# 2. Variables, expressions and statements¶

## 2.1. Values and data types¶

A **value** is one of the fundamental things — like a letter or a number —
that a program manipulates. The values we have seen so far are `4`

(the
result when we added `2 + 2`

), and `"Hello, World!"`

.

These values are classified into different **classes**, or **data types**: `4`

is an *integer*, and `"Hello, World!"`

is a *string*,
so-called because it contains a string of
letters. You (and the interpreter) can identify strings because they are
enclosed in quotation marks.

If you are not sure what class a value falls into, Python has a function
called **type** which can tell you.

>>> type("Hello, World!") <class 'str'> >>> type(17) <class 'int'>

Not surprisingly, strings belong to the class **str** and integers belong to the
class **int**. Less obviously, numbers with a decimal point belong to a class
called **float**, because these numbers are represented in a format called
*floating-point*. At this stage, you can treat the words *class* and *type*
interchangeably. We’ll come back to a deeper understanding of what a class
is in later chapters.

>>> type(3.2) <class 'float'>

What about values like `"17"`

and `"3.2"`

? They look like numbers, but they
are in quotation marks like strings.

>>> type("17") <class 'str'> >>> type("3.2") <class 'str'>

They’re strings!

Strings in Python can be enclosed in either single quotes (`'`

) or double quotes
(`"`

), or three of each (`'''`

or `"""`

)

>>> type('This is a string.') <class 'str'> >>> type("And so is this.") <class 'str'> >>> type("""and this.""") <class 'str'> >>> type('''and even this...''') <class 'str'>

Double quoted strings can contain single quotes inside them, as in
`"Bruce's beard"`

, and single quoted strings can have double quotes
inside them, as in `'The knights who say "Ni!"'`

.

Strings enclosed with three occurrences of either quote symbol are called triple quoted strings. They can contain either single or double quotes:

>>> print('''"Oh no", she exclaimed, "Ben's bike is broken!"''') "Oh no", she exclaimed, "Ben's bike is broken!" >>>

Triple quoted strings can even span multiple lines:

>>> message = """This message will ... span several ... lines.""" >>> print(message) This message will span several lines. >>>

Python doesn’t care whether you use single or double quotes or the three-of-a-kind quotes to surround your strings: once it has parsed the text of your program or command, the way it stores the value is identical in all cases, and the surrounding quotes are not part of the value. But when the interpreter wants to display a string, it has to decide which quotes to use to make it look like a string.

>>> 'This is a string.' 'This is a string.' >>> """And so is this.""" 'And so is this.'

So the Python language designers usually chose to surround their strings by single quotes. What do think would happen if the string already contained single quotes?

When you type a large integer, you might be tempted to use commas between
groups of three digits, as in `42,000`

. The same goes for entering Dutch-style
floating point numbers using a comma instead of a decimal dot.
This is not a legal integer in Python, but it does mean something else, which is legal:

>>> 42000 42000 >>> 42,000 (42, 0)

Well, that’s not what we expected at all! Because of the comma, Python chose to
treat this as a *pair* of values. We’ll come back to learn about pairs later.
But, for the moment, remember not to put commas or spaces in your integers, no matter
how big they are. Also revisit what we said in the previous chapter: formal languages are
strict, the notation is concise, and even the smallest change might
mean something quite different from what you intended.

## 2.2. Variables¶

One of the most powerful features of a programming language is the ability to
manipulate **variables**. A variable is a name that refers to a value.

The **assignment statement** gives a value to a variable:

