))Adding `.length`
after a string value will give us the length of that string. Thus, the
`while` loops keep adding zeros in front of the number strings until
they are at least three characters long.

Mission accomplished! But just as we are about to send the farmer the
code (along with a hefty invoice, of course), he calls and tells us
he's also started keeping pigs, and couldn't we please extend the
software to also print pigs?

(((copy-paste programming)))We sure can. But just as we're in the
process of copying and pasting those four lines one more time, we stop
and reconsider. There has to be a better way. Here's a first attempt:

[source,javascript]
----
function printZeroPaddedWithLabel(number, label) {
  var numberString = String(number);
  while (numberString.length < 3)
    numberString = "0" + numberString;
  console.log(numberString + " " + label);
}

function printFarmInventory(cows, chickens, pigs) {
  printZeroPaddedWithLabel(cows, "Cows");
  printZeroPaddedWithLabel(chickens, "Chickens");
  printZeroPaddedWithLabel(pigs, "Pigs");
}

printFarmInventory(7, 11, 3);
----

(((function,naming)))It works! But that name,
`printZeroPaddedWithLabel`, is a little awkward. It conflates three
things—printing, zero-padding, and adding a label—into a single
function.

(((zeroPad function)))Instead of lifting out the repeated part of our
program wholesale, let's try to pick out a single _concept_.

[source,javascript]
----
function zeroPad(number, width) {
  var string = String(number);
  while (string.length < width)
    string = "0" + string;
  return string;
}

function printFarmInventory(cows, chickens, pigs) {
  console.log(zeroPad(cows, 3) + " Cows");
  console.log(zeroPad(chickens, 3) + " Chickens");
  console.log(zeroPad(pigs, 3) + " Pigs");
}

printFarmInventory(7, 16, 3);
----

(((readability)))(((pure function)))A function with a nice, obvious
name like `zeroPad` makes it easier for someone who reads the code to
figure out what it does. And it is useful in more situations than just
this specific program. For example, you could use it to help print
nicely aligned tables of numbers.

(((interface,design)))How smart and versatile should our function be?
We could write anything from a terribly simple function that simply
pads a number so that it's three characters wide to a complicated
generalized number-formatting system that handles fractional numbers,
negative numbers, alignment of dots, padding with different
characters, and so on.

A useful principle is not to add cleverness unless you are absolutely
sure you're going to need it. It can be tempting to write general
“((framework))s” for every little bit of functionality you come
across. Resist that urge. You won't get any real work done, and you'll
end up writing a lot of code that no one will ever use.

[[pure]]
== Functions and side effects ==

(((side effect)))(((pure function)))(((function,purity)))Functions can
be roughly divided into those that are called for their side effects
and those that are called for their return value. (Though it is
definitely also possible to have both side effects and return a
value.)

(((reuse)))The first helper function in the ((farm example)),
`printZeroPaddedWithLabel`, is called for its side effect: it prints a
line. The second version, `zeroPad`, is called for its return value.
It is no coincidence that the second is useful in more situations than
the first. Functions that create values are easier to combine in new
ways than functions that directly perform side effects.

(((substitution)))A _pure_ function is a specific kind of
value-producing function that not only has no side effects but also
doesn't rely on side effects from other code—for example, it doesn't
read global variables that are occasionally changed by other code. A
pure function has the pleasant property that, when called with the
same arguments, it always produces the same value (and doesn't do
anything else). This makes it easy to reason about. A call to such a
function can be mentally substituted by its result, without changing
the meaning of the code. When you are not sure that a pure function is
working correctly, you can test it by simply calling it, and know that
if it works in that context, it will work in any context. Nonpure
functions might return different values based on all kinds of factors
and have side effects that might be hard to test and think about.

(((optimization)))(((console.log)))Still, there's no need to feel bad
when writing functions that are not pure or to wage a holy war to
purge them from your code. Side effects are often useful. There'd be
no way to write a pure version of `console.log`, for example, and
`console.log` is certainly useful. Some operations are also easier to
express in an efficient way when we use side effects, so computing
speed can be a reason to avoid purity.

== Summary ==

This chapter taught you how to write your own functions. The
`function` keyword, when used as an expression, can create a function
value. When used as a statement, it can be used to declare a variable
and give it a function as its value.

