Difference between revisions of "Context alias"
Basvandijk (talk  contribs) 
Basvandijk (talk  contribs) (Added some concluding remarks to the 'Class aliases with new methods' section) 

Line 165:  Line 165:  
fromInteger (n+1) = S n  You gotta love n+k patterns! 
fromInteger (n+1) = S n  You gotta love n+k patterns! 

−  In conclusion, a class alias is a name for a context plus optionally a new class. 
+  In conclusion, a class alias is a name for a context plus optionally a new class. The question is how useful this ability is. 
−  +  
+  The ''BoundedBelowJoinable'' could also be defined as a normal class with the necessary superclasses: 

+  
+  class (BoundedBelow a, SemiLatticeJoin a) => BoundedBelowJoinable a where 

+  joins :: [a] > a 

+  joins xs = foldl join bottom xs 

+  
+  However, user now don't get a ''BoundedBelowJoinable'' for free when they have defined instances for ''BoundedBelow'' and ''SemiLatticeJoin''. 

+  
+  The ''Num'' class alias could also be rewritten to a simple alias together with some functions that translate the original names to the new names: 

+  
+  class alias Num a = (Monoid a, Group a, Multiplicative a, FromInteger a) 

+  
+  (+) = mappend 

+  () = minus 

+  (*) = times 

+  negate = gnegate 

+  
=== Improvements === 
=== Improvements === 

Revision as of 12:34, 16 April 2009
Context aliases, also known as class aliases, are a longrequested feature of Haskell. This feature would allow class hierarchies to be restructured without breaking compatibility to a certain degree. Also, it would make finegrained class hierarchies usable.
Contents
The proposal
The original class alias proposal
The original proposal can be found on a page on John Meachem’s website.
Class aliases with new methods
I would like to emphasize an important point from the original proposal that was not emphasized enough:
Lets look at one of the examples from the original proposal:
class SemiLatticeJoin a where join :: a > a > a
class BoundedBelow a where bottom :: a
class BoundedBelowJoinable a = (BoundedBelow a, SemiLatticeJoin a) where joins :: [a] > a joins xs = foldl join bottom xs
Notice that BoundedBelowJoinable doesn't have the alias keyword. Is this a syntax error or is it allowed? It is allowed because BoundedBelowJoinable is not just an alias for (BoundedBelow a, SemiLatticeJoin a). It also declares a new method called joins.
So why is this usefull?
Users can declare instances for BoundedBelow and SemiLatticeJoin and get joins for free or they can declare an instance for BoundedBelowJoinable and define an optimized joins for their type.
Lets look at another example why this ability, to give a class alias new methods, is useful. Again I take an example from the original proposal but I slightly change it:
The current Num class in the Prelude is (more or less) this
class Num a where (+) :: a > a > a (*) :: a > a > a () :: a > a > a negate :: a > a fromInteger :: Integer > a
Ideally we would want to split it up using classes from the monoids package:
class Monoid a where mempty :: a mappend :: a > a > a class Monoid a => Group a where gnegate :: a > a minus :: a > a > a gsubtract :: a > a > a
gnegate = minus mempty a `minus` b = a `mappend` gnegate b a `gsubtract` b = gnegate a `mappend` b
class Multiplicative a where one :: a times :: a > a > a
class FromInteger a where fromInteger :: Integer > a
But this creates some problems as mentioned in the proposal:
 People using the new prelude have to write the ungainly (Monoid a, Group a, Multiplicative a, FromInteger a) and declare separate instances for all of them.
 If at some point a HasZero class is separated out then everyone needs to modify their instance declarations.
 Num still must be declared if you want it to work with old prelude functions, containing completely redundant information.
 All the problems mentioned in the second section of the proposal about alternate preludes in general.
We can solve all of them by creating a class alias:
class alias Num a = (Monoid a, Group a, Multiplicative a, FromInteger a)
Or can we? Unfortunately this Num is different than the original Num. Because instead of the methods (+), (), (*) and negate we have mappend, minus, times and gnegate.
Fortunately we can add the original names as new methods to the class alias and give them default definitions in terms of the new names:
