Variables

We cannot  go very far without variables. A variable is a value related to a name that we can bind  to have a particular value  and  then  later use in an expression. When  a variable is calculated in an statement, it is computed by looking  to see to what  value  it is bound.

An interpreter keeps track of which  variables are bound to what  values  in binding environments. An environment defines a mapping between variable values  and names.  The values  may be integers, ?oating point characters, numbers, or pointers to more hard  entities  such as procedures or larger  collections of data.

Here is an example binding environment:

Each row shows a binding: the entry  in the ?rst column is the variable name  and the entry  in the second  column is the value  it to which  it is bound.

When  you  start  up  the Python shell,  you  instantly start communicating with  a local binding environment.  You can include a binding or change  an existing  binding by evaluating an assignment statement of the form:

=

where is a variable name  (a string  of letters  or digits  or the character _, not starting with  a digit) and is a Python expression.14 Expressions are always  computed  in some environment.

We may  have the given interaction in a fresh Python shell:

>>> a = 3

>>> a

3

>>> b

Traceback (most recent call last):

File "", line 1, in

NameError: name 'b' is not defined

>>>

We started by assigning the variable value 3. That included a binding for a to the local environment.

Next, we computed the statement a. The value of a statement with one or more variable names in it cannot be determined unless we know with respect to what environment it is being computed. Thus, we will always speak  of evaluating expressions in an environment. In the mean while the program  of evaluating an expression in some environment E, if the interpreter takes a variable, it checks that  variable in E: if E contains a binding for the variable, then  the related value  is returned; if it does  not, then  an error  is provided. In the Python shell communication above,  we may see that the interpreter was  able to search a binding for a and  return a value,  but  it was  not able to ?nd  a binding for b.

Why do we bother de?ning values  for variables? They provide  us to reuse  an intermediate value in a calculation. We may  want  to calculate a formula in two parts, as in:

>>> c = 952**4

>>> c**2 + c / 2.0

6.7467650588636822e+23

They  will  also  play  a crucial  role  in abstraction and  the  de?nition of function.  By providing  a name  to a value,  we can isolate  the use of that  value  in other  calculation, so that  if we decide to modify  the value, we only have to change  the de?nition (and not change  a value several  places in the code).

It is ?ne to reassign the value  of a variable; although we use the equality symbol  = to stand for assignment, we are not  creating a mathematical equation of equality.  So, for program, we can write:

>>> a = 3

>>> a = a + 1

>>> a

4