Domain and Range

This activity introduces the notion of Contracts, which are a simple notation for keeping track of the set all of possible inputs and outputs for a function. They are also closely related to the concept of a function machine, which is introduced as well. Note: Contracts are based on the same notation found in Algebra!

Students should open code.pyret.org (CPO) in their browser, and click "Sign In". This will ask them to log in with a valid Google account (Gmail, Google Classroom, YouTube, etc.), and then show them the "Programs" page. This page is empty - they don’t have any programs yet! Have them click "Open Editor".

Source: Wikipedia 🖼Show image Functions are a lot like machines: values go in, something happens, and new values come out. Let’s start with an example of a function we all know: adding two numbers! Addition is like a machine that takes in pairs of numbers and produces a sum.

Consider the graphs on the right: for every input on the x-axis, a function will produce a single output. If we draw a vertical line and it hits the graph more than once, it means there is more than one output for the same input. Like any good machine, function machines must be reliable.

Whenever we use any machine, we always think about what goes in and what comes out. A coffee maker takes in coffee beans and water, and produces coffee. A toaster takes in bread and produces toast. We don’t have to know exactly how coffee makers or toasters work in order to use them. All we need to know is what type of thing goes in and what type of thing should come out!

In our coffee-maker example, we expect to get the exact same coffee out if we use the exact same beans and water each time. If you put bread in a toaster and got a bagel out, you’d be pretty surprised! Functions work the same way: no matter how many times you plug in the same number, you will always get the same result. And if you don’t? It’s not a function!

We use something called a Contract to keep track of what goes in and out of these machines called functions. Contracts are like a "cheat sheet" for using functions. Once you know how to read one, you can quickly figure out how to use a function just by looking at its contract!

Memorizing contracts is hard, and why memorize when we can just keep a log of them! Let’s write them down so we can use them later! At the back of your workbook, you’ll find pages with space to write down every contract you see in the course.

It would be silly to buy a coffee-maker that only works with one specific coffee! Similarly, Contracts don’t tell us specific inputs. They tell us the Datatype of input a function needs. For example, a Contract wouldn’t say that addition requires "3 and 4". Addition works on more than just those two inputs! Instead, it would tells us that addition requires "two Numbers". When we use a Contract, we plug specific numbers into a mathematical expression.

Students explore functions that go beyond numbers, producing all sorts of simple geometric shapes and images in the process. Making images is highly motivating, and encourages students to get better at both reading error messages and persisting in catching bugs.

Students have already seen Number values like 42,-91, 1/4 or 0.25, but computer programs can work with a much larger set of datatypes. Show students examples of the String datatype, by having them type various things in quotation marks:

Possible responses:

Possible responses:

You’ve seen two datatypes already: Numbers and Strings. Did we get back either on of those? The Range of star is a datatype we haven’t seen before: an Image!

Suppose we had never seen star before. How could we figure out how to use it, using the helpful error messages?

Give students time to investigate image functions and see how many they can discover, using the Contracts page to organize their findings.

This activity digs deeper into Contracts, and has students create their own Contracts trackers to take ownership of the concept and create an artifact they can refer back to.

star has three elements in its Domain: A Number, a String, and another String.

Where else have you heard the word "contract"? How can you connect that meaning to contracts in programming?

An actor signs a contract agreeing to perform in a film in exchange for compensation, a contractor makes an agreement with a homeowner to build or repair something in a set amount of time for compensation, or a parent agrees to pizza for dinner in exchange for the child completing their chores. Similarly, a contract in programming is an agreement between what the function is given and what it produces.