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Re: [Haskell-cafe] Type vs TypeClass duality

Subject: Re: [Haskell-cafe] Type vs TypeClass duality
From: Sterling Clover
Date: Wed, 24 Oct 2007 02:45:40 -0400
I'm relatively new to Haskell, so maybe this answer is a bit off, in that I'm sure there are times when some sort of auto-existential creation may have a point, but generally I've found that when I want it I've been thinking about the problem wrong.

The bigger issue is that as soon as you get fancier types classes, they'll probably be paramaterized over more than one type, not to mention with possible functional dependencies, etc., and very likely be polymorphic over return value as well. in fact, I suspect, Show and maybe fromIntegral or such aside, cases like you describe where you might even have the possibility of doing what you're looking for (i.e., a list of a typeclass such that a function in it is guaranteed a single return type) look fairly rare.

Integrals are a good example of what I ran into early on -- suppose you had a [Integral] rather than one of "Integral a => [a]". What would be the advantage of this? It would actually make your code messier -- instead of a case of, e.g. [x:x':xs] -> x+x' you wold need one of [x:x':xs] -> fromIntegral x + fromIntegral x', otherwise you would have no guarantee the types would match! And even then, what would the return type of this function be? Polymorphic over Integral? You'd just be spreading the fuzziness over type to the rest of your program, and probably introducing a load of potential inefficiencies to boot.

I suspect that you may still be trying to code with an OO mentality which thinks of the methods of a typeclass as "within" it as they are within an object, rather than as _on_ it.


On Oct 23, 2007, at 4:09 AM, TJ wrote:

Hi again,

Following up on my previous thread, I have figured out why it bothered
me that we cannot have a list such as the following: ["abc", 123, (1,
2)] :: Show a => [a]

It seems to me that there is an annoying duality in treating simple
algebraic data type vs type classes. As it stands, I can only have a
list where all the elements are of the same basic, ADT, type. There is
no way to express directly a list where all the elements satisfy a
given type class constraint.

If I am not mistaken, type classes are currently implemented in GHC like so:

Given a function "show" of type Show a => a -> string, and the
expression "show 10", GHC will pass the Int dictionary for class
Show's methods and the integer 10 to the function "show". In other
words, for each type class constraint in the function type, there will
be a hidden dictionary parameter managed entirely by the compiler.

What I find strange is, if we can have functions with hidden
parameters, why can't we have the same for, say, elements of a list?

Suppose that I have a list of type Show a => [a], I imagine that it
would not be particularly difficult to have GHC insert a hidden item
along with each value I cons onto the list, in effect making the
concrete type of the list [(Dictionary Show, a)]. I'm assuming that it
will not be particularly difficult because GHC will know the types of
the values I cons onto it, so it will most definitely be able to find
the Show dictionary implemented by that type, or report a type
mismatch error. No dynamic type information is necessary.

I am not an OO programming zealot, but I'd like to note here that this
is also how (class based) OO languages would allow the programmer to
mix types. e.g. I can have a List<Show> where the elements can be
instances of Show, or instances of subclasses of Show.

Why does this second rate treatment of type classes exist in Haskell?

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