# Think Python/Variables, expressions and statements



### Values and types

A **value** is one of the basic things a program works with, like a
letter or a number. The values we have seen so far are `1`, `2`, and
`'Hello, World!'`.

These values belong to different **types**: `2` 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.

The print statement also works for integers.

``` python
>>> print (4)
4
```

If you are not sure what type a value has, the interpreter can tell you.

``` python
>>> type('Hello, World!')
<type 'str'>
>>> type(17)
<type 'int'>
```

Not surprisingly, strings belong to the type `str` and integers belong
to the type `int`. Less obviously, numbers with a decimal point belong
to a type called `float`, because these numbers are represented in a
format called **floating-point**.

``` python
>>> type(3.2)
<type 'float'>
```

What about values like `'17'` and `'3.2'`? They look like numbers, but
they are in quotation marks like strings.

``` python
>>> type('17')
<type 'str'>
>>> type('3.2')
<type 'str'>
```

They\'re strings.

When you type a large integer, you might be tempted to use commas
between groups of three digits, as in `1,000,000`. This is not a legal
integer in Python, but it is legal:

``` python
>>> print 1,000,000
1 0 0
```

Well, that's not what we expected at all! Python interprets `1,000,000`
as a comma-separated sequence of integers, which it prints with spaces
between.

This is the first example we have seen of a semantic error: the code
runs without producing an error message, but it doesn\'t do the "right"
thing.

### 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.

An **assignment statement** creates new variables and gives them values:

``` python
>>> message = 'And now for something completely different'
>>> n = 17
>>> pi = 3.1415926535897931
```

This example makes three assignments. The first assigns a string to a
new variable named `message`; the second gives the integer `17` to `n`;
the third assigns the (approximate) value of π to `pi`.

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 diagram** because it shows what state each of the variables is
in (think of it as the variable's state of mind). This diagram shows the
result of the previous example:

  ----------- --------------- ------------------------------------------------
  `message`   $\rightarrow$   `'And now for something completely different'`
  `n`         $\rightarrow$   `17`
  `pi`        $\rightarrow$   `3.1415926535897931`
  ----------- --------------- ------------------------------------------------

To display the value of a variable, you can use a print statement:

``` python
>>> print n
17
>>> print pi
3.14159265359
```

The type of a variable is the type of the value it refers to.

``` python
>>> type(message)
<type 'str'>
>>> type(n)
<type 'int'>
>>> type(pi)
<type 'float'>
```

#### Exercise 1

If you type an integer with a leading zero, you might get a confusing
error:

``` python
>>> zipcode = 02492
                 ^
SyntaxError: invalid token
```

Other numbers seem to work, but the results are bizarre:

``` python
>>> zipcode = 02132
>>> print zipcode
1114
```

Can you figure out what is going on? Hint: print the values `01`, `010`,
`0100` and `01000`.

### Variable names and keywords

Programmers generally choose names for their variables that are
meaningful---they document what the variable is used for.

Variable names can be arbitrarily long. They can contain both letters
and numbers, but they have to begin with a letter. It is legal to use
uppercase letters, but it is a good idea to begin variable names with a
lowercase letter (you\'ll see why later).

The underscore character (`_`) can appear in a name. It is often used in
names with multiple words, such as `my_name` or
`airspeed_of_unladen_swallow`.

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

``` python
>>> 76trombones = 'big parade'
SyntaxError: invalid syntax
>>> more@ = 1000000
SyntaxError: invalid syntax
>>> class = 'Advanced Theoretical Zymurgy'
SyntaxError: invalid syntax
```

`76trombones` is illegal because it does not begin with a letter.
`more@` is illegal because it contains an illegal character, `@`. But
what\'s wrong with `class`?

It turns out that `class` is one of Python\'s **keywords**. The
interpreter uses keywords to recognize the structure of the program, and
they cannot be used as variable names.

Python has 31 keywords:

  ------------ ----------- ---------- ---------- ---------
  `and`        `del`       `from`     `not`      `while`
  `as`         `elif`      `global`   `or`       `with`
  `assert`     `else`      `if`       `pass`     `yield`
  `break`      `except`    `import`   `print`    
  `class`      `exec`      `in`       `raise`    
  `continue`   `finally`   `is`       `return`   
  `def`        `for`       `lambda`   `try`      
  ------------ ----------- ---------- ---------- ---------

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.

