Functor-Applicative-Monad Proposal
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− | The standard class hierarchy is a consequence of Haskell's historical development, rather than logic. The <hask>Functor</hask>, <hask>Applicative</hask>, and <hask>Monad</hask> type classes could be defined as: |
+ | Haskell calls a couple of historical accidents its own. While some of them, such as the "number classes" hierarchy, can be justified by pragmatism or lack of a strictly better suggestion, there is one thing that stands out as, well, not that: Applicative not being a superclass of Monad. |
− | <haskell> |
+ | The topic has been discussed multiple times in the past (cf. link section at the very end). '''This article was updated to describe the current, and very likely to succeed, Haskell 2014 Applicative => Monad proposal (AMP)'''. |
− | class Functor f where |
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− | map :: (a -> b) -> f a -> f b |
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− | class Functor f => Applicative f where |
+ | Some relevant links: |
− | return :: a -> f a |
+ | * [https://github.com/quchen/articles/blob/master/applicative_monad.md Initial text of the Haskell 2014 AMP] |
− | (<*>) :: f (a -> b) -> f a -> f b |
+ | * [http://article.gmane.org/gmane.comp.lang.haskell.libraries/19482 AMP mailing list discussion] |
− | (*>) :: f a -> f b -> f b |
+ | * Phase one: ticket [http://hackage.haskell.org/trac/ghc/ticket/8004 #8004] |
− | (<*) :: f a -> f b -> f a |
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− | class Applicative m => Monad m where |
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− | (>>=) :: m a -> (a -> m b) -> m b |
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− | f >>= x = join $ map f x |
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− | join :: m (m a) -> m a |
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− | join x = x >>= id |
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− | class Monad m => MonadFail m where |
+ | == Proposal contents == |
− | fail :: String -> m a |
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− | </haskell> |
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− | This would eliminate the necessity of declaring a Monad instance for every Applicative, and eliminate the need for sets of duplicate functions such as [<hask>fmap</hask>, <hask>liftM</hask>, <hask>map</hask>, <hask>liftA</hask>], [<hask>(<*>)</hask>, <hask>ap</hask>], and [<hask>concat</hask>, <hask>join</hask>]. |
+ | The list of changes is as follows: |
− | A monad which requires custom handling for pattern match failures can implement <hask>MonadFail</hask>; otherwise, a failed pattern match will error in the same way as is does for pure code. |
+ | # Applicative becomes a superclass of Monad, and is added to the Prelude. |
+ | # Alternative becomes a superclass of MonadPlus (in addition to Monad, of course). |
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+ | # <hask>join</hask> is promoted into the Monad typeclass. |
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− | <hask>Pointed</hask> has not been included due to controversy as to whether it should be a subclass of Functor, a superclass of Functor, independent of Functor, or perhaps it is not sufficiently useful to include at all. |
+ | The general rationale behind these changes: |
− | Backward compatibility could be eased with a legacy module, such as: |
+ | # ''Break as little code as possible.'' For example, do not move <hask>return</hask> to Applicative and remove <hask>pure</hask>. Instead, leave <hask>return</hask> in Monad, and give it <hask>pure</hask> as default implementation. |
+ | # ''Change only things that are closely related to the proposal.'' For example, using <hask>join</hask> in a monad definition requires it to be a functor, so it goes hand in hand with the AMP. On the other hand, removing <hask>fail</hask> has nothing to do with what we're trying to accomplish. |
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− | <haskell> |
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− | module Legacy where |
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− | fmap :: Functor f => (a -> b) -> f a -> f b |
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− | fmap = map |
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− | liftA :: Applicative f => (a -> b) -> f a -> f b |
+ | == How do programmers need to change their code? == |
− | liftA = map |
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− | liftM :: Monad m => (a -> b) -> m a -> m b |
+ | The following is a list of things you may have to change in your code so the AMP doesn't break it. |
− | liftM = map |
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− | ap :: Monad m => m (a -> b) -> m a -> m b |
+ | * Add Applicative/Functor instances for all your Monads. If you don't care about efficiency, you can simply derive these instances from the Monad by adding the following code: |
− | ap = (<*>) |
+ | <haskell> |
+ | -- Monad m |
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− | (>>) :: Monad m => m a -> m b -> m b |
+ | import Control.Monad (liftM, ap) |
− | (>>) = (*>) |
+ | import Control.Applicative (Applicative(..)) |
− | concat :: [[a]] -> [a] |
+ | instance Functor m where |
− | concat = join |
+ | fmap = liftM |
− | etc. |
+ | instance Applicative m where |
+ | pure = return |
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+ | (<*>) = ap |
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</haskell> |
</haskell> |
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− | And for those who really want a list map, |
+ | * Add an Alternative instance for all instances of MonadPlus. This can again be done easily using |