class Num a = (Monoid a, Group a, Multiplicative a, FromInteger a) where  Default implementations of existing methods: mempty = 0 mappend = (+)
one = 1 times = (*)
minus = () gnegate = negate
 New methods with default implementations: (+) :: a > a > a (+) = mappend
(*) :: a > a > a (*) = times
() :: a > a > a () = minus negate :: a > a negate = gnegate
The question is: how is the above translated?
The new methods from Num should be placed in a new "internal" class: Num_NEW_METHODS:
class Num_NEW_METHODS a where (+) :: a > a > a (*) :: a > a > a () :: a > a > a negate :: a > a
What happens when a user defines an instance for Num? Lets look at an example:
Say a user defines the natural numbers and makes them an instance of the Num class alias:
data N = Z  S N instance Num N where Z + y = y S x + y = S (x + y)
Z * _ = Z S Z * y = y S x * y = y + x * y
x  Z = x S x  S y = x  y
fromInteger 0 = Z fromInteger (n+1) = S n  You gotta love n+k patterns!
Note that the other methods of Num like mempty, mappend, one and times have default implementations in terms of the above.
First of all an instance for Num_NEW_METHODS will be defined:
instance Num_NEW_METHODS N where Z + y = y S x + y = S (x + y)
Z * _ = Z S Z * y = y S x * y = y + x * y
x  Z = x S x  S y = x  y
negate = gnegate
Then the other instances are defined using methods from Num_NEW_METHODS:
instance Monoid N where mempty = 0 mappend = (+)
instance Group N where minus = ()
instance Multiplicative N where one = 1 times = (*)
instance FromInteger N where fromInteger 0 = Z fromInteger (n+1) = S n  You gotta love n+k patterns!
In conclusion, a class alias is a name for a context plus optionally a new class. The question is how useful this ability is.
The BoundedBelowJoinable could also be defined as a normal class with the necessary superclasses:
class (BoundedBelow a, SemiLatticeJoin a) => BoundedBelowJoinable a where joins :: [a] > a joins xs = foldl join bottom xs
However, user now don't get a BoundedBelowJoinable for free when they have defined instances for BoundedBelow and SemiLatticeJoin.
The Num class alias could also be rewritten to a simple alias together with some functions that translate the original names to the new names:
class alias Num a = (Monoid a, Group a, Multiplicative a, FromInteger a)
(+) = mappend () = minus (*) = times negate = gnegate
Improvements
“Context alias” instead of “class alias”
A “class alias” actually doesn’t stand for a class but for a context (or a part of a context). So it might be better to choose a slightly different syntax:
context Foobar a = (Foo a, Bar a)
However if we allow class "aliases" to be extended with new methods then a class "alias" is not just a name for a context. (It is actually a context with a new class)
Maybe we should keep the syntax really light like:
class Foobar a = (Foo a, Bar a)
Superclass constraints
John Meacham proposes the following syntax for class aliases (context aliases) with superclass constraints:
class alias Num a = Eq a => (Additive a, Multiplicative a)
This is not consistent with the superclass syntax of class declarations. I think, we should use this syntax:
class alias Eq a => Num a = (Additive a, Multiplicative a)
Or better:
context Eq a => Num a = (Additive a, Multiplicative a)
Functional dependencies
Does the following make sense?
class alias A a b = (B a b, C a b)  a > b where ...
Associated data types and type synonyms
When {# LANGUAGE TypeFamilies #} is enabled, classes may declare associated data types or associated type synonyms.
If we allow class aliases to be extended with new methods, I think it make sense to also allow them to be extended with associated data types and type synonyms:
class A a = (B a, C a) where type T a data D a
Equality constraints
When {# LANGUAGE TypeFamilies #} is enabled, type contexts can include equality constraints (t1 ~ t2).
It makes sense to also allow them in class aliases (context aliases)
Things to have in mind
In order to get the context alias extension well, we should have an eye on problems we might want to solve with the help of context aliases. Here are some:

MonadPlus
should just be a combination ofAlternative
andMonad
(actually,Alternative f
should just be a combination ofApplicative f
andforall a. Monoid (f a)
)

Applicative
should be a superclass ofMonad
Implementation
Starting an implementation of context aliases is planned for the 5th Haskell Hackathon.