If you write your code in a text editor that understands Python, you may
find that it makes it easy for you to spot such keyword clashes by
displaying keywords in a different color to ordinary variables. This
feature is called *syntax highlighting*, and most programmers find it
indispensable. This book uses syntax highlighting for its example code,
so in the following example:

``` python
ok_variable = 42
yield = 42
```

you can see that `yield` has been recognized as a keyword and not as an
ordinary variable, since it is colored green.

### Statements

A statement is a unit of code that the Python interpreter can execute.
We have seen two kinds of statements: print and assignment.

When you type a statement in interactive mode, the interpreter executes
it and displays the result, if there is one.

A script usually contains a sequence of statements. If there is more
than one statement, the results appear one at a time as the statements
execute.

For example, the script

``` python
print 1
x = 2
print x
```

produces the output

``` python
1
2
```

The assignment statement produces no output.

### Operators and operands

**Operators** are special symbols that represent computations like
addition and multiplication. The values the operator is applied to are
called **operands**.

The operators `+`, `-`, `*`, `/` and `**` perform addition, subtraction,
multiplication, division and exponentiation, as in the following
examples:

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

In some other languages, `^` is used for exponentiation, but in Python
it is a bitwise operator called XOR. I won't cover bitwise operators in
this book, but you can read about them at
`wiki.python.org/moin/BitwiseOperators`.

The division operator might not do what you expect:

``` python
>>> minute = 59
>>> minute/60
0
```

The value of `minute` is 59, and in conventional arithmetic 59 divided
by 60 is 0.98333, not 0. The reason for the discrepancy is that Python
is performing **floor division**.[^1]

When both of the operands are integers, the result is also an integer;
floor division chops off the fraction part, so in this example it rounds
down to zero.

If either of the operands is a floating-point number, Python performs
floating-point division, and the result is a `float`:

``` python
>>> minute/60.0
0.98333333333333328
```

### Expressions

An **expression** is a combination of values, variables, and operators.
A value all by itself is considered an expression, and so is a variable,
so the following are all legal expressions (assuming that the variable
`x` has been assigned a value):

``` python
17
x
x + 17
```

If you type an expression in interactive mode, the interpreter
**evaluates** it and displays the result:

``` python
>>> 1 + 1
2
```

But in a script, an expression all by itself doesn't do anything! This
is a common source of confusion for beginners.

#### Exercise 2

Type the following statements in the Python interpreter to see what they
do:

``` python
5
x = 5
x + 1
```

Now put the same statements into a script and run it. What is the
output? Modify the script by transforming each expression into a print
statement and then run it again.

### Order of operations

When more than one operator appears in an expression, the order of
evaluation depends on the **rules of precedence**. For mathematical
operators, Python follows mathematical convention. The acronym
**PEMDAS** is a useful way to remember the rules:

-   **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 if it
    doesn\'t change the result.
-   **E**xponentiation has the next highest precedence, so `2**1+1` is
    3, not 4, and `3*1**3` is 3, not 27.
-   **M**ultiplication and **D**ivision have the same precedence, which
    is higher than **A**ddition and **S**ubtraction, which also have the
    same precedence. So `2*3-1` is 5, not 4, and `6+4/2` is 8, not 5.
-   Operators with the same precedence are evaluated from left to right.
    So in the expression `degrees / 2 * pi`, the division happens first
    and the result is multiplied by `pi`. To divide by 2 π, you can
    reorder the operands or use parentheses.

### String operations

In general, you cannot perform mathematical operations on strings, even
if the strings look like numbers, so the following are illegal:

``` python
'2'-'1'    'eggs'/'easy'    'third'*'a charm'
```

The `+` operator works with strings, but it might not do what you
expect: it performs **concatenation**, which means joining the strings
by linking them end-to-end. For example:

``` python
first = 'throat'
second = 'warbler'
print first + second
```

The output of this program is `throatwarbler`.

The `*` operator also works on strings; it performs repetition. For
example, `’Spam’*3` is `'SpamSpamSpam'`. If one of the operands is a
string, the other has to be an integer.