− | |||
<haskell> |
<haskell> |
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− | listMap :: (a -> b) -> [a] -> [b] |
+ | -- MonadPlus m |
− | listMap = map |
+ | |
+ | import Control.Monad (mzero, mplus) |
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+ | import Control.Applicative (Alternative(..)) |
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+ | |||
+ | instance Alternative m where |
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+ | (<|>) = mplus |
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+ | empty = mzero |
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</haskell> |
</haskell> |
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− | [[Context alias]] would also be a great help with backwards compatibility. |
+ | * Change your API to not define functions named <hask><*></hask>, <hask>join</hask> or <hask>pure</hask>. |
− | Another variant might be to split a <hask>Pointed</hask> class from the <hask>Applicative</hask> class. |
+ | Future versions of GHC will issue warnings if code doesn't comply to these rules; there will be a long enough transitional phase so Hackage can adapt to the AMP in advance before the above mentioned changes are actually enforced. |
− | <haskell> |
+ | == Discussion and consequences == |
− | class Pointed f where |
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− | return :: a -> f a |
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− | class (Functor f, Pointed f) => Applicative f where |
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− | (<*>) :: f (a -> b) -> f a -> f b |
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− | (*>) :: f a -> f b -> f b |
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− | (<*) :: f a -> f b -> f a |
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− | </haskell> |
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− | Such <hask>Pointed</hask> functionality by itself could be useful, for example, in a DSL in which it is only possible to embed values and not to lift functions to functions over those embedded values. |
+ | === It's the right thing to do™ === |
+ | |||
+ | Math. You've all heard this one, it's good and compelling so I don't need to spell it out. |
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+ | |||
+ | |||
+ | === Redundant functions === |
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+ | |||
+ | * <hask>pure</hask> and <hask>return</hask> do the same thing. |
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+ | * <hask>>></hask> and <hask>*></hask> are identical. |
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+ | * <hask>liftM</hask> and <hask>liftA</hask> are <hask>fmap</hask>. The <hask>liftM*</hask> are <hask>liftA*</hask>, <hask><*></hask> is <hask>ap</hask>. |
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+ | * Prelude's <hask>sequence</hask> requres <hask>Monad</hask> right now, while <hask>Applicative</hask> is sufficient to implement it. The more general version of this issue is captured by <hask>Data.Traversable</hask>, whose main typeclass implements the *same* functionality twice, namely <hask>traverse</hask> and <hask>mapM</hask>, and <hask>sequenceA</hask> and <hask>sequence</hask>. |
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+ | * The <hask>WrappedMonad</hask> type from <hask>Control.Applicative</hask> provides a semi-automatic way to using Functor/Applicative/Alternative functions for Monad/MonadPlus instances as a makeshift patch. |
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+ | |||
+ | That very much violates the "don't repeat yourself" principle, and even more so it ''forces'' the programmer to repeat himself to achieve maximal generality. It may be too late to take all redundancies out, but at least we can prevent new ones from being created. |
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+ | |||
+ | (Note that it is not proposed to remove any functions for compatibility reasons. Maybe some of them can be phased out in the long run, but that's beyond scope here.) |
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+ | |||
+ | |||
+ | === Using Functor/Applicative functions in monadic code === |
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+ | |||
+ | Whenever there's Monad code, you can use Functor/Applicative functions, without introducing an additional constraint. Keep in mind that "Functor/Applicative functions" does not only include what their typeclasses define but many more, for example <hask>void</hask>, <hask>(<$>)</hask>, <hask>(<**>)</hask>. |
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+ | |||
+ | Even if you think you have monadic code, strictly using the least restrictive functions may result in something that requires only Applicative. This is similar to writing a function that needs <hask>Int</hask>, but it turns out any <hask>Integral</hask> will do - more polymorphism for free. |
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+ | |||
+ | |||
+ | === Compatibility issues === |
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+ | |||
+ | These are the kinds of issues to be expected: |
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+ | |||
+ | # Monads lacking Functor or Applicative instances. This is easily fixable by either setting <hask>fmap = liftM</hask>, <hask>pure = return</hask> and <hask>(<*>) = ap</hask>, although more efficient implementations may exist, or by moving an already existing definition from <hask>Control.Applicative</hask> to the appropriate module. |
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+ | # This one is specific to building GHC: importing <hask>Control.Monad/Applicative</hask> introduces a circular module dependency. In this case, one can rely on handwritten implementations of the desired function, e.g. <hask>ap f x = f >>= ...</hask>. |
