[Haskell-cafe] typeclass woes...how to constain a typeclass to be "closed" under an operation....

[adam vogt]

Hi,

You can constrain the result type to be in the same class by writing
something like:

{-# LANGUAGE UndecidableInstances, FlexibleInstances #-}
{-# LANGUAGE TypeFamilies, FlexibleContexts #-}

class Foo_ a -- just to prevent a cycle in superclass constraints
instance Foo a => Foo_ a

class Foo_ (S a) => Foo a where
  type S a
  op :: a -> (S a)

-- and an example where you get a compile error if "op x" has an instance,
-- but "op (op x)" does not have an instance.
instance Foo Int where
    type S Int = Char
    op = toEnum

instance Foo Char where
    type S Char = (Char,Char)
    op x = (x,x)

instance Foo (Char,Char) where
    type S (Char,Char) = Int
    op (x,y) = fromEnum x


On Tue, Jan 6, 2015 at 1:53 PM, Nicholls, Mark <nicholls.mark at vimn.com> wrote:
> I will post the question again properly tomorrow but your example indeed is almost a good example, but is trivially closed
>
> If the operation on monoid was
>
> [a]->[b]->[c]
>
> That is also closed; ie [c] is also a monoid.... And the typeclass declaration follows the idiom ive suggested
>
> This only works for types of kind *->*
>
> If i wanted to do this over a type of kind * (ignoring the trivial a->a)
>
> Can i express this in a typeclass?
>
> Please ignore until i resubmit this question
>
> Ps i hate phones
>
> Excuse the spelling, sent from a phone with itty bitty keys, it like trying to sow a button on a shirt with a sausage.
>
>
>>> On 6 Jan 2015, at 18:10, Tom Ellis <tom-lists-haskell-cafe-2013 at jaguarpaw.co.uk> wrote:
>>>
>>> On Tue, Jan 06, 2015 at 05:43:47PM +0000, Nicholls, Mark wrote:
>>> Its quite common in maths to have operations in a theory that are (set)
>>> closed, i just want to translate that notion to a typeclass
>>
>> Do you really need a typeclass (or indeed any way) of doing this?  I suspect
>> it will not work.  If you consider the multiplication for the monoid of
>> concatenation of lists
>>
>>   (++) :: [a] -> [a] -> [a]
>>
>> you see that its type already implies that it is "closed".
>>
>> Tom
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