Contracts

Students learn how to apply functions in WeScheme, reinforcing concepts from standard Algebra, and practice reading error messages to diagnose errors in code.

In human languages, verbs do things to nouns. For example, I can "throw a ball", or "eat a sandwich". "Throw" and "Eat" are verbs, and "ball" and "sandwich" are nouns.

In programming languages, values are like nouns. You’ve learned about values in our programming language, like Numbers (42, -8.3, etc), Strings ("hello!"), and Booleans (true and false). In programming, our verbs are called functions. A function is like a machine, and it does three things:

Let’s play with a few functions, to get the hang of it.

Encourage students to try giving different arguments to sqrt. Does it only work with Numbers? Does it only take one Number?

Encourage students to try giving different arguments to string-length. Does it only work with Strings? Does it only take one String? What does it do?

Debrief the activity with the class. Be sure to discuss and analyze different error messages encountered.

This activity introduces the notion of Contracts, which are a simple notation for keeping track of the set of all 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!

When students typed (triangle 50 "solid" "red") into the editor, they created an example of a new data type, called an Image.

The triangle function can make lots of different triangles! The size, style and color are all determined by the specific inputs provided in the code, but, if we don’t provide the function with a number and two strings to define those parameters, we will get an error message instead of a triangle.

As you can imagine, there are many other functions for making images, each with a different set of arguments. For each of these functions, we need to keep track of three things:

The Name, Domain and Range are used to write a Contract.

Contracts tell us a lot about how to use a function. In fact, we can figure out how to use functions we’ve never seen before, just by looking at the contract! Most of the time, error messages occur when we’ve accidentally broken a contract.

Contracts don’t tell us specific inputs. They tell us the data type 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 or strings into the expression we are coding.

Let’s take a look at the Name, Domain, and Range of the functions we’ve seen before:

Optional: Have students make a Domain and Range Frayer model and use the visual organizer to explain the concepts of Domain and Range in their own words. You might also have students complete Function and Variable Frayer model.

This activity digs deeper into Contracts. Students explore image functions to take ownership of the concept and create an artifact they can refer back to. Making images is highly motivating, and encourages students to get better at both reading error messages and persisting in catching bugs.

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

Explain to students that at the back of their workbooks, they’ll find pages with space to write down a contract and example or other notes for every function in this course. (If your students do not have workbooks, print and copy the contracts pages.) A few contracts have been completed for them. Tell students that they will be adding to their contract pages and referring back to them for the remainder of this Bootstrap class!

Students are given contracts for some more interesting image functions and see how much more efficient it is to write code when starting with a contract.

You just investigated image functions by guessing and checking what the contract might be and responding to error messages until the images built. If you’d started with contracts, it would have been a lot easier!

Once students have discovered how to build a version of each image function that satisfies them, have them record the example code in their contracts table. Encourage students to explore what aspect of the image each of the inputs specifies. It may help students to jot down notes about their discoveries.

If students are ready to dig into more complex triangles, you can also have them work through Triangle Contracts (SAS & ASA).

Contracts that tell us more information about the arguments can be helpful, but are not a focal point of our work in this course. The Radial Star worksheet is designed to give students a taste of these more complex contracts. For more practice with detailed contracts, students can also complete Star Polygon. Both star-polygon and radial-star generate a wide range of interesting shapes!

Make sure that all students have completed the shape functions in their contracts pages with both contracts and example code so they have something to refer back to.

Students are very likely to randomly experiment, rather than to actually use the Contracts. You should plan to ask lots of direct questions to make sure students are making this connection, such as:

Diagnosing and fixing errors are skills that students will continue developing throughout this course. Some of the errors are syntax errors: a missing comma, an unclosed string, etc. All other errors are contract errors. If you see an error and you know the syntax is right, ask yourself these three questions: