Chapter 3: Boss Statements

Grammar Time So far every Python statement we have written is a grammatically complete imperative sentence with tacit subject "Python." Such statements are called worker statements.

The subject of this chapter is a new type of statement called a boss statement.

Python, like you, can only act when it is commanded with a complete sentence. Boss statements need a block of statements to complete them as a command that is coherent to Python. The appelation boss statement applies for two reasons.

• Boss statements have the power to alter the flow of execution in a program.
• Boss statements "own" a block of code that completes them as a grammatical sentence.

A typical boss statment has this form.

boss statement:
    line1
    line2 

    .
    .
    .
    lineN

The indented lines constitute the boss statement's block. A block must have at least one line of code. To do nothing in this block, use the pass keyword.

Can a boss statement appear in another boss statement's block? Yes, this is called nesting and it is ubiquitous in programming.

This chapter will introduce three types of boss statements: conditional logic statements, functions, and the while statement.

We will begin with functions.

Functions

So far, we have met variables, which allow us to store data under a name. Functions allow us to store a procedure under a name. Before we begin, let us review the mathemtical definition of function.

A function consists of three items: a domain, which is its allowable set of inputs, a codomain, which is an allowable set of outputs, and a rule tying each element of the domain to some element of the range.

If \(D\) is the domain of a a function \(f\) and \(R\) is its codomain, we write \(f:D\rightarrow R\). For an element \(x\in D\), we write \(f(x)\) to mean the rule \(f\) applied to \(x\).

One consequence of this definition is that when a function is given the same input, it must produce the same output every time. We say that mathematical functions are consistent.

Let's look at some built-in functions we have met so far. The domain of the len function is the set of all character strings. Its codomain is the nonegative integers. It is mathematically consistent; it calculates the number of characters in th string presented it.

The function bin accepts a nonnegative integer and it returns a string that is a binary representation of that integer.

Question What can you say about ord and chr?

Functions of two variables can be thought of as accepting a tuple containing the variables. For example the function

has domain the set of all two-tuples \((x,y)\) of real numbers and has codomain the real numbers. This principle generalizes to a function with any number of variables.

Python Functions

Mathematical functions can be reprsented as Python functions. However, there is a panoply of Python functions that are not mathematical functions. However, careful crafting of programs can cause many of your functions to be mathematical functions. This is desirable; understanding their actions and debugging with them is much simpler than with their messy brethern.

Let's begin with some examples.

inputs, parameters, and arguments

returning an output

side effects

A Very Un-Mathematical Function, input

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