For the 0.10.4 release, I worked on Functor deriving. This allows you to write a data type and derive a Functor instance for it. This obviously doesn’t work for all data types, but also doesn’t necessarily work for all data types that could have a valid Functor instance written for them. In this post I will demonstrate examples of the kinds of structures it works for, and those it doesn’t.

Recall the definition of the Functor type class:

class Functor f where
  map :: forall a. (a -> b) -> f a -> f b

Given a data type F :: * -> *, to derive the Functor instance, we would write a derived instance such as:

derive instance functorF :: Functor F

If the compiler is able to compute the implementation of map for the particular F data type, then it will do so; otherwise you will get a bad type error. We have a ticket to improve the error message here.

The following is a collection of example data types for which this deriving mechanism should work for. Each with a short comment describing the particular arrangement of types that is being demonstrated.

-- no mention of index
data Const c x = Const c

-- mention of index as argument
data Identity x = Identity x

-- index as multiple arguments
data Two x = Two x x

-- index as arguments across constructors
data Which x = This x | That x

-- index in records
data Rec x = Rec { field0 :: x, field1 :: x }

-- index nested under other functor types
data Wrapped x = Wrapped (Boolean -> Array x)

-- recursive
data List x = Nil | Cons x (List x)

-- dependency on functor of other argument
data Free f x = Pure x | Free (f (Free f x))
derive instance functorFreeF :: Functor f => Functor (Free f)

Note that the last example also requires a Functor instance on the index f. If we omitted this, we would end up with the type error similar to:

No type class instance was found for

    Data.Functor.Functor f

Algorithm

Implementing the map function is rather straight-forward. For each argument in each constructor:

  • if the argument is the type index, then apply the mapping function
  • if the argument is a record, then recurse on each field
  • if the argument is a type application, recurse on the argument and wrap the function in a call to map
  • otherwise, leave the argument alone

Records are somewhat special in PureScript, so we decided to add a special case for them.

Limitations

Given this algorithm, we can see some obvious limitations: we only recurse on the last argument in a type application - so we may miss the uses of the index in other argument positions.

We also only ever assume a Functor instance for a data type with the argument in the last index. If we have some contravariant data type C :: * -> * and a data type data F x = F (C (C x)), with this algorithm we are unable to derive a Functor F instance, even though a valid one exists via cmap <<< cmap.

Each of these limitations could potentially be overcome by a more interesting algorithm with access to more information about the types involved: such as index variance tracking. With variance tracking we could compute which sort of mapping to apply: map, cmap, bimap, dimap, etc.

Conclusion

Aside from those limitations, with such a simple algorithm we gained a useful and widely applicable code generating tool. As a next step, and following a similar algorithm, we would like to derive Foldable and Traversable (ticket here). Perhaps I will work on those some time soon if someone else doesn’t beat me to it :)