Notes (HPFP 16/31): Functor

16 Functor

16.4 Let’s talk about 4, baby

Excercises: Be Kind

  1. *
  2. b is `* -> ,Tis -> *`
  3. `* -> * -> *`

16.7 Commonly used functors

Exercises: Heavy Lifting

see HeavyLifting.hs

16.10 Exercises: Instances of Func

see FunctorInstances.hs

16.11 Ignoring possibilities

Exercise: Possibly

see PossiblyEither.hs

Short Exercise

  1. The a in First a might be a different type than the b in Second b. The function we pass to fmap can only operate on one of those types, but not both. In other words the function that fmap maps is of type b -> c and kind *. Furthermore, we have to apply the function to Second b rather than First a, because the structure that fmaps maps onto is of kind ` -> . Our structure is(Sum a)becauseSumis of kind* -> * -> *and it needs to have accepted every type constructor but the last before its something that fmap can work on. But that doesn't mean we're barred from writing another function that does something different toSum`, but something different wont be fmap.

16.7 Chapter Exercises

Determine if a valid Functor can be written for the datatype provided:

  1. No, Bool has kind * but fmap only works on `* -> *`
  2. Yes, note that False' and True' both take the same type a
  3. Yes, fmap can ignore Falsish
  4. Yes… but why…
  5. Nope, theres nothing to fmap over, kind *

Rearrange the arguments:

see Rearrange.hs

16.19 Follow-up resources

  1. Haskell Wikibook; The Functor class.
  2. Mark P. Jones; A system of constructor classes: overloading and implicit higher-order polymorphism.
  3. Gabriel Gonzalez; The functor design pattern.