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Lecture 14—Fold Functions

Before Lecture

Before lecture 14, you should:

• Use the m08-raining-eggs-refactor-starter.rkt as additional practice for use built-in abstract function problems.
AFTER you have worked it through, consult the solution to check your work - m08-raining-eggs-refactor-solution.rkt
• On edX work through the Fold Functions pt. 1 unit.

It is crucially important that you be totally comfortable with all of the Abstraction module up through Fold Functions pt. 1 before lecture because we will build on it significantly to make much more complicated programs get much much shorter.

During Lecture

The starters for this lecture are:

• m08-abstract-fold-definition-starter.rkt
• m08-abstract-fold-usages-starter.rkt
• m08-abstract-fold-complications-starter.rkt

After Lecture

The first thing to do is feel good for working through today's lecture - it is a difficult one. Feel good even if some of it was confusing! We are now past where many intro programming courses go. So don't be surprised if you need a couple of passes through today's material for it to truly sink in.

In terms of material we covered in module 8 it is very important to distinguish the different kinds of things we have done with abstract functions:

1. We designed abstract functions, in two different ways:
   • from examples (filter2, map2, andmap2)
   • from a template (foldr2, fold-course)

   As part of the design of these problems we used type inference to infer the signature of the function based on it's definition. These functions end up having a template origin like (listof X) or Course and (listof Course) for example.

2. We used abstract functions to write the definition of other functions we designed. In these cases the template origin of our function is either use-abstract-fn or fn-composition and use-abstract-fn.

Whenever you are working with an abstract functions problem it is very important to be sure which of the two you are doing - designing the abstract function, or using an abstract function. Note that the last step of any abstraction from examples is to rewrite the original function definition to use abstract function - but that is a separate and final phase of the abstraction frome examples.

As always, the best way to review today's material is to rework all three starters.

The solutions for this lecture are:

• m08-abstract-fold-definition-solution.rkt
• m08-abstract-fold-usages-solution.rkt
• m08-abstract-fold-complications-starter.rkt

Be sure to complete the before lecture section of Lecture 15 before that lecture.