Contracts: Making Tables and Displays

Students will be introduced to functions for working with tables, including: sort, count and first-n-rows. In the process they will review simple data types and be introduced to contracts for describing the Domain and Range of any function.

If you have time and interest in digging deeper into contracts, we have a whole lesson focused on contracts for image-producing functions, which students find highly motivating!

(If this is the first time your students are seeing a table in code.pyret.org (CPO), you may also want to acknowledge line 7 of the Definitions Area, where animals-table is defined along with the names of the 8 columns.)

As you can imagine, there are many other functions that work with tables, each with a different set of inputs. For each of these functions, we need to keep track of three things:

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

The Domain in the Contract for sort tells us exactly what kind of inputs it needs, and in what order. The Range tells us exactly what we’ll get back.

Students are likely to think that sort changes the table, when instead it produces a new, sorted table. Encourage students to say out loud what they think they will get if they type animals-table after evaluating sort​(​animals-table, "name", true​). By testing their hypothesis, students who are surprised at the outcome are much more likely to remember the difference later on.

Students learn to work with more than one function at once, by way of Circles of Evaluation, a visual representation of the underlying structure.

What if we wanted to see the ten youngest animals? How could the first-n-rows and sort functions work together? What order should we use the functions in?

One way to organize our thoughts is to diagram what we want to do, using the Circles of Evaluation. The rules are simple:

1) Every Circle of Evaluation must have one - and only one! - function, written at the top.

2) The arguments of the function are written left-to-right, in the middle of the Circle.

Values like Numbers, String, and Booleans are still written by themselves. It’s only when we want to use a function that we need to draw a Circle, and write the values inside from left-to-right.

3) Circles can contain other Circles!

If we want to see the ten youngest animals, our diagram would look like this.

To convert a Circle of Evaluation into code, we start at the outside and work our way in. After each function we write a pair of parentheses, and then convert each argument inside the Circle. The code for this Circle of Evaluation would be:

first-n-rows​(​sort​(​animals-table, "age", true​), 10​)

If we wanted to get extra fancy and see the species count for the youngest ten animals, we could add another layer to our Circle of Evaluation.

That would translate to the following code:

count​(​first-n-rows​(​sort​(​animals-table, "age", true​), 10​), "species"​)

Students will be introduced to functions for making one-variable displays in Pyret, including: pie-chart, bar-chart, box-plot and histogram.

The goal here is for students to become familiar with using Contracts to write expressions that will produce displays. Knowing how to make a histogram doesn’t mean a student really understands histograms!

Once students know how to use Contracts to write expressions to make these displays, we have dedicated, in-depth lessons focused on understanding Bar and Pie Charts, Histograms, Visualizing the "Shape" of Data, Box Plots, Scatter Plots, Linear Regression, Advanced Displays, etc.

The count function summarized the data for a single variable in a new table. But the same information could be communicated as a picture! This is called data visualization, and Pyret has functions that can make displays for us!

Optional:

Just as we can use Circles of Evaluation to help us combine sort, count, and first-n-rows, we can put Circles of Evaluation to work to help us write code to build more specific displays.

Optional: If your students would benefit from seeing a few more examples before drawing their own Circles of Evaluation, have them Match Display Descriptions to Circles of Evaluation.

Optional: For more practice making tables and displays by composing functions, have students complete Circles of Evaluation: Composing Functions to Make Displays (2)