Re: [Haskell-cafe] do we need types?
I'd say we don't really need subclasses. I mean, what's the difference:
class Eq a where (==) :: a - a - Bool
instance Eq a = Eq (Maybe a) where
Nothing == Nothing = True
Just x == Just y = x == y
_ == _ = False
sort :: Eq a = [a] - [a]
or
data Eq a = Eq {eq :: a - a - Bool}
eqMaybe :: Eq a - Eq (Maybe a)
eqMaybe e = Eq {eq = eqM} where
eqM Nothing Nothing = True
eqM (Just x) (Just y) = eq e x y
eqM _ _ = False
sort :: Eq a - [a] - [a]
Replacing classes with types, we only lose one thing: the compiler won't deduce
the right instances for us. I'll trade it for the ability to abstract over
them. After all, we CAN deduce the right
instances by hand, it's just a finite amount of work (not very big, in my
experience).
Pasqualino Titto Assini wrote:
Hi, just a silly question (or maybe more than one):
In Haskell we have data types (Integer,[a],...) as well as type
classes (Num, Ord...).
But, if we have type classes do we still need types?
Why shouldn't the objects that we process be defined only by their
'interfaces' (assuming that a type class is a kind of interface)?
Maybe the real question is: are type classes a more primitive concept
than data types?
And if so, in a language that had only type classes what would a data
declaration like the following map to:
data List a = Cons a (List a) | Nil
And what about pattern matching? Would that still be possible, and
what form would it take?
And finally, would having only type classes make the type system any simpler?
Thanks,
titto
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Re: [Haskell-cafe] do we need types?
s/subclasses/classes/
Sorry for the confusion.
Miguel Mitrofanov wrote:
I'd say we don't really need subclasses. I mean, what's the difference:
class Eq a where (==) :: a - a - Bool
instance Eq a = Eq (Maybe a) where
Nothing == Nothing = True
Just x == Just y = x == y
_ == _ = False
sort :: Eq a = [a] - [a]
or
data Eq a = Eq {eq :: a - a - Bool}
eqMaybe :: Eq a - Eq (Maybe a)
eqMaybe e = Eq {eq = eqM} where
eqM Nothing Nothing = True
eqM (Just x) (Just y) = eq e x y
eqM _ _ = False
sort :: Eq a - [a] - [a]
Replacing classes with types, we only lose one thing: the compiler won't
deduce the right instances for us. I'll trade it for the ability to
abstract over them. After all, we CAN deduce the right
instances by hand, it's just a finite amount of work (not very big, in
my experience).
Pasqualino Titto Assini wrote:
Hi, just a silly question (or maybe more than one):
In Haskell we have data types (Integer,[a],...) as well as type
classes (Num, Ord...).
But, if we have type classes do we still need types?
Why shouldn't the objects that we process be defined only by their
'interfaces' (assuming that a type class is a kind of interface)?
Maybe the real question is: are type classes a more primitive concept
than data types?
And if so, in a language that had only type classes what would a data
declaration like the following map to:
data List a = Cons a (List a) | Nil
And what about pattern matching? Would that still be possible, and
what form would it take?
And finally, would having only type classes make the type system any
simpler?
Thanks,
titto
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Re: [Haskell-cafe] do we need types?
This reminds me of an email posted to this list long ago
by Luke Palmer, describing a use of records-as-interfaces
in Agda.
--
Jason Dusek
-- Forwarded message --
From: Luke Palmer lrpal...@gmail.com
Date: 2009/12/29
Subject: Re: [Haskell-cafe] Alternatives to type classes.
To: Jason Dusek jason.du...@gmail.com
Cc: haskell haskell-cafe@haskell.org
On Tue, Dec 29, 2009 at 6:22 PM, Jason Dusek jason.du...@gmail.com wrote:
Consider the real numbers. They are a group. We have an
identity element `0', inverses and closure under the associative
operation `+'.
Group+ = (+, 0, -1 * _)
They are another group, too -- the group with `*':
Group* = (*, 1, 1 / _)
Ignoring 0 for sake of discussion.
This seems like a real problem with the whole notion of
typeclasses -- we can't really say a set/type is its
extension with some new operations.
One road to go on this is to make every extension of the set
with new ops a different type; but that seems really horribly
inconvenient. I wonder what approaches have been tried here?
I consider typeclasses a happy notational medium. They are not
perfect, they miss some cases, but they are pretty good.
For full generality at the expense of some verbosity, I like Agda's
solution pretty well. Agda allows you to open a record into a
scope.
record Group (a : Set) where
field
_+_ : a - a - a
-_ : a - a
0 : a
conj : {a : Set} - Group a - a - a - a
conj g x y = x + y + (-x)
where open g
Maybe I even got the syntax right :-P
The cool thing is that you can use this for the invariant-keeping
property of typeclasses, too. Eg. Data.Map relies on the fact that
there is at most one Ord instance per type. By parameterizing the
module over the Ord record, we can do the same:
record Ord (a : Set) where ...
module MapMod (a : Set) (ord : Ord a) where
Map : b - Set
Map = ...
insert : {b : Set} - a - b - Map b - Map b
insert = ...
...
So we have the liberty of being able to use different Ord instances,
but different Ord instances give rise to different Map types, so we
can not violate any invariants.
You can do something similar in Haskell using an existential type,
although it is very inconvenient:
data Ord a = ...
data MapMod map a b = MapMod { empty :: map a b, insert :: a - b -
map a b - map a b, ... }
withMap :: Ord a - (forall map. MapMod map a b - z) - z
withMap ord f = f ( {- implement MapMod here, using ord for ordering }- )
Then you could use maps on different Ords for the same type, but they
could not talk to each other.
Some syntax sugar could help the Haskell situation quite a lot.
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Re: [Haskell-cafe] do we need types?
On Fri, Feb 26, 2010 at 04:23:52PM +0300, Miguel Mitrofanov wrote:
I'd say we don't really need subclasses. I mean, what's the difference:
class Eq a where (==) :: a - a - Bool
instance Eq a = Eq (Maybe a) where
Nothing == Nothing = True
Just x == Just y = x == y
_ == _ = False
sort :: Eq a = [a] - [a]
or
data Eq a = Eq {eq :: a - a - Bool}
eqMaybe :: Eq a - Eq (Maybe a)
eqMaybe e = Eq {eq = eqM} where
eqM Nothing Nothing = True
eqM (Just x) (Just y) = eq e x y
eqM _ _ = False
sort :: Eq a - [a] - [a]
Replacing classes with types, we only lose one thing: the compiler won't
deduce the right instances for us. I'll trade it for the ability to abstract
over them. After all, we CAN deduce the right
instances by hand, it's just a finite amount of work (not very big, in my
experience).
But then we would lose the invarient that there is a unique pairing
between a type and a given class. for instance, you would no longer be
able to implement things like Set and Map,
For instance if you called the two following functions with different
ord arguments, you would suddenly break all the invarients of what 'Set'
means.
insert :: Ord a - a - Set a - Set a
member :: Ord a - a - Set a - Bool
The unique correspondence between types and classes (i.e. no local
instances) is a main _feature_ of type classes. Often when people think
they need local instances, they are just applying type classes when they
should be using a different idiom, such as the one you mention.
John
--
John Meacham - ⑆repetae.net⑆john⑈ - http://notanumber.net/
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