If you think of all the digital data and information stored in the cloud, on the web, on your phone, on your laptop, in hard and solid-state drives, and in every computer transaction, consideration comes down to just two things: 0 and 1.

These are bits, and with bits we can represent everything else in what we call “classical computers.” These systems date back to ideas from the 1940s. There is an additional concept for quantum computers, that of a qubit or “quantum bit.” The qubit extends the bit and is manipulated in quantum circuits and gates. Before we get to qubits, however, let’s consider the bit more closely.

First, we can interpret 0 as false and 1 as true. Thinking in terms of data, what would you say if I asked you the question, “Do you like Punk Rock?” We can store your response as 0 or 1 and then use it in further processing, such...

An expression is a written combination of data with operations to perform on that data. That sounds quite formal, so imagine a mathematical formula like:

15 × 6² + 3 × 6 – 4 .

This expression contains six pieces of data: 15, 6, 2, 3, 6, and 4. There are five operations: multiplication, exponentiation, addition, multiplication, and subtraction. If I rewrite this using symbols often used in programming languages, it is:

15 * 6**2 + 3 * 6 - 4

See that repeated 6? Suppose I want to consider different numbers in its place. I can write the formula:

15 × x² + 3 × x – 4

and the corresponding code expression:

15 * x**2 + 3 * x - 4

If I give x the value 6, I get the original expression. If I give it the value 11, I calculate:

15 * 11**2 + 3 * 11 - 4

We call x a variable and the process of giving it a value assignment. The expression...

The notion of “expression” includes functions and all that goes into writing and using them. The syntax of their definition varies significantly among programming languages, unlike simple arithmetic expressions. In words, I can say

The function maximum(x, y) returns x
if it is larger than y. Otherwise, it returns y.

Let’s consider this informal definition.

• It has a descriptive name: maximum.
• There are two variables within parentheses: x and y. These are the parameters of the function.
• A function may have zero, one, two, or more parameters. To remain readable, it shouldn’t have too many.
• When we employ the function as in maximum(3, -2) to get the larger value, we call the function maximum on the arguments 3 and -2.
• To repeat: x and y are parameters, and 3 and -2 are arguments. However, it’s not unusual...

While many books are now digital and available online, physical libraries are often still present in towns and cities. You can use a library to avoid doing something yourself, namely, buying a book. You can borrow it and read it. If it is a cookbook, you can use the recipes to make food.

A similar idea exists for programming languages and their environments. I can package together reusable data and functions, and then place them in a library. Via download or other sharing, coders can use my library to save themselves time. For example, if I built a library for math, it could contain functions like maximum, minimum, absolute_value, and is_prime. It could also include approximations to special values like π.

Once you have access to a library by installing it on your system, you need to tell your programming environment that you want to take advantage of it. Languages use...

Returning to the book analogy we started when discussing libraries, imagine that you own the seven volumes in the Chronicles of Narnia series by C. S. Lewis.

• The Lion, the Witch and the Wardrobe
• Prince Caspian: The Return to Narnia
• The Voyage of the Dawn Treader
• The Silver Chair
• The Horse and His Boy
• The Magician’s Nephew
• The Last Battle

The order I listed them is the order in which Lewis published the volumes from 1950 through 1956. In the list, the first book is the first published, the second is the second published, and so on. Had someone been maintaining the list in the 1950s, they would have appended a new title when Lewis released a new book in the series.

A programming language needs a structure like this so that you can store and insert objects as above. It...

When you write code, you create instructions for a computer that state what steps the computer must take to accomplish some task. In that sense, you are specifying a recipe. Depending on some conditions, like if a bank balance is positive or a car’s speed exceeds a stated limit, the sequence of steps may vary. We call how your code moves from one step to another its flow.

Let’s make some bread to show where a basic recipe has points where we should make choices.

Ingredients

• 1 ½ tablespoons sugar
• ¾ cup warm water (slightly warmer than body temperature)
• 2 ¼ teaspoons active dry yeast (1 package)
• 1 teaspoon salt
• ½ cup milk
• 1 tablespoon unsalted butter
• 2 cups all-purpose flour

Straight-through...

If I ask you to close your eyes, count to 10, then open them, the steps look like this:

1. Close your eyes
2. Set count to 1
3. While count is not equal 10, increment count by 1
4. Open your eyes

Steps 2 and 3 together constitute a loop. In this loop, we repeatedly do something while a condition is met. We do not move to step 4 from step 3 while the test returns true.

