I've been thinking about this idea for some time, which I'd call mutable lenses. So far, I haven't made it into a package, let me know, if you'd benefit from it.
First let's recall the generalized van Laarhoven Lenses (after some imports we'll need later):
{-# LANGUAGE RankNTypes #-}
import qualified Data.ByteString as BS
import Data.Functor.Constant
import Data.Functor.Identity
import Data.Traversable (Traversable)
import qualified Data.Traversable as T
import Control.Monad
import Control.Monad.STM
import Control.Concurrent.STM.TVar
type Lens s t a b = forall f . (Functor f) => (a -> f b) -> (s -> f t)
type Lens' s a = Lens s s a a
we can create such a lens from a "getter" and a "setter" as
mkLens :: (s -> a) -> (s -> b -> t) -> Lens s t a b
mkLens g s f x = fmap (s x) (f (g x))
and get a "getter"/"setter" from a lens back as
get :: Lens s t a b -> (s -> a)
get l = getConstant . l Constant
set :: Lens s t a b -> (s -> b -> t)
set l x v = runIdentity $ l (const $ Identity v) x
as an example, the following lens accesses the first element of a pair:
_1 :: Lens' (a, b) a
_1 = mkLens fst (\(x, y) x' -> (x', y))
-- or directly: _1 f (a,c) = (\b -> (b,c)) `fmap` f a
Now how a mutable lens should work? Getting some container's content involves a monadic action. And setting a value doesn't change the container, it remains the same, just as a mutable piece of memory does. So the result of a mutable lens will have to be monadic, and instead of the return type container t
we'll have just ()
. Moreover, the Functor
constraint isn't enough, since we need to interleave it with monadic computations. Therefore, we'll need Traversable
:
type MutableLensM m s a b
= forall f . (Traversable f) => (a -> f b) -> (s -> m (f ()))
type MutableLensM' m s a
= MutableLensM m s a a
(Traversable
is to monadic computations what Functor
is to pure computations).
Again, we create helper functions
mkLensM :: (Monad m) => (s -> m a) -> (s -> b -> m ())
-> MutableLensM m s a b
mkLensM g s f x = g x >>= T.mapM (s x) . f
mget :: (Monad m) => MutableLensM m s a b -> s -> m a
mget l s = liftM getConstant $ l Constant s
mset :: (Monad m) => MutableLensM m s a b -> s -> b -> m ()
mset l s v = liftM runIdentity $ l (const $ Identity v) s
As an example, let's create a mutable lens from a TVar
within STM
:
alterTVar :: MutableLensM' STM (TVar a) a
alterTVar = mkLensM readTVar writeTVar
These lenses are one-sidedly directly composable with Lens
, for example
alterTVar . _1 :: MutableLensM' STM (TVar (a, b)) a
Notes:
Mutable lenses could be made more powerful if we allow that the modifying function to include effects:
type MutableLensM2 m s a b = (Traversable f) => (a -> m (f b)) -> (s -> m (f ())) type MutableLensM2' m s a = MutableLensM2 m s a a mkLensM2 :: (Monad m) => (s -> m a) -> (s -> b -> m ()) -> MutableLensM2 m s a b mkLensM2 g s f x = g x >>= f >>= T.mapM (s x)
However, it has two major drawbacks:
- It isn't composable with pure
Lens
. - Since the inner action is arbitrary, it allows you to shoot yourself in the foot by mutating this (or other) lens during the mutating operation itself.
- It isn't composable with pure
There are other possibilities for monadic lenses. For example, we can create a monadic copy-on-write lens that preserves the original container (just as
Lens
does), but where the operation involves some monadic action:type LensCOW m s t a b = forall f . (Traversable f) => (a -> f b) -> (s -> m (f t))
I've made jLens - a Java library for mutable lenses, but the API is of course far from being as nice as Haskell lenses.