# Context alias

### From HaskellWiki

Basvandijk (Talk | contribs) |
Basvandijk (Talk | contribs) |
||

Line 77: | Line 77: | ||

class Num a = (Monoid a, Group a, Multiplicative a, FromInteger a) where | class Num a = (Monoid a, Group a, Multiplicative a, FromInteger a) where | ||

− | mempty = | + | |

+ | -- Default implementations of existing methods: | ||

+ | mempty = 0 | ||

mappend = (+) | mappend = (+) | ||

− | one = | + | one = 1 |

times = (*) | times = (*) | ||

Line 86: | Line 88: | ||

gnegate = negate | gnegate = negate | ||

+ | -- New methods with default implementations: | ||

(+) :: a -> a -> a | (+) :: a -> a -> a | ||

(+) = mappend | (+) = mappend |

## Revision as of 10:10, 16 April 2009

Context aliases, also known as class aliases, are a long-requested feature of Haskell. This feature would allow class hierarchies to be restructured without breaking compatibility to a certain degree. Also, it would make fine-grained class hierarchies usable.

## Contents |

## 1 The proposal

### 1.1 The original class alias proposal

The original proposal can be found on a page on John Meachem’s website.

#### 1.1.1 Class aliases with new methods

I would like to emphasize an important point from the 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: *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*. 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

### 1.2 Improvements

#### 1.2.1 “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)

#### 1.2.2 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)

#### 1.2.3 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)

#### 1.2.4 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:

- should just be a combination ofMonadPlusandAlternative(actually,Monadshould just be a combination ofAlternative fandApplicative f)forall a. Monoid (f a)

- should be a superclass ofApplicativeMonad

## 2 Implementation

Starting an implementation of context aliases is planned for the 5th Haskell Hackathon.