>>> message = "What's up, Doc?" >>> n = 17 >>> pi = 3.14159

This example makes three assignments. The first assigns the string value ```
"What's
up, Doc?"
```

to a variable named `message`

. The second gives the integer
`17`

to `n`

, and the third assigns the floating-point number `3.14159`

to
a variable called `pi`

.

The **assignment token**, `=`

, should not be confused with *equals*, which uses
the token `==`

. The assignment statement binds a *name*, on the
left-hand side of the operator, to a *value*, on the right-hand side.
Basically, an assignment is an order, and the equals operator can be read as a question mark.
This is why you will get an error if you enter:

>>> 17 = n File "<interactive input>", line 1 SyntaxError: can't assign to literalTip

When reading or writing code, say to yourself “n is assigned 17” or “n gets the value 17”. Don’t say “n equals 17”.

A common way to represent variables on paper is to write the name with an arrow
pointing to the variable’s value. This kind of figure is called a **state
snapshot** because it shows what state each of the variables is in at a particular
instant in time. (Think of it as the variable’s state of mind).
Some editors and programming environments do this for you, and allow you to
click through the state of the program saving you some paper.
This diagram shows the result of executing the assignment statements:

If you ask the interpreter to evaluate a variable, it will produce the value that is currently linked to the variable:

>>> message 'What's up, Doc?' >>> n 17 >>> pi 3.14159

We use variables in a program to “remember” things, perhaps the current score at the football game.
But variables are *variable*. This means they can change over time, just like the scoreboard at a football game.
You can assign a value to a variable, and later assign a different value to the same variable.
(*This is different from maths. In maths, if you give `x` the value 3, it
cannot change to link to a different value half-way through your calculations!*)

>>> day = "Thursday" >>> day 'Thursday' >>> day = "Friday" >>> day 'Friday' >>> day = 21 >>> day 21

You’ll notice we changed the value of `day`

three times, and on the third assignment we even
made it refer to a value that was of a different type.

A great deal of programming is about having the computer remember things, e.g. *The number of missed calls on your phone*,
and then arranging to update or change the variable when you miss another call.

## 2.3. Variable names and keywords¶

**Variable names** can be arbitrarily long. They can contain both letters and
digits, but they have to begin with a letter or an underscore. Although it is legal to use
uppercase letters, by convention we don’t. If you do, remember that case
matters. `Bruce`

and `bruce`

are different variables.

The underscore character ( `_`

) can appear in a name. It is often used in
names with multiple words, such as `my_name`

or `price_of_tea_in_china`

.

There are some situations in which names beginning with an underscore have special meaning, so a safe rule for beginners is to start all names with a letter.

If you give a variable an illegal name, you get a syntax error:

>>> 76trombones = "big parade" SyntaxError: invalid syntax >>> more$ = 1000000 SyntaxError: invalid syntax >>> class = "Computer Science 101" SyntaxError: invalid syntax

`76trombones`

is illegal because it does not begin with a letter. `more$`

is illegal because it contains an illegal character, the dollar sign. But
what’s wrong with `class`

?

It turns out that `class`

is one of the Python **keywords**. Keywords define
the language’s syntax rules and structure, and they cannot be used as variable names.

Python has thirty-something keywords (and every now and again improvements to Python introduce or eliminate one or two):

and | as | assert | break | class | continue |

def | del | elif | else | except | exec |

finally | for | from | global | if | import |

in | is | lambda | nonlocal | not | or |

pass | raise | return | try | while | with |

yield | True | False | None |

You might want to keep this list handy. If the interpreter complains about one of your variable names and you don’t know why, see if it is on this list.

Programmers generally choose names for their variables that are meaningful to the human readers of the program — they help the programmer document, or remember, what the variable is used for.

Caution

Beginners sometimes confuse “meaningful to the human readers” with “meaningful to the computer”.
So they’ll wrongly think that because they’ve called some variable `average`

or `pi`

, it will
somehow magically calculate an average, or magically know that the variable `pi`

should have a
value like 3.14159. No! The computer doesn’t understand what you intend the variable to mean.

So you’ll find some instructors who deliberately don’t choose meaningful
names when they teach beginners — not because we don’t think it is a good habit,
but because we’re trying to reinforce the message that you — the programmer — must
write the program code to calculate the average, and you must write an assignment
statement to give the variable `pi`

the value you want it to have.

```
e = 3.1415
ray = 10
size = e * ray ** 2
```

```
pi = 3.1415
radius = 10
area = pi * radius ** 2
```

The above two snippets do exactly the same thing, but the bottom one uses the right kind of variable names.
For the computer there is no difference at all, but for a human, using the names and letters that are part
of the conventional way of writing things make all the difference in the world. Using `e`

instead of `pi`

completely confuses people, while computers will just perform the calculation!

## 2.4. Statements¶

A **statement** is an instruction that the Python interpreter can execute. We
have only seen the assignment statement so far. Some other kinds of statements that
we’ll see shortly are `while`

statements, `for`

statements, `if`

statements,
and `import`

statements. (There are other kinds too!)

When you type a statement on the command line, Python executes it. Statements don’t produce any result.

## 2.5. Evaluating expressions¶

An **expression** is a combination of values, variables, operators, and calls to functions. If you
type an expression at the Python prompt, the interpreter **evaluates** it and
displays the result:

>>> 1 + 1 2 >>> len("hello") 5

In this example `len`

is a built-in Python function that returns the number of characters in a string.
We’ve previously seen the `print`

and the `type`

functions, so this is our third example of a function!

The *evaluation of an expression* produces a value, which is why expressions
can appear on the right hand side of assignment statements. A value all by
itself is a simple expression, and so is a variable.

>>> 17 17 >>> y = 3.14 >>> x = len("hello") >>> x 5 >>> y 3.14

## 2.6. Operators and operands¶

**Operators** are special tokens that represent computations like addition,
multiplication and division. The values the operator uses are called **operands**.

The following are all legal Python expressions whose meaning is more or less clear:

