Recall True and False are the two booleans in Python. It turns out they're pretty handy. For instance, what if we want to do something, but only if a particular condition is True? What if we want to repeat something until that condition is False? These sorts of problems come up all the time — whether you're programming a calculator, a video game, a Terminator robot, or anything in between.

# Comparisons

Now is a good time to learn about comparisons, which let us know which of two things is bigger or smaller. There are a few different comparisons Python supports:

• x > y if and only if x is bigger than y.
• x < y if and only if x is smaller than y.
• x >= y if and only if x is bigger than y, or x is equal to y.
• x <= y if and only if x is smaller than y, or x is equal to y.
• x == y if and only if x is equal to y.
• x != y if and only if x is not equal to y.

Notice we used two equals signs instead of one, to test whether x equals y. That's because one equals sign is used for assigning variables, not testing equality, so x == y is very different from x = y.

>>> x = 3
>>> x
3
>>> x == 3
True
>>> x == 3.14
False

You can also make several comparisons at once, as in the examples below. Every individual comparison must be True in order for the whole expression to evaluate to True. For instance, x < y < z requires x < y and y < z to both be True.

>>> 1 == 1 < 2 == 2
True
>>> 3.14 <= 30 % 9 >= 2.718
False

But comparisons aren't just for numbers. You can also compare strings to other strings, according to alphabetical order. Strings of numbers are less than strings of capital letters, which are less than strings of lowercase letters.

>>> '0' < '9' < 'A' < 'Z' < 'a' < 'z'
True

The == and != operators work for pointers at functions, too. Two pointers are equal if they point to the exact same thing, otherwise they are not equal. In the example below, f == g is True because f and g point to the exact same function. Meanwhile f == h is False because f and h point to two different functions. It doesn't matter that those two functions do the same thing.

>>> def f():
...     return 5
...
>>> g = f
>>> def h():
...     return 5
...
>>> f == g
True
>>> f == h
False

# Conditions

This is where things get exciting. We're about to see how to write code that makes decisions.

## The if and else statements

Using the if keyword, you can write code that does different things based on whether a condition is True or not. In particular, if the condition is True, then everything inside the if statement will happen. Otherwise it won't. Then, once everything within the if statement has happened, you move back outside and continue with the rest of the function.

>>> def example(n):
...     if n == 0:
...         print('zero') # This happens when n is 0.
...     return n          # This always happens.
...
>>> example(0)
zero
0
>>> example(1)
1

It may seem strange, but this could lead to some situations when you have multiple return statements in one function. That's fine — remember, we automatically stop as soon as we hit either one. In the next example we use the first one if n is even, otherwise we use the second one.

>>> def is_even(n):
...    if n % 2 == 0:
...        return True
...    return False
...
>>> is_even(2)
True
>>> is_even(-5)
False

You can also use the keyword else, which has to come right after an if statement. When you choose to have an else statement, your function will always execute either the if statement of the else statement but never both.

>>> def example(n):
...     if n == 0:
...         print('zero')    # This happens when n is 0.
...     else:
...         print('nonzero') # This happens when n isn't 0.
...     return n             # This always happens.
...
>>> example(0)
zero
0
>>> example(1)
nonzero
1

Here's an example of how to write an if / else statement on one line. It's called a ternary if.

>>> forecast = 50
>>> 'snow' if forecast < 30 else 'rain'
'rain'

Try not to do this too often, though. It can get really hard to read.

## The elif statement

This is cool so far, but it gets even cooler. When you have a lot of different conditions, and you only want to use one of them, you can use elif statements, short for "else if". You can have a bunch of elif statements in a row, if you want.

>>> def sign(n):
...     if n < 0:
...         return '-'
...     elif n > 0:
...         return '+'
...     else:
...         return 0
...
>>> sign(-1.1)
'-'
>>> sign(0) + 5
5

Below you'll find an equivalent way of expressing the function above, using only if and else statements. As you can see, it's a lot harder to read.

>>> def sign(n):
...     if n < 0:
...         return '-'
...     else:
...         if n > 0:
...             return '+'
...         else:
...             return 0
...
>>> sign(-1.1)
'-'
>>> sign(0) + 5
5

Be careful; elif is sometimes tricky. It is not the same as if! Why? In a bunch of if statements, you might end up executing more than one. In an elif chain, on the other hand, you only execute the first statement whose condition is True. For example, compare the two definitions of the size function below.