[source,javascript]
----
// Create a function value f
var f = function(a) {
  console.log(a + 2);
};

// Declare g to be a function
function g(a, b) {
  return a * b * 3.5;
}
----

A key aspect in understanding functions is understanding local scopes.
Parameters and variables declared inside a function are local to the
function, re-created every time the function is called, and not visible
from the outside. Functions declared inside another function have
access to the outer function's local scope.

Separating the tasks your program performs into different
functions is helpful. You won't have to repeat yourself as much, and
functions can make a program more readable by grouping code into
conceptual chunks, in the same way that chapters and sections help
organize regular text.

== Exercises ==

=== Minimum ===

(((Math object)))(((minimum (exercise))))(((Math.min
function)))(((minimum)))The
link:02_program_structure.html#return_values[previous chapter]
introduced the standard function `Math.min` that returns its smallest
argument. We can do that ourselves now. Write a function `min` that
takes two arguments and returns their minimum.

ifdef::interactive_target[]

// test: no

[source,javascript]
----
// Your code here.

console.log(min(0, 10));
// → 0
console.log(min(0, -10));
// → -10
----
endif::interactive_target[]

!!hint!!

(((minimum (exercise))))If you have trouble putting braces and
parentheses in the right place to get a valid function definition,
start by copying one of the examples in this chapter and modifying it.

(((return keyword)))A function may contain multiple `return`
statements.

!!hint!!

=== Recursion ===

(((recursion)))(((isEven (exercise))))(((even number)))We've seen
that `%` (the remainder operator) can be used to test whether a number
is even or odd by using `% 2` to check whether it's divisible by two.
Here's another way to define whether a positive whole number is even
or odd:

- Zero is even.

- One is odd.

- For any other number _N_, its evenness is the same as _N_ - 2.

Define a recursive function `isEven` corresponding to this
description. The function should accept a `number` parameter and
return a Boolean.

(((stack overflow)))Test it on 50 and 75. See how it behaves on -1.
Why? Can you think of a way to fix this?

ifdef::interactive_target[]

// test: no

[source,javascript]
----
// Your code here.

console.log(isEven(50));
// → true
console.log(isEven(75));
// → false
console.log(isEven(-1));
// → ??
----
endif::interactive_target[]

!!hint!!

(((isEven (exercise))))(((if keyword,chaining)))(((recursion)))Your
function will likely look somewhat similar to the inner `find`
function in the recursive `findSolution`
link:03_functions.html#recursive_puzzle[example] in this chapter, with
an `if`/`else if`/`else` chain that tests which of the three cases
applies. The final `else`, corresponding to the third case, makes the
recursive call. Each of the branches should contain a `return`
statement or in some other way arrange for a specific value to be
returned.

(((stack overflow)))When given a negative number, the function will
recurse again and again, passing itself an ever more negative number,
thus getting further and further away from returning a result. It will
eventually run out of stack space and abort.

!!hint!!

=== Bean counting ===

(((bean counting (exercise))))(((charAt
method)))(((string,indexing)))(((zero-based counting)))You can get the
Nth character, or letter, from a string by writing
`"string".charAt(N)`, similar to how you get its length with
`"s".length`. The returned value will be a string containing only one
character (for example, `"b"`). The first character has position zero,
which causes the last one to be found at position `string.length - 1`.
In other words, a two-character string has length 2, and its
characters have positions 0 and 1.

Write a function `countBs` that takes a string as its only argument
and returns a number that indicates how many uppercase “B” characters
are in the string.

Next, write a function called `countChar` that behaves like `countBs`,
except it takes a second argument that indicates the character that is
to be counted (rather than counting only uppercase “B” characters).
Rewrite `countBs` to make use of this new function.

ifdef::interactive_target[]

// test: no

[source,javascript]
----
// Your code here.

console.log(countBs("BBC"));
// → 2
console.log(countChar("kakkerlak", "k"));
// → 4
----
endif::interactive_target[]

!!hint!!

(((bean counting (exercise))))(((length property,for
string)))(((counter variable)))A ((loop)) in your function will have
to look at every character in the string by running an index from zero
to one below its length (`< string.length`). If the character at the
current position is the same as the one the function is looking for,
it adds 1 to a counter variable. Once the loop has finished, the
counter can be returned.

(((local variable)))Take care to make all the variables used in the
function _local_ to the function by using the `var` keyword.

!!hint!!