```
20+32 hour-1 hour*60+minute minute/60 5**2 (5+9)*(15-7)
```

The tokens `+`

, `-`

, and `*`

, and the use of parenthesis for grouping,
mean in Python what they mean in mathematics. The asterisk (`*`

) is the
token for multiplication, and `**`

is the token for exponentiation.

>>> 2 ** 3 8 >>> 3 ** 2 9

When a variable name appears in the place of an operand, it is replaced with its value before the operation is performed.

Addition, subtraction, multiplication, and exponentiation all do what you expect.

Example: so let us convert 645 minutes into hours:

>>> minutes = 645 >>> hours = minutes / 60 >>> hours 10.75

Oops! In Python 3, the division operator `/`

always yields a floating point result.
What we might have wanted to know was how many *whole* hours there are, and how many minutes remain.
Python gives us two different flavors of the division operator.
The second, called **floor division** uses the token //.
Its result is always a whole number — and if it has to adjust the number it always
moves it to the left on the number line. So 6 // 4 yields 1, but -6 // 4 might surprise you!

>>> 7 / 4 1.75 >>> 7 // 4 1 >>> minutes = 645 >>> hours = minutes // 60 >>> hours 10

Take care that you choose the correct flavor of the division operator. If you’re working with expressions where you need floating point values, use the division operator that does the division accurately.

## 2.7. Type converter functions¶

Here we’ll look at three more Python functions, `int`

, `float`

and `str`

, which will (attempt to)
convert their arguments into types `int`

, `float`

and `str`

respectively. We call these
**type converter** functions.

The `int`

function can take a floating point number or a string, and turn
it into an int. For floating point numbers, it *discards* the decimal portion
of the number — a process we call *truncation towards zero* on
the number line. Let us see this in action:

>>> int(3.14) 3 >>> int(3.9999) # This doesn't round to the closest int! 3 >>> int(3.0) 3 >>> int(-3.999) # Note that the result is closer to zero -3 >>> int(minutes / 60) 10 >>> int("2345") # Parse a string to produce an int 2345 >>> int(17) # It even works if arg is already an int 17 >>> int("23 bottles")

This last case doesn’t look like a number — what do we expect?

Traceback (most recent call last): File "<interactive input>", line 1, in <module> ValueError: invalid literal for int() with base 10: '23 bottles'

The type converter `float`

can turn an integer, a float, or a syntactically legal
string into a float:

>>> float(17) 17.0 >>> float("123.45") 123.45

The type converter `str`

turns its argument into a string:

>>> str(17) '17' >>> str(123.45) '123.45'

## 2.8. Order of operations¶

When more than one operator appears in an expression, the order of evaluation
depends on the **rules of precedence**. Python follows the same precedence
rules for its mathematical operators that mathematics does. The acronym PEMDAS
is a useful way to remember the order of operations:

**P**arentheses have the highest precedence and can be used to force an expression to evaluate in the order you want. Since expressions in parentheses are evaluated first,`2 * (3-1)`

is 4, and`(1+1)**(5-2)`

is 8. You can also use parentheses to make an expression easier to read, as in`(minute * 100) / 60`

, even though it doesn’t change the result.**E**xponentiation has the next highest precedence, so`2**1+1`

is 3 and not 4, and`3*1**3`

is 3 and not 27.**M**ultiplication and both**D**ivision operators have the same precedence, which is higher than**A**ddition and**S**ubtraction, which also have the same precedence. So`2*3-1`

yields 5 rather than 4, and`5-2*2`

is 1, not 6.Operators with the

*same*precedence are evaluated from left-to-right. In algebra we say they are*left-associative*. So in the expression`6-3+2`

, the subtraction happens first, yielding 3. We then add 2 to get the result 5. If the operations had been evaluated from right to left, the result would have been`6-(3+2)`

, which is 1. (The acronym PEDMAS could mislead you to thinking that division has higher precedence than multiplication, and addition is done ahead of subtraction - don’t be misled. Subtraction and addition are at the same precedence, and the left-to-right rule applies.)Due to some historical quirk, an exception to the left-to-right left-associative rule is the exponentiation operator

`**`

, so a useful hint is to always use parentheses to force exactly the order you want when exponentiation is involved:>>> 2 ** 3 ** 2 # The right-most ** operator gets done first! 512 >>> (2 ** 3) ** 2 # Use parentheses to force the order you want! 64

The immediate mode command prompt of Python is great for exploring and experimenting with expressions like this.

## 2.9. Operations on strings¶

In general, you cannot perform mathematical operations on strings, even if the
strings look like numbers. The following are illegal (assuming that `message`

has type string):

>>> message - 1 # Error >>> "Hello" / 123 # Error >>> message * "Hello" # Error >>> "15" + 2 # Error

Interestingly, the `+`

operator does work with strings, but for strings,
the `+`

