Fun with Functions! - Exercises Only

fun-with-functions.md

These exercises were part of a LambdaConf Outpost meetup. You may find the instructions here.

1. Develop a model for boolean values (Bool), which may be either true or false.

   Think: Do you need an if-then-else construct? Why or why not?

   Bonus: Develop a model for eithers (Either), whih can be one thing ("left") or another ("right"), and model a boolean as a partitioning of a set into two disjoint sets.

2. Develop a model for optional values (Maybe / Option), which are containers that are either empty ("nothing" / "none") or hold a single value ("just" / "some").

   Think: If you are wrote a parametric solution in a statically-typed language, can you prove the container holds exactly 0 or 1 element, based solely on its type signature? Why or why not?

   Bonus: Define a function, called optionMap, which takes an optional value, and a function which can transform the value, and returns another optional value.

3. Develop a model for a singly-linked list (List), which can be empty, or which can contain a head (the element at the start of the list) and a tail (the remainder of the list).

   Think: Do you need to define a left fold for this model? Why or why not?

   Bonus: Define a function, called listMap, which takes a list, and a function which can transform an element in the list, and returns another list.

4. Develop a model for a container of exactly two things (Tuple), which may individually have different structures.

   Think: How can you use only Tuple to define a Tuple3? What are the pros and cons of this approach?

   Bonus: Define Tuple3, Tuple4, and so on, up to Tuple10.

5. Develop a model for a container of either one thing ("left") or another ("right"), typically called Either.

   Think: What is the relationship of Either to Tuple?

   Bonus: Define Either3, Either4, and so on, up to Either10.

6. Develop a model for natural numbers (which start at 0 and count upwards in increments of 1). Hint: Try repeated application of some function to some initial value.

   Think: With this definition of natural number, how do you repeat something N times? How does this compare with repetition with a "native" natural number type?

   Bonus: Define addition and multiplication for natural numbers.

   2x Bonus: Model integers as a difference between two natural numbers, and define addition, subtraction, and multiplication.

7. Develop a model for a couple "write-only" commands, such as "print this number to the console." This model is purely descriptive, it doesn't need to do anything!

   Think: Why does the exercise insist these commands be "write-only"?

   Bonus: Think about approaches that might allow you to have "read" commands, that return information (for example, reading a line of input from the console).

8. Cheat and develop an "interpreter" which can take a list of write-only commands, and actually perform their effects!

For solutions, see here. Don't cheat!