The Way of the Program

15 minute read

The goal of this this class is to teach you to think like a computer scientist. This way of thinking combines some of the best features of mathematics, engineering, and natural science. Like mathematicians, computer scientists use formal languages to denote ideas (specifically computations). Like engineers, they design things, assembling components into systems and evaluating tradeoffs among alternatives. Like scientists, they observe the behavior of complex systems, form hypotheses, and test predictions.

The single most important skill for a computer scientist is problem solving. Problem solving means the ability to formulate problems, think creatively about solutions, and express a solution clearly and accurately. As it turns out, the process of learning to program is an excellent opportunity to practice problem-solving skills.

On one level, you will be learning to program, a useful skill by itself. On another level, you will use programming as a means to an end. As we go along, that end will become clearer.

What is a program?

A program is a sequence of instructions that specifies how to perform a computation. The computation might be something mathematical, such as solving a system of equations or finding the roots of a polynomial, but it can also be a symbolic computation, such as searching and replacing text in a document or something graphical, like processing an image or playing a video.

The details look different in different languages, but a few basic instructions appear in just about every language:

Basic Values
The basic building blocks that can be used in an algorithm. In Python, we will be using numeric values (e.g. 1, 2, 3) and textual values (e.g. "Harry Potter") a lot, but we will see many others.
Basic Operations
Simple operations on basic values such as addition and multiplication. Every programming language has basic operations built-in to the language, and we will learn them over time.
Temporary names for values. These are important since we often want to refer to a specific object by a shorter name. For example, we might have the swim times for three different swimmers and need to name them time1, time2, and time3. Later we might compute the average time and name that value time_avg.
Enable us to make decisions that depend on context. For example, you might need to include special cases if a value is equal to zero or handle a special scenario of a recipe depending on which ingredient you chose to use.
When you need to perform an operation repeatedly until some condition is satisfied. For example, if you are computing the average of 100 different swim times, you will need to repeatedly add all 100 numbers together before completing the average by dividing.
Named helper algorithms. We also sometimes refer to these as “procedures” or “functions”.
Values that are “passed into” the algorithm. For example, you might write an algorithm to add two numbers together. In order to execute the algorithm, you must provide two numbers to be added—these are the inputs to your algorithm. Inputs can be provided in many ways. We will initially ask the user of our program for inputs when needed, but they can also be provided from another file.
What the algorithm produces as a final product. How the output is presented by the program can vary. When working with Python, we will often print the output to the shell so that the user can read it. Later we will see other approaches like writing to a file or showing an image.

Believe it or not, that’s pretty much all there is to it. Every program you’ve ever used, no matter how complicated, is made up of instructions that look pretty much like these. So you can think of programming as the process of breaking a large, complex task into smaller and smaller subtasks until the subtasks are simple enough to be performed with one of these basic instructions.

Running Python

There are two versions of Python, called Python 2 and Python 3. They are very similar, so if you learn one, it is easy to switch to the other. In fact, there are only a few differences you will encounter as a beginner. Recently, support for Python 2 was discontinued, so we will be learning Python 3 .

Before you get started writing Python 3 programs, you first need to install an Integrated Development Environment (IDE). Since most programming languages are written in plain text, IDEs are essentially fancier Microsoft Notepad programs.

In this course, we will be using an IDE called Thonny. Thonny is especially convenient because it comes with everything you need to run Python 3 built-in as well as many useful features we will utilize.

The Python interpreter is a program that reads and executes Python code. Depending on your environment, you might start the interpreter by clicking on an icon, or by typing python on a command line. When it starts, you should see output like this:

Python 3.8.2

The first line contains the version number of the Python interpreter. You should check that the version number, which is 3.8.2 in this example, begins with 3, which indicates that you are running Python 3. If it begins with 2, you are running (you guessed it) Python 2.

The last line is a prompt that indicates that the interpreter is ready for you to enter code. If you type a line of code and hit Enter, the interpreter displays the result:

>>> 1 + 1

Thonny has a dedicated pane for the Python interpreter called the shell. We will use it extensively throughout the course.

Stop! Before continuing, follow the instructions for Installing Thonny. Most of the readings are designed to be interactive and require typing code into Thonny.

Hello, world!

Traditionally, the first program you write in a new language is called “Hello, world!” because all it does is display the words “Hello, World!”. In Python, it looks like this:

>>> print('Hello, world!')

This is an example of a print statement, although it doesn’t actually print anything on paper. It displays a result on the screen. In this case, the result is the words

Hello, world!

The quotation marks in the program mark the beginning and end of the text to be displayed; they don’t appear in the result.