operator represents **concatenation**, not addition.
Concatenation means joining the two operands by linking them end-to-end. For example:

1 2 3 fruit = "banana" baked_good = " nut bread" print(fruit + baked_good)

The output of this program is `banana nut bread`

. The space before the word
`nut`

is part of the string, and is necessary to produce the space between
the concatenated strings.

The `*`

operator also works on strings; it performs repetition. For example,
`'Fun'*3`

is `'FunFunFun'`

. One of the operands has to be a string; the
other has to be an integer.

On one hand, this interpretation of `+`

and `*`

makes sense by analogy with
addition and multiplication. Just as `4*3`

is equivalent to `4+4+4`

, we
expect `"Fun"*3`

to be the same as `"Fun"+"Fun"+"Fun"`

, and it is. On the
other hand, there is a significant way in which string concatenation and
repetition are different from integer addition and multiplication. Can you
think of a property that addition and multiplication have that string
concatenation and repetition do not?

## 2.10. Input¶

There is a built-in function in Python for getting input from the user:

1 name = input("Please enter your name: ")

The user of the program can enter the name and click OK, and when this happens
the text that has been entered is returned from the `input`

function, and in this
case assigned to the variable `name`

.

Even if you asked the user to enter their age, you would get back a string like `"17"`

.
It would be your job, as the programmer, to convert that string into a int or a float,
using the `int`

or `float`

converter functions we saw earlier.

## 2.11. Composition¶

So far, we have looked at the elements of a program — variables, expressions, statements, and function calls — in isolation, without talking about how to combine them.

One of the most useful features of programming languages is their ability to
take small building blocks and **compose** them into larger chunks.

For example, we know how to get the user to enter some input, we know how to convert the string we get into a float, we know how to write a complex expression, and we know how to print values. Let’s put these together in a small four-step program that asks the user to input a value for the radius of a circle, and then computes the area of the circle from the formula

Firstly, we’ll do the four steps one at a time:

1 2 3 4 response = input("What is your radius? ") r = float(response) area = 3.14159 * r**2 print("The area is ", area)

Now let’s compose the first two lines into a single line of code, and compose the second two lines into another line of code.

1 2 r = float( input("What is your radius? ") ) print("The area is ", 3.14159 * r**2)

If we really wanted to be tricky, we could write it all in one statement:

1 print("The area is ", 3.14159*float(input("What is your radius?"))**2)

Such compact code may not be most understandable for humans, but it does illustrate how we can compose bigger chunks from our building blocks.

If you’re ever in doubt about whether to compose code or fragment it into smaller steps, try to make it as simple as you can for the human to follow. My choice would be the first case above, with four separate steps.

## 2.12. The modulus operator¶

The **modulus operator** works on integers (and integer expressions) and gives
the remainder when the first number is divided by the second. In Python, the
modulus operator is a percent sign (`%`

). The syntax is the same as for other
operators. It has the same precedence as the multiplication operator.

>>> q = 7 // 3 # This is integer division operator >>> print(q) 2 >>> r = 7 % 3 >>> print(r) 1

So 7 divided by 3 is 2 with a remainder of 1.

The modulus operator turns out to be surprisingly useful. For example, you can
check whether one number is divisible by another—if `x % y`

is zero, then
`x`

is divisible by `y`

.

Also, you can extract the right-most digit or digits from a number. For
example, `x % 10`

yields the right-most digit of `x`

(in base 10).
Similarly `x % 100`

yields the last two digits.

It is also extremely useful for doing conversions, say from seconds, to hours, minutes and seconds. So let’s write a program to ask the user to enter some seconds, and we’ll convert them into hours, minutes, and remaining seconds.

1 2 3 4 5 6 7 8 total_secs = int(input("How many seconds, in total?")) hours = total_secs // 3600 secs_still_remaining = total_secs % 3600 minutes = secs_still_remaining // 60 secs_finally_remaining = secs_still_remaining % 60 print("Hrs=", hours, " mins=", minutes, "secs=", secs_finally_remaining)

## 2.13. Glossary¶

- assignment statement
A statement that assigns a value to a name (variable). To the left of the assignment operator,

`=`

, is a name. To the right of the assignment token is an expression which is evaluated by the Python interpreter and then assigned to the name. The difference between the left and right hand sides of the assignment statement is often confusing to new programmers. In the following assignment:number = number + 1

`number`

plays a very different role on each side of the`=`

