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Lecture 10—Mutual reference and mutual recursion

Before Lecture

Before lecture 10, please work through the videos in Module 6b: Mutually Recursive Data and Templating Mutual Recursion and complete the online questions for this module.

During Lecture

The starters for this lecture are:

• m06-regions-total-weight-starter.rkt
• m06-regions-all-with-color-v2-starter.rkt
• m06-regions-find-region-starter.rkt
• m06-regions-all-labels-starter.rkt
• m06-regions-render-starter.rkt

After Lecture

Today we covered what may seem like a complex concept — Mutual Reference. When Working with types that have mutual reference we are operating on data far more complicated than a few weeks ago.

But here's where all the work you have done so far really starts to pay off. We can use our notation for types, we can form templates for those types, we understand reference, self-reference and now mutual reference, we know about positions in templates, particularly base and combination positions, we have guidelines for forming tests for functions. And we know how to trust the natural recursions!

That means that we can write each of the functions in a mutual recursion without having to think through all the calls. Which makes these functions not much harder than functions on lists from module 4.

So the one really new thing we learned in this module really was that when we design functions on mutually referential data we group the signature/purpose/examples/definitions differently. The rest was just HtDF!

We also learned the backtracking template, which gets added into our type based templates to do a backtracking search over a tree. We will see this again and again as we go forward.

To review what you learned today:

• Review the data definitions for the regions structure. To test your knowledge, try constructing the DD for the Unit hierarchy without looking at the starter.
• Try redoing the functions we did in lecture from scratch.
• Then complete the remaining functions in the starter file. If you get stuck, do the steps described above to help yourself understand what to put in the ... section. Use the videos in Module 6b for help.
• Go to the Module 6b videos, download the starters and work ahead on the problem. Use the video to see if what you did was correct! Do NOT just watch the videos — this will not help you.
• After you work through the backtracking search video do the backtracking problem in today's starter file.

The solutions for this lecture are:

• m06-regions-total-weight-solution.rkt
• m06-regions-all-with-color-solution.rkt
• m06-regions-find-region-solution.rkt
• m06-regions-all-labels-solution.rkt
• m06-regions-render-solution.rkt

Be sure to complete the before lecture section of Lecture 11 before that lecture.