>>> def size(n):
...     if n > 1000:
...         print('big')
...     if n > 0:
...         print('meh')
...
>>> size(2000)
big
meh
>>> def size(n):
...     if n > 1000:
...         print('big')
...     elif n > 0:
...         print('meh')
...
>>> size(2000)
big

## Lazy evaluation

One last thing to know about conditions is that they are lazy. In other words, they only evaluate something if they absolutely have to. This goes for one-line if / else statements too. When we run lucky(4) in the code below, both conditions evaluate to False. That means there's no need to evaluate the part that says return 1 / 0 or the part that says return 'zebra' + 10, so we don't actually get an error. Instead we just keep going until we find a condition that works.

>>> def lucky(n):
...     if n == 7:
...         return 1 / 0
...     elif n == 13:
...         return 'zebra' + 10
...     else:
...         return True
...
>>> lucky(4)
True

# Boolean operators

There are three boolean operators: not, and, and or. Let's see how they work.

1. not negates a boolean expression.
>>> not True
False
>>> not False
True
2. and requires that both boolean expressions are True.
>>> True and True
True
>>> True and False
False
3. or requires that either of two boolean expressions is True.
>>> True or False
True
>>> False or False
False

## The order of evaluation

In grade school you probably learned that when you see an arithmetic expression like $1 + 2 \times 3$, it makes a big difference whether you do $(1 + 2) \times 3$ or $1 + (2 \times 3)$. This is a problem, because some people might read it as $(1 + 2) \times 3$ and get 9, whereas others might read it as $1 + (2 \times 3)$ and get 7. In order to avoid confusion, there's a well-established convention that you should do multiplication first, and addition second. So the correct way to read $1 + 2 \times 3$ is like $1 + (2 \times 3)$.

We face a similar problem with the boolean operators. For instance, does not True and False mean (not True) and False or does it mean not (True and False)? Let's try it out in the Python interpreter and find out:

>>> not True and False
False
>>> (not True) and False
False
>>> not (True and False)
True

It looks like not True and False agrees with the output for (not True) and False but disagrees with the output for not (True and False). That means (not True) and False is the right way to read it, which tells us not should come before and.

What about or? Let's try it out with False and False or True, which could mean (False and False) or True or False and (False or True). Here's how we might test it out in the Python interpreter:

>>> False and False or True
True
>>> (False and False) or True
True
>>> False and (False or True)
False

Since False and False or True matches with the output for (False and False) or True, we can see that and should come before or.

In summary, here's the proper order of boolean operations:

1. not
2. and
3. or

## Truthy and falsey values

So far we've only seen boolean expressions that evaluate to either True or False. But what if we have a boolean expression that evaluates to something else? Like, what if we see if 3.14: ...? That might be an issue, since 3.14 is not a boolean. Python solves this problem by automatically converting it to a boolean with the bool function that we saw when we learned about the primitive types.

Here's an example. It will help to recall bool(3.14) and bool('cowboys') are both True, bool('') is False, and bool(print('dinosaurs')) is False because print('dinosaurs') evaluates to None.

>>> if 3.14:
...     print('vs pirates')
...
vs pirates
>>> if 'cowboys':
...     print('vs aliens)
...
vs aliens
>>> if '':
...     print('vs a vacuum')
...
>>> if print('dinosaurs'):
...     print('vs ducks')
...
dinosaurs

Things like 3.14 and 'cowboys' are called truthy because you get True when you call bool on them. Similarly, things like '' and None are called falsey because you get False when you call bool on them. They behave just like True and False whenever you're dealing with boolean expressions or if / elif / else conditions. But keep in mind, truthy values do not equal True and falsey values do not equal False.

>>> 3.14 == True
False
>>> None == False
False

The numbers 1 and 0 are exceptions. That's because everything inside your computer is represented by 1's and 0's, so fundamentally True is just another name for 1 and False is just another name for 0.

>>> 1 == True
True
>>> 0 == False
True

## Short-circuiting

Consider a boolean expression like True or False. It evaluates to True, but we didn't have to read the entire thing to figure that out. What if we stopped right after the or, so all we saw was True or ____? Whether we fill in the blank with True or False, this expression has to be True. (Try it out! True or True and True or False both evaluate to True.) So, if we already know the answer is going to be True, is there any reason to finish reading the whole expression? No, not really. In fact, Python stops reading as soon as it knows the answer. In this example, that's right before it would've read False. This is called short-circuiting.