The parentheses indicate that print is a function. We’ll explain functions more in a later reading.

Arithmetic Operators

After “Hello, world!”, the next step is arithmetic. Python provides operators, which are special symbols that represent computations like addition and multiplication.

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

>>> 40 + 2
>>> 43 - 1
>>> 6 * 7

The operator / performs division:

>>> 84 / 2

You might wonder why the result is 42.0 instead of 42; we will see why in the next reading.

Finally, the operator ** performs exponentiation; that is, it raises a number to a power. For example, 6**2 is the same as $6^2$.

>>> 6**2 + 6

In some other languages, ^ is used for exponentiation, but in Python it is a bitwise operator called “exclusive or”. If you are not familiar with bitwise operators, the result will surprise you:

>>> 6 ^ 2

We won’t cover bitwise operators in this class, but you can read about them at

Note: You may notice that Python ignores some space characters. For example, 2*3+4 and 2 * 3 + 4 are interpreted in the same way.

Values and Types

A value is one of the basic things a program works with, like a letter or a number. Some values we have seen so far are 2, 42.0, and 'Hello, World!'.

These values belong to different types:

  • 2 is an integer,
  • 42.0 is a floating-point number, and
  • 'Hello, World!' is a string, so-called because the letters it contains are “strung together”.

If you are not sure what type a value has, you can use the built-in type function to figure it out:

>>> type(2)
<class 'int'>
>>> type(42.0)
<class 'float'>
>>> type('Hello, World!')
<class 'str'>

In these results, the word “class” is used in the sense of a category; a type is a category of values.

Not surprisingly, integers belong to the type int, strings belong to str and floating-point numbers belong to float.

What about values like '2' and '42.0'? They look like numbers, but they are in quotation marks like strings.

>>> type('2')
<class 'str'>
>>> type('42.0')
<class 'str'>

They’re strings.

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

>>> 1,000,000
(1, 0, 0)

That’s not what we expected at all! Python interprets 1,000,000 as a comma-separated sequence of integers. We’ll learn more about this kind of sequence later.

Formal and Natural Languages

Natural languages are the languages people speak, such as English, Spanish, and French. They were not designed by people (although people try to impose some order on them); they evolved naturally.

Formal languages are languages that are designed by people for specific applications. For example, the notation that mathematicians use is a formal language that is particularly good at denoting relationships among numbers and symbols. Chemists use a formal language to represent the chemical structure of molecules. And most importantly:

Programming languages are formal languages that have been designed to express computations.

Formal languages tend to have strict syntax rules that govern the structure of statements. For example, in mathematics the statement 3 + 3 = 6 has correct syntax, but 3 + = 3 $ 6 does not. In chemistry H2O is a syntactically correct formula, but 2Zz is not.

Syntax rules come in two flavors, pertaining to tokens and structure. Tokens are the basic elements of the language, such as words, numbers, and chemical elements. One of the problems with 3 += 3 $ 6 is that $ is not a legal token in mathematics (at least as far as I know). Similarly, 2Zz is not legal because there is no element with the abbreviation Zz.

The second type of syntax rule pertains to the way tokens are combined. The equation 3 +/ 3 is illegal because even though + and / are legal tokens, you can’t have one right after the other. Similarly, in a chemical formula the subscript comes after the element name, not before.

Here are a few more examples:

  • This is @ valid Engli$h sentence with invalid t*kens.
  • This sentence all valid tokens has, but invalid structure with.

When you read a sentence in English or a statement in a formal language, you have to figure out the structure (although in a natural language you do this subconsciously). This process is called parsing.

Although formal and natural languages have many features in common—tokens, structure, and syntax—there are some differences:

  • Ambiguity. Natural languages are full of ambiguity, which people deal with by using contextual clues and other information. Formal languages are designed to be nearly or completely unambiguous, which means that any statement has exactly one meaning, regardless of context.
  • Redundancy. In order to make up for ambiguity and reduce misunderstandings, natural languages employ lots of redundancy. As a result, they are often verbose. Formal languages are less redundant and more concise.
  • Literalness. Natural languages are full of idiom and metaphor. If I say, “The penny dropped”, there is probably no penny and nothing dropping (this idiom means that someone understood something after a period of co*nfusion). Formal languages mean exactly what they say.

Because we all grow up speaking natural languages, it is sometimes hard to adjust to formal languages. The difference between formal and natural language is like the difference between poetry and prose, but more so:

  • Poetry. Words are used for their sounds as well as for their meaning, and the whole poem together creates an effect or emotional response. Ambiguity is not only common but often deliberate.
  • Prose. The literal meaning of words is more important, and the structure contributes more meaning. Prose is more amenable to analysis than poetry but still often ambiguous.
  • Programs. The meaning of a computer program is unambiguous and literal, and can be understood entirely by analysis of the tokens and structure.

