Notes for Week 12 Applicative Functors Part 1 Functors and Functor Laws

Links:

• Chapter 11 Notes
• Online chapter

Exercises:

Exercise 1

* What are Functors useful for?
* What's the difference between fmap and (.) ?  Explain.

Exercise 2

Demonstrate using an IO action as a Functor.

Exercise 3

Make the following Tree type an instance of Functor:

     data Tree a = Node (Tree a) (Tree a) | Leaf a deriving (Show, Eq)

Use the following test to get it working (returns true):

     testFmap = (fmap (+1000) $ Node (Leaf 100) (Leaf 200)) == (Node (Leaf 1100) (Leaf 1200))

Prove that it follows the two Functor laws by writing the following tests:

     --testIdLaw = 
     --testComposeLaw = 

Links

• http://hackage.haskell.org/packages/archive/base/4.2.0.0/doc/html/Data-Functor.html
• http://www.haskell.org/haskellwiki/Category_theory/Functor
• http://www.catonmat.net/blog/on-functors/
• Deriving Functor http://www.mail-archive.com/[email protected]/msg02116.html

Questions raised during the group:

Answers to Exercises:

//TODO

Interesting Asides

//TODO