Now is a good time to mention boolean expressions don't always evaluate to True or False. They evaluate to the last value Python reads before it knows the answer, which will always be a corresponding truthy or falsey value. For instance consider the expression 4 or False. Since 4 is a truthy value, it's basically the same as our previous example True or False. Python doesn't have to finish reading it to know the expression is truthy. But in this case, it returns 4 instead of True because that's the last value Python had to read.

Let's take a closer look at short-circuiting with the and and or operators:

• and checks that every value is truthy, so if it comes across a falsey value it can stop right there. In the example below we reach the falsey value 0.0, where we stop and return 0.0. It doesn't matter that later values would cause an error.
>>> -1 and 'cake' and 0.0 and 'is a' and 1 / 0 and lie
0.0
Now let's see an example where every value is truthy, so we just return 'glados' since that's the last value Python looks at.
>>> 'portal' and 42 != 54 and 7 < 8 < 9 and 'glados'
'glados'
• or checks that at least one value is truthy, so if it comes across a truthy value it can stop right there. In the example below we reach the truthy value 'town', where we stop and return 'town'. It doesn't matter that later values would cause an error.
>>> None or 18 % 9 or print('flavor') or 'town' or 'one' * 0 or 1 / 0
'town'
Now let's see an example where every value is falsey, so we just return 0 since that's the last value Python looks at.
>>> 'one' * 0 or int(0.9) or '' or 2018 % 5 - 3 or bool(int(3.14) - 3) or 0
0

## Evaluating boolean expressions

Now that we have a good understanding of the mechanics behind boolean expressions, we can make a procedure for how to evaluate them.

1. Add parentheses to the original expression, according to the order of boolean operations: not, and, then or.
2. Simplify the leftmost thing in your expression. If you can stop now, then it's your final answer. Otherwise delete it and repeat this step with your new, shorter expression.

## Practice: miscellaneous boolean expressions

To make sure we have the hang of things, let's practice applying the procedure above. We'll start with the expression 'do' and 're' and 'mi' or None and not 0.

1. First we add parentheses for not, to get 'do' and 're' and 'mi' or None and (not 0). Then we add parentheses for and, to get ('do' and 're' and 'mi') or (None and (not 0)). It's not really necessary to add parentheses for or since it's the lowest-priority operator.
2. The leftmost thing in our expression is 'do' and 're' and 'mi'. It's an and operator where every value is truthy, so Python reads the whole thing and evaluates it to 'mi'. Now our expression looks like 'mi' or (None and (not 0)). 'mi' is truthy and we're evaluating an or operator, so we can stop here. Our final answer is 'mi'.

Let's look at a harder one, like 'a' and not not print('b') and 1 / 0 or 'c' + 123. We'll take it one step at a time, using the same process from before.

1. First we add parentheses for not, to get 'a' and (not (not print('b'))) and 1 / 0 or 'c' + 123. Then we add parentheses for and, to get ('a' and (not (not print('b'))) and 1 / 0) or 'c' + 123. Again, it's not really necessary to add parentheses for or since it's the lowest-priority operator.

2. The leftmost thing in our expression is 'a' and (not (not print('b'))) and 1 / 0. It's a bit complicated, so we'll apply our procedure to just this sub-expression in order to evaluate it.

1. For step 1 in the procedure above, we just add the parentheses. Conveniently we've already done this, so we can move on.
2. The leftmost thing in our sub-expression is 'a'. It's truthy and we're on an and operator, so we have to keep going. According to the procedure above, we'll delete it and move on to (not (not print('b'))) and 1 / 0.
3. Now the leftmost thing is (not (not print('b'))). print('b') returns None which is falsey, so (not print('b')) is True and (not (not print('b'))) is False. Now our expression is False and 1 / 0. We can stop here and return False, because at this point our expression will be False no matter what comes next. Notice how we didn't have to evaluate 1 / 0, which would've given us an error.

Now that we have evaluated 'a' and (not (not print('b'))) and 1 / 0 to False, we can rewrite our bigger expression like False or 'c' + 123.

3. The leftmost thing is False, and since we're evaluating an or operator we have to keep going to see if there are any truthy values. According to the procedure above, we delete the False and keep going with just 'c' + 123.

4. The leftmost thing is now 'c' + 123, which causes an error. Whoops.