This use of `+` and `*` makes sense by analogy with addition and
multiplication. Just as `4*3` is equivalent to `4+4+4`, we expect
`'Spam'*3` to be the same as `'Spam'+'Spam'+'Spam'`, 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 has that string concatenation does
not?

### Comments

As programs get bigger and more complicated, they get more difficult to
read. Formal languages are dense, and it is often difficult to look at a
piece of code and figure out what it is doing, or why.

For this reason, it is a good idea to add notes to your programs to
explain in natural language what the program is doing. These notes are
called **comments**, and they start with the `#` symbol:

``` python
# compute the percentage of the hour that has elapsed
percentage = (minute * 100) / 60
```

In this case, the comment appears on a line by itself. You can also put
comments at the end of a line:

``` python
percentage = (minute * 100) / 60     # percentage of an hour
```

Everything from the `#` to the end of the line is ignored---it has no
effect on the program.

Comments are most useful when they document non-obvious features of the
code. It is reasonable to assume that the reader can figure out *what*
the code does; it is much more useful to explain *why*.

This comment is redundant with the code and useless:

``` python
v = 5     # assign 5 to v
```

This comment contains useful information that is not in the code:

``` python
v = 5     # velocity in meters/second.
```

Good variable names can reduce the need for comments, but long names can
make complex expressions hard to read, so there is a tradeoff.

### Debugging

At this point the syntax error you are most likely to make is an illegal
variable name, like `class` and `yield`, which are keywords, or
`odd~job` and `US$`, which contain illegal characters.

If you put a space in a variable name, Python thinks it is two operands
without an operator:

``` python
>>> bad name = 5
SyntaxError: invalid syntax
```

For syntax errors, the error messages don't help much. The most common
messages are `SyntaxError: invalid syntax` and
`SyntaxError: invalid token`, neither of which is very informative.

The runtime error you are most likely to make is a "use before def;"
that is, trying to use a variable before you have assigned a value. This
can happen if you spell a variable name wrong:

``` python
>>> principal = 327.68
>>> interest = principle * rate
NameError: name 'principle' is not defined
```

Variables names are case sensitive, so `LaTeX` is not the same as
`latex`.

At this point the most likely cause of a semantic error is the order of
operations. For example, to evaluate 1/2 π, you might be tempted to
write

``` python
>>> 1.0 / 2.0 * pi
```

But the division happens first, so you would get π / 2, which is not the
same thing! There is no way for Python to know what you meant to write,
so in this case you don't get an error message; you just get the wrong
answer.