Formal languages are more dense than natural languages, so it takes longer to read them. Also, the structure is important, so it is not always best to read from top to bottom, left to right. Instead, learn to parse the program in your head, identifying the tokens and interpreting the structure. Finally, the details matter. Small errors in spelling and punctuation, which you can get away with in natural languages, can make a big difference in a formal language.


Programmers make mistakes. For whimsical reasons, programming errors are called bugs and the process of tracking them down is called debugging.

Programming, and especially debugging, sometimes brings out strong emotions. If you are struggling with a difficult bug, you might feel angry, despondent, or embarrassed.

There is evidence that people naturally respond to computers as if they were people. When they work well, we think of them as teammates, and when they are obstinate or rude, we respond to them the same way we respond to rude, obstinate people (Reeves and Nass, The Media Equation: How People Treat Computers, Television, and New Media Like Real People and Places).

Preparing for these reactions might help you deal with them. One approach is to think of the computer as an employee with certain strengths, like speed and precision, and particular weaknesses, like lack of empathy and inability to grasp the big picture.

Your job is to be a good manager: find ways to take advantage of the strengths and mitigate the weaknesses. And find ways to use your emotions to engage with the problem, without letting your reactions interfere with your ability to work effectively.

Learning to debug can be frustrating, but it is a valuable skill that is useful for many activities beyond programming. At the end of each chapter there is a section, like this one, with my suggestions for debugging. I hope they help!


problem solving
The process of formulating a problem, finding a solution, and expressing it.
high-level language
A programming language like Python that is designed to be easy for humans to read and write.
low-level language
A programming language that is designed to be easy for a computer to run; also called “machine language” or “assembly language”.
A property of a program that can run on more than one kind of computer.
A program that reads another program and executes it
Characters displayed by the interpreter to indicate that it is ready to take input from the user.
A set of instructions that specifies a computation.
print statement
An instruction that causes the Python interpreter to display a value on the screen.
A special symbol that represents a simple computation like addition, multiplication, or string concatenation.
One of the basic units of data, like a number or string, that a program manipulates.
A category of values. The types we have seen so far are integers (type int), floating-point numbers (type float), and strings (type str).
A type that represents whole numbers.
A type that represents numbers with fractional parts.
A type that represents sequences of characters.
natural language
Any one of the languages that people speak that evolved naturally.
formal language
Any one of the languages that people have designed for specific purposes, such as representing mathematical ideas or computer programs; all programming languages are formal languages.
One of the basic elements of the syntactic structure of a program, analogous to a word in a natural language.
The rules that govern the structure of a program.
To examine a program and analyze the syntactic structure.
An error in a program.
The process of finding and correcting bugs.

Self Checks

At the end of most readings, a few exercises will be included to give you a chance to apply what you’ve learned. When completing the exercises, it is important to have Thonny open and use it to work through the exercises. If you don’t have Thonny installed yet, go to the Installing Thonny page to install it.

Warning! After each reading, before coming to the corresponding class, you should attempt all of the self check exercises. You may be asked to share your answer/approach in class.

Check 1

Recall that we printed “Hello, world!” by executing the following into the Python interpreter:

>>> print('Hello, world!')

Answer the following questions by playing around in the Python interpreter.

  1. In a print statement, what happens if you leave out one of the parentheses, or both?

  2. If you are trying to print a string, what happens if you leave out one of the quotation marks, or both?

  3. You can use a minus sign to make a negative number like -2. What happens if you put a plus sign before a number? What about 2++2?

  4. In math notation, leading zeros are ok, as in 09. What happens if you try this in Python? What about 011?

  5. What happens if you have two values with no operator between them?

Check 2

Start the Python interpreter and use it as a calculator.

  1. How many seconds are there in 42 minutes 42 seconds?

  2. How many miles are there in 10 kilometers? Hint: there are 1.61 kilometers in a mile.

  3. If you run a 10 kilometer race in 42 minutes 42 seconds, what is your average pace (time per mile in minutes and seconds)? What is your average speed in miles per hour?


This reading was originally written by Allen Downey in his open source book Think Python 2e. Downey's book is licensed under the GNU Free Documentation License, which allows users to copy, modify, and distribute the book.

This reading was modified by Titus H. Klinge in 2021 and presented above under the same license in order to better serve the students of this course.