[Haskell-cafe] Sub class and model expansion

[Ryan Ingram]

On Tue, May 31, 2011 at 1:40 AM, Patrick Browne <patrick.browne at dit.ie>wrote:

> Continuing the thread on model expansion.
> I have changed the example trying to focus on expanding models of M in G
> Why is the operation ! ok or RHS but not visible on LHS of G?
> The equation itself does not seem to suffer from the dependent type
> problem of my previous post.
>
> class M a where
>  (!)  ::  a -> a -> a
>  e :: a
>
>
> class M a => G a where
>  (!-)  ::  a -> a -> a
> -- OK in G
>  a !- e = e ! a
>

This doesn't do what you think.  This is equivalent to

(!-) = (\a e -> e ! a)

That is, "e" is lambda-bound here, not the same "e" from M.  In this case
you've defined (!-) as "flip (!)"

When you define functions in a class declaration, you are just defining a
default implementation.  Generally this is used when you can implement some
functions in terms of the others, such as:

class Eq a where
   (==) :: a -> a -> a
   (/=) :: a -> a -> a

   a == b = not (a /= b)
   a /= b = not (a == b)

Now someone making an instance of this class need only define (==) or (/=);
the other one will be defined via the default instance.  (This has the
somewhat undesirable property that 'instance Eq X where' with no methods is
a valid instance declaration but in that instance == and /= are infinite
loops)

Maybe this will help you think about this: what code do you expect to write
for instances of this class?

instance M Int where
  e = 0
  (!) = +

instance G Int where
  -- do I need to write any code here?

It seems to me you are expecting the compiler to automatically derive the
definition 'inverse = negate'; there's no general way for the compiler to do
so, since it doesn't know the structure of your type.

Functions in Haskell, unlike, say, Prolog, only go from left of the = to the
right of the =.  Thanks to referential transparency, you can go backwards
from the point of view of proving properties about your code, but during
evaluation term rewriting only happens from left to right.

  -- ryan
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