Compare the simplicity of Figure 1.3 to

1. Close your eyes
2. Set count to 1
3. Increment count to 2
4. Increment count to 3
5. …
6. Increment count to 10
7. Open your eyes

If that doesn’t convince you, imagine if I asked you to count to 200. Here is how we do it in C++:

int n = 1;

while( n < 201 ) {
    n++;
}

In many science fiction stories, novels, movies, and television series, characters use “teleportation” to move people and objects from one place to another. For example, the protagonist could teleport from Toronto to Tokyo instantly, without going through the time-consuming hassle of air flight.

It is also used in such plots to allow characters to escape from dangerous and unexpected conditions. Perhaps a monster might have the team cornered in the back of a cave, and there is no way to fight their way to safety. A hurried call by the leader on a communications device might demand “get us out of here!” or “beam us up now!” The STAR TREK^® series and movies often featured the latter exclamation.

So, characters use teleportation for regular transportation, but also for exceptional situations that are usually life-threatening. Many programming languages...

Consider this one-sentence paragraph with some text formatted in bold and italics:

Some words are bold, some are italic, and some are both.

How could you represent this as data in a word processor, spreadsheet, or presentation application?

Let’s begin with the text itself for the paragraph. Maybe we just use a string.

"Some words are bold, some are italic, and some are both."

The words are there, but we lost the formatting. Let’s break the sentence into a list of the formatted and unformatted parts. I use square brackets “[ ]” around the list and commas to separate the parts.

[ "Some words are ",
  "bold",
  ",some are ",
  "italic",
  ", and some are ",
  "both",
  "." ]

Now we can focus on how to embellish each part with formatting. There are four options:

1. the text...

Let’s return to cooking. I recently ran out of bay leaves in our kitchen. Bay leaves are used to flavor many foods, most notably soups, stews, and other braised meat dishes. Okay, I thought, I’ll just order some bay leaves online. I found four varieties:

• Turkish or Mediterranean bay leaves, from the Bay Laurel tree,
• Indian bay leaves,
• California bay leaves, and
• Caribbean bay leaves.

I eventually discovered that what I wanted was Turkish bay leaves. I ordered six ounces. When they arrived, I realized that I had enough to last the rest of my life.

Let’s get back to the varieties. While numbers and strings are built into most programming languages, bay leaves most certainly are not. Nevertheless, I want to create a structure to represent bay leaves in a first-class way. Perhaps I’m building up a collection of ingredient ...

In the first section of this chapter, we looked at data. Starting with the bits 0 and 1, we built integers, and I indicated that we could also represent floating-point numbers. Let’s switch from the arithmetic and algebra of numbers to geometry.

A single point is 0-dimensional. Two points are just two 0-dimensional objects. Let’s label these points 0 and 1. When we draw an infinite line through the two points and consider all the points on the line, we get a 1-dimensional object. We can represent each such point as (x), or just x, where x is a real number. If we have another line drawn vertically and perpendicular to the first, we get a plane. A plane is 2-dimensional, and we can represent every point in it with coordinates (x, y). The point (0, 0) is the origin.

This is the...

Consider the expression maximum(2, 1 + round(x)), where maximum is the function we saw earlier in this chapter, and round rounds a number to the nearest integer. For example, round(1.3) equals 1. Figure 1.10 shows how processing flows as we evaluate the expression.

To fix terminology, we can call this a function application circuit. When we draw it like this, we call maximum, round, and “+” functions, operations, or gates.

The maximum and “+” gates each take two inputs and have one output. The round gate has one input and one output. In general, round is not reversible: you cannot go from the output answer it produced to its input.

Going to their lowest level, classical computer processors manipulate bits using logic operators. These are also...

In my coding career, I have used dozens of programming languages and created several. [AXM] When I have a new problem to solve or am considering a new project, I research how languages have evolved and improved. For each language I investigate, I ask myself,

• “can this language do what I have in mind?”,
• “can this language do what I want better than the others?”, and
• “what are the special features and idioms within the language that enable me to produce an elegant result?”.

This chapter introduced many of the ideas widely used today in languages for coding. It showed that you could think about features and functionality separately from what one specific language provides. In the next chapter, we get concrete and see how Python implements these and other concepts.