Varying lens properties by instance

arkeet edited this page Jan 27, 2013 · 3 revisions

Say we have a few types for things that have a "name", which is a String that may or may not be modifiable. We want to have a type class for these things that exposes a lens-like method for accessing the name in a type-safe manner, so that it may be a Lens or just a Getter depending on the instance.

First let's write some example types and some lenses for them:

{-# LANGUAGE MultiParamTypeClasses #-}
{-# LANGUAGE TypeFamilies, ConstraintKinds #-}

import Control.Lens
import GHC.Exts -- for the Constraint kind

newtype ReadWrite = ReadWrite String
newtype ReadOnly = ReadOnly String

       -- Functor f => LensLike' f ReadWrite String
rwName :: Lens' ReadWrite String
rwName f (ReadWrite s) = ReadWrite `fmap` f s

       -- Gettable f => LensLike' f ReadOnly String
roName :: Getter ReadOnly String
roName = to (\(ReadOnly a) -> a)

Now rwName is a full Lens, while roName can only be used as a Getter. We'd like to make a single class that lets us get and set the name of a ReadWrite, but only get the name of a ReadOnly.

Using a multi-parameter type class

Now the only difference between a Getter and a Lens is the restriction on the type of Functor it can be used with. So, the first idea is to let our class take that Functor as a parameter:

class NamedMPTC f a where
  nameMPTC :: LensLike' f a String

instance Functor f => NamedMPTC f ReadWrite where
  nameMPTC = rwName

instance Gettable f => NamedMPTC f ReadOnly where
  nameMPTC = roName

And now nameMPTC gives us a type-safe way to get what we want from both ReadOnly and ReadWrite:

ghci> ReadWrite "a" ^. nameMPTC
ghci> ReadWrite "a" & nameMPTC .~ "b"
ReadWrite "b"
ghci> ReadOnly "c" ^. nameMPTC
ghci> ReadOnly "c" & nameMPTC .~ "d"
-- No instance for (Gettable Mutator) arising from a use of `nameMPTC' ...

This appears to work pretty well. We can easily restrict to different types of Functors; for example, restricting to Applicative will make nameMPTC a Traversal, in case we had something with multiple names.

When we try to use this in practice, however, we run into problems. If NamedMPTC had another method that made no reference to f, then any time we tried to use it, the type checker would blow up with an ambiguous type error! The only way around this would be to have our lens-like method be in its own class, which sounds pretty undesirable. What we needed was a way to impose the constraint on f only on the lens-like method, not the entire class. So let's forget this and look at another approach.

Using the Constraint kind

This means we'll need at least GHC 7.4. Let's see the code first:

class Named a where
    type NameConstraint a f :: Constraint
    name :: NameConstraint a f => LensLike' f a String

instance Named ReadWrite where
    type NameConstraint ReadWrite f = Functor f
    name = rwName

instance Named ReadOnly where
    type NameConstraint ReadOnly f = Gettable f
    name = roName

Let's see how the types work. First let's look at the type of name:

name :: (NameConstraint a f, Named a) => LensLike' f a String

When we specialize to a = ReadOnly, the Named a constraint is satisfied and NameConstraint a f just becomes Gettable f, so we end up with

name :: Gettable f => LensLike' f ReadOnly String

which is exactly the type of roName we had before.

With this approach, name works exactly how nameMPTC did earlier. But notice that this time the constraint on f is only applied to name, not the entire class. This means we can easily add other methods to the class without causing any ambiguous type issues, and we can even add different lens-like methods with different constraints. Fantastic!