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+ | # Libraries using their own <hask>(<*>)</hask>. This one is potentially the most laborious consequence. For building GHC though, this only concerns Hoopl, and a handful of renames. |
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+ | |||
+ | |||
+ | |||
+ | === Beginner friendliness === |
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+ | |||
+ | How often did you say ... |
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+ | |||
+ | * "A Monad is always an Applicative but due to historical reasons it's not but you can easily verify it by setting <hask>pure = return</hask> and <hask>(<*>) = ap</hask>" |
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+ | * "<hask>liftM</hask> is <hask>fmap</hask> but not really." - "So when should I use <hask>fmap</hask> and when <hask>liftM</hask>?" - *sigh* |
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+ | |||
+ | With the new hierarchy, the answer would *always* be "use the least restrictive one". |
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+ | |||
+ | |||
+ | |||
+ | == Applying the AMP to GHC and then Haskell in practice == |
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+ | |||
+ | Proposed is a gradual introduction of the AMP in three phases: |
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+ | |||
+ | |||
+ | === '''Current stage''': Prepare GHC === |
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+ | |||
+ | Using a GHC fork with the full patch applied, find and fix all compilation errors introduced by the change by adding Functor/Applicative instances for all Monads. |
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+ | |||
+ | According to SPJ, adding an ad-hoc warning of sorts "Monad without Applicative detected" is not a problem, which will be crucial for the next phase. More specifically, issue a warning if: |
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+ | |||
+ | * Monad without Applicative |
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+ | * MonadPlus without Alternative |
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+ | * One of <hask><*></hask>, <hask>pure</hask>, <hask>join</hask> is defined in a different context to avoid naming conflicts, as these functions will go into the Prelude |
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+ | |||
+ | === Prepare Hackage === |
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+ | |||
+ | The warning just mentioned will hint to all authors that they should fix (or help others fix) the non-complying packages. This will ideally lead to libraries eventually adding Applicative instances, and changing their APIs if they redefine operators like <hask><*></hask>. |
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+ | |||
+ | After enough time has passed by so libraries adapted to the circumstances, move on to the next phase. |
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+ | |||
+ | |||
+ | === Apply the proposal === |
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+ | |||
+ | Once Hackage is prepared, applying the changes to the Base package is painless. However, this is not primarily a GHC, but a Haskell change. The previous steps were basically preparing the landscape, and when we've (hopefully) found out that it is a good idea to go through with it, it can be proposed to go into the Report. If we make it this far, the AMP should pass quite easily. |
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+ | |||
+ | |||
+ | |||
+ | == Previous proposals == |
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+ | |||
+ | * Early 2011: [http://hackage.haskell.org/trac/ghc/ticket/4834 GHC ticket] – changes similar to this proposal, but closed as "not GHC, but Haskell". See [http://thread.gmane.org/gmane.comp.lang.haskell.libraries/14883/focus=14905 here] for the associated discussion. |
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+ | * [[The Other Prelude]] |
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+ | |||
[[Category:Proposals]] |
[[Category:Proposals]] |
Revision as of 14:39, 22 June 2013
Haskell calls a couple of historical accidents its own. While some of them, such as the "number classes" hierarchy, can be justified by pragmatism or lack of a strictly better suggestion, there is one thing that stands out as, well, not that: Applicative not being a superclass of Monad.
The topic has been discussed multiple times in the past (cf. link section at the very end). This article was updated to describe the current, and very likely to succeed, Haskell 2014 Applicative => Monad proposal (AMP).
Some relevant links:
- Initial text of the Haskell 2014 AMP
- AMP mailing list discussion
- Phase one: ticket #8004
Contents |
1 Proposal contents
The list of changes is as follows:
- Applicative becomes a superclass of Monad, and is added to the Prelude.
- Alternative becomes a superclass of MonadPlus (in addition to Monad, of course).
- is promoted into the Monad typeclass.join
The general rationale behind these changes:
- Break as little code as possible. For example, do not move to Applicative and removereturn. Instead, leavepurein Monad, and give itreturnas default implementation.pure
- Change only things that are closely related to the proposal. For example, using in a monad definition requires it to be a functor, so it goes hand in hand with the AMP. On the other hand, removingjoinhas nothing to do with what we're trying to accomplish.fail
2 How do programmers need to change their code?
The following is a list of things you may have to change in your code so the AMP doesn't break it.