### Glossary

```{=html}
<DL CLASS="description">
```
```{=html}
<DT CLASS="dt-description">
```
**value:**

```{=html}
</DT>
```
```{=html}
<DD CLASS="dd-description">
```
One of the basic units of data, like a number or string, that a program
manipulates.

```{=html}
</DD>
```
```{=html}
<DT CLASS="dt-description">
```
**type:**

```{=html}
</DT>
```
```{=html}
<DD CLASS="dd-description">
```
A category of values. The types we have seen so far are integers (type
`int`), floating-point numbers (type `float`), and strings (type `str`).

```{=html}
</DD>
```
```{=html}
<DT CLASS="dt-description">
```
**integer:**

```{=html}
</DT>
```
```{=html}
<DD CLASS="dd-description">
```
A type that represents whole numbers.

```{=html}
</DD>
```
```{=html}
<DT CLASS="dt-description">
```
**floating-point:**

```{=html}
</DT>
```
```{=html}
<DD CLASS="dd-description">
```
A type that represents numbers with fractional parts.

```{=html}
</DD>
```
```{=html}
<DT CLASS="dt-description">
```
**string:**

```{=html}
</DT>
```
```{=html}
<DD CLASS="dd-description">
```
A type that represents sequences of characters.

```{=html}
</DD>
```
```{=html}
<DT CLASS="dt-description">
```
**variable:**

```{=html}
</DT>
```
```{=html}
<DD CLASS="dd-description">
```
A name that refers to a value.

```{=html}
</DD>
```
```{=html}
<DT CLASS="dt-description">
```
**statement:**

```{=html}
</DT>
```
```{=html}
<DD CLASS="dd-description">
```
A section of code that represents a command or action. So far, the
statements we have seen are assignments and print statements.

```{=html}
</DD>
```
```{=html}
<DT CLASS="dt-description">
```
**assignment:**

```{=html}
</DT>
```
```{=html}
<DD CLASS="dd-description">
```
A statement that assigns a value to a variable.

```{=html}
</DD>
```
```{=html}
<DT CLASS="dt-description">
```
**state diagram:**

```{=html}
</DT>
```
```{=html}
<DD CLASS="dd-description">
```
A graphical representation of a set of variables and the values they
refer to.

```{=html}
</DD>
```
```{=html}
<DT CLASS="dt-description">
```
**keyword:**

```{=html}
</DT>
```
```{=html}
<DD CLASS="dd-description">
```
A reserved word that is used by the compiler to parse a program; you
cannot use keywords like `if`, `def`, and `while` as variable names.

```{=html}
</DD>
```
```{=html}
<DT CLASS="dt-description">
```
**operator:**

```{=html}
</DT>
```
```{=html}
<DD CLASS="dd-description">
```
A special symbol that represents a simple computation like addition,
multiplication, or string concatenation.

```{=html}
</DD>
```
```{=html}
<DT CLASS="dt-description">
```
**operand:**

```{=html}
</DT>
```
```{=html}
<DD CLASS="dd-description">
```
One of the values on which an operator operates.

```{=html}
</DD>
```
```{=html}
<DT CLASS="dt-description">
```
**floor division:**

```{=html}
</DT>
```
```{=html}
<DD CLASS="dd-description">
```
The operation that divides two numbers and chops off the fraction part.

```{=html}
</DD>
```
```{=html}
<DT CLASS="dt-description">
```
**expression:**

```{=html}
</DT>
```
```{=html}
<DD CLASS="dd-description">
```
A combination of variables, operators, and values that represents a
single result value.

```{=html}
</DD>
```
```{=html}
<DT CLASS="dt-description">
```
**evaluate:**

```{=html}
</DT>
```
```{=html}
<DD CLASS="dd-description">
```
To simplify an expression by performing the operations in order to yield
a single value.

```{=html}
</DD>
```
```{=html}
<DT CLASS="dt-description">
```
**rules of precedence:**

```{=html}
</DT>
```
```{=html}
<DD CLASS="dd-description">
```
The set of rules governing the order in which expressions involving
multiple operators and operands are evaluated.

```{=html}
</DD>
```
```{=html}
<DT CLASS="dt-description">
```
**concatenate:**

```{=html}
</DT>
```
```{=html}
<DD CLASS="dd-description">
```
To join two operands end-to-end.

```{=html}
</DD>
```
```{=html}
<DT CLASS="dt-description">
```
**comment:**

```{=html}
</DT>
```
```{=html}
<DD CLASS="dd-description">
```
Information in a program that is meant for other programmers (or anyone
reading the source code) and has no effect on the execution of the
program.

```{=html}
</DD>
```
```{=html}
</DL>
```
### Exercises

#### Exercise 3

Assume that we execute the following assignment statements:

``` python
width = 17
height = 12.0
delimiter = '.'
```

For each of the following expressions, write the value of the expression
and the type (of the value of the expression).

``` python
width/2
width/2.0
height/3
1 + 2 * 5
delimiter * 5
```

Use the Python interpreter to check your answers.

#### Exercise 4

Practice using the Python interpreter as a calculator:

-   *The volume of a sphere with radius
    **\'`<I>`{=html}r`</I>`{=html}**\' is **\'4/3**\' π
    `<I>`{=html}r`</I>`{=html}*^*3*^\'\'.

What is the volume of a sphere with radius 5? Hint: 392.6 is wrong!\'\'

-   \'\'Suppose the cover price of a book is \$24.95, but bookstores get
    a

40% discount. Shipping costs \$3 for the first copy and 75 cents for
each additional copy. What is the total wholesale cost for 60
copies?\'\'

-   \'\'If I leave my house at 6:52 am and run 1 mile at an easy pace

(8:15 per mile), then 3 miles at tempo (7:12 per mile) and 1 mile at
easy pace again, what time do I get home for breakfast?\'\'

### Notes


[^1]: In Python 3.0, the result of this division is a `float`. The new
    operator `//` performs integer division.
