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

Oooo I'll have a go with this tomorrow Thanks 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 19:06, adam vogt wrote:

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 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 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".

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