- Add Applicative/Functor instances for all your Monads. If you don't care about efficiency, you can simply derive these instances from the Monad by adding the following code:
-- Monad m import Control.Monad (liftM, ap) import Control.Applicative (Applicative(..)) instance Functor m where fmap = liftM instance Applicative m where pure = return (<*>) = ap
- Add an Alternative instance for all instances of MonadPlus. This can again be done easily using
-- MonadPlus m import Control.Monad (mzero, mplus) import Control.Applicative (Alternative(..)) instance Alternative m where (<|>) = mplus empty = mzero
- Change your API to not define functions named ,<*>orjoin.pure
Future versions of GHC will issue warnings if code doesn't comply to these rules; there will be a long enough transitional phase so Hackage can adapt to the AMP in advance before the above mentioned changes are actually enforced.
3 Discussion and consequences
3.1 It's the right thing to do™
Math. You've all heard this one, it's good and compelling so I don't need to spell it out.
3.2 Redundant functions
- andpuredo the same thing.return
- and>>are identical.*>
- andliftMareliftA. ThefmapareliftM*,liftA*is<*>.ap
- Prelude's requressequenceright now, whileMonadis sufficient to implement it. The more general version of this issue is captured byApplicative, whose main typeclass implements the *same* functionality twice, namelyData.Traversableandtraverse, andmapMandsequenceA.sequence
- The type fromWrappedMonadprovides a semi-automatic way to using Functor/Applicative/Alternative functions for Monad/MonadPlus instances as a makeshift patch.Control.Applicative
That very much violates the "don't repeat yourself" principle, and even more so it forces the programmer to repeat himself to achieve maximal generality. It may be too late to take all redundancies out, but at least we can prevent new ones from being created.
(Note that it is not proposed to remove any functions for compatibility reasons. Maybe some of them can be phased out in the long run, but that's beyond scope here.)
3.3 Using Functor/Applicative functions in monadic code
Whenever there's Monad code, you can use Functor/Applicative functions, without introducing an additional constraint. Keep in mind that "Functor/Applicative functions" does not only include what their typeclasses define but many more, for example
3.4 Compatibility issues
These are the kinds of issues to be expected:
- Monads lacking Functor or Applicative instances. This is easily fixable by either setting ,fmap = liftMandpure = return, although more efficient implementations may exist, or by moving an already existing definition from(<*>) = apto the appropriate module.Control.Applicative
- This one is specific to building GHC: importing introduces a circular module dependency. In this case, one can rely on handwritten implementations of the desired function, e.g.Control.Monad/Applicative.ap f x = f >>= ...
- Libraries using their own . This one is potentially the most laborious consequence. For building GHC though, this only concerns Hoopl, and a handful of renames.(<*>)
3.5 Beginner friendliness
How often did you say ...
- "A Monad is always an Applicative but due to historical reasons it's not but you can easily verify it by setting andpure = return"(<*>) = ap
- "isliftMbut not really." - "So when should I usefmapand whenfmap?" - *sigh*liftM
With the new hierarchy, the answer would *always* be "use the least restrictive one".
4 Applying the AMP to GHC and then Haskell in practice
Proposed is a gradual introduction of the AMP in three phases:
4.1 Current stage: Prepare GHC
Using a GHC fork with the full patch applied, find and fix all compilation errors introduced by the change by adding Functor/Applicative instances for all Monads.
According to SPJ, adding an ad-hoc warning of sorts "Monad without Applicative detected" is not a problem, which will be crucial for the next phase. More specifically, issue a warning if:
- Monad without Applicative
- MonadPlus without Alternative
- One of ,<*>,pureis defined in a different context to avoid naming conflicts, as these functions will go into the Preludejoin
4.2 Prepare Hackage
The warning just mentioned will hint to all authors that they should fix (or help others fix) the non-complying packages. This will ideally lead to libraries eventually adding Applicative instances, and changing their APIs if they redefine operators likeAfter enough time has passed by so libraries adapted to the circumstances, move on to the next phase.
4.3 Apply the proposal
Once Hackage is prepared, applying the changes to the Base package is painless. However, this is not primarily a GHC, but a Haskell change. The previous steps were basically preparing the landscape, and when we've (hopefully) found out that it is a good idea to go through with it, it can be proposed to go into the Report. If we make it this far, the AMP should pass quite easily.
5 Previous proposals
- Early 2011: GHC ticket – changes similar to this proposal, but closed as "not GHC, but Haskell". See here for the associated discussion.
- The Other Prelude