2.8 Sub-expressions

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The expressions page introduced the idea of expressions as:

a recipe that returns a value.

When Python evaluates an expression, it follows the recipe to return the value.

In this page we go into a little more detail on expressions, and we consider sub-expressions.

We do this to get used to the more general idea in programming, of building complex things from simple building blocks, according to simple rules.

A large part of learning how to program is understanding what the computer is doing as a result of the code you type. You can do this by breaking down code into simpler building blocks, and understanding how the parts are combined.

Consider this expression:

(10.50 + 9.25) * 0.15

2.9625

Here is the full process that Python goes through, when evaluating (10.50 + 9.25) * 0.15. Python will:

  • evaluate the expression 10.50 to give the computer representation (CR) of 10.50;
  • evaluate the expression 9.25 to give the CR of 10.50;
  • evaluate the expression 10.50 + 9.25 to give the CR of 19.75;
  • evaluate the expression 19.75 * 0.15 to give the CR of 2.9625.

Sub-expressions

A compound expression is an expression made up of smaller sub-expressions.

A sub-expression is a smaller part of the compound expression, that Python will evaluate as part of evaluating the compound expression.

For example: here is a compound expression, made up of two sub-expressions:

10.50 + 9.25

19.75

The two sub-expressions are:

  • 10.50: an expression that returns the CR of the number 10.50;
  • 9.25: an expression that returns the CR of the number 9.25.

When Python evaluates 10.50 + 9.25, it first evaluates these two sub-expressions, then evaluates the final result by adding the results of these two sub-expressions.

Reconsider:

(10.50 + 9.25) * 0.15

2.9625

There are four sub-expressions here:

  • 10.50 as above;
  • 9.25 as above;
  • 0.15 returns the CR of the number 0.15;
  • (10.50 + 9.25) is a compound expression that is itself a sub-expression of the full expression above. It returns the CR of the number 19.75.

Each of these sub-expressions will be evaluated in the process of evaluating (10.50 + 9.25) * 0.15.

Now consider:

10.50 + 9.25 * 0.15

11.8875

Be careful - remember the rules of operator precedence.

Let’s think again what Python will do here. It will:

  • evaluate the expression 10.50 to gives the CR of 10.50;
  • evaluate the expression 9.25 to gives the CR of 10.50;
  • (because of the precedence rules) evaluate 9.25 * 1.15 to give the CR of 1.3875;
  • evaluate 10.50 * 1.3875 to give the CR of 11.8875.

So, these are the sub-expressions:

  • 10.50;
  • 9.25;
  • 0.15;
  • 9.25 * 0.15.

Note that 10.50 + 9.25 is not a sub-expression, because this does not return a value, in the process of evaluating the whole expression. The value that 9.25 is involved in is 9.25 * 1.3875, where 1.3875 is the value that comes back from 9.25 * 0.15 above.

Let’s say I have imported my cos function (see the functions page):

# Get the cos function from the numpy library.
from numpy import cos

Now consider:

cos(0)

1.0

cos(0) is an expression, because it is a recipe that returns a value. In fact, it is a call expression.

There is one sub-expression to this expression, which is:

  • 0 returns the CR of 0;
cos(0) + 2

3.0

has three sub-expressions:

  • 0 returns the CR of 0;
  • cos( ) with argument 0, from above, returns the CR of the number 1;
  • 2 returns the CR of 2.

Finally, let’s say I have defined this variable:

a = 10.50

Here is an expression:

a

10.5

It is an expression because it is a recipe that returns a value - in this case, the CR of the number 10.50.