. On the right it is a*value*and makes up part of the*expression*which will be evaluated by the Python interpreter before assigning it to the name on the left.- assignment token
`=`

is Python’s assignment token. Do not confuse it with*equals*, which is an operator for comparing values.- composition
- The ability to combine simple expressions and statements into compound statements and expressions in order to represent complex computations concisely.
- concatenate
- To join two strings end-to-end.
- data type
- A set of values. The type of a value determines how it can be used in
expressions. So far, the types you have seen are integers (
`int`

), floating-point numbers (`float`

), and strings (`str`

). - evaluate
- To simplify an expression by performing the operations in order to yield a single value.
- expression
- A combination of variables, operators, and values that represents a single result value.
- float
- A Python data type which stores
*floating-point*numbers. Floating-point numbers are stored internally in two parts: a*base*and an*exponent*. When printed in the standard format, they look like decimal numbers. Beware of rounding errors when you use`float`

s, and remember that they are only approximate values. - floor division
- An operator (denoted by the token
`//`

) that divides one number by another and yields an integer, or, if the result is not already an integer, it yields the next smallest integer. - int
- A Python data type that holds positive and negative whole numbers.
- keyword
- A reserved word that is used by the compiler to parse program; you
cannot use keywords like
`if`

,`def`

, and`while`

as variable names. - modulus operator
- An operator, denoted with a percent sign (
`%`

), that works on integers and yields the remainder when one number is divided by another. - operand
- One of the values on which an operator operates.
- operator
- A special symbol that represents a simple computation like addition, multiplication, or string concatenation.
- rules of precedence
- The set of rules governing the order in which expressions involving multiple operators and operands are evaluated.
- state snapshot
- A graphical representation of a set of variables and the values to which they refer, taken at a particular instant during the program’s execution.
- statement
- An instruction that the Python interpreter can execute. So far we have
only seen the assignment statement, but we will soon meet the
`import`

statement and the`for`

statement. - str
- A Python data type that holds a string of characters.
- value
- A number or string (or other things to be named later) that can be stored in a variable or computed in an expression.
- variable
- A name that refers to a value.
- variable name
- A name given to a variable. Variable names in Python consist of a
sequence of letters (a..z, A..Z, and _) and digits (0..9) that begins
with a letter. In best programming practice, variable names should be
chosen so that they describe their use in the program, making the
program
*self documenting*.

## 2.14. Exercises¶

Take the sentence:

*All work and no play makes Jack a dull boy.*Store each word in a separate variable, then print out the sentence on one line using`print`

.Add parenthesis to the expression

`6 * 1 - 2`

to change its value from 4 to -6.Place a comment before a line of code that previously worked, and record what happens when you rerun the program.

Start the Python interpreter and enter

`bruce + 4`

at the prompt. This will give you an error:NameError: name 'bruce' is not defined

Assign a value to

`bruce`

so that`bruce + 4`

evaluates to`10`

.The formula for computing the final amount if one is earning compound interest is given on Wikipedia as

Here, P is the principal amount (the amount that the interest is provided on), n the frequency that the interest is paid out (per year), and r the interest rate. The number of years that the interest is calculated for is t. Write a program that replaces these letters with something a bit more human-readable, and calculate the interest for some varying amounts of money at realistic interest rates such as 1%, and -0.05%. When you have that working, ask the user for the value of some of these variables and do the calculation.

Evaluate the following numerical expressions in your head, then use the Python interpreter to check your results:

`>>> 5 % 2`

`>>> 9 % 5`

`>>> 15 % 12`

`>>> 12 % 15`

`>>> 6 % 6`

`>>> 0 % 7`

`>>> 7 % 0`

What happened with the last example? Why? If you were able to correctly anticipate the computer’s response in all but the last one, it is time to move on. If not, take time now to make up examples of your own. Explore the modulus operator until you are confident you understand how it works.

You look at the clock and it is exactly 2pm. You set an alarm to go off in 51 hours. At what time does the alarm go off? (Hint: you could count on your fingers, but this is not what we’re after. If you are tempted to count on your fingers, change the 51 to 5100.)

Write a Python program to solve the general version of the above problem. Ask the user for the time now (in hours), and ask for the number of hours to wait. Your program should output what the time will be on the clock when the alarm goes off.